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version 1.1, 2003/09/26 15:28:53

version 1.2, 2003/11/20 18:08:02

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<s>LONDON, <lb/>Printed by WILLIAM LEYBOURNE, MDCLXI.</s><pb/><pb/>

<s>LONDON, <lb/>Printed by WILLIAM LEYBOURNE, MDCLXI.</s><pb xlink:href="068/01/002.jpg"/><pb xlink:href="068/01/003.jpg"/>

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<s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, 1661.</s><pb/><pb/>

<s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, 1661.</s><pb xlink:href="068/01/004.jpg"/><pb xlink:href="068/01/005.jpg"/>

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<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/>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>

<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>

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<s>A Monk of <emph type="italics"/>Ca&longs;&longs;ino.<emph.end type="italics"/></s><pb/>

<s>A Monk of <emph type="italics"/>Ca&longs;&longs;ino.<emph.end type="italics"/></s><pb xlink:href="068/01/007.jpg"/>

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<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><pb/>

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<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/><emph type="italics"/>to be Courted by &longs;undry Princes, and great Prelates. </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>

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<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/><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>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>

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<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/>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>

<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>

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<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/><emph type="italics"/>very &longs;peedily. </s>

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<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/>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>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>

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<s>29. <emph type="italics"/>r.<emph.end type="italics"/> con&longs;tant;.</s><pb pagenum="1"/>

<s>29. <emph type="italics"/>r.<emph.end type="italics"/> con&longs;tant;.</s><pb xlink:href="068/01/015.jpg" pagenum="1"/>

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<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 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>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>

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<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 pagenum="3"/>der&longs;tood nothing at all, of that which others pretended full and <lb/>clearly to under&longs;tand. </s>

<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>

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<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><pb pagenum="4"/>

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<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 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>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>

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<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 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>

<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>

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<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 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>

<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>

Line 1094

<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><pb pagenum="8"/>

Line 1126

<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 pagenum="9"/>the River, in &longs;uch a ca&longs;e there mu&longs;t follow very great and irre<lb/>pable innundations.</s>

<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>

Line 1146

<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 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>

<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>

Line 1162

<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 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>

<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>

Line 1174

<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 pagenum="12"/>ed, the water put therein would be more pre&longs;&longs;ed and crowded.</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>

Line 1202

<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 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>

<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>

Line 1210

<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 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>

<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>

Line 1218

<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 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>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>

Line 1238

<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><pb pagenum="16"/>

Line 1274

<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 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>

<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>

Line 1302

<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 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>

<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>

Line 1326

<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 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>

<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>

Line 1354

<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 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>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>

Line 1362

<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="fig6"></figure><lb/>is mea&longs;ured by the &longs;aid circumfe<lb/>rence. </s>

<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>

Line 1386

<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 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>

<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>

Line 1402

<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 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>

<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>

Line 1422

<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 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>

<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>

Line 1438

<s>Let the two mouths of the <lb/>Rivers be A, and B, and let <lb/><figure id="fig7"></figure><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>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>

Line 1446

<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 pagenum="24"/>&longs;elves, as have the mouths, which are the numbers 32 and 8 <lb/>in our example: Then this <lb/><figure id="fig8"></figure><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>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>

Line 1462

<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 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 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>

Line 1486

<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="fig9"></figure><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 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>

<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>

Line 1506

<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 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>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>

Line 1526

<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><pb pagenum="28"/>

Line 1542

<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 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>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>

Line 1570

<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 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>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>

Line 1598

<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 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>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>

Line 1614

<s>Continu<pb 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>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>

Line 1622

<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 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>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>

Line 1634

Line 1654

<s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed <emph type="italics"/>Anno Domini,<emph.end type="italics"/> MDCLXI.</s><pb/><pb pagenum="37"/>

<s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed <emph type="italics"/>Anno Domini,<emph.end type="italics"/> MDCLXI.</s><pb xlink:href="068/01/050.jpg"/><pb xlink:href="068/01/051.jpg" pagenum="37"/>

Line 1702

<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><pb pagenum="38"/>

Line 1758

<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><pb pagenum="37"/>

<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><pb xlink:href="068/01/053.jpg" pagenum="37"/>

Line 1770

<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="fig10"></figure><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>

<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>

Line 1782

<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 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="fig11"></figure><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>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>

Line 1794

<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><pb pagenum="41"/>

Line 1806

<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="fig12"></figure><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>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><pb pagenum="42"/>

<s>which was to be demon&longs;trated.</s><pb xlink:href="068/01/056.jpg" pagenum="42"/>

Line 1842

<s>Moreover, <lb/>as the breadth E F is to the breadth C B, &longs;o let the line H be to <pb 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="fig13"></figure><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>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><pb pagenum="44"/>

<s>which was <lb/>to be demon&longs;trated.</s><pb xlink:href="068/01/058.jpg" pagenum="44"/>

Line 1858

<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="fig14"></figure><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 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>

<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>

Line 1878

<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="fig15"></figure><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><pb/><pb pagenum="47"/>

<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><pb xlink:href="068/01/060.jpg"/><pb xlink:href="068/01/061.jpg" pagenum="47"/>

Line 1910

<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><pb pagenum="48"/>

Line 1926

<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="fig16"></figure><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>

<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>

Line 1950

<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><pb pagenum="49"/>

Line 1990

<s>The&longs;e things being pre-&longs;uppo&longs;ed, we will lay down &longs;ome fa<pb 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>

<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>

Line 2010

<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><pb pagenum="51"/>

Line 2026

<s>I &longs;ay, that all the <lb/>water G C &longs;hall be double in velocity to <lb/><figure id="fig17"></figure><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>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>

Line 2050

<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 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>

<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>

Line 2082

<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 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>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>

Line 2122

<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 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>

<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>

Line 2138

<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="fig18"></figure><lb/>line T. </s>

Line 2146

<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 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>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>

Line 2174

<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 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>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>

Line 2198

<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 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>

<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>

Line 2222

<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 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>

<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>

Line 2238

<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 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>

<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>

<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><figure></figure><pb pagenum="60"/>

Line 2266

<s>For upon &longs;uch like <emph type="italics"/>R<emph.end type="italics"/>ivers there are Wears, or Lockes made, <pb 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>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>

Line 2290

<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 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><figure></figure><pb pagenum="63"/>

<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><figure id="id.068.01.076.1.jpg" xlink:href="068/01/076/1.jpg"/><pb xlink:href="068/01/077.jpg" pagenum="63"/>

Line 2314

<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 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>

<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>

Line 2346

<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 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>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>

Line 2370

<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 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>

<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>

Line 2402

<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 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>

<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>

Line 2426

<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 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>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>

Line 2454

<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 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>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>

Line 2490

<s>As to the fir&longs;t, I am very certain that no man, let <pb 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>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>

Line 2526

<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 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 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>

Line 2558

<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><pb pagenum="72"/>

Line 2594

<s>The writing &longs;pake as followeth.</s><pb pagenum="73"/>

<s>The writing &longs;pake as followeth.</s><pb xlink:href="068/01/087.jpg" pagenum="73"/>

Line 2610

<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 pagenum="74"/>by the <emph type="italics"/>Plebeian<emph.end type="italics"/> Rout. </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>

Line 2630

<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><pb pagenum="75"/>

Line 2646

<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 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>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>

Line 2682

<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 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>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>

Line 2718

<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 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>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>

Line 2750

<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 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>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>

Line 2782

<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 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>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>

Line 2794

<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 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>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>

Line 2830

<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 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 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>

Line 2866

<s>D. BENEDETTO CASTELLI.</s><pb pagenum="83"/>

<s>D. BENEDETTO CASTELLI.</s><pb xlink:href="068/01/097.jpg" pagenum="83"/>

Line 2898

<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 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>

<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>

Line 2922

<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 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>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>

Line 2966

<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 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"/> 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>

Line 2998

<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 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>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>

Line 3026

<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 pagenum="88"/>Fen they fell more than fifteen Palmes. </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>

Line 3074

<s>When <lb/>it is &longs;topt up by the fury of the Sea waves, I affirm that it is a <pb 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>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>

Line 3118

<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><pb/><pb pagenum="91"/>

Line 3142

<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 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>

<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>

Line 3174

<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 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>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>

Line 3198

<s>And the better to ex<lb/>plain the example, let it be &longs;uppo&longs;ed, <lb/><figure id="fig19"></figure><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 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>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>

Line 3218

<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 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>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>

Line 3246

<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 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>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>

Line 3270

<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><figure></figure><pb pagenum="97"/>

Line 3282

<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 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>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>

Line 3294

<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 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>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>

Line 3318

<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><pb pagenum="100"/>

Line 3350

<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 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>

<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>

Line 3378

<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 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>

<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>

Line 3402

<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 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>

<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>

Line 3446

<s>On the contrary it is objected, That it is not convenient to <pb 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>

<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>

Line 3470

<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><pb pagenum="105"/>

Line 3486

<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 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>

<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>

Line 3506

<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 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>

<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>

Line 3526

<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 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>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>

Line 3562

<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 pagenum="109"/>time would be allowed, upon occa&longs;ion, to &longs;cowr and clean&longs;e <lb/>it.</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>

Line 3578

<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 pagenum="110"/>with the crime, than quit it thereof. </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>

Line 3598

<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><pb pagenum="111"/>

Line 3634

<s>But from its Removal, be&longs;ides the alleviation of the harm <pb 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><pb pagenum="113"/>

<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><pb xlink:href="068/01/127.jpg" pagenum="113"/>

Line 3654

<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 pagenum="432"/>tho&longs;e who finde therein &longs;ome kinde of ob&longs;curity.</s>

<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>

Line 3666

<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 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>

<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>

Line 3686

<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 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>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>

Line 3718

<s>The &longs;econd di&longs;order that happeneth, at pre&longs;ent, in the di&longs;tri<pb 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>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>

Line 3746

<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 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>

<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>

Line 3766

<s>FINIS.</s><pb/>

<s>FINIS.</s><pb xlink:href="068/01/133.jpg"/>

Line 3774

<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><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/><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/><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/><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/><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>

<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><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>

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