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DESpecs 2.0 Autumn 2009
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Thu, 02 May 2013 11:14:40 +0200 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Castelli, Benedetto</author> <title>Of the mensuration of running waters</title> <date>1661</date> <place>London</place> <translator>Salusbury</translator> <lang>en</lang> <cvs_file>caste_mensu_068_en_1661.xml</cvs_file> <locator>068.xml</locator> </info> <text> <front> <section> <pb xlink:href="068/01/001.jpg"/><p type="head"> <s>MATHEMATICAL <lb/>COLLECTIONS <lb/>AND <lb/>TRANSLATIONS: <lb/>THE SECOND <lb/>TOME.</s></p><p type="head"> <s>THE SECOND PART, <lb/>Containing,</s></p><p type="main"> <s>D. BENEDICTUS CASTELLUS, <emph type="italics"/>his DISCOURSE <lb/>of the MENSURATION of RUN­<lb/>NING WATERS.<emph.end type="italics"/></s></p> </section> </front> <body> <chap> <p type="main"> <s><emph type="italics"/>His Geometrical DEMONSTRATIONS of <lb/>the Mea&longs;ure of RUNNING WATERS.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>I. </s> <s>His LETTERS and CONSIDERATIONS <lb/>touching the Draining of FENNS, Diver&longs;ions of <lb/>RIVERS, &c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>V.<emph.end type="italics"/> D. CORSINUS, <emph type="italics"/>His RELATION of the &longs;tate of the <lb/>Inundations, &c. </s> <s>in the Territories of BOLOGNA, <lb/>and FERRARA.<emph.end type="italics"/></s></p><p type="head"> <s>By <emph type="italics"/>THOMAS SALUSBURY, <expan abbr="E&longs;q.">E&longs;que</expan><emph.end type="italics"/></s></p><p type="head"> <s>LONDON, <lb/>Printed by WILLIAM LEYBOURNE, MDCLXI.</s></p><pb xlink:href="068/01/002.jpg"/><pb xlink:href="068/01/003.jpg"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>RUNNING WATERS.</s></p><p type="head"> <s>An Excellent Piece <lb/><emph type="italics"/>Written in ITALIAN<emph.end type="italics"/><lb/>BY</s></p><p type="head"> <s>DON BENEDETTO CASTELLI, <lb/>Abbot of St. <emph type="italics"/>BENEDETTO ALOYSIO,<emph.end type="italics"/><lb/>and Profe&longs;&longs;our of the Mathematicks to <lb/>Pope <emph type="italics"/>URBAN VIII.<emph.end type="italics"/> in <emph type="italics"/>ROME.<emph.end type="italics"/></s></p><p type="head"> <s>Engli&longs;hed from the Third and be&longs;t Edition, with <lb/>the addition of a Second Book not before extant:</s></p><p type="head"> <s>By <emph type="italics"/>THOMAS SALUSBURY.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, 1661.</s></p><pb xlink:href="068/01/004.jpg"/><pb xlink:href="068/01/005.jpg"/><p type="head"> <s>THE <lb/>AUTHOURS EPISTLE <lb/>TO <lb/>Pope VRBAN VIII.</s></p><p type="main"> <s>I lay at the Feet of your Ho­<lb/>line&longs;&longs;e the&longs;e my Con&longs;ide­<lb/>rations concerning the <lb/>MENSURATION OF <lb/>RUNNING WATERS: <lb/>Wherein if I &longs;hall have &longs;ucceeded, being a <lb/>matter &longs;o difficult and unhandled by Wri­<lb/>ters both Ancient Modern, the di&longs;covery of <lb/>any thing of truth hath been the Effect of <lb/>Your Holine&longs;&longs;es Command; and if through <lb/>inability I have mi&longs;&longs;ed the Mark, the &longs;ame <pb xlink:href="068/01/006.jpg"/>Command will &longs;erve me for an Excu&longs;e with <lb/>Men of better Judgment, and more e&longs;peci­<lb/>ally with Your Holine&longs;&longs;e, to whom I humbly <lb/>pro&longs;trate my &longs;elf, and ki&longs;&longs;e Your Sacred <lb/>Feet.</s></p><p type="main"> <s><emph type="italics"/>From ROME.<emph.end type="italics"/></s></p><p type="main"> <s>Your Holine&longs;&longs;es</s></p><p type="main"> <s><emph type="italics"/>Mo&longs;t humble Servant<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>BENEDETTO.<emph.end type="italics"/></s></p><p type="main"> <s>A Monk of <emph type="italics"/>Ca&longs;&longs;ino.<emph.end type="italics"/></s></p><pb xlink:href="068/01/007.jpg"/><p type="head"> <s>AN <lb/>ACCOUNT <lb/>OF THE <lb/>Authour and Work.</s></p><p type="main"> <s>DON BENEDETTO CASTELLI, <lb/><emph type="italics"/>the famous Authour of the&longs;e en&longs;uing <lb/>Di&longs;cour&longs;es of the<emph.end type="italics"/> Men&longs;uration of <lb/>Running Waters, <emph type="italics"/>is de&longs;cended from <lb/>the Wor&longs;hipful FAMILY of the<emph.end type="italics"/><lb/>GASTELLII, <emph type="italics"/>and took his <lb/>fir&longs;t breath near to the lake THR A­<lb/>SIMENVS, (where<emph.end type="italics"/> Hanibal <emph type="italics"/>gave <lb/>a fatal overthrow to the<emph.end type="italics"/> Roman <lb/><emph type="italics"/>Legions) in that &longs;weet and fertile part <lb/>of happy<emph.end type="italics"/> ITALY, <emph type="italics"/>called the<emph.end type="italics"/> Territory <lb/><emph type="italics"/>of<emph.end type="italics"/> PERUGIA, <emph type="italics"/>a branch of the Dukedome of<emph.end type="italics"/> TUSCANY, <emph type="italics"/>which <lb/>at pre&longs;ent &longs;ubmitteth to the Juri&longs;diction of the Church, as being a <lb/>part of<emph.end type="italics"/> St. </s> <s>PETER'S Patrimony. <emph type="italics"/>His Parents, who were more <lb/>zealous of the good of his Soul than ob&longs;ervant of the Propen&longs;ion of <lb/>his Genius, dedicated him (according to the Devotion of that Coun­<lb/>try) to the Service of the Church; and entered him into the Flou­<lb/>ri&longs;hing Order of Black-Friers, called from the place Moncks <lb/>of<emph.end type="italics"/> Monte Ca&longs;ino, <emph type="italics"/>and from the Founder<emph.end type="italics"/> Benedictines. <emph type="italics"/>Na­<lb/>ture, that She might con&longs;ummate the Profu&longs;ion of her Fa­<lb/>vours upon him, &longs;ent him into the World in an Age that was &longs;o <lb/>ennobled and illuminated with Eminent Scholars in all Kinds of <lb/>Literature, that hardly any Century &longs;ince the Creation can boa&longs;t <lb/>the like.<emph.end type="italics"/></s></p><pb xlink:href="068/01/008.jpg"/><p type="main"> <s>§. <emph type="italics"/>In particular, the<emph.end type="italics"/> SCIENCES MATHEMATI­<lb/>CAL <emph type="italics"/>had then got that Fame and E&longs;teem in the Learned World, <lb/>that all men of Spirit or Quality became either Students in, or <lb/>Patrons of tho&longs;e Sublime Knowledges. </s> <s>On this occa&longs;ion the Curi­<lb/>o&longs;ity of our<emph.end type="italics"/> AUTHOUR <emph type="italics"/>being awakened, his Active Wit <lb/>could not endure to be any longer confined to the Slavi&longs;h Tuition <lb/>of Hermetical Pedagogues; but in concurrence with the Genius <lb/>of the Age, he al&longs;o betook him&longs;elf to tho&longs;e mo&longs;t Generous and <lb/>Liberal Studies. </s> <s>His helps in this his de&longs;ign were &longs;o many, and <lb/>&longs;o extraordinary, that had his Inclination been weaker, or his <lb/>Apprehen&longs;ion le&longs;&longs;er, he could hardly have failed attaining more <lb/>than a Common Eminency in the&longs;e Sciences. </s> <s>For be&longs;ides the De­<lb/>luge of Learned and V&longs;eful Books, which the Pre&longs;&longs;e at that <lb/>time &longs;ent forth from all parts of<emph.end type="italics"/> EUROPE, <emph type="italics"/>he had the good <lb/>Fortune to fall into the Acquaintance, and under the In&longs;truction <lb/>of the mo&longs;t Demon&longs;trative and mo&longs;t Familiar Man in the World, <lb/>the Famous<emph.end type="italics"/> GALILEO<emph type="italics"/>: who&longs;e &longs;ucce&longs;&longs;e being no le&longs;&longs;e upon <lb/>this his<emph.end type="italics"/> Pupil <emph type="italics"/>than upon the re&longs;t of tho&longs;e Illu&longs;trious and Ingeni­<lb/>ous Per&longs;ons that re&longs;orted from all parts to &longs;it under his Admi­<lb/>rable Lectures, he in a &longs;hort time attained to that Name in the <lb/>Mathematicks, that he was invited to<emph.end type="italics"/> ROME, <emph type="italics"/>Complemen­<lb/>ted, and Preferred by his then Holine&longs;&longs;e the Eighth<emph.end type="italics"/> URBAN, <lb/><emph type="italics"/>upon his very fir&longs;t Acce&longs;&longs;ion to the<emph.end type="italics"/> Papacy, <emph type="italics"/>which was in the <lb/>Year<emph.end type="italics"/> 1623.</s></p><p type="main"> <s>§. <emph type="italics"/>This Pope being moved with a Paternal Providence for the <lb/>Concerns of his Subjects in that part of<emph.end type="italics"/> ITALY <emph type="italics"/>about<emph.end type="italics"/> BO­<lb/>LOGNA, FERRARA, <emph type="italics"/>and<emph.end type="italics"/> COMMACHIO, <emph type="italics"/>ly­<lb/>ing between the Rivers of<emph.end type="italics"/> PO <emph type="italics"/>and<emph.end type="italics"/> RENO, <emph type="italics"/>which is part of<emph.end type="italics"/><lb/>Lo Stato della Chie&longs;a, <emph type="italics"/>or the Church Patrimony, appoints this <lb/>our<emph.end type="italics"/> CASTELLI <emph type="italics"/>in the Year 1625, to accompany the Right <lb/>Honourable<emph.end type="italics"/> Mon&longs;ignore GORSINI <emph type="italics"/>(a mo&longs;t ob&longs;ervant and <lb/>intelligent per&longs;on in the&longs;e affaires, and at that time Superinten­<lb/>dent of the General Draines, and Pre&longs;ident of<emph.end type="italics"/> ROMAGNA) <lb/><emph type="italics"/>in the Grand Vi&longs;itation which he was then ordered to make con­<lb/>cerning the di&longs;orders occa&longs;ioned by the Waters of tho&longs;e parts.<emph.end type="italics"/></s></p><p type="main"> <s>§. </s> <s>CASTELLI, <emph type="italics"/>having now an Opportunity to employ, <lb/>yea more, to improve &longs;uch Notions as he had imbued from the <lb/>Lectures of his Excellent<emph.end type="italics"/> MASTER, <emph type="italics"/>falls to his work with <lb/>all indu&longs;try: and in the time that his Occa&longs;ions detained him in<emph.end type="italics"/><lb/>ROMAGNA <emph type="italics"/>he perfected the Fir&longs;t Book of this his Di&longs;­<lb/>cour&longs;e concerning the<emph.end type="italics"/> Men&longs;uration of Running Waters. <emph type="italics"/>He con­<lb/>fe&longs;&longs;eth that he had &longs;ome years before applyed him&longs;elf to this part <lb/>of Practical Geometry, and from &longs;everal Ob&longs;ervations collected <lb/>part of that Doctrine which at this time he put into Method, and <lb/>which had procured him the Repute of &longs;o much Skill that he began<emph.end type="italics"/><pb xlink:href="068/01/009.jpg"/><emph type="italics"/>to be Courted by &longs;undry Princes, and great Prelates. </s> <s>In particu­<lb/>lar about the beginning of the Year 1623. and before his Invita­<lb/>tion to<emph.end type="italics"/> ROME <emph type="italics"/>he was employed by Prince<emph.end type="italics"/> Ferdinando I, <emph type="italics"/>Grand <lb/>Duke of<emph.end type="italics"/> TUSCANY, <emph type="italics"/>to remedy the Di&longs;orders which at that <lb/>time happened in the Valley of<emph.end type="italics"/> PISA <emph type="italics"/>in the Meadows that lye <lb/>upon the Banks of<emph.end type="italics"/> Serchio <emph type="italics"/>and<emph.end type="italics"/> Fiume Morto: <emph type="italics"/>and in the pre­<lb/>&longs;ence of the Grand Duke, Grand Dutche&longs;&longs;e Mother, the Commi&longs;­<lb/>&longs;ioners of Sewers, and &longs;undry other Per&longs;ons in a few hours he <lb/>made &longs;o great a progre&longs;&longs;e in that affair, as gave his Mo&longs;t Serene <lb/>Highne&longs;&longs;e high &longs;atisfaction, and gained him&longs;elf much Honour.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>No &longs;ooner had he in his fore-mentioned Voiage to<emph.end type="italics"/> RO­<lb/>MAGNA <emph type="italics"/>(which was but few Moneths after, in the &longs;ame <lb/>Year) committed his Conceptions to paper, but he communicated <lb/>them to certain of his Friends. </s> <s>In which number we finde<emph.end type="italics"/> Signo­<lb/>re Ciampoli <emph type="italics"/>Secretary of the Popes Private Affaires; whom in <lb/>the beginning of the Fir&longs;t Book he gratefully acknowledgeth to <lb/>have been contributary, in his Pur&longs;e, towards defraying the <lb/>charge of Experiments, and in his Per&longs;on, towards the debating <lb/>and compleating of Arguments upon this Subject. </s> <s>Some few years <lb/>after the Importunity of Friends, and the Zeal he had for the <lb/>Publique Good prevailed with him to pre&longs;ent the World with his <lb/>Fir&longs;t Di&longs;cour&longs;e, accompanied with a Treati&longs;e of the Geometrical <lb/>Demon&longs;trations of his whole Doctrine. </s> <s>What Reception it found <lb/>with the Judicious mu&longs;t needs be imagined by any one that hath <lb/>ob&longs;erved how<emph.end type="italics"/> Novelty <emph type="italics"/>and<emph.end type="italics"/> Facility <emph type="italics"/>in conjunction with<emph.end type="italics"/> Verity <lb/><emph type="italics"/>make a Charm of irre&longs;i&longs;table Operation.<emph.end type="italics"/></s></p><p type="main"> <s>§. </s> <s>New <emph type="italics"/>it was, for that no man before him had ever attemp­<lb/>ted to Demon&longs;trate all the three Dimen&longs;ions, to wit, the Length, <lb/>Breadth and Profundity, of this Fluid and Current Ele­<lb/>ment. </s> <s>And he detecteth &longs;uch gro&longs;&longs;e Errours in tho&longs;e few that <lb/>had untertook to write upon the Subject (of which he in&longs;tan­<lb/>ceth in<emph.end type="italics"/> Frontinus <emph type="italics"/>and<emph.end type="italics"/> Fontana, <emph type="italics"/>as tho&longs;e that include the rest) <lb/>and delivereth &longs;uch &longs;ingular and unheard-of Paradoxes (for &longs;o <lb/>they &longs;ound in Vulgar Eares) as cannot but procure un&longs;peakable <lb/>delight to his Reader.<emph.end type="italics"/></s></p><p type="main"> <s>§. </s> <s>Eafie <emph type="italics"/>it is likewi&longs;e and<emph.end type="italics"/> True; <emph type="italics"/>and that upon &longs;o Familiar <lb/>Experiments and Manife&longs;t Demon&longs;trations, that I have oft que­<lb/>&longs;tioned with my &longs;elf which merited the greater wonder, he, for <lb/>di&longs;covering, or all men that handled the Argument before him <lb/>for not di&longs;covering a Doctrine of &longs;uch &longs;trange Facility and Infal­<lb/>libility. </s> <s>But yet as if our Authour de&longs;igned to oblige the whole <lb/>World to him by &longs;o excellent a<emph.end type="italics"/> Pre&longs;ent, <emph type="italics"/>he &longs;elects a Subject that <lb/>he knew would be carre&longs;&longs;ed by all per&longs;ons of Nobler Souls, upon <lb/>the accounts afore-named, and by all Mankind in General, as <lb/>gratifying them in their much adored Idol<emph.end type="italics"/> Utility. <emph type="italics"/>And to ren-<emph.end type="italics"/><pb xlink:href="068/01/010.jpg"/><emph type="italics"/>der his Art the more profitable, he reduceth the lofty, and ea&longs;ie-to­<lb/>be-mi&longs;taken Speculations of the Theory, into certain and facile <lb/>Directions for Practice; teaching us how to prevent and repaire <lb/>the Breaches of Seas, and Inundations of Rivers; to draine <lb/>and recover Fenns and Marches; to divert, conveigh and di­<lb/>&longs;tribute Waters for the Flowing and Stercoration of Grounds, <lb/>&longs;trengthening of Fortifications, &longs;erving of Aquaducts, pre&longs;er­<lb/>ving of Health (by clean&longs;ing Streets, and &longs;cowring Sewers) and <lb/>maintaining of Commer&longs;e (by defending Bridges, cleering Ri­<lb/>vers, and opening Ports and Channels) with innumerable other <lb/>Benefits of the like nature. </s> <s>And, that I may omit no circum&longs;tance <lb/>that may recommend my Authour, the Fortune of this his Trea­<lb/>ti&longs;e hath been &longs;uch, that as if he intended a<emph.end type="italics"/> Plus ultra <emph type="italics"/>by it, <lb/>or as if all men de&longs;paired to out-do it, or la&longs;tly, as if<emph.end type="italics"/> CA­<lb/>STELLI <emph type="italics"/>hath been &longs;o great a<emph.end type="italics"/> Ma&longs;ter <emph type="italics"/>that none have pre&longs;u­<lb/>med to take Pencil in hand for the fini&longs;hing of what he<emph.end type="italics"/> Pour­<lb/>foild, <emph type="italics"/>this &longs;mall Tract like the Arabian Phœnix (of which it is <lb/>&longs;aid<emph.end type="italics"/> Unica &longs;emper Avis) <emph type="italics"/>did for &longs;everal years together continue <lb/>&longs;ingle in the World, till that to verifie it to be truly<emph.end type="italics"/> Phœnician, <lb/><emph type="italics"/>it renewed its Age by undergoing a &longs;econd Impre&longs;&longs;ion. </s> <s>And as if <lb/>this did not make out the Immortal vertue of it, it hath had<emph.end type="italics"/><lb/>Anno 1660 <emph type="italics"/>a third Circulation, and ri&longs;en in this la&longs;t Edition as <lb/>it were from the Vrne of its Authour; and that &longs;o improved by <lb/>the Addition of a &longs;econd part, that it promi&longs;eth to perpetuate <lb/>his Merits to all Po&longs;terity. </s> <s>To be brief, the meer Fame of this <lb/>Work re&longs;ounded the Honourable Name of<emph.end type="italics"/> CASTELLI <emph type="italics"/>in­<lb/>to all the Corners of<emph.end type="italics"/> Italy, <emph type="italics"/>I may &longs;ay of<emph.end type="italics"/> Europe; <emph type="italics"/>in&longs;omuch, <lb/>that, in hopes to reap great benefit by his Art, the re&longs;pective <lb/>Grandees of the adjacent Countries courted his Judgment and <lb/>Advice about their Draining of Fenns, Diver&longs;ion of Rivers, <lb/>Evacuation of Ports, Preventing of Inundations, &c. </s> <s>So that <lb/>every Summer he made one or more of the&longs;e Journies or Vi&longs;itati­<lb/>ons. </s> <s>Particularly, the Senate of<emph.end type="italics"/> Venice <emph type="italics"/>con&longs;ulted him about their <lb/>Lake; to whom he delivered his Opinion in<emph.end type="italics"/> May 1641. <emph type="italics"/>and up­<lb/>on farther thoughts he pre&longs;ented them with another Paper of Con­<lb/>&longs;iderations the<emph.end type="italics"/> 20 December <emph type="italics"/>following. </s> <s>Prince<emph.end type="italics"/> LEOPOLDO <lb/><emph type="italics"/>of<emph.end type="italics"/> TUSCANY <emph type="italics"/>likewi&longs;e reque&longs;ted his Advice in the begin­<lb/>ning of the en&longs;uing year 1642, which occa&longs;ioned his Letter to <lb/>Father<emph.end type="italics"/> France&longs;co di San Giu&longs;eppe, <emph type="italics"/>bearing date<emph.end type="italics"/> February 1, <lb/><emph type="italics"/>To which<emph.end type="italics"/> Signore Bartolotti <emph type="italics"/>oppo&longs;ing, he writes a &longs;econd Let­<lb/>ter, directed to one of the Commi&longs;&longs;ioners of Sewers, vindicating <lb/>his former, and refuting<emph.end type="italics"/> Bartolotti, <emph type="italics"/>both which I here give <lb/>you.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>The Preferments which his Merits recommended him unto, <lb/>were fir&longs;t to be Abbot of<emph.end type="italics"/> Ca&longs;&longs;ino, <emph type="italics"/>from which he was removed<emph.end type="italics"/><pb xlink:href="068/01/011.jpg"/>Anno 1640, <emph type="italics"/>or thereabouts, unto the Abbey of<emph.end type="italics"/> Santo Benedet­<lb/>to Aloy&longs;io; <emph type="italics"/>and much about the &longs;ame time preferred to the Dig­<lb/>nity of Chief Mathematician to his grand Patron Pope<emph.end type="italics"/> URBAN <lb/>VIII. <emph type="italics"/>and Publique Profe&longs;&longs;our of Mathematicks in the Vni­<lb/>ver&longs;ity of<emph.end type="italics"/> ROME.</s></p><p type="main"> <s>§. <emph type="italics"/>Here a Stop was put to the Carier of his Fortunes, and be­<lb/>ing fuller of Honour than of Years, was by Death, the Importu­<lb/>nate Intrerupter of Generous De&longs;igns, prevented in doing that <lb/>farther Good which the World had good rea&longs;on to promi&longs;e it &longs;elf <lb/>from &longs;o Profound and Indu&longs;trious a Per&longs;onage, leaving many <lb/>Friends and Di&longs;ciples of all Degrees and Qualities to lament <lb/>his lo&longs;&longs;e, and honour his Memory.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>His &longs;ingular Virtues and Abilities had gained him the <lb/>Friend&longs;hip of very many; as to in&longs;tance in &longs;ome, he had con­<lb/>racted &longs;trict Amity with<emph.end type="italics"/> Mon&longs;ignore Maffei Barberino <emph type="italics"/>a Floren­<lb/>tine, Præfect of the Publique Wayes, and afterwards Pope with <lb/>the Name of<emph.end type="italics"/> URBAN VIII. <emph type="italics"/>as was &longs;aid before; with the <lb/>above-named<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini <emph type="italics"/>Superintendant of the General <lb/>Draines: with<emph.end type="italics"/> Mon&longs;ignore Piccolomini <emph type="italics"/>Arch-Bi&longs;hop of<emph.end type="italics"/> Siena<emph type="italics"/>: <lb/>with Cardinal<emph.end type="italics"/> Serra: <emph type="italics"/>with Cardinal<emph.end type="italics"/> Caponi, <emph type="italics"/>who hath &longs;tudied <lb/>much and writ well upon this Subject; and with Cardinal<emph.end type="italics"/> Gae­<lb/>tano <emph type="italics"/>who frequently con&longs;ulted with him in his de&longs;ign of Drain­<lb/>ing the Fenns of<emph.end type="italics"/> ROMAGNA. <emph type="italics"/>Moreover Prince<emph.end type="italics"/> LEO­<lb/>POLDO, <emph type="italics"/>and his Brother the Grand Duke had very great <lb/>kindne&longs;&longs;e for him; which &longs;peaks no &longs;mall attractions in him, <lb/>con&longs;idering him as a favourite of the Family of<emph.end type="italics"/> Barberini, <emph type="italics"/>be­<lb/>tween whom and the Hou&longs;e of<emph.end type="italics"/> Medeci <emph type="italics"/>there is an inveterate <lb/>Fewd. </s> <s>Among&longs;t per&longs;ons of a lower Quality he acknowledgeth<emph.end type="italics"/><lb/>Signore Ciampoli <emph type="italics"/>the Popes Secretary,<emph.end type="italics"/> Sig. </s> <s>Ferrante Ce&longs;arini, <lb/>Sig. </s> <s>Giovanni Ba&longs;adonna <emph type="italics"/>Senator of<emph.end type="italics"/> Venice; <emph type="italics"/>and I find menti­<lb/>oned<emph.end type="italics"/> Sig. </s> <s>Lana, Sig. </s> <s>Albano, Padre Serafino, Pad. </s> <s>France&longs;co <lb/>de San. </s> <s>Giu&longs;eppe, <emph type="italics"/>and many others.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>The Works in which he will &longs;urvive to all &longs;ucceeding Ages <lb/>are fir&longs;t His &longs;olid and &longs;ober Confutation of the Arguments of<emph.end type="italics"/><lb/>Signore Lodovico dell Columbo, <emph type="italics"/>and<emph.end type="italics"/> Signore Vincentio di <lb/>Gratia <emph type="italics"/>again&longs;t the Tract of<emph.end type="italics"/> Galileo Delle co&longs;e che &longs;tanno &longs;opra <lb/>Aqua, <emph type="italics"/>wherein he vindicates bis &longs;aid<emph.end type="italics"/> Ma&longs;ter <emph type="italics"/>with a Gratitude <lb/>that Tutors very rarely reap from the pains they take in Culti­<lb/>vating their Pupils. </s> <s>This Apology was fir&longs;t Printed<emph.end type="italics"/> Anno 1615. <lb/><emph type="italics"/>and was a &longs;econd time publi&longs;hed, as al&longs;o tho&longs;e of his Antago­<lb/>ni&longs;ts, among&longs;t the Works of<emph.end type="italics"/> GALILEO, <emph type="italics"/>&longs;et forth by the <lb/>Learned<emph.end type="italics"/> Viviani 1656. <emph type="italics"/>He hath likewi&longs;e writ &longs;everal other <lb/>curious Pieces, as I am informed by the mo&longs;t Courteous<emph.end type="italics"/> Carolo <lb/>Manole&longs;&longs;i <emph type="italics"/>of<emph.end type="italics"/> Bologna; <emph type="italics"/>among&longs;t others an excellent Treati&longs;e <lb/>concerning<emph.end type="italics"/> Colours, <emph type="italics"/>which he putteth me in hopes to &longs;ee printed<emph.end type="italics"/><pb xlink:href="068/01/012.jpg"/><emph type="italics"/>very &longs;peedily. </s> <s>And la&longs;t of all the&longs;e Di&longs;cour&longs;es and Reflections <lb/>upon the<emph.end type="italics"/> Men&longs;uration of Running Waters, <emph type="italics"/>with the addition of <lb/>a Second Book, three Epi&longs;tles, and four Con&longs;iderations upon <lb/>the &longs;ame Argument, which conduce much to Illu&longs;trate his Do­<lb/>ctrine and Facilitate the Practice of it; and which with a Rela­<lb/>tion of<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini, <emph type="italics"/>make the &longs;econd part of my Fir&longs;t <lb/>Tome.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>I might here &longs;ally forth into the Citation of &longs;undry Au­<lb/>thours of Good Account, that have tran&longs;mitted his Character <lb/>to Po&longs;terity, but &longs;hall confine my &longs;elf to onely two; the one is <lb/>of his<emph.end type="italics"/> Ma&longs;ter, <emph type="italics"/>the other of his<emph.end type="italics"/> Scholar; <emph type="italics"/>than whom there can­<lb/>not be two more competent Judges of his Accompli&longs;hments. </s> <s>To <lb/>begin with his<emph.end type="italics"/> Ma&longs;ter, <emph type="italics"/>the Quick-&longs;ighted, and truly Lyncean<emph.end type="italics"/><lb/>GALILEO, <emph type="italics"/>who &longs;peaking of his Abilities in A&longs;tronomy &longs;aith<emph.end type="italics"/><lb/><arrow.to.target n="marg961"></arrow.to.target><lb/><emph type="italics"/>(a)<emph.end type="italics"/> Che la felicità del &longs;uo ingegno non la fà bi&longs;ogno&longs;a dell' o­<lb/>pera &longs;uo. <emph type="italics"/>And again, &longs;ubmitting a certain Demon&longs;tration, <lb/>which he intended to divulge, to the Judgment of this our Abbot, he<emph.end type="italics"/><lb/><arrow.to.target n="marg962"></arrow.to.target><lb/><emph type="italics"/>writes to him in this manner: (b)<emph.end type="italics"/> Que&longs;to lo comunico a V. S. <lb/>per lettera prima che ad alcun altro, con attenderne principal­<lb/>mente il parer &longs;uo, e doppo quello de' no&longs;tri Amici di&longs;co&longs;ti, <lb/>conpen&longs;iero d' inviarne poi altre Copie ad altri Amici d' Italia, <lb/>e di Francia, quando io ne venga da lei con&longs;igliato: e qui pre­<lb/>gandola a farci parte d' alcuna delle &longs;ue peregrine &longs;peculationi; <lb/>con &longs;inceri&longs;&longs;imo affetto, &c. <emph type="italics"/>And the mo&longs;t acute Mathematician<emph.end type="italics"/><lb/>Signore Evangeli&longs;ta Terricelli, <emph type="italics"/>late Profe&longs;&longs;our to the Grand <lb/>Duke in immediate Succe&longs;&longs;ion after<emph.end type="italics"/> GALILEO, <emph type="italics"/>maketh this<emph.end type="italics"/><lb/><arrow.to.target n="marg963"></arrow.to.target><lb/><emph type="italics"/>Honourable and Grateful Mention of him, and his Book: (c)<emph.end type="italics"/> O­<lb/>mitto magnum illum nutantis Maris motum; Prætereo etiam <lb/>omnem Fluminum, Aquarumque Currentium tum men&longs;urum, <lb/>tum u&longs;um, quarum omnis doctrina reperta primum fuit ab <lb/>Abbate BENEDICTO CASTELLIO Preceptore <lb/>meo. </s> <s>Scrip&longs;it ille Scientiam &longs;uam, & illam non &longs;olum demon&longs;tra­<lb/>tione, verum etiam opere confirmavit, maxima cum Princi­<lb/>pum & populorum utilitatate, majore cum admiratione Phylo­<lb/>&longs;ophorum. </s> <s>Extat illius Liber, vere aureus.</s></p><p type="margin"> <s><margin.target id="marg961"></margin.target><emph type="italics"/>(a)<emph.end type="italics"/>Nella continu­<lb/>atione dell Nun­<lb/>tio &longs;iderio.</s></p><p type="margin"> <s><margin.target id="marg962"></margin.target><emph type="italics"/>(b)<emph.end type="italics"/> Lettera al P. <lb/></s> <s>Abbate D. B. </s> <s>Ca­<lb/>&longs;telli D'Arcetro; <lb/>li. </s> <s>3. Decemb. <lb/></s> <s>1639.</s></p><p type="margin"> <s><margin.target id="marg963"></margin.target><emph type="italics"/>(c)<emph.end type="italics"/> De Motu A­<lb/>quarum. </s> <s>Lib. 2. <lb/>Prop. </s> <s>37. p. </s> <s>191.</s></p><p type="main"> <s>§. <emph type="italics"/>I have onely two particulars more to offer the Engli&longs;h Rea­<lb/>der: The one concerns the Book, and it is this, That after the <lb/>general Aprobation it hath had in<emph.end type="italics"/> Italy, <emph type="italics"/>I cannot but think it <lb/>de&longs;erveth the &longs;ame Civil Entertainment with us, in regard that <lb/>it cometh with no le&longs;&longs;e<emph.end type="italics"/> Novelty, Facility, Verity, and Utility <emph type="italics"/>to <lb/>us than to tho&longs;e whom the Authour favoured with the Original. <lb/></s> <s>Our Rivers and Sewers through Publique Di&longs;tractions and Pri­<lb/>vate Incroachments are in great di&longs;order, as tho&longs;e Channels for <lb/>iu&longs;tance which formerly were Navigable unto the very Walls of<emph.end type="italics"/><pb xlink:href="068/01/013.jpg"/>York <emph type="italics"/>and<emph.end type="italics"/> Salisbury, <emph type="italics"/>&c: Our Ports are choaked and ob&longs;tructed <lb/>by Shelfes and Setlements: Our Fenns do in a great part lie wa&longs;te <lb/>and unimproved: Now all the&longs;e may be (and, as I find by the <lb/>Confe&longs;&longs;ion of &longs;ome who&longs;e Practi&longs;es upon the Copy of the Fir&longs;t <lb/>Book onely of our Authour hath got them both Money and Repu­<lb/>tation, in part have been) remedied by the Ways and Means he <lb/>here &longs;ets down. </s> <s>The truth is the Argument hath been pa&longs;t over <lb/>with an Vniver&longs;al Silence; &longs;o that to this day I have not &longs;een <lb/>any thing that hath been written Demon&longs;tratively and with Ma­<lb/>thematical Certainty concerning the &longs;ame, &longs;ave onely what this <lb/>Learned Prelate hath delivered of his Own Invention in the&longs;e <lb/>Treati&longs;es: who yet hath &longs;o fully and plainly handled the Whole <lb/>Doctrine, that I may affirm his Work to be every way ab&longs;olute. </s> <s>It <lb/>mu&longs;t be confe&longs;t the Demon&longs;tration of the Second Propo&longs;ition of the <lb/>Second Book did not well plea&longs;e the Authour, and had he lived <lb/>he would have &longs;upplyed that defect, but being prevented by <lb/>Death, the Reader mu&longs;t content him&longs;elf with the Mechanical <lb/>Proof that he giveth you of the truth of &longs;o Excellent a Con­<lb/>clu&longs;ion.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>The other particular that I am to offer is, that out of my de­<lb/>&longs;ire to contribute what lyeth in me to the compleating of this Piece <lb/>for Engli&longs;h Practice, I have exeeded my promi&longs;e not onely in gi­<lb/>ving you the Second and following Books which were not extant at <lb/>the time of tendring my Overtures, but al&longs;o in that I have added <lb/>a Map or Plat of all the Rivers, Lakes, Fenns, &c. </s> <s>mentioned <lb/>thorow out the Work. </s> <s>And if I have not kept touch in point of <lb/>Time, let it be con&longs;idered that I am the Tran&longs;lator and not the <lb/>Printer. </s> <s>To conclude, according to your acceptance of the&longs;e my <lb/>endeavours, you may expect &longs;ome other Tracts of no le&longs;&longs;e Profit <lb/>and Delight.<emph.end type="italics"/> Farewell.</s></p><p type="head"> <s><emph type="italics"/>T. S.<emph.end type="italics"/></s></p><pb xlink:href="068/01/014.jpg"/><p type="head"> <s>ERRATA of the <emph type="italics"/>&longs;econd<emph.end type="italics"/> PART of the <emph type="italics"/>fir&longs;t<emph.end type="italics"/> TOME.</s></p><p type="main"> <s>In PREFACE, I cad <emph type="italics"/>Ferdinando II.<emph.end type="italics"/> ibid. <emph type="italics"/>l' Aqua.<emph.end type="italics"/></s></p><p type="main"> <s>PAGE 2. LINE 26, <emph type="italics"/>for<emph.end type="italics"/> mu&longs;t <emph type="italics"/>read<emph.end type="italics"/> much. </s> <s>P. 3. l. </s> <s>22, <emph type="italics"/>r.<emph.end type="italics"/> and let. </s> <s>l. </s> <s>25. <emph type="italics"/>r.<emph.end type="italics"/> water, from l. </s> <s>41. <lb/><emph type="italics"/>r.<emph.end type="italics"/> Tappe, (<emph type="italics"/>as every where el&longs;e).<emph.end type="italics"/> Page 4. l. </s> <s>18. <emph type="italics"/>r<emph.end type="italics"/> cords. </s> <s>Page 6. l. </s> <s>9. <emph type="italics"/>r.<emph.end type="italics"/> acquire, or. <lb/></s> <s>Page 9. l. </s> <s>1. <emph type="italics"/>r.<emph.end type="italics"/> irreperable. </s> <s>P. 10. l. </s> <s>13. <emph type="italics"/>r.<emph.end type="italics"/> di&longs;&longs;imboguement. <emph type="italics"/>For<emph.end type="italics"/> Page 17. <emph type="italics"/>r.<emph.end type="italics"/> P. 15. <lb/>P. 15. l. </s> <s>27, <emph type="italics"/>r.<emph.end type="italics"/> in. </s> <s>l. </s> <s>36, <emph type="italics"/>r.<emph.end type="italics"/> is as. </s> <s>l. </s> <s>38, <emph type="italics"/>r. </s> <s>Panaro.<emph.end type="italics"/> P. 17. l. </s> <s>12, <emph type="italics"/>Giulio.<emph.end type="italics"/> l. </s> <s>17. <emph type="italics"/>r.<emph.end type="italics"/> Mea&longs;urers. </s> <s>l. <lb/></s> <s>25, <emph type="italics"/>r.<emph.end type="italics"/> mea&longs;ured it,. <emph type="italics"/>r.<emph.end type="italics"/> nece&longs;&longs;arily. </s> <s>P. 23. l. </s> <s>19. <emph type="italics"/>r.<emph.end type="italics"/> for help. <emph type="italics"/>for<emph.end type="italics"/> Page 31. <emph type="italics"/>r.<emph.end type="italics"/> P. 32. P. 24. <lb/>l. </s> <s>14, <emph type="italics"/>r.<emph.end type="italics"/> to. </s> <s>l. </s> <s>17, <emph type="italics"/>r.<emph.end type="italics"/> namly, of the. </s> <s>l. </s> <s>23, <emph type="italics"/>r.<emph.end type="italics"/> ea&longs;ie. </s> <s>P. 25. l. </s> <s>38. <emph type="italics"/>r.<emph.end type="italics"/> Cock. </s> <s>p. </s> <s>29. l. </s> <s>7. <emph type="italics"/>r.<emph.end type="italics"/> la&longs;ted,. <lb/>p. </s> <s>31. l. </s> <s>32. <emph type="italics"/>r.<emph.end type="italics"/> Soe. </s> <s>p. </s> <s>41. l. </s> <s>20. <emph type="italics"/>r.<emph.end type="italics"/> to the line. </s> <s>p. </s> <s>48. l. </s> <s>19. <emph type="italics"/>r.<emph.end type="italics"/> us the ^{*}. id. <emph type="italics"/>Figure fal&longs;e<emph.end type="italics"/> p. </s> <s>52. <lb/>l. </s> <s>30, and 31. <emph type="italics"/>for<emph.end type="italics"/> Theorem <emph type="italics"/>r.<emph.end type="italics"/> Propo&longs;ition. </s> <s>p. </s> <s>53. l. </s> <s>29. <emph type="italics"/>r.<emph.end type="italics"/> again. </s> <s>p. </s> <s>57. l. </s> <s>19, <emph type="italics"/>r.<emph.end type="italics"/> &longs;ame if. <lb/></s> <s>l. </s> <s>44. <emph type="italics"/>r.<emph.end type="italics"/> bodily. </s> <s>p. </s> <s>58. l. </s> <s>9, <emph type="italics"/>r.<emph.end type="italics"/> gathering. </s> <s>l. </s> <s>40. <emph type="italics"/>omit<emph.end type="italics"/>;. </s> <s>p. </s> <s>60. l. </s> <s>2. <emph type="italics"/>omit,<emph.end type="italics"/> if. </s> <s>p. </s> <s>65. l. </s> <s>1. <emph type="italics"/>r.<emph.end type="italics"/> tide <lb/><emph type="italics"/>dele<emph.end type="italics"/>;. </s> <s>p. </s> <s>66. l. </s> <s>35. <emph type="italics"/>r.<emph.end type="italics"/> Stoppage of. </s> <s>p. </s> <s>68. l. </s> <s>12, <emph type="italics"/>for<emph.end type="italics"/> Lords the <emph type="italics"/>r.<emph.end type="italics"/> Lords. </s> <s>l. <emph type="italics"/>ult. </s> <s>for<emph.end type="italics"/> they <lb/><emph type="italics"/>r.<emph.end type="italics"/> it. </s> <s>p. </s> <s>69. l. </s> <s>14. <emph type="italics"/>r.<emph.end type="italics"/> to one. <emph type="italics"/>id.<emph.end type="italics"/> carried <emph type="italics"/>dele<emph.end type="italics"/> to. </s> <s>p. </s> <s>71. l. </s> <s>20, <emph type="italics"/>r.<emph.end type="italics"/> and that. </s> <s>l. </s> <s>25, <emph type="italics"/>r.<emph.end type="italics"/> Braces; it. </s> <s>l. <lb/></s> <s>29. <emph type="italics"/>r.<emph.end type="italics"/> Braces. </s> <s>l. </s> <s>44, <emph type="italics"/>r.<emph.end type="italics"/> the <emph type="italics"/>Brent.<emph.end type="italics"/> p. </s> <s>72. l. </s> <s>23. <emph type="italics"/>r. </s> <s>Serene Highne&longs;&longs;e.<emph.end type="italics"/> p. </s> <s>73. l. </s> <s>24, <emph type="italics"/>r.<emph.end type="italics"/> deliberation:. <lb/>l. </s> <s>26, <emph type="italics"/>for<emph.end type="italics"/> &longs;umme <emph type="italics"/>r.<emph.end type="italics"/> Moddel. </s> <s>l. </s> <s>40. <emph type="italics"/>r.<emph.end type="italics"/> Months. </s> <s>p. </s> <s>79. l. </s> <s>18. <emph type="italics"/>r.<emph.end type="italics"/> that into. </s> <s>p. </s> <s>82. l. </s> <s>22. <emph type="italics"/>dele<emph.end type="italics"/>;. </s> <s>p. <lb/></s> <s>85. l. </s> <s>9, 10. <emph type="italics"/>dele<emph.end type="italics"/> a free drame. </s> <s>p. </s> <s>88. l. </s> <s>5. <emph type="italics"/>r.<emph.end type="italics"/> Palmes. </s> <s>p. </s> <s>89. l. </s> <s>8. <emph type="italics"/>r.<emph.end type="italics"/> Princes. </s> <s>p. </s> <s>92. l. </s> <s>3. <emph type="italics"/>r.<emph.end type="italics"/> Di&longs;­<lb/>cour&longs;es. </s> <s>p. </s> <s>93. l. </s> <s>31. <emph type="italics"/>r.<emph.end type="italics"/> Tautologie. </s> <s>p. </s> <s>94. l. </s> <s>9. <emph type="italics"/>r.<emph.end type="italics"/> miracle;. </s> <s>p. </s> <s>97. l. </s> <s>13. <emph type="italics"/>r,<emph.end type="italics"/> weighty. </s> <s>p. </s> <s>101. <lb/>l. </s> <s>21. <emph type="italics"/>r.<emph.end type="italics"/> Marrara. </s> <s>p. </s> <s>107. l. </s> <s>28, <emph type="italics"/>r.<emph.end type="italics"/> Patrimony. </s> <s>l. </s> <s>40, <emph type="italics"/>r.<emph.end type="italics"/> above. </s> <s>p. </s> <s>111. l. </s> <s>16. <emph type="italics"/>r.<emph.end type="italics"/> &longs;aid. <emph type="italics"/>For<emph.end type="italics"/> p. </s> <s>432. <lb/><emph type="italics"/>r.<emph.end type="italics"/> p. </s> <s>114. p. </s> <s>114. l. </s> <s>35. <emph type="italics"/>r.<emph.end type="italics"/> of 200, l. </s> <s>41. <emph type="italics"/>r.<emph.end type="italics"/> clo&longs;ed. </s> <s>p. </s> <s>115. l. </s> <s>29. <emph type="italics"/>r.<emph.end type="italics"/> con&longs;tant;.</s></p><pb xlink:href="068/01/015.jpg" pagenum="1"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s><emph type="italics"/>LIB.<emph.end type="italics"/> I.</s></p><p type="main"> <s>What, and of how great moment the confi­<lb/>deration of <emph type="italics"/>Motion<emph.end type="italics"/> is in natural things, <lb/>is &longs;o manife&longs;t, that the Prince of <emph type="italics"/>Peri­<lb/>pateticks<emph.end type="italics"/> pronounced that in his Schools <lb/>now much u&longs;ed Sentence: <emph type="italics"/>Ignorato mo­<lb/>tu, ignoratur natura.<emph.end type="italics"/> Thence it is that <lb/>true Philo&longs;ophers have &longs;o travailed in the <lb/>contemplation of the Cele&longs;tial motions, <lb/>and in the &longs;peculation of the motions of <lb/>Animals, that they have arrived to a wonderful height and &longs;ub­<lb/>limity of under&longs;tanding. </s> <s>Under the &longs;ame Science of <emph type="italics"/>Motion<emph.end type="italics"/><lb/>is comprehended all that which is written by Mechanitians con­<lb/>cerning Engines moving of them&longs;elves, <emph type="italics"/>Machins<emph.end type="italics"/> moving by the <lb/>force of Air, and tho&longs;e which &longs;erve to move weights and im­<lb/>men&longs;e magnitudes with &longs;mall force. </s> <s>There appertaineth to the <lb/>Science of <emph type="italics"/>Motion<emph.end type="italics"/> all that which hath been written of the <lb/>alteration not onely of Bodies, but of our Minds al&longs;o; and <lb/>in &longs;um, this ample matter of <emph type="italics"/>Motion<emph.end type="italics"/> is &longs;o extended and di­<lb/>lated, that there are few things which fall under mans no­<lb/>tice, which are not conjoyned with <emph type="italics"/>Motion,<emph.end type="italics"/> or at lea&longs;t de­<lb/>pending thereupon, or to the knowledge thereof directed; <lb/>and of almo&longs;t every of them, there hath been written and <lb/>compo&longs;ed by &longs;ublime wits, learned Treati&longs;es and In&longs;tructions. <pb xlink:href="068/01/016.jpg" pagenum="2"/>And becau&longs;e that in the years pa&longs;t I had occa&longs;ion by Order of <lb/>our Lord Pope <emph type="italics"/>Vrban<emph.end type="italics"/> 8. to apply my thoughts to the motion of <lb/>the Waters of Rivers, (a matter difficult, mo&longs;t important, and <lb/>little handled by others) having concerning the &longs;ame ob&longs;erved <lb/>&longs;ome particulars not well ob&longs;erved, or con&longs;idered till now, but of <lb/>great moment both in publick and private affairs; I have thought <lb/>good to publi&longs;h them, to the end that ingenious &longs;pirits might <lb/>have occa&longs;ion to di&longs;cu&longs;&longs;e more exactly then hitherto hath been <lb/>done, &longs;o nece&longs;&longs;ary and profitable a matter, and to &longs;upply al&longs;o my <lb/>defects in this &longs;hort and difficult Tractate. </s> <s>Difficult I &longs;ay, for <lb/>the truth is, the&longs;e knowledges, though of things next our &longs;en&longs;es, <lb/>are &longs;ometimes more ab&longs;truce and hidden, then the knowledge of <lb/>things more remote; and much better, and with greater exqui&longs;it­<lb/>ne&longs;s are known the motions of the Planets, and Periods of the <lb/>Stars, than tho&longs;e of Rivers and Seas: As that &longs;ingular light of <lb/>Philo&longs;ophie of our times, and my Ma&longs;ter <emph type="italics"/>Signore Galileo Galilei<emph.end type="italics"/><lb/>wi&longs;ely ob&longs;erveth in his Book concerning the Solar &longs;pots. </s> <s>And <lb/>to proceed with a due order in Sciences, I will take &longs;ome &longs;uppo­<lb/>&longs;itions and cognitions &longs;ufficiently clear; from which I will after­<lb/>wards proceed to the deducing of the principal conclu&longs;ions. </s> <s>But <lb/>to the end that what I have written at the end of this di&longs;cour&longs;e in <lb/>a demon&longs;trative and Geometrical method, may al&longs;o be under­<lb/>&longs;tood of tho&longs;e which never have applyed their thoughts to the <lb/>&longs;tudy of Geometry; I have endeavoured to explain my conceit <lb/>by an example, and with the con&longs;ideration of the natural things <lb/>them&longs;elves, mu&longs;t after the &longs;ame order in which I began to doubt <lb/>in this matter; and have placed this particular Treati&longs;e here in <lb/>the beginning, adverting neverthele&longs;s, that he who de&longs;ires more <lb/>full and ab&longs;olute &longs;olidity of Rea&longs;ons, may overpa&longs;s this prefatory <lb/>di&longs;cour&longs;e, and onely con&longs;ider what is treated of in the demon&longs;tra­<lb/>tions placed towards the end, and return afterwards to the con&longs;i­<lb/>deration of the things collected in the <emph type="italics"/>Corollaries<emph.end type="italics"/> and Appendices; <lb/>which demon&longs;trations notwith&longs;tanding, may be pretermitted by <lb/>him that hath not &longs;een at lea&longs;t the fir&longs;t &longs;ix Books of the Elements <lb/>of Euclid; &longs;o that he diligently ob&longs;erveth that which fol­<lb/>loweth.</s></p><p type="main"> <s>I &longs;ay therefore, that having in times pa&longs;t, on divers occa&longs;i­<lb/>ons heard &longs;peak of the mea&longs;ures of the waters of Rivers, and <lb/>Fountains, &longs;aying, &longs;uch a River is two or three thou&longs;and feet of <lb/>water; &longs;uch a &longs;pring-water is twenty, thirty, or forty inches, <emph type="italics"/>&c.<emph.end type="italics"/><lb/>Although in &longs;uch manner I have found all to treat thereof in <lb/>word and writing, without variety, and as we are wont to &longs;ay, <lb/><emph type="italics"/>con&longs;tanti &longs;ermone,<emph.end type="italics"/> yea even Arti&longs;ts and Ingeneers, as if it were <lb/>a thing that admitted not of any doubt, yet how&longs;oever I re­<lb/>mained &longs;till infolded in &longs;uch an ob&longs;curity, that I well knew I un­<pb xlink:href="068/01/017.jpg" pagenum="3"/>der&longs;tood nothing at all, of that which others pretended full and <lb/>clearly to under&longs;tand. </s> <s>And my doubt aro&longs;e from my frequent <lb/>ob&longs;ervation of many Trenches and Channels, which carry <lb/>water to turn Mills, in which Trenches, and Channels, the <lb/>water being mea&longs;ured, was found pretty deep; but if afterwards <lb/>the &longs;ame water was mea&longs;ured in the fall it made to turn the <lb/>Wheel of the Mill, it was much le&longs;&longs;e, not amounting often to the <lb/>tenth part, nor &longs;ometimes to the twentieth, in&longs;omuch, that the <lb/>&longs;ame running water came to be one while more, another while le&longs;s <lb/>in mea&longs;ure, in divers parts of its Channel; and for that rea&longs;on this <lb/>vulgar manner of mea&longs;uring running Waters, as indeterminate and <lb/>uncertain, was by me ju&longs;tly &longs;u&longs;pected, the mea&longs;ure being to be de­<lb/>terminate, and the &longs;ame. </s> <s>And here I freely confe&longs;&longs;e that I had fin­<lb/>gular help to re&longs;olve this difficulty from the excellent & accurate <lb/>way of di&longs;cour&longs;ing, as in allother matters, &longs;o al&longs;o in this, of the <lb/>Right Honourable and Truly Noble Signior <emph type="italics"/>Ciampoli,<emph.end type="italics"/> Secretary <lb/>of the Popes &longs;ecret affairs. </s> <s>Who moreover, not &longs;paring &longs;or the co&longs;ts <lb/>of the &longs;ame, generou&longs;ly gave me occa&longs;ion a few years pa&longs;t to try by <lb/>exact experiments that which pa&longs;t concerning this particular. </s> <s>And <lb/>to explain all more clearly with an example; we &longs;uppo&longs;e a Ve&longs;&longs;el <lb/>filled with Water, as for in&longs;tance a Butt, which is kept full, though <lb/>&longs;till water runneth out, and the Water run out by two Taps equal <lb/>of bigne&longs;&longs;e, one put in the bottom of the Ve&longs;&longs;el, and the other in <lb/>the upper part; it is manife&longs;t that in the time wherein from the <lb/>upper part &longs;hall i&longs;&longs;ue a determinate mea&longs;ure of water &longs;rom <lb/>the inferiour part there &longs;hall i&longs;&longs;ue four, five, and many more of <lb/>the &longs;ame mea&longs;ures, according to the difference of the height of <lb/>the Taps, and the di&longs;tance of the upper Tap from the Superfici­<lb/>es and level of the water of the Ve&longs;&longs;el: and all this will alwayes <lb/>follow, though, as hath been &longs;aid, the Taps be equal, and the <lb/>water in di&longs;charging keep the &longs;aid Taps alwayes full. </s> <s>Where fir&longs;t <lb/>we note, that, although the mea&longs;ure of the Taps be equal, never­<lb/>thele&longs;&longs;e there i&longs;&longs;ueth from them in equal times unequal quantities <lb/>of water, And if we &longs;hould more attentively con&longs;ider this bu&longs;i­<lb/>ne&longs;&longs;e, we &longs;hould find, that the water by the lower Tap, run­<lb/>neth and pa&longs;&longs;eth with much greater velocity, then it doth by the <lb/>upper, whatever is the rea&longs;on. </s> <s>If therefore we would have <lb/>&longs;uch a quantity of Water di&longs;charge from the upper tap, as <lb/>would di&longs;charge from the neather in the &longs;ame time, it is plain, that <lb/>either the upper Taps mu&longs;t be multiplyed in &longs;uch &longs;ort, that &longs;o <lb/>many more Taps in number be placed above than below, as the <lb/>neather tap &longs;hall be more &longs;wift than the upper, or the upper Tap <lb/>made &longs;o much bigger than the nether, by how much that be­<lb/>neath &longs;hall be more &longs;wift than that above; and &longs;o then in equal <lb/>times, the &longs;ame quantity of Water &longs;hall di&longs;charge from the upper, <lb/>as doth from the neather part.</s></p><pb xlink:href="068/01/018.jpg" pagenum="4"/><p type="main"> <s>I will declare my &longs;elf by another example. </s> <s>If we &longs;hould ima­<lb/>gine, that two cords or lines of equal thickne&longs;s, be drawn through <lb/>two holes of equal bore; but &longs;o that the fir&longs;t pa&longs;s with quadruple <lb/>velocity to the &longs;econd: It is manife&longs;t, that if in a determinate <lb/>time, we &longs;hall by the fir&longs;t bore have drawn four Ells of the line, <lb/>in the &longs;ame time, by the &longs;econd hole we &longs;hall have drawn but one <lb/>Ell of cord onely; and if by the fir&longs;t there pa&longs;&longs;e twelve Ells, then <lb/>through the &longs;econd there &longs;hall pa&longs;&longs;e onely three Ells; and in <lb/>&longs;hort the quantity of cord &longs;hall have the &longs;ame proportion to the <lb/>cord, that the volocity hath to the velocity. </s> <s>And therefore we <lb/>de&longs;iring to compen&longs;ate the tardity of the &longs;econd cord, and main­<lb/>taining the &longs;ame tardity to draw through the &longs;econd hole as much <lb/>cord as through the fir&longs;t, it will be nece&longs;&longs;ary to draw through the <lb/>&longs;econd bore four ends of cord; &longs;o that the thickne&longs;s of all the <lb/>cords by the &longs;econd hole, have the &longs;ame proportion to the thick­<lb/>ne&longs;s of the cord which pa&longs;&longs;eth onely by the fir&longs;t, as the velocity <lb/>of the cord by the fir&longs;t hole hath reciprocally to the velocity of <lb/>the codrs by the &longs;econd hole. </s> <s>And thus its clear, that when <lb/>there is drawn through two holes equal quantity of cords in <lb/>equal time, but with unequal velocity, it will be nece&longs;&longs;ary, that <lb/>the thickne&longs;s of all the four cords &longs;hall have the &longs;ame reciprocal <lb/>proportion to the thickne&longs;s of the &longs;wifter cord, that the velo­<lb/>city of the &longs;wifter cord hath to the velocity of the &longs;lower. </s> <s>The <lb/>which is verified likewi&longs;e in the fluid Element of Water.</s></p><p type="main"> <s>And to the end that this principal fundamental be well under­<lb/>&longs;tood, I will al&longs;o note a certain ob&longs;ervation made my me in the <lb/>Art of Wyer-drawing, or &longs;pinning Gold, Silver, Bra&longs;s, and Iron, <lb/>and it is this; That &longs;uch Artificers de&longs;iring more and more to <lb/>di&longs;gro&longs;&longs;e and &longs;ubtillize the &longs;aid Metals, having would about a <lb/><emph type="italics"/>R<emph.end type="italics"/>ocket or Barrel, the thread of the Metal, they place the Roc­<lb/>ket in a frame upon a &longs;tedfa&longs;t Axis, in &longs;uch &longs;ort that the Rocket <lb/>may turn about in it &longs;elf; then making one end of the thread to <lb/>pa&longs;&longs;e by force through a Plate of Steel pierced with divers holes, <lb/>greater and le&longs;&longs;er, as need requireth, fa&longs;tning the &longs;ame end of the <lb/>thread to another Rocket, they wind up the thread, which pa&longs;­<lb/>&longs;ing through a bore le&longs;s than the thickne&longs;&longs;e of the thread, is of <lb/>force con&longs;trained to di&longs;gro&longs;&longs;e and &longs;ubtillize. </s> <s>Now that which is <lb/>inten&longs;ly to be ob&longs;erved in this bu&longs;ine&longs;s, is this, That the parts of <lb/>the thread before the hole, are of &longs;uch a thickne&longs;&longs;e, but the parts <lb/>of the &longs;ame thread after it is pa&longs;&longs;ed the hole, are of a le&longs;&longs;er thick­<lb/>ne&longs;&longs;e: and yet neverthele&longs;&longs;e the ma&longs;&longs;e and weight of the thread <lb/>which is drawn forth, is ever equal to the ma&longs;&longs;e and weight of the <lb/>thread which is winded up. </s> <s>But if we &longs;hould well con&longs;ider the mat­<lb/>ter, we &longs;hould finde, that the thicker the thread before the hole is, <lb/>than the thread pa&longs;&longs;ed the hole, the greater reciprocally is the <pb xlink:href="068/01/019.jpg" pagenum="5"/>velocity of the parts of the thread pa&longs;&longs;ed the hole, than the volo­<lb/>city of the parts before the hole: In&longs;omuch that if <emph type="italics"/>verbi gratia<emph.end type="italics"/><lb/>the thickne&longs;&longs;e of the thread before the hole, were double to the <lb/>thickne&longs;&longs;e after the hole, in &longs;uch ca&longs;e the velocity of the parts of <lb/>the thread pa&longs;&longs;ed the hole, &longs;hould be double to the velocity of the <lb/>parts of the thread before the hole; and thus the thickne&longs;&longs;e <lb/>compen&longs;ates the velocity, and the velocity compen&longs;ates the thick­<lb/>ne&longs;&longs;e. </s> <s>So that the &longs;ame occurreth in the &longs;olid Metals of Gold, <lb/>Silver, Bra&longs;s, Iron, &c. </s> <s>that eveneth al&longs;o in the fluid Element of <lb/>Water, and other liquids, namely, That the velocity beareth the <lb/>&longs;ame proportion to the velocity, that the thickne&longs;&longs;e of the Me­<lb/>tal, or Water, hath to the thickne&longs;&longs;e.</s></p><p type="main"> <s>And therefore granting this di&longs;cour&longs;e, we may &longs;ay, that as of­<lb/>ten as two Taps with different velocity di&longs;charge equal quanti­<lb/>ties of Water in equal times, it will be nece&longs;&longs;ary that the Tap <lb/>le&longs;&longs;e &longs;wift be &longs;o much greater, and larger, than the Tap more <lb/>&longs;wift, by how much the &longs;wifter &longs;uperates in velocity the &longs;lower; <lb/>and to pronounce the Propo&longs;ition in more proper terms, we &longs;ay; <lb/>That if two Taps of unequal velocity, di&longs;charge in equal times <lb/>equal quantities of Water, the greatne&longs;&longs;e of the fir&longs;t &longs;hall be to <lb/>the greatne&longs;&longs;e of the &longs;econd, in reciprocal proportion, as the ve­<lb/>locity of the &longs;econd to the velocity of the fir&longs;t. </s> <s>As for example, <lb/>if the fir&longs;t Tap &longs;hall be ten times &longs;wifter than the &longs;econd Tap, it <lb/>will be nece&longs;&longs;ary, that the &longs;econd be ten times bigger and larger <lb/>than the fir&longs;t; and in &longs;uch ca&longs;e the Taps &longs;hall di&longs;charge equall <lb/>quantities of water in equal times; and this is the principal and <lb/>mo&longs;t important point, which ought to be kept alwayes in minde, <lb/>for that on it well under&longs;tood depend many things profitable, <lb/>and worthy of our knowledge.</s></p><p type="main"> <s>Now applying all that hath been &longs;aid neerer to our purpo&longs;e, I <lb/>con&longs;ider, that it being mo&longs;t true, that in divers parts of the &longs;ame <lb/>River or Current of running water, there doth always pa&longs;&longs;e equal <lb/>quantity of Water in equal time (which thing is al&longs;o demon­<lb/>&longs;trated in out fir&longs;t Propo&longs;ition) and it being al&longs;o true, that in di­<lb/>vers parts the &longs;ame River may have various and different veloci­<lb/>ty; it follows of nece&longs;&longs;ary con&longs;equence, that where the River <lb/>hath le&longs;&longs;e velocity, it &longs;hall be of greater mea&longs;ure, and in tho&longs;e <lb/>parts, in which it hath greater velocity, it &longs;hall be of le&longs;&longs;e mea­<lb/>&longs;ure; and in &longs;um, the velocity of &longs;everal parts of the &longs;aid River, <lb/>&longs;hall have eternally reciprocall and like proportion with <lb/>their mea&longs;ures. </s> <s>This principle and fundamental well e&longs;tabli&longs;h­<lb/>ed, that the &longs;ame Current of Water changeth mea&longs;ure, accor­<lb/>ding to its varying of velocity; that is, le&longs;&longs;ening the mea&longs;ure, <lb/>when the velocity encrea&longs;eth, and encrea&longs;ing the mea&longs;ure, when <lb/>the velocity decrea&longs;eth; I pa&longs;&longs;e to the con&longs;ideration of many <pb xlink:href="068/01/020.jpg" pagenum="6"/>particular accidents in this admirable matter, and all depending <lb/>on this &longs;ole Propo&longs;ition, the &longs;en&longs;e of which I have oft repeated, <lb/>that it might be well under&longs;tood.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> I.</s></p><p type="main"> <s>And fir&longs;t, we hence conclude, that the &longs;ame Streams of a <lb/>Torrent, namely, tho&longs;e &longs;treams which carry equal quantity of <lb/>Water in equal times, make not the &longs;ame depths or mea&longs;ures in <lb/>the River, in which they enter, unle&longs;&longs;e when in the entrance in­<lb/>to the River they acquire; or to &longs;ay better, keep the &longs;ame velo­<lb/>city; becau&longs;e if the velocicities acquired in the River &longs;hall be <lb/>different, al&longs;o the mea&longs;ures &longs;hall be diver&longs;e; and con&longs;equently <lb/>the depths, as is demon&longs;trated.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> II.</s></p><p type="main"> <s>And becau&longs;e &longs;ucce&longs;&longs;ively, as the River is more and more full, <lb/>it is con&longs;tituted ordinarily in greater & greater velocity: hence <lb/>it is that the &longs;ame &longs;treams of the Torrent, that enter into the Ri­<lb/>ver, make le&longs;&longs;e and le&longs;&longs;e depths, as the River grows more and <lb/>more full; &longs;ince that al&longs;o the Waters of the Torrent being en­<lb/>tered into the River, go acquiring greater and greater velocities, <lb/>and therefore dimini&longs;h in mea&longs;ure and height.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> III.</s></p><p type="main"> <s>We ob&longs;erve al&longs;o, that while the main River is &longs;hallow, if there <lb/>fall but a gentle rain, it &longs;uddenly much increa&longs;eth and ri&longs;eth; <lb/>but when the River is already &longs;welled, though there fall again a­<lb/>nother new violent &longs;hower, yet it increa&longs;eth not at the &longs;ame rate <lb/>as before, proportionably to the rain which fell: which thing <lb/>we may affirm particularly to depend on this, that in the fir&longs;t <lb/>ca&longs;e, while the River is low, it is found al&longs;o very &longs;low, and there­<lb/>fore the little water which entereth into it, pa&longs;&longs;eth and runs with <lb/>little velocity, and con&longs;equently occupieth a great mea&longs;ure: <lb/>But when the River is once augmented, by new water being al&longs;o <lb/>made more &longs;wift, it cau&longs;eth the great Flood of water which fal­<lb/>leth, to bear a le&longs;&longs;e mea&longs;ure, and not to make &longs;uch a depth.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> IV.</s></p><p type="main"> <s>From the things demon&longs;trated is manife&longs;t al&longs;o, that whil&longs;t a <lb/>Torrent entereth into a River, at the time of Ebbe, then the <lb/>Torrent moveth with &longs;uch a certain velocity, what ever it be, <pb xlink:href="068/01/021.jpg" pagenum="7"/>pa&longs;&longs;ing by its extreame&longs;t parts, wherewith it communicateth with <lb/>the River; in which parts, the Torrent being mea&longs;ured, &longs;hall <lb/>have &longs;uch a certain mea&longs;ure: but the River &longs;welling and ri&longs;ing, <lb/>al&longs;o tho&longs;e parts of the Torrent augment in greatne&longs;&longs;e and mea­<lb/>&longs;ure, though the Torrent, in that in&longs;tant, di&longs;-imbogue no more <lb/>water than it did before: &longs;o that the River being &longs;welled, we <lb/>are to con&longs;ider two mouths of the &longs;ame Torrent, one le&longs;&longs;e be­<lb/>fore the ri&longs;ing, the other greater after the ri&longs;ing, which mouths <lb/>di&longs;charge equal quantities of water in equal times; therefore the <lb/>velocity by the le&longs;&longs;er mouth &longs;hall be greater than the velocity by <lb/>the greater mouth; and thus the Torrent &longs;hall be retarded from <lb/>its ordinary cour&longs;e.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> V.</s></p><p type="main"> <s>From which operation of Nature proceedeth another effect <lb/>worthy of con&longs;ideration; and it is, that the cour&longs;e of the water <lb/>retarding, as hath been &longs;aid in tho&longs;e ultimate parts of the Tor­<lb/>rent, if it &longs;hall happen that the Torrent grow torbid and mud­<lb/>dy, and its &longs;treame be retarded in &longs;uch a degree, that it is not <lb/>able to carry away tho&longs;e minute grains of Earth, which com­<lb/>po&longs;e the muddine&longs;&longs;e; in this ca&longs;e the Torrent &longs;hall clear away <lb/>the mud, and carry away the Sand at the bottome of its own <lb/>Chanel, in the extream parts of its mouth, which rai&longs;ed and <lb/>voided Sand, &longs;hall again afterwards be carried away, when the <lb/>River abating, the Torrent &longs;hall return to move with its primitive <lb/>velocity.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> VI.</s></p><p type="main"> <s>Whil&longs;t it is demon&longs;trated, that the &longs;ame water hath different <lb/>mea&longs;ures in its Chanel or cour&longs;e, according as it varieth in <lb/>velocity; &longs;o that the mea&longs;ure of the water is alwayes greater, where <lb/>the velocity is le&longs;&longs;er; and on the contrary, the mea&longs;ure le&longs;&longs;er, <lb/>where the velocity is greater: from hence we may mo&longs;t ele­<lb/>gantly render the rea&longs;on of the u&longs;ual Proverb, <emph type="italics"/>Take heed of the <lb/>&longs;till waters:<emph.end type="italics"/> For that if we con&longs;ider the &longs;elf &longs;ame water of a <lb/>River in tho&longs;e parts, wherein it is le&longs;s &longs;wift, and thence called <emph type="italics"/>&longs;till<emph.end type="italics"/><lb/>or <emph type="italics"/>&longs;mooth<emph.end type="italics"/> water, it &longs;hall be, of nece&longs;&longs;ity, of greater mea&longs;ure <lb/>than in tho&longs;e parts, in which it is more &longs;wift, and therefore ordi­<lb/>narily &longs;hall be al&longs;o more deep and dangerous for pa&longs;&longs;engers; <lb/>whence it is well &longs;aid, <emph type="italics"/>Take heed of the &longs;till Waters<emph.end type="italics"/>; and this <lb/>&longs;aying hath been &longs;ince applied to things moral.</s></p><pb xlink:href="068/01/022.jpg" pagenum="8"/><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> VII.</s></p><p type="main"> <s>Likewi&longs;e, from the things demon&longs;trated may be concluded, <lb/>that the windes, which &longs;top a <emph type="italics"/>R<emph.end type="italics"/>iver, and blowing again&longs;t the <lb/>Current, retard its cour&longs;e and ordinary velocity &longs;hall nece&longs;&longs;arily <lb/>amplifie the mea&longs;ure of the &longs;ame River, and con&longs;equently &longs;hall <lb/>be, in great part, cau&longs;es; or we may &longs;ay, potent con-cau&longs;es of <lb/>making the extraordinary inundations which Rivers u&longs;e to make. <lb/></s> <s>And its mo&longs;t certain, that as often as a &longs;trong and continual wind <lb/>&longs;hall blow again&longs;t the Current of a River, and &longs;hall reduce the <lb/>water of the River to &longs;uch tardity of motion, that in the time <lb/>wherein before it run five miles, it now moveth but one, &longs;uch a <lb/>River will increa&longs;e to five times the mea&longs;ure, though there &longs;hould <lb/>not be added any other quantity of water; which thing indeed <lb/>hath in it &longs;omething of &longs;trange, but it is mo&longs;t certain, for that <lb/>look what proportion the waters velocity before the winde, hath <lb/>to the velocity after the winde, and &longs;uch reciprocally is the mea­<lb/>&longs;ure of the &longs;ame water after the winde, to the mea&longs;ure before <lb/>the winde; and becau&longs;e it hath been &longs;uppo&longs;ed in our ca&longs;e that the <lb/>velocity is dimini&longs;hed to a fifth part, therefore the mea&longs;ure &longs;hall <lb/>be increa&longs;ed five times more than that, which it was before.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> VIII.</s></p><p type="main"> <s>We have al&longs;o probable the cau&longs;e of the inundations of <emph type="italics"/>Tyber,<emph.end type="italics"/><lb/>which befel at <emph type="italics"/>Rome,<emph.end type="italics"/> in the time of <emph type="italics"/>Alexander<emph.end type="italics"/> the Sixth, & of <lb/><emph type="italics"/>Clement<emph.end type="italics"/> the Seventh; which innundations came in a &longs;erene time, <lb/>and without great thaws of the Snows; which therefore much <lb/>puzzled the wits of tho&longs;e times. </s> <s>But we may with much pro­<lb/>bability affirm, That the River ro&longs;e to &longs;uch a height and excre&longs;­<lb/>cence, by the retardation of the Waters dependant on the <lb/>boi&longs;trous and con&longs;tant Winds, that blew in tho&longs;e times, as is no­<lb/>red in the memorials.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/> IX.</s></p><p type="main"> <s>It being mo&longs;t manife&longs;t, that by the great abundance of Water <lb/>the Torrents may increa&longs;e, and of them&longs;elves alone exorbitantly <lb/>&longs;well the River; and having demon&longs;trated that al&longs;o without new <lb/>Water, but onely by the notable retardment the River ri&longs;eth and <lb/>increa&longs;eth in mea&longs;ure, in proportion as the velocity decrea&longs;eth: <lb/>hence it is apparent, that each of the&longs;e cau&longs;es being able of it &longs;elf, <lb/>and &longs;eparate from the other to &longs;well the River; when it &longs;hall <lb/>happen that both the&longs;e two cau&longs;es con&longs;pire the augmentation of <pb xlink:href="068/01/023.jpg" pagenum="9"/>the River, in &longs;uch a ca&longs;e there mu&longs;t follow very great and irre­<lb/>pable innundations.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> X.</s></p><p type="main"> <s>From what hath been demon&longs;trated, we may with facility re­<lb/>&longs;olve the doubt which hath troubled, and &longs;till po&longs;eth the mo&longs;t <lb/>diligent, but incautelous ob&longs;ervers of Rivers, who mea&longs;uring <lb/>the Streams and Torrents which fall into another River; as tho&longs;e <lb/>for in&longs;tance, which enter into the <emph type="italics"/>Po,<emph.end type="italics"/> or tho&longs;e which fall into <emph type="italics"/>Ti­<lb/>ber<emph.end type="italics"/>; and having &longs;ummed the total of the&longs;e mea&longs;ures, and con­<lb/>ferring the mea&longs;ures of the Rivers and Brooks, which fall into <lb/><emph type="italics"/>Tiber,<emph.end type="italics"/> with the mea&longs;ure of <emph type="italics"/>Tiber,<emph.end type="italics"/> and the mea&longs;ures of tho&longs;e which <lb/>di&longs;imbogue into <emph type="italics"/>Po,<emph.end type="italics"/> with the mea&longs;ure of <emph type="italics"/>Po,<emph.end type="italics"/> they find them not <lb/>equal, as, it &longs;eems to them, they ought to be, and this is becau&longs;e <lb/>they have not well noted the mo&longs;t important point of the varia­<lb/>tion of velocity, and how that it is the mo&longs;t potent cau&longs;e of won­<lb/>derfully altering the mea&longs;ures of running Waters; but we mo&longs;t <lb/>facilly re&longs;olving the doubt, may &longs;ay that the&longs;e Waters dimini&longs;h <lb/>the mea&longs;ure, being once entered the principal Channel, becau&longs;e <lb/>they increa&longs;e in velocity.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XI.</s></p><p type="main"> <s>Through the ignorance of the force of the velocity of the Wa­<lb/>ter, in altering its mea&longs;ure, & augmenting it when the velocity <lb/>dimini&longs;heth; and dimini&longs;hing it when the velocity augmenteth: <lb/>The Architect <emph type="italics"/>Giovanni Fontana,<emph.end type="italics"/> endeavoured to mea&longs;ure, and <lb/>and to cau&longs;e to be mea&longs;ured by his Nephew, all the Brooks and <lb/>Rivers which di&longs;charged their Waters into <emph type="italics"/>Tiber,<emph.end type="italics"/> at the time of <lb/>the Innundation; which happened at <emph type="italics"/>Rome<emph.end type="italics"/> in the year 1598, <lb/>and publi&longs;hed a &longs;mall Treati&longs;e thereof, wherein he &longs;ummeth up <lb/>the mea&longs;ures of the extraordinary Water which fell into <emph type="italics"/>Tiber,<emph.end type="italics"/><lb/>and made account that it was about five hundred Ells more than <lb/>ordinary; and in the end of that Treati&longs;e concludeth, that to re­<lb/>move the Innundation wholly from <emph type="italics"/>Rome,<emph.end type="italics"/> it would be nece&longs;&longs;ary <lb/>to make two other Channels, equal to that at pre&longs;ent, and that <lb/>le&longs;&longs;e would not &longs;uffice; and finding afterwards that the whole <lb/>Stream pa&longs;&longs;ed under the Bridge <emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> (the Arch where­<lb/>of is of a far le&longs;s mea&longs;ure then five hundred Ells) concludeth, <lb/>that under the &longs;aid Bridge pa&longs;t a hundred fifty one Ells of Water <lb/>compre&longs;&longs;ed, (I have &longs;et down the preci&longs;e term of compre&longs;t Wa­<lb/>ter, written by <emph type="italics"/>Fontana<emph.end type="italics"/>) wherein I finde many errors.</s></p><p type="main"> <s>The fir&longs;t of which is to think that the mea&longs;ures of the&longs;e Wa­<lb/>ters compre&longs;&longs;ed in the Channels of tho&longs;e Brooks and Rivers, <pb xlink:href="068/01/024.jpg" pagenum="10"/>&longs;hould maintain them&longs;elves the &longs;ame in <emph type="italics"/>Tiber,<emph.end type="italics"/> which by his leave, <lb/>is mo&longs;t fal&longs;e, when ever tho&longs;e waters reduced into <emph type="italics"/>Tiber,<emph.end type="italics"/> retain <lb/>not the &longs;ame velocity which they had in the place in which <emph type="italics"/>Fon­<lb/>tana<emph.end type="italics"/> and his Nephew mea&longs;ured them: And all this is manife&longs;t <lb/>from the things which we have above explained; for, if the Wa­<lb/>ters reduced into <emph type="italics"/>Tiber<emph.end type="italics"/> increa&longs;e in velocity, they decrea&longs;e in mea­<lb/>&longs;ure; and if they decrea&longs;e in velocity, they increa&longs;e in mea­<lb/>&longs;ure.</s></p><p type="main"> <s>Secondly, I con&longs;ider that the mea&longs;ures of tho&longs;e Brooks and <lb/>Rivers, which enter into <emph type="italics"/>Tiber<emph.end type="italics"/> at the time of Innundation, are <lb/>not between them&longs;elves really the &longs;ame, when their velocities are <lb/>not equal, though they have the &longs;ame names of Ells and Feet; <lb/>for that its po&longs;&longs;ible that a di&longs;inboguement of ten Ells requadrated <lb/>(to &longs;peak in the phra&longs;e of <emph type="italics"/>Fontana<emph.end type="italics"/>) of one of tho&longs;e Brooks, <lb/>might di&longs;charge into <emph type="italics"/>Tiber<emph.end type="italics"/> at the time of Innundation, four, ten, <lb/>and twenty times le&longs;s Water, than another mouth equal to the <lb/>fir&longs;t in greatne&longs;s, as would occur when the fir&longs;t mouth were four, <lb/>ten, or twenty times le&longs;s &longs;wift than the &longs;econd. </s> <s>Whereupon, <lb/>whil&longs;t <emph type="italics"/>Fontana<emph.end type="italics"/> &longs;ummes up the Ells and Feet of the mea&longs;ures of <lb/>tho&longs;e Brooks and Rivers into a total aggregate, he commits the <lb/>&longs;ame error with him, which would add into one &longs;umme diver&longs;e <lb/>moneys of diver&longs;e values, and diver&longs;e places, but that had the <lb/>&longs;ame name; as if one &longs;hould &longs;ay ten Crowns of <emph type="italics"/>Roman<emph.end type="italics"/> money, <lb/>four Crowns of Gold, thirteen Crowns of <emph type="italics"/>Florence,<emph.end type="italics"/> five Growns <lb/>of <emph type="italics"/>Venice,<emph.end type="italics"/> and eight Crowns of <emph type="italics"/>Mantua,<emph.end type="italics"/> &longs;hould make the &longs;ame <lb/>&longs;umme with forty Crowns of Gold, or forty Crowns of <emph type="italics"/>Mantua.<emph.end type="italics"/></s></p><p type="main"> <s>Thirdly, It might happen that &longs;ome River or Current in the <lb/>parts nearer <emph type="italics"/>Rome,<emph.end type="italics"/> in the time of its flowing, did not &longs;end forth <lb/>more Water than ordinary; and however, its a thing very clear, <lb/>that whil&longs;t the &longs;tream came from the &longs;uperior parts, that &longs;ame <lb/>Brook or River would be augmented in mea&longs;ure, as hath been <lb/>noted in the fourth <emph type="italics"/>Corollary<emph.end type="italics"/>; in &longs;uch &longs;ort, that <emph type="italics"/>Fontana<emph.end type="italics"/> might <lb/>have inculcated, and noted that &longs;ame River or Current as con­<lb/>curring to the Innundation, although it were therein altogether <lb/>unconcerned.</s></p><p type="main"> <s>Moreover, in the fourth place we mu&longs;t note, That it might <lb/>&longs;o fall out, that &longs;uch a River not onely was unintere&longs;&longs;ed in the <lb/>Innundation, though augmented in mea&longs;ure, but it might I &longs;ay <lb/>happen, that it was in&longs;trumental to the a&longs;&longs;waging the Innunda­<lb/>tion, by augmenting in the mea&longs;ure of its own Channel; which <lb/>matter is &longs;ufficiently evident; for if it be &longs;uppo&longs;ed that the Ri­<lb/>ver in the time of flood, had not had of it &longs;elf, and from its pro­<lb/>per &longs;prings more Water than ordinary, its a thing certain, that <lb/>the Water of <emph type="italics"/>Tiber<emph.end type="italics"/> ri&longs;ing and increa&longs;ing; al&longs;o that River, to le­<lb/>vel it &longs;elf with the Water of <emph type="italics"/>Tiber,<emph.end type="italics"/> would have retained &longs;ome of <pb xlink:href="068/01/025.jpg" pagenum="11"/>its Waters in its own Chanel, without di&longs;charging them into <emph type="italics"/>Ty­<lb/>ber,<emph.end type="italics"/> or el&longs;e would have ingorged and &longs;wallowed (if I may &longs;o &longs;ay) <lb/>&longs;ome of the water of <emph type="italics"/>Tyber<emph.end type="italics"/>; and in this ca&longs;e, at the time of In­<lb/>undation, le&longs;&longs;e abundance of water would have come to <emph type="italics"/>Rome,<emph.end type="italics"/><lb/>and yet neverthele&longs;&longs;e the mea&longs;ure of that River would have been <lb/>increa&longs;ed.</s></p><p type="main"> <s>Fifthly, <emph type="italics"/>Fontana<emph.end type="italics"/> deceiveth him&longs;elf, when he concludeth, that <lb/>to remove the Inundation from <emph type="italics"/>Rome,<emph.end type="italics"/> it would be nece&longs;&longs;ary to <lb/>make two other Chanels of Rivers, that were as large as that, <lb/>which is the pre&longs;ent one, and that le&longs;s would not &longs;uffice, which, <lb/>I &longs;ay, is a fallacy: and to convince him ea&longs;ily of his errour, it <lb/>&longs;ufficeth to &longs;ay, that all the Streams being pa&longs;&longs;ed under the Bridge <lb/><emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> as he him&longs;elf atte&longs;ts, a Channel would &longs;uffice on­<lb/>ly of the capacity of the &longs;aid Bridge, provided that the water <lb/>there might run with the &longs;ame velocity, as it did under the Bridge <lb/>at the time of Inundation; and on the contrary, twenty Cur­<lb/>rents of capacity equal to the pre&longs;ent one, would not &longs;uffice, if <lb/>the water &longs;hould run with twenty times le&longs;s velocity, than it made <lb/>at the time of the Inundation.</s></p><p type="main"> <s>Sixthly, to me it &longs;eemeth a great weakne&longs;&longs;e to &longs;ay, that there <lb/>&longs;hould pa&longs;&longs;e under the Bridge <emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> an hundred fifty one <lb/>ells of water compre&longs;&longs;ed; for that I do not under&longs;tand that wa­<lb/>ter is like Cotton or Wool, which matters may be pre&longs;t and trod, <lb/>as it happeneth al&longs;o to the air, which receiveth compre&longs;&longs;ion in <lb/>&longs;uch &longs;ort, that after that in &longs;ome certain place a quantity of air <lb/>&longs;hall be reduced to its natural con&longs;titution; and having taken up <lb/>all the &longs;aid place, yet neverthele&longs;&longs;e compre&longs;&longs;ing the fir&longs;t Air <lb/>with force and violence, it is reduced into far le&longs;s room, and will <lb/>admit four or &longs;ix times as much air, as before, as is experimen­<lb/>tally ^{*} &longs;een in the Wind-Gun, invented in our dayes by <emph type="italics"/>M. Vin,<emph.end type="italics"/><lb/><arrow.to.target n="marg964"></arrow.to.target><lb/><emph type="italics"/>cenzo Vincenti<emph.end type="italics"/> of <emph type="italics"/>Vrbin,<emph.end type="italics"/> which property of the Air of admit­<lb/>ting conden&longs;ation, is al&longs;o &longs;een in the portable Fountains of the <lb/>&longs;ame <emph type="italics"/>M. Vincenzo:<emph.end type="italics"/> which Fountains &longs;pirt the Water on high, <lb/>by force of the Air compre&longs;&longs;ed, which whil&longs;t it &longs;eeks to reduce <lb/>its &longs;elf to its natural con&longs;titution, in the dilation cau&longs;eth that vi­<lb/>olence. </s> <s>But the water can never, for any thing I know, crowd, <lb/>or pre&longs;s &longs;o, as that if before the compre&longs;&longs;ion it held or po&longs;&longs;e&longs;t a <lb/>place, being in its natural con&longs;titution, I believe not, I &longs;ay, that it <lb/>is po&longs;&longs;ible, by pre&longs;&longs;ing and crowding to make it po&longs;&longs;e&longs;s le&longs;s room, <lb/>for if it were po&longs;&longs;ible to compre&longs;s the Water, and make it to oc­<lb/>cupy a le&longs;s place, it would thence follow, that two Ve&longs;&longs;els of e­<lb/>qual mea&longs;ure, but of unequal height, &longs;hould be of unequal capa­<lb/>city, and that &longs;hould hold more water which was higher; al&longs;o a <lb/>Cylinder, or other Ve&longs;&longs;el more high than broad, would containe <lb/>more water erected, than being laid along; for that being erect­<pb xlink:href="068/01/026.jpg" pagenum="12"/>ed, the water put therein would be more pre&longs;&longs;ed and crowded.</s></p><p type="margin"> <s><margin.target id="marg964"></margin.target>* And as is at <lb/>large demon&longs;trated <lb/>by that mo&longs;t excel­<lb/>lent and lonour­<lb/>able per&longs;onage Mr. <lb/><emph type="italics"/>Botle<emph.end type="italics"/> in the indu­<lb/>&longs;trious experiment <lb/>of his Pneumatical <lb/>Engine.</s></p><p type="main"> <s>And therefore, in our ca&longs;e, according to our principles we will <lb/>&longs;ay, that the water of that Stream pa&longs;seth all under the &longs;aid <lb/>Bridge <emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> for that being there mo&longs;t &longs;wift, it ought of <lb/>con&longs;equence to be le&longs;s in mea&longs;ure.</s></p><p type="main"> <s>And here one may &longs;ee, into how many errours a man may run <lb/>through ignorance of a true and real Principle, which once known <lb/>and well under&longs;tood, takes away all mi&longs;ts of doubting, and ea­<lb/>&longs;ily re&longs;olveth all difficulties.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/> XII.</s></p><p type="main"> <s>Through the &longs;ame inadvertency of not regarding the variation <lb/>of velocity in the &longs;ame Current, therea re committed by Ingi­<lb/>neers and Learned men, errours of very great moment (and I <lb/>could thereof produce examples, but for good rea&longs;ons I pa&longs;s <lb/>them over in &longs;ilence) when they think, and propo&longs;e, by deriving <lb/>new Channels from great Rivers, to dimini&longs;h the mea&longs;ure of the <lb/>water in the River, and to dimini&longs;h it proportionally, according <lb/>to the mea&longs;ure of the Water which they make to pa&longs;s through <lb/>the Channel, as making <emph type="italics"/>v.g<emph.end type="italics"/> a Channel fifty foot broad, in which <lb/>the derived water is to run wa&longs;te, ten foot deep, they think they <lb/>have dimini&longs;hed the mea&longs;ure of the Water in the River five hun­<lb/>dred feet, which thing doth not indeed &longs;o fall out; and the rea­<lb/>&longs;on is plain; for that the Chanel being derived, the re&longs;t of the <lb/>main River, dimini&longs;heth in velocity, and therefore retains a grea­<lb/>ter mea&longs;ure than it had at fir&longs;t before the derivation of the Cha­<lb/>nel; and moreover, if the Chanel being derived, it &longs;hall not <lb/>con&longs;erve the &longs;ame velocity which it had at fir&longs;t in the main Ri­<lb/>ver, but &longs;hall dimini&longs;h it, it will be nece&longs;&longs;ary, that it hath a grea­<lb/>ter mea&longs;ure than it had before in the River; and therefore <lb/>to accompt aright, there &longs;hall not be &longs;o much water derived into <lb/>the Channel, as &longs;hall dimini&longs;h the River, according to the quanti­<lb/>ty of the water in the Channel, as is pretended.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XIII.</s></p><p type="main"> <s>This &longs;ame con&longs;ideration giveth me occa&longs;ion to di&longs;cover a mo&longs;t <lb/>ordinary errour, ob&longs;erved by me in the bu&longs;ine&longs;&longs;e of the wa­<lb/>ter of <emph type="italics"/>Ferara,<emph.end type="italics"/> when I was in tho&longs;e parts, in &longs;ervice of the mo&longs;t <lb/>Reverend and Illu&longs;trious Monfignor <emph type="italics"/>Cor&longs;ini<emph.end type="italics"/>; the &longs;ublime wit of <lb/>whom hath been a very great help to me in the&longs;e contemplations; <lb/>its very true, I have been much perplexed, whether I &longs;hould <lb/>commit this particular to paper, or pa&longs;&longs;e it over in &longs;ilence, for <lb/>that I have ever doubted, that the opinion &longs;o common and <pb xlink:href="068/01/027.jpg" pagenum="13"/>moreover confirmed with a mo&longs;t manife&longs;t experiment, may not <lb/>onely make this my conjecture to be e&longs;teemed far from true, <lb/>but al&longs;o to di&longs;credit with the World the re&longs;t of this my Treati&longs;e: <lb/>Neverthele&longs;&longs;e I have at la&longs;t re&longs;olved not to be wanting to my <lb/>&longs;elf, and to truth in a matter of it &longs;elf, and for other con&longs;e­<lb/>quences mo&longs;t important; nor doth it &longs;eem to me requi&longs;ite in <lb/>difficult matters, &longs;uch as the&longs;e we have in hand, to refigne our <lb/>&longs;elves to the common opinion, &longs;ince it would be very &longs;trange if <lb/>the multitude in &longs;uch matters &longs;hould hit on the truth, nor ought <lb/>that to be held difficult, in which even the vulgar do know the <lb/>truth and right; be&longs;ides that I hope morever to prove all in &longs;uch <lb/>&longs;ort, that per&longs;ons of &longs;olid judgment, &longs;hall re&longs;t fully per&longs;waded, <lb/>&longs;o that they but keep in mind the principal ground and foundation <lb/>of all this Treati&longs;e; and though that which I will propo&longs;e, be a par­<lb/>ticular, as I have &longs;aid, pertaining onely to the intere&longs;ts of <emph type="italics"/>Ferara<emph.end type="italics"/>; <lb/>yet neverthele&longs;&longs;e from this particular Doctrine well under&longs;tood, <lb/>good judgement may be made of other the like ca&longs;es in general.</s></p><p type="main"> <s>I &longs;ay then, for greater per&longs;pecuity, and better under&longs;tanding <lb/>of the whole, That about thirteen miles above <emph type="italics"/>Ferara,<emph.end type="italics"/> near to <lb/><emph type="italics"/>Stellata,<emph.end type="italics"/> the main of P<emph type="italics"/>o,<emph.end type="italics"/> branching it &longs;elf into two parts, with one <lb/>of its Arms it cometh clo&longs;e to <emph type="italics"/>Ferara,<emph.end type="italics"/> retaining the name of the <lb/>P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/>; and here again it divideth it &longs;elf into two other <lb/>branches, and that which continueth on the right hand, is called <lb/>the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> and of <emph type="italics"/>Primaro<emph.end type="italics"/>; and that on the left the P<emph type="italics"/>o<emph.end type="italics"/><lb/>of <emph type="italics"/>Volana.<emph.end type="italics"/> But for that the bed of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being here­<lb/>tofore augmented and rai&longs;ed, it followeth that it re&longs;teth wholly <lb/>deprived of the Water of the great P<emph type="italics"/>o,<emph.end type="italics"/> except in the time of its <lb/>greater &longs;welling; for in that ca&longs;e, this P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being re­<lb/>&longs;trained with a Bank near to <emph type="italics"/>Bondeno,<emph.end type="italics"/> would come al&longs;o in the <lb/>overflowings of the main P<emph type="italics"/>o,<emph.end type="italics"/> to be free from its Waters: But the <lb/>Lords of <emph type="italics"/>Ferara<emph.end type="italics"/> are wont at &longs;uch time as the P<emph type="italics"/>o<emph.end type="italics"/> threateneth to <lb/>break out, to cut the bank; by which cutting, there di&longs;­<lb/>gorgeth &longs;uch a Torrent of Water, that it is ob&longs;erved, that the <lb/>main P<emph type="italics"/>o<emph.end type="italics"/> in the &longs;pace of &longs;ome few hours abateth near a foot, and <lb/>all per&longs;ons that I have &longs;poken with hitherto, moved by this ex­<lb/>periment, think that it is of great profit and benefit to keep ready <lb/>this Vent, and to make u&longs;e of it in the time of its fullne&longs;&longs;e. </s> <s>And <lb/>indeed, the thing con&longs;idered &longs;imply, and at the fir&longs;t appearance, <lb/>it &longs;eemeth that none can think otherwi&longs;e; the rather, for that <lb/>many examining the matter narrowly, mea&longs;ure that body of <lb/>Water which runneth by the Channel, or Bed of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Fera­<lb/>ra,<emph.end type="italics"/> and make account, that the body of the Water of the great <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> is dimini&longs;hed the quantity of the body of the Water which <lb/>runneth by the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara.<emph.end type="italics"/> But if we well remember what <lb/>hath been &longs;aid in the beginning of the Treati&longs;e, and how much <pb xlink:href="068/01/028.jpg" pagenum="14"/>the variety of the velocities of the &longs;aid Water importeth, and the <lb/>knowledge of them is nece&longs;&longs;ary to conclude the true quantity of <lb/>the running Water, we &longs;hall finde it manife&longs;t, that the benefit of <lb/>this Vent is far le&longs;&longs;e than it is generally thought: And mereover, <lb/>we &longs;hall finde, if I deceive not my &longs;elf, that there follow from <lb/>thence &longs;o many mi&longs;chiefs, that I could greatly incline to believe, <lb/>that it were more to the purpo&longs;e wholly to &longs;top it up, than to <lb/>maintain it open: yet I am not &longs;o wedded to my opinion, but <lb/>that I am ready to change my judgement upon &longs;trength of better <lb/>rea&longs;ons; e&longs;pecially of one that &longs;hall have fir&longs;t well under&longs;tood <lb/>the beginning of this my di&longs;cour&longs;e, which I frequently inculcate, <lb/>becau&longs;e its ab&longs;olutely impo&longs;&longs;ible without this adverti&longs;ement to <lb/>treat of the&longs;e matters, and not commit very great errours.</s></p><p type="main"> <s>I propo&longs;e therefore to con&longs;ideration, that although it be true, <lb/>that whil&longs;t the water of the main P<emph type="italics"/>o<emph.end type="italics"/> is at its greate&longs;t height, the <lb/>Bank and Dam then cut of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara,<emph.end type="italics"/> and the &longs;uperior <lb/>waters having a very great fall into the Channel of <emph type="italics"/>Ferara,<emph.end type="italics"/> they <lb/>precipitate into the &longs;ame with great violence and velocity, and <lb/>with the &longs;ame in the beginning, or little le&longs;&longs;e, they run towards <lb/>the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Volana,<emph.end type="italics"/> and of <emph type="italics"/>Argenta<emph.end type="italics"/> on the &longs;ea coa&longs;ts; yet after the <lb/>&longs;pace of &longs;ome few hours, the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being full, and the &longs;u­<lb/>perior Waters not finding &longs;o great a diclivity there, as they had <lb/>at the beginning of the cutting, they fall not into the &longs;ame with <lb/>the former velocity, but with far le&longs;&longs;e, and thereby a great deal <lb/>le&longs;&longs;e Water begins to i&longs;&longs;ue from the great P<emph type="italics"/>o<emph.end type="italics"/>; and if we dili­<lb/>gently compare the velocity at the fir&longs;t cutting, with the velocity <lb/>of the Water after the cutting made, and when the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/><lb/>&longs;hall be full of Water, we &longs;hall finde perhaps that to be fifteen or <lb/>twenty times greater than this, and con&longs;equently the Water <lb/>which i&longs;&longs;ues from the great P<emph type="italics"/>o,<emph.end type="italics"/> that fir&longs;t impetuo&longs;ity being pa&longs;t, <lb/>&longs;hall be onely the fifteenth or twentieth part of that which i&longs;&longs;ued <lb/>at the beginning; and therefore the Waters of the main P<emph type="italics"/>o<emph.end type="italics"/> will <lb/>return in a &longs;mall time almo&longs;t to the fir&longs;t height. </s> <s>And here I will <lb/>pray tho&longs;e who re&longs;t not wholly &longs;atisfied with what hath been &longs;aid, <lb/>that for the love of truth, and the common good, they would <lb/>plea&longs;e to make diligent ob&longs;ervation whether in the time of great <lb/>Floods, the &longs;aid Bank or Dam at <emph type="italics"/>Bondeno<emph.end type="italics"/> is cut, and that in few <lb/>hours the main P<emph type="italics"/>o<emph.end type="italics"/> dimini&longs;heth, as hath been &longs;aid about a foot in <lb/>its height; that they would ob&longs;erve I &longs;ay, whether, a day or two <lb/>being pa&longs;t, the Waters of the main P<emph type="italics"/>o<emph.end type="italics"/> return almo&longs;t to their fir&longs;t <lb/>height; for if this &longs;hould follow, it would be very clear, that the <lb/>benefit which re&longs;ulteth from this diver&longs;ion or Vent, is not &longs;o great <lb/>as is univer&longs;ally pre&longs;umed; I &longs;ay, it is not &longs;o great as is <lb/>pre&longs;umed; becau&longs;e, though it be granted for true, that <lb/>the Waters of the main P<emph type="italics"/>o,<emph.end type="italics"/> abate at the beginning of <pb xlink:href="068/01/029.jpg" pagenum="17"/>the Vent, yet this benefit happens to be but temporary and for a <lb/>few hours: If the ri&longs;ing of P<emph type="italics"/>o,<emph.end type="italics"/> and the dangers of breaking forth <lb/>were of &longs;hort duration, as it ordinarily befalleth in the overflow­<lb/>ings of Torrents, in &longs;uch a ca&longs;e the profit of the Vent would be <lb/>of &longs;ome e&longs;teem: But becau&longs;e the &longs;wellings of P<emph type="italics"/>o<emph.end type="italics"/> continue for <lb/>thirty, or &longs;ometimes for forty dayes, therefore the gain which <lb/>re&longs;ults from the Vent proveth to be incon&longs;iderable. </s> <s>It remain­<lb/>eth now to con&longs;ider the notable harms which follow the &longs;aid <lb/>Sluice or Vent, that &longs;o reflection being made, and the profit and <lb/>the detriment compared, one may rightly judge, and choo&longs;e that <lb/>which &longs;hall be mo&longs;t convenient. </s> <s>The fir&longs;t prejudice therefore <lb/>which ari&longs;eth from this Vent or Sluice, is; That the Channels of <lb/><emph type="italics"/>Ferara, Primaro,<emph.end type="italics"/> and <emph type="italics"/>Volana<emph.end type="italics"/> filling with Water, all tho&longs;e parts <lb/>from <emph type="italics"/>Bondeno<emph.end type="italics"/> to the Sea &longs;ide are allarmed and endangered <lb/>thereby. </s> <s>Secondly, The Waters of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro<emph.end type="italics"/> having <lb/>free ingre&longs;&longs;e into the upper Valleys, they fill them to the great <lb/>damage of the Fields adjacent, and ob&longs;truct the cour&longs;e of the <lb/>ordinary Trenches in the &longs;ame Valleys; in&longs;omuch that all the <lb/>care, co&longs;t, and labour about the draining, and freeing the upper <lb/>Valleys from Water, would al&longs;o become vain and ineffectual. <lb/></s> <s>Thirdly, I con&longs;ider that the&longs;e Waters of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being <lb/>pa&longs;&longs;ed downwards towards the Sea, at the time that the main P<emph type="italics"/>o<emph.end type="italics"/><lb/>was in its greater excre&longs;cences and heights, it is manife&longs;t by expe­<lb/>rience, that when the great P<emph type="italics"/>o<emph.end type="italics"/> dimini&longs;heth, then the&longs;e Waters <lb/>pa&longs;&longs;ed by the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> begin to retard in their cour&longs;e, and <lb/>finally come to turn the current upwards towards <emph type="italics"/>Stellata,<emph.end type="italics"/> re&longs;ting <lb/>fir&longs;t iu the intermediate time, almo&longs;t fixed and &longs;tanding, and <lb/>therefore depo&longs;ing the muddine&longs;&longs;e, they fill up the Channel of <lb/>the River or Current of <emph type="italics"/>Ferara.<emph.end type="italics"/> Fourthly and la&longs;tly, There <lb/>followeth from this &longs;ame diver&longs;ion another notable damage, and <lb/>it is like to that which followeth the breaches made by Rivers; <lb/>near to which breaches in the lower parts, namely below the <lb/>breach, there is begot in the Channel of the River, a certain ridge <lb/>or &longs;helf, that is, the bottom of the River is rai&longs;ed, as if &longs;ufficiently <lb/>manife&longs;t by experience; and thus ju&longs;t in the &longs;ame manner cutting <lb/>the Bank at <emph type="italics"/>Bondeno,<emph.end type="italics"/> there is at it were a breach made, from which <lb/>followeth the ri&longs;ing in the lower parts of the main P<emph type="italics"/>o,<emph.end type="italics"/> being pa&longs;t <lb/>the mouth of <emph type="italics"/>Pamaro<emph.end type="italics"/>; which thing, how pernitious it is, let any one <lb/>judge that under&longs;tandeth the&longs;e matters. </s> <s>And therefore both for <lb/>the &longs;mall benefit, and &longs;o many harms that en&longs;ue from maintain­<lb/>ing this diver&longs;ion, I &longs;hould think it were more &longs;ound advice to <lb/>keep that Bank alwaies whole at <emph type="italics"/>Bondeno,<emph.end type="italics"/> or in any other conve­<lb/>nient place, and not to permit that the Water of the Grand P<emph type="italics"/>o<emph.end type="italics"/><lb/>&longs;hould ever come near to <emph type="italics"/>Ferara.<emph.end type="italics"/></s></p><pb xlink:href="068/01/030.jpg" pagenum="16"/><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XIV.<lb/><arrow.to.target n="marg965"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg965"></margin.target>* <emph type="italics"/>Arte&longs;ia.<emph.end type="italics"/></s></p><p type="main"> <s>In the Grand Rivers, which fall into the Sea, as here in <emph type="italics"/>Italy <lb/>Po, Adige,<emph.end type="italics"/>^{*} and <emph type="italics"/>Arno,<emph.end type="italics"/> which are armed with Banks again&longs;t their <lb/>excre&longs;cencies, its ob&longs;erved that far from the Sea, they need <lb/>Banks of a notable height; which height goeth afterwards by <lb/>degrees dimini&longs;hing, the more it approacheth to the Sea-coa&longs;ts: <lb/>in &longs;uch &longs;ort, that the P<emph type="italics"/>o,<emph.end type="italics"/> di&longs;tant from the Sea about fifty or &longs;ixty <lb/>miles at <emph type="italics"/>Ferara,<emph.end type="italics"/> &longs;hall have Banks that be above twenty feet <lb/>higher than the ordinary Water marks; but ten or twelve miles <lb/>from the Sea, the Banks are not twelve feet higher than the &longs;aid <lb/>ordinary Water-marks, though the breadth of the River be the <lb/>&longs;ame, &longs;o that the excre&longs;cence of the &longs;ame Innundation happens <lb/>to be far greater in mea&longs;ure remote from the Sea, then near; and <lb/>yet it &longs;hould &longs;eem, that the &longs;ame quantity of Water pa&longs;&longs;ing by <lb/>every piace, the River &longs;hould need to have the &longs;ame altitude of <lb/>Banks in all places: But we by our Principles and fundamentals <lb/>may be able to render the rea&longs;on of that effect, and &longs;ay; That <lb/>that exce&longs;&longs;e of quantity of Water, above the ordinary Water, <lb/>goeth alwaies acquiring greater velocity; the nearer it approach­<lb/>eth the Sea, and therefore decrea&longs;eth in mea&longs;ure, and con&longs;equenly <lb/>in height. </s> <s>And this perhaps might have been the cau&longs;e in great <lb/>part, why the <emph type="italics"/>Tyber<emph.end type="italics"/> in the Innundation <emph type="italics"/>Anno<emph.end type="italics"/> 1578. i&longs;&longs;ued not <lb/>forth of its Channel below <emph type="italics"/>Rome<emph.end type="italics"/> towards the Sea.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XV.</s></p><p type="main"> <s>From the &longs;ame Doctrine may be rendred a mo&longs;t manife&longs;t rea­<lb/>&longs;on why the falling Waters go le&longs;&longs;ening in their de&longs;cent, &longs;o <lb/>that the &longs;ame falling Water, mea&longs;ured at the beginning of <lb/>its fall, is greater, and bigger, and afterwards by degrees le&longs;&longs;eneth <lb/>in mea&longs;ure the more it is remote from the beginning of the fall. <lb/></s> <s>Which dependeth on no other, than on the acqui&longs;ition, which <lb/>it &longs;ucce&longs;&longs;ively makes of greater velocity; it being a mo&longs;t fami­<lb/>liar conclu&longs;ion among Philo&longs;ophers, that grave bodies falling, <lb/>the more they remove from the beginning of their motion, the <lb/>more they acquire of &longs;wiftne&longs;&longs;e; and therefore the Water, as a <lb/>grave body, falling, gradually velocitates, and therefore de­<lb/>crea&longs;eth in mea&longs;ure, and le&longs;&longs;eneth.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XVI.</s></p><p type="main"> <s>And on the contrary, the &longs;pirtings of a Fountain of Water, <lb/>which &longs;pring on high, work a contrary effect; namely <pb xlink:href="068/01/031.jpg" pagenum="17"/>in the beginning they are &longs;mall, and afterwards become greater <lb/>and bigge; and the rea&longs;on is mo&longs;t manife&longs;t, becau&longs;e in the be­<lb/>ginning they are very &longs;wift, and afterwards gradually relent <lb/>their impetuo&longs;ity, and motion, &longs;o that in the beginning of the <lb/>excur&longs;ion that they make, they ought to be &longs;mall, and after­<lb/>wards to grow bigger, as in the effect is &longs;een.</s></p><p type="head"> <s>APPENDIX. I.</s></p><p type="main"> <s>Into the errour of not con&longs;idering how much the different <lb/>velocities of the &longs;ame running water in &longs;everal places of <lb/>its current, are able to change the mea&longs;ure of the &longs;ame <lb/>water, and to make it greater, or le&longs;&longs;e, I think, if I be not <lb/>deceived, that <emph type="italics"/>Ginlio Frontino<emph.end type="italics"/> a noble antient Writer, may <lb/>have faln in the Second Book which he writ, of the Aqueducts <lb/>of the City of <emph type="italics"/>Rome<emph.end type="italics"/>: Whil&longs;t finding the mea&longs;ure of the Water <lb/>^{*}<emph type="italics"/>Commentaries<emph.end type="italics"/> le&longs;&longs;e than it was <emph type="italics"/>in erogatione 1263. Quinaries,<emph.end type="italics"/> he </s></p><p type="main"> <s><arrow.to.target n="marg966"></arrow.to.target><lb/>thought that &longs;o much difference might proceed from the negligence <lb/>of the Mea&longs;ures; and when afterwards with his own indu&longs;try he <lb/>mea&longs;ured the &longs;ame water at the beginnings of the Aqueducts, <lb/>finding it neer 10000. <emph type="italics"/>Quinaries<emph.end type="italics"/> bigger than it was <emph type="italics"/>in Commenta­<lb/>riis<emph.end type="italics"/> he judged, that the overplus was imbeziled by Mini&longs;ters and <lb/>Partakers; which in part might be &longs;o, for it is but too true, that <lb/>the publique is almo&longs;t alwayes defrauded; yet neverthele&longs;&longs;e, I <lb/>verily believe withal, that be&longs;ides the frauds of the&longs;e Officers, <lb/>the velocities of the water in the place wherein <emph type="italics"/>Frontino<emph.end type="italics"/> mea&longs;u­<lb/>red, it might be different from tho&longs;e velocities, which are <lb/>found in other places before mea&longs;ured by others; and there­<lb/>fore the mea&longs;ures of the waters might, yea ought nec&longs;&longs;arily to <lb/>be diffcrent, it having been by us demon&longs;trated, that the mea­<lb/>&longs;ures of the &longs;ame running water have reciprocal proportion to <lb/>their velocities. </s> <s>Which <emph type="italics"/>Frontino<emph.end type="italics"/> not well con&longs;idering, and find­<lb/>ing the water <emph type="italics"/>in Commentariis 12755. Quinaries in erogati­<lb/>one<emph.end type="italics"/> 14018, and in his own mea&longs;ure <emph type="italics"/>ad capita ductuum,<emph.end type="italics"/> at the <lb/>head of the fountain 22755. <emph type="italics"/>Quinaries,<emph.end type="italics"/> or thereabouts, he <lb/>thought, that in all the&longs;e places there pa&longs;t different quantities of <lb/>water; namely, greater at the fountain head then that which was <lb/><emph type="italics"/>in Erogatione,<emph.end type="italics"/> and this he judged greater than that which was <lb/><emph type="italics"/>in Commentariis.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg966"></margin.target>+ <emph type="italics"/>Commentarius<emph.end type="italics"/><lb/>beareth many &longs;en­<lb/>&longs;es, but in this <lb/>place &longs;ignifieth a <lb/>certain Regi&longs;ter of <lb/>the quantities of <lb/>the Waters in the <lb/>&longs;everal publique A­<lb/>qu ducts of <emph type="italics"/>Rome<emph.end type="italics"/>; <lb/>which word I find <lb/>frequently u&longs;ed in <lb/>the Law-books of <lb/>antient Civilians: <lb/>Andby errogation <lb/>we are to under­<lb/>&longs;tand the di&longs;tribu­<lb/>tion or delivering <lb/>out of tho&longs;e &longs;tores <lb/>of Water.</s></p><p type="head"> <s>APPENDIX II.</s></p><p type="main"> <s>Alike mi&longs;take chanced lately in the Aqueduct of <emph type="italics"/>Acqua­<lb/>Paola,<emph.end type="italics"/> which Water &longs;hould be 2000 Inches, and &longs;o many <lb/>effectively ought to be allowed; and it hath been given in <pb xlink:href="068/01/032.jpg" pagenum="18"/>&longs;o to be by the Signors of <emph type="italics"/>Bracciano<emph.end type="italics"/> to the <emph type="italics"/>Apo&longs;tolick-Chamber<emph.end type="italics"/>; <lb/>and there was a mea&longs;ure thereof made at the beginning of the <lb/>Aqueduct; which mea&longs;ure proved afterwards much le&longs;&longs;e and <lb/>&longs;hort, con&longs;idered and taken in <emph type="italics"/>Rome,<emph.end type="italics"/> and thence followed di&longs;­<lb/>contents and great di&longs;orders, and all becau&longs;e this property of <lb/>Running-Waters, of increa&longs;ing in mea&longs;ure, where the velocity <lb/>decrea&longs;ed; and of dimini&longs;hing in mea&longs;ure, where the velocity <lb/>augmented, was not lookt into.</s></p><p type="head"> <s>APPENDIX III.</s></p><p type="main"> <s>Alike errour, in my judgement, hath beeen committed by <lb/>all tho&longs;e learned men, which to prevent the diver&longs;ion of <lb/>the <emph type="italics"/>Reno<emph.end type="italics"/> of <emph type="italics"/>Bologna<emph.end type="italics"/> into P<emph type="italics"/>o<emph.end type="italics"/> by the Channels, through <lb/>which it at pre&longs;ent runneth, judged, that the <emph type="italics"/>Reno<emph.end type="italics"/> being in its <lb/>greater excre&longs;cence about 2000 feet, and the P<emph type="italics"/>o<emph.end type="italics"/> being near <lb/>1000 feet broad, they judged, I &longs;ay, that letting the <emph type="italics"/>Reno<emph.end type="italics"/> into <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> it would have rai&longs;ed the Water of P<emph type="italics"/>o<emph.end type="italics"/> two feet; from which <lb/>ri&longs;e, they concluded afterwards mo&longs;t exorbitant di&longs;orders, either <lb/>of extraordinary Inundations, or el&longs;e of immen&longs;e and intolera­<lb/>ble expences to the people in rai&longs;ing the Banks of P<emph type="italics"/>o<emph.end type="italics"/> and <emph type="italics"/>Reno,<emph.end type="italics"/><lb/>and with &longs;uch like weakne&longs;&longs;es, often vainly di&longs;turbed the minds <lb/>of the per&longs;ons concerned: But now from the things demon&longs;tra­<lb/>ted, it is manife&longs;t, That the mea&longs;ure of the <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno,<emph.end type="italics"/> would <lb/>be different from the mea&longs;ure of <emph type="italics"/>Reno<emph.end type="italics"/> in P<emph type="italics"/>o<emph.end type="italics"/>; in ca&longs;e that the <lb/>velocity of the <emph type="italics"/>Reno<emph.end type="italics"/> in P<emph type="italics"/>o,<emph.end type="italics"/> &longs;hould differ from the velocity <lb/>of <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno,<emph.end type="italics"/> as is more exactly determined in the fourth Pro­<lb/>po&longs;ition.</s></p><p type="head"> <s>APPENDIX IV.</s></p><p type="main"> <s>No le&longs;s likewi&longs;e are tho&longs;e Ingeneers and Arti&longs;ts deceived, <lb/>that have affirmed, That letting the <emph type="italics"/>Reno<emph.end type="italics"/> into P<emph type="italics"/>o,<emph.end type="italics"/> there <lb/>would be no ri&longs;e at all in the Water of P<emph type="italics"/>o<emph.end type="italics"/>: For the truth <lb/>is, That letting <emph type="italics"/>Reno<emph.end type="italics"/> into P<emph type="italics"/>o,<emph.end type="italics"/> there would alwaies be a ri&longs;ing; but <lb/>&longs;ometimes greater, &longs;ometimes le&longs;&longs;e, as the P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall have a &longs;wifter <lb/>or &longs;lower Current; &longs;o that if the P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall be con&longs;tituted in a great <lb/>velocity, the ri&longs;e will be very &longs;mall; and if the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall be <lb/>&longs;low in its cour&longs;e, then the ri&longs;e will be notable.</s></p><p type="head"> <s>APPENDIX V.</s></p><p type="main"> <s>And here it will not be be&longs;ides the purpo&longs;e to adverti&longs;e, That <lb/>the mea&longs;ures, partments, and di&longs;tributions of the Waters <lb/>of Fountains, cannot be made exactly, unle&longs;s there be con­<pb xlink:href="068/01/033.jpg" pagenum="19"/>fidered, be&longs;ides the mea&longs;ure, the velocity al&longs;o of the Water; <lb/>which particular not being thorowly ob&longs;erved, is the cau&longs;e of <lb/>continual mi&longs;cariages in &longs;uch like affairs.</s></p><p type="head"> <s>APPENDIX VI.</s></p><p type="main"> <s>Like con&longs;ideration ought to be had with the greater diligence, <lb/>for that an errour therein is more prejudicial; I &longs;ay, ought to <lb/>be had by tho&longs;e which part and divide Waters; for the <lb/>watering of fields, as is done in the Territories of <emph type="italics"/>Bre&longs;cia, Ber­<lb/>gama, Crema, Pavia, Lodigiano, Cremona,<emph.end type="italics"/> and other places: <lb/>For if they have not regard to the mo&longs;t important point of the <lb/>variation of the velocity of the Water, but onely to the bare <lb/>Vulgar mea&longs;ure, there will alwaies very great di&longs;orders and pre­<lb/>judices en&longs;ue to the per&longs;ons concerned.</s></p><p type="head"> <s>APPENDIX VII.</s></p><p type="main"> <s>It &longs;eemeth that one may ob&longs;erve, that whil&longs;t the Water run­<lb/>neth along a Channel, Current, or Conduit, its velocity is <lb/>retarded, withheld, and impeded by its touching the Bank or <lb/>&longs;ide of the &longs;aid Channel or Current; which, as immoveable, not <lb/>following the motion of the Water, interrupteth its velocity: <lb/>From which particular, being true, as I believe it to be mo&longs;t <lb/>true, and from our con&longs;iderations, we have an occa&longs;ion of di&longs;­<lb/>covering a very nice mi&longs;take, into which tho&longs;e commonly fall <lb/>who divide the Waters of Fountains. </s> <s>Which divi&longs;ion is wont <lb/>to be, by what I have &longs;een here in <emph type="italics"/>Rome,<emph.end type="italics"/> performed two wayes; <lb/>The fir&longs;t of which is with the mea&longs;ures of like figures, as Cir­<lb/>cles, or Squares, having cut through a Plate of metal &longs;everal <lb/>Circles or Squares, one of half an inch, another of one inch, <lb/>another of two, of three, of four, <emph type="italics"/>&c.<emph.end type="italics"/> with which they after­<lb/>wards adju&longs;t the Cocks to di&longs;pence the Waters. </s> <s>The other <lb/>manner of dividing the Waters of Fountains, is with rectangle <lb/>paralellograms, of the &longs;ame height, but of different Ba&longs;es, in &longs;uch <lb/>&longs;ort likewi&longs;e, that one paralellogram be of half an inch, another <lb/>of one, two, three, <emph type="italics"/>&c.<emph.end type="italics"/> In which manner of mea&longs;uring and <lb/>dividing the Water, it &longs;hould &longs;eem that the Cocks being placed <lb/>in one and the &longs;ame plain, equidi&longs;tant from the level, or &longs;uperior <lb/>&longs;uperficies of the water of the Well; and the &longs;aid mea&longs;ures be­<lb/>ing mo&longs;t exactly made, the Water ought con&longs;equently al&longs;o to <lb/>be equally divided, and parted according to the proportion of <lb/>the mea&longs;ures. </s> <s>But if we well con&longs;ider every particular, we &longs;hall <lb/>finde, that the Cocks, as they &longs;ucce&longs;&longs;ively are greater, di&longs;charge <lb/>alwaies more Water than the ju&longs;t quantity, in compari&longs;on of <pb xlink:href="068/01/034.jpg" pagenum="20"/>the le&longs;&longs;er; that is, to &longs;peak more properly, The Water which <lb/>pa&longs;&longs;eth through the greater Cock, hath alwaies a greater pro­<lb/>portion to that which pa&longs;&longs;eth through the le&longs;&longs;er, than the greater <lb/>Cock hath to the le&longs;&longs;er. </s> <s>All which I will declare by an exam­<lb/>ple.</s></p><p type="main"> <s>Let there be &longs;uppo&longs;ed for more plainne&longs;s two Squares; (the <lb/>&longs;ame may be under&longs;tood of Circles, and other like Figures) The <lb/>fir&longs;t Square is, as we will &longs;uppo&longs;e, quadruple to the other, and <lb/>the&longs;e Squares are the mouths of two Cocks.; one of four inches, <lb/>the other of one: Now its manife&longs;t by what hath been &longs;aid, that <lb/>the Water which pa&longs;&longs;eth by the le&longs;s Cock, findeth its velocity <lb/>impeded in the circumference of the Cock; which impediment <lb/><figure id="id.068.01.034.1.jpg" xlink:href="068/01/034/1.jpg"/><lb/>is mea&longs;ured by the &longs;aid circumfe­<lb/>rence. </s> <s>Now it is to be con&longs;ider­<lb/>ed, that if we would have the Wa­<lb/>ter which pa&longs;&longs;eth through the <lb/>greater Cock, to be onely qua­<lb/>druple to that which pa&longs;&longs;eth <lb/>through the le&longs;&longs;e, in equal &longs;paces of time, it would be nece&longs;&longs;ary, <lb/>that not onely the capacity and the mea&longs;ure of the greater Cock <lb/>be quadruple to the le&longs;&longs;er Cock, but that al&longs;o the impediment be <lb/>quadrupled. </s> <s>Now in our ca&longs;e it is true, That the belly and <lb/>mouth of the Cock is quadrupled, and yet the impediment is not <lb/>quadrupled, but is onely doubled; &longs;eeing that the circumference <lb/>of the greater Square, is onely double to the circumference of <lb/>the le&longs;ier Square; for the greater circumference containeth eight <lb/>of tho&longs;e parts, of which the le&longs;&longs;er containeth but four, as is ma­<lb/>nife&longs;t by the de&longs;cribed Figure; and for that cau&longs;e there &longs;hall <lb/>pa&longs;s by the greater Cock, above four times as much Water, as <lb/>&longs;hall pa&longs;s by the le&longs;&longs;er Cock.</s></p><p type="main"> <s>The like errour occurreth al&longs;o in the other manner of mea&longs;u­<lb/>ring the Water of a Fountain, as may ea&longs;ily be collected from <lb/>what hath been &longs;aid and ob&longs;erved above.</s></p><p type="head"> <s>APPENDIX VIII.</s></p><p type="main"> <s>The &longs;ame contemplation di&longs;covereth the errour of tho&longs;e <lb/>Architects, who being to erect a Bridge of &longs;undry Arches <lb/>over a River, con&longs;ider the ordinary breadth of the River; <lb/>which being <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> fourty fathom, and the Bridge being to con&longs;i&longs;t <lb/>of four Arches, it &longs;ufficeth them, that the breadth of all the four <lb/>Arches taken together, be fourty fathom; not con&longs;idering that <lb/>in the ordinary Channel of the River, the Water hath onely <lb/>two impediments which retard its velocity; namely, the touching <lb/>and gliding along the two &longs;ides or &longs;hores of the River: but <pb xlink:href="068/01/035.jpg" pagenum="21"/>the &longs;ame water in pa&longs;&longs;ing under the Bridge, in our ca&longs;e meeteth <lb/>with eight of the &longs;ame impediments, bearing, and thru&longs;ting upon <lb/>two &longs;ides of each Arch (to omit the impediment of the bottom, <lb/>for that it is the &longs;ame in the River, and under the Bridge) from <lb/>which inadvertency &longs;ometimes follow very great di&longs;orders, as <lb/>quotidian practice &longs;hews us.</s></p><p type="head"> <s>APPENDIX IX.</s></p><p type="main"> <s>It is al&longs;o worthy to con&longs;ider the great and admirable benefit <lb/>that tho&longs;e fields receive, which are wont to drink up the Rain­<lb/>water with difficulty, through the height of the water in the <lb/>principal Ditches; in which ca&longs;e the careful Husbandman cutteth <lb/>away the reeds and ru&longs;hes in the Ditches, through which the <lb/>waters pa&longs;s; whereupon may be pre&longs;ently &longs;een, &longs;o &longs;oon as the <lb/>reeds and ru&longs;hes are cut, a notable Ebb in the level of the water <lb/>in the Ditches; in&longs;omuch that &longs;ometimes it is ob&longs;erved, that the <lb/>water is abated after the &longs;aid cutting a third and more, of what it <lb/>was before the cutting. </s> <s>The which effect &longs;eemingly might de­<lb/>pend on this, That, before tho&longs;e weeds took up room in the <lb/>Ditch, and for that cau&longs;e the water kept a higher level, and the <lb/>&longs;aid Plants being afterwards cut and removed, the water came to <lb/>abate, po&longs;&longs;e&longs;&longs;ing the place that before was occupied by the <lb/>weeds: Which opinion, though probable, and at fir&longs;t &longs;ight &longs;a­<lb/>tisfactory, is neverthele&longs;s in&longs;ufficient to give the total rea&longs;on of <lb/>that notable abatement which hath been &longs;poken of: But it is ne­<lb/>ce&longs;&longs;ary to have recour&longs;e to our confideration of the velocity in <lb/>the cour&longs;e of the water, the chiefe&longs;t and true cau&longs;e of the vari­<lb/>ation of the mea&longs;ure of the &longs;ame Running-Water; for, that <lb/>multitudes of reeds, weeds, and plants di&longs;per&longs;ed through the cur­<lb/>rent of the Ditch, do chance notably to retard the cour&longs;e of the <lb/>water, and therefore the mea&longs;ure of the water increa&longs;eth; and <lb/>tho&longs;e impediments removed, the &longs;ame water gaineth velocity, <lb/>and therefore decrea&longs;eth in mea&longs;ure, and con&longs;equently in <lb/>height.</s></p><p type="main"> <s>And perhaps this point well under&longs;tood, may be of great <lb/>profit to the fields adjacent to the <emph type="italics"/>Pontine<emph.end type="italics"/> Fens, and I doubt not <lb/>but if the River <emph type="italics"/>Ninfa,<emph.end type="italics"/> and the other principal Brooks of tho&longs;e <lb/>Territories were kept well clean&longs;ed from weeds, their waters <lb/>would be at a lower level, and con&longs;equently the drains of the <lb/>fields would run into them more readily; it being alwayes to be <lb/>held for undoubted, that the mea&longs;ure of the water before the <lb/>clean&longs;ing, hath the &longs;ame proportion to the mea&longs;ure after clean­<lb/>&longs;ing, that the velocity after the clean&longs;ing hath to the velocity <lb/>before the clean&longs;ing: An dbecau&longs;e tho&longs;e weeds being clean&longs;ed <pb xlink:href="068/01/036.jpg" pagenum="22"/>away, the cour&longs;e ef the water notably increa&longs;eth, it is therefore <lb/>nece&longs;&longs;ary that the &longs;aid water abate in mea&longs;ure, and become <lb/>lower.</s></p><p type="head"> <s>APPENDIX. X.</s></p><p type="main"> <s>We having above ob&longs;erved &longs;ome errors that are commit­<lb/>ted in di&longs;tributing the waters of Fountains, and tho&longs;e <lb/>that &longs;erve to water fields; it &longs;eemeth now fit, by way of <lb/>a clo&longs;e to this di&longs;cour&longs;e, to adverti&longs;e by what means the&longs;e divi­<lb/>&longs;ions may be made ju&longs;tly and without error. </s> <s>I therefore think <lb/>that one might two &longs;everal wayes exqui&longs;itly divide the water of <lb/>Fountains; The fir&longs;t would be by diligently examining, Fir&longs;t, <lb/>how much water the whole Fountain di&longs;chargeth in a determi­<lb/>nate time, as for in&longs;tance: How many Barrels, or Tuns it carri­<lb/>eth in a &longs;et time; and in ca&longs;e you are afterwards to di&longs;tribute <lb/>the water, di&longs;tribute it at the rate of &longs;omany Barrels or Tuns, in <lb/>that &longs;ame time; and in this ca&longs;e the participants would have <lb/>their punctual &longs;hares: Nor could it ever happen to &longs;end out more <lb/>water, than is reckoned to be in the principal Fountain; as befel <lb/><emph type="italics"/>Giulio Frontino,<emph.end type="italics"/> and as al&longs;o it frequently happeneth in the Mo­<lb/>dern Aqueducts, to the publick and private detriment.</s></p><p type="main"> <s>The other way of dividing the &longs;ame waters of a Fountain, is <lb/>al&longs;o &longs;ufficiently exact and ea&longs;ie, and may be, by having one one­<lb/>ly &longs;ize for the Cock or Pipe, as &longs;uppo&longs;e of an inch, or of half an <lb/>inch; and when the ca&longs;e requireth to di&longs;pence two, three, and <lb/>more inches, take &longs;o many Cocks of the &longs;aid mea&longs;ure as do eva­<lb/>cuate the water, which is to be emitted; and if we are to make <lb/>u&longs;e onely of one greater Cock, we being to place one to di&longs;­<lb/>charge for example four inches; and having the former &longs;ole mea­<lb/>&longs;ure of an inch, we mu&longs;t make a Cock that is bigger, its true, than <lb/>the Cock of one inch; but not &longs;imply in a quadruple propor­<lb/>tion, for that it would di&longs;charge more than ju&longs;t &longs;o much water, <lb/>as hath been &longs;aid above; but we ought to examine diligently <lb/>how much water the little Cock emitteth in an hour; and then <lb/>enlarge, and contract the greater Cock, &longs;o, that it may di&longs;­<lb/>charge four times as much water as the le&longs;&longs;er in the &longs;ame time; <lb/>and by this means we &longs;hall avoid the di&longs;order hinted in the <lb/>&longs;eventh Appendix. </s> <s>It would be nece&longs;&longs;ary neverthele&longs;s, to ac­<lb/>commodate the Cocks of the Ci&longs;tern &longs;o, that the level of the <lb/>water in the Ci&longs;tern may alwayes re&longs;t at one determinate mark <lb/>above the Cock, otherwi&longs;e the Cocks will emit &longs;ometimes <lb/>greater, and &longs;ometimes le&longs;&longs;e abundance of water: And becau&longs;e <lb/>it may be that the &longs;ame water of the Fountain may be &longs;ometimes <lb/>more abundant, &longs;ometimes le&longs;s; in &longs;uch ca&longs;e it will be nece&longs;&longs;ary <pb xlink:href="068/01/037.jpg" pagenum="23"/>to adju&longs;t the Ci&longs;tern &longs;o, that the exce&longs;s above the ordinary wa­<lb/>ter, di&longs;charge into the publick Fountains, that &longs;o the particular <lb/>participants may have alwayes the &longs;ame abundance of <lb/>water.</s></p><p type="head"> <s>APPENDIX XI.</s></p><p type="main"> <s>Much more difficult is the divi&longs;ion of the waters which <lb/>&longs;erve to water the fields, it not being po&longs;&longs;ible to ob&longs;erve <lb/>&longs;o commodiou&longs;ly, what quantity of water the whole <lb/>Ditch &longs;ends forth in one determinate time, as may be done in <lb/>Fountains: Yet neverthele&longs;s, if the &longs;econd propo&longs;ition by us a <lb/>little below demon&longs;trated, be well under&longs;tood, there may be <lb/>thence taken a very &longs;afe and ju&longs;t way to di&longs;tribute &longs;uch waters. <lb/></s> <s>The Propo&longs;ition therefore by us demon&longs;trated is this: If there <lb/>be two Sections, (namely two mouths of Rivers) the quantity of <lb/>the water which pa&longs;&longs;eth by the fir&longs;t, hath a proportion to that <lb/>which pa&longs;&longs;eth by the &longs;econd, compounded of the proportions of <lb/>the fir&longs;t Section to the &longs;econd, and of the velocity through <lb/>the fir&longs;t, to the velocity through the &longs;econd: As I will declare <lb/>for example by help of practice, that I may be under&longs;tood by <lb/>all, in a matter &longs;o important. </s> <s>Let the two mouths of the <lb/>Rivers be A, and B, and let <lb/><figure id="id.068.01.037.1.jpg" xlink:href="068/01/037/1.jpg"/><lb/>the mouth A be in mea&longs;ure <lb/>and content thirty two feet, <lb/>and the mouth B, eight feet. <lb/></s> <s>Here you mu&longs;t take notice, <lb/>that it is not alwayes true, that <lb/>the Water which pa&longs;&longs;eth by A, <lb/>hath the &longs;ame proportion to that which pa&longs;&longs;eth by B, that the <lb/>mouth A hath to the mouth B; but onely when the velocityes <lb/>by each of tho&longs;e pa&longs;&longs;ages are equal: But if the velocityes &longs;hall <lb/>be unequal, it may be that the &longs;aid mouths may emit equal <lb/>quantity of Water in equal times, though their mea&longs;ure be un­<lb/>equal; and it may be al&longs;o, that the bigger doth di&longs;charge a great­<lb/>er quantity of Water: And la&longs;tly, it may be, that the le&longs;s mouth <lb/>di&longs;chargeth more Water than the greater; and all this is mani­<lb/>fe&longs;t by the things noted in the beginning of this di&longs;cour&longs;e, and <lb/>by the &longs;aid &longs;econd Propo&longs;ition. </s> <s>Now to examine the propor­<lb/>tion of the Water that pa&longs;&longs;eth by one Ditch, to that which pa&longs;­<lb/>&longs;eth by another, that this being known, the &longs;ame Waters and <lb/>mouths of Ditches may be then adju&longs;ted; we are to keep ac­<lb/>count not onely of the greatne&longs;s of the mouths or pa&longs;&longs;ages of the <lb/>Water, but of the velocity al&longs;o; which we will do, by fir&longs;t find­<lb/>ing two numbers that have the &longs;ame proportion between them­<pb xlink:href="068/01/038.jpg" pagenum="24"/>&longs;elves, as have the mouths, which are the numbers 32 and 8 <lb/>in our example: Then this <lb/><figure id="id.068.01.038.1.jpg" xlink:href="068/01/038/1.jpg"/><lb/>being done, let the velocity <lb/>of the Water by the pa&longs;&longs;a­<lb/>ges A and B, be examined <lb/>(which may be done keeping <lb/>account what &longs;pace a piece <lb/>of Wood, or other body that <lb/>&longs;wimmeth, is carried by the &longs;tream in one determinate time; as <lb/>for in&longs;tance in 50 pul&longs;es) and then work by the golden Rule, as <lb/>the velocity by A, is to the velocity by B, &longs;o is the number 8, to <lb/>another number, which is 4. It is clear by what is demon&longs;tra­<lb/>ted in the &longs;aid &longs;econd Propo&longs;ition, that the quantity of water, <lb/>which pa&longs;&longs;eth by the mouth A, &longs;hall have the &longs;ame proportion of <lb/>that which pa&longs;&longs;eth by the mouth B, that 8 hath to 1. Such pro­<lb/>portion being compo&longs;ed of the proportions of 32 to 8, and of 8 to <lb/>4; namely, tothe greatne&longs;s of the mouth A, to the greatne&longs;s of the <lb/>mouth B, and of the velocity in A, to the velocity in B. </s> <s>This being <lb/>done, we mu&longs;t then contract the mouth which di&longs;chargeth more <lb/>then its ju&longs;t quantity of water, or enlarge the other which di&longs;char­<lb/>geth le&longs;s, as &longs;hal be mo&longs;t commodious in practice, which to him that <lb/>hath under&longs;tood this little that hath been delivered, will be very <lb/>afie.</s></p><p type="head"> <s>APPENDIX XII.</s></p><p type="main"> <s>The&longs;e opperations about Water, as I have hitherto on &longs;un­<lb/>dry occa&longs;ions ob&longs;erved, are involved in &longs;o many difficul­<lb/>ties, and &longs;uch a multiplicity of mo&longs;t extravagant accidents, <lb/>that it is no marvel if continually many, and very important er­<lb/>rours be therein committed by many, and even by Ingeneers <lb/>them&longs;elves, and Learned-men; and becau&longs;e many times they <lb/>concern not onely the publique, but private intere&longs;ts: Hence it <lb/>is, that it not onely belongeth to Arti&longs;ts to treat thereof, but very <lb/>oft even the vulgar them&longs;elves pretend to give their judgement <lb/>therein: And I have been troubled many times with a nece&longs;&longs;ity <lb/>of treating, not onely with tho&longs;e, which either by practice, or <lb/>particular &longs;tudy, under&longs;tood &longs;omewhat in the&longs;e matters; but al&longs;o <lb/>with people wholly void of tho&longs;e notions, which are nece&longs;&longs;ary for <lb/>one that would on good grounds di&longs;cour&longs;e about this particular; <lb/>and thus many times have met with more difficulty in the thick <lb/>skulls of men, than in precipitous Torrents, and va&longs;t Fennes. <lb/></s> <s>And in particular, I had occafion &longs;ome years pa&longs;t to go &longs;ee the <lb/>Gave or Emi&longs;&longs;ary of the Lake of <emph type="italics"/>Perugia,<emph.end type="italics"/> made many years agon <lb/>by <emph type="italics"/>Braccio Fortobraccio,<emph.end type="italics"/> but for that it was with great ruines by <lb/>Time decayed, and rendred unu&longs;eful, it was repaired with in­<pb xlink:href="068/01/039.jpg" pagenum="25"/>du&longs;try truly heroicall and admirable, by Mon&longs;ignor <emph type="italics"/>Maffei Bar­<lb/>herino,<emph.end type="italics"/> then Prefect for the Wayes, and now Pope. </s> <s>And being <lb/>nece&longs;&longs;itated, that I might be able to walk in the Cave, and for <lb/>other cau&longs;es, I let down the Sluices of the &longs;aid Cave, at the mouth <lb/>of the Lake: No &longs;ooner were they &longs;topt, but a great many of the <lb/>people of the Towns and Villages coa&longs;ting upon the <emph type="italics"/>L<emph.end type="italics"/>ake <lb/>flocking thither, began to make grievous complaints, that if tho&longs;e <lb/>Sluices were kept &longs;hut, not onely the Lake would want its due <lb/>Vent, but al&longs;o the parts adjacent to the Lake would be over <lb/>flown to their very great detriment. </s> <s>And becau&longs;e at fir&longs;t appea­<lb/>rance their motion &longs;eemed very rea&longs;onable, I found my &longs;elf hard <lb/>put to it, &longs;eeing no way to per&longs;wade &longs;uch a multitude, that the <lb/>prejudice which they pretended I &longs;hould do them by keeping <lb/>the Sluices &longs;hut for two dayes, was ab&longs;olutely in&longs;en&longs;ible; and that <lb/>by keeping them open, the Lake did not ebb in the &longs;ame time &longs;o <lb/>much as the thickne&longs;s of a &longs;heet of Paper: And therefore I was <lb/>nece&longs;&longs;itated to make u&longs;e of the authority I had, and &longs;o followed <lb/>my bu&longs;ine&longs;s as cau&longs;e required, without any regard to that Rab­<lb/>ble tumultuou&longs;ly a&longs;&longs;embled. </s> <s>Now when I am not working with <lb/>Mattock or Spade, but with the Pen and Di&longs;cour&longs;e, I intend to <lb/>demon&longs;trate clearly to tho&longs;e that are capable of rea&longs;on, and that <lb/>have well under&longs;tood the ground of this my Treati&longs;e, that the <lb/>fear was altogether vain which tho&longs;e people conceited. </s> <s>And <lb/>therefore I &longs;ay, that the Emi&longs;&longs;ary or Sluice of the Lake of <emph type="italics"/>Peru­<lb/>gia,<emph.end type="italics"/> &longs;tanding in the &longs;ame mannner as at pre&longs;ent, and the water <lb/>pa&longs;&longs;ing thorow it with the &longs;ame velocity as now; to examine <lb/>how much the Lake may abate in two days &longs;pace, we ought to <lb/>con&longs;ider, what proportion the &longs;uperficies of the whole Lake hath <lb/>to the mea&longs;ure of the Section of the Emi&longs;&longs;ary, and afterwards to <lb/>infer, that the velocity of the water by the Emi&longs;&longs;ary or Sluice, <lb/>&longs;hall have the &longs;ame proportion to the abatement of the Lake, <lb/>and to prove thorowly and clearly this di&longs;cour&longs;e, I intend to <lb/>demon&longs;trate the following Propo&longs;ition.</s></p><p type="main"> <s>Suppo&longs;e a Ve&longs;&longs;el of any bigne&longs;&longs;e, and that it hath an Emi&longs;&longs;ary <lb/>or Cock, by which it di&longs;chargeth its water. </s> <s>And look what pro­<lb/>portion the &longs;uper&longs;icies of the <lb/>ve&longs;&longs;el hath to the mea&longs;ure of <lb/><figure id="id.068.01.039.1.jpg" xlink:href="068/01/039/1.jpg"/><lb/>the &longs;ection of the cock, &longs;uch pro­<lb/>portion &longs;hall the velocity of the <lb/>Water in the Cock have to the <lb/>abatement of the Lake Let the <lb/>Ve&longs;&longs;el be A B C D, H I L B, through which the Water runneth, <lb/>the &longs;uperficies of the Water in the Ve&longs;&longs;el A D, and the &longs;ection <lb/>of the Cock H L: and let the Water in the Ve&longs;&longs;el <lb/>be &longs;uppo&longs;ed to have falne in one determinate time from A to F. <pb xlink:href="068/01/040.jpg" pagenum="26"/>I &longs;ay that the proportion of the &longs;uperficies of the Ve&longs;&longs;el A D is <lb/>in proportion to the mea&longs;ure of the &longs;ection of the Emi&longs;&longs;ary <lb/>H L, as the velocity of the Emi&longs;&longs;ary or Cock to the line A F; <lb/>which is manife&longs;t, for that the Water in the Ve&longs;sel moving by <lb/>the line A F; as far as F, and the whole ma&longs;s of Water A G <lb/>di&longs;charging it &longs;elf, and in the &longs;ame time the &longs;ame quantity of <lb/>Water being di&longs;charged by the &longs;ection of the Emi&longs;&longs;ary H L; it <lb/>is nece&longs;&longs;ary by what I have demon&longs;trated in the third Propo&longs;ition, <lb/>and al&longs;o explained in the beginning of this Treati&longs;e, that the ve­<lb/>locity by the Emi&longs;&longs;ary or Cock be in proportion to the velocity <lb/>of the abatement, as the &longs;uperficies of the Ve&longs;&longs;el to the mea­<lb/>&longs;ure of the &longs;ection of the Emi&longs;&longs;ary, which was to be demon­<lb/>&longs;trated.</s></p><p type="main"> <s>That which hath been demon&longs;trated in the Ve&longs;&longs;el, falls out ex­<lb/>actly al&longs;o in our Lake of <emph type="italics"/>Perugia,<emph.end type="italics"/> and its Emi&longs;sary; and becau&longs;e <lb/>the immen&longs;ity of the &longs;uperficies of the Lake is in proportion to <lb/>the &longs;uperficies of the Emi&longs;sary or Sluice, as many millions to <lb/>one, as may be ea&longs;ily calculated; it is manife&longs;t, that &longs;uch abate­<lb/>ment &longs;hall be imperceptible, and almo&longs;t nothing, in two dayes <lb/>&longs;pace, nay in four or &longs;ix: and all this will be true, when we <lb/>&longs;uppo&longs;e that for that time there entreth no other Water into the <lb/>Lake from Ditches or Rivolets, which falling into the Lake would <lb/>render &longs;uch abatement yet le&longs;s.</s></p><p type="main"> <s>Now we &longs;ee, that it's nece&longs;sary to examine &longs;uch abatements <lb/>and ri&longs;ings, with excellent rea&longs;ons, or at lea&longs;t, with accurate ex­<lb/>periments, before we re&longs;olve and conclude any thing; and how <lb/>farre the vulgar are di&longs;tant from a right judgment in &longs;uch <lb/>matters.</s></p><p type="head"> <s>APPENDIX XIII.</s></p><p type="main"> <s>For greater confirmation of all this which I have &longs;aid, I <lb/>will in&longs;tance in another like ca&longs;e, which al&longs;o I met with here­<lb/>tofore, wherein, for that the bu&longs;ine&longs;s was not rightly un­<lb/>der&longs;tood, many di&longs;orders, va&longs;t expences, and con&longs;iderable mi&longs;­<lb/>chiefs have followed. </s> <s>There was heretofore an Emi&longs;sary or <lb/>Sluice made to drain the Waters, which from Rains, Springs, and <lb/>Rivolets fall into a Lake; to the end, the &longs;hores adjoyning on <lb/>the Lake, &longs;hould be free from the overflowing of the Waters; <lb/>but becau&longs;e perhaps the enterprize was not well managed and <lb/>carried on, it fell out, that the Fields adjacent to the &longs;aid Chanel <lb/>could not drain, but continued under water; to which di&longs;orders <lb/>a pre&longs;ent remedy hath been u&longs;ed, namely, in a time convenient <lb/>to &longs;top up the Sluice, by meanes of certain Floodgates kept on <lb/>purpo&longs;e for that end; and thus abating the Level of the Water <pb xlink:href="068/01/041.jpg" pagenum="27"/>in the Emi&longs;&longs;ary, in the &longs;pace of three or four dayes, the Fields <lb/>have been haply drained. </s> <s>But on the other part, the proprietors <lb/>bordering on the Lake oppo&longs;ed this, grievou&longs;ly complaining, that <lb/>whil&longs;t the Floodgates are &longs;hut, and the cour&longs;e of the Water of <lb/>the Sluice hindered, the Lake overflowes the Lands adjacent, by <lb/>meanes of the Rivers that fell into it, to their very great damage; <lb/>and &longs;o continuing their &longs;uits, they got more of vexation than &longs;a­<lb/>tisfaction. </s> <s>Now, being asked my opinion herein, I judged it <lb/>requi&longs;ite (&longs;ince the point in controver&longs;ie was about the ri&longs;ing <lb/>and falling of the Lake) that the &longs;aid abatement, when the <lb/>Floodgates are open, and increa&longs;e when they are &longs;hut &longs;hould be <lb/>exactly mea&longs;ured, and told them, that it might be ea&longs;ily done at <lb/>a time when no extraordinary Waters fell into the Lake, neither <lb/>of Rain, or otherwi&longs;e; and the Lake was undi&longs;turbed by winds <lb/>that might drive the Water to any &longs;ide, by planting neer to an <lb/>I&longs;let, which is about the middle of the Lake, a thick po&longs;t, on <lb/>which &longs;hould be made the marks of the Lakes ri&longs;ing and falling <lb/>for two or three dayes. </s> <s>I would not, at that time, pawn, or re­<lb/>&longs;olutely declare, my judgment, in regard I might be, by divers <lb/>accidents mi&longs;led. </s> <s>But this I told them, that (by what I have <lb/>demon&longs;trated, and particularly that which I have &longs;aid above <lb/>touching the Lake of <emph type="italics"/>Perugia<emph.end type="italics"/>) I inclined greatly to think, <lb/>that the&longs;e ri&longs;ings and fallings would prove imperceptible, and <lb/>incon&longs;iderable; and therefore, that in ca&longs;e experience &longs;hould <lb/>make good my rea&longs;on, it would be to no purpo&longs;e for them to <lb/>continue di&longs;puting and wrangling, which cau&longs;eth, (according <lb/>to the Proverb) <emph type="italics"/>A great deal of cry,<emph.end type="italics"/> but produceth not much <lb/><emph type="italics"/>Wool.<emph.end type="italics"/></s></p><p type="main"> <s>La&longs;tly, it importing very much to know what a Rain conti­<lb/>nued for many dayes can do in rai&longs;ing the&longs;e Lakes, I will here in­<lb/>&longs;ert the Copy of a Letter, which I writ formerly to <emph type="italics"/>Signior Ga­<lb/>lilæo Galilæi,<emph.end type="italics"/> chief Philo&longs;opher to the Grand Duke of <emph type="italics"/>Tu&longs;cany,<emph.end type="italics"/><lb/>wherein I have delivered one of my conceits in this bu&longs;ine&longs;&longs;e, and <lb/>it may be, by this Letter, I may, more &longs;trongly, confirm what I <lb/>have &longs;aid above.</s></p><pb xlink:href="068/01/042.jpg" pagenum="28"/><p type="main"> <s><emph type="italics"/>The Copy of a Letter to<emph.end type="italics"/> Signore GALILÆO <lb/>GALILÆI, <emph type="italics"/>Chief Philo&longs;opher to the mo&longs;t Serene <lb/>Great Duke of TVSCANY.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Worthy and mo&longs;t Excellent<emph.end type="italics"/> SIR,</s></p><p type="main"> <s>In &longs;atisfaction of my promi&longs;e, in my former Letters of <lb/>repre&longs;enting unto you &longs;ome of my Con&longs;iderations <lb/>made upon the Lake <emph type="italics"/>Thra&longs;imeno,<emph.end type="italics"/> I &longs;ay, That in times <lb/>pa&longs;t, being in <emph type="italics"/>Perugia,<emph.end type="italics"/> where we held our General <lb/>Convention, having under&longs;tood that the Lake <emph type="italics"/>Thra&longs;imeno,<emph.end type="italics"/> by <lb/>the great drought of many Moneths was much abated, It came <lb/>into my head, to go privately and &longs;ee this novelty, both for my <lb/>particular &longs;atisfaction, as al&longs;o that might I be able to relate the <lb/>whole to my Patrons, upon the certitude of my own &longs;ight of the <lb/>place. </s> <s>And &longs;o being come to the Emi&longs;&longs;ary of the Lake, I found <lb/>that the Level of the Lakes &longs;urface was ebbed about five Ro­<lb/>man Palmes of its wonted watermark, in&longs;omuch that it was lower <lb/>than the tran&longs;ome of the mouth of the Emi&longs;&longs;ary, by the length <lb/>of ----------------------------this de&longs;cribed line, and there­<lb/>fore no Water i&longs;&longs;ued out of the Lake, to the great prejudice of <lb/>all the places and villages circumjacent, in regard that the Wa­<lb/>ter which u&longs;ed to run from the &longs;aid Lake turned 22 Mills, which <lb/>not going, nece&longs;&longs;itated the inhabitants of tho&longs;e parts to go a <lb/>dayes journey and more, to grinde upon the <emph type="italics"/>Tiber.<emph.end type="italics"/> Being retur­<lb/>ned to <emph type="italics"/>Perugia,<emph.end type="italics"/> there followed a Rain, not very great, but con­<lb/>&longs;tant, and even, which la&longs;ted for the &longs;pace of eight hours, or <lb/>thereabouts; and it came into my thoughts to examine, being <lb/>in <emph type="italics"/>Perugia,<emph.end type="italics"/> how much the Lake was increa&longs;ed and railed by this <lb/>Rain, &longs;uppo&longs;ing (as it was probable enough) that the Rain had <lb/>been univer&longs;al over all the Lake; and like to that which fell in <lb/><emph type="italics"/>Perugia,<emph.end type="italics"/> and to this purpo&longs;e I took a Gla&longs;&longs;e formed like a Cy­<lb/>linder, about a palme high, and half a palme broad; and having <lb/>put in water &longs;nfficient to cover the bottome of the Gla&longs;&longs;e, I no­<lb/>ted diligently the mark of the height of the Water in the Gla&longs;&longs;e, <lb/>and afterwards expo&longs;ed it to the open weather, to receive the <lb/>Raine-water, which fell into it; and I let it &longs;tand for the <lb/>&longs;pace of an hour; and having ob&longs;erved that in that time the Wa­<lb/>ter was ri&longs;en in the Ve&longs;&longs;el the height of the following line---, <lb/>I con&longs;idered that if I had expo&longs;ed to the &longs;ame rain &longs;uch other ve&longs;­<lb/>&longs;els equal to that, the Water would have ri&longs;en in them all accor­<lb/>ding to that mea&longs;ure: And thereupon concluded, that al&longs;o in all <pb xlink:href="068/01/043.jpg" pagenum="29"/>the whole extent of the Lake, it was nece&longs;&longs;ary the Water &longs;hould <lb/>be rai&longs;ed in the &longs;pace of an hour the &longs;ame mea&longs;ure. </s> <s>Yet here I <lb/>con&longs;idered two difficulties that might di&longs;tutb and altar &longs;uch an <lb/>effect, or at lea&longs;t render it inob&longs;erveable, which afterwards well <lb/>weighed, and re&longs;olved, left me (as I will tell you anon) in the <lb/>conclu&longs;ion the more confirmed; that the Lake ought to be in­<lb/>crea&longs;ed in the &longs;pace of eight hours, that the rain la&longs;ted eight <lb/>times that mea&longs;ure. </s> <s>And whil&longs;t I again expo&longs;ed the Gla&longs;s to re­<lb/>peat the experiment, there came unto me an Ingeneer to talk <lb/>with me touching certain affairs of our Mona&longs;tary of <emph type="italics"/>Perugia,<emph.end type="italics"/> and <lb/>di&longs;cour&longs;ing with him, I &longs;hewed him the Gla&longs;s out at my Cham­<lb/>ber-window, expo&longs;ed in a Court-yard; and communicated to <lb/>him my fancy, relacing unto him all that I had done. </s> <s>But I <lb/>&longs;oon perceived that this brave fellow conceited me to be but of <lb/>a dull brain, for he &longs;milling &longs;aid unto me; Sir, you deceive <lb/>your &longs;elf: I am of opinion that the Lake will not be increa&longs;­<lb/>ed by this rain, &longs;o much as the thickne&longs;&longs;e of a ^{*} <emph type="italics"/>Julio.<emph.end type="italics"/><lb/><arrow.to.target n="marg967"></arrow.to.target><lb/>Hearing him pronounce this his opinion with freene&longs;s and <lb/>confidence, I urged him to give me &longs;ome rea&longs;on for what he <lb/>&longs;aid, a&longs;&longs;uring him, that I would change my judgement, when I <lb/>&longs;aw the &longs;trength of his Arguments: To which he an&longs;wered, that <lb/>he had been very conver&longs;ant about the Lake, and was every day <lb/>upon it, and was well a&longs;&longs;ured that it was not at all increa&longs;ed. </s> <s>And <lb/>importuning him further, that he would give me &longs;ome rea&longs;on <lb/>for his &longs;o thinking, he propo&longs;ed to my con&longs;ideration the great <lb/>drought pa&longs;&longs;ed, and that that &longs;ame rain was nothing for the <lb/>great parching: To which I an&longs;wered, I believe Sir that the &longs;ur­<lb/>face of the Lake, on which the rain had fallen was moi&longs;tned; and <lb/>therefore &longs;aw not how its drought, which was nothing at all, <lb/>could have drunk up any part of the rain. </s> <s>For all this he per­<lb/>&longs;i&longs;ting in his conceit, without yielding in the lea&longs;t to my allega­<lb/>tion; he granted in the end (I believe in civility to me) that <lb/>my rea&longs;on was plau&longs;ible and good, but that in practi&longs;e it could <lb/>not hold. </s> <s>At la&longs;t to clear up all, I made one be called, and <lb/>&longs;ent him to the mouth of the Emi&longs;&longs;ary of the Lake, with order <lb/>to bring me an exact account, how he found the water of the <lb/>Lake, in re&longs;pect of the Tran&longs;ome of the Sluice. </s> <s>Now here, <lb/>Signore <emph type="italics"/>Galilo,<emph.end type="italics"/> I would not have you think that I had brought <lb/>the matter in hand to concern me in my honour; but believe me <lb/>(and there are witne&longs;&longs;es of the &longs;ame &longs;till living) that my me&longs;&longs;en­<lb/>ger returning in the evening to <emph type="italics"/>Perugia,<emph.end type="italics"/> he brought me word, <lb/>that the water of the Lake began to run through the Cave; and <lb/>that it was ri&longs;en almo&longs;t a fingers breadth above the Tran&longs;ome: <lb/>In&longs;omuch, that adding this mea&longs;ure, to that of the lowne&longs;s of <lb/>the &longs;urface of the Lake, beneath the Tran&longs;ome before the rain, <pb xlink:href="068/01/044.jpg" pagenum="30"/>it was manife&longs;t that the ri&longs;ing of the Lake cau&longs;ed by the rain, was <lb/>to a hair tho&longs;e four fingers breadth that I had judged it to be. <lb/></s> <s>Two dayes after I had another bout with the Ingeneer, and re­<lb/>lated to him the whole bu&longs;ine&longs;s, to which he knew not what to <lb/>an&longs;wer.</s></p><p type="margin"> <s><margin.target id="marg967"></margin.target>* A Coyn of Pope <lb/><emph type="italics"/>Julius<emph.end type="italics"/> worth &longs;ix <lb/>pence.</s></p><p type="main"> <s>Now the two difficulties which I thought of, able to impede <lb/>my conclu&longs;ion, were the&longs;e following: Fir&longs;t, I con&longs;idered that <lb/>it might be, that the Wind blowing from the &longs;ide where the <lb/>Sluice &longs;tood, to the Lake-ward; the mole and ma&longs;s of the Wa­<lb/>ter of the Lake might be driven to the contrary &longs;hore; on which <lb/>the Water ri&longs;ing, it might be fallen at the mouth of the Emi&longs;&longs;a­<lb/>ry, and &longs;o the ob&longs;ervation might be much ob&longs;cured. </s> <s>But this <lb/>difficulty wholly vani&longs;hed by rea&longs;on of the Aires great tranqui­<lb/>lity; which it kept at that time, for no Wind was &longs;tirring on any <lb/>&longs;ide, neither whil&longs;t it rained, nor afterwards.</s></p><p type="main"> <s>The &longs;econd difficulty which put the ri&longs;ing in doubt, was, That <lb/>having ob&longs;erved in <emph type="italics"/>Florence,<emph.end type="italics"/> and el&longs;ewhere, tho&longs;e Ponds into <lb/>which the rain-water, falling from the hou&longs;e, is conveyed <lb/>through the Common-&longs;hores: And that they are not thereby <lb/>ever filled, but that they &longs;wallow all that abundance of water, <lb/>that runs into them by tho&longs;e conveyances which &longs;erve them with <lb/>water; in&longs;omuch that tho&longs;e conveyances which in time of <lb/>drought maintain the Pond, when there comes new abundance <lb/>of water into the Pond, they drink it up, and &longs;wallow it: A like <lb/>effect might al&longs;o fall out in the Lake, in which there being many <lb/>veins (as it is very likely) that maintain and feed the Lake; the&longs;e <lb/>veins might imbibe the new addition of the Rain-water, and &longs;o <lb/>by that means annuall the ri&longs;ing; or el&longs;e dimini&longs;h it in &longs;uch &longs;ort, as <lb/>to render it inob&longs;ervable. </s> <s>But this difficulty was ea&longs;ily re&longs;olved <lb/>by con&longs;idering my Treati&longs;e of the mea&longs;ure of Running-Waters; <lb/>fora&longs;much as having demon&longs;trated, that the abatement of a Lake <lb/>beareth the reciprocal proportion to the velocity of the Emi&longs;&longs;a­<lb/>ry, which the mea&longs;ure of the Section of the Emi&longs;&longs;ary of the Lake, <lb/>hath to the mea&longs;ure of the &longs;urface of the Lake: making the <lb/>calculation and account, though in gro&longs;s; by &longs;uppo&longs;ing that its <lb/>veins were &longs;ufficiently large, and that the velocity in them were <lb/>notable in drinking up the water of the Lake; yet I found never­<lb/>thele&longs;s, that many weeks and moneths would be &longs;pent in drink­<lb/>ing up the new-come abundance of water by the rain, &longs;o that <lb/>I re&longs;ted &longs;ure, that the ri&longs;ing would en&longs;ue, as in effect it did.</s></p><p type="main"> <s>And becau&longs;e many of accurate judgement, have again cau&longs;ed <lb/>me to que&longs;tion this ri&longs;ing, &longs;etting before me, that the Earth be­<lb/>ing parched by the great drought, that had &longs;o long continued, it <lb/>might be, that that Bank of Earth which environed the brink of <lb/>the Lake, being dry, and imbibing great abundance of Water <pb xlink:href="068/01/045.jpg" pagenum="31"/>from the increa&longs;ing Lake, would not &longs;uffer it to increa&longs;e in <lb/>height: I &longs;ay therefore, that if we would rightly con&longs;ider this <lb/>doubt here propo&longs;ed, we &longs;hould, in the very con&longs;ideration of it, <lb/>&longs;ee it re&longs;olved; for, it being &longs;uppo&longs;ed that that li&longs;t or border of <lb/>Banks which was to be occupied by the increa&longs;e of the Lake, be <lb/>a Brace in breadth quite round the Lake, and that by rea&longs;on of <lb/>its dryne&longs;s it &longs;ucks in water, and that by that means this propor­<lb/>tion of water co-operates not in rai&longs;ing of the Lake: It is ab&longs;o­<lb/>lutely nece&longs;&longs;ary on the other hand, that we con&longs;ider, That the <lb/>Circuit of the water of the Lake being thirty miles, as its com­<lb/>monly held, that is to &longs;ay, Ninety thou&longs;and Braces of <emph type="italics"/>Florence<emph.end type="italics"/><lb/>in compa&longs;s; and therefore admitting for true, that each Brace of <lb/>this Bank drink two quarts of water, and that for the &longs;pieading <lb/>it require three quarts more, we &longs;hall finde, that the whole agre­<lb/>gate of this portion of water, which is not imployed in the rai&longs;ing <lb/>of the Lake, will be four hundred and fifty thou&longs;and Quarts of <lb/>water; and &longs;uppo&longs;ing that the Lake be &longs;ixty &longs;quare miles, three <lb/>thou&longs;and Braces long, we &longs;hall finde, that to di&longs;pence the water <lb/>po&longs;&longs;e&longs;t by the Bank about the Lake, above the total &longs;urface of <lb/>the Lake, it ought to be &longs;pread &longs;o thin, that one &longs;ole quart of <lb/>water may over-&longs;pread ten thou&longs;and &longs;quare Braces of &longs;urface: <lb/>&longs;uch a thinne&longs;s, as mu&longs;t much exceed that of a leaf of beaten <lb/>Gold, and al&longs;o le&longs;s than that skin of water which covers the Bub­<lb/>bles of it: and &longs;uch would that be, which tho&longs;e men would have <lb/>&longs;ub&longs;tracted from the ri&longs;ing of the Lake: But again, in the &longs;pace <lb/>of a quarter of an hour at the beginning of the rain, all that <lb/>Bank is &longs;oaked by the &longs;aid rain, &longs;o that we need not for the <lb/>moi&longs;tning of it, imploy a drop of that water which falleth into <lb/>the Lake. </s> <s>Be&longs;ides we have not brought to account that abun­<lb/>dance of water which runs in time of rain into the Lake, from <lb/>the &longs;teepne&longs;s of the adjacent Hills and Mountains; which would <lb/>be enough to &longs;upply all our occa&longs;ions: So that, neither ought <lb/>we for this rea&longs;on to que&longs;tion our pretended ri&longs;ing. </s> <s>And this <lb/>is what hath fallen in my way touching the con&longs;ideration of the <lb/><emph type="italics"/>Thra&longs;imenian<emph.end type="italics"/> Lake.</s></p><p type="main"> <s>After which, perhaps &longs;omewhat ra&longs;hly, wandring beyond my <lb/>bounds, I proceeded to another contemplation, which I will re­<lb/>late to you, hoping that you will receive it, as collected with <lb/>the&longs;e cautions requi&longs;ite in &longs;uch like affairs; wherein we ought <lb/>not too po&longs;itively to affirm any thing of our own heads for cer­<lb/>tain, but ought to &longs;ubmit all to the &longs;ound and &longs;ecure delibera­<lb/>tion of the Holy Mother-Church, as I do this of mine, and all <lb/>others; mo&longs;t ready to change my judgement, and conform my <lb/>&longs;elf alwaies to the deliberations of my Superiors. </s> <s>Continu­<pb xlink:href="068/01/046.jpg" pagenum="32"/>ing therefore my above-&longs;aid conceit about the ri&longs;ing of the wa­<lb/>ter in the gla&longs;s tried before, it came into my minde, that the <lb/>forementioned rain having been very gentle, it might well be, <lb/>that if there &longs;hould have faln a Rain fifty, an hundred, or a thou­<lb/>&longs;and times greater than this, and much more inten&longs;e (which <lb/>would in&longs;ue as oft as tho&longs;e falling drops were four, &longs;ive or ten <lb/>times bigger than tho&longs;e of the above-mentioned rain, keeping <lb/>the &longs;ame number) in &longs;uch a ca&longs;e its manife&longs;t, that in the &longs;pace <lb/>of an hour the Water would ri&longs;e in our Gla&longs;s, two, three, and <lb/>perhaps more Yards or Braces; and con&longs;equently, if &longs;uch a <lb/>Raine &longs;hould fall upon a Lake, that the &longs;aid Lake would <lb/>ri&longs;e, according to the &longs;ame rate: And likewi&longs;e, if &longs;uch a <lb/>Rain were univer&longs;all, over the whole Terre&longs;triall Globe, it <lb/>would nece&longs;&longs;arily, in the &longs;pace of an hour, make a ri­<lb/>&longs;ing of two, or three braces round about the &longs;aid Globe, <lb/>And becau&longs;e we have from Sacred Records, that in the <lb/>time of the Deluge, it rained fourty dayes and fourty nights; <lb/>namely, for the &longs;pace of 960 houres; its clear, that if the &longs;aid <lb/>Rain had been ten times bigger than ours at <emph type="italics"/>Perugia,<emph.end type="italics"/> the ri&longs;ing <lb/>of the Waters above the Terre&longs;trial Globe would reach and pa&longs;s <lb/>a mile higher than the tops of the Hills and Mountains that are <lb/>upon the &longs;uperficies of the Earth; and they al&longs;o would concur <lb/>to increa&longs;e the ri&longs;e. </s> <s>And therefore I conclude, that the ri&longs;e of <lb/>the Waters of the Deluge have a rational congruity with natural <lb/>Di&longs;cour&longs;es, of which I know very well that the eternal truths of <lb/>the Divine leaves have no need; but however I think &longs;o clear an <lb/>agreement is worthy of our con&longs;ideration, which gives us occa­<lb/>&longs;ion to adore and admire the greatne&longs;&longs;e of God in his mighty <lb/>Works, in that we are &longs;ometimes able, in &longs;ome &longs;ort, to mea&longs;ure <lb/>them by the &longs;hort Standard of our Rea&longs;on.</s></p><p type="main"> <s>Many Le&longs;&longs;ons al&longs;o may be deduced from the &longs;ame Doctrine, <lb/>which I pa&longs;&longs;e by, for that every man of him&longs;elf may ea&longs;ily know <lb/>them, having once &longs;tabli&longs;hed this Maxime; That it is not po&longs;&longs;i­<lb/>ble to pronounce any thing, of a certainty, touching the quantity <lb/>of Running Waters, by con&longs;idering only the &longs;ingle vulgar mea­<lb/>&longs;ure of the Water wichout the velocity; and &longs;o on the contrary, <lb/>he that computes only the velocity, without the mea&longs;ure, &longs;hall <lb/>commit very great errours; for treating of the mea&longs;ure of Run­<lb/>ning Waters, it is nece&longs;&longs;ary, the water being a body, in handling <lb/>its quantity, to con&longs;ider in it all the three dimen&longs;ions of breadth, <lb/>depth, and length: the two fir&longs;t dimen&longs;ions are ob&longs;erved by all <lb/>in the common manner, and ordinary way of mea&longs;uring Running <lb/>Waters; but the third dimen&longs;ion of length is omitted; and hap­<lb/>ly &longs;uch an over&longs;ight is committed, by rea&longs;on the length of Run­<pb xlink:href="068/01/047.jpg" pagenum="33"/>ning Water is reputed in &longs;ome &longs;en&longs;e infinite, in that it never cea­<lb/>&longs;eth to move away, and as infinite is judged incomprehen&longs;ible; <lb/>and &longs;uch as that there is no exact knowledge to be had thereof; <lb/>& &longs;o there comes to be no account made thereof; but if we &longs;hould <lb/>make &longs;trict reflection upon our con&longs;ideration of the velocity of <lb/>Water, we &longs;hould find, that keeping account of the &longs;ame, there <lb/>is a reckoning al&longs;o made of the length; fora&longs;much as whil&longs;t we <lb/>&longs;ay, the Water of &longs;uch a Spring runs with the velocity of pa&longs;&longs;ing <lb/>a thou&longs;and or two thou&longs;and paces an hour: this in &longs;ub&longs;tance is <lb/>no other than if we had &longs;aid, &longs;uch a Fountain di&longs;chargeth in an <lb/>hour a Water of a thou&longs;and or two thou&longs;and paces long. </s> <s>So <lb/>that, albeit the total length of Running water be incomprehen­<lb/>&longs;ible, as being infinite, yet neverthele&longs;&longs;e its rendered intelligible <lb/>by parts in its velocity. </s> <s>And &longs;o much &longs;ufficeth to have hinted <lb/>about this matter, hoping to impart on &longs;ome other occa&longs;ion other <lb/>more accurate Ob&longs;ervations in this affair.</s></p><p type="head"> <s><emph type="italics"/>LAVS DEO.<emph.end type="italics"/></s></p><figure id="id.068.01.047.1.jpg" xlink:href="068/01/047/1.jpg"/><pb xlink:href="068/01/048.jpg"/><pb xlink:href="068/01/049.jpg"/><p type="head"> <s>GEOMETRICAL <lb/>DEMONSTRATIONS <lb/>OF THE <lb/>MEASURE <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s>BY <lb/>D. BENEDETTO CASTELLI, <lb/>Abbot of CASSINA, and Mathematician to <lb/>P. <emph type="italics"/>VRBAN. VIII.<emph.end type="italics"/></s></p><p type="head"> <s>DEDICATED <lb/><emph type="italics"/>To the mo&longs;t Illu&longs;trious, and mo&longs;t Excellent Prince<emph.end type="italics"/></s></p><p type="head"> <s>DON THADDEO BARBERINI, <lb/>PRINCE OF <lb/>PALESTRINA, <lb/>AND <lb/>GENERAL of the HOLY CHURCH.</s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed <emph type="italics"/>Anno Domini,<emph.end type="italics"/> MDCLXI.</s></p><pb xlink:href="068/01/050.jpg"/><pb xlink:href="068/01/051.jpg" pagenum="37"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>Let it be &longs;uppo&longs;ed, that the banks of the Rivers of which <lb/>we &longs;peak be erected perpendicular to the plane of the up­<lb/>per &longs;uperficies of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>We &longs;uppo&longs;e that the plane of the bottome of the River, of <lb/>which we &longs;peak is at right angles with the banks.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>It is to be &longs;uppo&longs;ed, that we &longs;peak of Rivers, when they are at <lb/>ebbe, in that &longs;tate of &longs;hallowne&longs;&longs;e, or at flowing in that &longs;tate <lb/>of deepne&longs;&longs;e, and not in their tran&longs;ition from the ebbe to the <lb/>flowing, or fr m the flowing to the ebbe.</s></p><p type="head"> <s><emph type="italics"/>Declaration of Termes.<emph.end type="italics"/></s></p><p type="head"> <s>FIRST.</s></p><p type="main"> <s>If a River &longs;hall be cut by a Plane at right angles to the &longs;urface <lb/>of the water of the River, and to the banks of the River, <lb/>that &longs;ame dividing Plane we call the Section of the River; and <lb/>this Section, by the Suppo&longs;itions above, &longs;hall be a right angled <lb/>Parallelogram.</s></p><p type="head"> <s>SECOND.</s></p><p type="main"> <s>We call tho&longs;e Sections equally Swift, by which the water runs <lb/>with equal velocity; and more &longs;wift and le&longs;s &longs;wift that <lb/>Section of another, by which the water runs with greater or le&longs;&longs;e <lb/>velocity.</s></p><pb xlink:href="068/01/052.jpg" pagenum="38"/><p type="head"> <s>AXIOME I.</s></p><p type="main"> <s>Sections equal, and equally &longs;wift, di&longs;charge equal quantities <lb/>of Water in equal times.</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s>Sections equally &longs;wift, and that di&longs;charge equal quantity of <lb/>Water, in equal time, &longs;hall be equal.</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s>Sections equal, and that di&longs;charge equal quantities of Water <lb/>in equal times, &longs;hall be equally &longs;wift.</s></p><p type="head"> <s>AXIOME IV.</s></p><p type="main"> <s>When Sections are unequal, but equally &longs;wift, the quanti­<lb/>ty of the Water that pa&longs;&longs;eth through the fir&longs;t Section, <lb/>&longs;hall have the &longs;ame proportion to the quantity that pa&longs;­<lb/>&longs;eth through the Second, that the fir&longs;t Section hath to the &longs;econd <lb/>Section. </s> <s>Which is manife&longs;t, becau&longs;e the velocity being the <lb/>&longs;ame, the difference of the Water that pa&longs;&longs;eth &longs;hall be according <lb/>to the difference of the Sections.</s></p><p type="head"> <s>AXIOME V.</s></p><p type="main"> <s>If the Sections &longs;hall be equal, and of unequal velocity, the <lb/>quantity of the Water that pa&longs;&longs;eth through the fir&longs;t, &longs;hall <lb/>have the &longs;ame proportion to that which pa&longs;&longs;eth through the <lb/>&longs;econd, that the velocity of the fir&longs;t Section, &longs;hall have to the <lb/>velocity of the &longs;econd Section. </s> <s>Which al&longs;o is manife&longs;t, becau&longs;e <lb/>the Sections being equal, the difference of the Water which <lb/>pa&longs;&longs;eth, dependeth on the velocity.</s></p><p type="head"> <s><emph type="italics"/>PETITION.<emph.end type="italics"/></s></p><p type="main"> <s>A Section of a River being given, we may &longs;uppo&longs;e another <lb/>equal to the given, of different breadth, heigth, and ve­<lb/>locity.</s></p><pb xlink:href="068/01/053.jpg" pagenum="37"/><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s><emph type="italics"/>The Sections of the &longs;ame River di&longs;charge equal quan­<lb/>tities of Water in equal times, although the Secti­<lb/>ons them&longs;elves he unequal.<emph.end type="italics"/></s></p><p type="main"> <s>Let the two Sections be A and B, in the River C, running <lb/>from A, towards B; I &longs;ay, that they di&longs;charge equal quan­<lb/>tity of Water in equal times; for if greater quantity of Wa­<lb/>ter &longs;hould pa&longs;s through A, than pa&longs;&longs;eth through B, it would <lb/><figure id="id.068.01.053.1.jpg" xlink:href="068/01/053/1.jpg"/><lb/>follow that the Water in the intermediate &longs;pace of the River C, <lb/>would increa&longs;e continually, which is manife&longs;tly fal&longs;e, but if <lb/>more Water &longs;hould i&longs;&longs;ue through the Section B, than entreth at <lb/>the Section A, the Water in the intermediate &longs;pace C, would <lb/>grow continually le&longs;s, and alwaies ebb, which is likewi&longs;e fal&longs;e; <lb/>therefore the quantity of Water that pa&longs;&longs;eth through the Secti­<lb/>on B, is equal to the quantity of Water which pa&longs;&longs;eth through <lb/>the Section A, and therefore the Sections of the &longs;ame River di&longs;­<lb/>charge, <emph type="italics"/>&c.<emph.end type="italics"/> Which w s to be demon&longs;trated.</s></p><p type="head"> <s>PROPOSITION II.</s></p><p type="main"> <s><emph type="italics"/>In two Sections of Rivers, the quantity of the Water <lb/>which pa&longs;&longs;eth by one Section, is to that which pa&longs;­<lb/>&longs;eth by the &longs;econd, in a Proportion compounded of <lb/>the proportions of the fir&longs;t Section to the &longs;econd, and <lb/>of the velocitie through the first, to the velocitie <lb/>of the &longs;econd.<emph.end type="italics"/></s></p><p type="main"> <s>I Et A, and B be two Sections of a River; I &longs;ay, that the <lb/>quantity of Water which pa&longs;&longs;eth through A, is to that which <lb/>pa&longs;&longs;eth through B, in a proportion compounded of the pro­<lb/>portions of the fir&longs;t Section A, to the Section B; and of the velo­<lb/>city through A, to the velocity through B: Let a Section be <pb xlink:href="068/01/054.jpg" pagenum="40"/>&longs;uppo&longs;ed equal to the Section A, in magnitude; but of velocity <lb/>equal to the Section B, and let it be G, and as the Section A is <lb/><figure id="id.068.01.054.1.jpg" xlink:href="068/01/054/1.jpg"/><lb/>to the Section B, &longs;o let the line F be to the line D; and as the <lb/>velocity A, is to the velocity by B, &longs;o let the line D be to the <lb/>line R: Therefore the Water which pa&longs;&longs;eth thorow A, &longs;hall be <lb/>to that which pa&longs;&longs;eth through G (in regard the Sections A and <lb/>G are of equal bigne&longs;s, but of unequal velocity) as the velocity <lb/>through A, to the velocity through G; But as the velocity <lb/>through A, is to the velocity through G, &longs;o is the velocity through <lb/>A, to the velocity through B; namely, as the line D, to the <lb/>line R: therefore the quantity of the Water which pa&longs;&longs;e the <lb/>through A, &longs;hall be to the quantity which pa&longs;&longs;eth through G, as <lb/>the line D is to the line R; but the quantity which pa&longs;&longs;eth <lb/>through G, is to that which pa&longs;&longs;eth through B, (in regard the <lb/>Sections G, and B, are equally &longs;wift) as the Section G to the Se­<lb/>ction B; that is, as the Section A, to the Section B; that is, as <lb/>the line F, to the line D: Therefore by the equal and perturbed <lb/>proportionality, the quantity of the Water which pa&longs;&longs;eth through <lb/>A, hath the &longs;ame proportion to that which pa&longs;&longs;eth through B, <lb/>that the line F hath to the line R; but F to R, hath a proportion <lb/>compounded of the proportions of F to D, and of D to R; that <lb/>is, of the Section A to the Section B; and of the velocity through <lb/>A, to the velocity through B. </s> <s>Therefore al&longs;o the quantity of <lb/>Water which pa&longs;&longs;eth through the Section A, &longs;hall have a propor­<lb/>tion to that which pa&longs;&longs;eth through the Section B, compounded of <lb/>the proportions of the Section A, to the Section B; and of <lb/>the velocity through A, to the velocity through B: And <lb/>therefore in two Sections of Rivers, the quantity of Water which <lb/>pa&longs;&longs;eth by the fir&longs;t, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be demon&longs;trated.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/></s></p><p type="main"> <s>The &longs;ame followeth, though the quantity of the Water which <lb/>pa&longs;&longs;eth through the Section A, be equal to the quantity of <lb/>Water which pa&longs;&longs;eth through the Section B, as is manife&longs;t by the <lb/>&longs;ame demon&longs;tration.</s></p><pb xlink:href="068/01/055.jpg" pagenum="41"/><p type="head"> <s>PROPOSITION III.</s></p><p type="main"> <s><emph type="italics"/>In two Sections unequal, through which pa&longs;s equal <lb/>quantities of Water in equal times, the Sections <lb/>have to one another, reciprocal proportion to their <lb/>velocitie.<emph.end type="italics"/></s></p><p type="main"> <s>Let the two unequal Sections, by which pa&longs;s equal quantities <lb/>of Water in equal times be A, the greater; and B, the le&longs;&longs;er: <lb/>I &longs;ay, that the Section A, &longs;hall have the &longs;ame Proportion <lb/>to the Section B, that reciprocally the velocity through B, hath to <lb/>the velocity through A; for &longs;uppo&longs;ing that as the Water that <lb/>pa&longs;&longs;eth through A, is to that which pa&longs;&longs;eth through B, &longs;o is the <lb/><figure id="id.068.01.055.1.jpg" xlink:href="068/01/055/1.jpg"/><lb/>line E to the line F: therefore the quantity of water which pa&longs;­<lb/>&longs;eth through A, being equal to that which pa&longs;&longs;eth through B, <lb/>the line E &longs;hall al&longs;o be equal to the line F: Suppo&longs;ing moreover, <lb/>That as the Section A, is to the Section B, &longs;o is the line F, to the <lb/>line G; and becau&longs;e the quantity of water which pa&longs;&longs;eth <lb/>through the Section A, is to that which pa&longs;&longs;eth through the <lb/>Section B, in a proportion compo&longs;ed of the proportions of the <lb/>Section A, to the Section B, and of the velocity through A, to the <lb/>velocity through B; therefore the line E, &longs;hall be the line to F, in <lb/>a proportion compounded of the &longs;ame proportions; namely, of <lb/>the proportion of the Section A, to the Section B, and of the ve­<lb/>locity through A, to the velocity through B; but the line E, hath <lb/>to the line G, the proportion of the Section A, to the Section B, <lb/>therefore the proportion remaining of the line G, to the line F, <lb/>&longs;hall be the proportion of the velocity through A, to the velocity <lb/>through B; therefore al&longs;o the line G, &longs;hall be to the line E, as <lb/>the velocity by A, to the velocity by B: And conver&longs;ly, the ve­<lb/>locity through B, &longs;hall be to the velocity through A, as the line <lb/>E, to the line G; that is to &longs;ay, as the Section A, to the Section B, <lb/>and therefore in two Sections, &c. </s> <s>which was to be demon&longs;trated.</s></p><pb xlink:href="068/01/056.jpg" pagenum="42"/><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/></s></p><p type="main"> <s>Hence it is manife&longs;t, that Sections of the &longs;ame River (which <lb/>are no other than the vulgar mea&longs;ures of the River) have <lb/>betwixt them&longs;elves reciprocal proportions to their veloci­<lb/>ties; for in the fir&longs;t Propo&longs;ition we have demon&longs;trated that the <lb/>Sections of the &longs;ame River, di&longs;charge equal quantities of Water <lb/>in equal times; therefore, by what hath now been demon&longs;trated <lb/>the Sections of the &longs;ame River &longs;hall have reciprocal proportion <lb/>to their velocities; And therefore the &longs;ame running water chan­<lb/>geth mea&longs;ure, when it changeth velocity; namely, increa&longs;eth the <lb/>mea&longs;ure, when it decrea&longs;eth the velocity, and decrea&longs;eth the <lb/>mea&longs;ure, when it increa&longs;eth the velocity.</s></p><p type="main"> <s>On which principally depends all that which hath been &longs;aid <lb/>above in the <emph type="italics"/>Di&longs;cour&longs;e,<emph.end type="italics"/> and ob&longs;erved in the <emph type="italics"/>Corollaries<emph.end type="italics"/> and <emph type="italics"/>Ap­<lb/>pendixes<emph.end type="italics"/>; and therefore is worthy to be well under&longs;tood and <lb/>heeded.</s></p><p type="head"> <s>PROPOSITION IV.</s></p><p type="main"> <s><emph type="italics"/>If a River fall into another River, the height of the <lb/>fir&longs;t in its own Chanel &longs;hall be to the height that it <lb/>&longs;hall make in the &longs;econd Chanel, in a proportion <lb/>compounded of the proportions of the breadth of <lb/>the Chanel of the &longs;econd, to the breadth of the <lb/>Chanel of the fir&longs;t, and of the velocitie acquired in <lb/>the Chanel of the &longs;econd, to that which it had in <lb/>its proper and first Chanel.<emph.end type="italics"/></s></p><p type="main"> <s>Let the River A B, who&longs;e height is A C, and breadth C B, <lb/>that is, who&longs;e Section is A C B; let it enter, I &longs;ay, into a­<lb/>nother River as broad as the line E F, and let it therein make <lb/>the ri&longs;e or height D E, that is to &longs;ay, let it have its Section in <lb/>the River whereinto it falls D E F; I &longs;ay, that the height A C <lb/>hath to the height D E the proportion compounded of the pro­<lb/>portions of the breadth E F, to the breadth C B, and of the ve­<lb/>locity through D F, to the velocity through A B. </s> <s>Let us &longs;up­<lb/>po&longs;e the Section G, equal in velocity to the Section A B, and in <lb/>breadth equal to E F, which carrieth a quantity of Water e­<lb/>qual to that which the Section A B carrieth, in equal times, <lb/>and con&longs;equently, equal to that which D F carrieth. </s> <s>Moreover, <lb/>as the breadth E F is to the breadth C B, &longs;o let the line H be to <pb xlink:href="068/01/057.jpg" pagenum="43"/>the line I; and as the velocity of D F is to the velocity of A B, <lb/>&longs;o let the line I be to the line L; becau&longs;e therefore the two <lb/>Sections A B and G are equally &longs;wift, and di&longs;charge equal quan­<lb/>tity of Water in equal times, they &longs;hall be equal Sections; and <lb/><figure id="id.068.01.057.1.jpg" xlink:href="068/01/057/1.jpg"/><lb/>therefore the height of A <emph type="italics"/>B<emph.end type="italics"/> to the height of G, &longs;hall be as the <lb/>breadth of G, to the breadth of A <emph type="italics"/>B,<emph.end type="italics"/> that is, as E F to C <emph type="italics"/>B,<emph.end type="italics"/><lb/>that is, as the line H to the line I: but becau&longs;e the Water which <lb/>pa&longs;&longs;eth through G, is equal to that which pa&longs;&longs;eth through D E F, <lb/>therefore the Section G, to the Section D E F, &longs;hall have the re­<lb/>ciprocal proportion of the velocity through D E F, to the velo­<lb/>city through G; but al&longs;o the height of G, is to the height D E, <lb/>as the Section G, to the Section D E F: Therefore the height of <lb/>G, is to the height D E, as the velocity through D E F, is to the <lb/>velocity through G; that is, as the velocity through D E F, is to <lb/>the velocity through A <emph type="italics"/>B<emph.end type="italics"/>; That is, finally, as the line I, to the <lb/>line L; Therefore, by equal proportion, the height of <emph type="italics"/>A B,<emph.end type="italics"/> that <lb/>is, A C, &longs;hall be to the height D E; as H to L, that is, com­<lb/>pounded of the proportions of the breadth E F, to the breadth <lb/>C <emph type="italics"/>B,<emph.end type="italics"/> and of the velocity through D F, to the velocity through <lb/>A <emph type="italics"/>B<emph.end type="italics"/>: So that if a River fall into another River, &c. </s> <s>which was <lb/>to be demon&longs;trated.</s></p><pb xlink:href="068/01/058.jpg" pagenum="44"/><p type="head"> <s>PROPOSITION V.</s></p><p type="main"> <s><emph type="italics"/>If a River di&longs;charge a certain quantitie of Water <lb/>in a certain time; and after that there come into it <lb/>a Flood, the quantity of Water which is di&longs;char­<lb/>ged in as much time at the Flood, is to that which <lb/>was di&longs;charged before, whil&longs;t the River was low, <lb/>in a proportion compounded of the proportions of <lb/>the velocity of the Flood, to the velocity of the first <lb/>Water, and of the height of the Flood, to the <lb/>height of the first Water.<emph.end type="italics"/></s></p><p type="main"> <s>Suppo&longs;e a River, which whil&longs;t it is low, runs by the Section <lb/>AF; and after a Flood cometh into the &longs;ame, and runneth <lb/>through the Section D F, I &longs;ay, that the quantity of the Wa­<lb/>ter which is di&longs;charged through D F, is to that which is di&longs;charged <lb/><figure id="id.068.01.058.1.jpg" xlink:href="068/01/058/1.jpg"/><lb/>through A F, in a proportion compounded of the proportions of <lb/>the velocity through D F, to the velocity through A F, and of <lb/>the height D <emph type="italics"/>B,<emph.end type="italics"/> to the height A <emph type="italics"/>B<emph.end type="italics"/>; As the velocity through DF <lb/>is to the velocity through A F, &longs;o let the line R, to the line S; <lb/>and as the height D <emph type="italics"/>B<emph.end type="italics"/> is to the height A <emph type="italics"/>B,<emph.end type="italics"/> &longs;o let the line S, to <lb/>the line T; and let us &longs;uppo&longs;e a Section L M N, equal to D F <lb/>in height and breadth; that is L M equal to D <emph type="italics"/>B,<emph.end type="italics"/> and M N equal <lb/>to <emph type="italics"/>B F<emph.end type="italics"/>; but let it be in velocity equal to the Section A F, there­<lb/>fore the quantity of Water which runneth through D F, &longs;hall be <lb/>to that which runneth through LN, as the velocity through DF, <lb/>is to the velocity through L N, that is, to the velocity through <lb/><emph type="italics"/>A F<emph.end type="italics"/>; and the line R being to the line S, as the velocity through <lb/>D <emph type="italics"/>F,<emph.end type="italics"/> to the velocity through <emph type="italics"/>A F<emph.end type="italics"/>; therefore the quantity which <lb/>runneth through D <emph type="italics"/>F,<emph.end type="italics"/> to that which runneth through L N, &longs;hall <lb/>have the proportion of R to S; but the quantity which runneth <lb/>through L N, to that which runneth through <emph type="italics"/>A F,<emph.end type="italics"/> (the Sections <pb xlink:href="068/01/059.jpg" pagenum="45"/>being equally &longs;wift) &longs;hall be in proportion as the Section <emph type="italics"/>L<emph.end type="italics"/> N, to <lb/>the Section A F; that is, as D B, to A B; that is as the line S, to <lb/>the line T: Therefore by equal proportion, the quantity of the <lb/>water which runneth through D F, &longs;hall be in proportion to that <lb/>which runneth through A F, as R is to T; that is, compounded of <lb/>the proportions of the height D B, to the height A B, and of the <lb/>velocity through <emph type="italics"/>D F,<emph.end type="italics"/> to the velocity through <emph type="italics"/>A F<emph.end type="italics"/>; and therefore <lb/>if a River di&longs;charge a certain quantity, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be de­<lb/>mon&longs;trated.</s></p><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>The &longs;ame might have been demon&longs;trated by the &longs;econd <lb/>Propo&longs;ition above demon&longs;trated, as is manife&longs;t.</s></p><p type="head"> <s>PROPOSITION VI.</s></p><p type="main"> <s><emph type="italics"/>If two equal &longs;treams of the &longs;ame Torrent, fall into a <lb/>River at divers times, the heights made in the Ri­<lb/>ver by the Torrent, &longs;hall have between them­<lb/>&longs;elves the reciprocal proportion of the velocities <lb/>acquired in the River.<emph.end type="italics"/></s></p><p type="main"> <s>Let A and B, be two equal &longs;treams of the &longs;ame Torrent, <lb/>which falling into a River at divers times, make the heights <lb/>C D, and F G; that is the &longs;tream A, maketh the height <lb/>C D, and the &longs;tream B, maketh the height F G; that is, Let <lb/>their Sections in the River, into which they are fallen, be C E, <lb/>and FH; I &longs;ay, that the height C D, &longs;hall be to the height F G, <lb/>in reciprocal proportion, as the velocity through F H, to the ve­<lb/>locity through C E; for the quantity of water which pa&longs;&longs;eth <lb/>through A, being equal to the quantity which pa&longs;&longs;eth through B, <lb/>in equal times; al&longs;o the quantity which pa&longs;&longs;eth through C E, &longs;hall <lb/><figure id="id.068.01.059.1.jpg" xlink:href="068/01/059/1.jpg"/><lb/>be equal to that which pa&longs;&longs;eth through F H: And therefore the <lb/>proportion that the Section C E, hath to the Section F H; &longs;hall <lb/>be the &longs;ame that the velocity through F H, hath to the velocity <lb/>through C E; But the Section C E, is to the Section F H, as <lb/>C D, to F G, by rea&longs;on they are of the &longs;ame breadth: Therefore <lb/>C D, &longs;hall be to F G, in reciprocal proportion, as the velocity <lb/>through F H, is to the velocity through C E, and therefore if two <lb/>equal &longs;treams of the &longs;ame Torrent, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be de­<lb/>mon&longs;trated.</s></p><pb xlink:href="068/01/060.jpg"/><pb xlink:href="068/01/061.jpg" pagenum="47"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s><emph type="italics"/>Lib.<emph.end type="italics"/> II.</s></p><p type="main"> <s>Having, in the clo&longs;e of my Treati&longs;e of the <lb/>Men&longs;uration of Running Waters promi&longs;ed <lb/>to declare upon another occa&longs;ion other par­<lb/>ticulars more ob&longs;cure, and of very great <lb/>concern upon the &longs;ame argumement: I now <lb/>do perform my promi&longs;e on the occa&longs;ion <lb/>that I had the pa&longs;t year 1641. to propound <lb/>my thoughts touching the &longs;tate of the Lake <lb/>of <emph type="italics"/>Venice,<emph.end type="italics"/> a bu&longs;ine&longs;s certainly mo&longs;t important, as being the <lb/>concernment of that mo&longs;t noble and mo&longs;t admirable City; and <lb/>indeed of all <emph type="italics"/>Italy,<emph.end type="italics"/> yea of all <emph type="italics"/>Europe, A&longs;ia, & Africa<emph.end type="italics"/>; & one may <lb/>truly &longs;ay of all the whole World. </s> <s>And being to proceed according <lb/>to the method nece&longs;&longs;ary in Sciences, I wil propo&longs;e, in the fir&longs;t place <lb/>certain Definitions of tho&longs;e Terms whereof we are to make u&longs;e <lb/>in our Di&longs;cour&longs;e: and then, laying down certain Principles we <lb/>will demon&longs;trate &longs;ome Problemes and Theoremes nece&longs;&longs;ary for <lb/>the under&longs;tanding of tho&longs;e things which we are to deliver; and <lb/>moreover, recounting &longs;undry ca&longs;es that have happened, we will <lb/>prove by practice, of what utility this contemplation of the <lb/>Mea&longs;ure of Running Waters is in the more important affairs both <lb/>Publique and Private.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s>Two Rivers are &longs;aid to move with equal velocity, when in e­<lb/>qual times they pa&longs;&longs;e &longs;paces of equal length.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s>Rivers are &longs;aid to move with like velocity, when their propor­<lb/>tional parts do move alike, that is, the upper parts alike to <lb/>the upper, and the lower to the lower; &longs;o that if the upper <lb/>part of one River &longs;hall be more &longs;wift than the upper part of ano­<lb/>ther; then al&longs;o the lower part of the former &longs;hall be more &longs;wift <lb/>than the part corre&longs;pondent to it in the &longs;econd, proportionally.</s></p><pb xlink:href="068/01/062.jpg" pagenum="48"/><p type="head"> <s>DEFINITON III.</s></p><p type="main"> <s>To mea&longs;ure a River, or running Water, is in our &longs;en&longs;e to finde <lb/>out how many determinate mea&longs;ures, or weights of Water <lb/>in a given time pa&longs;&longs;eth through the River, or Channel of the <lb/>Water that is to be mea&longs;ured.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s>If a Machine be made either of Brick, or of Stone, or of <lb/>Wood, &longs;o compo&longs;ed that two &longs;ides of the &longs;aid Machine be <lb/>placed at right angles upon the ends of a third &longs;ide, that is <lb/>&longs;uppo&longs;ed to be placed in the bottom of a River, parallel to the <lb/>Horizon, in &longs;uch a manner, that all the water which runneth <lb/>through the &longs;aid River, pa&longs;&longs;eth thorow the &longs;aid Machine: And <lb/>if all the water coming to be diverted <lb/><figure id="id.068.01.062.1.jpg" xlink:href="068/01/062/1.jpg"/><lb/>that runneth through the &longs;aid River, the <lb/>upper &longs;uperficies of that third &longs;ide placed <lb/>in the bottom do remain uncovered <lb/>and dry, and that the dead water be not <lb/>above it; This &longs;ame Machine &longs;hall be <lb/><arrow.to.target n="marg968"></arrow.to.target><lb/>called by us ^{*} REGULATOR: And that third &longs;ide of the <lb/>Machine which &longs;tandeth Horizontally is called the bottom of <lb/>the Regulator; and the other two &longs;ides, are called the banks of <lb/>the Regulator; as is &longs;een in this fir&longs;t Figure: A B C D, &longs;hall be <lb/>the Regulator; B C the bottom; and the other two &longs;ides A B, <lb/>and C D are its banks.</s></p><p type="margin"> <s><margin.target id="marg968"></margin.target>* Or Sluice.</s></p><p type="head"> <s>DEFINITION V.</s></p><p type="main"> <s>By the quick height, we mean the Perpendicular from the upper <lb/>&longs;uperficies of the River, unto the upper &longs;uperficies of the bot­<lb/>tom of the Regulator; as in the foregoing Figure the line. </s> <s>G H.</s></p><p type="head"> <s>DEFINITION VI.</s></p><p type="main"> <s>If the water of a <emph type="italics"/>R<emph.end type="italics"/>iver be &longs;uppo&longs;ed to be marked by three <lb/>&longs;ides of a Regulator, that Rightangled Parallelogram compre­<lb/>hended between the banks of the Regulator, and the bottom, <lb/>and the &longs;uperficies of the Water is called a Section of the <lb/>River.</s></p><pb xlink:href="068/01/063.jpg" pagenum="49"/><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>Here it is to be noted, that the River it &longs;elf may have &longs;undry <lb/>and divers heights, in &longs;everal parts of its Chanel, by rea&longs;on of <lb/>the various velocities of the water, and its mea&longs;ures; as hath <lb/>been demon&longs;trated in the fir&longs;t book.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>It is &longs;uppo&longs;ed, that the Rivers equal in breadth, and quick <lb/>height, that have the &longs;ame inclination of bed or bottom, ought <lb/>al&longs;o to have equal velocities, the accidental impediments being <lb/>removed that are di&longs;per&longs;ed throughout the cour&longs;e of the water, <lb/>and ab&longs;tracting al&longs;o from the external windes, which may velo­<lb/>citate, and retard the cour&longs;e of the water of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>Let us &longs;uppo&longs;e al&longs;o, that if there be two Rivers that are in <lb/>their beds of equal length, and of the &longs;ame inclination, but of <lb/>quick heights unequal, they ought to move with like velocity, <lb/>according to the &longs;en&longs;e explained in the &longs;econd definition.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>Becau&longs;e it will often be requi&longs;ite to mea&longs;ure the time exactly <lb/>in the following Problems, we take that to be an excellent <lb/>way to mea&longs;ure the time, which was &longs;hewed me many years &longs;ince <lb/>by <emph type="italics"/>Signore Galilæo Galilæi,<emph.end type="italics"/> which is as followeth.</s></p><p type="main"> <s>A &longs;tring is to be taken three Roman feet long, to the end of <lb/>which a Bullet of Lead is to be hanged, of about two or three <lb/>ounces; and holding it by the other end, the Plummet is to be <lb/>removed from its perpendicularity a Palm, more or le&longs;s, and then <lb/>let go, which will make many &longs;wings to and again, pa&longs;&longs;ing and <lb/>repa&longs;&longs;ing the Perpendicular, before that it &longs;tay in the &longs;ame: Now <lb/>it being required to mea&longs;ure the time that is &longs;pent in any what­<lb/>&longs;oever operation, tho&longs;e vibrations are to be numbred, that are <lb/>made whil&longs;t the work la&longs;teth; and they &longs;hall be &longs;o many &longs;econd <lb/>minutes of an hour, if &longs;o be, that the &longs;tring be three Roman feet <lb/>long, but in &longs;horter &longs;trings, the vibrations are more frequent, and <lb/>in longer, le&longs;s frequent; and all this &longs;till followeth, whether the <lb/>Plummet be little or much removed from its Perpendicularity, or <lb/>whether the weight of the Lead be greater or le&longs;&longs;er.</s></p><p type="main"> <s>The&longs;e things being pre-&longs;uppo&longs;ed, we will lay down &longs;ome fa­<pb xlink:href="068/01/064.jpg" pagenum="50"/>miliar Problems, from which we &longs;hall pa&longs;s to the Notions and <lb/>que&longs;tions more &longs;ubtil and curious; which will al&longs;o prove profi­<lb/>table, and not to be &longs;leighted in this bu&longs;ine&longs;s of Waters.</s></p><p type="head"> <s>PROPOSITION I. PROBLEME I.</s></p><p type="main"> <s><emph type="italics"/>Achanel of Running-Water being given, the breadth <lb/>of which pa&longs;sing through a Regulator, is three <lb/>Palms; and the height one Palm, little more or <lb/>le&longs;s, to mea&longs;ure what water pa&longs;&longs;eth through the <lb/>Regulator in a time given.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t, we are to dam up the Chanel; &longs;o that there pa&longs;s not any <lb/>water below the Dam; then we mu&longs;t place in the &longs;ide of the <lb/>Chanel, in the parts above the Regulator three, or four, or five <lb/>Bent-pipes, or Syphons, according to the quantity of the water <lb/>that runneth along the Chanel; in &longs;uch &longs;ort, as that they may <lb/>drink up, or draw out of the Chanel all the water that the Cha­<lb/>nel beareth (and then &longs;hall we know that the Syphons drink up <lb/>all the water, when we &longs;ee that the water at the Dam doth nei­<lb/>ther ri&longs;e higher, nor abate, but alwaies keepeth in the &longs;ame Le­<lb/>vel.) The&longs;e things being prepared, taking the In&longs;trument to <lb/>mea&longs;ure the time, we will examine the quantity of the water that <lb/>i&longs;&longs;ueth by one of tho&longs;e Syphons in the &longs;pace of twenty vibrations, <lb/>and the like will we do one by one with the other Syphons; and <lb/>then collecting the whole &longs;umme, we will &longs;ay, that &longs;o much is <lb/>the water that pa&longs;&longs;eth and runneth thorow the Regulator or <lb/>Chanel (the Dam being taken away) in the &longs;pace of twenty &longs;e­<lb/>cond minutes of an hour; and calculating, we may ea&longs;ily reduce <lb/>it to hours, dayes, months, and years: And it hath fallen to my <lb/>turn to mea&longs;ure this way the waters of Mills and Fountains, and I <lb/>have been well a&longs;&longs;ured of its exactne&longs;s, by often repeating the <lb/>&longs;ame work.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>And this method mu&longs;t be made u&longs;e of in mea&longs;uring the waters, <lb/>that we are to bring into Conducts, and carry into Cities <lb/>and Ca&longs;tles, for Fountains; and that we may be able afterwards <lb/>to divide and &longs;hare them to particular per&longs;ons ju&longs;tly; which will <lb/>prevent infinite &longs;uits and controver&longs;ies that every day happen in <lb/>the&longs;e matters..</s></p><pb xlink:href="068/01/065.jpg" pagenum="51"/><p type="head"> <s>PROPOSITION II. THEOREM I.</s></p><p type="main"> <s><emph type="italics"/>If a River moving with &longs;uch a certain velocitie <lb/>through its Regulator, &longs;hall have a given quick <lb/>height, and afterwards by new water &longs;hall increa&longs;e <lb/>to be double, it &longs;hall al&longs;o increa&longs;e double in ve­<lb/>locitie.<emph.end type="italics"/></s></p><p type="main"> <s>Let the quick height of a River in the Regulator A B C D, <lb/>be the perpendicular F B, and afterwards, by new water that <lb/>is added to the River, let the water be &longs;uppo&longs;ed to be rai&longs;­<lb/>ed to G, &longs;o that G B may be double to E B. </s> <s>I &longs;ay, that all the <lb/>water G C &longs;hall be double in velocity to <lb/><figure id="id.068.01.065.1.jpg" xlink:href="068/01/065/1.jpg"/><lb/>that of E C: For the water G F, having <lb/>for its bed the bottom E F, equally in­<lb/>clined as the bed B C, and its quick <lb/>height G E being equal to the quick <lb/>height E C, and having the &longs;ame breadth <lb/>B C, it &longs;hall have of it &longs;elf a velocity e­<lb/>qual to the velocity of the fir&longs;t water <lb/>F C: but becau&longs;e, be&longs;ides its own moti­<lb/>on, which is imparted to it by the motion of the water E C, it <lb/>hath al&longs;o over and above its own motion, the motion of E C. </s> <s>And <lb/>becau&longs;e the two waters G C, and E C, are alike in velocity, by <lb/>the third Suppo&longs;ition; therefore the whole water G C &longs;hall be <lb/>double in velocity to the water E C; which was that which we <lb/>were to demon&longs;trate.</s></p><p type="main"> <s><emph type="italics"/>This demon&longs;tration is not here in&longs;erted, as perfect, the Authour ha­<lb/>ving by &longs;everal letters to his friends confe&longs;&longs;ed him&longs;elf un&longs;atisfi­<lb/>ed therewith; and that he intended not to publi&longs;h the<emph.end type="italics"/> Theorem <lb/><emph type="italics"/>without a more &longs;olid demon&longs;tration, which he was in hope to light <lb/>upon. </s> <s>But being overtaken by Death, he could not give the <lb/>fini&longs;hing touch either to this, or to the rest of the &longs;econd Book. </s> <s>In <lb/>con&longs;ideration of which, it &longs;eemed good to the Publi&longs;her of the <lb/>&longs;ame, rather to omit it, than to do any thing contrary to the mind of <lb/>the Authour. </s> <s>And this he hints, by way of adverti&longs;ement, to <lb/>tho&longs;e that have Manu&longs;cript Copies of this Book, with the &longs;aid de­<lb/>mon&longs;tration. </s> <s>For this time let the Reader content him&longs;elf with <lb/>the knowledge of &longs;o ingenious and profitable a Conclu&longs;ion; of the <lb/>truth of which he may, with &longs;mall expence and much plea&longs;ure, be <lb/>a&longs;&longs;ured by means of the experiment to be made in the &longs;ame man­<lb/>ner, with that which is laid down in the &longs;econd Corollary of<emph.end type="italics"/><pb xlink:href="068/01/066.jpg" pagenum="52"/><emph type="italics"/>the fourth<emph.end type="italics"/> Theorem <emph type="italics"/>of this, with its Table, and the u&longs;e there­<lb/>of annexed.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/></s></p><p type="main"> <s>Hence it followeth, that when a River increa&longs;eth in quick <lb/>height by the addition of new water, it al&longs;o increa&longs;eth in ve­<lb/>locity; &longs;o that the velocity hath the &longs;ame proportion to the velo­<lb/>city that the quick height hath to the quick height; as may be <lb/>demon&longs;trated in the &longs;ame manner.</s></p><p type="head"> <s>PROPOS. III. PROBLEME II.</s></p><p type="main"> <s><emph type="italics"/>Achanel of Water being given who&longs;e breadth exceeds not <lb/>twenty Palms, or thereabouts, and who&longs;e quick beight <lb/>is le&longs;s than five Palms, to mea&longs;ure the quantity of the <lb/>Water that runneth thorow the Chanel in a time <lb/>given.<emph.end type="italics"/></s></p><p type="main"> <s>Place in the Chanel a Regulator, and ob&longs;erve the quick <lb/>height in the &longs;aid Regulator; then let the water be turned <lb/>away from the Chanel by a Chanellet of three or four Palms <lb/>in breadth, or thereabouts: And that being done, mea&longs;ure the <lb/>quantity of the water which pa&longs;&longs;eth thorow the &longs;aid Chanellet, <lb/>as hath been taught in the &longs;econd Propo&longs;ition; and at the &longs;ame <lb/>time ob&longs;erve exactly how much the quick height &longs;hall be abated <lb/>in the greater Chanel, by means of the diver&longs;ion of the Chancl­<lb/>let; and all the&longs;e particulars being performed, multiply the quick <lb/>height of the greater Chanel into it &longs;elf, and likewi&longs;e multiply <lb/>into it &longs;elf the le&longs;&longs;er height of the &longs;aid bigger Chanel, and the <lb/>le&longs;&longs;er &longs;quare being taken, from the greater, the remainder &longs;hall <lb/>have the &longs;ame proportion to the whole greater &longs;quare, as the wa­<lb/>ter of the Chanellet diverted, hath to the water of the bigger <lb/>Chanel: And becau&longs;e the water of the Chanellet is known by <lb/>the Method laid down in the fir&longs;t Theorem, and the terms of the <lb/>Theorem being al&longs;o known, the quantity of the water which run­<lb/>neth thorow the bigger Chanel, &longs;hall be al&longs;o known by the Gol­<lb/>den <emph type="italics"/>R<emph.end type="italics"/>ule, which was that that was de&longs;ired to be known. </s> <s>We <lb/>will explain the whole bu&longs;ine&longs;s by an example.</s></p><p type="main"> <s>Let a Chanel be, for example, 15 Palms broad, its quick height <lb/>before its diver&longs;ion by the Chanellet &longs;hall be &longs;uppo&longs;ed to be 24 <lb/>inches; but after the diver&longs;ion, let the quick height of the Chanel <lb/>be onely 22 inches. </s> <s>Therefore the greater height to the le&longs;&longs;er, <lb/>is as the number 11. to 12. But the &longs;quare of 11. is 121, and the <lb/>&longs;quare of 12. is 144, the difference between the &longs;aid le&longs;&longs;er <pb xlink:href="068/01/067.jpg" pagenum="53"/>&longs;quare and the greater is 23. Therefore the diverted water, is <lb/>to the whole water, as 23. to 144: which is well near as 1 to <lb/>6 6/23: and that is the proportion that the quantity of the water <lb/>which runneth through the Chanellet &longs;hall have, to all the water <lb/>that runneth thorow the great Chanel. </s> <s>Now if we &longs;hould finde <lb/>by the Rule mentioned above in the fir&longs;t Propo&longs;ition, that the <lb/>quantity of the water that runneth through the Chanellet, is <lb/><emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> an hundred Barrels, in the &longs;pace of 15 &longs;econd minutes of <lb/>an hour, it is manife&longs;t, that the water which runneth through the <lb/>great Chanel in the &longs;aid time of 35 min. </s> <s>&longs;ec. </s> <s>&longs;hall be about 600 <lb/>Barrels.</s></p><p type="head"> <s><emph type="italics"/>The &longs;ame operation performed another way.<emph.end type="italics"/></s></p><p type="main"> <s>And becau&longs;e very often in applying the Theory to Practice <lb/>it happeneth, that all the nece&longs;&longs;ary particulars in the The­<lb/>ory cannot &longs;o ea&longs;ily be put in execution; therefore we will <lb/>here add another way of performing the &longs;ame Problem, if it &longs;hould <lb/>chance to happen that the Chanellet could not commodiou&longs;ly be <lb/>diverted from the great Chanel, but that it were ea&longs;ier for the <lb/>water of another &longs;maller Chanel to be brought into the greater <lb/>Chanel; which water of the &longs;maller Chanel might be ea&longs;ily mea­<lb/>&longs;ured, as hath been &longs;hewen in the fir&longs;t Probleme; or in ca&longs;e that <lb/>there did fall into a greater Chanel, a le&longs;&longs;er Chanel that might <lb/>be diverted and mea&longs;ured. </s> <s>Therefore I &longs;ay in the fir&longs;t ca&longs;e, If <lb/>we would mea&longs;ure the quantity of the water that runneth in a <lb/>certain time thorow the greater Chanel, into which another le&longs;&longs;er <lb/>Chanel that is mea&longs;urable may be brought, we mu&longs;t fir&longs;t exactly <lb/>mea&longs;ure the Chanellet, and then ob&longs;erve the quick height of the <lb/>greater Chanel, before the introduction of the le&longs;&longs;er; and having <lb/>brought in the &longs;aid Chanellet, we mu&longs;t agnin find the propor­<lb/>tion that the water of the Chanellet hath to all the water of the <lb/>great Ghanel; for the&longs;e terms of the proportion being known, as <lb/>al&longs;o the quantity of the water of the Chanellet, we &longs;hall al&longs;o <lb/>come to know the quantity of the water that runneth thorow <lb/>the great Chanel. </s> <s>It is likewi&longs;e manife&longs;t, that we &longs;hall obtain <lb/>our intent, if the ca&longs;e were that there entered into the great <lb/>Chanel, another le&longs;&longs;er Chanel that was mea&longs;urable, and that <lb/>might be diverted.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>It would be nece&longs;&longs;ary to make u&longs;e of this Doctrine in the di­<lb/>&longs;tribution of the waters that are imploy'd to overflow the fields, <lb/>as is u&longs;ed in the <emph type="italics"/>Bre&longs;ciau, Cremone&longs;e, Bergama&longs;e, Lodigian, Mila-<emph.end type="italics"/><pb xlink:href="068/01/068.jpg" pagenum="54"/><emph type="italics"/>ne&longs;e<emph.end type="italics"/> territories, and many other places, where very great &longs;uits <lb/>and differences ari&longs;e, which not being to be determined with in­<lb/>telligible rea&longs;ons, come oftentimes to be decided, by force of <lb/>armes; and in&longs;tead of flowing their Grounds with Waters, they <lb/>cruelly flow them with the &longs;hedding of humane blood, impiou&longs;ly <lb/>inverting the cour&longs;e of Peace and Ju&longs;tice, &longs;owing &longs;uch di&longs;orders <lb/>and feuds, as that they are &longs;ometimes accompanied with the ru­<lb/>ine of whole Cities, or el&longs;e unprofitably charge them with vain, <lb/>and &longs;ometimes prejudicial expences.</s></p><p type="head"> <s>PROPOS. IV. THEOR. II.</s></p><p type="main"> <s><emph type="italics"/>If a River increa&longs;e in quick height, the quantitie of <lb/>Water which the River di&longs;chargeth after the in­<lb/>crea&longs;e, hath the Proportion compounded of the <lb/>Proportions of the Quick height to the Quick <lb/>height, and of the velocity to the velocity.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a River, which whil&longs;t it is low, runneth thorow <lb/>the Regulator D F, with the Quick height A B, and after­<lb/>wards let a Flood come; and then let it run with the height <lb/>D B, I &longs;ay, that the quantity of the Water that is di&longs;charged <lb/>through D F, to that which di&longs;chargeth through A F, hath the <lb/>proportion compounded of the proportions of the velocity <lb/>through D F to the velocity through A F, and of the height <lb/>D B to the height A B. </s> <s>As the velocity through D F is to the <lb/>velocity through A F, &longs;o let the line R be to the line S; and as <lb/>the height D B is to the height A B; &longs;o let the line S be to the <lb/><figure id="id.068.01.068.1.jpg" xlink:href="068/01/068/1.jpg"/><lb/>line T. </s> <s>And let a Section be &longs;uppo&longs;ed L M N equal to the <lb/>Section D F in height and length, but let it be in velocity equal <lb/>to the Section AF. </s> <s>Therefore the quantity of the Water that run­<lb/>neth through D F to that which runneth through L N, &longs;hall be <pb xlink:href="068/01/069.jpg" pagenum="55"/>as the velocity through D F, to the velocity of L N, that is, to <lb/>the velocity through L N, that is, to the velocity through <emph type="italics"/>A F.<emph.end type="italics"/><lb/>therefore the quantity of Water which runneth through D <emph type="italics"/>F,<emph.end type="italics"/><lb/>to that which pa&longs;&longs;eth through L N, &longs;hall have the proportion <lb/>that R hath to S; but the quantity of the Water that runneth <lb/>through L N, to that which runneth through <emph type="italics"/>A F<emph.end type="italics"/>; (the Sections <lb/>being equally &longs;wift) &longs;hall have the proportion that the Section <lb/>L N hath to the Section A F, that is, that the height <emph type="italics"/>B<emph.end type="italics"/> D hath to <lb/>the height <emph type="italics"/>B<emph.end type="italics"/> A, that is, that S hath to T. Therefore, by equal <lb/>proportion, the quantity of the Water which runneth by D F, <lb/>to that which runneth by A F, &longs;hall have the proportion of R to <lb/>T, that is, &longs;hall be compounded of the proportions of the height <lb/>D <emph type="italics"/>B,<emph.end type="italics"/> to the height A <emph type="italics"/>B<emph.end type="italics"/>; and of the velocity through D F, to <lb/>the velocity through A F. </s> <s>And therefore if a River increa&longs;e in <lb/>quick height, the quantity of the Water that runneth after the <lb/>increa&longs;e, to that which runneth before the increa&longs;e, hath the <lb/>proportion compounded, &c. </s> <s>Which was to be demon&longs;trated.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE I.<emph.end type="italics"/></s></p><p type="main"> <s>Hence it followeth, that we having &longs;hewn, that the quantity of <lb/>the Water which runneth, whil&longs;t the River is high, to that <lb/>which ran, whil&longs;t it was low, hath the proportion compounded <lb/>of the velocity to the velocity, and of the height to the height. <lb/></s> <s>And it having been demon&longs;trated, that the velocity to the velo­<lb/>city is as the height to the height; it followeth, I &longs;ay, that the <lb/>quantity of the Water that runneth, whil&longs;t the River is high, to <lb/>that which runneth, whil&longs;t it is low, hath duplicate proportion of <lb/>the height to the height, that is, the proportion that the &longs;quares <lb/>of the heights have.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE II.<emph.end type="italics"/></s></p><p type="main"> <s>Vpon which things dependeth the rea&longs;on of that which I have <lb/>&longs;aid, in my &longs;econd Con&longs;ideration, that if by the diver&longs;ion of <lb/>5/9 of the Water that entereth by the Rivers into the Moor or <lb/>Fen, the Water be abated &longs;uch a mea&longs;ure, that &longs;ame &longs;hall be <lb/>only one third of its whole height; but moreover diverting the 4/9, it <lb/>&longs;hall abate two other thirds, a mo&longs;t principal point; and &longs;uch, <lb/>that its not having been well under&longs;tood, hath cau&longs;ed very great <lb/>di&longs;orders, and there would now, more than ever, follow extream <lb/>dammage, if one &longs;hould put in execution the diver&longs;ion of the <emph type="italics"/>Sile<emph.end type="italics"/><lb/>and other Rivers; and it is manife&longs;t, that in the &longs;ame manner, <lb/>wherewith it hath been demon&longs;trated, that the quantity of the <lb/>Water increa&longs;ing quadruple, the height would increa&longs;e onely <pb xlink:href="068/01/070.jpg" pagenum="56"/>double, and the quantity increa&longs;ing nonuple, the height increa­<lb/>&longs;eth triple; &longs;o that, by adding to units all the odde numbers, ac­<lb/>cording to their Series, the heights increa&longs;e according to the na­<lb/>tural progre&longs;&longs;ion of all the numbers, from units. </s> <s>As for exam­<lb/>ple, there pa&longs;&longs;ing thorow a Regulator &longs;uch a certain quantity of <lb/>Water in one time; adding three of tho&longs;e mea&longs;ures, the quick <lb/>height is two of tho&longs;e parts, which at fir&longs;t was one; and con­<lb/>tinuing to adde five of tho&longs;e &longs;aid mea&longs;ures, the height is three of <lb/>tho&longs;e parts which at fir&longs;t were one; and thus adding &longs;even, and <lb/>then nine, and then 11. and then 13, &c. </s> <s>the heights &longs;hall be 4. <lb/>then 5, then 6. then 7, &c. </s> <s>And for the greater facility of the <lb/>Work, we have de&longs;cribed the following Table, of which we will <lb/>declare the u&longs;e: The Table is divided into three Series or Pro­<lb/>gre&longs;&longs;ions of Numbers: the fir&longs;t Series containeth all the Num­<lb/>bers in the Natural Progre&longs;&longs;ion, beginning at a Unit, and is called <lb/>the Series of the Heights; the &longs;econd containeth all the odde <lb/>numbers, beginning at an unit, and is called the Series of the <lb/>Additions: the third containeth all the &longs;quare numbers, begin­<lb/>ning at an unit, and is called the Series of Quantity.<lb/><arrow.to.target n="table73"></arrow.to.target></s></p><table><table.target id="table73"></table.target><row><cell>Heights.</cell><cell>1</cell><cell>2</cell><cell>3</cell><cell>4</cell><cell>5</cell><cell>6</cell><cell>7</cell><cell>8</cell><cell>9</cell><cell>10</cell><cell>11</cell></row><row><cell>Additions.</cell><cell>1</cell><cell>3</cell><cell>5</cell><cell>7</cell><cell>9</cell><cell>11</cell><cell>13</cell><cell>15</cell><cell>17</cell><cell>19</cell><cell>21</cell></row><row><cell>Quantities.</cell><cell>1</cell><cell>4</cell><cell>9</cell><cell>16</cell><cell>25</cell><cell>36</cell><cell>49</cell><cell>64</cell><cell>81</cell><cell>100</cell><cell>121</cell></row></table><p type="head"> <s><emph type="italics"/>The u&longs;e of the afore-mentioned Table.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t, if we &longs;uppo&longs;e the whole quick height of a River of Run­<lb/>ning Water to be divided into any number of equal parts, at <lb/>plea&longs;ure, and would abate the &longs;ame one fift, by means of a divi­<lb/>&longs;ron; let there be found in the Table in the Series of heights the <lb/>number 5. the denominator of the part which the River is to a­<lb/>bate, and take the number that is immediately under it in the <lb/>row of Additions, which is 9. which let be &longs;ub&longs;tracted from the <lb/>number 25. placed underneath the &longs;ame in the row of Quanti­<lb/>ties, the remainder 16. &longs;ignifieth that of the 25. parts of Water <lb/>that ran in the River, whil&longs;t it was 5 mea&longs;ures high, there do <lb/>onely run 16. parts; &longs;o that to make it abate 1/5 it is nece&longs;&longs;ary to <lb/>take 9/25 from the Water that the whole River did carry; &longs;o that <lb/>with &longs;ub&longs;tracting &longs;omewhat more than one third of the Water of <lb/>the River, it is abated but only one fift.</s></p><p type="main"> <s>2. And thus, in the &longs;econd place, if on the contrary, one would <lb/>know how much water is to be added to the &longs;aid River to make <lb/>it increa&longs;e one fift more in height, &longs;o as that it may run in the <pb xlink:href="068/01/071.jpg" pagenum="57"/>Regulator 6. of tho&longs;e parts high; of which it ran before but 5. let <lb/>6 be found in the row of heights, and let the number 11. &longs;tand­<lb/>ing under the &longs;ame be taken and added to the number 25. <lb/>that is placed under the number 9. in the Additions, and 5. in <lb/>the heights, and you &longs;hall have 36; which is the quantity of the <lb/>water that runneth with the height of the River, when it is high <lb/>6 of tho&longs;e parts, whereof it was before but 5.</s></p><p type="main"> <s>3. But if it &longs;hould be de&longs;ired, to know how much water it is <lb/>requi&longs;ite to add to make the River ri&longs;e &longs;o, as that it may run in <lb/>height 8. of tho&longs;e parts of which before it ran but 5; one <lb/>ought to take the &longs;um of the number of the Series of Additions <lb/>&longs;tanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39. <lb/>and this &longs;hall be the &longs;umme that mu&longs;t be added to 25: So that <lb/>to make the River to run 8. of tho&longs;e parts in height, of which it <lb/>before did run 5, it will be nece&longs;&longs;ary to add 39. of tho&longs;e parts, <lb/>of which the River before was 25.</s></p><p type="main"> <s>4. Likewi&longs;e the &longs;ame Table giveth the quantity of water <lb/>that runneth from time to time through a River, that increa&longs;eth <lb/>by the addition of new water to the &longs;ame in one of its heights, the <lb/>quantity of its water be known. </s> <s>As for example: If we knew that <lb/>the River in one minute of an hour di&longs;chargeth 2500. of tho&longs;e mea­<lb/>&longs;ures of water, and runneth in height 5. parts in the Regulator, and <lb/>afterwards &longs;hould &longs;ee that it runneth 8 Palms high, finding in the <lb/>row of quantity the number placed under 8. which is 64. we would <lb/>&longs;ay that the River heightned, carrieth of water 64. of tho&longs;e parts <lb/>whereof it carried before but 25; and becau&longs;e before it carried <lb/>2500. mea&longs;ures, by the Golden Rule we will &longs;ay, that the River <lb/>carrieth 6400. of tho&longs;e mea&longs;ures, of which before it carried 2500.</s></p><p type="main"> <s>In this progre&longs;s of Nature, is one thing really curious, and that <lb/>at fir&longs;t &longs;ight &longs;eemeth to be &longs;omewhat Paradoxal, that we pro­<lb/>ceeding ordinately in the diver&longs;ions and additions, with additi­<lb/>ons and diver&longs;ions &longs;o unequal, the abatings do notwith&longs;tanding <lb/>alwaies prove equal, and &longs;o do the ri&longs;ings: And who would ever <lb/>think that a River in height, <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> 10. Palms, running and carry­<lb/>ing an hundred mea&longs;ures in a minute of an hour, is to abate but <lb/>one Palm, onely by the diver&longs;ion of 19. of tho&longs;e mea&longs;ures; and <lb/>then again, that the bui&longs;ine&longs;s cometh to that pa&longs;s, that it abateth <lb/>likewi&longs;e a Palm by the diver&longs;ion of three onely of tho&longs;e mea&longs;ures, <lb/>nay, by the diver&longs;ion of but one mea&longs;ure? </s> <s>and yet it is mo&longs;t <lb/>certain: And this truth meets with &longs;o manife&longs;t proofs in experi­<lb/>ence, that it is very admirable! And for the full &longs;atisfaction of <lb/>tho&longs;e, who not being able to comprehend &longs;ubtil demon&longs;trati­<lb/>ons, desire to be clearly inform'd by the matters of fact, and to <lb/>&longs;ee with their bobily eyes, and touch with their hands, what their <lb/>under&longs;tanding and rea&longs;on cannot reach unto: I will hear add <lb/>another very ea&longs;ie way to reduce all to an experiment, the <pb xlink:href="068/01/072.jpg" pagenum="58"/>which may be made in little, in great, or in very great; of <lb/>which I make u&longs;e frequently, to the admiration of &longs;uch as &longs;ee it.</s></p><p type="main"> <s>I prepared an hundred Siphons, or, if you will, bowed Pipes, <lb/>all equal; and placed them at the brim of a Ve&longs;&longs;el, wherein the <lb/>water is kept at one and the &longs;ame level (whether all the Syphons <lb/>work, or but a certain number of them) the mouths by which <lb/>the water i&longs;&longs;ueth being all placed in the &longs;ame level, parallel to <lb/>the Horizon; but lower in level than the water in the Ve&longs;&longs;el; and <lb/>gathered all the water falling from the Syphons into another <lb/>Ve&longs;&longs;el &longs;tanding lower than the former, I made it to run away <lb/>thorow a Chanel, in &longs;uch manner inclined, that wanting water <lb/>from the Syphons, the &longs;aid Chanel remained quite dry.</s></p><p type="main"> <s>And this done, I mea&longs;ured the quick height of the Chanel <lb/>with care, and afterwards divided it exactly into 10 equal parts, <lb/>and cau&longs;ing 19. of tho&longs;e Syphons to be taken away, &longs;o that the <lb/>Chanel did not run water, &longs;ave onely with 81 of tho&longs;e Syphons, <lb/>I again ob&longs;erved the quick height of the water in the &longs;ame &longs;ite <lb/>ob&longs;erved before, and found that its height was dimini&longs;hed pre­<lb/>ci&longs;ely the tenth part of all its fir&longs;t height; and thus continuing to <lb/>take away 17. other Syphons, the height was likewi&longs;e dimini&longs;h­<lb/>ed 1/1. of all its fir&longs;t quick height; and trying to take away 15. <lb/>Syphons, then 13, then 11, then 9, then 7, then 5, and then 3. <lb/>alwaies in the&longs;e diver&longs;ions, made in order as hath been &longs;aid, there <lb/>en&longs;ued &longs;till an abatement of 1/1. of the whole height.</s></p><p type="main"> <s>And here was one thing worthy of ob&longs;ervation, that the water <lb/>encrea&longs;ing in [<emph type="italics"/>or through<emph.end type="italics"/>] the Chanel, its quick height was diffe­<lb/>rent in different &longs;ites of the Chanel, that is &longs;till le&longs;&longs;er, the more <lb/>one approached to the Out-let; notwith&longs;tanding which the abate­<lb/>ment followed in all places proportionably, that is in all its &longs;ites <lb/>the fir&longs;t part of the height of that &longs;ite dimini&longs;hed: And more­<lb/>over the water i&longs;&longs;ued from the Chanel, and dilated into a broader <lb/>cour&longs;e, from which likewi&longs;e having divers Out-lets and Mouths; <lb/>yet neverthele&longs;s in that breadth al&longs;o the quick heights &longs;ucce&longs;&longs;ive­<lb/>ly varied and altered in the &longs;ame proportions. </s> <s>Nor did I here <lb/>de&longs;i&longs;t my ob&longs;ervation, but the water being dimini&longs;hed, that i&longs;&longs;u­<lb/>ed from the Syphons, and there being but one of them left that <lb/>di&longs;charged water; I ob&longs;erved the quick height that it made in the <lb/>above-&longs;aid &longs;ites, (the which was likewi&longs;e 1/1. of all the fir&longs;t height) <lb/>there being added to the water of that Syphon, the water of <lb/>three other Syphons; &longs;o that all the water was of 4 Syphons, <lb/>and con&longs;equently quadruple to the fir&longs;t Syphon; but the quick <lb/>height was onely double, and adding five Siphons, the quick <lb/>height became triple, and with adding &longs;even Syphons, the height <lb/>increa&longs;ed quadruple; and &longs;o by adding of 9. it increa&longs;ed quin­<lb/>tuple, and by adding of 11. it increa&longs;ed &longs;extuple, and by ad­<pb xlink:href="068/01/073.jpg" pagenum="59"/>ding of 13. it increa&longs;ed &longs;eptuple, and by adding of 15. octuple, <lb/>and by adding of 17. nonuple, and la&longs;tly by adding 19. Syphons; <lb/>&longs;o that all the water was centuple to the water of one Syphon, <lb/>yet neverthele&longs;s the quick height of all this water was onely de­<lb/>cuple to the fir&longs;t height conjoyned by the water that i&longs;&longs;ued from <lb/>one onely Syphon.</s></p><p type="main"> <s>For the more clear under&longs;tanding of all which, I have made <lb/>the following Figure; in which we have the mouth A, that <lb/>maintaineth the water of the Ve&longs;&longs;el B C in the &longs;ame level; though <lb/>it continually run; to the brim of the Ve&longs;&longs;el are put 25. Sy­<lb/>phons (and there may be many more) divided into 5 Cla&longs;&longs;es, <lb/>D E F G H, and the fir&longs;t D, are of one onely Syphon; the &longs;econd <lb/>E, of three Syphons; the third F, of five; the fourth G, of 7; the <lb/>fifth H, of 9; and one may &longs;uppo&longs;e the &longs;ixth of 11, the &longs;eventh <lb/>of 13 Syphons, and &longs;o of the other Cla&longs;&longs;es, all containing in con­<lb/>&longs;equent odd numbers &longs;ucce&longs;&longs;ively (we are content to repre&longs;ent in <lb/>the Figure no more but the five forenamed Cla&longs;&longs;es to avoid con­<lb/>fu&longs;ion) the gathered water D E F G H, which runneth thorow <lb/>the Chanel I K L, and falleth into the out-let M N O P; and &longs;o <lb/>much &longs;ufficeth for the explanation of this experiment.</s></p><figure id="id.068.01.073.1.jpg" xlink:href="068/01/073/1.jpg"/><pb xlink:href="068/01/074.jpg" pagenum="60"/><p type="head"> <s>PROPOS. V. PROB. III.</s></p><p type="main"> <s><emph type="italics"/>Any River of any bigne&longs;s, if being given to examine the <lb/>quantity of the Water that runneth thorow the River <lb/>in a time a&longs;&longs;igned.<emph.end type="italics"/></s></p><p type="main"> <s>By what we have &longs;aid already in the two preceding Pro­<lb/>blems, we may al&longs;o re&longs;olve this that we have now before <lb/>us; and it is done, by diverting in the fir&longs;t place from the <lb/>great River a good big mea&longs;urable Chanel, as is taught in the <lb/>&longs;econd Probleme, and ob&longs;erving the abatement of the River, <lb/>cau&longs;ed by the diver&longs;ion of the Chanel; and finding the proporti­<lb/>on that the Water of the Chanel hath to that of the River, then <lb/>let the Water of the Chanel be mea&longs;ured by the &longs;econd Pro­<lb/>bleme, and work as above, and you &longs;hall have your de&longs;ire.</s></p><p type="head"> <s>CONSIDERATION. I.</s></p><p type="main"> <s>And although it &longs;eemeth as if it might prove difficult, and <lb/>almo&longs;t impo&longs;&longs;ible to make u&longs;e of the Regulator number, if <lb/>one be about to mea&longs;ure the water of &longs;ome great River, <lb/>and con&longs;equently would be impo&longs;&longs;ible, or at lea&longs;t very difficult <lb/>to reduce the Theory of the fir&longs;t Probleme into practice: Yet ne­<lb/>verthele&longs;s, I could &longs;ay that &longs;uch great conceits of mea&longs;uring the <lb/>water of a great River, are not to come into the minds of any <lb/>but great Per&longs;onages, and potent Princes; of whom it is expected <lb/>for their extraordinary concerns, that they will make the&longs;e kinde <lb/>of enquiries; as if here in <emph type="italics"/>Italy<emph.end type="italics"/> it &longs;hould be of the Rivers <emph type="italics"/>Tyber, <lb/>Velino, Chiana, Arno, Serchio, Adice,<emph.end type="italics"/> in which it &longs;eemeth real­<lb/>ly difficult to apply the <emph type="italics"/>R<emph.end type="italics"/>egulator, to finde exactly the quick <lb/>height of the <emph type="italics"/>R<emph.end type="italics"/>iver: But becau&longs;e in &longs;uch like ca&longs;es &longs;ometimes <lb/>it would turn to account to be at &longs;ome charge, to come to the <lb/>exact and true knowledge of the quantity of water which that <lb/><emph type="italics"/>R<emph.end type="italics"/>iver carrieth, by knowledge whereof, other greater di&longs;­<lb/>bur&longs;ments might afterwards be avoided, that would oft times be <lb/>made in vain; and prevent the di&longs;gu&longs;ts, which &longs;ometimes happen <lb/>among&longs;t Princes: Upon this ground I think it will be well to <lb/>&longs;hew al&longs;o the way how to make u&longs;e of the <emph type="italics"/>R<emph.end type="italics"/>egulator in the&longs;e <lb/>great <emph type="italics"/>R<emph.end type="italics"/>ivers; in which if we will but open our eyes, we &longs;hall meet <lb/>with good ones, and tho&longs;e made without great co&longs;t or labour, <lb/>which will &longs;erve our turn.</s></p><p type="main"> <s>For upon &longs;uch like <emph type="italics"/>R<emph.end type="italics"/>ivers there are Wears, or Lockes made, <pb xlink:href="068/01/075.jpg" pagenum="61"/>to cau&longs;e the Waters to ri&longs;e, and to turn them for the &longs;ervice of <lb/>Mills, or the like. </s> <s>Now in the&longs;e Ca&longs;es it is &longs;ufficient, that one <lb/>erect upon the two extreames of the Weare two Pila&longs;ters either <lb/>of Wood or Brick, which with the bottome of the Weare do <lb/>compo&longs;e our Regulator, wherewith we may make our de&longs;ired <lb/>operation, yea the Chanel it &longs;elf diverted &longs;hall &longs;erve, without <lb/>making any other diver&longs;ion or union. </s> <s>And in brief, if the bu­<lb/>fine&longs;&longs;es be but managed by a judicious per&longs;on, there may wayes <lb/>and helps be made u&longs;e of, according to occa&longs;ion, of which it <lb/>would be too tedious to &longs;peak, and therefore this little that hath <lb/>been hinted &longs;hall &longs;u&longs;&longs;ice.</s></p><p type="head"> <s>CONSIDERATION II.</s></p><p type="main"> <s>From what hath been declared, if it &longs;hall be well under­<lb/>&longs;tood, may be deduced many benefits and conveniences, <lb/>not onely in dividing of Running Waters for infinite u&longs;es <lb/>that they are put to in turning of Corne-Mills, Paper-Mills, <lb/>Gins, Powder-Mills, Rice-Mills, Iron Mills, Oil-Mills, Saw­<lb/>ing-Mills, Mirtle-Mills, Felling-Mills, Fulling-Mills, Silk-Mills, <lb/>and &longs;uch other Machines; but al&longs;o in ordering Navigable Cha­<lb/>nels, diverting Rivers and Chanels of Waters, or terminating <lb/>and limiting the &longs;izes of Pipes for Fountains: In all which af­<lb/>fairs there are great errours committed, to the lo&longs;&longs;e of much <lb/>expence, the Chanels and Pipes that are made, &longs;ometimes not <lb/>being &longs;ufficient to carry the de&longs;igned Waters, and &longs;ometimes they <lb/>are made bigger than is nece&longs;&longs;ary; which di&longs;orders &longs;hall be <lb/>avoided, if the Engineer be advi&longs;ed of the things above&longs;aid: and <lb/>in ca&longs;e that to the&longs;e Notions there be added the knowledge of <lb/>Philo&longs;ophy and Mathematicks, agreeable to the &longs;ublime Di&longs;co­<lb/>veries of <emph type="italics"/>Signore Galilæo,<emph.end type="italics"/> and the further improvement thereof <lb/>by <emph type="italics"/>Signore Evangeli&longs;ta Torricelli,<emph.end type="italics"/> Mathematician to the Grand <lb/><emph type="italics"/>Duke of Tu&longs;cany,<emph.end type="italics"/> who hath &longs;ubtilly and admirably handled this <lb/>whole bu&longs;ine&longs;&longs;e of Motion, one &longs;hall then come to the know­<lb/>ledge of particular notions of great curio&longs;ity in the Theoricks, <lb/>and of extraordinary benefit in the Practicks that daily occur in <lb/>the&longs;e bu&longs;ine&longs;&longs;es.</s></p><p type="main"> <s>And to &longs;hew, in effect, of what utility the&longs;e Notions are, I <lb/>have thought fit to in&longs;ert, in this place, the Con&longs;iderations by <lb/>me made upon the Lake of <emph type="italics"/>Venice,<emph.end type="italics"/> and to repre&longs;ent, <lb/>at large, by the experience of the la&longs;t year 1641. the mo&longs;t Se­<lb/>rene <emph type="italics"/>Erizzo,<emph.end type="italics"/> then Duke of the &longs;aid Republique. </s> <s>Being <lb/>therefore at <emph type="italics"/>Venice,<emph.end type="italics"/> in the year afore&longs;aid, I was reque&longs;ted by the <lb/>mo&longs;t Illu&longs;trious and mo&longs;t Excellent <emph type="italics"/>Signore Giovanni Ba&longs;a-<emph.end type="italics"/><pb xlink:href="068/01/076.jpg" pagenum="62"/><emph type="italics"/>donna,<emph.end type="italics"/> a Senatour of great worth and merit, that I would inge­<lb/>nuou&longs;ly deliver my opinion touching the &longs;tate of the Lake <lb/>of <emph type="italics"/>Venice<emph.end type="italics"/>; and after I had di&longs;cour&longs;ed with his Honour &longs;eve­<lb/>ral times, in the end I had order to &longs;et down the whole <lb/>bu&longs;ine&longs;&longs;e in writing, who having afterwards read it privately, <lb/>the &longs;aid <emph type="italics"/>Signore<emph.end type="italics"/> imparted the &longs;ame, with like privacy, to the <lb/>mo&longs;t Serene PRINCE, and I received order to repre&longs;ent the <lb/>&longs;ame to the full <emph type="italics"/>Colledge,<emph.end type="italics"/> as accordingly I did in the Moneth <lb/>of <emph type="italics"/>May,<emph.end type="italics"/> the &longs;ame year, and it was as followeth.</s></p><figure id="id.068.01.076.1.jpg" xlink:href="068/01/076/1.jpg"/><pb xlink:href="068/01/077.jpg" pagenum="63"/><p type="head"> <s>CONSIDER ATIONS <lb/>Concerning the <lb/>LAKE <lb/>OF <lb/>VENICE. <lb/>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, <lb/>Abbot of S. <emph type="italics"/>Benedetto Aloy&longs;io,<emph.end type="italics"/> Mathematician to <lb/>Pope <emph type="italics"/>VR BAN VIII.<emph.end type="italics"/> and Profe&longs;&longs;or in <lb/>ROME.</s></p><p type="head"> <s><emph type="italics"/>CONSIDERATION I.<emph.end type="italics"/></s></p><p type="main"> <s>Though the principal cau&longs;e be but one <lb/>onely, that in my judgment threatneth <lb/>irreparable ruine to the Lake of <lb/><emph type="italics"/>Venice,<emph.end type="italics"/> in the pre&longs;ent &longs;tate in which it <lb/>now &longs;tands; Yet neverthele&longs;&longs;e, I think <lb/>that two Heads may be con&longs;idered. <lb/></s> <s>And this Con&longs;ideration may peradven­<lb/>ture &longs;erve us for to facilitate and explain <lb/>the opportune remedies, though not to <lb/>render the &longs;tate of things ab&longs;olutely unchangeable and eternal: <lb/>an enterprize impo&longs;&longs;ible, and e&longs;pecially in that which having had <lb/>&longs;ome beginning, ought likewi&longs;e nece&longs;&longs;arily to have its end; or <lb/>at lea&longs;t to prevent the danger for many hundreds of years; and <lb/>po&longs;&longs;ibly it may, in the mean time, by the mutation it &longs;elf be <lb/>brought into a better condition.</s></p><p type="main"> <s>I &longs;ay therefore, that the pre&longs;ent di&longs;order may be con&longs;idered <lb/>under two Heads; One is the very notable di&longs;covery of Land <lb/>that is ob&longs;erved at the time of low Water, the which, be&longs;ides <lb/>the ob&longs;tructing of Navigation in the Lake and al&longs;o in the <lb/>Chanels, doth likewi&longs;e threaten another mi&longs;chief and di&longs;order <pb xlink:href="068/01/078.jpg" pagenum="64"/>worthy of very particular con&longs;ideration, which is, That the Sun <lb/>drying up that mudde, e&longs;pecially in the times of hot Summers, <lb/>doth rai&longs;e thence the putrified and pernicious vapours, fogs, and <lb/>exhalations that infect the Air, and may render the City unha­<lb/>bitable.</s></p><p type="main"> <s>The &longs;econd Head is the great Stoppage that daily is grow­<lb/>ing in the Ports, e&longs;pecially of <emph type="italics"/>Venice,<emph.end type="italics"/> at <emph type="italics"/>Malamoco<emph.end type="italics"/>; concerning <lb/>which matters I will hint certain general points, and then <lb/>will proceed to the more particular and important affairs.</s></p><p type="main"> <s>And fir&longs;t, I &longs;ay, that I hold it altogether impo&longs;&longs;ible to effect <lb/>any thing, though never &longs;o profitable, which doth not bring with <lb/>it &longs;ome mi&longs;chief; and therefore the good and the hurt ought to <lb/>be very well weighed, and then the le&longs;&longs;e harmful part to be im­<lb/>braced.</s></p><p type="main"> <s>Secondly, I propo&longs;e to con&longs;ideration, that the &longs;o notable di&longs;­<lb/>covery of Earth & Mud, hath not been long ob&longs;erved, as I under­<lb/>&longs;tand, from old per&longs;ons that can remember pa&longs;&longs;ages for fifty <lb/>years pa&longs;t; which thing being true, as to me it &longs;eemeth mo&longs;t <lb/>true, it &longs;hould appear that it could not but be good to reduce <lb/>matters to that pa&longs;&longs;e that they were at formerly, (laying a&longs;ide <lb/>all affection or pa&longs;&longs;ion that &longs;elf-flattering minds have entertained <lb/>for their own conceits) or at lea&longs;t it &longs;hall be nece&longs;&longs;ary &longs;peedily to <lb/>con&longs;ult the whole.</s></p><p type="main"> <s>Thirdly, I hold that it is nece&longs;&longs;ary to weigh, whether from the <lb/>fore&longs;aid di&longs;covery of Land, it followeth, that onely the Earth ri­<lb/>&longs;eth, as it is commonly thought by all, without di&longs;pute; or whe­<lb/>ther the Waters are abated and faln away; or el&longs;e whether it <lb/>proceedeth from both the one and other cau&longs;e. </s> <s>And here it would <lb/>be &longs;ea&longs;onable to enquire, what &longs;hare the &longs;aid cau&longs;es may have, <lb/>each con&longs;idered apart in the fore&longs;aid effect. </s> <s>For, in the fir&longs;t <lb/>ca&longs;e, if the Earth have been rai&longs;ed, it would be nece&longs;&longs;ary to <lb/>con&longs;ider of taking it down, and removing it: But if the Wa­<lb/>ters have failed or abated, I believe that it would be extreamly ne­<lb/>ce&longs;&longs;ary to re&longs;tore and rai&longs;e them: And if both the&longs;e rea&longs;ons have <lb/>con&longs;pired in this effect, it will be nece&longs;&longs;ary to remedy them each <lb/>apart. </s> <s>And I do, for my part, think, that the &longs;o notable appea­<lb/>rance of Shelves at the time of low Water, proceeds principally <lb/>from the decrea&longs;e and abatement of the Waters, which may <lb/>confidently be affirmed to need no other proof, in regard that the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> hath been actually diverted which did formerly di&longs;charge <lb/>its Water into the Lake.</s></p><p type="main"> <s>As to the other point of the great Stoppage of Ports, I hold, <lb/>that all proceedeth from the violence of the Sea, which being <lb/>&longs;ometimes di&longs;turbed by windes, e&longs;pecially at the time of the wa­<lb/>ters flowing, doth continually rai&longs;e from its bottome immen&longs;e <pb xlink:href="068/01/079.jpg" pagenum="65"/>heaps of &longs;and, carrying them by the tide; and force of the waves <lb/>into the Lake; it not having on its part any &longs;ttength of current <lb/>that may rai&longs;e and carry them away, they &longs;ink to the bottom, and <lb/>&longs;o they choke up the Ports. </s> <s>And that this effect happeneth in <lb/>this manner, we have mo&longs;t frequent experiences thereof along the <lb/>Sea-coa&longs;ts: And I have ob&longs;erved in <emph type="italics"/>Tu&longs;cany<emph.end type="italics"/> on the <emph type="italics"/>Roman­<lb/>&longs;hores,<emph.end type="italics"/> and in the Kingdom of of <emph type="italics"/>Naples,<emph.end type="italics"/> that when a river fal­<lb/>leth into the Sea, there is alwaies &longs;een in the Sea it &longs;elf, at the place <lb/>of the rivets out-let, the re&longs;emblance, as it were, of an half-Moon, <lb/>or a great &longs;helf of &longs;ettled &longs;and under water, much higher then the <lb/>re&longs;t of the &longs;hore, and it is called in <emph type="italics"/>Tu&longs;cany, il Cavallo<emph.end type="italics"/>; and here <lb/>in <emph type="italics"/>Venice, lo Scanto<emph.end type="italics"/>: the which cometh to be cut by the current <lb/>of the river, one while on the right &longs;ide, another while on the <lb/>left, and &longs;ometimes in the mid&longs;t, according as the Wind fits. </s> <s>And <lb/>a like effect I have ob&longs;erved in certain little Rillets of water, <lb/>along the Lake of <emph type="italics"/>Bol&longs;ena<emph.end type="italics"/>; with no other difference, &longs;ave that of <lb/>&longs;mall and great.</s></p><p type="main"> <s>Now who&longs;o well con&longs;idereth this effect, plainly &longs;eeth that it <lb/>proceeds from no other, than from the contrariety of the &longs;tream <lb/>of the River, to the <emph type="italics"/>impetus<emph.end type="italics"/> of the Sea waves; &longs;eeing that <lb/>great abundance of &longs;and which the Sea continually throws upon <lb/>the &longs;hore, cometh to be driven into the Sea by the &longs;tream of the <lb/>river; and in that place where tho&longs;e two impediments meet <lb/>with equal force, the &longs;and &longs;etleth under water, and thereupon is <lb/>made that &longs;ame Shelf or <emph type="italics"/>Cavallo<emph.end type="italics"/>; the which if the river carry <lb/>water, and that any con&longs;iderable &longs;tore, it &longs;hall be thereby cut <lb/>and broken; one while in one place, and another while in ano­<lb/>ther; as hath been &longs;aid, according as the Wind blows: And <lb/>through that Chanel it is that Ve&longs;&longs;els fall down into the Sea, and <lb/>again make to the river, as into a Port. </s> <s>But if the Water of <lb/>the river &longs;hall not be continual or &longs;hall be weak, in that ca&longs;e the <lb/>force of the Sea-Wind &longs;hall drive &longs;uch a quantity of &longs;and into <lb/>the mouth of the Port, and of the river, as &longs;hall wholly choak it <lb/>up. </s> <s>And hereupon there are &longs;een along the Sea-&longs;ide, very many <lb/>Lakes and Meers, which at certain times of the year abound with <lb/>waters, and the Lakes bear down that enclo&longs;ure, and run into <lb/>the Sea.</s></p><p type="main"> <s>Now it is nece&longs;&longs;ary to make the like reflections on our Ports <lb/>of <emph type="italics"/>Venice, Malamocco, Bondolo,<emph.end type="italics"/> and <emph type="italics"/>Chiozza<emph.end type="italics"/>; which in a certain <lb/>&longs;en&longs;e are no other than Creeks, mouths, and openings of the &longs;hore <lb/>that parts the Lake from the main Sea; and therefore I hold that <lb/>if the Waters in the Lake were plentiful, they would have <lb/>&longs;trength to &longs;cowr the mouths of the Ports thorowly, & with great <lb/>force; but the Water in the Lake failing, the Sea will with­<lb/>out any oppo&longs;al, bring &longs;uch a drift of &longs;and into the Ports; that if <pb xlink:href="068/01/080.jpg" pagenum="66"/>it doth not wholly choke them up, it &longs;hall render them at lea&longs;t <lb/>unprofitable, and impo&longs;&longs;ible for Barks and great Ve&longs;&longs;els.</s></p><p type="main"> <s>Many other con&longs;iderations might be propounded concerning <lb/>the&longs;e two heads of the &longs;toppage of the Ports, and of the appea­<lb/>rance of the Ouze and Mud in the Lakes, but &longs;o much &longs;hall &longs;uf­<lb/>fice us to have hinted, to make way for di&longs;cour&longs;ing of the opera­<lb/>tions about the oportune remedies.</s></p><p type="main"> <s>Yet before that I propound my opinion, I &longs;ay, That I know <lb/>very well that my propo&longs;al, at fir&longs;t &longs;ight, will &longs;eem ab&longs;urd and in­<lb/>convenient; and therefore, as &longs;uch, will perhaps be rejected by <lb/>the mo&longs;t: and &longs;o much the rather, for that it will prove directly <lb/>contrary to what hath hitherto been, and as I hear, is intended to <lb/>be done. </s> <s>And I am not &longs;o wedded to my opinions, but that I <lb/>do con&longs;ider what others may judge thereof: But be it as it will, <lb/>I am obliged to &longs;peak my thoughts freely, and that being done, <lb/>I will leawe it to wi&longs;er men than my &longs;elf; when they &longs;hall have <lb/>well con&longs;idered my rea&longs;ons, to judge and deliberate of the <emph type="italics"/>quid <lb/>agendum:<emph.end type="italics"/> And if the &longs;entence &longs;hall go again&longs;t me, I appeal to the <lb/>mo&longs;t equitable and inexorable Tribunal of Nature, who not <lb/>caring in the lea&longs;t to plea&longs;e either one party or another, will be <lb/>alwaies a punctual and inviolable executrix of her eternal De­<lb/>crees, again&longs;t which neither humane deliberations, nor our vain <lb/>de&longs;ires; &longs;hall ever have power to rebell. </s> <s>I added by word of <lb/>mouth that which followeth.</s></p><p type="main"> <s>Though your Highne&longs;s intere&longs;t your &longs;elf in this Noble Col­<lb/>ledge, and cau&longs;e it to be confirmed in the ^{*} Senate by univer&longs;al <lb/><arrow.to.target n="marg969"></arrow.to.target><lb/>Vote, that the Winds do not blow, that the Sea doth not fluctuate, <lb/>that the Rivers do not run; yet &longs;hall the Winds be alwaies deaf, <lb/>the Sea &longs;hall be con&longs;tant in its incon&longs;tancy, and the Rivers mo&longs;t <lb/>ob&longs;tinate: And the&longs;e &longs;hall be my Judges, and to their determi­<lb/>nation I refer my &longs;elf.</s></p><p type="margin"> <s><margin.target id="marg969"></margin.target>* In <emph type="italics"/>Pregadi,<emph.end type="italics"/> a <lb/>particular Coun­<lb/>cil, the Senators of <lb/>which have great <lb/>Authority.</s></p><p type="main"> <s>By what hath been &longs;aid, in my opinion, that is made very clear <lb/>and manife&longs;t, which in the beginning of this di&longs;cour&longs;e I glanced <lb/>at; namely, That the whole di&longs;order, although it be divided into <lb/>two heads, into the di&longs;covery of the Mud, and of the &longs;toppage <lb/>Ports, yet neverthele&longs;s, by the application of one onely remedy, <lb/>and that in my e&longs;teem very ea&longs;ie, the whole &longs;hall be removed: <lb/>And this it is; That there be re&longs;tored into the Lake as much <lb/>Water as can be po&longs;&longs;ible, and in particular from the upper parts <lb/>of <emph type="italics"/>Venice,<emph.end type="italics"/> taking care that the Water be as free from Mud as is <lb/>po&longs;&longs;ible. </s> <s>And that this is the true and real remedy of the prece­<lb/>dent di&longs;orders, is manife&longs;t: For in the pa&longs;&longs;age that this Water <lb/>&longs;hall make thorow the Lakes, it &longs;hall of it &longs;elf by degrees clear <lb/>the Chanels in &longs;undry parts of them, according to the currents <lb/>that it &longs;hall &longs;ucce&longs;&longs;ively acquire, and in this manner being di&longs;­<pb xlink:href="068/01/081.jpg" pagenum="67"/>per&longs;ed thorow the Lake, it &longs;hall maintain the waters in the &longs;ame, <lb/>and in the Chanels much higher, as I &longs;hall prove hereafter; a <lb/>thing that will make Navigation commodious; and that, which <lb/>moreover is of great moment in our bu&longs;ine&longs;&longs;e; tho&longs;e Shelves <lb/>of Mud which now di&longs;cover them&longs;elves at the time of Low­<lb/>Waters &longs;hall be alwayes covered, &longs;o that the putrefaction of <lb/>the Air &longs;hall al&longs;o be remedied.</s></p><p type="main"> <s>And la&longs;tly, this abundance of Water being alwayes to di&longs;­<lb/>charge it &longs;elf into the Sea by the Ports, I do not doubt, but that <lb/>their bottomes will be &longs;coured. </s> <s>And that the&longs;e effects mu&longs;t fol­<lb/>low, Nature her &longs;elf &longs;eemeth to per&longs;wade, there remaining onely <lb/>one great doubt, whether that abundance of Water that &longs;hall be <lb/>brought into the Lake may be really &longs;ufficient to make the Wa­<lb/>ters ri&longs;e &longs;o much as to keep the Shelves covered, and to facilitate <lb/>Navigation, which ought to be at lea&longs;t half a ^{*} Brace, or there­<lb/><arrow.to.target n="marg970"></arrow.to.target><lb/>abouts. </s> <s>And indeed it &longs;eemeth at fir&longs;t &longs;ight to be impo&longs;&longs;ible, <lb/>that the &longs;ole Water of the ^{*} <emph type="italics"/>Brent<emph.end type="italics"/> let into the Lake, and di&longs;­<lb/><arrow.to.target n="marg971"></arrow.to.target><lb/>per&longs;ed over the &longs;ame, can occa&longs;ion &longs;o notable an height of water; <lb/>and the more to confirm the difficulties, one might &longs;ay, reducing <lb/>the rea&longs;on to calculation, that in ca&longs;e the <emph type="italics"/>Brent<emph.end type="italics"/> were 40. Bra­<lb/>ces broad, and two and an half high, and the breadth of the <lb/>Lake were 20000. Braces, it would &longs;eem nece&longs;&longs;ary that the <lb/>height of the water of the <emph type="italics"/>Brent<emph.end type="italics"/> dilated and di&longs;tended thorow <lb/>the Lake would be but onely 1/200 of a Brace in height, which is <lb/>imperceptible, and would be of no avail to our purpo&longs;e; nay <lb/>more, it being very certain that the <emph type="italics"/>Brent<emph.end type="italics"/> runneth very muddy <lb/>and foul, this would occa&longs;ion very great mi&longs;chief, filling and <lb/>contracting the Lake, and for that rea&longs;on this remedy ought, as <lb/>pernicious, to be totally excluded and condemned.</s></p><p type="margin"> <s><margin.target id="marg970"></margin.target>* A <emph type="italics"/>Venice<emph.end type="italics"/> Brace <lb/>is 11/16 of our yard.</s></p><p type="margin"> <s><margin.target id="marg971"></margin.target>* A River of <lb/>that name.</s></p><p type="main"> <s>I here confe&longs;&longs;e that I am &longs;urprized at the forme of the Argu­<lb/>ment, as if I were in a certain manner convinced, that I dare not <lb/>adventure to &longs;ay more, or open my mouth in this matter; but <lb/>the &longs;trength it &longs;elf of the Argument, as being founded upon <lb/>the means of Geometrical and Arithmetical Calculation, hath <lb/>opened me the way to di&longs;cover a very crafty fraud that is couch­<lb/>ed in the &longs;ame Argument, which fraud I will make out to any <lb/>one that hath but any in&longs;ight in <emph type="italics"/>Geometry<emph.end type="italics"/> and <emph type="italics"/>Arithmetick.<emph.end type="italics"/><lb/>And as it is impo&longs;&longs;ible, that &longs;uch an argument &longs;hould be produced <lb/>by any but &longs;uch as have ta&longs;ted of the&longs;e, in &longs;uch affairs, mo&longs;t pro­<lb/>fitable, and mo&longs;t nece&longs;&longs;ary Sciences; &longs;o do not I pretend to make <lb/>my &longs;elf under&longs;tood, &longs;ave onely by &longs;uch, to whom I will evince <lb/>&longs;o clearly, as that more it cannot be de&longs;ired, the errour and fraud <lb/>wherein tho&longs;e Ancients and Moderns have been, and alwayes <lb/>are intangled, that have in any way yet handled this matter of <lb/>con&longs;idering the Mea&longs;ure and Quantity of the Waters that move. <pb xlink:href="068/01/082.jpg" pagenum="68"/>And &longs;o great is the e&longs;teem that I have for that which I am now <lb/>about to &longs;ay touching this particular, that I am content that all <lb/>the re&longs;t of my Di&longs;cour&longs;e be rejected; provided, that that be per­<lb/>fectly under&longs;tood, which I am hereafter to propo&longs;e, I holding <lb/>and knowing it to be a main Principle, upon which all that is <lb/>founded that can be &longs;aid either well or hand&longs;omely on this parti­<lb/>cular. </s> <s>The other Di&longs;cour&longs;es may have an appearance of being <lb/>probable, but this hits the mark as full as can be de&longs;ired, arriving <lb/>at the highe&longs;t degree of certainty.</s></p><p type="main"> <s>I have, &longs;eventeen years &longs;ince, as I repre&longs;ented to the mo&longs;t Se­<lb/>rene Prince, and to the Right Honourable the Pre&longs;ident of the <lb/>Lords the Commi&longs;&longs;ioners of the ^{*}Sewers, written a Treati&longs;e of the <lb/><arrow.to.target n="marg972"></arrow.to.target><lb/>Mea&longs;ure of the waters that move, in which I Geometrically de­<lb/>mon&longs;trate and declare this bu&longs;ine&longs;&longs;e, and they who &longs;hall have <lb/>well under&longs;tood the ground of my Di&longs;cour&longs;e, will re&longs;t fully &longs;a­<lb/>tisfied with that which I am now about to propo&longs;e: But that all <lb/>may become rhe more ea&longs;ie, I will more briefly explicate and <lb/>declare &longs;o much thereof as I have demon&longs;trated in the Di&longs;cour&longs;e, <lb/>which will &longs;uffice for our purpo&longs;e: And if that &longs;hould not be <lb/>enough, we have alwayes the experiment of a very ea&longs;ie and <lb/>cheap way to clear up the whole bu&longs;ine&longs;&longs;e. </s> <s>And moreover I <lb/>will take the boldne&longs;&longs;e to affirm, that in ca&longs;e there &longs;hould not for <lb/>the pre&longs;ent any deliberation be made concerning this affair, ac­<lb/>cording to my opinion; yet neverthele&longs;&longs;e it will be, at &longs;ome <lb/>time or other; or if it be not, things will grow wor&longs;e and <lb/>wor&longs;e.</s></p><p type="margin"> <s><margin.target id="marg972"></margin.target>* <emph type="italics"/>I. </s> <s>Savii dell' <lb/>Acque,<emph.end type="italics"/> a particu­<lb/>lar Council that <lb/>take care of the <lb/>Lakes and other <lb/>Aquatick affairs.</s></p><p type="main"> <s>For more clear under&longs;tanding, therefore, it ought to be known, <lb/>that it being required, as it is generally u&longs;ed, to mea&longs;ure the wa­<lb/>ters of a River, its breadth and its depth is taken, and the&longs;e two <lb/>dimen&longs;ions being multiplied together, the product is affirmed to <lb/>be the quantity of that River: As for example, if a River &longs;hall <lb/>be 100. feet broad, and 20. feet high, it will be &longs;aid, that that <lb/>River is 2000 feet of Water, and &longs;o if a Ditch &longs;hall be 15. feet <lb/>broad, and 5. feet high, this &longs;ame Ditch will be affirmed to be <lb/>75. feet of Water: And this manner of mea&longs;uring Running <lb/>Water hath been u&longs;ed by the Ancients, and by Moderns, with <lb/>no other difference, &longs;ave onely that &longs;ome have made u&longs;e of the <lb/>Foot, others of the Palme, others of the Brace, and others of <lb/>other mea&longs;ures.</s></p><p type="main"> <s>Now becau&longs;e that in ob&longs;erving the&longs;e Waters that move, I fre­<lb/>quently found, that the &longs;ame Water of the &longs;ame River was in <lb/>&longs;ome &longs;ites of its Chanel pretty big, and in others much le&longs;&longs;e, <lb/>not arriving in &longs;ome places to the twentieth, nor to the hundreth <lb/>part of that which it is &longs;een to be in other places; therefore this <lb/>vulgar way of mea&longs;uring the Waters that move, for that they did <pb xlink:href="068/01/083.jpg" pagenum="69"/>not give me a certain and &longs;table mea&longs;ure and quantity of Water, <lb/>began de&longs;ervedly to be &longs;u&longs;pected by me, as difficult and defective, <lb/>being alwayes various, and the mea&longs;ure, on the contrary, being <lb/>to be alwayes determinate, and the &longs;ame; it is therefore written, <lb/>that <emph type="italics"/>Pondus & Pondus, Men&longs;ura & Men&longs;ura, utrumque abomi­<lb/>nabile e&longs;t apud Deum,<emph.end type="italics"/> Exod. </s> <s>I con&longs;idered that in the Terri­<lb/>tory of <emph type="italics"/>Bre&longs;cia,<emph.end type="italics"/> my native Countrey, and in other places, where <lb/>Waters are divided to overflow the Grounds, by the like way of <lb/>mea&longs;uring them, there were committed grievous and mo&longs;t impor­<lb/>tant errours, to the great prejudice of the Publique and of Pri­<lb/>vate per&longs;ons, neither they that &longs;ell, nor they that buy under­<lb/>&longs;tanding the true quantity of that which is &longs;old and bought: In <lb/>regard that the &longs;ame &longs;quare mea&longs;ure, as is accu&longs;tomed in tho&longs;e <lb/>parts, a&longs;&longs;igned one particular per&longs;on, carried to &longs;ometimes above <lb/>twice or thrice as much water, as did the &longs;ame &longs;quare mea&longs;ure a&longs;­<lb/>&longs;igned to another. </s> <s>Which thing proveth to be the &longs;ame incon­<lb/>venience, as if the mea&longs;ure wherewith Wine and Oil is bought <lb/>and &longs;old, &longs;hould hold twice or thrice as much Wine or Oil at one <lb/>time as at another. </s> <s>Now this Con&longs;ideration invited my minde <lb/>and curio&longs;ity to the finding out of the true mea&longs;ure of Running <lb/>Waters. </s> <s>And in the end, by occa&longs;ion of a mo&longs;t important bu­<lb/>&longs;ine&longs;&longs;e that I was imployed in &longs;ome years &longs;ince, with great in­<lb/>ten&longs;ene&longs;&longs;e of minde, and with the &longs;ure direction of <emph type="italics"/>Geometry,<emph.end type="italics"/> I <lb/>have di&longs;covered the mi&longs;take, which was, that we being upon the <lb/>bu&longs;ine&longs;&longs;e of taking the mea&longs;ure of the Waters that move, do make <lb/>u&longs;e of two dimen&longs;ions onely, namely, breadth and depth, keep­<lb/>ing no account of the length. </s> <s>And yet the Water being, though <lb/>running, a Body, it is nece&longs;&longs;ary in forming a conceit of its quan­<lb/>tity, in relation to another, to keep account of all the three Di­<lb/>men&longs;ions, that is of length, breadth, and depth.</s></p><p type="main"> <s>Here an objection hath been put to me, in behalf of the ordi­<lb/>nary way of mea&longs;uring Running Waters, in oppo&longs;ition to what <lb/>I have above con&longs;idered and propo&longs;ed: and I was told, Its true, <lb/>that in mea&longs;uring a Body that &longs;tands &longs;till, one ought to take all <lb/>the three Dimen&longs;ions; but in mea&longs;uring a Body that continually <lb/>moveth, as the Water, the ca&longs;e is not the &longs;ame: For the length <lb/>is not to be had, the length of the water that moveth being infi­<lb/>nite, as never fini&longs;hing its running; and con&longs;equently is incom­<lb/>prehen&longs;ible by humane under&longs;tanding, and therefore with rea&longs;on, <lb/>nay upon nece&longs;&longs;ity it cometh to be omitted.</s></p><p type="main"> <s>In an&longs;wer to this, I &longs;ay, that in the above&longs;aid Di&longs;cour&longs;e, two <lb/>things are to be con&longs;idered di&longs;tinctly; Fir&longs;t, whether it be po&longs;&longs;ible <lb/>to frame any conceit of the quantity of the Body of the Water <lb/>with two Dimen&longs;ions onely. </s> <s>And &longs;econdly, whether this length <lb/>be to be found. </s> <s>As to the fir&longs;t, I am very certain that no man, let <pb xlink:href="068/01/084.jpg" pagenum="70"/>him be never &longs;o great a Wit, can never promi&longs;e to frame a con­<lb/>ceit of the quantity of the Body of Water, without the third <lb/>Dimen&longs;ion of length: and hereupon I return to affirm, that the <lb/>vulgar Rule of mea&longs;uring Running water is vain and erroneous. <lb/></s> <s>This point being agreed on, I come to the &longs;econd, which is, Whe­<lb/>ther the third Dimen&longs;ion of length may be mea&longs;ured. </s> <s>And I &longs;ay, <lb/>that if one would know the whole length of the water of a <lb/>Fountain or River, thereby to come to know the quantity of all <lb/>the Water, it would prove an impo&longs;&longs;ible enterprize, nay the <lb/>knowing of it would not be u&longs;eful. </s> <s>But if one would know how <lb/>much water a Fountain, or a River carrieth in a determinate time <lb/>of an hour, of a day, or of a moneth, &c. </s> <s>I &longs;ay, that it is a very <lb/>po&longs;&longs;ible and profitable enquiry, by rea&longs;on of the innumerable <lb/>benefits that may be derived thence, it much importing to know <lb/>how much Water a Chanel carrieth in a time given; and I have <lb/>demon&longs;trated the &longs;ame above in the beginning of this Book; and <lb/>of this we &longs;tand in need in the bu&longs;ine&longs;&longs;e of the Lake, that &longs;o we <lb/>may be able to determine how much &longs;hall be the height of the <lb/><emph type="italics"/>Brent,<emph.end type="italics"/> when it is &longs;pread all over the Lake: For the three dimen­<lb/>&longs;ions of a Body being given, the Body is known; and the quan­<lb/>tity of a Body being given, if you have but two dimen&longs;ions, the <lb/>third &longs;hall be known. </s> <s>And thus diving farther and farther into <lb/>this Con&longs;ideration, I found that the Velocity of the cour&longs;e of the <lb/>water may be an hundred times greater or le&longs;&longs;er in one part of <lb/>its Chanel than in another. </s> <s>And therefore although there &longs;hould <lb/>be two mouths of Waters equal in bigne&longs;&longs;e; yet neverthele&longs;s it <lb/>might come to pa&longs;&longs;e, that one might di&longs;charge an hundred or a <lb/>thou&longs;and times more water than another: and this would be, if <lb/>the water in one of the mouths &longs;hould run with an hundred or a <lb/>thou&longs;and times greater velocity, than the other; for that it <lb/>would be the &longs;ame as to &longs;ay, that the &longs;wifter was an hundred or <lb/>a thou&longs;and times longer, than the &longs;lower: and in this manner I <lb/>di&longs;covered that to keep account of the velocity, was the keeping <lb/>account of the Length.</s></p><p type="main"> <s>And therefore it is manife&longs;t, that when two Mouths di&longs;charge <lb/>the &longs;ame quantity of Wa r in an equal velocity, it is nece&longs;&longs;ary <lb/>that the le&longs;s &longs;wift Mouth be &longs;o much bigger than the more &longs;wift; <lb/>as the more &longs;wift exceedeth in velocity the le&longs;s &longs;wift; as for <lb/>example.</s></p><p type="main"> <s>In ca&longs;e two Rivers &longs;hould carry equal quantity of water in <lb/>equal times, but that one of them &longs;hould be four times more <lb/>&longs;wift than the other, the more &longs;low &longs;hould of nece&longs;&longs;ity be four <lb/>times more large. </s> <s>And becau&longs;e the &longs;ame River in any part <lb/>thereof alwaies di&longs;chargeth the &longs;ame quantity of Water in equal <lb/>times (as is demon&longs;trated in the fir&longs;t Propo&longs;ition of the fir&longs;t <pb xlink:href="068/01/085.jpg" pagenum="71"/><arrow.to.target n="marg973"></arrow.to.target><lb/>Book^{*} of the mea&longs;ure of Running Watets;) but yet doth not <lb/>run thorowout with the &longs;ame velocity: Hence it is, that the vul­<lb/>gar mea&longs;ures of the &longs;aid River, in divers parts of its Chanel, are <lb/>alwaies divers; in&longs;omuch, that if a River pa&longs;&longs;ing through its cha­<lb/>nel had &longs;uch velocity, that it ran 100 Braces in the 1/60 of an hour­<lb/>and afterwards the &longs;aid River &longs;hould be reduced to &longs;o much tardi, <lb/>ty of motion, as that in the &longs;ame time it &longs;hould not run more than <lb/>one Brace, it would be nece&longs;&longs;ary that that &longs;ame River &longs;hould be­<lb/>come 100. times bigger in that place where it was retarded; I <lb/>mean, 100. times bigger than it was in the place where it was <lb/>&longs;wifter. </s> <s>And let it be kept well in mind, that this point rightly <lb/>under&longs;tood, will clear the under&longs;tanding to di&longs;cover very many <lb/>accidents worthy to be known. </s> <s>But for this time let it &longs;uffice, <lb/>that we have onely declared that which makes for our purpo&longs;e, <lb/>referring apprehen&longs;ive and &longs;tudious Wits to the peru&longs;al of my <lb/>aforenamed Treati&longs;e; for therein he &longs;hall finde profit and delight <lb/>both together.</s></p><p type="margin"> <s><margin.target id="marg973"></margin.target>* He here intends <lb/>the Demon&longs;trati­<lb/>ons following, at <lb/>the end of the fir&longs;t <lb/>Book</s></p><p type="main"> <s>Now applying all to our principal intent, I &longs;ay, That by what <lb/>hath been declared it is manife&longs;t, that if the <emph type="italics"/>Brent<emph.end type="italics"/> were 40. Bra­<lb/>ces broad, and 2 1/2 high, in &longs;ome one part of its Chanel, that after­<lb/>wards the &longs;ame Water of the <emph type="italics"/>Brent<emph.end type="italics"/> falling into the Lake, andpa&longs;­<lb/>&longs;ing thorow the &longs;ame to the Sea, it &longs;hould lo&longs;e &longs;o much of its ve­<lb/>locity, that it &longs;hould run but one Brace, in the time wherein <lb/>whil&longs;t it was in its Chanel at the place afore&longs;aid, it ran 100. Bra­<lb/>ces. </s> <s>It would be ab&longs;olutely nece&longs;&longs;ary, that increa&longs;ing in mea­<lb/>&longs;ure, it &longs;hould become an hundred times ^{*} thicker; and therefore <lb/><arrow.to.target n="marg974"></arrow.to.target><lb/>if we &longs;hould &longs;uppo&longs;e that the Lake were 20000. Braces, the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> that already hath been &longs;uppo&longs;ed in its Chanel 100. Braces, <lb/>being brought into the Lake, &longs;hould be 100. times 100. Brates; <lb/>that is, &longs;hall be 10000. Braces in thickne&longs;s, and con&longs;equently &longs;hall <lb/>be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a <lb/>Brace, as was concluded in the Argument.</s></p><p type="margin"> <s><margin.target id="marg974"></margin.target>* Deeper.</s></p><p type="main"> <s>Now one may &longs;ee into what a gro&longs;s errour of 99. in 100. one <lb/>may fall through the not well under&longs;tanding the true quantity <lb/>of Running Water, which being well under&longs;tood, doth open a <lb/>direct way to our judging aright in this mo&longs;t con&longs;iderable affair.</s></p><p type="main"> <s>And therefore admitting that wich hath been demon&longs;trated, <lb/>I fay, that I would (if it did concern me) greatly encline to con­<lb/>&longs;ult upon the returning of the <emph type="italics"/>Brent<emph.end type="italics"/> again into the Lake: For it <lb/>being mo&longs;t evident, that the <emph type="italics"/>Brent<emph.end type="italics"/> in the Chanel of its mouth, is <lb/>much &longs;wifter than the <emph type="italics"/>Brent<emph.end type="italics"/> being brought into the Lake, it will <lb/>certainly follow thereupon, that the thickne&longs;s of the Water of <lb/><emph type="italics"/>Brent<emph.end type="italics"/> in the Lake, &longs;hall be &longs;o much greater than that of <emph type="italics"/>Brent<emph.end type="italics"/> in <lb/><emph type="italics"/>Brent,<emph.end type="italics"/> by how much the <emph type="italics"/>Bront<emph.end type="italics"/> in <emph type="italics"/>Brent<emph.end type="italics"/> is &longs;wifter than thh <emph type="italics"/>Brent<emph.end type="italics"/><lb/>in the Lake.</s></p><pb xlink:href="068/01/086.jpg" pagenum="72"/><p type="main"> <s>1. From which operation doth follow in the fir&longs;t place, that <lb/>the Lake being filled and increa&longs;ed by tbe&longs;e Waters, &longs;hall be <lb/>more Navigable, and pa&longs;&longs;ible, than at pre&longs;ent we &longs;ee it to be.</s></p><p type="main"> <s>2. By the current of the&longs;e Waters, the Chanels will be &longs;cour­<lb/>ed, and will be kept clean from time to time.</s></p><p type="main"> <s>3. There will not appear at the times of low-waters &longs;o many <lb/>Shelves, and &longs;uch heaps of Mud, as do now appear.</s></p><p type="main"> <s>4. The Ayr will become more whole&longs;om, for that it &longs;hall not <lb/>be &longs;o infected by putrid vapours exhaled by the Sun, &longs;o long as <lb/>the Miery Ouze &longs;hall be covered by the Waters.</s></p><p type="main"> <s>5. La&longs;tly, in the current of the&longs;e advantagious Waters,, which <lb/>mu&longs;t i&longs;&longs;ue out of the Lake into the Sea, be&longs;ides tho&longs;e of the Tyde, <lb/>the Ports will be kept &longs;coured, and clear: And this is as much as <lb/>I &longs;hall offer for the pre&longs;ent, touching this weighty bui&longs;ine&longs;s; al­<lb/>waies &longs;ubmitting my &longs;elf to &longs;ounder judgements.</s></p><p type="main"> <s>Of the above-&longs;aid Writing I pre&longs;ented a Copy at <emph type="italics"/>Venice,<emph.end type="italics"/> at a <lb/>full Colledge, in which I read it all, and it was hearkned to with <lb/>very great attention; and at la&longs;t I pre&longs;ented it to the Duke, and <lb/>left &longs;ome Copies thereof with &longs;undry Senators, and went my way, <lb/>promi&longs;ing with all inten&longs;ene&longs;s to apply my pains with reiterated <lb/>&longs;tudies in the publick &longs;ervice; and if any other things &longs;hould come <lb/>into my minde, I promi&longs;ed to declare them &longs;incerely, and &longs;o took <lb/>leave of <emph type="italics"/>His &longs;erenity,<emph.end type="italics"/> and that Noble Council. </s> <s>When I was <lb/>returned to <emph type="italics"/>Rome,<emph.end type="italics"/> this bu&longs;ine&longs;s night and day continually run­<lb/>ning in my mind, I hapned to think of another admirable and <lb/>mo&longs;t important conceit, which with effectual rea&longs;ons, confirmed <lb/>by exact operations, I with the Divine a&longs;&longs;i&longs;tance, made clear and <lb/>manife&longs;t; and though the thing at fir&longs;t &longs;ight &longs;eemed to me a mo&longs;t <lb/>extravagant Paradox, yet notwith&longs;tanding, having &longs;atisfied my <lb/>&longs;elf of the whole bu&longs;ine&longs;s, I &longs;ent it in writing to the mo&longs;t Illu&longs;tri­<lb/>ous and mo&longs;t Noble <emph type="italics"/>Signore Gio. </s> <s>Ba&longs;adonna<emph.end type="italics"/>; who after he had <lb/>well con&longs;idered my Paper, carried it to the Council; and after <lb/>that tho&longs;e Lords had for many months maturely con&longs;idered <lb/>thereon, they in the end re&longs;olved to &longs;u&longs;pend the execution of the <lb/>diver&longs;ion which they had before con&longs;ulted to make of the River <lb/><emph type="italics"/>Sile,<emph.end type="italics"/> and of four other Rivers, which al&longs;o fall into the Lake; a <lb/>thing by me blamed in this &longs;econd Paper, as mo&longs;t prejudicial, <lb/>and harmful. </s> <s>The writing &longs;pake as followeth.</s></p><pb xlink:href="068/01/087.jpg" pagenum="73"/><p type="head"> <s>CONSIDERATIONS <lb/>Concerning the <lb/>LAKE <lb/>OF <lb/>VENICE.</s></p><p type="head"> <s><emph type="italics"/>CONSIDERATION II.<emph.end type="italics"/></s></p><p type="main"> <s>If the di&longs;cour&longs;ing well about the truth of <lb/>things, Mo&longs;t Serene Prince, were as the <lb/>carrying of Burdens, in which we &longs;ee <lb/>that an hundred Hor&longs;es carry a greater <lb/>weight than one Hor&longs;e onely; it would <lb/>&longs;eem that one might make more account <lb/>of the opinion of many men, than of <lb/>one alone; But becau&longs;e that di&longs;cour&longs;ing <lb/>more re&longs;embleth running, than carrying <lb/>Burdens, in which we &longs;ee that one Barb alone runneth fa&longs;ter <lb/>than an hundred heavy-heel'd Jades; therefore I have ever more <lb/>e&longs;teemed one Conclu&longs;ion well managed, and well con&longs;idered by <lb/>one under&longs;tanding man, although alone, than the common and <lb/>Vulgar opinions; e&longs;pecially, when they concern ab&longs;truce and <lb/>arduous points: Nay in &longs;uch ca&longs;es the opinions moulded and <lb/>framed by the mo&longs;t ignorant and &longs;tupid Vulgar, have been ever <lb/>&longs;u&longs;pected by me as fal&longs;e, for that it would be a great wonder if <lb/>in difficult matters a common capacity &longs;hould hit upon that <lb/>which is hand&longs;om, good, and true. </s> <s>Hence I have, and do hold <lb/>in very great veneration the &longs;umme of the Government of the <lb/>mo&longs;t Serene, and eternal Republick of <emph type="italics"/>Venice<emph.end type="italics"/>; which although, <lb/>as being in nature a Common-wealth, it ought to be governed by <lb/>the greater part; yet neverthele&longs;s, in arduous affairs, it is alwaies <lb/>directed by the Grave Judgement of few, and not judged blindly <pb xlink:href="068/01/088.jpg" pagenum="74"/>by the <emph type="italics"/>Plebeian<emph.end type="italics"/> Rout. </s> <s>Tis true, that he that propoundeth Pro­<lb/>po&longs;itions far above the reach of common capacity, runneth a <lb/>great hazard of being very often condemned without further Pro­<lb/>ce&longs;s, or knowledge of the Cau&longs;e; but yet for all that, the truth <lb/>is not to be de&longs;erted in mo&longs;t weighty affairs, but ought rather to <lb/>be explained in due place and time with all po&longs;&longs;ible per&longs;picuity; <lb/>that &longs;o being well under&longs;tood, and con&longs;idered, it may come after­<lb/>wards for the Common good to be embraced.</s></p><p type="main"> <s>This which I &longs;peak in general, hath often been my fortune in <lb/>very many particulars, not onely when I have kept within the <lb/>bounds of meer &longs;peculation, but al&longs;o when I have chanced to de­<lb/>&longs;cend to Practice, and to Operations: and your Highne&longs;s know­<lb/>eth very well what befel me the la&longs;t Summer 1641. when in obe­<lb/>dience to your Soveraign Command, I did in full Colledge repre­<lb/>&longs;ent my thoughts touching the &longs;tate of the Lake of <emph type="italics"/>Venice<emph.end type="italics"/>; for <lb/>there not being &longs;uch wanting, who without &longs;o much as vouch­<lb/>&longs;afing to under&longs;tand me, but having onely had an inkling, and <lb/>bad apprehen&longs;ion of my opinion, fell furiou&longs;ly upon me, and by <lb/>violent means both with the Pen and Pre&longs;s, full of Gall, did abu&longs;e <lb/>me in reward of the readine&longs;s that I had expre&longs;t to obey and <lb/>&longs;erve them: But I was above mea&longs;ure encouraged and plea&longs;ed, to <lb/>&longs;ee that tho&longs;e few who vouch&longs;afed to hear me, were all either <lb/>thorowly per&longs;waded that my opinion was well grounded, or at <lb/>lea&longs;t &longs;u&longs;pended their prudent verdict to more mature deliberati­<lb/>on. </s> <s>And though at the fir&longs;t bout I chanced to propo&longs;e a thing <lb/>that was totally contrary to the mo&longs;t received and antiquated <lb/>opinion, and to the re&longs;olutions and con&longs;ultations taken above an <lb/>hundred years ago: Moved by the&longs;e things, and to &longs;atisfie al&longs;o <lb/>to the promi&longs;e that I had made of tendering unto them what <lb/>&longs;hould farther offer it &longs;elf unto me touching the &longs;ame bu&longs;ine&longs;s; I <lb/>have re&longs;olved to pre&longs;ent to the Throne of your Highne&longs;s, another <lb/>Con&longs;ideration of no le&longs;s importance, which perhaps at fir&longs;t &longs;ight <lb/>will appear a &longs;tranger Paradox; but yet brought to the Te&longs;t and <lb/>Touch-&longs;tone of experience, it &longs;hall prove mo&longs;t clear and evident. <lb/></s> <s>If it &longs;hall be accounted of, &longs;o that it &longs;ucceedeth to the benefit of <lb/>your Highne&longs;s, I &longs;hall have obtained my defire and intent: And <lb/>if not, I &longs;hall have &longs;atisfied my &longs;elf, and &longs;hall not have been <lb/>wanting to the Obligation of your mo&longs;t faithful Servant, and na­<lb/>tive &longs;ubject.</s></p><p type="main"> <s>That which I propounded in the Mouths pa&longs;s, touching the <lb/>mo&longs;t important bu&longs;ine&longs;s of the Lake, though it did onely expre&longs;­<lb/>ly concern the point of the diver&longs;ion of the Mouth of the Lake, <lb/>already made and put in execution; yet it may be under&longs;tood <lb/>and applyed al&longs;o to the diver&longs;ion under debate, to be made of <lb/>the other five Rivers, and of the <emph type="italics"/>Sile<emph.end type="italics"/> in particular.</s></p><pb xlink:href="068/01/089.jpg" pagenum="75"/><p type="main"> <s>Now touching this, I had the fortune to offer an admirable <lb/>accident that we meet with when we come to the effect, which <lb/>I verily believe will be an utter ruine to the Lake of <emph type="italics"/>Ve­<lb/>nice.<emph.end type="italics"/></s></p><p type="main"> <s>I &longs;ay therefore, that by diverting the&longs;e five Rivers that re­<lb/>main, although their water that they di&longs;charge for the pre&longs;ent in­<lb/>to the Lake is not all taken together 4/5 parts of what the <emph type="italics"/>Brent<emph.end type="italics"/><lb/>alone did carry, yet neverthele&longs;&longs;e the abatement of the water of <lb/>the Lake which &longs;hall en&longs;ue upon this la&longs;t diver&longs;ion of four parts, <lb/>which was the whole water, &longs;hall prove double to that which hath <lb/>happened by the diver&longs;ion of <emph type="italics"/>Brent<emph.end type="italics"/> onely, although that the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> alone carried five parts of that water, of which the Rivers <lb/>that are to be diverted carry four: A wonder really great, and <lb/>altogether unlikely; for the reducing all this Propo&longs;ition to be <lb/>under&longs;tood, is as if we &longs;hould &longs;ay, that there being given us <lb/>three Rivers, of which the fir&longs;t di&longs;chargeth five parts, the &longs;econd <lb/>three, and the third one, and that from the diver&longs;ion of the <lb/>fir&longs;t, there did follow &longs;uch a certain abatement or fall; from <lb/>the taking away of the &longs;econd there ought to follow al&longs;o &longs;o <lb/>much more abatement; And la&longs;tly, from the withdrawing of <lb/>the third the water ought to fall &longs;o much more, which is wholly <lb/>impo&longs;&longs;ible: And yet it is mo&longs;t certain, and be&longs;ides the demon­<lb/>&longs;tration that per&longs;wades me to it, which I &longs;hall explain in due <lb/>time, I can &longs;et before your eyes &longs;uch an experiment as is not to <lb/>be denied by any one, although ob&longs;tinate: and I will make it <lb/>plainly &longs;een and felt, that by taking away only four parts of the <lb/>five, which &longs;hall have been taken away, the abatement proveth <lb/>double to the abatement en&longs;uing upon the diverting fir&longs;t of the <lb/>five onely; which thing being true, as mo&longs;t certainly it is, it <lb/>will give us to under&longs;tand how pernicious this diver&longs;ion of five <lb/>Rivers is like to prove, if it &longs;hall be put in execution.</s></p><p type="main"> <s>By this little that I have hinted, and the much that I could <lb/>&longs;ay, let your Highne&longs;&longs;e gather with what circum&longs;pection this bu­<lb/>&longs;ine&longs;&longs;e ought to be managed, and with how great skill he ought <lb/>to be furni&longs;hed who would behave him&longs;elf well in the&longs;e difficult <lb/>affairs.</s></p><p type="main"> <s>I have not at this time explained the demon&longs;tration, nor have <lb/>I &longs;o much as propounded the way to make the Experiment, that <lb/>I am able to make in confirmation of what I have &longs;aid, that &longs;o <lb/>by &longs;ome one or others mi&longs;-apprehending the Demon&longs;tration, <lb/>and maiming the Experiment, the truth may not happen to &longs;hine <lb/>with le&longs;&longs;e clarity than it doth, when all mi&longs;ts of difficulty are re­<lb/>moved: and if &longs;o be, no account &longs;hould be made of the Rea&longs;ons <lb/>by me alledged, and that men &longs;hould &longs;hut their eyes again&longs;t the <lb/>Experiments that without co&longs;t or charge may be made, I do de­<pb xlink:href="068/01/090.jpg" pagenum="76"/>clare and prote&longs;t that there &longs;hall follow very great dammages <lb/>to the Fields of the main Land, and extraordinary &longs;ummes <lb/>&longs;hall be expended to no purpo&longs;e. </s> <s>The Lake undoubtedly will <lb/>become almo&longs;t dry, and will prove impa&longs;&longs;ible for Navigation, <lb/>with a manife&longs;t danger of corrupting the Air: And in the la&longs;t <lb/>place there will unavoidably en&longs;ue the choaking and &longs;toppage of <lb/>the Ports of <emph type="italics"/>Venice.<emph.end type="italics"/></s></p><p type="main"> <s>Upon the 20th. </s> <s>of <emph type="italics"/>December,<emph.end type="italics"/> 1641. I imparted this my &longs;econd <lb/>Con&longs;ideration to the mo&longs;t Excellent <emph type="italics"/>Signore Ba&longs;adonna,<emph.end type="italics"/> pre&longs;en­<lb/>ting him with a Copy thereof among&longs;t other Writings, which I <lb/>have thought good to in&longs;ert, although they &longs;eem not to belong <lb/>directly to our bu&longs;ine&longs;&longs;e of the Lake.</s></p><p type="head"> <s>The way to examine the MUD and SAND <lb/>that entereth and remaineth in the <lb/>LAKE of <emph type="italics"/>VENICE.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>To the mo&longs;t Excellent<emph.end type="italics"/></s></p><p type="head"> <s>SIGNORE GIO. BASADONNA.</s></p><p type="main"> <s>Two very con&longs;iderable Objections have been made a­<lb/>gain&longs;t my opinion concerning the Lake of <emph type="italics"/>Venice:<emph.end type="italics"/> One <lb/>was that, of which I have &longs;poken at large in my fir&longs;t <lb/>Con&longs;ideration, namely, that the <emph type="italics"/>Brents<emph.end type="italics"/> having been taken out of <lb/>the Lake, cannot have been the occa&longs;ion of the notable fall of <lb/>the Waters in the Lake, as I pretend, and con&longs;equently, that <lb/>the turning <emph type="italics"/>Brent<emph.end type="italics"/> into the Lake would be no con&longs;iderable reme­<lb/>dy, in regard that the water of <emph type="italics"/>Brent,<emph.end type="italics"/> and the great expan&longs;ion <lb/>of the Lake over which the water of <emph type="italics"/>Brent<emph.end type="italics"/> is to diffu&longs;e and <lb/>&longs;pread being con&longs;idered, it is found that the ri&longs;e proveth in­<lb/>&longs;en&longs;ible.</s></p><p type="main"> <s>The &longs;econd Objection was, that the <emph type="italics"/>Brent<emph.end type="italics"/> is very muddy, and <lb/>therefore if it &longs;hould fall muddy into the Lake, the Sand would <lb/>&longs;ink and fill up the &longs;ame.</s></p><p type="main"> <s>Touching the fir&longs;t Query, enough hath been &longs;aid in my fir&longs;t <lb/>Con&longs;ideration, where I have plainly di&longs;covered the deceipt of the <lb/>Argument, and &longs;hewn its fallacy; It remaineth now to examine <pb xlink:href="068/01/091.jpg" pagenum="77"/>the &longs;econd: to which in the fir&longs;t place I &longs;ay, that one of the fir&longs;t <lb/>things that I propo&longs;ed in this affair was, that I held it impo&longs;&longs;ible <lb/>to do any act, though never &longs;o beneficial, that was not al&longs;o ac­<lb/>companied by &longs;ome inconvenience and mi&longs;chief; and therefore <lb/>we are to con&longs;ider well the profit, and the lo&longs;&longs;e and prejudice; <lb/>and they both being weighed, we &longs;hall be able to choo&longs;e the le&longs;­<lb/>&longs;er evil: Secondly, I admit it to be mo&longs;t true, that <emph type="italics"/>Brent<emph.end type="italics"/> is at &longs;ome <lb/>times muddy, but it is al&longs;o true, that for the greater part of the <lb/>year it is not muddy. </s> <s>Thirdly, I do not &longs;ee nor under&longs;tand <lb/>what &longs;trength this objection hath, being taken &longs;o at large, and in <lb/>general; and methinks that it is not enough to &longs;ay, that the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> runneth muddy, and to a&longs;&longs;ert that it depo&longs;eth its Muddi­<lb/>ne&longs;&longs;e in the Lake, but we ought moreover to proceed to particu­<lb/>lars, and &longs;hew how much this Mud is, and in what time this <lb/>choaking up of the Ports may be effected. </s> <s>For the Rea&longs;ons are <lb/>but too apparent and particular, that conclude the ruine of the <lb/>Lake, and that in a very &longs;hort time, (for mention is made of <lb/>dayes) the Waters diver&longs;ion being made, and moreover we <lb/>have the circum&longs;tance of an Experiment, the &longs;tate of things be­<lb/>ing ob&longs;erved to have grown wor&longs;e &longs;ince the &longs;aid diver&longs;ion. </s> <s>And <lb/>I have demon&longs;trated, that in ca&longs;e the Diver&longs;ion of the <emph type="italics"/>Sile<emph.end type="italics"/> and <lb/>the other Rivers &longs;hould be put in execution, the Lake would in a <lb/>few dayes become almo&longs;t dry; and the Ports would be lo&longs;t, with <lb/>other mi&longs;chievous con&longs;equences. </s> <s>But on the other &longs;ide, al­<lb/>though that we did grant the choaking of them, we may very <lb/>probably &longs;ay, that it will not happen, &longs;ave onely in the &longs;ucce&longs;&longs;ion <lb/>of many and many Centuries of years. </s> <s>Nor can I think it pru­<lb/>dent coun&longs;el to take a re&longs;olution and imbrace a De&longs;igne now, to <lb/>obtain a benefit very uncertain, and more than that, which only <lb/>&longs;hall concern tho&longs;e who are to come very many Ages after us, <lb/>and thereby bring a certain inconvenience upon our &longs;elves, and <lb/>upon our children that are now alive and pre&longs;ent.</s></p><p type="main"> <s>Let it be alledged therefore, (although I hold it fal&longs;e) that by <lb/>the diver&longs;ions of the Rivers the Lake may be kept in good con­<lb/>dition for &longs;everal years to come.</s></p><p type="main"> <s>But I &longs;ay confidently, and hope to demon&longs;trate it; That the <lb/>Diver&longs;ions will bring the Lake, even in our dayes, to be almo&longs;t <lb/>dry, and at lea&longs;t will leave &longs;o little water in it, that it &longs;hall cea&longs;e <lb/>to be Navigable, and the Ports &longs;hall mo&longs;t infallibly be choaked <lb/>up. </s> <s>I will therefore &longs;ay upon experience, in an&longs;wer to this Ob­<lb/>jection, that it is very nece&longs;&longs;ary fir&longs;t well to di&longs;cour&longs;e, and ratio­<lb/>nally to particularize and a&longs;certain the be&longs;t that may be this <lb/>point of the quantity of this &longs;inking Mud or Sand.</s></p><p type="main"> <s>Now I fear I &longs;hall make my &longs;elf ridiculous to tho&longs;e, who mea­<lb/>&longs;uring the things of Nature with the &longs;hallowne&longs;&longs;e of their brains <pb xlink:href="068/01/092.jpg" pagenum="78"/>do think that it is ab&longs;olutely impo&longs;&longs;ible to make this enquiry, and <lb/>will &longs;ay unto me, <emph type="italics"/>Quis men&longs;us e&longs;t pugillo aquas, & terram palmo <lb/>ponderavit<emph.end type="italics"/>? </s> <s>Yet neverthele&longs;s I will propound a way whereby, <lb/>at lea&longs;t in gro&longs;s, one may find out the &longs;ame.</s></p><p type="main"> <s>Take a Ve&longs;&longs;el of Cylindrical Figure, holding two barrels of <lb/>water, or thereabouts; and then fill it with the water of <emph type="italics"/>Brent,<emph.end type="italics"/><lb/>at its Mouth or Fall into the Lake; but in the Lake at the time <lb/>that the <emph type="italics"/>Brent<emph.end type="italics"/> runneth muddy, and after it hath begun to run <lb/>muddy for eight or ten hours, to give the mud time to go as far <lb/>as S. <emph type="italics"/>Nicolo,<emph.end type="italics"/> to i&longs;&longs;ue into the Sea; and at the &longs;ame time take <lb/>another Ve&longs;&longs;el, like, and equal to the fir&longs;t, and fill it with the wa­<lb/>ter of the Lake towards S. <emph type="italics"/>Nicolo,<emph.end type="italics"/> (but take notice that this ope­<lb/>ration ought to be made at the time when the waters go out, <lb/>and when the Sea is calm) and then, when the waters &longs;hall have <lb/>&longs;etled in the afore&longs;aid Ve&longs;&longs;els, take out the clear water, and con­<lb/>&longs;ider the quantity of Sand that remains behind, and let it be &longs;et <lb/>down, or kept in mind: And I am ea&longs;ily induced to think, that <lb/>that &longs;hall be a greater quantity of Sand which &longs;hall be left in the <lb/>fir&longs;t Ve&longs;&longs;el, than that left in the &longs;econd Ve&longs;&longs;el. </s> <s>Afterwards <lb/>when the <emph type="italics"/>Brent<emph.end type="italics"/> &longs;hall come to be clear, let both the operations be <lb/>repeated, and ob&longs;erve the quantity of Sand in the afore&longs;aid Ve&longs;­<lb/>&longs;els; for if the Sand in the fir&longs;t Ve&longs;&longs;el &longs;hould be mo&longs;t, it would <lb/>be a &longs;ign, that in the revolution of a year the <emph type="italics"/>Brent<emph.end type="italics"/> would depo&longs;e <lb/>Sand in the Lake: And in this manner one may calculate to a <lb/>&longs;mall matter what proportion the Sand that entreth into the Lake, <lb/>hath to that which remains: And by that proportion one may <lb/>judge how expedient it &longs;hall be for publick benefit. </s> <s>And if at <lb/>&longs;everal times of the year you carefully repeat the &longs;ame operati­<lb/>ons, or rather ob&longs;ervations, you would come to a more exact <lb/>knowledge in this bu&longs;ine&longs;s: And it would be good to make the <lb/>&longs;aid operations at tho&longs;e times, when the Lake is di&longs;turbed by <lb/>&longs;trong high Winds, and made muddy by its own Mud, rai&longs;ed by <lb/>the commotion of the Waters.</s></p><p type="main"> <s>This notion would give us great light, if the &longs;ame ob&longs;ervations <lb/>&longs;hould be made towards the Mouth of <emph type="italics"/>Lio,<emph.end type="italics"/> at &longs;uch time as the <lb/>waters flow and ebb, in calm &longs;ea&longs;ons; for &longs;o one &longs;hould come to <lb/>know whether the waters of the Lake are more thick at the going <lb/>out, than at the entrance. </s> <s>I have propounded the foregoing <lb/>way of mea&longs;uring Sands and Mud, to &longs;hew that we are not &longs;o <lb/>generally, and incon&longs;iderately to pronounce any &longs;entence, but <lb/>proceed to &longs;tricter inquiries, and then deliberate what &longs;hall be <lb/>mo&longs;t expedient to be done. </s> <s>Others may propo&longs;e more exqui­<lb/>&longs;ite examinations, but this &longs;hall &longs;erve me for the pre&longs;ent.</s></p><p type="main"> <s>I will add onely, that if any one had greater curio&longs;ity (it would <lb/>be profitable to have it) in inve&longs;tigating more exactly the quan­<pb xlink:href="068/01/093.jpg" pagenum="79"/>tity of the Water that entereth into the Lake, by the means that <lb/>I have &longs;hewen in the beginning of this Book: When he &longs;hall <lb/>have found the proportion of the quantity of water to the quan­<lb/>tity of Sand or Mud, he &longs;hall come to know how much Sand the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> &longs;hall leave in the Lake in the &longs;pace of a year. </s> <s>But to <lb/>perform the&longs;e things, there are required per&longs;ons of di&longs;cretion, and <lb/>fidelity, and that are imployed by publick Order; for there <lb/>would thence re&longs;ult eminent benefit and profit.</s></p><p type="main"> <s><emph type="italics"/>Here are wanting<emph.end type="italics"/> LETTERS <emph type="italics"/>from &longs;everal per&longs;ons.<emph.end type="italics"/></s></p><p type="head"> <s>To the Reverend Father, <emph type="italics"/>France&longs;co di<emph.end type="italics"/></s></p><p type="head"> <s>S. GIUSEPPE.</s></p><p type="main"> <s>In execution of the command that you laid upon me in your <lb/>former Letters, by order from the mo&longs;t Serene, my Lord, <lb/><emph type="italics"/>Prince Leopold<emph.end type="italics"/>; that I &longs;hould &longs;peak my judgment concern­<lb/>ing the di&longs;imboguement of the River called <emph type="italics"/>Fiume morto,<emph.end type="italics"/> whe­<lb/>ther it ought to be let into the Sea, or into <emph type="italics"/>Serchio<emph.end type="italics"/>; I &longs;ay, that <lb/>I chanced 18. years &longs;ince to be pre&longs;ent, when the &longs;aid Mouth was <lb/>opened into the Sea, and that of <emph type="italics"/>Serchio<emph.end type="italics"/> &longs;topt; which work was <lb/>done to remedy the great Innundation that was made in all that <lb/>Country, and Plain of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> that lyeth between the River <emph type="italics"/>Arno,<emph.end type="italics"/><lb/>and the Mountains of <emph type="italics"/>S. Giuliano,<emph.end type="italics"/> and the River <emph type="italics"/>Serchio<emph.end type="italics"/>; which <lb/>Plain continued long under water, in&longs;omuch that not onely in the <lb/>Winter, but al&longs;o for a great part of the Summer, tho&longs;e fields <lb/>were overflowed; and when that the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> was <lb/>effectually opened into the Sea, the place was pre&longs;ently freed from <lb/>the waters. </s> <s>and drained, to the great &longs;atisfaction of the Owners <lb/>of tho&longs;e Grounds. </s> <s>And here I judge it worth your notice, that <lb/>for the generality of tho&longs;e that po&longs;&longs;e&longs;s e&longs;tates in tho&longs;e parts, they <lb/>de&longs;ired that the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> might &longs;tand open to the <lb/>Sea, and tho&longs;e who would have it open into <emph type="italics"/>Serchio,<emph.end type="italics"/> are per&longs;ons <lb/>that have no other concernment there, &longs;ave the hopes of gaining <lb/>by having the di&longs;po&longs;e of Commi&longs;&longs;ions, and the like, &c,</s></p><p type="main"> <s>But for the more plain under&longs;tanding of that which is to be <lb/>&longs;aid, it mu&longs;t be known, That the re&longs;olution of opening the &longs;aid <lb/>Mouth into <emph type="italics"/>Serchio,<emph.end type="italics"/> was taken in the time of the Great Duke <lb/><emph type="italics"/>Ferdinando<emph.end type="italics"/> the fir&longs;t, upon the &longs;ame motives that are at this time <lb/>again propo&longs;ed, as your Letters tell me, Since that, it manife&longs;t­<lb/>ly appearing, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> had, and hath its Mouth open to <lb/>the Sea, the Plain hathbeen kept dry; and it being al&longs;o true, that <pb xlink:href="068/01/094.jpg" pagenum="80"/>the fury of the South, and South-We&longs;t-Winds carryed &longs;uch <lb/>abundance of &longs;and into the Mouth, or Out-let of <emph type="italics"/>Fiume morto,<emph.end type="italics"/><lb/>that it wholly &longs;topt it up: e&longs;pecially when the waters on <emph type="italics"/>Pi&longs;a<emph.end type="italics"/><lb/>&longs;ide were low and &longs;hallow, And they think, that turning the <lb/>Lake of <emph type="italics"/>Fiume morto<emph.end type="italics"/> into <emph type="italics"/>Serchio,<emph.end type="italics"/> and the <emph type="italics"/>Serchio<emph.end type="italics"/> maintaining <lb/>continually its own Mouth with the force of its waters open to the <lb/>Sea, and con&longs;equently al&longs;o <emph type="italics"/>Fiume morto,<emph.end type="italics"/> they would have had the <lb/>Out-let clear and open; and in this manner they think, that the <lb/>Plain of <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> would have been freed from the waters. </s> <s>The bu­<lb/>&longs;ine&longs;s pa&longs;&longs;eth for current, at fir&longs;t &longs;ight; but experience proveth <lb/>the contrary, and Rea&longs;on confirmeth the &longs;ame: For the height <lb/>of the water of tho&longs;e Plains, was regulated by the height of the <lb/>waters in the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/>; that is, The waters at the <lb/>Mouth being high, the waters al&longs;o do ri&longs;e in the fields; and when <lb/>the waters at the Mouth are low, the waters of the fields do like­<lb/>wi&longs;e abate: Nor is it enough to &longs;ay, That the Out-let or Vent <lb/>of <emph type="italics"/>Fiume morto<emph.end type="italics"/> is continual, but it mu&longs;t be very low: Now if <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> did determine in <emph type="italics"/>Serchio,<emph.end type="italics"/> it is manife&longs;t that it <lb/>would determine high; for <emph type="italics"/>Serchio<emph.end type="italics"/> terminating in the Sea, when <lb/>ever it more and more aboundeth with water, and ri&longs;eth, it is ne­<lb/>ce&longs;lary that al&longs;o <emph type="italics"/>Fiume morto<emph.end type="italics"/> hath its level higher, and con&longs;e­<lb/>quently &longs;hall keep the waters in the Plains higher. </s> <s>Nay, it hath <lb/>happened &longs;ometimes (and I &longs;peak it upon my own &longs;ight) that <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> hath rever&longs;ed its cour&longs;e upwards towards <emph type="italics"/>Pi&longs;a<emph.end type="italics"/>; <lb/>which ca&longs;e will ever happen, when&longs;oever the <emph type="italics"/>Pi&longs;an<emph.end type="italics"/> waters chance <lb/>to be lower than the level of tho&longs;e of <emph type="italics"/>Serchio<emph.end type="italics"/>; for in that ca&longs;e <lb/>the waters of <emph type="italics"/>Serchio<emph.end type="italics"/> return back upon the Plains thorow <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> in &longs;uch &longs;ort, that the Muddine&longs;&longs;es, and the <emph type="italics"/>Serchio<emph.end type="italics"/> have <lb/>been ob&longs;erved to be carried by this return as farr as the Walls of <lb/><emph type="italics"/>Pi&longs;a<emph.end type="italics"/>; and then before &longs;uch time as &longs;o great waters can be a&longs;­<lb/>&longs;waged, which come in with great fury, and go out by little and <lb/>little, there do pa&longs;s very many days, and moneths, nay &longs;ome­<lb/>times one being never able to find the waters of <emph type="italics"/>Serchio,<emph.end type="italics"/><lb/>when at the &longs;hallowe&longs;t, &longs;o low as the Sea in level; (which is the <lb/>lowe&longs;t place of the waters) it thence doth follow, that the wa­<lb/>ters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hould never at any time of the year, &longs;o long <lb/>as they determine in <emph type="italics"/>Serchio,<emph.end type="italics"/> be &longs;o low, as they come to be when <lb/>the &longs;ame <emph type="italics"/>Fiume morto<emph.end type="italics"/> determineth in the Sea. </s> <s>Tis true indeed, <lb/>that the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> opened into the Sea, is &longs;ubject to <lb/>the inconvenience of being &longs;topt up by the force of Winds: But <lb/>in this ca&longs;e, it is nece&longs;&longs;ary to take &longs;ome pains in opening it; which <lb/>may ea&longs;ily be done, by cutting that Sand a little which &longs;tayeth <lb/>in the Mouth, after that the Wind is laid; and it is enough if you <lb/>make a Trench little more than two Palms in breadth; for the <lb/>water once beginning to run into it, it will in a few hours carry <pb xlink:href="068/01/095.jpg" pagenum="81"/>that Sand away with it, and there will en&longs;ue a deep and broad <lb/>Trench that will drain away all the water of the Plains in very lit­<lb/>tle time. </s> <s>And I have found by practice, that there having been <lb/>a great quantity of Sand driven back, by the fury of the South­<lb/>We&longs;t-Wind, into the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> I having cau&longs;ed the <lb/>little gutter to be made in the Morning, &longs;omewhat before Noon, <lb/>a Mouth hath been opened of 40. Braces wide, and notably deep, <lb/>in&longs;omuch that the water, which before had incommoded all the <lb/>Champian ran away in le&longs;s than three dayes, and left the Coun­<lb/>try free and dry, to the admiration of all men. </s> <s>There was pre­<lb/>&longs;ent upon the place, at this bu&longs;ine&longs;s, on the &longs;ame day that I <lb/>opened the Mouth, the mo&longs;t Serene great Duke, the mo&longs;t Serene <lb/>Arch-Dutche&longs;s Mother, all the Commi&longs;&longs;ioners of Sewers, with <lb/>many other Per&longs;ons and Pea&longs;ants of tho&longs;e parts; and they all &longs;aw <lb/>very well, that it was never po&longs;&longs;ible that a little Bark of eight <lb/>Oars, which was come from <emph type="italics"/>Legorn<emph.end type="italics"/> to wait upon the great <lb/>Duke, &longs;hould ever be able to ma&longs;ter the Current, and to make <lb/>up into <emph type="italics"/>Fiume morto<emph.end type="italics"/>; and his Highne&longs;s, who came with an intent <lb/>to cau&longs;e the &longs;aid Mouth towards the Sea to be &longs;topt; and that <lb/>into <emph type="italics"/>Serchio<emph.end type="italics"/> to be opened, changed his judgement, giving order <lb/>that it &longs;hould be left open towards the Sea, as it was done. </s> <s>And <lb/>if at this day it &longs;hall return into <emph type="italics"/>Serchio,<emph.end type="italics"/> I am very certain that it <lb/>will be nece&longs;&longs;ary to open it again into the Sea. </s> <s>And there was <lb/>al&longs;o charge and order given to a per&longs;on appointed for the pur­<lb/>po&longs;e, that he &longs;hould take care to open the &longs;aid Mouth, as hath <lb/>been &longs;aid upon occa&longs;ion. </s> <s>And thus things have &longs;ucceeded very <lb/>well unto this very time. </s> <s>But from the middle of <emph type="italics"/>October,<emph.end type="italics"/> until <lb/>this fir&longs;t of <emph type="italics"/>February,<emph.end type="italics"/> there having continued high South, and <lb/>South-We&longs;t-Winds, with frequent and abundant Rains; it is no <lb/>wonder that &longs;ome innundation hath happened; but yet I will <lb/>affirm, that greater mi&longs;chiefs would have followed, if the Mouth <lb/>had been opened into <emph type="italics"/>Serchio.<emph.end type="italics"/> This which I have hitherto &longs;aid, <lb/>is very clear and intelligible to all &longs;uch as have but competent in­<lb/>&longs;ight, and indifferent skill in the&longs;e affairs. </s> <s>But that which I am <lb/>now about to propo&longs;e farther, will, I am very certain, be under­<lb/>&longs;tood by your &longs;elf, but it will &longs;eem &longs;trange and unlikely to many <lb/>others. </s> <s>The point is, that I &longs;ay, That by rai&longs;ing the level of <lb/><emph type="italics"/>Fiume morto,<emph.end type="italics"/> one half Brace, onely at its Mouth, (it will peni­<lb/>penitrate into <emph type="italics"/>Serchio<emph.end type="italics"/> farther than it would into the Sea) it &longs;hall <lb/>cau&longs;e the waters to ri&longs;e three, or perhaps more Braces upon the <lb/>fields towards <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and &longs;till more by degrees as they &longs;hall recede <lb/>farther from the Sea-&longs;ide; and thus there will follow very great <lb/>Innundations, and con&longs;iderable mi&longs;chiefs. </s> <s>And to know that <lb/>this is true, you are to take notice of an accident, which I give <lb/>warning of in my di&longs;cour&longs;e of the Mea&longs;ure of Running Waters: <pb xlink:href="068/01/096.jpg" pagenum="82"/>where al&longs;o I give the rea&longs;on thereof, ^{*} <emph type="italics"/>Coroll.<emph.end type="italics"/> 14. The ac­<lb/>cident is this, That there coming a Land-Flood, for example, <lb/>into <emph type="italics"/>Arno,<emph.end type="italics"/> which maketh it to ri&longs;e above its ordinary Mouth <lb/>wthin <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> or a little above or below the City &longs;ix or &longs;even Bra­<lb/>ces; this &longs;ame height becometh alwaies le&longs;&longs;er and le&longs;&longs;er, the more <lb/>we approach towards the Sea-&longs;ide; in&longs;omuch, that near to the <lb/>Sea the &longs;aid River &longs;hall be rai&longs;ed hardly half a Brace: Whence <lb/>it followeth of nece&longs;&longs;ary con&longs;equence, that &longs;hould I again be at <lb/>the Sea-&longs;ide, and knowing nothing of what hapneth, &longs;hould &longs;ee <lb/>the River <emph type="italics"/>Arno<emph.end type="italics"/> rai&longs;ed by the acce&longs;&longs;ion of a Land-flood, one third <lb/>of a Brace; I could certainly infer, that the &longs;ame River was rai&longs;ed <lb/>in <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> tho&longs;e &longs;ame &longs;ix or &longs;even Braces. </s> <s>And that which I &longs;ay of <lb/><emph type="italics"/>Arno,<emph.end type="italics"/> is true of all Rivers that fall into the Sea. </s> <s>Which thing <lb/>being true, it is nece&longs;&longs;ary to make great account of every &longs;mall <lb/>ri&longs;ing, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> maketh towards the Sea-&longs;ide by fal­<lb/>ling into <emph type="italics"/>Serchio.<emph.end type="italics"/> For although the ri&longs;ing of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> by <lb/>being to di&longs;gorge its Waters into <emph type="italics"/>Serchio,<emph.end type="italics"/> towards the Sea, were <lb/>onely a quarter of a Brace; we might very well be &longs;ure, that fart <lb/>from the Sea, about <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and upon tho&longs;e fields the ri&longs;e &longs;hall be <lb/>much greater, and &longs;hall become two or three Braces: And be­<lb/>cau&longs;e the Countrey lyeth low, that &longs;ame ri&longs;e will cau&longs;e a conti­<lb/>nual Innundation of the Plains, like as it did before; I cau&longs;ed the <lb/>Mouth to be opened into the Sea. </s> <s>And therefore I conclude <lb/>that the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> ought by no means to be opened <lb/>into <emph type="italics"/>Serchio<emph.end type="italics"/>; but ought to be continued into the Sea, u&longs;ing all <lb/>diligence to keep it open after the manner afore&longs;aid, &longs;o &longs;oon as <lb/>ever the Wind &longs;hall be laid. </s> <s>And if they &longs;hall do otherwi&longs;e, I <lb/>confidently affirm, that there will daily follow greater damages; <lb/>not onely in the Plains, but al&longs;o in the whole&longs;omne&longs;s of the <lb/>Air; as hath been &longs;een in times pa&longs;t. </s> <s>And again, It ought with <lb/>all care to be procured, that no waters do by any means run or <lb/>fall from the Trench of <emph type="italics"/>Libra,<emph.end type="italics"/> into the Plain of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> for the&longs;e <lb/>Waters being to di&longs;charge into <emph type="italics"/>Fiume morto,<emph.end type="italics"/> they maintain it <lb/>much higher than is imagined, according to that which I have de­<lb/>mon&longs;trated in my con&longs;ideration upon the &longs;tate of the Lake of <lb/><emph type="italics"/>Venice.<emph.end type="italics"/> I have &longs;aid but little, but I &longs;peak to you, who under­<lb/>&longs;tandeth much, and I &longs;ubmit all to the mo&longs;t refined judgment of <lb/>our mo&longs;t Serene Prince <emph type="italics"/>Leopold,<emph.end type="italics"/> who&longs;e hands I be&longs;eech you in all <lb/>humility to ki&longs;s in my name, and implore the continuance of his <lb/>Princely favour to me; and &longs;o de&longs;iring your prayers to God for <lb/>me, I take my leave.</s></p><p type="main"> <s><emph type="italics"/>Rome<emph.end type="italics"/> 1. Feb. <lb/></s> <s>1642.</s></p><p type="main"> <s><emph type="italics"/>Your mo&longs;t affectionate Servant,<emph.end type="italics"/></s></p><p type="main"> <s>D. BENEDETTO CASTELLI.</s></p><pb xlink:href="068/01/097.jpg" pagenum="83"/><p type="head"> <s>The an&longs;wer to a Letter written by BAR­<lb/>TOLOTTI, touching the <lb/>difficultyes ob&longs;erved.</s></p><p type="head"> <s><emph type="italics"/>The former part of the Letter is omitted, and the di&longs;cour&longs;e <lb/>beginneth at the fir&longs;t Head.<emph.end type="italics"/></s></p><p type="main"> <s>And fir&longs;t I &longs;ay, Whereas I &longs;uppo&longs;e that the level of the <emph type="italics"/>Ser­<lb/>chio<emph.end type="italics"/> is higher than that of <emph type="italics"/>Fiume morto<emph.end type="italics"/>; this is mo&longs;t true, <lb/>at &longs;uch time as the waters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> are di&longs;charged in­<lb/>to the Sea; but I did never &longs;ay that things could never be brought <lb/>to that pa&longs;s, as that the level of <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hould be higher than <lb/><emph type="italics"/>Serchio<emph.end type="italics"/>: and &longs;o I grant that it will follow, that the waters of <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hall go into <emph type="italics"/>Serchio,<emph.end type="italics"/> and its very po&longs;&longs;ible, that the <lb/>Drain of <emph type="italics"/>Fiume morto<emph.end type="italics"/> into <emph type="italics"/>Serchio<emph.end type="italics"/> may be continuate; and I far­<lb/>ther grant, that its po&longs;&longs;ible, that the <emph type="italics"/>Serchio<emph.end type="italics"/> doth never di&longs;gorge <lb/>thorow <emph type="italics"/>Fiume morto<emph.end type="italics"/> towards <emph type="italics"/>Pi&longs;a<emph.end type="italics"/>; Nay, I will yet farther grant <lb/>that it might have happened, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> might have had <lb/>&longs;uch a fall into <emph type="italics"/>Serchio,<emph.end type="italics"/> as would have &longs;ufficed to have turned <lb/>Mills: But then I add withall, that the Plains of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and the <lb/>City it &longs;elf mu&longs;t be a meer Lake.</s></p><p type="main"> <s>2. <emph type="italics"/>Signore Bartololti<emph.end type="italics"/> &longs;aith confidently, that when the Sea &longs;wel­<lb/>leth by the South-We&longs;t, or other Winds, the level of <emph type="italics"/>Serchio<emph.end type="italics"/> in <lb/>the place marked A in the Platt, di&longs;tant about 200. Braces, ri&longs;eth <lb/>very little: But that <emph type="italics"/>Fiume morto<emph.end type="italics"/> in D, and in E, many miles <lb/>more up into Land ri&longs;eth very much, and that certain Fi&longs;hermen <lb/>confirm this, and &longs;hew him the &longs;ignes of the ri&longs;ing of the Water. <lb/></s> <s>I grant it to be very true, and I have &longs;een it with my own eyes: <lb/>But this cometh to pa&longs;s, when the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> is &longs;topt <lb/>up by the Sea; as I &longs;hall &longs;hew by and by. </s> <s>And this ri&longs;ing near <lb/>the Sea-&longs;ide, is of no con&longs;iderable prejudice to the fields. </s> <s>And <lb/>this is as much as I find to be true in the a&longs;&longs;ertion of <emph type="italics"/>Signore Bar­<lb/>tolotti,<emph.end type="italics"/> (without his confirming it by any other proof; as indeed <lb/>it needs none) That the level of <emph type="italics"/>Fiume morto<emph.end type="italics"/> ri&longs;eth in E, and ma­<lb/>ny miles farther upwards it ri&longs;eth much; nor did I ever affirm the <lb/>contrary.</s></p><p type="main"> <s>3. Concerning the difficulty of opening the Mouth of <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> into the Sea, that which <emph type="italics"/>Il Ca&longs;tellano<emph.end type="italics"/> &longs;aith is mo&longs;t certain; <lb/>namely, That at the entrance upon the opening of the Mouth, it <lb/>is nece&longs;&longs;ary to make a deep Trench: But I &longs;ay, that at that time <lb/>it is difficult to open it, unle&longs;s upon great occa&longs;ions; for that the <pb xlink:href="068/01/098.jpg" pagenum="84"/>difficulty proceedeth from the waters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> being low, <lb/>and the fields drained.</s></p><p type="main"> <s>4. As to the particular of the Cau&longs;es that you tell me men <lb/>pre&longs;s &longs;o much unto the mo&longs;t <emph type="italics"/>Serene Grand Duke,<emph.end type="italics"/> and to the <lb/>Prince, I have not much to &longs;ay, becau&longs;e it is not my profe&longs;&longs;ion; <lb/>nor have I con&longs;idered of the &longs;ame: Yet I believe, that when the <lb/>Prince and his Highne&longs;&longs;e &longs;ee the benefit of his People and Sub­<lb/>jects in one &longs;cale of the Ballance, and the accomodation of <lb/>Hunt&longs;men in the other, his Highne&longs;&longs;e will incline to the profit <lb/>of his &longs;ubjects; &longs;uch have I alwayes found his Clemency and <lb/>Noblene&longs;&longs;e of minde. </s> <s>But if I were to put in my vote upon <lb/>this bu&longs;ine&longs;&longs;e, I would &longs;ay, that the points of Spears, and the <lb/>mouths of Guns, the yelping of Dogs, the wilyne&longs;&longs;e of Hunt&longs;­<lb/>men, who run thorow and narrowly &longs;earch all tho&longs;e Woods, <lb/>Thickets and Heathes, are the true de&longs;troyers of Bucks and <lb/>Boares, and not a little Salt-water, which &longs;etleth at la&longs;t in &longs;ome <lb/>low places, and &longs;preadeth not very far. </s> <s>Yet neverthele&longs;&longs;e, I will <lb/>not enter upon any &longs;uch point, but confine my &longs;elf &longs;olely to the <lb/>bu&longs;ine&longs;&longs;e before me.</s></p><p type="main"> <s>5. That Experiment of joyning together the water of <emph type="italics"/>Fiume <lb/>morto,<emph.end type="italics"/> and that of <emph type="italics"/>Serchio<emph.end type="italics"/> by a little trench to &longs;ee what advan­<lb/>tage the Level E hath upon the Level I, doth not give me full <lb/>&longs;atisfaction, taken &longs;o particularly, for it may come to pa&longs;&longs;e, that <lb/>&longs;ometimes E may be higher, and &longs;ometimes A lower, and I do <lb/>not que&longs;tion but that when <emph type="italics"/>Serchio<emph.end type="italics"/> is low, and <emph type="italics"/>Fiume morto<emph.end type="italics"/> full <lb/>of Water, the level of <emph type="italics"/>Fiume morto<emph.end type="italics"/> will be higher than that of <lb/><emph type="italics"/>Serchio.<emph.end type="italics"/> But <emph type="italics"/>Serchio<emph.end type="italics"/> being full, and <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;cant of Wa­<lb/>ter, the contrary will follow, if the Mouth &longs;hall be opened to <lb/>the Sea. </s> <s>And here it &longs;hould &longs;eem to me, that it ought to be <lb/>con&longs;idered, that there is as much advantage from E to the Sea <lb/>through the little Trench opened anew into <emph type="italics"/>Serchio,<emph.end type="italics"/> as from E to <lb/>the Sea by the Mouth of <emph type="italics"/>Fiume morto.<emph.end type="italics"/> But the difficulty (which <lb/>is that we are to regard in our ca&longs;e) is, that the cour&longs;e of the <lb/>Waters thorow the Trench is three times longer than the cour&longs;e <lb/>of the Mouth of <emph type="italics"/>Fiums morto,<emph.end type="italics"/> as appeareth by the Draught or <lb/>Plat which you &longs;ent me, which I know to be very exactly drawn, <lb/>for that the &longs;ituation of tho&longs;e places are fre&longs;h in my memory. <lb/></s> <s>Here I mu&longs;t give notice, that the waters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> determi­<lb/>ning thorow the Trench in <emph type="italics"/>Serchio<emph.end type="italics"/> (the waters of which <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> are, for certain, never &longs;o low as the Sea) their pendency or <lb/>declivity &longs;hall, for two cau&longs;es, be le&longs;&longs;e than the pendency of tho&longs;e <lb/>waters through the Mouth towards the Sea, that is, becau&longs;e of <lb/>the length of the line through the Trench, and becau&longs;e of the <lb/>height of their entrance into <emph type="italics"/>Serchio,<emph.end type="italics"/> a thing which is of very <lb/>great import in di&longs;charging the waters which come &longs;uddenly, as <pb xlink:href="068/01/099.jpg" pagenum="85"/>he &longs;hall plainly &longs;ee, who &longs;hall have under&longs;tood my Book of the <lb/>Mea&longs;ure of Running Waters And this was the Rea&longs;on why all <lb/>the Countrey did grow dry upon the opening of the Mouth into <lb/>the Sea. </s> <s>And here I propo&longs;e to con&longs;ideration that which the Pea­<lb/>&longs;ants about <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> relate, namely, That the Water in the Fields <lb/>doth no con&longs;iderable harm by continuing there five or &longs;ix, yea, or <lb/>eight dayes. </s> <s>And therefore the work of the Countrey is to o­<lb/>pen the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> in &longs;uch manner, that the Water <lb/>being come, they may have the Trench free and ready, when that <lb/>the Water cometh it may have a free drain, and may not &longs;tay <lb/>there above eight or nine dayes, for then the overflowings be­<lb/>come hurtful. </s> <s>It is to be de&longs;ired al&longs;o, that if any Propo&longs;ition is <lb/>produced touching the&longs;e affairs, it might be propounded the mo&longs;t <lb/>di&longs;tinctly that may be po&longs;&longs;ible, and not con&longs;i&longs;t in generals, e&longs;pe­<lb/>cially when the Di&longs;pute is of the ri&longs;ings, of velocity, of tardity, <lb/>of much and little water; things that are all to be &longs;pecified by <lb/>mea&longs;ures.</s></p><p type="main"> <s>6. Your Letter &longs;aith, in the next place, that <emph type="italics"/>Signore Barto­<lb/>lotti<emph.end type="italics"/> confe&longs;&longs;eth, that if the Mouth of the <emph type="italics"/>Fiume morto<emph.end type="italics"/> might al­<lb/>wayes be kept open, it would be better to let it continue as it is: <lb/>the which, that I may not yield to him in courte&longs;ie, I confe&longs;&longs;e, <lb/>for the keeping it &longs;topt on all &longs;ides would be a thing mo&longs;t per­<lb/>nicious. </s> <s>But admitting of his confe&longs;&longs;ion I again reply, that <emph type="italics"/>Fi­<lb/>ume morto<emph.end type="italics"/> ought not to be let into <emph type="italics"/>Serchio,<emph.end type="italics"/> but immediately in­<lb/>to the Sea; becau&longs;e although &longs;ometimes the Mouth to Sea­<lb/>wards be &longs;topt up, yet for all that, the rai&longs;ing of the Bank above <lb/>the Plains (which is all the bu&longs;ine&longs;&longs;e of importance) &longs;hall be ever <lb/>le&longs;&longs;er, if we make u&longs;e of the Mouth leading to the Sea, than u­<lb/>&longs;ing that of <emph type="italics"/>Serchio.<emph.end type="italics"/></s></p><p type="main"> <s>7. I will not omit to mention a kinde of &longs;cruple that I have <lb/>concerning the po&longs;ition of <emph type="italics"/>Sign. </s> <s>Bartolotti,<emph.end type="italics"/> that is, where he &longs;aith <lb/>that the two Mouths A and D are equal to the like Mouths into <lb/>the Sea; Now it &longs;eems to me, that the Mouth A of <emph type="italics"/>Fiume morto<emph.end type="italics"/><lb/>into <emph type="italics"/>Serchio<emph.end type="italics"/> is ab&longs;olutely within <emph type="italics"/>Serchio,<emph.end type="italics"/> nor can it be made low­<lb/>er, and is regulated by the height of <emph type="italics"/>Serchio<emph.end type="italics"/>: But the Mouth <lb/>of <emph type="italics"/>Fiume morto<emph.end type="italics"/> terminates, and ought to be under&longs;tood to ter­<lb/>minate in the Sea it &longs;elf, the lowe&longs;t place. </s> <s>And this I believe <lb/>was very well peroeived by <emph type="italics"/>Sig. </s> <s>Bartolotti,<emph.end type="italics"/> but I cannot tell why <lb/>he pa&longs;t it over without declaring it: and we &longs;ee not that the <lb/>Mouth D falleth far from the Sea, which Mouth ought to be let <lb/>into the Sea it &longs;elf, and &longs;o the advantage of the <emph type="italics"/>M<emph.end type="italics"/>outh into the <lb/>Sea more clearly appeareth.</s></p><p type="main"> <s>8. That which <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> addeth, that when it is high <lb/>Waters, at &longs;uch time as the Waters are out, and when Winds <lb/>choak up <emph type="italics"/>Fiume morto,<emph.end type="italics"/> they not only retard it, but return the <pb xlink:href="068/01/100.jpg" pagenum="86"/>cour&longs;e of the Waters upwards very lea&longs;urely, per&longs;wadeth me <lb/>more readily to believe that <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> knoweth very well, <lb/>that the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> let into <emph type="italics"/>Serchio<emph.end type="italics"/> is hurtful: for <lb/>by this he acknowledgeth that the Mouth towards the Sea doth <lb/>in &longs;uch &longs;ort drain the Countrey of the Waters, as that they be­<lb/>come very low; and therefore upon every little <emph type="italics"/>impetus<emph.end type="italics"/> the wa­<lb/>ters turn their cour&longs;e: And from the motions, being exceeding <lb/>&longs;low, is inferred, that the abundance of Sea-water that com­<lb/>eth into <emph type="italics"/>Fiume morto,<emph.end type="italics"/> is &longs;o much as is believed, and as <emph type="italics"/>Sig. </s> <s>Bat­<lb/>tolotti<emph.end type="italics"/> affirmeth.</s></p><p type="main"> <s>9. After that <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> hath &longs;aid what he promi&longs;eth a­<lb/>bove, namely, that when the Windes blowing &longs;trongly do &longs;top <lb/>up <emph type="italics"/>Fiume morto,<emph.end type="italics"/> and not onely retard but turn the cour&longs;e up­<lb/>wards, the time being Rainy, and the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hut <lb/>up, the Waves of the Sea pa&longs;&longs;e over the Bank of <emph type="italics"/>Fiume morto<emph.end type="italics"/>; at <lb/>that time, &longs;aith <emph type="italics"/>Signore Bartolotti,<emph.end type="italics"/> the Champain &longs;hall know the <lb/>benefit of <emph type="italics"/>Fiume morto<emph.end type="italics"/> di&longs;charged into <emph type="italics"/>Serchio,<emph.end type="italics"/> and the mouth A <lb/>&longs;hall &longs;tand alwayes open; and <emph type="italics"/>Fiume morto<emph.end type="italics"/> may alwayes con­<lb/>&longs;tantly run out, as al&longs;o the Rains and Rain-waters, although the <lb/>hurtful Tempe&longs;t &longs;hould la&longs;t many dayes, &c. </s> <s>And I reply, that <lb/>all the Art con&longs;i&longs;ts in this; for the benefit of tho&longs;e Fields doth <lb/>not depend on, or con&longs;i&longs;t in &longs;aying, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> is alwayes <lb/>open, and <emph type="italics"/>Fiume morto<emph.end type="italics"/> draineth continually; But all the bu&longs;i­<lb/>ne&longs;&longs;e of profit lyeth and con&longs;i&longs;teth in maintaining the Waters <lb/>low in tho&longs;e Plaines, and tho&longs;e Ditches, which &longs;hall never be ef­<lb/>fected whil&longs;t the World &longs;tands, if you let <emph type="italics"/>Fiume morto<emph.end type="italics"/> into <emph type="italics"/>Ser­<lb/>chio<emph.end type="italics"/>; but yet it may, by opening the mouth into the Sea: and <lb/>&longs;o much rea&longs;on and nature proveth, and (which importeth) Ex­<lb/>perience confirmeth.</s></p><p type="main"> <s>10. In the tenth place I come to con&longs;ider the an&longs;wer that <lb/>was made to another Propo&longs;ition in the Letter which I writ to <lb/>Father <emph type="italics"/>France&longs;co,<emph.end type="italics"/> which prudently of it &longs;elf alone might &longs;erve <lb/>to clear this whole bu&longs;ine&longs;&longs;e. </s> <s>I &longs;aid in my Letter, That great <lb/>account is to be made of every &longs;mall ri&longs;ing and ebbing of the <lb/>Waters neer to the Sea in <emph type="italics"/>Fiume morto,<emph.end type="italics"/> for that the&longs;e ri&longs;ings and <lb/>fallings, although that they be &longs;mall neer to the Sea-&longs;ide, yet ne­<lb/>verthele&longs;&longs;e, they operate and are accompanied by notable ri&longs;ings <lb/>and fallings within Land, and far from the Sea-&longs;ide, and I have <lb/>declared by an example of <emph type="italics"/>Arno,<emph.end type="italics"/> in which a Land-flood falling, <lb/>that made it increa&longs;e above its ordinary height within <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> &longs;ix or <lb/>&longs;even Braces, that this height of the &longs;ame Flood becometh &longs;till <lb/>le&longs;&longs;er, the neerer we approach to the Sea-coa&longs;ts. </s> <s>Nor &longs;hall the <lb/>&longs;aid River be rai&longs;ed hardly half a Brace; whereupon it nece&longs;&longs;­<lb/>rily followeth, that if I &longs;hould return to the Sea-&longs;ide, and not <lb/>knowing any think of that which happeneth at <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and &longs;eeing <pb xlink:href="068/01/101.jpg" pagenum="87"/>the River <emph type="italics"/>Arno<emph.end type="italics"/> rai&longs;ed by a Land-flood half a Brace, I might con­<lb/>fidently affirm the &longs;aid River to be rai&longs;ed in <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> tho&longs;e &longs;ix or &longs;e­<lb/>ven Braces, &c. </s> <s>From &longs;uch like accidents I conclude in the &longs;ame <lb/>Letter, that it is nece&longs;&longs;ary to make great account of every little <lb/>ri&longs;e that <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hall make towards the Sea. </s> <s>Now cometh <lb/><emph type="italics"/>Bartolotti<emph.end type="italics"/> (and perhaps becau&longs;e I knew not how to expre&longs;s my <lb/>&longs;elf better, under&longs;tandeth not my Propo&longs;ition) and &longs;peaketh that <lb/>which indeed is true, but yet be&longs;ides our ca&longs;e: Nor have I ever <lb/>&longs;aid the contrary; and withall doth not apply it to his purpo&longs;e. <lb/></s> <s>Nay I &longs;ay, that if he had well applyed it, this alone had been a­<lb/>ble to have made him change his opinion. </s> <s>And becau&longs;e he &longs;aith, <lb/>that I &longs;aid, that it is true, when the abatement proceedeth from <lb/>&longs;ome cau&longs;e above, as namely by Rain, or opening of Lakes; <lb/>But when the cau&longs;e is from below, that is, by &longs;ome &longs;top, as for <lb/>in&longs;tance &longs;ome Fi&longs;hers Wears or Locks, or &longs;ome impediment re­<lb/>mote from the Sea, although at the Level it &longs;hall ri&longs;e &longs;ome Braces <lb/>where the impediment is, yet that ri&longs;ing &longs;hall go upwards; and <lb/>here he fini&longs;heth his Di&longs;cour&longs;e, and concludeth not any thing <lb/>more. </s> <s>To which I &longs;ay fir&longs;t, that I have al&longs;o &longs;aid the &longs;ame in the <lb/>Propo&longs;ition, namely, that a Flood coming (which maketh <emph type="italics"/>Arno<emph.end type="italics"/><lb/>to ri&longs;e in <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> &longs;ix or &longs;even Braces (which I take to be a &longs;uperiour <lb/>cau&longs;e whether it be Rain or the opening of Lakes, as be&longs;t plea­<lb/>&longs;eth <emph type="italics"/>Bartolotti<emph.end type="italics"/>) in &longs;uch a ca&longs;e I &longs;ay, and in no other (for towards <lb/>the Sea-coa&longs;ts it &longs;hall not cau&longs;e a ri&longs;ing of full half a Brace; and <lb/>therefore &longs;eeing <emph type="italics"/>Arno<emph.end type="italics"/> at the Sea-&longs;ide to be rai&longs;ed by a Flood, whe­<lb/>ther of Rain, or of opening of Lakes half a Brace) it may be <lb/>inferred, that at <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> it &longs;hall be rai&longs;ed tho&longs;e &longs;ix or &longs;even Braces; <lb/>which variety, well con&longs;idered, explaineth all this affair in favour <lb/>of my opinion: For the ri&longs;ing that is made by the impediment <lb/>placed below, of Fi&longs;hing Weares and Locks, operateth at the be­<lb/>ginning, rai&longs;ing the Waters that are neer to the impediment; <lb/>and afterwards le&longs;s and le&longs;s, as we retire upwards from the im­<lb/>pediment: provided yet that we &longs;peak not of a Flood that com­<lb/>meth by acce&longs;&longs;ion, but onely of the ordinary Water impeded. <lb/></s> <s>But there being a new acce&longs;&longs;ion, as in our ca&longs;e, then the Water <lb/>of the Flood, I &longs;ay, &longs;hall make a greater ri&longs;ing in the parts &longs;uperi­<lb/>our, far from the impediment; and the&longs;e impediments &longs;hall <lb/>come to be tho&longs;e that &longs;hall overflow the Plains, as happened <lb/>eighteen or nineteen years ago, before the opening of <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> into the Sea, The &longs;ame will certainly follow, if <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> be let into <emph type="italics"/>Serchio.<emph.end type="italics"/> Here I could alledge a very pretty <lb/>ca&longs;e that befell me in <emph type="italics"/>la ^{*} Campagna di Roma,<emph.end type="italics"/> neer to the Sea­<lb/><arrow.to.target n="marg975"></arrow.to.target><lb/>&longs;ide. </s> <s>where I drained a Bog or Fen, of the nature of the Wa­<lb/>ters of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and I &longs;ucceeded in the enterprize, the Waters in their <lb/>&longs;ite towards the Sea abating only three Palmes, and yet in the <pb xlink:href="068/01/102.jpg" pagenum="88"/>Fen they fell more than fifteen Palmes. </s> <s>But the bu&longs;ine&longs;&longs;e <lb/>would be long, and not &longs;o ea&longs;ily to be declared, and I am cer­<lb/>tain that <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> having con&longs;idered this, would alter his <lb/>judgment, and withall would know that remitting that impedi­<lb/>ment anew, which I had left for le&longs;&longs;e than three Palmes towards <lb/>the Sea, the Waters in the Fen would return with the fir&longs;t Floods <lb/>and Raines to the &longs;ame height as before, as likewi&longs;e <emph type="italics"/>Fiume morto<emph.end type="italics"/><lb/>will do if it &longs;hall be let again into <emph type="italics"/>Serchio.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg975"></margin.target>* The Countrey <lb/>or Province lying <lb/>round the City, <lb/>heretofore called <lb/><emph type="italics"/>Latium<emph.end type="italics"/></s></p><p type="main"> <s>Here I intreat your Honour to do me the favour to importune <lb/><emph type="italics"/>P. France&longs;co<emph.end type="italics"/> in my behalf, that he would be plea&longs;ed to deelare <lb/>my meaning in the afore&longs;aid Letter to <emph type="italics"/>Sig. </s> <s>Bartolotti,<emph.end type="italics"/> for I hope <lb/>that if he will under&longs;tand this point, he will be no longer &longs;o te­<lb/>nacious in his opinion.</s></p><p type="main"> <s>Next that the&longs;e Lords in the Commi&longs;&longs;ion of Sewers, with the <lb/>Right Honourable the Marque&longs;&longs;e of S. <emph type="italics"/>Angelo,<emph.end type="italics"/> and your Honour <lb/>do approve of my judgment, doth very much rejoyce me; but <lb/>becau&longs;e that I know that they do it not in de&longs;ign to complement <lb/>me, but onely to &longs;erve his Highne&longs;s our Grand Duke, I freely <lb/>profe&longs;s that I will pretend no farther obligations from them there­<lb/>in, than I account my &longs;elf to owe to tho&longs;e who&longs;e opinions are <lb/>contrary to mine, for that I know that they have the &longs;ame end. <lb/></s> <s>The definitive &longs;entence of this whole bu&longs;ine&longs;s is, that they give <lb/>the&longs;e Plains, the&longs;e Draines, and the&longs;e Waters farre fetcht ap­<lb/>pellations.</s></p><p type="main"> <s>11. As to the quantity of the Water that <emph type="italics"/>Fiume morto<emph.end type="italics"/> di&longs;­<lb/>chargeth into the Sea, there are very great di&longs;putes about it, and <lb/>I have been pre&longs;ent at &longs;ome of them. </s> <s>But let your Honour be­<lb/>lieve me, that as this is not continual, but only during a few <lb/>dayes, &longs;o it will never be of any great prejudice to the&longs;e Fields; <lb/>and if your Lord&longs;hip would be a&longs;certained thereof, you may <lb/>plea&longs;e to go to <emph type="italics"/>Fiume morto<emph.end type="italics"/> at about a mile's di&longs;tance from the <lb/>Sea, in the time of the&longs;e &longs;trong Windes, and ob&longs;erve the cur­<lb/>rent from thence upwards, for you &longs;hall finde it extream &longs;low, <lb/>and con&longs;equently will know that the quantity of the Water that <lb/>is repuls'd is very &longs;mall. </s> <s>And this &longs;eems to be contradicted by the <lb/>rule of Ri&longs;ings proceeding from cau&longs;es below, which occa&longs;ion no <lb/>con&longs;iderable alteration far from the Sea.</s></p><p type="main"> <s>I am nece&longs;&longs;itated to go to morrow out of <emph type="italics"/>Rome<emph.end type="italics"/> with his Emi­<lb/>nence Cardinal <emph type="italics"/>Gaetano<emph.end type="italics"/> about certain affairs touching Waters, <lb/>therefore I &longs;hall not farther inlarge, but for a clo&longs;e to this tedious <lb/>Di&longs;cour&longs;e, I conclude in few words, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> is by no <lb/>means to be let into <emph type="italics"/>Serchio,<emph.end type="italics"/> nor are there any means intermedi­<lb/>ate cour&longs;es to be taken, for they will alwayes be prejudicial; but <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> is to be di&longs;charged immediately into the Sea. </s> <s>When <lb/>it is &longs;topt up by the fury of the Sea waves, I affirm that it is a <pb xlink:href="068/01/103.jpg" pagenum="89"/>&longs;ign that there is no need of opening it; and if there be any oc­<lb/>ca&longs;ion to open it, it is ea&longs;ily done. </s> <s>As for the re&longs;t your Lord&longs;hip <lb/>may plea&longs;e to keep account of all the particulars that occur, for <lb/>the memory of things pa&longs;t is our Tutre&longs;&longs;e in tho&longs;e that are to <lb/>come. </s> <s>If occa&longs;ion &longs;hall offer, I intreat you to bow humbly in <lb/>my name to His Highne&longs;s the Grand Duke, and the mo&longs;t Serene <lb/>Prince <emph type="italics"/>Leopold<emph.end type="italics"/>; and to attend the &longs;ervice of Their Highne&longs;&longs;es, for <lb/>you &longs;erve I rinces of extraordinary merit; And to whom I my <lb/>&longs;elf am al&longs;o exceedingly obliged. </s> <s>In the controver&longs;ies that ari&longs;e <lb/>re&longs;pect the pious end of &longs;peaking the Truth, for then every <lb/>thing will &longs;ucceed happily. </s> <s>I ki&longs;s the hands of <emph type="italics"/>Padre France&longs;co,<emph.end type="italics"/><lb/>of <emph type="italics"/>Sig. </s> <s>Bartolotti,<emph.end type="italics"/> and of your Lord&longs;hip.</s></p><p type="main"> <s><emph type="italics"/>Rome, 14. March<emph.end type="italics"/> 1642.</s></p><p type="main"> <s><emph type="italics"/>Your Honours<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>most Obliged Servant<emph.end type="italics"/></s></p><p type="main"> <s>D. <emph type="italics"/>BENEDETTO CASTELLI.<emph.end type="italics"/></s></p><p type="main"> <s>Vpon this occa&longs;ion I will here in&longs;ert a Di&longs;cour&longs;e that I made <lb/>upon the Draining and improvement of the <emph type="italics"/>Pontine Fens,<emph.end type="italics"/><lb/>for that I think that what&longs;oever may be done well and to pur­<lb/>po&longs;e in this matter hath ab&longs;olute dependance on the perfect know­<lb/>ledge of that &longs;o important Propo&longs;ition, by me demon&longs;trated and <lb/>explained in my Treati&longs;e of the <emph type="italics"/>Men&longs;uration<emph.end type="italics"/> of <emph type="italics"/>Running Wa­<lb/>ters,<emph.end type="italics"/> namely, That the &longs;ame water of a River doth continually <lb/>change Mea&longs;ures, according as it altereth and changeth the ve­<lb/>locity of its cour&longs;e; &longs;o that the mea&longs;ure of the thickne&longs;&longs;e of a <lb/>River in one Site, to the mea&longs;ure of the &longs;ame River in another <lb/>Site, hath the &longs;ame proportion reciprocally that the velocity in <lb/>this &longs;ite hath to the velocity in the fir&longs;t &longs;ite. </s> <s>And this is a Truth <lb/>&longs;o con&longs;tant and unchangeable, that it altereth not in the lea&longs;t <lb/>point on any occurrences of the Waters that change: and <lb/>being well under&longs;tood, it openeth the way to the knowledge of <lb/>&longs;undry adverti&longs;ements in the&longs;e matters, which are all re&longs;olved by <lb/>this &longs;ole Principle; and from it are derived very con&longs;iderable be­<lb/>nefits; and without the&longs;e it is impo&longs;&longs;ible to do any thing with <lb/>ab&longs;olute perfection</s></p><pb xlink:href="068/01/104.jpg"/><pb xlink:href="068/01/105.jpg" pagenum="91"/><p type="head"> <s>A <lb/>CONSIDERATION <lb/>Upon the <lb/>DRAINING <lb/>OF THE <lb/>Pontine Fenns. <lb/></s> <s>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, Abbot <lb/>of S. BENEDETTO ALOISIO, and Profe&longs;&longs;or <lb/>of the <emph type="italics"/>Mathematicks<emph.end type="italics"/> to P. <emph type="italics"/>Urban<emph.end type="italics"/> VIII. in the <lb/>Univer&longs;ity of <emph type="italics"/>ROME.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>CONSIDERATION<emph.end type="italics"/> III.</s></p><p type="main"> <s>Among&longs;t the enterprizes by me e&longs;teemed, if not ab­<lb/>&longs;olutely impo&longs;&longs;ible, , at lea&longs;t exceeding difficult, <lb/>one was that famous one of Draining the <emph type="italics"/>Pontine <lb/>Fenns<emph.end type="italics"/>; and therefore I was thorowly re&longs;olved <lb/>never to apply my minde thereunto, although <lb/>by my Patrons I &longs;hould be commanded to the <lb/>&longs;ame: accounting that it was an occa&longs;ion rather of lo&longs;ing repu­<lb/>tation by the mi&longs;carriage of the attempt, than of gaining fame by <lb/>reducing things to a better pa&longs;s then they now are at. </s> <s>Yet never­<lb/>thele&longs;s, having of late years ob&longs;erved the place, and &longs;ailed through <lb/>tho&longs;e Chanels, and tho&longs;e Waters; after I had made &longs;ome reflection <lb/>thereupon, I thought that the enterprize was not &longs;o difficult as <lb/>I had at fir&longs;t conceited it to be; and I am the more confirmed in <lb/>this opinion, upon the inducement of that which I have written <pb xlink:href="068/01/106.jpg" pagenum="92"/>Geometrically in my Treati&longs;e of the Men&longs;uration of Running <lb/>Waters; &longs;o that talking with &longs;everal per&longs;ons, I adventured to <lb/>affirm, in di&longs;coures, that this improvement might po&longs;&longs;ibly be <lb/>brought into a good e&longs;tate.</s></p><p type="main"> <s>Now I have re&longs;olved to &longs;et down my thoughts in writing, and <lb/>to honour this my Paper with the Noble Name of your Lord&longs;hip, <lb/>to render it the more credible and con&longs;picuous at the fir&longs;t view, <lb/>if it &longs;hould chance that the Subject I treat of, were not of &longs;uch <lb/>moment, as that it did de&longs;erve to be valued for any other rea&longs;on. <lb/></s> <s>Pardon me, Sir, if I have been too bold, and continue me in the <lb/>number of your Servants.</s></p><p type="main"> <s>The enterprize of Draining a great part of the Territories of <lb/>the <emph type="italics"/>Pontine Fenns,<emph.end type="italics"/> hath been undertaken both in the time of <lb/>the antient <emph type="italics"/>Romans,<emph.end type="italics"/> and la&longs;t of all, in our days; yea in the late <lb/>times by <emph type="italics"/>Sixtus<emph.end type="italics"/> V. </s> <s>I do not doubt in the lea&longs;t, but that it will <lb/>be po&longs;&longs;ible yet to reduce things to a very good pa&longs;s; and if I be not <lb/>mi&longs;taken, with a very &longs;mall charge in compari&longs;on of the profit that <lb/>would be received from tho&longs;e rich Grounds. </s> <s>This improvement <lb/>was of great expence in the time of <emph type="italics"/>Sixtus Quintus,<emph.end type="italics"/> but by rea­<lb/>&longs;on the thing was not rightly under&longs;tood, there were made many <lb/>Drains; a great part of which were unprofitable and vain: and <lb/>among&longs;t &longs;o many operations, there hapned &longs;ome to be made that <lb/>&longs;ucceeded, as was de&longs;ired; but not being under&longs;tood, they were <lb/>held in no account; and thus the bu&longs;ine&longs;s being neglected, the <lb/>waters are returned into the &longs;ame &longs;tate as they were at fir&longs;t, be­<lb/>fore the improvement. </s> <s>Here I have by familiar di&longs;cour&longs;es <lb/>with my friends, explained this enterprize undertaken by <emph type="italics"/>Six­<lb/>tus<emph.end type="italics"/> V. and haply al&longs;o by &longs;ome more antient, with the example of <lb/>the Fable of <emph type="italics"/>Orilo,<emph.end type="italics"/> in <emph type="italics"/>Ario&longs;to.<emph.end type="italics"/> This Mon&longs;ter was made up with <lb/>&longs;uch enchantment, that men fought with him alwayes in vain; <lb/>for though in the Combate he were cut in pieces, tho&longs;e divided <lb/>Members pre&longs;ently re-united, and returned to the fight more <lb/>fierce then ever. </s> <s>But the <emph type="italics"/>Paladine A&longs;tolfo<emph.end type="italics"/> coming to undertake <lb/>him, after a long di&longs;pute, at the end he cut his head &longs;heer off <lb/>from the &longs;houlders at one blow; and nimbly alighting from his <lb/>Hor&longs;e, took the Mon&longs;trous head, and mounting again, as he rid <lb/>away he fell to &longs;have the Pole of that Mon&longs;ter, and &longs;o he lo&longs;t <lb/>the Lock of Hair, in which alone the enchantment lay; and then <lb/>the horrible Head in an in&longs;tant manife&longs;ted &longs;igns of death, and the <lb/>trunk which ran, &longs;eeking to reunite to it anew, gave the la&longs;t ga&longs;p, <lb/>and in this manner the enchantment ended. </s> <s>The Book of Fate <lb/>&longs;erved admirably to the <emph type="italics"/>Paladine,<emph.end type="italics"/> whereby he came to under­<lb/>&longs;tand that Charm; for by &longs;having his whole head, the enchanted <lb/>hairs came to be cut off among&longs;t the re&longs;t: In the &longs;ame manner, I <lb/>&longs;ay, that it hath &longs;ometimes happened in Draining tho&longs;e Fields; <pb xlink:href="068/01/107.jpg" pagenum="93"/>for that among&longs;t &longs;o many tryals as have been made, that al&longs;o <lb/>was light upon, on which the improvement and remedy to the <lb/>di&longs;order did depend. </s> <s>And to us my fore-named Treati&longs;e &longs;hall <lb/>&longs;erve for a Rule, which being well under&longs;tood, &longs;hall make us to <lb/>know wherein con&longs;i&longs;teth, and whereon dependeth this mi&longs;carri­<lb/>age, and con&longs;equently it will be ea&longs;ie to apply thereunto a &longs;ea&longs;o­<lb/>nable remedy.</s></p><p type="main"> <s>And fir&longs;t I &longs;ay, That there is no doubt but that the waters <lb/>continue &longs;o high on tho&longs;e Plains becau&longs;e they are &longs;o high in the <lb/>principal River, which ought to receive them, and carry them <lb/>into the Sea. </s> <s>Now the Cau&longs;es of the height of the River, may <lb/>in my judgement be reduced to one alone; which is that by me <lb/>&longs;o often mentioned for the mo&longs;t Potent one, and declared in my <lb/>afore-named Tractate; to wit, The tardity of the motion of the <lb/>waters, which doth alwayes infallibly, and preci&longs;ely cau&longs;e the <lb/>&longs;elf &longs;ame Running Water to change the mea&longs;ure of its thickne&longs;s <lb/>at &longs;uch a rate, that the more it encrea&longs;eth in velocity, the more <lb/>it decrea&longs;eth in mea&longs;ure; and the more it decrea&longs;eth in velocity, <lb/>the more it encrea&longs;eth in mea&longs;ure: As for example; If a River <lb/>run in &longs;uch a place with the velocity of moving a mile in the <lb/>&longs;pace of an hour, and afterwards the &longs;ame River in another place <lb/>doth encrea&longs;e in velocity, &longs;o as to make three miles an hour; <lb/>that &longs;ame River &longs;hall dimini&longs;h in thickne&longs;s two thirds: And on <lb/>the contrary, If it &longs;hall dimini&longs;h in velocity &longs;o, as that it runneth <lb/>but half a mile in the &longs;ame time, it &longs;hall encrea&longs;e the double in <lb/>thickne&longs;s and mea&longs;ure. </s> <s>And in a word, look what proportion <lb/>the velocity in the fir&longs;t place, hath to the velocity in the &longs;econd, <lb/>and &longs;uch hath reciprocally the mea&longs;ure of the thickne&longs;s in the <lb/>&longs;econd place, to the mea&longs;ure in the fir&longs;t; as I have clearly demon­<lb/>&longs;trated in my Treati&longs;e: Which I repeat &longs;o frequently, that I <lb/>fear the Profe&longs;&longs;ors of Polite Learning will charge me with Tua­<lb/>tologie, and vain Repetition. </s> <s>But I am &longs;o de&longs;irous in this mo&longs;t <lb/>important point to be well under&longs;tood, becau&longs;e it will then be <lb/>ea&longs;ie to comprehend all the re&longs;t; and without this it is impo&longs;&longs;ible <lb/>(I will not &longs;ay difficult, but ab&longs;olutely impo&longs;&longs;ible) to under&longs;tand, <lb/>or ever to effect any thing to purpo&longs;e. </s> <s>And the better to ex­<lb/>plain the example, let it be &longs;uppo&longs;ed, <lb/><figure id="id.068.01.107.1.jpg" xlink:href="068/01/107/1.jpg"/><lb/>That the water of a River A D, <lb/>runneth high at the level of A F, <lb/>with &longs;uch a certain velocity; and let <lb/>it, by the &longs;ame water, be velocitated <lb/>three times more; I &longs;ay, that it will <lb/>abate 1/3, and &longs;hall &longs;tand at the level <lb/>in B E; and if it &longs;hall more veloci­<lb/>tate, it will abate the more at the Sea; But if it &longs;hould retard <pb xlink:href="068/01/108.jpg" pagenum="94"/>more than it did at the level AF, it would ri&longs;e yet more above <lb/>the &longs;aid level A F; although that the &longs;elf &longs;ame quantity of water <lb/>runneth all the while. </s> <s>By the above-named &longs;olid Principle I <lb/>re&longs;olve extravagant Problems in my Treati&longs;e, and a&longs;&longs;ign the Rea­<lb/>&longs;ons of admirable effects of Running Waters: But as for what <lb/>concerneth our purpo&longs;e of the <emph type="italics"/>Pontine Fenns,<emph.end type="italics"/> we have the Cau­<lb/>&longs;es very plain and clear; for which, by the trampling of Cattle <lb/>which pa&longs;s thorow the <emph type="italics"/>Draining River,<emph.end type="italics"/> the waters abate &longs;o nota­<lb/>bly, that it is as it were a miracle for tho&longs;e Reeds, Flags, and <lb/>Weeds that &longs;pring up, encrea&longs;e, and &longs;pread all over the River, <lb/>&longs;top and impede that velocity of the waters which they would <lb/>have by means of their declivity. </s> <s>But that pa&longs;&longs;age of tho&longs;e Bea&longs;ts, <lb/>treading down tho&longs;e Weeds unto the bottom of the River, in &longs;uch <lb/>&longs;ort, as that they no longer hinder the Current of the Water; <lb/>and the &longs;ame Waters increa&longs;ing in their cour&longs;e, they do dimi­<lb/>ni&longs;h in mea&longs;ure and height; and by this meanes the Ditches of the <lb/>Plains empty into the &longs;ame &longs;ucce&longs;sfully, and leave them free <lb/>from Waters, and Drained. </s> <s>But the&longs;e Weeds in a &longs;hort <lb/>time &longs;prouting up anew, and rai&longs;ing their &longs;talkes thorow the <lb/>body of the Waters, they reduce things to the &longs;ame evil <lb/>&longs;tate, as before, retarding the velocity of the Water, ma­<lb/>king it to increa&longs;e in height, and perhaps do occa&longs;ion grea­<lb/>ter mi&longs;chiefs; &longs;eeing that tho&longs;e many knots which each plant <lb/>&longs;hoots forth, begets a greater multitude of Stalks, which much <lb/>more incumbering the Water of the River, are a greater impe­<lb/>diment unto its velocity, and con&longs;equently make the height <lb/>of the waters to encrea&longs;e &longs;o much the more, and do more mi&longs;chief <lb/>than before.</s></p><p type="main"> <s>Another head to which the&longs;e harms may be reduced, but pro­<lb/>ceeding from the &longs;ame Root, which hath a great part in this <lb/>di&longs;order, is the impediment of tho&longs;e Wears in the River which <lb/>are made by heightning the bed of the &longs;ame, for placing of fi&longs;h­<lb/>ing-nets; of which <emph type="italics"/>Pi&longs;caries<emph.end type="italics"/> I reckoned above ten, when I made <lb/>a voyage thorow tho&longs;e waters to <emph type="italics"/>Sandolo.<emph.end type="italics"/> And the&longs;e Fi&longs;hing­<lb/>Wears are &longs;uch impediments, that &longs;ome one of them makes the <lb/>water of the River in the upper part to ri&longs;e half a Palm, and <lb/>&longs;ometimes a whole Palm, and more; &longs;o that when they are all <lb/>gathered together, the&longs;e impediments amount to more than &longs;even, <lb/>or po&longs;&longs;ibly than eight Palms.</s></p><p type="main"> <s>There concurreth for a third mo&longs;t Potent Cau&longs;e of the waters <lb/>continuing high in the evacuating, or Draining Chanel, and con­<lb/>&longs;equently on the Plains; The great abundance of water that i&longs;&longs;u­<lb/>eth from <emph type="italics"/>Fiume Si&longs;to,<emph.end type="italics"/> the waters of which do not keep within its <lb/>Banks when they are abundant; but encrea&longs;ing above its Chanel, <lb/>they unite with tho&longs;e of the Evacuator, and di&longs;per&longs;ing thorow <pb xlink:href="068/01/109.jpg" pagenum="95"/>the Fens are rai&longs;ed with great prejudice, and much grea­<lb/>ter than is conceived, according to what hath been demon­<lb/>&longs;trated in the Second Con&longs;ideration upon the <emph type="italics"/>Lake of Venice.<emph.end type="italics"/><lb/>Nor is it to any purpo&longs;e to &longs;ay, that if we &longs;hould mea&longs;ure <lb/>all the Waters that disimbogue from <emph type="italics"/>Fiume Si&longs;to,<emph.end type="italics"/> and gather <lb/>them into one &longs;umme, we &longs;hould not finde them to be &longs;uch, <lb/>as that they &longs;hall be able to make the Waters of the Fens <lb/>to increa&longs;e, by rea&longs;on of the great expan&longs;ion of them, over <lb/>which that body of water is to di&longs;tend: for to this in&longs;tance we <lb/>an&longs;wer wich that which we have given notice of in the Fir&longs;t Con­<lb/>&longs;ideration touching the <emph type="italics"/>Lake of Venice,<emph.end type="italics"/> treating of the abate­<lb/>ment that is cau&longs;ed by the <emph type="italics"/>Brent<emph.end type="italics"/> let into the Lake. </s> <s>And more­<lb/>over, if I &longs;hall adde thereto that which I write in the Second <lb/>Con&longs;ideration, it will be very apparent how greatly harmfull <lb/>and prejudicial the&longs;e excurfions of Waters from <emph type="italics"/>Fiume Si&longs;to<emph.end type="italics"/><lb/>may be, which are not kept under, and confined within the <lb/>River: Therefore, proceeding to the provi&longs;ions, and ope­<lb/>rations that are to be accounted Principall, I reduce them to <lb/>three Heads.</s></p><p type="main"> <s>In the fir&longs;t place it is nece&longs;&longs;ary to throw down tho&longs;e Weares, <lb/>and to take the Pi&longs;ciaries quite away, ob&longs;erving a Maxime, in <lb/>my judgment, infallible, that Fi&longs;hing and Sowing are two things <lb/>that can never con&longs;i&longs;t together; Fi&longs;hing being on the Water, and <lb/>Sowing on land.</s></p><p type="main"> <s>Secondly, it will be nece&longs;&longs;ary to cut under Water in the bot­<lb/>tome of the River tho&longs;e Weeds and Plants that grow and in­<lb/>crea&longs;e in the River, and leave them to be carried into the Sea by <lb/>the Stream; for by this means the&longs;e Reeds &longs;hall not &longs;pring up <lb/>and di&longs;tend along the bottome of the River, by means of the <lb/>Bea&longs;ts treading upon them; And the &longs;ame ought to be done <lb/>often, and with care, and mu&longs;t not be delaied till the mi&longs;­<lb/>chief increa&longs;e, and the Champain Grounds be drowned, but <lb/>one ought to order matters &longs;o, as that they may not drown. <lb/></s> <s>And I will affirm, that otherwi&longs;e this principal point would be­<lb/>come a mo&longs;t con&longs;iderable inconvenience.</s></p><p type="main"> <s>Thirdly, it is nece&longs;&longs;ary to make good the Banks of <emph type="italics"/>Fiume Si&longs;to<emph.end type="italics"/><lb/>on the left hand, and to procure that tho&longs;e Waters may run in <lb/>the Chanel, and not break forth. </s> <s>And it is to be noted, that <lb/>it is not enough to do one or two of tho&longs;e things, but we are to <lb/>put them all in execution; for omitting any thing, the whole <lb/>machine will be out of tune, and &longs;poiled. </s> <s>But proceeding with <lb/>due care, you &longs;hall not only Drain the <emph type="italics"/>Pontine Fens,<emph.end type="italics"/> but by <lb/>means of this la&longs;t particular the Current of <emph type="italics"/>Fiums Sisto<emph.end type="italics"/> &longs;hall <lb/>&longs;cowr its own Chanel of its &longs;elf, even to the carrying part of it <lb/>away: and haply with this abundance of water that it &longs;hall <pb xlink:href="068/01/110.jpg" pagenum="96"/>bear, the Mouth <emph type="italics"/>della Torre<emph.end type="italics"/> may be opened, and kept open <lb/>into the Sea. </s> <s>And it would, la&longs;t of all, be of admirable bene­<lb/>fit to clean&longs;e <emph type="italics"/>Fiume Sisto<emph.end type="italics"/> from many Trees and Bu&longs;hes where­<lb/>with it is overgrown.</s></p><p type="main"> <s>And with this I conclude, that the Improvement or Drain <lb/>po&longs;&longs;ible to be made con&longs;i&longs;teth in the&longs;e three particulars. </s> <s>Fir&longs;t, <lb/>in taking away the Fi&longs;hing Weares, leaving the Cour&longs;e <lb/>of the Waters free. </s> <s>Secondly, in keeping the Principal <lb/>Rivers clear from Weeds and Plants. </s> <s>Thirdly, in keeping <lb/>the water of <emph type="italics"/>Fiume Sisto<emph.end type="italics"/> in its own Chanel. </s> <s>All which are <lb/>things that may be done with very little charge, and to the <lb/>manife&longs;t benefit of the whole Country, and to the rendering <lb/>the Air whol&longs;omer in all tho&longs;e Places adjoyning to the <emph type="italics"/>Pon­<lb/>tine Fens.<emph.end type="italics"/></s></p><figure id="id.068.01.110.1.jpg" xlink:href="068/01/110/1.jpg"/><pb xlink:href="068/01/111.jpg" pagenum="97"/><p type="head"> <s>A <lb/>CONSIDERATION <lb/>Upon the <lb/>DRAINING <lb/>Of the Territories of <lb/>Bologna, Ferrara, <lb/>AND <lb/>Romagna.</s></p><p type="head"> <s>BY <lb/>D. BENEDETTO CASTELLI, Abbot <lb/>of S. BENEDETTO ALOISIO, <emph type="italics"/>Mathematician<emph.end type="italics"/><lb/>to P. <emph type="italics"/>Vrban<emph.end type="italics"/> VIII. and Profe&longs;&longs;or in the <lb/>Univer&longs;ity of <emph type="italics"/>ROME.<emph.end type="italics"/></s></p><p type="main"> <s>The weghty bu&longs;ine&longs;&longs;e of the Draining of <lb/>the Territories of <emph type="italics"/>Bologna, Ferrara,<emph.end type="italics"/><lb/>and <emph type="italics"/>Romagna<emph.end type="italics"/> having been punctually <lb/>handled and declared in writing from <lb/>the excellent memory of the Right Ho­<lb/>nourable and Noble <emph type="italics"/>Mon&longs;ignore Cor&longs;ini,<emph.end type="italics"/><lb/>who was heretofore Deputed Commi&longs;­<lb/>&longs;ary General, and Vi&longs;itor of tho&longs;e Wa­<lb/>ters; I am not able to make &longs;uch ano­<lb/>ther Di&longs;cour&longs;e upon the &longs;ame Subject, but will only &longs;ay &longs;ome­<lb/>what for farther confirmation of that which I have &longs;aid in this <lb/>Book upon the <emph type="italics"/>Lake of Venice,<emph.end type="italics"/> upon the <emph type="italics"/>Pontine Fens,<emph.end type="italics"/> and up­<lb/>on the Draining of tho&longs;e Plains of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> lying between the Ri­<lb/>vers <emph type="italics"/>Arno<emph.end type="italics"/> and <emph type="italics"/>Serchio<emph.end type="italics"/>; whereby it is manife&longs;t, that in all the <pb xlink:href="068/01/112.jpg" pagenum="98"/>aforementioned Ca&longs;es, and in the pre&longs;ent one that we are in hand <lb/>with, there have, in times pa&longs;t, very gro&longs;&longs;e Errours been com­<lb/>mitted, through the not having ever well under&longs;tood the true <lb/>mea&longs;ure of Running waters; and here it is to be noted, that the <lb/>bu&longs;ine&longs;&longs;e is, that in <emph type="italics"/>Venice,<emph.end type="italics"/> the diver&longs;ion of the waters of the <lb/>Lake, by diverting the <emph type="italics"/>Brent<emph.end type="italics"/> was debated, and in part executed, <lb/>without con&longs;ideration had how great abatement of water might <lb/>follow in the Lake, if the <emph type="italics"/>Brent<emph.end type="italics"/> were diverted, as I have &longs;hewn <lb/>in the fir&longs;t Con&longs;ideration upon this particular, from which act <lb/>there hath in&longs;ued very bad con&longs;equences, not only the difficulty <lb/>of Navigation, but it hath infected the whol&longs;omne&longs;&longs;e of the Air, <lb/>and cau&longs;ed the &longs;toppage of the Ports of <emph type="italics"/>Venice.<emph.end type="italics"/> And on the <lb/>contrary, the &longs;ame inadvertency of not con&longs;idering what ri&longs;ing of <lb/>the Water the <emph type="italics"/>Reno,<emph.end type="italics"/> and other Rivers being opened into the Val­<lb/>leys of <emph type="italics"/>Bologna<emph.end type="italics"/> and <emph type="italics"/>Ferrara,<emph.end type="italics"/> might cau&longs;e in the &longs;aid Valleys, is <lb/>the certain cau&longs;e that &longs;o many rich and fertile Fields are drown­<lb/>ed under water, converting the happy habitations and dwellings <lb/>of men into mi&longs;erable receptacles for Fi&longs;hes: Things which <lb/>doubtle&longs;&longs;e would never have happened, if tho&longs;e Rivers had been <lb/>kept at their height, and <emph type="italics"/>Reno<emph.end type="italics"/> had been turn'd into <emph type="italics"/>Main-Po,<emph.end type="italics"/><lb/>and the other Rivers into that of <emph type="italics"/>Argenta,<emph.end type="italics"/> and of <emph type="italics"/>Volano.<emph.end type="italics"/> Now <lb/>there having &longs;ufficient been &longs;poken by the above-named <emph type="italics"/>Mon&longs;ig. <lb/></s> <s>Cor&longs;ini<emph.end type="italics"/> in his Relation, I will only adde one conceit of my own, <lb/>which after the Rivers &longs;hould be regulated, as hath been &longs;aid, I <lb/>verily believe would be of extraordinary profit, I much doubt in­<lb/>deed that I &longs;hall finde it a hard matter to per&longs;wade men to be of <lb/>my mind, but yet neverthele&longs;s I will not que&longs;tion, but that tho&longs;e, <lb/>at lea&longs;t, who &longs;hall have under&longs;tood what I have &longs;aid and demon­<lb/>&longs;trated concerning the manners and proportions, according to <lb/>which the abatements and ri&longs;ings of Running waters proceed, <lb/>that are made by the Diver&longs;ions and Introductions of Waters, <lb/>will apprehend that my conjecture is grounded upon Rea&longs;on. <lb/></s> <s>And although I de&longs;cend not to the exactne&longs;&longs;e of particulars, I <lb/>will open the way to others, who having ob&longs;erved the requi&longs;ite <lb/>Rules of con&longs;idering the quantity of the waters that are intro­<lb/>duced, or that happen to be diverted, &longs;hall be able with punctu­<lb/>ality to examine the whole bu&longs;ine&longs;&longs;e, and then re&longs;olve on that <lb/>which &longs;hall be expedient to be done.</s></p><p type="main"> <s>Reflecting therefore upon the fir&longs;t Propo&longs;ition, that the <lb/>Ri&longs;ings of a Running Water made by the acce&longs;&longs;ion of new water <lb/>into the River, are to one another, as the Square-Roots of the <lb/>quantity of the water that runneth; and con&longs;equently, that the <lb/>&longs;ame cometh to pa&longs;s in the Diver&longs;ions: In&longs;omuch, that a River <lb/>running in height one &longs;uch a certain mea&longs;ure, to make it encrea&longs;e <lb/>double in height, the water is to be encrea&longs;ed to three times as <pb xlink:href="068/01/113.jpg" pagenum="99"/>much as it ran before; &longs;o that when the water &longs;hall be quadru­<lb/>ple, the height &longs;hall be double; and if the water were centuple, <lb/>the height would be decuple onely, and &longs;o from one quantity <lb/>to another: And on the contrary, in the Diver&longs;ions; If of the <lb/>100. parts of water that run thorow a River, there &longs;hall be di­<lb/>verted 19/160, the height of the River dimini&longs;heth onely 1/10, and con­<lb/>tinuing to divert 17/100, the height of the River abateth likewi&longs;e 1/10, <lb/>and &longs;o proceeding to divert 15/100 and then 13/100, and then 11/100, and <lb/>then 9/100, and then 7/100, and then 5/100, and then 3/106, alwaies by <lb/>each of the&longs;e diver&longs;ions, the height of the Running Water di­<lb/>mini&longs;heth the tenth part: although that the diver&longs;ions be &longs;o une. <lb/></s> <s>qual. </s> <s>Reflecting I &longs;ay upon this infallible Truth, I have had a <lb/>conceit, that though the <emph type="italics"/>Reno<emph.end type="italics"/> and other Rivers were diverted <lb/>from the Valleyes, and there was onely left the <emph type="italics"/>Chanel of Navi­<lb/>gation,<emph.end type="italics"/> which was onely the 1/20 part of the whole water that fal­<lb/>leth into the Valleys; yet neverthele&longs;s, the water in tho&longs;e &longs;ame <lb/>Valleyes would retain a tenth part of that height that became <lb/>conjoyned by the concour&longs;e of all the Rivers: And therefore I <lb/>&longs;hould think that it were the be&longs;t re&longs;olution to maintain the <emph type="italics"/>Gha­<lb/>nel of Navigation<emph.end type="italics"/> (if it were po&longs;&longs;ible) continuate unto the P<emph type="italics"/>o<emph.end type="italics"/> of <lb/><emph type="italics"/>Ferrara,<emph.end type="italics"/> and from thence to carry it into the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Volano<emph.end type="italics"/>; for <lb/>be&longs;ides that it would be of very great ea&longs;e in the Navigation of <lb/><emph type="italics"/>Bologna,<emph.end type="italics"/> and <emph type="italics"/>Ferrara,<emph.end type="italics"/> the &longs;aid water would render the P<emph type="italics"/>o<emph.end type="italics"/> o&longs; <lb/><emph type="italics"/>Volano<emph.end type="italics"/> navigable as far as to the very Walls of <emph type="italics"/>Ferrara,<emph.end type="italics"/> and con­<lb/>&longs;equently the Navigation would be continuate from <emph type="italics"/>Bologna<emph.end type="italics"/> to <lb/>the Sea-&longs;ide.</s></p><p type="main"> <s>But to manage this enterprize well, it is nece&longs;&longs;ary to mea&longs;ure <lb/>the quantity of the Water that the Rivers di&longs;charge into the Val­<lb/>leys, and that which the <emph type="italics"/>Chanel of Navigation<emph.end type="italics"/> carryeth, in man­<lb/>ner as I have demon&longs;trated at the beginning of this Book; for this <lb/>once known, we &longs;hall al&longs;o come to know, how profitable this di­<lb/>ver&longs;ion of the <emph type="italics"/>Chanel of Navigation<emph.end type="italics"/> from the Valleys is like to <lb/>prove; which yet would &longs;till be unprofitable, if &longs;o be that all <lb/>the Rivers that di&longs;charge their waters into the Valleys, &longs;hould <lb/>not &longs;ir&longs;t be Drained, according to what hath been above ad­<lb/>verti&longs;ed.</s></p><p type="main"> <s>Abbot CASTELLI, <emph type="italics"/>in the pre&longs;ent con&longs;ideration referring <lb/>himfelf to the Relation of<emph.end type="italics"/> Mon&longs;ig. </s> <s>Cor&longs;ini, <emph type="italics"/>grounded upon the Ob­<lb/>&longs;ervations and Precepts of the &longs;aid Abbot; as is &longs;een in the pre­<lb/>&longs;ent Di&longs;cour&longs;e. </s> <s>I thought it convenient for the compleating of the <lb/>Work of our Aulhour, upon the&longs;e &longs;ubjects, to in&longs;ert it in this <lb/>place.<emph.end type="italics"/></s></p><pb xlink:href="068/01/114.jpg" pagenum="100"/><p type="head"> <s>A <lb/>Relation of the Waters in the Territories <lb/>of <emph type="italics"/>Bologna<emph.end type="italics"/> and <emph type="italics"/>Ferrara.<emph.end type="italics"/><lb/>BY</s></p><p type="head"> <s>The Right Honourable and Illu&longs;trious, <emph type="italics"/>Mon&longs;ig­<lb/>nore<emph.end type="italics"/> CORSINI, a Native of <emph type="italics"/>Ju&longs;cany,<emph.end type="italics"/> Su­<lb/>perintendent of the general DRAINS, <lb/>and Pre&longs;ident of <emph type="italics"/>Romagna-<emph.end type="italics"/></s></p><p type="main"> <s>The <emph type="italics"/>Rheno,<emph.end type="italics"/> and other Brooks of <emph type="italics"/>Romagna,<emph.end type="italics"/> were by the <lb/>advice of <emph type="italics"/>P. </s> <s>Ago&longs;tino Spernazzati<emph.end type="italics"/> the Je&longs;uite, towards <lb/>the latter end of the time of <emph type="italics"/>Pope Clement<emph.end type="italics"/> VIII. notwith­<lb/>&longs;tanding the oppo&longs;ition of the <emph type="italics"/>Bologne&longs;i,<emph.end type="italics"/> and others concerned <lb/>therein, diverted from their Chanels, for the more commodious <lb/>clean&longs;ing of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferrara,<emph.end type="italics"/> and of its two Branches of <emph type="italics"/>Prima­<lb/>ro,<emph.end type="italics"/> and <emph type="italics"/>Volano<emph.end type="italics"/>; in order to the introducing the water of the <lb/><emph type="italics"/>Main-Po<emph.end type="italics"/> into them, to the end that their wonted Torrents being <lb/>re&longs;tored, they might carry the Muddy-water thence into the Sea, <lb/>and re&longs;tore to the City the Navigation which was la&longs;t, as is ma­<lb/>nife&longs;t by the Brief of the &longs;aid <emph type="italics"/>Pope Clement,<emph.end type="italics"/> directed to the <emph type="italics"/>Car­<lb/>dinal San Clemence,<emph.end type="italics"/> bearing date the 22. of <emph type="italics"/>Augu&longs;t,<emph.end type="italics"/> 1604.</s></p><p type="main"> <s>The work of the &longs;aid clean&longs;ing, and introducing of the &longs;aid <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> either as being &longs;uch in it &longs;elf, or by the contention of the <lb/><emph type="italics"/>Cardinal Legates<emph.end type="italics"/> then in the&longs;e parts; and the jarrings that hap­<lb/>ned betwixt them, proved &longs;o difficult, that after the expence of <lb/>va&longs;t &longs;umms in the &longs;pace of 21. years, there hath been nothing <lb/>done, &longs;ave the rendring of it the more difficult to be effected.</s></p><p type="main"> <s>Interim, the Torrents with their waters, both muddy and <lb/>clear, have damaged the Grounds lying on the right hand of the <lb/>P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> and the <emph type="italics"/>Rheno<emph.end type="italics"/> tho&longs;e on its Banks; of which I <lb/>will &longs;peak in the fir&longs;t place, as of that which is of greater impor­<lb/>tance, and from which the principal cau&longs;e of the mi&longs;chiefs that <lb/>re&longs;ult from the re&longs;t doth proceed.<lb/><arrow.to.target n="marg976"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg976"></margin.target>* Or Lord&longs;hip.</s></p><p type="main"> <s>This <emph type="italics"/>Rbeno<emph.end type="italics"/> having overflowed the ^{*} Tennency of <emph type="italics"/>Sanmartina,<emph.end type="italics"/><lb/>in circumference about fourteen miles given it before, and part <lb/>of that of <emph type="italics"/>Cominale<emph.end type="italics"/> given it afterwards, as it were, for a recepta­<lb/>cle; from whence, having depo&longs;ed the matter of its muddine&longs;s, <lb/>it i&longs;&longs;ued clear by the Mouths of <emph type="italics"/>Ma&longs;i,<emph.end type="italics"/> and of <emph type="italics"/>Lievaloro,<emph.end type="italics"/> into <lb/>the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro,<emph.end type="italics"/> and of <emph type="italics"/>Volano<emph.end type="italics"/>; did break down the encom­<pb xlink:href="068/01/115.jpg" pagenum="101"/>pa&longs;&longs;ing Bank or Dam towards S. <emph type="italics"/>Martino,<emph.end type="italics"/> and that of its new <lb/>Chanel on the right hand neer to <emph type="italics"/>Torre del Fondo.<emph.end type="italics"/></s></p><p type="main"> <s>By the breaches on this &longs;ide it &longs;treamed out in great abun­<lb/>dance from the upper part of <emph type="italics"/>Cominale,<emph.end type="italics"/> and in the parts about <lb/><emph type="italics"/>Raveda, Pioggio, Caprara, Chiare di Reno, Sant' Ago&longs;tino, San <lb/>Pro&longs;pero, San Vincenzo,<emph.end type="italics"/> and others, and made them to become <lb/>incultivable: it made al&longs;o tho&longs;e places above but little fruitful, <lb/>by rea&longs;on of the impediments that their Draines received, finding <lb/>the Conveyances called <emph type="italics"/>Riolo<emph.end type="italics"/> and <emph type="italics"/>Scor&longs;uro,<emph.end type="italics"/> not only filled by <emph type="italics"/>la <lb/>Motta<emph.end type="italics"/> and <emph type="italics"/>la Belletta,<emph.end type="italics"/> but that they turned backwards of them­<lb/>&longs;elves.</s></p><p type="main"> <s>But by the Mouths in the inclo&longs;ing Bank or Dam at <emph type="italics"/>Borgo di<emph.end type="italics"/><lb/>S. <emph type="italics"/>Martino<emph.end type="italics"/> i&longs;&longs;uing with violence, it fir&longs;t gave ob&longs;truction to the <lb/>ancient Navigation of <emph type="italics"/>la Torre del la Fo&longs;&longs;a,<emph.end type="italics"/> and afterwards to <lb/>the moderne of the mouth of <emph type="italics"/>Ma&longs;i,<emph.end type="italics"/> &longs;o that at pre&longs;ent the Com­<lb/>merce between <emph type="italics"/>Bologna<emph.end type="italics"/> and <emph type="italics"/>Ferrara<emph.end type="italics"/> is lo&longs;t, nor can it ever be <lb/>in any durable way renewed, whil&longs;t that this exceeds its due <lb/>bounds, and what ever moneys &longs;hall be imployed about the &longs;ame <lb/>&longs;hall be without any equivalent benefit, and to the manife&longs;t </s></p><p type="main"> <s><arrow.to.target n="marg977"></arrow.to.target><lb/>and notable prejudice of the ^{*} Apo&longs;tolick Chamber.</s></p><p type="margin"> <s><margin.target id="marg977"></margin.target>* The Popes <lb/>Exchequer.</s></p><p type="main"> <s>Thence pa&longs;&longs;ing into the Valley of <emph type="italics"/>Marzara,<emph.end type="italics"/> it &longs;welleth high­<lb/>er, not only by the ri&longs;ing of the water, but by the rai&longs;ing of the <lb/>bottome, by rea&longs;on of the matter &longs;unk thither after Land­<lb/>floods, and dilateth &longs;o, that it covereth all the Meadows there­<lb/>abouts, nor doth it receive with the wonted facility the Drains of <lb/>the upper Grounds, of which the next unto it lying under the wa­<lb/>ters that return upwards by the Conveyances, and the more re­<lb/>mote, not finding a pa&longs;&longs;age for Rain-waters that &longs;ettle, become <lb/>either altogether unpro&longs;itable or little better.</s></p><p type="main"> <s>From this Valley, by the Trench or Ditch of <emph type="italics"/>Marzara,<emph.end type="italics"/> or of <lb/><emph type="italics"/>la Duca<emph.end type="italics"/> by <emph type="italics"/>la Buova,<emph.end type="italics"/> or mouth of <emph type="italics"/>Ca&longs;taldo de Ro&longs;&longs;i,<emph.end type="italics"/> and by the <lb/>new pa&longs;&longs;age it falleth into the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> which being to re­<lb/>ceive it clear, that &longs;o it may &longs;ink farther therein, and receiving <lb/>it muddy, becau&longs;e it hath acquired a quicker cour&longs;e, there will <lb/>ari&longs;e a very contrary effect.</s></p><p type="main"> <s>Here therefore the &longs;uperficies of the water keeping high, until <lb/>it come to the Sea, hindereth the Valleys of <emph type="italics"/>Ravenna,<emph.end type="italics"/> where <lb/>the River <emph type="italics"/>Senio,<emph.end type="italics"/> tho&longs;e of <emph type="italics"/>San Bernardino<emph.end type="italics"/> where <emph type="italics"/>Santerno<emph.end type="italics"/> was <lb/>turned, tho&longs;e of <emph type="italics"/>Buon' acqui&longs;to,<emph.end type="italics"/> and tho&longs;e of <emph type="italics"/>Marmorto,<emph.end type="italics"/> where <lb/>the <emph type="italics"/>Idice, Quaderna, Sellero<emph.end type="italics"/> &longs;all in, from &longs;wallowing and taking <lb/>in their Waters by their u&longs;ual In-lets, yet many times, as I my <lb/>&longs;elf have &longs;een in the <emph type="italics"/>Vi&longs;itation,<emph.end type="italics"/> they drink them up plentifully, <lb/>whereupon, being conjoyned with the muddine&longs;&longs;e of tho&longs;e Ri­<lb/>vers that fall into the &longs;ame, they &longs;well, and dilate, and overflow <lb/>&longs;ome grounds, and deprive others of their Drains in like manner <pb xlink:href="068/01/116.jpg" pagenum="102"/>as hath been &longs;aid of that of <emph type="italics"/>Marrara,<emph.end type="italics"/> in&longs;omuch that from the <lb/>Point of S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> as far as S. <emph type="italics"/>Alberto<emph.end type="italics"/> all tho&longs;e that are between <lb/>the Valleys and P<emph type="italics"/>o<emph.end type="italics"/> are &longs;poiled, of tho&longs;e that are between Valley <lb/>and Valley many are in a very bad condition, and tho&longs;e that are <lb/>&longs;ome con&longs;iderable &longs;pace above not a little damnified.</s></p><p type="main"> <s>In fine, by rai&longs;ing the bottom or &longs;and of the Valleys, and the <lb/>bed of <emph type="italics"/>Reno,<emph.end type="italics"/> and the too great repletion of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro<emph.end type="italics"/><lb/>with waters, the Valleys of <emph type="italics"/>Comacchio<emph.end type="italics"/> (on which &longs;ide the Banks <lb/>are very bad) and ^{*} <emph type="italics"/>Pole&longs;ine di<emph.end type="italics"/> S. <emph type="italics"/>Giorgio<emph.end type="italics"/> are threatned with a <lb/><arrow.to.target n="marg978"></arrow.to.target><lb/>danger, that may in time, if it be not remedied, become irrepa­<lb/>rable, and at pre&longs;ent feeleth the incommodity of the Waters, <lb/>which penetrating thorow the pores of the Earth do &longs;pring up in <lb/>the &longs;ame, which they call <emph type="italics"/>Purlings,<emph.end type="italics"/> which is all likely to redound <lb/>to the prejudice of <emph type="italics"/>Ferrara,<emph.end type="italics"/> &longs;o noble a City of <emph type="italics"/>Italy,<emph.end type="italics"/> and &longs;o im­<lb/>portant to the <emph type="italics"/>Eccle&longs;ta&longs;tick State.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg978"></margin.target>+ <emph type="italics"/>Pole&longs;ine<emph.end type="italics"/> is a <lb/>plat of Ground al­<lb/>mo&longs;t &longs;urrounded <lb/>with Bogs or wa­<lb/>ters, like an I&longs;land</s></p><p type="main"> <s>Which particulars all appear to be atte&longs;ted under the hand of <lb/>a Notary in the <emph type="italics"/>Vi&longs;itation<emph.end type="italics"/> which I made upon the command of <lb/>His Holine&longs;&longs;e, and are withall known to be true by the ^{*}<emph type="italics"/>Ferrare&longs;t<emph.end type="italics"/><lb/><arrow.to.target n="marg979"></arrow.to.target><lb/>them&longs;elves, of whom (be&longs;ides the reque&longs;t of the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/>) the <lb/>greater part beg compa&longs;&longs;ion with &longs;undry <emph type="italics"/>Memorials,<emph.end type="italics"/> and reme­<lb/>dies, a&longs;well for the mi&longs;chiefs pa&longs;t, as al&longs;o for tho&longs;e in time to <lb/>come, from which I hold it a duty of Con&longs;cience, and of Cha­<lb/>rity to deliver them.</s></p><p type="margin"> <s><margin.target id="marg979"></margin.target>* People of <emph type="italics"/>Fer­<lb/>rara.<emph.end type="italics"/></s></p><p type="main"> <s>Pope <emph type="italics"/>Clement<emph.end type="italics"/> judged, that the &longs;ufficient means to effect this <lb/>was the &longs;aid Introduction of the <emph type="italics"/>Main Po<emph.end type="italics"/> into the Chancl of <lb/><emph type="italics"/>Ferrara<emph.end type="italics"/>; a re&longs;olution truly Heroical, and of no le&longs;&longs;e beauty <lb/>than benefit to that City, of which I &longs;peak not at pre&longs;ent, be­<lb/>cau&longs;e I think that there is need of a readier and more acco­<lb/>modate remedy.</s></p><p type="main"> <s>So that I &longs;ee not how any other thing can be &longs;o much con&longs;ide­<lb/>rable as the removal of <emph type="italics"/>Reno,<emph.end type="italics"/> omitting for this time to &longs;peak of <lb/><arrow.to.target n="marg980"></arrow.to.target><lb/>^{*} inclo&longs;ing it from Valley to Valley untill it come to the Sea, as <lb/>the Dukes of <emph type="italics"/>Ferrara<emph.end type="italics"/> did de&longs;ign, fora&longs;much as all tho&longs;e <emph type="italics"/>Ferra­<lb/>re&longs;i<emph.end type="italics"/> that have intere&longs;t in the <emph type="italics"/>Pole&longs;ine di<emph.end type="italics"/> S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> and on the <lb/>right hand of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta<emph.end type="italics"/> do not de&longs;ire it, and do, but too <lb/>openly, prote&longs;t again&longs;t it; and becau&longs;e that before the Chanel <lb/>were made as far as the Sea, many hundreds of years would be <lb/>&longs;pent, and yet would not remedy the dammages of tho&longs;e who <lb/>now are agrieved, but would much increa&longs;e them, in regard the <lb/>Valleys would continue &longs;ubmerged, the Drains &longs;topped, and the <lb/>other Brooks ob&longs;tructed, which would of nece&longs;&longs;ity drown not a <lb/>few Lands that lie between Valley and Valley; and in fine, in <lb/>regard it hath not from <emph type="italics"/>San Martina<emph.end type="italics"/> to the Sea for a &longs;pace of &longs;if­<lb/>ty miles a greater fall then 19, 8, 6, feet, it would want that force <lb/>which they them&longs;elves who propound this project do require it to <pb xlink:href="068/01/117.jpg" pagenum="103"/>have, that &longs;o it may not depo&longs;e the matter of the muddine&longs;s when <lb/>it is intended to be let into <emph type="italics"/>Volana.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg980"></margin.target>* In Chanels <lb/>made by hand.</s></p><p type="main"> <s>So that making the Line of the bottome neer to <emph type="italics"/>Vigarano,<emph.end type="italics"/> it <lb/>would ri&longs;e to tho&longs;e prodigious termes that they do make bigger, <lb/>and they may thence expect tho&longs;e mi&longs;chiefs, for which they <lb/>will not admit of introducing it into the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Volana.<emph.end type="italics"/></s></p><p type="main"> <s>Among&longs;t the wayes therefore that I have thought of for effect­<lb/>ing that &longs;ame remotion, and which I have cau&longs;ed to be viewed by <lb/>skilful men that have taken a level thereof, (with the a&longs;&longs;i&longs;tance of <lb/>the venerable Father, <emph type="italics"/>D. </s> <s>Benedetto Ca&longs;telli<emph.end type="italics"/> of <emph type="italics"/>Ca&longs;ina,<emph.end type="italics"/> a man of <lb/>much fidelity and hone&longs;ty, and no le&longs;s expert in &longs;uch like affairs <lb/>touching waters, than perfect in the <emph type="italics"/>Mathematick<emph.end type="italics"/> Di&longs;ciplines) two <lb/>onely, the re&longs;t being either too tedious, or too dangerous to the <lb/>City, have &longs;eemed to me worthy, and one of them al&longs;o more than <lb/>the other, to offer to your Lord&longs;hip.</s></p><p type="main"> <s>The one is to remit it into the Chanel of <emph type="italics"/>Volana,<emph.end type="italics"/> thorow which <lb/>it goeth of its own accord to the Sea.</s></p><p type="main"> <s>The other is to turn it into <emph type="italics"/>Main-Po<emph.end type="italics"/> at <emph type="italics"/>Stellata,<emph.end type="italics"/> for, as at other <lb/>times it hath done, it will carry it to the Sea happily.</s></p><p type="main"> <s>As to what concerns the making choice of the fir&longs;t way, that <lb/>which &longs;eemeth to per&longs;wade us to it is, that we therein do nothing <lb/>that is new, in that it is but re&longs;tored to the place whence it was <lb/>removed in the year 1522. in the time of Pope <emph type="italics"/>Adrian,<emph.end type="italics"/> by an <lb/>agreement made in way of contract, between <emph type="italics"/>Alfon&longs;o,<emph.end type="italics"/> Duke of <lb/><emph type="italics"/>Ferrara,<emph.end type="italics"/> and the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/>; and that it was diverted for rea&longs;ons, <lb/>that are either out of date, or el&longs;e have been too long time <lb/>deferred.</s></p><p type="main"> <s>In like manner the facility wherewith it may be effected, let­<lb/>ting it run into the divided P<emph type="italics"/>o,<emph.end type="italics"/> whereby it will be turned to <emph type="italics"/>Fer­<lb/>rara,<emph.end type="italics"/> or el&longs;e carrying it by <emph type="italics"/>Torre del Fondo,<emph.end type="italics"/> to the mouth of <emph type="italics"/>Ma&longs;i,<emph.end type="italics"/><lb/>and from thence thorow the Trench made by the <emph type="italics"/>Ferrare&longs;i,<emph.end type="italics"/><lb/>along by <emph type="italics"/>Panaro,<emph.end type="italics"/> where al&longs;o finding an ample Bed, and high and <lb/>thick Banks, that will &longs;erve at other times for it, and for the wa­<lb/>ters of P<emph type="italics"/>o,<emph.end type="italics"/> there may a great expence be &longs;pared.</s></p><p type="main"> <s>That what ever its Fall be, it would maintain the &longs;ame, not <lb/>having other Rivers, which with their Floods can hinder it; and <lb/>that running confined between good Banks, without doubt it <lb/>would not leave <emph type="italics"/>la Motto<emph.end type="italics"/> by the way; but e&longs;pecially, that it <lb/>would be &longs;ufficient if it came to <emph type="italics"/>Codigoro,<emph.end type="italics"/> where being a&longs;&longs;i&longs;ted by <lb/>the Ebbing and Flowing of the Sea, it would run no hazard of <lb/>having its Chanel filled up from thence downwards.</s></p><p type="main"> <s>That there might thence many benefits be derived to the City, <lb/>by means of the Running Waters, and al&longs;o no mean Navigation <lb/>might be expected.</s></p><p type="main"> <s>On the contrary it is objected, That it is not convenient to <pb xlink:href="068/01/118.jpg" pagenum="104"/>think of returning this Torrent into the divided P<emph type="italics"/>o,<emph.end type="italics"/> by rea&longs;on of <lb/>the peril that would thence redound to this City.</s></p><p type="main"> <s>And that going by <emph type="italics"/>Torre del Fondo,<emph.end type="italics"/> through <emph type="italics"/>Sanmartina<emph.end type="italics"/> to <lb/>the Mouth <emph type="italics"/>de Ma&longs;i<emph.end type="italics"/> by the Chappel of <emph type="italics"/>Vigarano<emph.end type="italics"/> unto the Sea, it is <lb/>by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, &longs;o <lb/>that it would come to fall but 4. inches & an half, or thereabouts <lb/>in a mile; whereas the common opinion of the skilfull (to the <lb/>end that the Torrents may not depo&longs;e their &longs;and that they bring <lb/>with them in Land-Floods) requireth the twenty fourth part of <lb/>the hundredth part of their whole length, which in our ca&longs;e, <lb/>accounting according to the mea&longs;ure of the&longs;e places, is 16. inches <lb/><arrow.to.target n="marg981"></arrow.to.target><lb/>a ^{*} mile; whereupon the &longs;inking of the Mud and Sand would <lb/>mo&longs;t certainly follow, and &longs;o an immen&longs;e heightning of the Line <lb/>of the Bottom, and con&longs;equently a nece&longs;&longs;ity of rai&longs;ing the Banks, <lb/>the impo&longs;&longs;ibility of maintaining them, the danger of breaches <lb/>and decayes, things very prejudicial to the <emph type="italics"/>I&longs;lets<emph.end type="italics"/> of this City, and <lb/>of <emph type="italics"/>San Giorgio,<emph.end type="italics"/> the ob&longs;truction of the Drains, which from the <lb/>Tower of <emph type="italics"/>Tienne<emph.end type="italics"/> downwards, fall into the &longs;aid Chanel; to wit, <lb/>tho&longs;e of the Sluices of <emph type="italics"/>Goro,<emph.end type="italics"/> and the Drains, of the Meadows of <lb/><emph type="italics"/>Ferrara<emph.end type="italics"/>: And moreover, the damages that would ari&longs;e unto the <lb/>&longs;aid <emph type="italics"/>I&longs;let<emph.end type="italics"/> of S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> and the Valleys of <emph type="italics"/>Comachio,<emph.end type="italics"/> by the wa­<lb/>ters that &longs;hould enter into the <emph type="italics"/>Goro<emph.end type="italics"/> or Dam of the Mills of <emph type="italics"/>Belri­<lb/>guardo,<emph.end type="italics"/> thorow the Trenches of <emph type="italics"/>Quadrea,<emph.end type="italics"/> which cannot be &longs;topt, <lb/>becau&longs;e they belong to the Duke of <emph type="italics"/>Modena,<emph.end type="italics"/> who hath right of <lb/>diverting the waters of that place at his plea&longs;ure to the work of <lb/>turning Mills.</s></p><p type="margin"> <s><margin.target id="marg981"></margin.target>* The inch of <lb/>the&longs;e places is <lb/>&longs;omewhat bigger <lb/>than ours.</s></p><p type="main"> <s>The greater part of which Objections, others pretend to prove <lb/>frivolous, by &longs;aying, that its running there till at the la&longs;t it was <lb/>turned another way, is a &longs;ign that it had made &longs;uch an elevation <lb/>of the Line, of its Bed as it required; denying that it needeth <lb/>&longs;o great a declivity as is mentioned above; and that for the fu­<lb/>ture it would ri&longs;e no more.</s></p><p type="main"> <s>That the &longs;aid Dra ns and Ditches did empty into the &longs;ame, <lb/>whil&longs;t P<emph type="italics"/>o<emph.end type="italics"/> was there; &longs;o that they mu&longs;t needs be more able to do <lb/>&longs;o when onely <emph type="italics"/>Reno<emph.end type="italics"/> runs that way.</s></p><p type="main"> <s>That there would no Breaches follow, or if they did, they <lb/>would be onely of the water of <emph type="italics"/>Reno,<emph.end type="italics"/> which in few hours might <lb/>be taken away (in tho&longs;e parts they call damming up of Breaches, <lb/>and mending the Bank, <emph type="italics"/>taking away the Breaches<emph.end type="italics"/>) and its a que­<lb/>&longs;tion whether they would procure more inconvenience than bene­<lb/>fit, for that its Mud and Sand might in many places, by filling <lb/>them up, occa&longs;ion a &longs;ea&longs;onable improvement.</s></p><p type="main"> <s>Now omitting to di&longs;cour&longs;e of the &longs;olidity of the rea&longs;ons on the <lb/>one&longs;ide, or on the other, I will produce tho&longs;e that move me to <lb/>&longs;u&longs;pend my allowance of this de&longs;ign.</s></p><pb xlink:href="068/01/119.jpg" pagenum="105"/><p type="main"> <s>The fir&longs;t is, that although I dare not &longs;ub&longs;cribe to the opinion <lb/>of tho&longs;e that require 16. inches Declivity in a mile to <emph type="italics"/>Reno,<emph.end type="italics"/> to <lb/>prevent its depo&longs;ing of Mud; yet would I not be the Author that <lb/>&longs;hould make a trial of it with &longs;o much hazard, for having to &longs;a­<lb/>tisfie my &longs;elf in &longs;ome particulars cau&longs;ed a Level to be taken of <lb/>the Rivers <emph type="italics"/>L'amone, Senio,<emph.end type="italics"/> and <emph type="italics"/>Santerno,<emph.end type="italics"/> by <emph type="italics"/>Bernardino Aleotti,<emph.end type="italics"/><lb/>we found that they have more Declivity by much than Arti&longs;ts re­<lb/>quire, as al&longs;o the <emph type="italics"/>Reno<emph.end type="italics"/> hath from <emph type="italics"/>la Botta de Ghi&longs;lieri<emph.end type="italics"/> to the <lb/>Chappel of <emph type="italics"/>Vigarano,<emph.end type="italics"/> for in the &longs;pace of four miles its Bottom­<lb/>Line falleth five feet and five inches. </s> <s>So that I hold it greater <lb/>prudence to depend upon that example, than to go contrary to a <lb/>common opinion, e&longs;pecially &longs;ince, that the effects cau&longs;ed by <emph type="italics"/>Reno<emph.end type="italics"/><lb/>it &longs;elf do confirm me in the &longs;ame, for when it was for&longs;aken by <lb/>the P<emph type="italics"/>o,<emph.end type="italics"/> after a few years, either becau&longs;e it had choaked up its <lb/>Chanel with Sand, or becau&longs;e its too long journey did increa&longs;e <lb/>it, it al&longs;o naturally turned a&longs;ide, and took the way of the &longs;aid <lb/>P<emph type="italics"/>o<emph.end type="italics"/> towards <emph type="italics"/>Stellata.<emph.end type="italics"/> Nay, in tho&longs;e very years that it did run that <lb/>way, it only began (as relations &longs;ay) to make Breaches, an evi­<lb/>dent &longs;ign that it doth depo&longs;e Sand, and rai&longs;e its Bed; which a­<lb/>greeth with the te&longs;timony of &longs;ome that were examined in the <lb/><emph type="italics"/>Vi&longs;itation<emph.end type="italics"/> of the Publique Notary, who found great benefit by <lb/>having Running Water, and &longs;ome kind of pa&longs;&longs;age for Boats, <lb/>and yet neverthele&longs;s affirm that it for want of Running Water <lb/>had made too high Stoppages and Shelfes of Sand; &longs;o that if <lb/>it &longs;hould be re&longs;tored to the Cour&longs;e that it for&longs;ook, I much fear <lb/>that after a &longs;hort time, if not &longs;uddenly, it would leave it a­<lb/>again.</s></p><p type="main"> <s>The &longs;econd I take from the ob&longs;ervation of what happened to <lb/><emph type="italics"/>Panaro,<emph.end type="italics"/> when with &longs;o great applau&longs;e of the <emph type="italics"/>Ferare&longs;i,<emph.end type="italics"/> it was <lb/>brought by Cardinal <emph type="italics"/>Serra<emph.end type="italics"/> into the &longs;aid Chanel of <emph type="italics"/>Volana<emph.end type="italics"/>; for <lb/>that notwith&longs;tanding that it had Running Waters in much grea­<lb/>ter abundance than <emph type="italics"/>Reno<emph.end type="italics"/>; yet in the time that it continued in <lb/>that Chanel it rai&longs;ed its Bed well neer five feet, as is to be &longs;een <lb/>below the Sluice made by Cardinal <emph type="italics"/>Capponi<emph.end type="italics"/> to his new Chanel; <lb/>yea, the &longs;aid Cardinal <emph type="italics"/>Serra<emph.end type="italics"/> who de&longs;ired that this his under taking <lb/>&longs;hould appear to have been of no danger nor damage, was con­<lb/>&longs;trained at its Overflowings, to give it Vent into <emph type="italics"/>Sanmartina,<emph.end type="italics"/> that <lb/>it might not break in upon, and prejudice the City; which dan­<lb/>ger I &longs;hould more fear from <emph type="italics"/>Reno,<emph.end type="italics"/> in regard it carrieth a greater <lb/>abundance of Water and Sand</s></p><p type="main"> <s>Thirdly, I am much troubled (in the uncertainty of the &longs;uc­<lb/>ce&longs;s of the affair) at the great expence thereto required; For in <lb/>regard I do not approve of letting it in, neer to the Fortre&longs;&longs;e, <lb/>for many re&longs;pects, and carrying it by <emph type="italics"/>la Torre del Fondo<emph.end type="italics"/> to the <lb/>Month <emph type="italics"/>de Ma&longs;t,<emph.end type="italics"/> it will take up eight miles of double Banks, a <pb xlink:href="068/01/120.jpg" pagenum="106"/>thing not ea&longs;ie to be procured, by rea&longs;on that the Grounds lie <lb/>under Water; but from the Mouth <emph type="italics"/>de Ma&longs;i<emph.end type="italics"/> unto <emph type="italics"/>Codigoro,<emph.end type="italics"/> it <lb/>would al&longs;o be nece&longs;&longs;ary to make new Scowrings of the Chanel; <lb/>to the end, that the Water approaching (by wearing and carry­<lb/>ing away the Earth on both &longs;hores, might make a Bed &longs;ufficient <lb/>for its Body, the depth made for <emph type="italics"/>Panaro<emph.end type="italics"/> not &longs;erving the turn, as <lb/>I conceive; and if it &longs;hould &longs;uffice, when could the people of <lb/><emph type="italics"/>Ferrara<emph.end type="italics"/> hope to be re-imbur&longs;ed and &longs;atisfied for the charge <lb/>thereof?</s></p><p type="main"> <s>Fourthly, it &longs;erves as an Argument with me, to &longs;ee that the <lb/>very individual per&longs;ons concerned in the Remotion or Diver&longs;ion <lb/>of the &longs;aid Torrent, namely, the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/> do not incline unto it, <lb/>and that the whole City of <emph type="italics"/>Ferrara,<emph.end type="italics"/> even tho&longs;e very per&longs;ons who <lb/>at pre&longs;ent receive damage by it, cannot indure to hear thereof. <lb/></s> <s>The rea&longs;on that induceth the&longs;e la&longs;t named to be &longs;o aver&longs;e thereto, <lb/>is, either becau&longs;e that this undertaking will render the introducti­<lb/>on of the Water of <emph type="italics"/>Main-Po<emph.end type="italics"/> more difficult; or becau&longs;e they fear <lb/>the danger thereof; The others decline the Project, either for <lb/>that they know that <emph type="italics"/>Reno<emph.end type="italics"/> cannot long continue in that Cour&longs;e, <lb/>or becau&longs;e they fear that it is too much expo&longs;ed to tho&longs;e mens re­<lb/>vengeful Cutting of it who do not de&longs;ire it &longs;hould; and if a <lb/>man have any other wayes, he ought, in my opinion, to forbear <lb/>that, which to &longs;uch as &longs;tand in need of its Removal, is le&longs;&longs;e &longs;ati&longs;­<lb/>factory, and to &longs;uch as oppo&longs;e it, more prejudicial.</s></p><p type="main"> <s>To conclude, I exceedingly honour the judgment of Cardinal <lb/><emph type="italics"/>Capponi,<emph.end type="italics"/> who having to his Natural Ability and Prudence added <lb/>a particular Study, Ob&longs;ervation, and Experience of the&longs;e Wa­<lb/>ters for the &longs;pace of three years together, doth not think that <lb/><emph type="italics"/>Reno<emph.end type="italics"/> can go by <emph type="italics"/>Volana<emph.end type="italics"/>; to which agreeth the opinion of Car­<lb/>dinal S. <emph type="italics"/>Marcello,<emph.end type="italics"/> Legate of this City, of whom, for his exqui­<lb/>&longs;ite under&longs;tanding, we ought to make great account. </s> <s>But if e­<lb/>ver this &longs;hould be re&longs;olved on, it would be materially nece&longs;&longs;ary <lb/>to unite the Quick and Running Waters of the little Chanel of <lb/><emph type="italics"/>Cento,<emph.end type="italics"/> of the Chanel <emph type="italics"/>Navilio,<emph.end type="italics"/> of <emph type="italics"/>Guazzaloca,<emph.end type="italics"/> and at its very <lb/>beginning tho&longs;e of <emph type="italics"/>Dardagna,<emph.end type="italics"/> which at pre&longs;ent, is one of the <lb/>Springs or Heads of <emph type="italics"/>Panaro,<emph.end type="italics"/> that &longs;o they might a&longs;&longs;i&longs;t it in carry­<lb/>ing its Sand, and the matter of its Muddine&longs;s into the Sea; and <lb/>then there would not fail to be a greater evacuation and &longs;cowr­<lb/>ing; but withall the Proprietors in the I&longs;let of <emph type="italics"/>San Giorgio<emph.end type="italics"/> and <lb/>of <emph type="italics"/>Ferrara<emph.end type="italics"/> mu&longs;t prepare them&longs;elves to indure the inconveniences <lb/>of Purlings or Sewings of the Water from the River thorow <lb/>the Boggy Ground thereabouts.</s></p><p type="main"> <s>I &longs;hould more ea&longs;ily incline therefore to carry it into <emph type="italics"/>Main-Po<emph.end type="italics"/><lb/>at <emph type="italics"/>Stellata,<emph.end type="italics"/> for the Rea&longs;ons that Cardinal <emph type="italics"/>Capponi<emph.end type="italics"/> mo&longs;t ingeni­<lb/>ou&longs;ly enumerates in a &longs;hort, but well-grounded Tract of his: not <pb xlink:href="068/01/121.jpg" pagenum="107"/>becau&longs;e that indeed it would not both by Purlings and by Brea­<lb/>ches occa&longs;ion &longs;ome inconvenience; e&longs;pecially, in the beginning: <lb/>but becau&longs;e I hold this for the incomodities of it, to be a far le&longs;s <lb/>evil than any of the re&longs;t; and becau&longs;e that by this means there is <lb/>no occa&longs;ion given to them of <emph type="italics"/>Ferrara,<emph.end type="italics"/> to explain that they are <lb/>deprived of the hope of ever &longs;eeing the P<emph type="italics"/>o<emph.end type="italics"/> again under the Walls <lb/>of their City: To whom, where it may be done, it is but rea&longs;on <lb/>that &longs;atisfaction &longs;hould be given.</s></p><p type="main"> <s>It is certain that P<emph type="italics"/>o<emph.end type="italics"/> was placed by Nature in the mid&longs;t of this <lb/>great Valley made by the <emph type="italics"/>Appennine<emph.end type="italics"/> Hills, and by the Alps, to <lb/>carry, as the Ma&longs;ter-Drain to the Sea, that is the grand receptacle <lb/>of all Waters; tho&longs;e particular &longs;treams which de&longs;cend from <lb/>them.</s></p><p type="main"> <s>That the <emph type="italics"/>Reno<emph.end type="italics"/> by all Geographers, <emph type="italics"/>Strabo, Pliuy, Solimas, <lb/>Mella,<emph.end type="italics"/> and others is enumerated among the Rivers that fall into <lb/>the &longs;aid P<emph type="italics"/>o.<emph.end type="italics"/></s></p><p type="main"> <s>That although P<emph type="italics"/>o<emph.end type="italics"/> &longs;hould of it &longs;elf change its cour&longs;e, yet would <lb/><emph type="italics"/>Reno<emph.end type="italics"/> go to look it out, if the works erected by humane ind u&longs;try <lb/>did not ob&longs;truct its pa&longs;&longs;age; &longs;o that it neither is, nor ought to <lb/>&longs;eem &longs;trange, if one for the greater common good &longs;hould turn it <lb/>into the &longs;ame.</s></p><p type="main"> <s>Now at <emph type="italics"/>Stellata<emph.end type="italics"/> it may go &longs;everal waies into P<emph type="italics"/>o,<emph.end type="italics"/> as appeareth <lb/>by the levels that were taken by my Order; of all which I &longs;hould <lb/>be&longs;t like the turning of it to <emph type="italics"/>la Botta de' Ghi&longs;lieri,<emph.end type="italics"/> carrying it <lb/>above <emph type="italics"/>Bondeno<emph.end type="italics"/> to the Church of <emph type="italics"/>Gambarone,<emph.end type="italics"/> or a little higher or <lb/>lower, as &longs;hall be judged lea&longs;t prejudicial, when it cometh to the <lb/>execution, and this for two principal rea&longs;ons: The one becau&longs;e <lb/>that then it will run along by the confines of the Church P tri­<lb/>mony, without &longs;eparating <emph type="italics"/>Ferrara<emph.end type="italics"/> from the re&longs;t of it; The other <lb/>is, Becau&longs;e the Line is &longs;horter, and con&longs;equently the fall greater; <lb/>for that in a &longs;pace of ten miles and one third, it falleth twenty &longs;ix <lb/>feet, more by much than is required by Arti&longs;ts; and would go <lb/>by places where it could do but little hurt, notwith&longs;tanding that <lb/>the per&longs;ons interre&longs;&longs;ed &longs;tudy to amplifie it incredibly.</s></p><p type="main"> <s>On the contrary, there are but onely two objections that are <lb/>worthy to be examined; One, That the Drains and Ditches of <lb/>S. <emph type="italics"/>Bianca,<emph.end type="italics"/> of the Chanel of <emph type="italics"/>Cento,<emph.end type="italics"/> and of <emph type="italics"/>Burana,<emph.end type="italics"/> and all tho&longs;e <lb/>others that enter into P<emph type="italics"/>o,<emph.end type="italics"/> do hinder this diver&longs;ion of <emph type="italics"/>Reno,<emph.end type="italics"/> by the <lb/>encrea&longs;ing of the waters in the P<emph type="italics"/>o.<emph.end type="italics"/> The other is that P<emph type="italics"/>o<emph.end type="italics"/> ri&longs;ing <lb/>about the Tran&longs;om of the <emph type="italics"/>Pila&longs;ter<emph.end type="italics"/>-Sluice, very near 20 feet, the <lb/><emph type="italics"/>Reno<emph.end type="italics"/> would have no fall into the &longs;ame; whereupon it would ri&longs;e <lb/>to a terrible height, at which it would not be po&longs;&longs;ible to make, or <lb/>keep the Banks made, &longs;o that it would break out and drown <lb/>the Meadowes, and cau&longs;e mi&longs;chiefs, and damages un&longs;peakable <lb/>and irreparable; as is evident by the experiment made upon <pb xlink:href="068/01/122.jpg" pagenum="108"/><emph type="italics"/>Panaro,<emph.end type="italics"/> which being confined between Banks, that it might go <lb/>into P<emph type="italics"/>o,<emph.end type="italics"/> this not being neither in its greate&longs;t excre&longs;cen&longs;e, it broke <lb/>out into the territories of <emph type="italics"/>Final,<emph.end type="italics"/> and of <emph type="italics"/>Ferrara.<emph.end type="italics"/> And though <lb/>that might be done, it would thereupon en&longs;ue, that there being <lb/>let into the Chanel of P<emph type="italics"/>o,<emph.end type="italics"/> 2800, &longs;quare feet of water (for &longs;o much <lb/>we account tho&longs;e of <emph type="italics"/>Reno<emph.end type="italics"/> and <emph type="italics"/>Panaro,<emph.end type="italics"/> taken together in their <lb/>greate&longs;t heights) the &longs;uperficies of it would ri&longs;e at lea&longs;t four feet, <lb/>in&longs;omuch that either it would be requi&longs;ite to rai&longs;e its Banks all the <lb/>way unto the Sea, to the &longs;ame height, which the trea&longs;ures of the <lb/><emph type="italics"/>Indies<emph.end type="italics"/> would not &longs;uffice to effect; or el&longs;e there would be a nece&longs;­<lb/>&longs;ity of enduring exce&longs;&longs;ive Breaches. </s> <s>To the&longs;e two Heads are the <lb/>Arguments reduced, which are largely amplified again&longs;t our opi­<lb/>nion; and I &longs;hall an&longs;wer fir&longs;t to the la&longs;t, as mo&longs;t material.</s></p><p type="main"> <s>I &longs;ay therefore, that there are three ca&longs;es to be con&longs;idered: <lb/>Fir&longs;t, P<emph type="italics"/>o<emph.end type="italics"/> high, and <emph type="italics"/>Reno<emph.end type="italics"/> low. </s> <s>Secondly, <emph type="italics"/>Reno<emph.end type="italics"/> high, and P<emph type="italics"/>o<emph.end type="italics"/><lb/>low. </s> <s>Thirdly, <emph type="italics"/>Reno<emph.end type="italics"/> and P<emph type="italics"/>o<emph.end type="italics"/> both high together.</s></p><p type="main"> <s>As to the fir&longs;t and &longs;econd, there is no difficulty in them; for if <lb/>P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall not be at its greate&longs;t height, <emph type="italics"/>Reno<emph.end type="italics"/> &longs;hall ever have a fall <lb/>into it, and there &longs;hall need no humane Artifice about the Banks: <lb/>And if <emph type="italics"/>Reno<emph.end type="italics"/> &longs;hall be low, P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall regurgitate and flow up into <lb/>the Chanel of it; and al&longs;o from thence no inconvenience &longs;hall <lb/>follow. </s> <s>The third remains, from which there are expected ma­<lb/>ny mi&longs;chiefs; but it is a mo&longs;t undoubted truth, that the excre&longs;cen­<lb/>cies of <emph type="italics"/>Reno,<emph.end type="italics"/> as coming from the adjacent <emph type="italics"/>Appennines<emph.end type="italics"/> and Rains, <lb/>are to continue but &longs;even, or eight hours at mo&longs;t, and &longs;o would <lb/>never, or very rarely happen to be at the &longs;ame time with tho&longs;e of <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> cau&longs;ed by the melting of the &longs;nowes of the Alps, at lea&longs;t 400. <lb/>miles di&longs;tance from thence. </s> <s>But becau&longs;e it &longs;ometimes may hap­<lb/>pen, I reply, that when it cometh to pa&longs;s, <emph type="italics"/>Reno<emph.end type="italics"/> &longs;hall not go into <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> but it &longs;hall have allowed it one or two Vents; namely, into <lb/>the Chanel of <emph type="italics"/>Ferrara,<emph.end type="italics"/> as it hath ever had; and into <emph type="italics"/>Sanmartina,<emph.end type="italics"/><lb/>where it runneth at pre&longs;ent, and wherewith there is no doubt, but <lb/>that the per&longs;ons concerned will be well plea&longs;ed, it being a great <lb/>benefit to them, to have the water over-flow their grounds once <lb/>every four or five years, in&longs;tead of &longs;eeing it anoy them continu­<lb/>ally. </s> <s>Yea, the Vent may be regulated, re&longs;erving for it the Cha­<lb/>nel in which <emph type="italics"/>Reno<emph.end type="italics"/> at pre&longs;ent runneth; and in&longs;tead of turning it <lb/>by a Dam at <emph type="italics"/>la Betta de Chi&longs;lieri,<emph.end type="italics"/> perhaps, to turn it by help of <lb/>&longs;trong Sluices, that may upon all occa&longs;ions be opened and &longs;hut. <lb/></s> <s>And for my part, I do not que&longs;tion but that the Proprietors <lb/>them&longs;elves in <emph type="italics"/>Sanmartina<emph.end type="italics"/> would make a Chanel for it; which <lb/>receiving, and confining it in the time of the Vents, might carry <lb/>the Sand into the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro:<emph.end type="italics"/> Nor need there thence be fear­<lb/>ed any &longs;toppage by Mud and Sand, &longs;ince that it is &longs;uppo&longs;ed that <lb/>there will but very &longs;eldom be any nece&longs;&longs;ity of u&longs;ing it; &longs;o that <pb xlink:href="068/01/123.jpg" pagenum="109"/>time would be allowed, upon occa&longs;ion, to &longs;cowr and clean&longs;e <lb/>it.</s></p><p type="main"> <s>And in this manner all tho&longs;e Prodigies vani&longs;h that are rai&longs;ed <lb/>with &longs;o much fear from the enterance of the Water of <emph type="italics"/>Reno<emph.end type="italics"/><lb/>&longs;welled into P<emph type="italics"/>o,<emph.end type="italics"/> when it is high, to which there needeth no other <lb/>an&longs;wer; yet neverthele&longs;&longs;e we do not take that quantity of Wa­<lb/>ter, that is carried by <emph type="italics"/>Reno,<emph.end type="italics"/> and by <emph type="italics"/>Panaro,<emph.end type="italics"/> to be &longs;o great as is affir­<lb/>med: For that P. D. <emph type="italics"/>Benedetto Ca&longs;telli<emph.end type="italics"/> hath no le&longs;&longs;e accutely <lb/>than accurately ob&longs;erved the mea&longs;ures of this kind, noting that <lb/>the breadth and depth of a River is not enough to re&longs;olve the <lb/>que&longs;tion truly, but that there is re&longs;pect to be had to the velocity <lb/>of the Waters, and the term of time, things hitherto not con&longs;i­<lb/>dered by the Skilful in the&longs;e affairs; and therefore they are not <lb/>able to &longs;ay what quantity of Waters the &longs;aid Rivers carry, nor <lb/>to conclude of the ri&longs;ings that will follow thereupon. </s> <s>Nay, it <lb/>is mo&longs;t certain, that if all the Rivers that fall into <emph type="italics"/>Po,<emph.end type="italics"/> which are <lb/>above thirty, &longs;hould ri&longs;e at the rate that the&longs;e compute <emph type="italics"/>Reno<emph.end type="italics"/> to <lb/>do, an hundred feet of Banks would not &longs;uffice, and yet they <lb/>have far fewer: So that this confirmes the Rule of R. P. D. <emph type="italics"/>Bene­<lb/>detto,<emph.end type="italics"/> namely, that the proportion of the height of the Water <lb/>of <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno<emph.end type="italics"/> to the height of the Water of <emph type="italics"/>Reno<emph.end type="italics"/> in P<emph type="italics"/>o,<emph.end type="italics"/> is <lb/>compounded of the proportion of the breadth of the Chanel of <lb/><emph type="italics"/>Po<emph.end type="italics"/> to that of <emph type="italics"/>Reno,<emph.end type="italics"/> and of the velocity of the Water of <emph type="italics"/>Reno<emph.end type="italics"/><lb/>in <emph type="italics"/>Po<emph.end type="italics"/> to the velccity of the Water of <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno<emph.end type="italics"/>; a manife&longs;t <lb/>argument that there cannot in it, by this new augmentation of <lb/>Waters follow any alteration that nece&longs;&longs;itates the rai&longs;ing of its <lb/>Banks, as appeareth by the example of <emph type="italics"/>Panaro,<emph.end type="italics"/> which hath been <lb/>&longs;o far from &longs;welling P<emph type="italics"/>o,<emph.end type="italics"/> that it hath rather a&longs;&longs;waged it, for it hath <lb/>carried away many Shelfs and many I&longs;lets that had grown in its <lb/>Bed, for want of Waters &longs;ufficient to bear away the matter of <lb/>Land-floods in &longs;o broad a Chanel; and as is learnt by the trial <lb/>made by us in <emph type="italics"/>Panaro<emph.end type="italics"/> with the Water of <emph type="italics"/>Burana<emph.end type="italics"/>; for erecting <lb/>in the River &longs;tanding marks, and &longs;hutting the &longs;aid Sluice, we could <lb/>&longs;ee no &longs;en&longs;ible abatement, nor much le&longs;s after we had opened it <lb/>&longs;en&longs;ible increa&longs;ment; by which we judge that the &longs;ame is to &longs;uc­<lb/>ceed to P<emph type="italics"/>o,<emph.end type="italics"/> by letting in of <emph type="italics"/>Reno, Burana<emph.end type="italics"/> having greater pro­<lb/>portion to <emph type="italics"/>Panaro<emph.end type="italics"/> than <emph type="italics"/>Reno<emph.end type="italics"/> to P<emph type="italics"/>o,<emph.end type="italics"/> con&longs;idering the &longs;tate of tho&longs;e <lb/>Rivers in which the Ob&longs;ervation was made. </s> <s>So that there is no <lb/>longer any occa&longs;ion for tho&longs;e great rai&longs;ings of Banks, and the <lb/>danger of the ruptures as well of <emph type="italics"/>Reno<emph.end type="italics"/> as of P<emph type="italics"/>o<emph.end type="italics"/> do vani&longs;h, as al­<lb/>&longs;o the fear le&longs;t that the Sluices which empty into P<emph type="italics"/>o<emph.end type="italics"/> &longs;hould re­<lb/>ceive ob&longs;truction: which if they &longs;hould, yet it would be over in <lb/>a few hours. </s> <s>And as to the Breaches of <emph type="italics"/>Panaro<emph.end type="italics"/> which happened <lb/>in 1623. I know not why, &longs;eeing that it is confe&longs;&longs;ed that the P<emph type="italics"/>o<emph.end type="italics"/><lb/>was not, at that time, at its height, one &longs;hould rather charge it <pb xlink:href="068/01/124.jpg" pagenum="110"/>with the crime, than quit it thereof. </s> <s>The truth is, that the <lb/>Bank was not made of proof, &longs;ince that the &longs;ame now continu­<lb/>eth whole and good, and <emph type="italics"/>Panaro<emph.end type="italics"/> doth not break out; nay, there <lb/>was, when it brake more than a foot and half of its Banks above <lb/>the Water, and to &longs;pare; but it broke thorow by a Moles wor­<lb/>king, or by the hole of a Water-Rat, or &longs;ome &longs;uch vermine; <lb/>and by occa&longs;ion of the badne&longs;s of the &longs;aid Banks, as I finde by <lb/>the te&longs;timony of &longs;ome witne&longs;&longs;es examined by my command, that <lb/>I might know the truth thereof. </s> <s>Nor can I here forbear to &longs;ay, <lb/>that it would be better, if in &longs;uch matters men were more candid <lb/>and &longs;incere. </s> <s>But to &longs;ecure our &longs;elves neverthele&longs;&longs;e, to the ut­<lb/>mo&longs;t of our power, from &longs;uch like Breaches which may happen <lb/>at the fir&longs;t, by rea&longs;on of the newne&longs;&longs;e of the Banks, I pre&longs;uppo&longs;e <lb/>that from P<emph type="italics"/>o<emph.end type="italics"/> unto the place whence <emph type="italics"/>Reno<emph.end type="italics"/> is cut, there ought to <lb/>be a high and thick Fence made with its Banks, &longs;o that there <lb/>would be no cau&longs;e to fear any what&longs;oever acce&longs;&longs;ions of Water, <lb/>although that concurrence of three Rivers, which was by &longs;ome <lb/>more ingeniou&longs;ly aggravated than faithfully &longs;tated by that which <lb/>was &longs;aid above were true; to whom I think not my &longs;elf bound <lb/>to make any farther reply, neither to tho&longs;e who &longs;ay that <emph type="italics"/>Po<emph.end type="italics"/> will <lb/>a&longs;cend upwards into <emph type="italics"/>Reno,<emph.end type="italics"/> &longs;ince that the&longs;e are the &longs;ame per&longs;ons <lb/>who would introduce a &longs;mall branch of the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> into the <lb/>Chanel of <emph type="italics"/>Ferrara,<emph.end type="italics"/> that &longs;o it may conveigh to the Sea, not <emph type="italics"/>Reno<emph.end type="italics"/><lb/>onely, but al&longs;o all the other Brooks of which we complained; <lb/>and becau&longs;e that withal it is impo&longs;&longs;ible, that a River &longs;o capacious <lb/>as <emph type="italics"/>Po<emph.end type="italics"/> &longs;hould be incommoded by a Torrent, that, as I may &longs;ay, <lb/>hath no proportion to it.</s></p><p type="main"> <s>I come now to the bu&longs;ine&longs;&longs;e of the Ditches and Draines; and <lb/>as to the Conveyance of <emph type="italics"/>Burana,<emph.end type="italics"/> it hath heretofore been deba­<lb/>ted to turn it into <emph type="italics"/>Main-Po,<emph.end type="italics"/> &longs;o that in this ca&longs;e it will receive no <lb/>harm, and though it were not removed, yet would it by a Trench <lb/>under ground pur&longs;ue the cour&longs;e that it now holdeth, and al&longs;o <lb/>would be able to di&longs;-imbogue again into the &longs;aid new Chanel of <lb/><emph type="italics"/>Reno,<emph.end type="italics"/> which conforming to the &longs;uperficies of the Water of <emph type="italics"/>Po,<emph.end type="italics"/><lb/>would continue at a lower level than that which <emph type="italics"/>Panara<emph.end type="italics"/> had <lb/>when it came to <emph type="italics"/>Ferrara,<emph.end type="italics"/> into which <emph type="italics"/>Burana<emph.end type="italics"/> did neverthele&longs;&longs;e <lb/>empty it &longs;elf for &longs;ome time.</s></p><p type="main"> <s>The Conveyance or Drain of <emph type="italics"/>Santa Bianca,<emph.end type="italics"/> and the little <lb/>Chanel of <emph type="italics"/>Cento<emph.end type="italics"/> may al&longs;o empty them&longs;elves by two &longs;ubterranean <lb/>Trenches, without any prejudice where they run at pre&longs;ent, or <lb/>without any more works of that nature, they may be turned into <lb/>the &longs;aid new Chanel, although with &longs;omewhat more of incon­<lb/>venience; and withall, the Chanel of <emph type="italics"/>Ferrara,<emph.end type="italics"/> left dry, would <lb/>be a &longs;ufficient receptacle for any other Sewer or Drain what&longs;oe­<lb/>ver, that &longs;hould remain there.</s></p><pb xlink:href="068/01/125.jpg" pagenum="111"/><p type="main"> <s>All which Operations might be brought to perfection with <lb/>150. thou&longs;and Crowns, well and faithfully laid out; which &longs;umm <lb/>the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/> will not be unwilling to provide; be&longs;ides that tho&longs;e <lb/><emph type="italics"/>Ferrare&longs;i<emph.end type="italics"/> ought to contribute to it, who &longs;hall partake of the <lb/>benefit.</s></p><p type="main"> <s>Let me be permitted in this place to propo&longs;e a thing which I <lb/>have thought of, and which peradventure might occa&longs;ion two <lb/>benefits at once, although it be not wholly new. </s> <s>It was in the <lb/>time of <emph type="italics"/>Pope Paul<emph.end type="italics"/> V. propounded by one <emph type="italics"/>Cre&longs;cenzio<emph.end type="italics"/> an Ingi­<lb/>neer, to cut the <emph type="italics"/>Main-Po,<emph.end type="italics"/> above <emph type="italics"/>le Papozze<emph.end type="italics"/>; and having made a <lb/>&longs;ufficient evacuation to derive the water thereof into the P<emph type="italics"/>o<emph.end type="italics"/> of <lb/><emph type="italics"/>Adriano,<emph.end type="italics"/> and &longs;o to procure it to be Navigable, which was not at <lb/>that time effected, either by rea&longs;on of the oppo&longs;itions of tho&longs;e, <lb/>who&longs;e po&longs;&longs;e&longs;&longs;ions were to be cut thorow, or by rea&longs;on of the <lb/>great &longs;um of money that was nece&longs;&longs;ary for the effecting of it: But <lb/>in viewing tho&longs;e Rivers, we have ob&longs;erved, that the &longs;edge cutting <lb/>might ea&longs;ily be made below <emph type="italics"/>le Papozze,<emph.end type="italics"/> in digging thorow the <lb/>Bank called <emph type="italics"/>Santa Maria,<emph.end type="italics"/> & drawing a Trench of the bigne&longs;s that <lb/>skilful Arti&longs;ts &longs;hall judge meet unto the P<emph type="italics"/>o<emph.end type="italics"/> ^{*} of <emph type="italics"/>Ariano,<emph.end type="italics"/> below the <lb/><arrow.to.target n="marg982"></arrow.to.target><lb/><emph type="italics"/>Secche<emph.end type="italics"/> of the &longs;aid S. <emph type="italics"/>Maria<emph.end type="italics"/>; which as being a work of not <lb/>above 160. Perches in length, would be fini&longs;hed with onely <lb/>12000. Crowns.</s></p><p type="margin"> <s><margin.target id="marg982"></margin.target>* Of <emph type="italics"/>Adriano.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t; it is to be believed, that the waters running that way, <lb/>would not fail to open that Mouth into the Sea, which at pre­<lb/>&longs;ent is almo&longs;t choakt up by the Shelf of Sand, which the new <lb/>Mouth of <emph type="italics"/>Ponto Virro<emph.end type="italics"/> hath brought thither; and that it would <lb/>again bring into u&longs;e the Port <emph type="italics"/>Goro,<emph.end type="italics"/> and its Navigation.</s></p><p type="main"> <s>And haply experience might teach us, that the &longs;uperficies of <lb/>P<emph type="italics"/>o<emph.end type="italics"/> might come to fall by this a&longs;&longs;wagement of Water, &longs;o that the <lb/>acce&longs;&longs;ion of <emph type="italics"/>Reno<emph.end type="italics"/> would que&longs;tionle&longs;s make no ri&longs;ing in it: <lb/>Whereupon, if it &longs;hould &longs;o fall out, tho&longs;e Princes would have <lb/>no rea&longs;on to complain; who &longs;eem to que&longs;tion, le&longs;t by this new <lb/>acce&longs;&longs;ion of water into P<emph type="italics"/>o,<emph.end type="italics"/> the Sluices might be endangered. <lb/></s> <s>Which I thought not fit to omit to repre&longs;ent to your Lord&longs;hip; <lb/>not, that I propo&longs;e it to you as a thing ab&longs;olutely certain, but that <lb/>you might, if you &longs;o plea&longs;ed, lay it before per&longs;ons who&longs;e judge­<lb/>ments are approved in the&longs;e affairs.</s></p><p type="main"> <s>I return now from where I degre&longs;t, and affirm it as indubita­<lb/>ble, that <emph type="italics"/>Reno<emph.end type="italics"/> neither can, nor ought to continue longer where <lb/>it at this day is; and that it cannot go into any other place but <lb/>that, whither <emph type="italics"/>Cardinal Capponi<emph.end type="italics"/> de&longs;igned to carry it, and which <lb/>at pre&longs;ent plea&longs;eth me better than any other; or into <emph type="italics"/>Volana,<emph.end type="italics"/><lb/>whence it was taken away; the vigilance of Men being able to <lb/>obviate part of tho&longs;e mi&longs;chiefs, which it may do there.</s></p><p type="main"> <s>But from its Removal, be&longs;ides the alleviation of the harm <pb xlink:href="068/01/126.jpg" pagenum="112"/>which by it &longs;elf is cau&longs;ed, there would al&longs;o re&longs;ult the diminution <lb/>of that which is occa&longs;ioned by the other Brooks, to the right hand <lb/>of the <emph type="italics"/>Po<emph.end type="italics"/> of <emph type="italics"/>Argenta<emph.end type="italics"/>; fora&longs;much as the &longs;aid <emph type="italics"/>Po<emph.end type="italics"/> wanting all the <lb/>water of <emph type="italics"/>Reno,<emph.end type="italics"/> it would of nece&longs;&longs;ity come to ebb in &longs;uch man­<lb/>ner, that the Valleys would have a greater Fall into the &longs;ame, <lb/>and con&longs;equently it would take in, and &longs;wallow greater abun­<lb/>dance of water; and by this means the Ditches and Draines <lb/>of the Up-Lands would likewi&longs;e more ea&longs;ily Fall into them; e&longs;­<lb/>pecially if the &longs;couring of <emph type="italics"/>Zenzalino<emph.end type="italics"/> were brought to perfection, <lb/>by which the waters of <emph type="italics"/>Marrara<emph.end type="italics"/> would fall into <emph type="italics"/>Marmorta<emph.end type="italics"/>: And <lb/>if al&longs;o that of <emph type="italics"/>Ba&longs;tia<emph.end type="italics"/> were enlarged, and fini&longs;hed, by which there <lb/>might enter as much water into the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> as is taken <lb/>from it by the removal of <emph type="italics"/>Reno<emph.end type="italics"/>; although that by that meanes <lb/>the water of the Valleys would a&longs;&longs;wage double: Nor would the <lb/>people of <emph type="italics"/>Argenta,<emph.end type="italics"/> the I&longs;les of S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> and <emph type="italics"/>Comacchio<emph.end type="italics"/> have any <lb/>cau&longs;e to complain; for that there would not be given to them <lb/>more water than was taken away: Nay &longs;ometimes whereas they <lb/>had Muddy waters, they would have clear; nor need they to fear <lb/>any ri&longs;ing: And furthermore, by this means a very great quan­<lb/>tity of ground would be re&longs;tored to culture; For the effecting of <lb/>all which, the &longs;umm of 50. thou&longs;and Crowns would go very far, <lb/>and would &longs;erve the turn at pre&longs;ent touching tho&longs;e Brooks, car­<lb/>rying them a little farther in the mean time, to fill up the greater <lb/>cavities of the Valleys, that we might not enter upon a va&longs;ter <lb/>and harder work, that would bring with it the difficulties of other <lb/>operations, and &longs;o would hinder the benefit which the&longs;e people <lb/>expect from the paternal charity of His Holine&longs;s.</s></p><pb xlink:href="068/01/127.jpg" pagenum="113"/><p type="head"> <s>TO <lb/>The Right Honourable, <lb/>MONSIGNORE <lb/>D. </s> <s>Ferrante Ce&longs;arini.</s></p><p type="main"> <s>My Treati&longs;e of the MENSURATION of RUN­<lb/>NING WATERS, Right Honourable, and <lb/>mo&longs;t Noble Sir, hath not a greater Preroga­<lb/>tive than its having been the production of the <lb/>command of Pope <emph type="italics"/>Vrban<emph.end type="italics"/> VIII. when His Ho­<lb/>line&longs;s was plea&longs;ed to enjoyn me to go with <lb/><emph type="italics"/>Mon&longs;ignore Cor&longs;ini,<emph.end type="italics"/> in the Vi&longs;itation that was <lb/>impo&longs;ed upon him in the year 1625. of the Waters of <emph type="italics"/>Ferrara, <lb/>Bologna, Romagna,<emph.end type="italics"/> and <emph type="italics"/>Romagnola<emph.end type="italics"/>; for that, on that occa&longs;ion <lb/>applying my whole Study to my &longs;ervice and duty, I publi&longs;hed in <lb/>that Treati&longs;e &longs;ome particulars till then not rightly under&longs;tood and <lb/>con&longs;idered (that I knew) by any one; although they be in them­<lb/>&longs;elves mo&longs;t important, and of extraordinary con&longs;equence. </s> <s>Yet <lb/>I mu&longs;t render thanks to Your Lord&longs;hip for the honour you have <lb/>done to that my Tract; but wi&longs;h withal, that your E&longs;teem of it <lb/>may not prejudice the univer&longs;al E&longs;teem that the World hath of <lb/>Your Honours mo&longs;t refined judgement.</s></p><p type="main"> <s>As to that Point which I touch upon in the Conclu&longs;ion, name­<lb/>ly, That the con&longs;ideration of the Velocity of Running Water &longs;up­<lb/>plyeth the con&longs;ideration of the ^{*} Length omitted in the common <lb/><arrow.to.target n="marg983"></arrow.to.target><lb/>way of mea&longs;uring Running Waters; Your Lord&longs;hip having com­<lb/>manded me that in favour of <emph type="italics"/>Practi&longs;e,<emph.end type="italics"/> and for the perfect di&longs;co­<lb/>very of the di&longs;order that commonly happeneth now adayes in <lb/>the di&longs;tribution of the Waters of Fountains, I &longs;hould demon­<lb/>&longs;trate that the knowledge of the Velocity &longs;erveth for the finding <lb/>of the Length: I have thought fit to &longs;atisfie your Command by <lb/>relating a Fable; which, if I do not deceive my &longs;elf, will make <lb/>out to us the truth thereof; in&longs;omuch that the re&longs;t of my Treati&longs;e <lb/>&longs;hall thereby al&longs;o become more manife&longs;t and intelligible, even to <pb xlink:href="068/01/128.jpg" pagenum="432"/>tho&longs;e who finde therein &longs;ome kinde of ob&longs;curity.</s></p><p type="margin"> <s><margin.target id="marg983"></margin.target>* Larghezza, but <lb/>mi&longs;printed.</s></p><p type="main"> <s>In the dayes of yore, before that the admirable Art of Wea­<lb/>ving was in u&longs;e, there was found in <emph type="italics"/>Per&longs;ia<emph.end type="italics"/> a va&longs;tand unvaluable <lb/>Trea&longs;ure, which con&longs;i&longs;ted in an huge multitude of pieces of Er­<lb/>me&longs;in, or Damask, I know not whether; which, as I take it, <lb/>amounted to near two thou&longs;and pieces; which were of &longs;uch a <lb/>nature, that though their Breadth and Thickne&longs;s were finite and <lb/>determinate, as they u&longs;e to be at this day; yet neverthele&longs;s, their <lb/>Length was in a certain &longs;en&longs;e infinite, for that tho&longs;e two thou&longs;and <lb/>pieces, day and night without cea&longs;ing, i&longs;&longs;ued out with their ends <lb/>at &longs;uch a rate, that of each piece there i&longs;&longs;ued 100. Ells a day, from <lb/>a deep and dark Cave, con&longs;ecrated by the Super&longs;tition of tho&longs;e <lb/>people, to the fabulous <emph type="italics"/>Arachne.<emph.end type="italics"/> In tho&longs;e innocent and early <lb/>times (I take it to have been, in that &longs;o much applauded and <lb/>de&longs;ired Golden age) it was left to the liberty of any one, to cut <lb/>off of tho&longs;e pieces what quantity they plea&longs;ed without any diffi­<lb/>culty: But that felicity decaying and degenerating, which was <lb/>altogether ignorant of <emph type="italics"/>Meum<emph.end type="italics"/> and <emph type="italics"/>Tuum<emph.end type="italics"/>; terms certainly mo&longs;t <lb/>pernicious, the Original of all evils, and cau&longs;e of all di&longs;cords; <lb/>there were by tho&longs;e people &longs;trong and vigilant Guards placed <lb/>upon the Cave, who re&longs;olved to make merchandize of the Stuffes; <lb/>and in this manner they began to &longs;et a price upon that ine&longs;tima­<lb/>ble Trea&longs;ure, &longs;elling the propriety in tho&longs;e pieces to divers Mer­<lb/>chants; to &longs;ome they &longs;old a right in one, to &longs;ome in two, and to <lb/>&longs;ome in more. </s> <s>But that which was the wor&longs;t of all, There was <lb/>found out by the in&longs;atiable avarice of the&longs;e men crafty inventions <lb/>to deceive the Merchants al&longs;o; who came to buy the afore&longs;aid <lb/>commodity, and to make them&longs;elves Ma&longs;ters, &longs;ome of one <lb/>&longs;ome of two, and &longs;ome of more ends of tho&longs;e pieces of &longs;tuff; <lb/>and in particular, there were certain ingenuous Machines placed <lb/>in the more &longs;ecret places of the Cave, with which at the plea&longs;ure <lb/>of the Guards, they did retard the velocity of tho&longs;e Stuffs, in <lb/>their i&longs;&longs;uing out of the Cave; in&longs;omuch, that he who ought to have <lb/>had 100. Ells of Stuff in a day, had not above 50, and he who <lb/>&longs;hould have had 400, enjoyed the benefit of 50. onely; and &longs;o all <lb/>the re&longs;t were defrauded of their Rights, the &longs;urplu&longs;age being &longs;old, <lb/>appropriated, and &longs;hared at the will of the corrupt Officers: So <lb/>that the bu&longs;ine&longs;s was without all order or ju&longs;tice, in&longs;omuch that <lb/>the Godde&longs;s <emph type="italics"/>Arachne<emph.end type="italics"/> being di&longs;plea&longs;ed at tho&longs;e people, deprived <lb/>every one of their benefit, and with a dreadful Earthquake for <lb/>ever clo&longs;ing the mouth of the Cave, in puni&longs;hment of &longs;o much <lb/>impiety and malice: Nor did it avail them to excu&longs;e them&longs;elves, <lb/>by &longs;aying that they allowed the Buyer the Breadth and Thick­<lb/>ne&longs;s bargained for; and that of the Length, which was infinite, <pb xlink:href="068/01/129.jpg" pagenum="115"/>there could no account be kept: For the wi&longs;e and prudent <lb/>Prie&longs;t of the Sacred <emph type="italics"/>Grotto<emph.end type="italics"/> an&longs;wered, That the deceit lay in the <lb/>length, which they were defrauded of, in that the velocity of the <lb/>ftuffe was retarded, as it i&longs;&longs;ued out of the Cave: and although <lb/>the total length of the Piece was infinite, for that it never cea­<lb/>&longs;ed coming forth, and &longs;o was not to be computed; yet never­<lb/>thele&longs;s its length con&longs;idered, part by part, as it came out of the <lb/>Cave, and was bargained for, continued &longs;till finite, and might <lb/>be one while greater, and another while le&longs;&longs;er, according as the <lb/>Piece was con&longs;tituted in greater or le&longs;&longs;er velocity; and he added <lb/>withall, that exact Ju&longs;tice required, that when they &longs;old a piece <lb/>of &longs;tuff, and the propriety or dominion therein, they ought not <lb/>only to have a&longs;certained the breadth and thickne&longs;&longs;e of the Piece, <lb/>but al&longs;o to have determined the length, determining its ve­<lb/>locity.</s></p><p type="main"> <s>The &longs;ame di&longs;order and confu&longs;ion, that was repre&longs;ented in the <lb/>Fable, doth come to pa&longs;&longs;e in the Hi&longs;tory of the Di&longs;tribution of <lb/>the Waters of Conduits and Fountains, &longs;eeing that they are &longs;old <lb/>and bought, having regard only to the two Dimen&longs;ions, I mean <lb/>of Breadth and Height of the Mouth that di&longs;chargeth the Wa­<lb/>ter; and to remedy &longs;uch an inconvenience, it is nece&longs;&longs;ary to de­<lb/>termine the length in the velocity; for never &longs;hall we be able to <lb/>make a gue&longs;&longs;e at the quantity of the Body of Running Water, <lb/>with the two Dimen&longs;ions only of Breadth and Height, without <lb/>Length.</s></p><p type="main"> <s>And to the end, that the whole bu&longs;ine&longs;s may be reduced <lb/>to a mo&longs;t ea&longs;ie practice, by which the waters of Aqueducts <lb/>may be bought and &longs;old ju&longs;tly, and with mea&longs;ures alwayes ex­<lb/>act and con&longs;tant.</s></p><p type="main"> <s>Fir&longs;t, the quantity of the Water ought diligently to be exa­<lb/>mined, which the whole principal ^{*} Pipe di&longs;chargeth in a time <lb/>certain, as for in&longs;tance, in an hour, in half an hour, or in a le&longs;&longs;e <lb/>interval of time, (for knowing which I have a mo&longs;t exact and <lb/>ea&longs;ie Rule) and finding that the whole principal pipe di&longs;char­<lb/>geth <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> a thou&longs;and Tuns of Water in the &longs;pace of one or <lb/>more hours, in &longs;elling of this water, it ought not to be uttered by <lb/>the ordinary and fal&longs;e mea&longs;ure, but the di&longs;tribution is to be <lb/>made with agreement to give and maintain to the buyer ten or <lb/>twenty, or a greater number of Tuns, as the bargain &longs;hall be <lb/>made, in the &longs;pace of an hour, or of &longs;ome other &longs;et and deter­<lb/>minate time. </s> <s>And here I adde, that if I were to undertake to <lb/>make &longs;uch an adju&longs;tment, I would make u&longs;e of a way to divide <lb/>and mea&longs;ure the time with &longs;uch accuratene&longs;&longs;e, that the &longs;pace of <lb/>an hour &longs;hould be divided into four, &longs;ix, or eight thou&longs;and parts <pb xlink:href="068/01/130.jpg" pagenum="116"/>without the lea&longs;t errour; which Rule was taught me by my <lb/>Ma&longs;ter <emph type="italics"/>Sign. </s> <s>Galilæo Galilæi,<emph.end type="italics"/> Chief Philo&longs;opher to the mo&longs;t Se­<lb/>rene <emph type="italics"/>Grand Duke<emph.end type="italics"/> of <emph type="italics"/>Tu&longs;cany.<emph.end type="italics"/> And this way will &longs;erve ea&longs;ily and <lb/>admirably to our purpo&longs;e and occa&longs;ion; &longs;o that we &longs;hall <lb/>thereby be able to know how many Quarts of Water an A­<lb/>queduct will di&longs;charge in a given time of hours, moneths, or <lb/>years. </s> <s>And in this manner we may con&longs;titute a Cock that &longs;hall <lb/>di&longs;charge a certain and determinate quantity of water in a time <lb/>given.</s></p><p type="main"> <s>And becau&longs;e daily experience &longs;hews us, that the Springs of A­<lb/>queducts do not maintain them alwayes equally high, and full <lb/>of Water, but that &longs;ometimes they increa&longs;e, and &longs;ometimes de­<lb/>crea&longs;e, which accident might po&longs;&longs;ibly procure &longs;ome difficulty in <lb/>our di&longs;tribution: Therefore, to the end that all manner of &longs;cru­<lb/>ple may be removed, I conceive that it would be convenient to <lb/>provide a Ci&longs;tern, according to the occa&longs;ion, into which there <lb/>might alwayes fall one certain quantity of water, which &longs;hould <lb/>not be greater than that which the principal pipe di&longs;chargeth in <lb/>times of drought, when the Springs are bare of water, that &longs;o in <lb/>this Ci&longs;tern the water might alwayes keep at one con&longs;tant height. <lb/></s> <s>Then to the Ci&longs;tern &longs;o prepared we are to fa&longs;ten the Cocks of <lb/>particular per&longs;ons, to whom the Water is &longs;old by the Reverend <lb/>Apo&longs;tolique Chamber, according to what hath been ob&longs;erved <lb/>before; and that quantity of Water which remaineth over and <lb/>above, is to be di&longs;charged into another Ci&longs;tern, in which the <lb/>Cocks of the Waters for publick &longs;ervices, and of tho&longs;e which <lb/>people buy upon particular occa&longs;ions are to be placed. </s> <s>And <lb/>when the bu&longs;ine&longs;&longs;e &longs;hall have been brought to this pa&longs;&longs;e, there <lb/>will likewi&longs;e a remedy be found to the &longs;o many di&longs;orders that <lb/>continually happen; of which, for brevity &longs;ake, I will in&longs;tance <lb/>in but four only, which concern both publique and private bene­<lb/>fit, as being, in my judgment, the mo&longs;t enormous and intole­<lb/>rable.</s></p><p type="main"> <s>The fir&longs;t inconvenience is, that in the common way of mea&longs;u­<lb/>ring, di&longs;pen&longs;ing, and &longs;elling the Waters of Aqueducts, it is not <lb/>under&longs;tood, neither by the Buyer nor Seller, what the quantity <lb/>truly is that is bought and &longs;old; nor could I ever meet with any <lb/>either Engineer or Architect, or Arti&longs;t, or other that was able to <lb/>decypher to me, what one, or two, or ten inches of water was. <lb/></s> <s>But by our above declared Rule, for di&longs;pen&longs;ing the Waters of <lb/>Aqueducts we may very ea&longs;ily know the true quantity of Water <lb/>that is bought or &longs;old, as that it is &longs;o many Tuns an hour, &longs;o ma­<lb/>ny a day, &longs;o many in a year, &c.</s></p><p type="main"> <s>The &longs;econd di&longs;order that happeneth, at pre&longs;ent, in the di&longs;tri­<pb xlink:href="068/01/131.jpg" pagenum="117"/>bution of Aqueducts is, that as the bu&longs;ine&longs;&longs;e is now governed, it <lb/>lieth in the power of a &longs;ordid Ma&longs;on to take unju&longs;tly from one, <lb/>and give unde&longs;ervedly to another more or le&longs;&longs;e Water than be­<lb/>longeth to them of right: And I have &longs;een it done, of my <lb/>own experience. </s> <s>But in our way of mea&longs;uring and di&longs;tri­<lb/>buting Waters, there can no fraud be committed; and put­<lb/>ting the ca&longs;e that they &longs;hould be committed, its an ea&longs;ie mat­<lb/>ter to know it, and amend it, by repairing to the Tribunal <lb/>appointed.</s></p><p type="main"> <s>Thirdly, it happens very often, (and we have examples there­<lb/>of both antient and modern) that in di&longs;pen&longs;ing the Water after <lb/>the common and vulgar way; there is &longs;ometimes more Water di&longs;­<lb/>pended than there is in the Regi&longs;ter, in which there will be regi­<lb/>&longs;tred, as they &longs;ay, two hundred inches (for example) and there <lb/>will be di&longs;pen&longs;ed two hundred and fifty inches, or more. </s> <s>Which <lb/>pa&longs;&longs;age happened in the time of <emph type="italics"/>Nerva<emph.end type="italics"/> the Emperour, as <emph type="italics"/>Giulio <lb/>Frontino<emph.end type="italics"/> writes, in his 2. Book, <emph type="italics"/>De Aquaductibus Vrbis Romæ,<emph.end type="italics"/><lb/>where he ob&longs;erveth that they had <emph type="italics"/>in Commentariis 12755. Qui­<lb/>naries<emph.end type="italics"/> of Water; and found that they di&longs;pen&longs;ed 14018. <emph type="italics"/>Qui­<lb/>naries.<emph.end type="italics"/> And the like Errour hath continued, and is in u&longs;e al&longs;o <lb/>modernly until our times. </s> <s>But if our Rule &longs;hall be ob&longs;erved, <lb/>we &longs;hall incur no &longs;uch di&longs;order, nay there will alwayes be given <lb/>to every one his &longs;hare, according to the holy end of exact ju&longs;tice, <lb/>which <emph type="italics"/>dat unicuique quod &longs;uum e&longs;t.<emph.end type="italics"/> As on the contrary, it is <lb/>manife&longs;t, that His Divine Maje&longs;ty hateth and abominateth <emph type="italics"/>Pon­<lb/>dus & pondus, Men&longs;ura & men&longs;ura,<emph.end type="italics"/> as the Holy Gho&longs;t &longs;peak­<lb/>eth by the mouth of <emph type="italics"/>Solomon<emph.end type="italics"/> in the <emph type="italics"/>Proverbs, Chap. </s> <s>20. Pondus <lb/>& Pondus, Men&longs;ura & Men&longs;ura, utrumque abominabile e&longs;t apud <lb/>Deum.<emph.end type="italics"/> And therefore who is it that &longs;eeth not that the way of <lb/>dividing and mea&longs;uring of Waters, commonly u&longs;ed, is expre&longs;ly <lb/>again&longs;t the Law of God. </s> <s>Since that thereby the &longs;ame mea&longs;ure <lb/>is made &longs;ometimes greater, and &longs;ometimes le&longs;&longs;er; A di&longs;order &longs;o <lb/>enormous and execrable, that I &longs;hall take the boldne&longs;s to &longs;ay, that <lb/>for this &longs;ole re&longs;pect it ought to be condemned and prohibited like­<lb/>wi&longs;e by human Law, which &longs;hould Enact that in this bu&longs;ine&longs;s there <lb/>&longs;hould be imployed either this our Rule, or &longs;ome other that <lb/>is more exqui&longs;ite and practicable, whereby the mea&longs;ure <lb/>might keep one con&longs;tant and determinate tenor, as we make it, <lb/>and not, as it is now, to make <emph type="italics"/>Pondus & Pondus, Men&longs;ur a & <lb/>Men&longs;ura.<emph.end type="italics"/></s></p><p type="main"> <s>And this is all that I had to offer to Your mo&longs;t Illu&longs;trious <lb/>Lord&longs;hip, in obedience to your commands, re&longs;erving to my &longs;elf <lb/>the giving of a more exact account of this my invention, when <lb/>the occa&longs;ion &longs;hall offer, of reducing to practice &longs;o holy, ju&longs;t, and <pb xlink:href="068/01/132.jpg" pagenum="118"/>nece&longs;&longs;ary a reformation of the Mea&longs;ure of Running Waters and <lb/>of Aqueducts in particular: which Rule may al&longs;o be of great <lb/>benefit in the divi&longs;ion of the greater Waters to over-flow <lb/>Grounds, and for other u&longs;es: I humbly bow,</s></p><p type="main"> <s><emph type="italics"/>Your Most Devoted,<emph.end type="italics"/><lb/>and <lb/><emph type="italics"/>Mo&longs;t Obliged Servant,<emph.end type="italics"/></s></p><p type="main"> <s>D. </s> <s>Benedetto Ca&longs;telli, <emph type="italics"/>Abb. </s> <s>Ca&longs;in.<emph.end type="italics"/></s></p><p type="head"> <s>FINIS.</s></p><pb xlink:href="068/01/133.jpg"/><p type="head"> <s>A TABLE</s></p><p type="head"> <s>Of the mo&longs;t ob&longs;ervable matters in this Treati&longs;e of the <lb/>MENSURATION of RUNNING <lb/>WATERS.<lb/><arrow.to.target n="table74"></arrow.to.target></s></p><table><table.target id="table74"></table.target><row><cell>A</cell><cell></cell></row><row><cell>Abatements <emph type="italics"/>of a River in different and unequal Diver&longs;ions, is alwaies equal, which is proved with<emph.end type="italics"/> 100. Syphons.</cell><cell><emph type="italics"/>Page<emph.end type="italics"/> 75</cell></row><row><cell>Arno <emph type="italics"/>River when it ri&longs;eth upon a Land-Flood near the Sea one third of a Brace, it ri&longs;eth about<emph.end type="italics"/> Pi&longs;a 6. <emph type="italics"/>or 7. Braces.<emph.end type="italics"/></cell><cell>82</cell></row><row><cell>B</cell><cell></cell></row><row><cell><emph type="italics"/>Banks near to the Sea lower, than far from thence. Corollary<emph.end type="italics"/> XIV.</cell><cell>16</cell></row><row><cell>Brent <emph type="italics"/>River diverted from the Lake o<emph.end type="italics"/>f Venice, <emph type="italics"/>and its effects.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell>Brent <emph type="italics"/>&longs;uppo&longs;ed in&longs;ufficient to remedy the inconveniences of the Lake, and the fal&longs;ity of that &longs;uppo&longs;ition.<emph.end type="italics"/></cell><cell>67</cell></row><row><cell>Brent, <emph type="italics"/>and its benefits in the Lake.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell><emph type="italics"/>Its Depo&longs;ition of Sand in the Lake, bow great it is.<emph.end type="italics"/></cell><cell>78, 79</cell></row><row><cell><emph type="italics"/>Bridges over Rivers, and how they are to be made. Appendix<emph.end type="italics"/> VIII.</cell><cell>20</cell></row><row><cell>Burana <emph type="italics"/>River, its ri&longs;ing, and falling in<emph.end type="italics"/> Panaro.</cell><cell>110</cell></row><row><cell>C</cell><cell></cell></row><row><cell>Ca&longs;telli <emph type="italics"/>applyed him&longs;elf to this Study by Order of<emph.end type="italics"/> Urban VIII.</cell><cell>2</cell></row><row><cell>Chanel of Navigation <emph type="italics"/>in the Valleys of<emph.end type="italics"/> Bologna, <emph type="italics"/>and its inconveniences.<emph.end type="italics"/></cell><cell>99</cell></row><row><cell><emph type="italics"/>Carried into the<emph.end type="italics"/> Po <emph type="italics"/>of<emph.end type="italics"/> Ferrara, <emph type="italics"/>and its benefits<emph.end type="italics"/></cell><cell>ibid.</cell></row><row><cell>Ciampoli <emph type="italics"/>alover of the&longs;e Ob&longs;ervations of Waters.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell>D</cell><cell></cell></row><row><cell><emph type="italics"/>Difficulty of this bu&longs;ine&longs;s of Mea&longs;uring Waters.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Di&longs;orders that happen in the di&longs;tribution of the Waters of Aqueducts, and their re-medies.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Di&longs;tribution of the Waters of Fountains, and Aqueducts. Appendix<emph.end type="italics"/> X.</cell><cell>22</cell></row><row><cell><emph type="italics"/>Di&longs;tribution of Water to over-flow Grounds. Appendix<emph.end type="italics"/> XI.</cell><cell>23, 69, 70</cell></row><row><cell><emph type="italics"/>Diver&longs;ion of<emph.end type="italics"/> Reno <emph type="italics"/>and other Brooks of<emph.end type="italics"/> Romagna, <emph type="italics"/>advi&longs;ed by<emph.end type="italics"/> P. Spernazzati <emph type="italics"/>to what end it was.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>Drains and Ditches, the benefit they receive by cutting away the Weeds and Reeds. Appendix<emph.end type="italics"/> IX.</cell><cell>21</cell></row><row><cell><emph type="italics"/>Drains and Sewers ob&longs;tructed, in the Diver&longs;ion of<emph.end type="italics"/> Reno <emph type="italics"/>into<emph.end type="italics"/> Main Po, <emph type="italics"/>and a remedy for the &longs;ame.<emph.end type="italics"/></cell><cell>110</cell></row><row><cell>E</cell><cell></cell></row><row><cell><emph type="italics"/>Engineers unver&longs;'d in the matters of Waters.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Erour found in the common way of Mea&longs;uring Running Waters.<emph.end type="italics"/></cell><cell>68, 69</cell></row><row><cell><emph type="italics"/>Errour in deriving the Water of<emph.end type="italics"/> Acqua Paola. <emph type="italics"/>Appendix<emph.end type="italics"/> II.</cell><cell>17, 18</cell></row><pb xlink:href="068/01/134.jpg"/><row><cell><emph type="italics"/>Errour of<emph.end type="italics"/> Bartolotti.</cell><cell>86, 87</cell></row><row><cell><emph type="italics"/>Errours of Engineers in the Derivation of Chenels. Corollary<emph.end type="italics"/> XII.</cell><cell>12</cell></row><row><cell><emph type="italics"/>Errour of Engineers in Mea&longs;uring of<emph.end type="italics"/> Reno <emph type="italics"/>in<emph.end type="italics"/> Po. <emph type="italics"/>Appendix<emph.end type="italics"/> III.</cell><cell>ibid.</cell></row><row><cell><emph type="italics"/>Errour of other Engineers, contrary to the precedent. Appendix<emph.end type="italics"/> IV.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Errour of<emph.end type="italics"/> Giovanni Fontana <emph type="italics"/>in Mea&longs;uring Waters, Corollary<emph.end type="italics"/> XI.</cell><cell>9</cell></row><row><cell><emph type="italics"/>Errour of<emph.end type="italics"/> Giulio Frontino <emph type="italics"/>in Mea&longs;uring the Waters of Aqueducts. Appen-dix<emph.end type="italics"/> I.</cell><cell>17</cell></row><row><cell><emph type="italics"/>Errours committed in cutting the Bank at<emph.end type="italics"/> Bondeno, <emph type="italics"/>in the &longs;wellings of<emph.end type="italics"/> Po: <emph type="italics"/>Corollary<emph.end type="italics"/>XIII.</cell><cell>81</cell></row><row><cell>F</cell><cell></cell></row><row><cell><emph type="italics"/>Fenns<emph.end type="italics"/> Pontine, <emph type="italics"/>Drained by Pope<emph.end type="italics"/> Sixtus Quintus, <emph type="italics"/>with va&longs;t expence.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>The ruine and mi&longs;carriage thereof.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Tardity of the principal Chanel that Drains them, cau&longs;e of the Drowning.<emph.end type="italics"/></cell><cell>ibid.</cell></row><row><cell><emph type="italics"/>They are ob&longs;tructed by the Fi&longs;hing-Wears, which &longs;uell the River.<emph.end type="italics"/></cell><cell>94</cell></row><row><cell><emph type="italics"/>Waters of<emph.end type="italics"/> Fiume Si&longs;to, <emph type="italics"/>which flow in great abundance into the<emph.end type="italics"/> Evacuator <emph type="italics"/>of the &longs;aid Fenns.<emph.end type="italics"/></cell><cell>94, 95</cell></row><row><cell><emph type="italics"/>Remedies to the di&longs;orders of tho&longs;e Fenns.<emph.end type="italics"/></cell><cell>95, 96</cell></row><row><cell>Fontana Giovanni, <emph type="italics"/>his errours in Mea&longs;uring Waters. Corollary<emph.end type="italics"/> XI.</cell><cell>9</cell></row><row><cell>Fiume Morto, <emph type="italics"/>whether it ought to fall into the Sea, or into<emph.end type="italics"/> Serchio,</cell><cell>79</cell></row><row><cell><emph type="italics"/>Let into<emph.end type="italics"/> Serchio <emph type="italics"/>and its inconveniences.<emph.end type="italics"/></cell><cell>79, 80</cell></row><row><cell><emph type="italics"/>The dangerous ri&longs;ing of its Waters, when to be expected.<emph.end type="italics"/></cell><cell>81</cell></row><row><cell><emph type="italics"/>Its inconveniences when it is higher in level than<emph.end type="italics"/> Serchio, <emph type="italics"/>and why it ri&longs;eth mo&longs;t On the Sea-coa&longs;ts, at &longs;uch time as the Winds make the Sea to &longs;uell.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell>G</cell><cell></cell></row><row><cell>Galilæo Galilæi. <emph type="italics"/>hoxourably mentioned.<emph.end type="italics"/></cell><cell><emph type="italics"/>Page<emph.end type="italics"/> 2, 28</cell></row><row><cell><emph type="italics"/>His Rule for mea&longs;uring the time.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell>H</cell><cell></cell></row><row><cell><emph type="italics"/>Height,<emph.end type="italics"/> vide <emph type="italics"/>Quick<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Heights different, made by the &longs;ame &longs;tream of a Brock or Torrent, according to the divers Velocities in the entrance of the River. Corollary<emph.end type="italics"/> I.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Heights different, made by the Torrent in the River, according to the different heights of the River. Corollary<emph.end type="italics"/> II.</cell><cell>ibid.</cell></row><row><cell>K</cell><cell></cell></row><row><cell><emph type="italics"/>Knowledge of Motion how much it importeth.<emph.end type="italics"/></cell><cell>1</cell></row><row><cell>L</cell><cell></cell></row><row><cell><emph type="italics"/>t<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Lake of<emph.end type="italics"/> Perugia, <emph type="italics"/>and, he Ob&longs;ervation made on it. Appendix<emph.end type="italics"/> XII.</cell><cell>42</cell></row><row><cell><emph type="italics"/>Lake of<emph.end type="italics"/> Thra&longs;imenus <emph type="italics"/>and Con&longs;iderations upon it, a Letter written to<emph.end type="italics"/> Sig. Galilæo Galilæi.</cell><cell>28</cell></row><row><cell><emph type="italics"/>Lake of<emph.end type="italics"/> Venice, <emph type="italics"/>and Con&longs;iderations upon it.<emph.end type="italics"/></cell><cell>63, 73</cell></row><row><cell><emph type="italics"/>Low Waters which let the bottom of it be di&longs;covered.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>The &longs;toppage and choaking of the Ports, a main cau&longs;e of the di&longs;orders of the Lake, and the grand remedy to tho&longs;e di&longs;orders what it is.<emph.end type="italics"/></cell><cell>66</cell></row><row><cell><emph type="italics"/>Lakes and Metrs along the Sea-coa&longs;ts, and the cau&longs;es thereof.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Length of Waters, how it is to be Mea&longs;ured.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell>M</cell><cell></cell></row><row><cell><emph type="italics"/>Mea&longs;ure and Di&longs;tributions of Waters. Appendix<emph.end type="italics"/> V.</cell><cell>18</cell></row><pb xlink:href="068/01/135.jpg"/><row><cell><emph type="italics"/>Mea&longs;ure of Rivers that fall into others difficult. Coroll.<emph.end type="italics"/> X:</cell><cell>9</cell></row><row><cell><emph type="italics"/>Mea&longs;ure of the Running Water of a Chanel of an height known by a<emph.end type="italics"/> Regulator <emph type="italics"/>of a Mea-&longs;ure given, in a time a&longs;&longs;igned. Propo&longs;ition<emph.end type="italics"/> I. <emph type="italics"/>Problem<emph.end type="italics"/> I.</cell><cell>50</cell></row><row><cell><emph type="italics"/>Mea&longs;ure of the Water of any River, of any greatne&longs;s, in a time given. Propo&longs;ition<emph.end type="italics"/> V. <emph type="italics"/>Problem<emph.end type="italics"/> III.</cell><cell>60</cell></row><row><cell><emph type="italics"/>Mea&longs;ure that &longs;hewes how much Water a River di&longs;chargeth in a time given.<emph.end type="italics"/></cell><cell>48</cell></row><row><cell><emph type="italics"/>Mole-holes,<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Motion the principal &longs;ubject of Philo&longs;ophy.<emph.end type="italics"/></cell><cell>1</cell></row><row><cell><emph type="italics"/>Mud.<emph.end type="italics"/> Vide <emph type="italics"/>Sand.<emph.end type="italics"/></cell><cell></cell></row><row><cell>N</cell><cell></cell></row><row><cell><emph type="italics"/>Navigation from<emph.end type="italics"/> Bologna <emph type="italics"/>to<emph.end type="italics"/> Ferrara, <emph type="italics"/>is become impo&longs;&longs;ible, till &longs;uch time as<emph.end type="italics"/> Reno <emph type="italics"/>be diverted.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Navigation in the Lake of<emph.end type="italics"/> Venice <emph type="italics"/>endangered, and how restored.<emph.end type="italics"/></cell><cell>65, 70</cell></row><row><cell>P</cell><cell></cell></row><row><cell><emph type="italics"/>Perpendicularity of the Banks of the River, to the upper &longs;uperficies of it.<emph.end type="italics"/></cell><cell>37</cell></row><row><cell><emph type="italics"/>Perpendicularity of the Banks to the bottom.<emph.end type="italics"/></cell><cell>37</cell></row><row><cell><emph type="italics"/>Perugia.<emph.end type="italics"/> Vide <emph type="italics"/>Lake.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Pontine.<emph.end type="italics"/> Vide <emph type="italics"/>Fenns.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Ports of<emph.end type="italics"/> Venice, Malamocco, Bondolo, <emph type="italics"/>and<emph.end type="italics"/> Chiozza, <emph type="italics"/>choaked up for want of Water in the Lake.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Proportions of unequal Sections of equal Velocity, and of equal Sections of unequal Velo-city. Axiome<emph.end type="italics"/> IV. <emph type="italics"/>and<emph.end type="italics"/> V.</cell><cell>38</cell></row><row><cell><emph type="italics"/>Proportions of equal and unequal quantities of Water, which pa&longs;s by the Sections of dif-ferent Rivers. Propo&longs;ition<emph.end type="italics"/> II.</cell><cell>39</cell></row><row><cell><emph type="italics"/>Proportions of unequal Sections that in equal times di&longs;charge equal quantities of Water. Propo&longs;ition<emph.end type="italics"/> III.</cell><cell>41</cell></row><row><cell><emph type="italics"/>Proportion wherewith one River falling into another, varieth in height. Propo-&longs;ition<emph.end type="italics"/> IV.</cell><cell>44</cell></row><row><cell><emph type="italics"/>Proportion of the Water di&longs;charged by a River in the time of Flood, to the Water di&longs;charged in an equal time by the &longs;aid River, before or after the Flood. Propo&longs;ition<emph.end type="italics"/> V.</cell><cell>44</cell></row><row><cell><emph type="italics"/>Proportion of the Heights made by two equal Brooks or Streams falling into the &longs;ame River. Propo&longs;ition<emph.end type="italics"/> VI.</cell><cell>45</cell></row><row><cell><emph type="italics"/>Proportion of the Water which a River di&longs;chargeth encrea&longs;ing in Quick-height by the ad-dition of new Water, to that which it di&longs;chargeth after the encrea&longs;e is made. Propo-&longs;ition<emph.end type="italics"/> IV. <emph type="italics"/>Theor.<emph.end type="italics"/> II.</cell><cell>54</cell></row><row><cell><emph type="italics"/>Proportion of a River when high, to it &longs;elf when low. Coroll.<emph.end type="italics"/> I.</cell><cell>55</cell></row><row><cell>Q</cell><cell></cell></row><row><cell><emph type="italics"/>Quantity of Running Waters is never certain, if with the Vulgar way of Mea&longs;uring them, their Velocities be not con&longs;idered.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Quantities of Waters which are di&longs;charged by a River, an&longs;wer in equality to the Velocities and times in which they are di&longs;charged. Axiome<emph.end type="italics"/> I, II, III.</cell><cell>38</cell></row><row><cell>Quick-Height <emph type="italics"/>of a River, what it is. Definition<emph.end type="italics"/> V.</cell><cell>48</cell></row><row><cell>R</cell><cell></cell></row><row><cell><emph type="italics"/>Rea&longs;on of the Proverb,<emph.end type="italics"/> Take heed of the &longs;till Waters. <emph type="italics"/>Coroll.<emph.end type="italics"/> VI.</cell><cell>7</cell></row><row><cell><emph type="italics"/>Rea&longs;ons of<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini <emph type="italics"/>again&longs;t the diver&longs;ion of<emph.end type="italics"/> Reno <emph type="italics"/>into the<emph.end type="italics"/> Po <emph type="italics"/>of<emph.end type="italics"/>Volano.</cell><cell>105</cell></row><row><cell><emph type="italics"/>Rea&longs;ons of<emph.end type="italics"/> Cardinal Capponi <emph type="italics"/>and<emph.end type="italics"/> Mon&longs;ig. Cor&longs;ini, <emph type="italics"/>for the turning of<emph.end type="italics"/> Reno <emph type="italics"/>into Main<emph.end type="italics"/> Po.</cell><cell>106</cell></row><pb xlink:href="068/01/136.jpg"/><row><cell><emph type="italics"/>Two objections on the contrary, and an&longs;wers to them.<emph.end type="italics"/></cell><cell>104 <emph type="italics"/>&<emph.end type="italics"/> 105</cell></row><row><cell><emph type="italics"/>What ought to be the proportion of the Heights of<emph.end type="italics"/> Reno <emph type="italics"/>in<emph.end type="italics"/> Reno, <emph type="italics"/>and of<emph.end type="italics"/> Reno <emph type="italics"/>in<emph.end type="italics"/>Po.</cell><cell>110</cell></row><row><cell><emph type="italics"/>Regulator what it is. Definition<emph.end type="italics"/> IV.</cell><cell>48</cell></row><row><cell><emph type="italics"/>Relation of the Waters of<emph.end type="italics"/> Bologna <emph type="italics"/>and<emph.end type="italics"/> Ferrara, <emph type="italics"/>by<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini</cell><cell>100</cell></row><row><cell>Reno <emph type="italics"/>in the Valleys, and its bad effects.<emph.end type="italics"/></cell><cell>100, 101</cell></row><row><cell><emph type="italics"/>Two wayes to divert it.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>The facility and utility of tho&longs;e wayes.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>The difficulties objected.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Reply to<emph.end type="italics"/> Bartolotti <emph type="italics"/>touching the dangers of turning<emph.end type="italics"/> Fiume Morto <emph type="italics"/>into<emph.end type="italics"/> Serchio.</cell><cell>83</cell></row><row><cell><emph type="italics"/>Retardment of the cour&longs;e of a River cau&longs;ed by its Banks. Appendix<emph.end type="italics"/> VII.</cell><cell>19</cell></row><row><cell><emph type="italics"/>Ri&longs;ings made by Flood-Gates but &longs;mall. Appendix<emph.end type="italics"/> XIII.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Rivers that are &longs;hallow &longs;well much upon &longs;mall &longs;howers, &longs;uch as are deep ri&longs;e but little upon great Floods. Corollary<emph.end type="italics"/> III.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Rivers the higher they are, the &longs;wifter.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Rivers the higher they are, thele&longs;&longs;e they encrea&longs;e upon Floods.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell><emph type="italics"/>Rivers when they are to have equal and when like Velocity.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Rivers in falling into the Sea, form a Shelf of Sand called<emph.end type="italics"/> Cavallo.</cell><cell>65</cell></row><row><cell><emph type="italics"/>Five Rivers to be diverted from the Lake of<emph.end type="italics"/> Venice, <emph type="italics"/>and the inconveniences that would en&longs;ue thereupon.<emph.end type="italics"/></cell><cell>74, 75</cell></row><row><cell><emph type="italics"/>A River of Quick-height, and Velocity in its Regulator being given, if the Height be redoubled by new Water, it redoubleth al&longs;o in Velocity. Propo&longs;ition<emph.end type="italics"/> II. <emph type="italics"/>The-orem<emph.end type="italics"/> I.</cell><cell>51</cell></row><row><cell><emph type="italics"/>Keepeth the proportion of the heights, to the Velocities. Corollary<emph.end type="italics"/></cell><cell>52</cell></row><row><cell>S</cell><cell></cell></row><row><cell><emph type="italics"/>Sand and Mud that entereth into the Lake of<emph.end type="italics"/> Venice, <emph type="italics"/>and the way to examine it.<emph.end type="italics"/></cell><cell>76</cell></row><row><cell><emph type="italics"/>Seas agitated and driven by the Winds &longs;top up the Ports.<emph.end type="italics"/></cell><cell>64, 65</cell></row><row><cell><emph type="italics"/>Sections of a River what they are. Definition<emph.end type="italics"/> I.</cell><cell>37</cell></row><row><cell><emph type="italics"/>Sections equally &longs;wift what they are. Definition<emph.end type="italics"/> II.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Sections of a River being given, to conceive others equal to them, of different breadth, height and Velocity. Petition.<emph.end type="italics"/></cell><cell>38</cell></row><row><cell><emph type="italics"/>Sections of the &longs;ame River, and their Proportions to their Velocities. Coroll.<emph.end type="italics"/> I.</cell><cell>42</cell></row><row><cell><emph type="italics"/>Sections of a River di&longs;charge in any what&longs;oever place of the &longs;aid River, equal quantities of Water in equal times. Propo&longs;ition<emph.end type="italics"/> I.</cell><cell>39</cell></row><row><cell>Sile <emph type="italics"/>River what mi&longs;chiefes it threatneth, diverted from the Lake.<emph.end type="italics"/></cell><cell>74</cell></row><row><cell><emph type="italics"/>Spirtings of Waters grow bigger the higher they go. Coroll.<emph.end type="italics"/> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"/>Sreams of Rivers how they encrea&longs;e and vary. Coroll.<emph.end type="italics"/> I.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Streams retarded, and the effects thereof. Coroll.<emph.end type="italics"/> IX.</cell><cell>8</cell></row><row><cell>T</cell><cell></cell></row><row><cell><emph type="italics"/>Table of the Heights, Additions, and Quantities of Waters, and its u&longs;e.<emph.end type="italics"/></cell><cell>56</cell></row><row><cell><emph type="italics"/>Thra&longs;imenus.<emph.end type="italics"/> Vide <emph type="italics"/>Lake.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Time how its mea&longs;ured in the&longs;e Operations of the Waters.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell><emph type="italics"/>Torrents encrea&longs;e at the encrea&longs;ing of a River, though they carry no more Water than before: Coroll.<emph.end type="italics"/> IV.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Torrents when they depo&longs;e and carry away the Sand. Coroll.<emph.end type="italics"/> V.</cell><cell>7</cell></row><row><cell><emph type="italics"/>Torrents and their effects in a River.<emph.end type="italics"/></cell><cell>6, 7</cell></row><row><cell><emph type="italics"/>Torrents that fall into the Valleys, or into<emph.end type="italics"/> Po <emph type="italics"/>of<emph.end type="italics"/> Volano, <emph type="italics"/>and their mi&longs;chiefs prevent-ed, by the diverting of<emph.end type="italics"/> Reno <emph type="italics"/>into<emph.end type="italics"/> Main Po.</cell><cell>100</cell></row><row><cell><emph type="italics"/>Tyber and the cau&longs;es of its inundations. Coroll.<emph.end type="italics"/> VIII.</cell><cell>8</cell></row><pb xlink:href="068/01/137.jpg"/><row><cell>V</cell><cell></cell></row><row><cell><emph type="italics"/>Valleys of<emph.end type="italics"/> Bologna <emph type="italics"/>and<emph.end type="italics"/> Ferrara, <emph type="italics"/>their inundations and di&longs;orders, whence they pro-ceed.<emph.end type="italics"/></cell><cell>97</cell></row><row><cell><emph type="italics"/>Velocity of the Water &longs;hewn by &longs;everal Examples.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Its proportion to the Mea&longs;ure.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Velocities equal, what they are.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Velocities like, what they are.<emph.end type="italics"/></cell><cell>47, 48</cell></row><row><cell><emph type="italics"/>Velocities of Water known, how they help us in finding the Lengths.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>A Fable to explain the truth thereof.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Venice.<emph.end type="italics"/> Vide <emph type="italics"/>Lake.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>V&longs;e of the<emph.end type="italics"/> Regulator <emph type="italics"/>in mea&longs;uring great Rivers. Con&longs;ideration I.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell>W</cell><cell></cell></row><row><cell><emph type="italics"/>Waters falling, why they di&longs;groß. Coroll.<emph.end type="italics"/> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"/>Waters, how the Length of them is Mea&longs;ured.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell><emph type="italics"/>Waters that are imployed to flow Grounds, how they are to be di&longs;tributed.<emph.end type="italics"/></cell><cell>19, 53, 54</cell></row><row><cell><emph type="italics"/>Waters to be carryed in Pipes, to &longs;erve Aquaducts and Conduits, how they are to be Mea-&longs;ured.<emph.end type="italics"/></cell><cell>115, 116</cell></row><row><cell><emph type="italics"/>Way to know the ri&longs;ing of Lakes by Raines.<emph.end type="italics"/></cell><cell>28</cell></row><row><cell><emph type="italics"/>Way of the Vulgar to Mea&longs;ure the Waters of Rivers.<emph.end type="italics"/></cell><cell>68</cell></row><row><cell><emph type="italics"/>Wind Gun, and Tortable Fountain of<emph.end type="italics"/> Vincenzo Vincenti <emph type="italics"/>of<emph.end type="italics"/> Urbin.</cell><cell>11</cell></row><row><cell><emph type="italics"/>Windes contrary, retard, and make Rivers encrea&longs;e. Coroll.<emph.end type="italics"/> VII.</cell><cell>8</cell></row></table><p type="head"> <s>The END of the TABLE of the Second Part <lb/>of the Fir&longs;t TOME.</s></p> </chap> </body> <back></back> </text></archimedes>