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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Castelli, Benedetto</author> <title>Of the mensuration of running waters</title> <date>1661</date> <place>London</place> <translator>Salusbury</translator> <lang>en</lang> <cvs_file>caste_mensu_068_en_1661.xml</cvs_file> <locator>068.xml</locator> </info> <text> <front> <section> <pb xlink:href="068/01/001.jpg"></pb><p type="head"> <s>MATHEMATICAL <lb></lb>COLLECTIONS <lb></lb>AND <lb></lb>TRANSLATIONS: <lb></lb>THE SECOND <lb></lb>TOME.</s></p><p type="head"> <s>THE SECOND PART, <lb></lb>Containing,</s></p><p type="main"> <s>D. BENEDICTUS CASTELLUS, <emph type="italics"></emph>his DISCOURSE <lb></lb>of the MENSURATION of RUN<lb></lb>NING WATERS.<emph.end type="italics"></emph.end></s></p> </section> </front> <body> <chap> <p type="main"> <s><emph type="italics"></emph>His Geometrical DEMONSTRATIONS of <lb></lb>the Meaſure of RUNNING WATERS.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>I. </s> <s>His LETTERS and CONSIDERATIONS <lb></lb>touching the Draining of FENNS, Diverſions of <lb></lb>RIVERS, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>V.<emph.end type="italics"></emph.end> D. CORSINUS, <emph type="italics"></emph>His RELATION of the ſtate of the <lb></lb>Inundations, &c. </s> <s>in the Territories of BOLOGNA, <lb></lb>and FERRARA.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>By <emph type="italics"></emph>THOMAS SALUSBURY, <expan abbr="Eſq.">Eſque</expan><emph.end type="italics"></emph.end></s></p><p type="head"> <s>LONDON, <lb></lb>Printed by WILLIAM LEYBOURNE, MDCLXI.</s></p><pb xlink:href="068/01/002.jpg"></pb><pb xlink:href="068/01/003.jpg"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>RUNNING WATERS.</s></p><p type="head"> <s>An Excellent Piece <lb></lb><emph type="italics"></emph>Written in ITALIAN<emph.end type="italics"></emph.end><lb></lb>BY</s></p><p type="head"> <s>DON BENEDETTO CASTELLI, <lb></lb>Abbot of St. <emph type="italics"></emph>BENEDETTO ALOYSIO,<emph.end type="italics"></emph.end><lb></lb>and Profeſſour of the Mathematicks to <lb></lb>Pope <emph type="italics"></emph>URBAN VIII.<emph.end type="italics"></emph.end> in <emph type="italics"></emph>ROME.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>Engliſhed from the Third and beſt Edition, with <lb></lb>the addition of a Second Book not before extant:</s></p><p type="head"> <s>By <emph type="italics"></emph>THOMAS SALUSBURY.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, 1661.</s></p><pb xlink:href="068/01/004.jpg"></pb><pb xlink:href="068/01/005.jpg"></pb><p type="head"> <s>THE <lb></lb>AUTHOURS EPISTLE <lb></lb>TO <lb></lb>Pope VRBAN VIII.</s></p><p type="main"> <s>I lay at the Feet of your Ho<lb></lb>lineſſe theſe my Conſide<lb></lb>rations concerning the <lb></lb>MENSURATION OF <lb></lb>RUNNING WATERS: <lb></lb>Wherein if I ſhall have ſucceeded, being a <lb></lb>matter ſo difficult and unhandled by Wri<lb></lb>ters both Ancient Modern, the diſcovery of <lb></lb>any thing of truth hath been the Effect of <lb></lb>Your Holineſſes Command; and if through <lb></lb>inability I have miſſed the Mark, the ſame <pb xlink:href="068/01/006.jpg"></pb>Command will ſerve me for an Excuſe with <lb></lb>Men of better Judgment, and more eſpeci<lb></lb>ally with Your Holineſſe, to whom I humbly <lb></lb>proſtrate my ſelf, and kiſſe Your Sacred <lb></lb>Feet.</s></p><p type="main"> <s><emph type="italics"></emph>From ROME.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Your Holineſſes</s></p><p type="main"> <s><emph type="italics"></emph>Moſt humble Servant<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>BENEDETTO.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>A Monk of <emph type="italics"></emph>Caſſino.<emph.end type="italics"></emph.end></s></p><pb xlink:href="068/01/007.jpg"></pb><p type="head"> <s>AN <lb></lb>ACCOUNT <lb></lb>OF THE <lb></lb>Authour and Work.</s></p><p type="main"> <s>DON BENEDETTO CASTELLI, <lb></lb><emph type="italics"></emph>the famous Authour of theſe enſuing <lb></lb>Diſcourſes of the<emph.end type="italics"></emph.end> Menſuration of <lb></lb>Running Waters, <emph type="italics"></emph>is deſcended from <lb></lb>the Worſhipful FAMILY of the<emph.end type="italics"></emph.end><lb></lb>GASTELLII, <emph type="italics"></emph>and took his <lb></lb>firſt breath near to the lake THR A<lb></lb>SIMENVS, (where<emph.end type="italics"></emph.end> Hanibal <emph type="italics"></emph>gave <lb></lb>a fatal overthrow to the<emph.end type="italics"></emph.end> Roman <lb></lb><emph type="italics"></emph>Legions) in that ſweet and fertile part <lb></lb>of happy<emph.end type="italics"></emph.end> ITALY, <emph type="italics"></emph>called the<emph.end type="italics"></emph.end> Territory <lb></lb><emph type="italics"></emph>of<emph.end type="italics"></emph.end> PERUGIA, <emph type="italics"></emph>a branch of the Dukedome of<emph.end type="italics"></emph.end> TUSCANY, <emph type="italics"></emph>which <lb></lb>at preſent ſubmitteth to the Juriſdiction of the Church, as being a <lb></lb>part of<emph.end type="italics"></emph.end> St. </s> <s>PETER'S Patrimony. <emph type="italics"></emph>His Parents, who were more <lb></lb>zealous of the good of his Soul than obſervant of the Propenſion of <lb></lb>his Genius, dedicated him (according to the Devotion of that Coun<lb></lb>try) to the Service of the Church; and entered him into the Flou<lb></lb>riſhing Order of Black-Friers, called from the place Moncks <lb></lb>of<emph.end type="italics"></emph.end> Monte Caſino, <emph type="italics"></emph>and from the Founder<emph.end type="italics"></emph.end> Benedictines. <emph type="italics"></emph>Na<lb></lb>ture, that She might conſummate the Profuſion of her Fa<lb></lb>vours upon him, ſent him into the World in an Age that was ſo <lb></lb>ennobled and illuminated with Eminent Scholars in all Kinds of <lb></lb>Literature, that hardly any Century ſince the Creation can boaſt <lb></lb>the like.<emph.end type="italics"></emph.end></s></p><pb xlink:href="068/01/008.jpg"></pb><p type="main"> <s>§. <emph type="italics"></emph>In particular, the<emph.end type="italics"></emph.end> SCIENCES MATHEMATI<lb></lb>CAL <emph type="italics"></emph>had then got that Fame and Eſteem in the Learned World, <lb></lb>that all men of Spirit or Quality became either Students in, or <lb></lb>Patrons of thoſe Sublime Knowledges. </s> <s>On this occaſion the Curi<lb></lb>oſity of our<emph.end type="italics"></emph.end> AUTHOUR <emph type="italics"></emph>being awakened, his Active Wit <lb></lb>could not endure to be any longer confined to the Slaviſh Tuition <lb></lb>of Hermetical Pedagogues; but in concurrence with the Genius <lb></lb>of the Age, he alſo betook himſelf to thoſe moſt Generous and <lb></lb>Liberal Studies. </s> <s>His helps in this his deſign were ſo many, and <lb></lb>ſo extraordinary, that had his Inclination been weaker, or his <lb></lb>Apprehenſion leſſer, he could hardly have failed attaining more <lb></lb>than a Common Eminency in theſe Sciences. </s> <s>For beſides the De<lb></lb>luge of Learned and Vſeful Books, which the Preſſe at that <lb></lb>time ſent forth from all parts of<emph.end type="italics"></emph.end> EUROPE, <emph type="italics"></emph>he had the good <lb></lb>Fortune to fall into the Acquaintance, and under the Inſtruction <lb></lb>of the moſt Demonſtrative and moſt Familiar Man in the World, <lb></lb>the Famous<emph.end type="italics"></emph.end> GALILEO<emph type="italics"></emph>: whoſe ſucceſſe being no leſſe upon <lb></lb>this his<emph.end type="italics"></emph.end> Pupil <emph type="italics"></emph>than upon the reſt of thoſe Illuſtrious and Ingeni<lb></lb>ous Perſons that reſorted from all parts to ſit under his Admi<lb></lb>rable Lectures, he in a ſhort time attained to that Name in the <lb></lb>Mathematicks, that he was invited to<emph.end type="italics"></emph.end> ROME, <emph type="italics"></emph>Complemen<lb></lb>ted, and Preferred by his then Holineſſe the Eighth<emph.end type="italics"></emph.end> URBAN, <lb></lb><emph type="italics"></emph>upon his very firſt Acceſſion to the<emph.end type="italics"></emph.end> Papacy, <emph type="italics"></emph>which was in the <lb></lb>Year<emph.end type="italics"></emph.end> 1623.</s></p><p type="main"> <s>§. <emph type="italics"></emph>This Pope being moved with a Paternal Providence for the <lb></lb>Concerns of his Subjects in that part of<emph.end type="italics"></emph.end> ITALY <emph type="italics"></emph>about<emph.end type="italics"></emph.end> BO<lb></lb>LOGNA, FERRARA, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> COMMACHIO, <emph type="italics"></emph>ly<lb></lb>ing between the Rivers of<emph.end type="italics"></emph.end> PO <emph type="italics"></emph>and<emph.end type="italics"></emph.end> RENO, <emph type="italics"></emph>which is part of<emph.end type="italics"></emph.end><lb></lb>Lo Stato della Chieſa, <emph type="italics"></emph>or the Church Patrimony, appoints this <lb></lb>our<emph.end type="italics"></emph.end> CASTELLI <emph type="italics"></emph>in the Year 1625, to accompany the Right <lb></lb>Honourable<emph.end type="italics"></emph.end> Monſignore GORSINI <emph type="italics"></emph>(a moſt obſervant and <lb></lb>intelligent perſon in theſe affaires, and at that time Superinten<lb></lb>dent of the General Draines, and Preſident of<emph.end type="italics"></emph.end> ROMAGNA) <lb></lb><emph type="italics"></emph>in the Grand Viſitation which he was then ordered to make con<lb></lb>cerning the diſorders occaſioned by the Waters of thoſe parts.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. </s> <s>CASTELLI, <emph type="italics"></emph>having now an Opportunity to employ, <lb></lb>yea more, to improve ſuch Notions as he had imbued from the <lb></lb>Lectures of his Excellent<emph.end type="italics"></emph.end> MASTER, <emph type="italics"></emph>falls to his work with <lb></lb>all induſtry: and in the time that his Occaſions detained him in<emph.end type="italics"></emph.end><lb></lb>ROMAGNA <emph type="italics"></emph>he perfected the Firſt Book of this his Diſ<lb></lb>courſe concerning the<emph.end type="italics"></emph.end> Menſuration of Running Waters. <emph type="italics"></emph>He con<lb></lb>feſſeth that he had ſome years before applyed himſelf to this part <lb></lb>of Practical Geometry, and from ſeveral Obſervations collected <lb></lb>part of that Doctrine which at this time he put into Method, and <lb></lb>which had procured him the Repute of ſo much Skill that he began<emph.end type="italics"></emph.end><pb xlink:href="068/01/009.jpg"></pb><emph type="italics"></emph>to be Courted by ſundry Princes, and great Prelates. </s> <s>In particu<lb></lb>lar about the beginning of the Year 1623. and before his Invita<lb></lb>tion to<emph.end type="italics"></emph.end> ROME <emph type="italics"></emph>he was employed by Prince<emph.end type="italics"></emph.end> Ferdinando I, <emph type="italics"></emph>Grand <lb></lb>Duke of<emph.end type="italics"></emph.end> TUSCANY, <emph type="italics"></emph>to remedy the Diſorders which at that <lb></lb>time happened in the Valley of<emph.end type="italics"></emph.end> PISA <emph type="italics"></emph>in the Meadows that lye <lb></lb>upon the Banks of<emph.end type="italics"></emph.end> Serchio <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Fiume Morto: <emph type="italics"></emph>and in the pre<lb></lb>ſence of the Grand Duke, Grand Dutcheſſe Mother, the Commiſ<lb></lb>ſioners of Sewers, and ſundry other Perſons in a few hours he <lb></lb>made ſo great a progreſſe in that affair, as gave his Moſt Serene <lb></lb>Highneſſe high ſatisfaction, and gained himſelf much Honour.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>No ſooner had he in his fore-mentioned Voiage to<emph.end type="italics"></emph.end> RO<lb></lb>MAGNA <emph type="italics"></emph>(which was but few Moneths after, in the ſame <lb></lb>Year) committed his Conceptions to paper, but he communicated <lb></lb>them to certain of his Friends. </s> <s>In which number we finde<emph.end type="italics"></emph.end> Signo<lb></lb>re Ciampoli <emph type="italics"></emph>Secretary of the Popes Private Affaires; whom in <lb></lb>the beginning of the Firſt Book he gratefully acknowledgeth to <lb></lb>have been contributary, in his Purſe, towards defraying the <lb></lb>charge of Experiments, and in his Perſon, towards the debating <lb></lb>and compleating of Arguments upon this Subject. </s> <s>Some few years <lb></lb>after the Importunity of Friends, and the Zeal he had for the <lb></lb>Publique Good prevailed with him to preſent the World with his <lb></lb>Firſt Diſcourſe, accompanied with a Treatiſe of the Geometrical <lb></lb>Demonſtrations of his whole Doctrine. </s> <s>What Reception it found <lb></lb>with the Judicious muſt needs be imagined by any one that hath <lb></lb>obſerved how<emph.end type="italics"></emph.end> Novelty <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Facility <emph type="italics"></emph>in conjunction with<emph.end type="italics"></emph.end> Verity <lb></lb><emph type="italics"></emph>make a Charm of irreſiſtable Operation.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. </s> <s>New <emph type="italics"></emph>it was, for that no man before him had ever attemp<lb></lb>ted to Demonſtrate all the three Dimenſions, to wit, the Length, <lb></lb>Breadth and Profundity, of this Fluid and Current Ele<lb></lb>ment. </s> <s>And he detecteth ſuch groſſe Errours in thoſe few that <lb></lb>had untertook to write upon the Subject (of which he inſtan<lb></lb>ceth in<emph.end type="italics"></emph.end> Frontinus <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Fontana, <emph type="italics"></emph>as thoſe that include the rest) <lb></lb>and delivereth ſuch ſingular and unheard-of Paradoxes (for ſo <lb></lb>they ſound in Vulgar Eares) as cannot but procure unſpeakable <lb></lb>delight to his Reader.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. </s> <s>Eafie <emph type="italics"></emph>it is likewiſe and<emph.end type="italics"></emph.end> True; <emph type="italics"></emph>and that upon ſo Familiar <lb></lb>Experiments and Manifeſt Demonſtrations, that I have oft que<lb></lb>ſtioned with my ſelf which merited the greater wonder, he, for <lb></lb>diſcovering, or all men that handled the Argument before him <lb></lb>for not diſcovering a Doctrine of ſuch ſtrange Facility and Infal<lb></lb>libility. </s> <s>But yet as if our Authour deſigned to oblige the whole <lb></lb>World to him by ſo excellent a<emph.end type="italics"></emph.end> Preſent, <emph type="italics"></emph>he ſelects a Subject that <lb></lb>he knew would be carreſſed by all perſons of Nobler Souls, upon <lb></lb>the accounts afore-named, and by all Mankind in General, as <lb></lb>gratifying them in their much adored Idol<emph.end type="italics"></emph.end> Utility. <emph type="italics"></emph>And to ren-<emph.end type="italics"></emph.end><pb xlink:href="068/01/010.jpg"></pb><emph type="italics"></emph>der his Art the more profitable, he reduceth the lofty, and eaſie-to<lb></lb>be-miſtaken Speculations of the Theory, into certain and facile <lb></lb>Directions for Practice; teaching us how to prevent and repaire <lb></lb>the Breaches of Seas, and Inundations of Rivers; to draine <lb></lb>and recover Fenns and Marches; to divert, conveigh and di<lb></lb>ſtribute Waters for the Flowing and Stercoration of Grounds, <lb></lb>ſtrengthening of Fortifications, ſerving of Aquaducts, preſer<lb></lb>ving of Health (by cleanſing Streets, and ſcowring Sewers) and <lb></lb>maintaining of Commerſe (by defending Bridges, cleering Ri<lb></lb>vers, and opening Ports and Channels) with innumerable other <lb></lb>Benefits of the like nature. </s> <s>And, that I may omit no circumſtance <lb></lb>that may recommend my Authour, the Fortune of this his Trea<lb></lb>tiſe hath been ſuch, that as if he intended a<emph.end type="italics"></emph.end> Plus ultra <emph type="italics"></emph>by it, <lb></lb>or as if all men deſpaired to out-do it, or laſtly, as if<emph.end type="italics"></emph.end> CA<lb></lb>STELLI <emph type="italics"></emph>hath been ſo great a<emph.end type="italics"></emph.end> Maſter <emph type="italics"></emph>that none have preſu<lb></lb>med to take Pencil in hand for the finiſhing of what he<emph.end type="italics"></emph.end> Pour<lb></lb>foild, <emph type="italics"></emph>this ſmall Tract like the Arabian Phœnix (of which it is <lb></lb>ſaid<emph.end type="italics"></emph.end> Unica ſemper Avis) <emph type="italics"></emph>did for ſeveral years together continue <lb></lb>ſingle in the World, till that to verifie it to be truly<emph.end type="italics"></emph.end> Phœnician, <lb></lb><emph type="italics"></emph>it renewed its Age by undergoing a ſecond Impreſſion. </s> <s>And as if <lb></lb>this did not make out the Immortal vertue of it, it hath had<emph.end type="italics"></emph.end><lb></lb>Anno 1660 <emph type="italics"></emph>a third Circulation, and riſen in this laſt Edition as <lb></lb>it were from the Vrne of its Authour; and that ſo improved by <lb></lb>the Addition of a ſecond part, that it promiſeth to perpetuate <lb></lb>his Merits to all Poſterity. </s> <s>To be brief, the meer Fame of this <lb></lb>Work reſounded the Honourable Name of<emph.end type="italics"></emph.end> CASTELLI <emph type="italics"></emph>in<lb></lb>to all the Corners of<emph.end type="italics"></emph.end> Italy, <emph type="italics"></emph>I may ſay of<emph.end type="italics"></emph.end> Europe; <emph type="italics"></emph>inſomuch, <lb></lb>that, in hopes to reap great benefit by his Art, the reſpective <lb></lb>Grandees of the adjacent Countries courted his Judgment and <lb></lb>Advice about their Draining of Fenns, Diverſion of Rivers, <lb></lb>Evacuation of Ports, Preventing of Inundations, &c. </s> <s>So that <lb></lb>every Summer he made one or more of theſe Journies or Viſitati<lb></lb>ons. </s> <s>Particularly, the Senate of<emph.end type="italics"></emph.end> Venice <emph type="italics"></emph>conſulted him about their <lb></lb>Lake; to whom he delivered his Opinion in<emph.end type="italics"></emph.end> May 1641. <emph type="italics"></emph>and up<lb></lb>on farther thoughts he preſented them with another Paper of Con<lb></lb>ſiderations the<emph.end type="italics"></emph.end> 20 December <emph type="italics"></emph>following. </s> <s>Prince<emph.end type="italics"></emph.end> LEOPOLDO <lb></lb><emph type="italics"></emph>of<emph.end type="italics"></emph.end> TUSCANY <emph type="italics"></emph>likewiſe requeſted his Advice in the begin<lb></lb>ning of the enſuing year 1642, which occaſioned his Letter to <lb></lb>Father<emph.end type="italics"></emph.end> Franceſco di San Giuſeppe, <emph type="italics"></emph>bearing date<emph.end type="italics"></emph.end> February 1, <lb></lb><emph type="italics"></emph>To which<emph.end type="italics"></emph.end> Signore Bartolotti <emph type="italics"></emph>oppoſing, he writes a ſecond Let<lb></lb>ter, directed to one of the Commiſſioners of Sewers, vindicating <lb></lb>his former, and refuting<emph.end type="italics"></emph.end> Bartolotti, <emph type="italics"></emph>both which I here give <lb></lb>you.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>The Preferments which his Merits recommended him unto, <lb></lb>were firſt to be Abbot of<emph.end type="italics"></emph.end> Caſſino, <emph type="italics"></emph>from which he was removed<emph.end type="italics"></emph.end><pb xlink:href="068/01/011.jpg"></pb>Anno 1640, <emph type="italics"></emph>or thereabouts, unto the Abbey of<emph.end type="italics"></emph.end> Santo Benedet<lb></lb>to Aloyſio; <emph type="italics"></emph>and much about the ſame time preferred to the Dig<lb></lb>nity of Chief Mathematician to his grand Patron Pope<emph.end type="italics"></emph.end> URBAN <lb></lb>VIII. <emph type="italics"></emph>and Publique Profeſſour of Mathematicks in the Vni<lb></lb>verſity of<emph.end type="italics"></emph.end> ROME.</s></p><p type="main"> <s>§. <emph type="italics"></emph>Here a Stop was put to the Carier of his Fortunes, and be<lb></lb>ing fuller of Honour than of Years, was by Death, the Importu<lb></lb>nate Intrerupter of Generous Deſigns, prevented in doing that <lb></lb>farther Good which the World had good reaſon to promiſe it ſelf <lb></lb>from ſo Profound and Induſtrious a Perſonage, leaving many <lb></lb>Friends and Diſciples of all Degrees and Qualities to lament <lb></lb>his loſſe, and honour his Memory.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>His ſingular Virtues and Abilities had gained him the <lb></lb>Friendſhip of very many; as to inſtance in ſome, he had con<lb></lb>racted ſtrict Amity with<emph.end type="italics"></emph.end> Monſignore Maffei Barberino <emph type="italics"></emph>a Floren<lb></lb>tine, Præfect of the Publique Wayes, and afterwards Pope with <lb></lb>the Name of<emph.end type="italics"></emph.end> URBAN VIII. <emph type="italics"></emph>as was ſaid before; with the <lb></lb>above-named<emph.end type="italics"></emph.end> Monſignore Corſini <emph type="italics"></emph>Superintendant of the General <lb></lb>Draines: with<emph.end type="italics"></emph.end> Monſignore Piccolomini <emph type="italics"></emph>Arch-Biſhop of<emph.end type="italics"></emph.end> Siena<emph type="italics"></emph>: <lb></lb>with Cardinal<emph.end type="italics"></emph.end> Serra: <emph type="italics"></emph>with Cardinal<emph.end type="italics"></emph.end> Caponi, <emph type="italics"></emph>who hath ſtudied <lb></lb>much and writ well upon this Subject; and with Cardinal<emph.end type="italics"></emph.end> Gae<lb></lb>tano <emph type="italics"></emph>who frequently conſulted with him in his deſign of Drain<lb></lb>ing the Fenns of<emph.end type="italics"></emph.end> ROMAGNA. <emph type="italics"></emph>Moreover Prince<emph.end type="italics"></emph.end> LEO<lb></lb>POLDO, <emph type="italics"></emph>and his Brother the Grand Duke had very great <lb></lb>kindneſſe for him; which ſpeaks no ſmall attractions in him, <lb></lb>conſidering him as a favourite of the Family of<emph.end type="italics"></emph.end> Barberini, <emph type="italics"></emph>be<lb></lb>tween whom and the Houſe of<emph.end type="italics"></emph.end> Medeci <emph type="italics"></emph>there is an inveterate <lb></lb>Fewd. </s> <s>Amongſt perſons of a lower Quality he acknowledgeth<emph.end type="italics"></emph.end><lb></lb>Signore Ciampoli <emph type="italics"></emph>the Popes Secretary,<emph.end type="italics"></emph.end> Sig. </s> <s>Ferrante Ceſarini, <lb></lb>Sig. </s> <s>Giovanni Baſadonna <emph type="italics"></emph>Senator of<emph.end type="italics"></emph.end> Venice; <emph type="italics"></emph>and I find menti<lb></lb>oned<emph.end type="italics"></emph.end> Sig. </s> <s>Lana, Sig. </s> <s>Albano, Padre Serafino, Pad. </s> <s>Franceſco <lb></lb>de San. </s> <s>Giuſeppe, <emph type="italics"></emph>and many others.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>The Works in which he will ſurvive to all ſucceeding Ages <lb></lb>are firſt His ſolid and ſober Confutation of the Arguments of<emph.end type="italics"></emph.end><lb></lb>Signore Lodovico dell Columbo, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Signore Vincentio di <lb></lb>Gratia <emph type="italics"></emph>againſt the Tract of<emph.end type="italics"></emph.end> Galileo Delle coſe che ſtanno ſopra <lb></lb>Aqua, <emph type="italics"></emph>wherein he vindicates bis ſaid<emph.end type="italics"></emph.end> Maſter <emph type="italics"></emph>with a Gratitude <lb></lb>that Tutors very rarely reap from the pains they take in Culti<lb></lb>vating their Pupils. </s> <s>This Apology was firſt Printed<emph.end type="italics"></emph.end> Anno 1615. <lb></lb><emph type="italics"></emph>and was a ſecond time publiſhed, as alſo thoſe of his Antago<lb></lb>niſts, amongſt the Works of<emph.end type="italics"></emph.end> GALILEO, <emph type="italics"></emph>ſet forth by the <lb></lb>Learned<emph.end type="italics"></emph.end> Viviani 1656. <emph type="italics"></emph>He hath likewiſe writ ſeveral other <lb></lb>curious Pieces, as I am informed by the moſt Courteous<emph.end type="italics"></emph.end> Carolo <lb></lb>Manoleſſi <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Bologna; <emph type="italics"></emph>amongſt others an excellent Treatiſe <lb></lb>concerning<emph.end type="italics"></emph.end> Colours, <emph type="italics"></emph>which he putteth me in hopes to ſee printed<emph.end type="italics"></emph.end><pb xlink:href="068/01/012.jpg"></pb><emph type="italics"></emph>very ſpeedily. </s> <s>And laſt of all theſe Diſcourſes and Reflections <lb></lb>upon the<emph.end type="italics"></emph.end> Menſuration of Running Waters, <emph type="italics"></emph>with the addition of <lb></lb>a Second Book, three Epiſtles, and four Conſiderations upon <lb></lb>the ſame Argument, which conduce much to Illuſtrate his Do<lb></lb>ctrine and Facilitate the Practice of it; and which with a Rela<lb></lb>tion of<emph.end type="italics"></emph.end> Monſignore Corſini, <emph type="italics"></emph>make the ſecond part of my Firſt <lb></lb>Tome.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>I might here ſally forth into the Citation of ſundry Au<lb></lb>thours of Good Account, that have tranſmitted his Character <lb></lb>to Poſterity, but ſhall confine my ſelf to onely two; the one is <lb></lb>of his<emph.end type="italics"></emph.end> Maſter, <emph type="italics"></emph>the other of his<emph.end type="italics"></emph.end> Scholar; <emph type="italics"></emph>than whom there can<lb></lb>not be two more competent Judges of his Accompliſhments. </s> <s>To <lb></lb>begin with his<emph.end type="italics"></emph.end> Maſter, <emph type="italics"></emph>the Quick-ſighted, and truly Lyncean<emph.end type="italics"></emph.end><lb></lb>GALILEO, <emph type="italics"></emph>who ſpeaking of his Abilities in Aſtronomy ſaith<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg961"></arrow.to.target><lb></lb><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> Che la felicità del ſuo ingegno non la fà biſognoſa dell' o<lb></lb>pera ſuo. <emph type="italics"></emph>And again, ſubmitting a certain Demonſtration, <lb></lb>which he intended to divulge, to the Judgment of this our Abbot, he<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg962"></arrow.to.target><lb></lb><emph type="italics"></emph>writes to him in this manner: (b)<emph.end type="italics"></emph.end> Queſto lo comunico a V. S. <lb></lb>per lettera prima che ad alcun altro, con attenderne principal<lb></lb>mente il parer ſuo, e doppo quello de' noſtri Amici diſcoſti, <lb></lb>conpenſiero d' inviarne poi altre Copie ad altri Amici d' Italia, <lb></lb>e di Francia, quando io ne venga da lei conſigliato: e qui pre<lb></lb>gandola a farci parte d' alcuna delle ſue peregrine ſpeculationi; <lb></lb>con ſinceriſſimo affetto, &c. <emph type="italics"></emph>And the moſt acute Mathematician<emph.end type="italics"></emph.end><lb></lb>Signore Evangeliſta Terricelli, <emph type="italics"></emph>late Profeſſour to the Grand <lb></lb>Duke in immediate Succeſſion after<emph.end type="italics"></emph.end> GALILEO, <emph type="italics"></emph>maketh this<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg963"></arrow.to.target><lb></lb><emph type="italics"></emph>Honourable and Grateful Mention of him, and his Book: (c)<emph.end type="italics"></emph.end> O<lb></lb>mitto magnum illum nutantis Maris motum; Prætereo etiam <lb></lb>omnem Fluminum, Aquarumque Currentium tum menſurum, <lb></lb>tum uſum, quarum omnis doctrina reperta primum fuit ab <lb></lb>Abbate BENEDICTO CASTELLIO Preceptore <lb></lb>meo. </s> <s>Scripſit ille Scientiam ſuam, & illam non ſolum demonſtra<lb></lb>tione, verum etiam opere confirmavit, maxima cum Princi<lb></lb>pum & populorum utilitatate, majore cum admiratione Phylo<lb></lb>ſophorum. </s> <s>Extat illius Liber, vere aureus.</s></p><p type="margin"> <s><margin.target id="marg961"></margin.target><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end>Nella continu<lb></lb>atione dell Nun<lb></lb>tio ſiderio.</s></p><p type="margin"> <s><margin.target id="marg962"></margin.target><emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> Lettera al P. <lb></lb></s> <s>Abbate D. B. </s> <s>Ca<lb></lb>ſtelli D'Arcetro; <lb></lb>li. </s> <s>3. Decemb. <lb></lb></s> <s>1639.</s></p><p type="margin"> <s><margin.target id="marg963"></margin.target><emph type="italics"></emph>(c)<emph.end type="italics"></emph.end> De Motu A<lb></lb>quarum. </s> <s>Lib. 2. <lb></lb>Prop. </s> <s>37. p. </s> <s>191.</s></p><p type="main"> <s>§. <emph type="italics"></emph>I have onely two particulars more to offer the Engliſh Rea<lb></lb>der: The one concerns the Book, and it is this, That after the <lb></lb>general Aprobation it hath had in<emph.end type="italics"></emph.end> Italy, <emph type="italics"></emph>I cannot but think it <lb></lb>deſerveth the ſame Civil Entertainment with us, in regard that <lb></lb>it cometh with no leſſe<emph.end type="italics"></emph.end> Novelty, Facility, Verity, and Utility <emph type="italics"></emph>to <lb></lb>us than to thoſe whom the Authour favoured with the Original. <lb></lb></s> <s>Our Rivers and Sewers through Publique Diſtractions and Pri<lb></lb>vate Incroachments are in great diſorder, as thoſe Channels for <lb></lb>iuſtance which formerly were Navigable unto the very Walls of<emph.end type="italics"></emph.end><pb xlink:href="068/01/013.jpg"></pb>York <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Salisbury, <emph type="italics"></emph>&c: Our Ports are choaked and obſtructed <lb></lb>by Shelfes and Setlements: Our Fenns do in a great part lie waſte <lb></lb>and unimproved: Now all theſe may be (and, as I find by the <lb></lb>Confeſſion of ſome whoſe Practiſes upon the Copy of the Firſt <lb></lb>Book onely of our Authour hath got them both Money and Repu<lb></lb>tation, in part have been) remedied by the Ways and Means he <lb></lb>here ſets down. </s> <s>The truth is the Argument hath been paſt over <lb></lb>with an Vniverſal Silence; ſo that to this day I have not ſeen <lb></lb>any thing that hath been written Demonſtratively and with Ma<lb></lb>thematical Certainty concerning the ſame, ſave onely what this <lb></lb>Learned Prelate hath delivered of his Own Invention in theſe <lb></lb>Treatiſes: who yet hath ſo fully and plainly handled the Whole <lb></lb>Doctrine, that I may affirm his Work to be every way abſolute. </s> <s>It <lb></lb>muſt be confeſt the Demonſtration of the Second Propoſition of the <lb></lb>Second Book did not well pleaſe the Authour, and had he lived <lb></lb>he would have ſupplyed that defect, but being prevented by <lb></lb>Death, the Reader muſt content himſelf with the Mechanical <lb></lb>Proof that he giveth you of the truth of ſo Excellent a Con<lb></lb>cluſion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>The other particular that I am to offer is, that out of my de<lb></lb>ſire to contribute what lyeth in me to the compleating of this Piece <lb></lb>for Engliſh Practice, I have exeeded my promiſe not onely in gi<lb></lb>ving you the Second and following Books which were not extant at <lb></lb>the time of tendring my Overtures, but alſo in that I have added <lb></lb>a Map or Plat of all the Rivers, Lakes, Fenns, &c. </s> <s>mentioned <lb></lb>thorow out the Work. </s> <s>And if I have not kept touch in point of <lb></lb>Time, let it be conſidered that I am the Tranſlator and not the <lb></lb>Printer. </s> <s>To conclude, according to your acceptance of theſe my <lb></lb>endeavours, you may expect ſome other Tracts of no leſſe Profit <lb></lb>and Delight.<emph.end type="italics"></emph.end> Farewell.</s></p><p type="head"> <s><emph type="italics"></emph>T. S.<emph.end type="italics"></emph.end></s></p><pb xlink:href="068/01/014.jpg"></pb><p type="head"> <s>ERRATA of the <emph type="italics"></emph>ſecond<emph.end type="italics"></emph.end> PART of the <emph type="italics"></emph>firſt<emph.end type="italics"></emph.end> TOME.</s></p><p type="main"> <s>In PREFACE, I cad <emph type="italics"></emph>Ferdinando II.<emph.end type="italics"></emph.end> ibid. <emph type="italics"></emph>l' Aqua.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>PAGE 2. LINE 26, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> muſt <emph type="italics"></emph>read<emph.end type="italics"></emph.end> much. </s> <s>P. 3. l. </s> <s>22, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> and let. </s> <s>l. </s> <s>25. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> water, from l. </s> <s>41. <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Tappe, (<emph type="italics"></emph>as every where elſe).<emph.end type="italics"></emph.end> Page 4. l. </s> <s>18. <emph type="italics"></emph>r<emph.end type="italics"></emph.end> cords. </s> <s>Page 6. l. </s> <s>9. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> acquire, or. <lb></lb></s> <s>Page 9. l. </s> <s>1. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> irreperable. </s> <s>P. 10. l. </s> <s>13. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> diſſimboguement. <emph type="italics"></emph>For<emph.end type="italics"></emph.end> Page 17. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> P. 15. <lb></lb>P. 15. l. </s> <s>27, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> in. </s> <s>l. </s> <s>36, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> is as. </s> <s>l. </s> <s>38, <emph type="italics"></emph>r. </s> <s>Panaro.<emph.end type="italics"></emph.end> P. 17. l. </s> <s>12, <emph type="italics"></emph>Giulio.<emph.end type="italics"></emph.end> l. </s> <s>17. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Meaſurers. </s> <s>l. <lb></lb></s> <s>25, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> meaſured it,. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> neceſſarily. </s> <s>P. 23. l. </s> <s>19. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> for help. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Page 31. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> P. 32. P. 24. <lb></lb>l. </s> <s>14, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to. </s> <s>l. </s> <s>17, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> namly, of the. </s> <s>l. </s> <s>23, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> eaſie. </s> <s>P. 25. l. </s> <s>38. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Cock. </s> <s>p. </s> <s>29. l. </s> <s>7. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> laſted,. <lb></lb>p. </s> <s>31. l. </s> <s>32. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Soe. </s> <s>p. </s> <s>41. l. </s> <s>20. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to the line. </s> <s>p. </s> <s>48. l. </s> <s>19. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> us the ^{*}. id. <emph type="italics"></emph>Figure falſe<emph.end type="italics"></emph.end> p. </s> <s>52. <lb></lb>l. </s> <s>30, and 31. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Theorem <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Propoſition. </s> <s>p. </s> <s>53. l. </s> <s>29. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> again. </s> <s>p. </s> <s>57. l. </s> <s>19, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> ſame if. <lb></lb></s> <s>l. </s> <s>44. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> bodily. </s> <s>p. </s> <s>58. l. </s> <s>9, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> gathering. </s> <s>l. </s> <s>40. <emph type="italics"></emph>omit<emph.end type="italics"></emph.end>;. </s> <s>p. </s> <s>60. l. </s> <s>2. <emph type="italics"></emph>omit,<emph.end type="italics"></emph.end> if. </s> <s>p. </s> <s>65. l. </s> <s>1. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> tide <lb></lb><emph type="italics"></emph>dele<emph.end type="italics"></emph.end>;. </s> <s>p. </s> <s>66. l. </s> <s>35. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Stoppage of. </s> <s>p. </s> <s>68. l. </s> <s>12, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Lords the <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Lords. </s> <s>l. <emph type="italics"></emph>ult. </s> <s>for<emph.end type="italics"></emph.end> they <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> it. </s> <s>p. </s> <s>69. l. </s> <s>14. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to one. <emph type="italics"></emph>id.<emph.end type="italics"></emph.end> carried <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> to. </s> <s>p. </s> <s>71. l. </s> <s>20, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> and that. </s> <s>l. </s> <s>25, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Braces; it. </s> <s>l. <lb></lb></s> <s>29. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Braces. </s> <s>l. </s> <s>44, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Brent.<emph.end type="italics"></emph.end> p. </s> <s>72. l. </s> <s>23. <emph type="italics"></emph>r. </s> <s>Serene Highneſſe.<emph.end type="italics"></emph.end> p. </s> <s>73. l. </s> <s>24, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> deliberation:. <lb></lb>l. </s> <s>26, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> ſumme <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Moddel. </s> <s>l. </s> <s>40. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Months. </s> <s>p. </s> <s>79. l. </s> <s>18. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> that into. </s> <s>p. </s> <s>82. l. </s> <s>22. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end>;. </s> <s>p. <lb></lb></s> <s>85. l. </s> <s>9, 10. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> a free drame. </s> <s>p. </s> <s>88. l. </s> <s>5. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Palmes. </s> <s>p. </s> <s>89. l. </s> <s>8. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Princes. </s> <s>p. </s> <s>92. l. </s> <s>3. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Diſ<lb></lb>courſes. </s> <s>p. </s> <s>93. l. </s> <s>31. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Tautologie. </s> <s>p. </s> <s>94. l. </s> <s>9. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> miracle;. </s> <s>p. </s> <s>97. l. </s> <s>13. <emph type="italics"></emph>r,<emph.end type="italics"></emph.end> weighty. </s> <s>p. </s> <s>101. <lb></lb>l. </s> <s>21. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Marrara. </s> <s>p. </s> <s>107. l. </s> <s>28, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Patrimony. </s> <s>l. </s> <s>40, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> above. </s> <s>p. </s> <s>111. l. </s> <s>16. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> ſaid. <emph type="italics"></emph>For<emph.end type="italics"></emph.end> p. </s> <s>432. <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> p. </s> <s>114. p. </s> <s>114. l. </s> <s>35. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> of 200, l. </s> <s>41. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> cloſed. </s> <s>p. </s> <s>115. l. </s> <s>29. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> conſtant;.</s></p><pb xlink:href="068/01/015.jpg" pagenum="1"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s><emph type="italics"></emph>LIB.<emph.end type="italics"></emph.end> I.</s></p><p type="main"> <s>What, and of how great moment the confi<lb></lb>deration of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is in natural things, <lb></lb>is ſo manifeſt, that the Prince of <emph type="italics"></emph>Peri<lb></lb>pateticks<emph.end type="italics"></emph.end> pronounced that in his Schools <lb></lb>now much uſed Sentence: <emph type="italics"></emph>Ignorato mo<lb></lb>tu, ignoratur natura.<emph.end type="italics"></emph.end> Thence it is that <lb></lb>true Philoſophers have ſo travailed in the <lb></lb>contemplation of the Celeſtial motions, <lb></lb>and in the ſpeculation of the motions of <lb></lb>Animals, that they have arrived to a wonderful height and ſub<lb></lb>limity of underſtanding. </s> <s>Under the ſame Science of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end><lb></lb>is comprehended all that which is written by Mechanitians con<lb></lb>cerning Engines moving of themſelves, <emph type="italics"></emph>Machins<emph.end type="italics"></emph.end> moving by the <lb></lb>force of Air, and thoſe which ſerve to move weights and im<lb></lb>menſe magnitudes with ſmall force. </s> <s>There appertaineth to the <lb></lb>Science of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> all that which hath been written of the <lb></lb>alteration not onely of Bodies, but of our Minds alſo; and <lb></lb>in ſum, this ample matter of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is ſo extended and di<lb></lb>lated, that there are few things which fall under mans no<lb></lb>tice, which are not conjoyned with <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> or at leaſt de<lb></lb>pending thereupon, or to the knowledge thereof directed; <lb></lb>and of almoſt every of them, there hath been written and <lb></lb>compoſed by ſublime wits, learned Treatiſes and Inſtructions. <pb xlink:href="068/01/016.jpg" pagenum="2"></pb>And becauſe that in the years paſt I had occaſion by Order of <lb></lb>our Lord Pope <emph type="italics"></emph>Vrban<emph.end type="italics"></emph.end> 8. to apply my thoughts to the motion of <lb></lb>the Waters of Rivers, (a matter difficult, moſt important, and <lb></lb>little handled by others) having concerning the ſame obſerved <lb></lb>ſome particulars not well obſerved, or conſidered till now, but of <lb></lb>great moment both in publick and private affairs; I have thought <lb></lb>good to publiſh them, to the end that ingenious ſpirits might <lb></lb>have occaſion to diſcuſſe more exactly then hitherto hath been <lb></lb>done, ſo neceſſary and profitable a matter, and to ſupply alſo my <lb></lb>defects in this ſhort and difficult Tractate. </s> <s>Difficult I ſay, for <lb></lb>the truth is, theſe knowledges, though of things next our ſenſes, <lb></lb>are ſometimes more abſtruce and hidden, then the knowledge of <lb></lb>things more remote; and much better, and with greater exquiſit<lb></lb>neſs are known the motions of the Planets, and Periods of the <lb></lb>Stars, than thoſe of Rivers and Seas: As that ſingular light of <lb></lb>Philoſophie of our times, and my Maſter <emph type="italics"></emph>Signore Galileo Galilei<emph.end type="italics"></emph.end><lb></lb>wiſely obſerveth in his Book concerning the Solar ſpots. </s> <s>And <lb></lb>to proceed with a due order in Sciences, I will take ſome ſuppo<lb></lb>ſitions and cognitions ſufficiently clear; from which I will after<lb></lb>wards proceed to the deducing of the principal concluſions. </s> <s>But <lb></lb>to the end that what I have written at the end of this diſcourſe in <lb></lb>a demonſtrative and Geometrical method, may alſo be under<lb></lb>ſtood of thoſe which never have applyed their thoughts to the <lb></lb>ſtudy of Geometry; I have endeavoured to explain my conceit <lb></lb>by an example, and with the conſideration of the natural things <lb></lb>themſelves, muſt after the ſame order in which I began to doubt <lb></lb>in this matter; and have placed this particular Treatiſe here in <lb></lb>the beginning, adverting nevertheleſs, that he who deſires more <lb></lb>full and abſolute ſolidity of Reaſons, may overpaſs this prefatory <lb></lb>diſcourſe, and onely conſider what is treated of in the demonſtra<lb></lb>tions placed towards the end, and return afterwards to the conſi<lb></lb>deration of the things collected in the <emph type="italics"></emph>Corollaries<emph.end type="italics"></emph.end> and Appendices; <lb></lb>which demonſtrations notwithſtanding, may be pretermitted by <lb></lb>him that hath not ſeen at leaſt the firſt ſix Books of the Elements <lb></lb>of Euclid; ſo that he diligently obſerveth that which fol<lb></lb>loweth.</s></p><p type="main"> <s>I ſay therefore, that having in times paſt, on divers occaſi<lb></lb>ons heard ſpeak of the meaſures of the waters of Rivers, and <lb></lb>Fountains, ſaying, ſuch a River is two or three thouſand feet of <lb></lb>water; ſuch a ſpring-water is twenty, thirty, or forty inches, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end><lb></lb>Although in ſuch manner I have found all to treat thereof in <lb></lb>word and writing, without variety, and as we are wont to ſay, <lb></lb><emph type="italics"></emph>conſtanti ſermone,<emph.end type="italics"></emph.end> yea even Artiſts and Ingeneers, as if it were <lb></lb>a thing that admitted not of any doubt, yet howſoever I re<lb></lb>mained ſtill infolded in ſuch an obſcurity, that I well knew I un<pb xlink:href="068/01/017.jpg" pagenum="3"></pb>derſtood nothing at all, of that which others pretended full and <lb></lb>clearly to underſtand. </s> <s>And my doubt aroſe from my frequent <lb></lb>obſervation of many Trenches and Channels, which carry <lb></lb>water to turn Mills, in which Trenches, and Channels, the <lb></lb>water being meaſured, was found pretty deep; but if afterwards <lb></lb>the ſame water was meaſured in the fall it made to turn the <lb></lb>Wheel of the Mill, it was much leſſe, not amounting often to the <lb></lb>tenth part, nor ſometimes to the twentieth, inſomuch, that the <lb></lb>ſame running water came to be one while more, another while leſs <lb></lb>in meaſure, in divers parts of its Channel; and for that reaſon this <lb></lb>vulgar manner of meaſuring running Waters, as indeterminate and <lb></lb>uncertain, was by me juſtly ſuſpected, the meaſure being to be de<lb></lb>terminate, and the ſame. </s> <s>And here I freely confeſſe that I had fin<lb></lb>gular help to reſolve this difficulty from the excellent & accurate <lb></lb>way of diſcourſing, as in allother matters, ſo alſo in this, of the <lb></lb>Right Honourable and Truly Noble Signior <emph type="italics"></emph>Ciampoli,<emph.end type="italics"></emph.end> Secretary <lb></lb>of the Popes ſecret affairs. </s> <s>Who moreover, not ſparing ſor the coſts <lb></lb>of the ſame, generouſly gave me occaſion a few years paſt to try by <lb></lb>exact experiments that which paſt concerning this particular. </s> <s>And <lb></lb>to explain all more clearly with an example; we ſuppoſe a Veſſel <lb></lb>filled with Water, as for inſtance a Butt, which is kept full, though <lb></lb>ſtill water runneth out, and the Water run out by two Taps equal <lb></lb>of bigneſſe, one put in the bottom of the Veſſel, and the other in <lb></lb>the upper part; it is manifeſt that in the time wherein from the <lb></lb>upper part ſhall iſſue a determinate meaſure of water ſrom <lb></lb>the inferiour part there ſhall iſſue four, five, and many more of <lb></lb>the ſame meaſures, according to the difference of the height of <lb></lb>the Taps, and the diſtance of the upper Tap from the Superfici<lb></lb>es and level of the water of the Veſſel: and all this will alwayes <lb></lb>follow, though, as hath been ſaid, the Taps be equal, and the <lb></lb>water in diſcharging keep the ſaid Taps alwayes full. </s> <s>Where firſt <lb></lb>we note, that, although the meaſure of the Taps be equal, never<lb></lb>theleſſe there iſſueth from them in equal times unequal quantities <lb></lb>of water, And if we ſhould more attentively conſider this buſi<lb></lb>neſſe, we ſhould find, that the water by the lower Tap, run<lb></lb>neth and paſſeth with much greater velocity, then it doth by the <lb></lb>upper, whatever is the reaſon. </s> <s>If therefore we would have <lb></lb>ſuch a quantity of Water diſcharge from the upper tap, as <lb></lb>would diſcharge from the neather in the ſame time, it is plain, that <lb></lb>either the upper Taps muſt be multiplyed in ſuch ſort, that ſo <lb></lb>many more Taps in number be placed above than below, as the <lb></lb>neather tap ſhall be more ſwift than the upper, or the upper Tap <lb></lb>made ſo much bigger than the nether, by how much that be<lb></lb>neath ſhall be more ſwift than that above; and ſo then in equal <lb></lb>times, the ſame quantity of Water ſhall diſcharge from the upper, <lb></lb>as doth from the neather part.</s></p><pb xlink:href="068/01/018.jpg" pagenum="4"></pb><p type="main"> <s>I will declare my ſelf by another example. </s> <s>If we ſhould ima<lb></lb>gine, that two cords or lines of equal thickneſs, be drawn through <lb></lb>two holes of equal bore; but ſo that the firſt paſs with quadruple <lb></lb>velocity to the ſecond: It is manifeſt, that if in a determinate <lb></lb>time, we ſhall by the firſt bore have drawn four Ells of the line, <lb></lb>in the ſame time, by the ſecond hole we ſhall have drawn but one <lb></lb>Ell of cord onely; and if by the firſt there paſſe twelve Ells, then <lb></lb>through the ſecond there ſhall paſſe onely three Ells; and in <lb></lb>ſhort the quantity of cord ſhall have the ſame proportion to the <lb></lb>cord, that the volocity hath to the velocity. </s> <s>And therefore we <lb></lb>deſiring to compenſate the tardity of the ſecond cord, and main<lb></lb>taining the ſame tardity to draw through the ſecond hole as much <lb></lb>cord as through the firſt, it will be neceſſary to draw through the <lb></lb>ſecond bore four ends of cord; ſo that the thickneſs of all the <lb></lb>cords by the ſecond hole, have the ſame proportion to the thick<lb></lb>neſs of the cord which paſſeth onely by the firſt, as the velocity <lb></lb>of the cord by the firſt hole hath reciprocally to the velocity of <lb></lb>the codrs by the ſecond hole. </s> <s>And thus its clear, that when <lb></lb>there is drawn through two holes equal quantity of cords in <lb></lb>equal time, but with unequal velocity, it will be neceſſary, that <lb></lb>the thickneſs of all the four cords ſhall have the ſame reciprocal <lb></lb>proportion to the thickneſs of the ſwifter cord, that the velo<lb></lb>city of the ſwifter cord hath to the velocity of the ſlower. </s> <s>The <lb></lb>which is verified likewiſe in the fluid Element of Water.</s></p><p type="main"> <s>And to the end that this principal fundamental be well under<lb></lb>ſtood, I will alſo note a certain obſervation made my me in the <lb></lb>Art of Wyer-drawing, or ſpinning Gold, Silver, Braſs, and Iron, <lb></lb>and it is this; That ſuch Artificers deſiring more and more to <lb></lb>diſgroſſe and ſubtillize the ſaid Metals, having would about a <lb></lb><emph type="italics"></emph>R<emph.end type="italics"></emph.end>ocket or Barrel, the thread of the Metal, they place the Roc<lb></lb>ket in a frame upon a ſtedfaſt Axis, in ſuch ſort that the Rocket <lb></lb>may turn about in it ſelf; then making one end of the thread to <lb></lb>paſſe by force through a Plate of Steel pierced with divers holes, <lb></lb>greater and leſſer, as need requireth, faſtning the ſame end of the <lb></lb>thread to another Rocket, they wind up the thread, which paſ<lb></lb>ſing through a bore leſs than the thickneſſe of the thread, is of <lb></lb>force conſtrained to diſgroſſe and ſubtillize. </s> <s>Now that which is <lb></lb>intenſly to be obſerved in this buſineſs, is this, That the parts of <lb></lb>the thread before the hole, are of ſuch a thickneſſe, but the parts <lb></lb>of the ſame thread after it is paſſed the hole, are of a leſſer thick<lb></lb>neſſe: and yet nevertheleſſe the maſſe and weight of the thread <lb></lb>which is drawn forth, is ever equal to the maſſe and weight of the <lb></lb>thread which is winded up. </s> <s>But if we ſhould well conſider the mat<lb></lb>ter, we ſhould finde, that the thicker the thread before the hole is, <lb></lb>than the thread paſſed the hole, the greater reciprocally is the <pb xlink:href="068/01/019.jpg" pagenum="5"></pb>velocity of the parts of the thread paſſed the hole, than the volo<lb></lb>city of the parts before the hole: Inſomuch that if <emph type="italics"></emph>verbi gratia<emph.end type="italics"></emph.end><lb></lb>the thickneſſe of the thread before the hole, were double to the <lb></lb>thickneſſe after the hole, in ſuch caſe the velocity of the parts of <lb></lb>the thread paſſed the hole, ſhould be double to the velocity of the <lb></lb>parts of the thread before the hole; and thus the thickneſſe <lb></lb>compenſates the velocity, and the velocity compenſates the thick<lb></lb>neſſe. </s> <s>So that the ſame occurreth in the ſolid Metals of Gold, <lb></lb>Silver, Braſs, Iron, &c. </s> <s>that eveneth alſo in the fluid Element of <lb></lb>Water, and other liquids, namely, That the velocity beareth the <lb></lb>ſame proportion to the velocity, that the thickneſſe of the Me<lb></lb>tal, or Water, hath to the thickneſſe.</s></p><p type="main"> <s>And therefore granting this diſcourſe, we may ſay, that as of<lb></lb>ten as two Taps with different velocity diſcharge equal quanti<lb></lb>ties of Water in equal times, it will be neceſſary that the Tap <lb></lb>leſſe ſwift be ſo much greater, and larger, than the Tap more <lb></lb>ſwift, by how much the ſwifter ſuperates in velocity the ſlower; <lb></lb>and to pronounce the Propoſition in more proper terms, we ſay; <lb></lb>That if two Taps of unequal velocity, diſcharge in equal times <lb></lb>equal quantities of Water, the greatneſſe of the firſt ſhall be to <lb></lb>the greatneſſe of the ſecond, in reciprocal proportion, as the ve<lb></lb>locity of the ſecond to the velocity of the firſt. </s> <s>As for example, <lb></lb>if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it <lb></lb>will be neceſſary, that the ſecond be ten times bigger and larger <lb></lb>than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall <lb></lb>quantities of water in equal times; and this is the principal and <lb></lb>moſt important point, which ought to be kept alwayes in minde, <lb></lb>for that on it well underſtood depend many things profitable, <lb></lb>and worthy of our knowledge.</s></p><p type="main"> <s>Now applying all that hath been ſaid neerer to our purpoſe, I <lb></lb>conſider, that it being moſt true, that in divers parts of the ſame <lb></lb>River or Current of running water, there doth always paſſe equal <lb></lb>quantity of Water in equal time (which thing is alſo demon<lb></lb>ſtrated in out firſt Propoſition) and it being alſo true, that in di<lb></lb>vers parts the ſame River may have various and different veloci<lb></lb>ty; it follows of neceſſary conſequence, that where the River <lb></lb>hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe <lb></lb>parts, in which it hath greater velocity, it ſhall be of leſſe mea<lb></lb>ſure; and in ſum, the velocity of ſeveral parts of the ſaid River, <lb></lb>ſhall have eternally reciprocall and like proportion with <lb></lb>their meaſures. </s> <s>This principle and fundamental well eſtabliſh<lb></lb>ed, that the ſame Current of Water changeth meaſure, accor<lb></lb>ding to its varying of velocity; that is, leſſening the meaſure, <lb></lb>when the velocity encreaſeth, and encreaſing the meaſure, when <lb></lb>the velocity decreaſeth; I paſſe to the conſideration of many <pb xlink:href="068/01/020.jpg" pagenum="6"></pb>particular accidents in this admirable matter, and all depending <lb></lb>on this ſole Propoſition, the ſenſe of which I have oft repeated, <lb></lb>that it might be well underſtood.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> I.</s></p><p type="main"> <s>And firſt, we hence conclude, that the ſame Streams of a <lb></lb>Torrent, namely, thoſe ſtreams which carry equal quantity of <lb></lb>Water in equal times, make not the ſame depths or meaſures in <lb></lb>the River, in which they enter, unleſſe when in the entrance in<lb></lb>to the River they acquire; or to ſay better, keep the ſame velo<lb></lb>city; becauſe if the velocicities acquired in the River ſhall be <lb></lb>different, alſo the meaſures ſhall be diverſe; and conſequently <lb></lb>the depths, as is demonſtrated.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>And becauſe ſucceſſively, as the River is more and more full, <lb></lb>it is conſtituted ordinarily in greater & greater velocity: hence <lb></lb>it is that the ſame ſtreams of the Torrent, that enter into the Ri<lb></lb>ver, make leſſe and leſſe depths, as the River grows more and <lb></lb>more full; ſince that alſo the Waters of the Torrent being en<lb></lb>tered into the River, go acquiring greater and greater velocities, <lb></lb>and therefore diminiſh in meaſure and height.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>We obſerve alſo, that while the main River is ſhallow, if there <lb></lb>fall but a gentle rain, it ſuddenly much increaſeth and riſeth; <lb></lb>but when the River is already ſwelled, though there fall again a<lb></lb>nother new violent ſhower, yet it increaſeth not at the ſame rate <lb></lb>as before, proportionably to the rain which fell: which thing <lb></lb>we may affirm particularly to depend on this, that in the firſt <lb></lb>caſe, while the River is low, it is found alſo very ſlow, and there<lb></lb>fore the little water which entereth into it, paſſeth and runs with <lb></lb>little velocity, and conſequently occupieth a great meaſure: <lb></lb>But when the River is once augmented, by new water being alſo <lb></lb>made more ſwift, it cauſeth the great Flood of water which fal<lb></lb>leth, to bear a leſſe meaſure, and not to make ſuch a depth.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> IV.</s></p><p type="main"> <s>From the things demonſtrated is manifeſt alſo, that whilſt a <lb></lb>Torrent entereth into a River, at the time of Ebbe, then the <lb></lb>Torrent moveth with ſuch a certain velocity, what ever it be, <pb xlink:href="068/01/021.jpg" pagenum="7"></pb>paſſing by its extreameſt parts, wherewith it communicateth with <lb></lb>the River; in which parts, the Torrent being meaſured, ſhall <lb></lb>have ſuch a certain meaſure: but the River ſwelling and riſing, <lb></lb>alſo thoſe parts of the Torrent augment in greatneſſe and mea<lb></lb>ſure, though the Torrent, in that inſtant, diſ-imbogue no more <lb></lb>water than it did before: ſo that the River being ſwelled, we <lb></lb>are to conſider two mouths of the ſame Torrent, one leſſe be<lb></lb>fore the riſing, the other greater after the riſing, which mouths <lb></lb>diſcharge equal quantities of water in equal times; therefore the <lb></lb>velocity by the leſſer mouth ſhall be greater than the velocity by <lb></lb>the greater mouth; and thus the Torrent ſhall be retarded from <lb></lb>its ordinary courſe.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> V.</s></p><p type="main"> <s>From which operation of Nature proceedeth another effect <lb></lb>worthy of conſideration; and it is, that the courſe of the water <lb></lb>retarding, as hath been ſaid in thoſe ultimate parts of the Tor<lb></lb>rent, if it ſhall happen that the Torrent grow torbid and mud<lb></lb>dy, and its ſtreame be retarded in ſuch a degree, that it is not <lb></lb>able to carry away thoſe minute grains of Earth, which com<lb></lb>poſe the muddineſſe; in this caſe the Torrent ſhall clear away <lb></lb>the mud, and carry away the Sand at the bottome of its own <lb></lb>Chanel, in the extream parts of its mouth, which raiſed and <lb></lb>voided Sand, ſhall again afterwards be carried away, when the <lb></lb>River abating, the Torrent ſhall return to move with its primitive <lb></lb>velocity.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> VI.</s></p><p type="main"> <s>Whilſt it is demonſtrated, that the ſame water hath different <lb></lb>meaſures in its Chanel or courſe, according as it varieth in <lb></lb>velocity; ſo that the meaſure of the water is alwayes greater, where <lb></lb>the velocity is leſſer; and on the contrary, the meaſure leſſer, <lb></lb>where the velocity is greater: from hence we may moſt ele<lb></lb>gantly render the reaſon of the uſual Proverb, <emph type="italics"></emph>Take heed of the <lb></lb>ſtill waters:<emph.end type="italics"></emph.end> For that if we conſider the ſelf ſame water of a <lb></lb>River in thoſe parts, wherein it is leſs ſwift, and thence called <emph type="italics"></emph>ſtill<emph.end type="italics"></emph.end><lb></lb>or <emph type="italics"></emph>ſmooth<emph.end type="italics"></emph.end> water, it ſhall be, of neceſſity, of greater meaſure <lb></lb>than in thoſe parts, in which it is more ſwift, and therefore ordi<lb></lb>narily ſhall be alſo more deep and dangerous for paſſengers; <lb></lb>whence it is well ſaid, <emph type="italics"></emph>Take heed of the ſtill Waters<emph.end type="italics"></emph.end>; and this <lb></lb>ſaying hath been ſince applied to things moral.</s></p><pb xlink:href="068/01/022.jpg" pagenum="8"></pb><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> VII.</s></p><p type="main"> <s>Likewiſe, from the things demonſtrated may be concluded, <lb></lb>that the windes, which ſtop a <emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver, and blowing againſt the <lb></lb>Current, retard its courſe and ordinary velocity ſhall neceſſarily <lb></lb>amplifie the meaſure of the ſame River, and conſequently ſhall <lb></lb>be, in great part, cauſes; or we may ſay, potent con-cauſes of <lb></lb>making the extraordinary inundations which Rivers uſe to make. <lb></lb></s> <s>And its moſt certain, that as often as a ſtrong and continual wind <lb></lb>ſhall blow againſt the Current of a River, and ſhall reduce the <lb></lb>water of the River to ſuch tardity of motion, that in the time <lb></lb>wherein before it run five miles, it now moveth but one, ſuch a <lb></lb>River will increaſe to five times the meaſure, though there ſhould <lb></lb>not be added any other quantity of water; which thing indeed <lb></lb>hath in it ſomething of ſtrange, but it is moſt certain, for that <lb></lb>look what proportion the waters velocity before the winde, hath <lb></lb>to the velocity after the winde, and ſuch reciprocally is the mea<lb></lb>ſure of the ſame water after the winde, to the meaſure before <lb></lb>the winde; and becauſe it hath been ſuppoſed in our caſe that the <lb></lb>velocity is diminiſhed to a fifth part, therefore the meaſure ſhall <lb></lb>be increaſed five times more than that, which it was before.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> VIII.</s></p><p type="main"> <s>We have alſo probable the cauſe of the inundations of <emph type="italics"></emph>Tyber,<emph.end type="italics"></emph.end><lb></lb>which befel at <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> in the time of <emph type="italics"></emph>Alexander<emph.end type="italics"></emph.end> the Sixth, & of <lb></lb><emph type="italics"></emph>Clement<emph.end type="italics"></emph.end> the Seventh; which innundations came in a ſerene time, <lb></lb>and without great thaws of the Snows; which therefore much <lb></lb>puzzled the wits of thoſe times. </s> <s>But we may with much pro<lb></lb>bability affirm, That the River roſe to ſuch a height and excreſ<lb></lb>cence, by the retardation of the Waters dependant on the <lb></lb>boiſtrous and conſtant Winds, that blew in thoſe times, as is no<lb></lb>red in the memorials.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end> IX.</s></p><p type="main"> <s>It being moſt manifeſt, that by the great abundance of Water <lb></lb>the Torrents may increaſe, and of themſelves alone exorbitantly <lb></lb>ſwell the River; and having demonſtrated that alſo without new <lb></lb>Water, but onely by the notable retardment the River riſeth and <lb></lb>increaſeth in meaſure, in proportion as the velocity decreaſeth: <lb></lb>hence it is apparent, that each of theſe cauſes being able of it ſelf, <lb></lb>and ſeparate from the other to ſwell the River; when it ſhall <lb></lb>happen that both theſe two cauſes conſpire the augmentation of <pb xlink:href="068/01/023.jpg" pagenum="9"></pb>the River, in ſuch a caſe there muſt follow very great and irre<lb></lb>pable innundations.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> X.</s></p><p type="main"> <s>From what hath been demonſtrated, we may with facility re<lb></lb>ſolve the doubt which hath troubled, and ſtill poſeth the moſt <lb></lb>diligent, but incautelous obſervers of Rivers, who meaſuring <lb></lb>the Streams and Torrents which fall into another River; as thoſe <lb></lb>for inſtance, which enter into the <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> or thoſe which fall into <emph type="italics"></emph>Ti<lb></lb>ber<emph.end type="italics"></emph.end>; and having ſummed the total of theſe meaſures, and con<lb></lb>ferring the meaſures of the Rivers and Brooks, which fall into <lb></lb><emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> with the meaſure of <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> and the meaſures of thoſe which <lb></lb>diſimbogue into <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> with the meaſure of <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> they find them not <lb></lb>equal, as, it ſeems to them, they ought to be, and this is becauſe <lb></lb>they have not well noted the moſt important point of the varia<lb></lb>tion of velocity, and how that it is the moſt potent cauſe of won<lb></lb>derfully altering the meaſures of running Waters; but we moſt <lb></lb>facilly reſolving the doubt, may ſay that theſe Waters diminiſh <lb></lb>the meaſure, being once entered the principal Channel, becauſe <lb></lb>they increaſe in velocity.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XI.</s></p><p type="main"> <s>Through the ignorance of the force of the velocity of the Wa<lb></lb>ter, in altering its meaſure, & augmenting it when the velocity <lb></lb>diminiſheth; and diminiſhing it when the velocity augmenteth: <lb></lb>The Architect <emph type="italics"></emph>Giovanni Fontana,<emph.end type="italics"></emph.end> endeavoured to meaſure, and <lb></lb>and to cauſe to be meaſured by his Nephew, all the Brooks and <lb></lb>Rivers which diſcharged their Waters into <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> at the time of <lb></lb>the Innundation; which happened at <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> in the year 1598, <lb></lb>and publiſhed a ſmall Treatiſe thereof, wherein he ſummeth up <lb></lb>the meaſures of the extraordinary Water which fell into <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end><lb></lb>and made account that it was about five hundred Ells more than <lb></lb>ordinary; and in the end of that Treatiſe concludeth, that to re<lb></lb>move the Innundation wholly from <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> it would be neceſſary <lb></lb>to make two other Channels, equal to that at preſent, and that <lb></lb>leſſe would not ſuffice; and finding afterwards that the whole <lb></lb>Stream paſſed under the Bridge <emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> (the Arch where<lb></lb>of is of a far leſs meaſure then five hundred Ells) concludeth, <lb></lb>that under the ſaid Bridge paſt a hundred fifty one Ells of Water <lb></lb>compreſſed, (I have ſet down the preciſe term of compreſt Wa<lb></lb>ter, written by <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end>) wherein I finde many errors.</s></p><p type="main"> <s>The firſt of which is to think that the meaſures of theſe Wa<lb></lb>ters compreſſed in the Channels of thoſe Brooks and Rivers, <pb xlink:href="068/01/024.jpg" pagenum="10"></pb>ſhould maintain themſelves the ſame in <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> which by his leave, <lb></lb>is moſt falſe, when ever thoſe waters reduced into <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> retain <lb></lb>not the ſame velocity which they had in the place in which <emph type="italics"></emph>Fon<lb></lb>tana<emph.end type="italics"></emph.end> and his Nephew meaſured them: And all this is manifeſt <lb></lb>from the things which we have above explained; for, if the Wa<lb></lb>ters reduced into <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> increaſe in velocity, they decreaſe in mea<lb></lb>ſure; and if they decreaſe in velocity, they increaſe in mea<lb></lb>ſure.</s></p><p type="main"> <s>Secondly, I conſider that the meaſures of thoſe Brooks and <lb></lb>Rivers, which enter into <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> at the time of Innundation, are <lb></lb>not between themſelves really the ſame, when their velocities are <lb></lb>not equal, though they have the ſame names of Ells and Feet; <lb></lb>for that its poſſible that a diſinboguement of ten Ells requadrated <lb></lb>(to ſpeak in the phraſe of <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end>) of one of thoſe Brooks, <lb></lb>might diſcharge into <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> at the time of Innundation, four, ten, <lb></lb>and twenty times leſs Water, than another mouth equal to the <lb></lb>firſt in greatneſs, as would occur when the firſt mouth were four, <lb></lb>ten, or twenty times leſs ſwift than the ſecond. </s> <s>Whereupon, <lb></lb>whilſt <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end> ſummes up the Ells and Feet of the meaſures of <lb></lb>thoſe Brooks and Rivers into a total aggregate, he commits the <lb></lb>ſame error with him, which would add into one ſumme diverſe <lb></lb>moneys of diverſe values, and diverſe places, but that had the <lb></lb>ſame name; as if one ſhould ſay ten Crowns of <emph type="italics"></emph>Roman<emph.end type="italics"></emph.end> money, <lb></lb>four Crowns of Gold, thirteen Crowns of <emph type="italics"></emph>Florence,<emph.end type="italics"></emph.end> five Growns <lb></lb>of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> and eight Crowns of <emph type="italics"></emph>Mantua,<emph.end type="italics"></emph.end> ſhould make the ſame <lb></lb>ſumme with forty Crowns of Gold, or forty Crowns of <emph type="italics"></emph>Mantua.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Thirdly, It might happen that ſome River or Current in the <lb></lb>parts nearer <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> in the time of its flowing, did not ſend forth <lb></lb>more Water than ordinary; and however, its a thing very clear, <lb></lb>that whilſt the ſtream came from the ſuperior parts, that ſame <lb></lb>Brook or River would be augmented in meaſure, as hath been <lb></lb>noted in the fourth <emph type="italics"></emph>Corollary<emph.end type="italics"></emph.end>; in ſuch ſort, that <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end> might <lb></lb>have inculcated, and noted that ſame River or Current as con<lb></lb>curring to the Innundation, although it were therein altogether <lb></lb>unconcerned.</s></p><p type="main"> <s>Moreover, in the fourth place we muſt note, That it might <lb></lb>ſo fall out, that ſuch a River not onely was unintereſſed in the <lb></lb>Innundation, though augmented in meaſure, but it might I ſay <lb></lb>happen, that it was inſtrumental to the aſſwaging the Innunda<lb></lb>tion, by augmenting in the meaſure of its own Channel; which <lb></lb>matter is ſufficiently evident; for if it be ſuppoſed that the Ri<lb></lb>ver in the time of flood, had not had of it ſelf, and from its pro<lb></lb>per ſprings more Water than ordinary, its a thing certain, that <lb></lb>the Water of <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> riſing and increaſing; alſo that River, to le<lb></lb>vel it ſelf with the Water of <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> would have retained ſome of <pb xlink:href="068/01/025.jpg" pagenum="11"></pb>its Waters in its own Chanel, without diſcharging them into <emph type="italics"></emph>Ty<lb></lb>ber,<emph.end type="italics"></emph.end> or elſe would have ingorged and ſwallowed (if I may ſo ſay) <lb></lb>ſome of the water of <emph type="italics"></emph>Tyber<emph.end type="italics"></emph.end>; and in this caſe, at the time of In<lb></lb>undation, leſſe abundance of water would have come to <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end><lb></lb>and yet nevertheleſſe the meaſure of that River would have been <lb></lb>increaſed.</s></p><p type="main"> <s>Fifthly, <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end> deceiveth himſelf, when he concludeth, that <lb></lb>to remove the Inundation from <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> it would be neceſſary to <lb></lb>make two other Chanels of Rivers, that were as large as that, <lb></lb>which is the preſent one, and that leſs would not ſuffice, which, <lb></lb>I ſay, is a fallacy: and to convince him eaſily of his errour, it <lb></lb>ſufficeth to ſay, that all the Streams being paſſed under the Bridge <lb></lb><emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> as he himſelf atteſts, a Channel would ſuffice on<lb></lb>ly of the capacity of the ſaid Bridge, provided that the water <lb></lb>there might run with the ſame velocity, as it did under the Bridge <lb></lb>at the time of Inundation; and on the contrary, twenty Cur<lb></lb>rents of capacity equal to the preſent one, would not ſuffice, if <lb></lb>the water ſhould run with twenty times leſs velocity, than it made <lb></lb>at the time of the Inundation.</s></p><p type="main"> <s>Sixthly, to me it ſeemeth a great weakneſſe to ſay, that there <lb></lb>ſhould paſſe under the Bridge <emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> an hundred fifty one <lb></lb>ells of water compreſſed; for that I do not underſtand that wa<lb></lb>ter is like Cotton or Wool, which matters may be preſt and trod, <lb></lb>as it happeneth alſo to the air, which receiveth compreſſion in <lb></lb>ſuch ſort, that after that in ſome certain place a quantity of air <lb></lb>ſhall be reduced to its natural conſtitution; and having taken up <lb></lb>all the ſaid place, yet nevertheleſſe compreſſing the firſt Air <lb></lb>with force and violence, it is reduced into far leſs room, and will <lb></lb>admit four or ſix times as much air, as before, as is experimen<lb></lb>tally ^{*} ſeen in the Wind-Gun, invented in our dayes by <emph type="italics"></emph>M. Vin,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg964"></arrow.to.target><lb></lb><emph type="italics"></emph>cenzo Vincenti<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Vrbin,<emph.end type="italics"></emph.end> which property of the Air of admit<lb></lb>ting condenſation, is alſo ſeen in the portable Fountains of the <lb></lb>ſame <emph type="italics"></emph>M. Vincenzo:<emph.end type="italics"></emph.end> which Fountains ſpirt the Water on high, <lb></lb>by force of the Air compreſſed, which whilſt it ſeeks to reduce <lb></lb>its ſelf to its natural conſtitution, in the dilation cauſeth that vi<lb></lb>olence. </s> <s>But the water can never, for any thing I know, crowd, <lb></lb>or preſs ſo, as that if before the compreſſion it held or poſſeſt a <lb></lb>place, being in its natural conſtitution, I believe not, I ſay, that it <lb></lb>is poſſible, by preſſing and crowding to make it poſſeſs leſs room, <lb></lb>for if it were poſſible to compreſs the Water, and make it to oc<lb></lb>cupy a leſs place, it would thence follow, that two Veſſels of e<lb></lb>qual meaſure, but of unequal height, ſhould be of unequal capa<lb></lb>city, and that ſhould hold more water which was higher; alſo a <lb></lb>Cylinder, or other Veſſel more high than broad, would containe <lb></lb>more water erected, than being laid along; for that being erect<pb xlink:href="068/01/026.jpg" pagenum="12"></pb>ed, the water put therein would be more preſſed and crowded.</s></p><p type="margin"> <s><margin.target id="marg964"></margin.target>* And as is at <lb></lb>large demonſtrated <lb></lb>by that moſt excel<lb></lb>lent and lonour<lb></lb>able perſonage Mr. <lb></lb><emph type="italics"></emph>Botle<emph.end type="italics"></emph.end> in the indu<lb></lb>ſtrious experiment <lb></lb>of his Pneumatical <lb></lb>Engine.</s></p><p type="main"> <s>And therefore, in our caſe, according to our principles we will <lb></lb>ſay, that the water of that Stream paſseth all under the ſaid <lb></lb>Bridge <emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> for that being there moſt ſwift, it ought of <lb></lb>conſequence to be leſs in meaſure.</s></p><p type="main"> <s>And here one may ſee, into how many errours a man may run <lb></lb>through ignorance of a true and real Principle, which once known <lb></lb>and well underſtood, takes away all miſts of doubting, and ea<lb></lb>ſily reſolveth all difficulties.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end> XII.</s></p><p type="main"> <s>Through the ſame inadvertency of not regarding the variation <lb></lb>of velocity in the ſame Current, therea re committed by Ingi<lb></lb>neers and Learned men, errours of very great moment (and I <lb></lb>could thereof produce examples, but for good reaſons I paſs <lb></lb>them over in ſilence) when they think, and propoſe, by deriving <lb></lb>new Channels from great Rivers, to diminiſh the meaſure of the <lb></lb>water in the River, and to diminiſh it proportionally, according <lb></lb>to the meaſure of the Water which they make to paſs through <lb></lb>the Channel, as making <emph type="italics"></emph>v.g<emph.end type="italics"></emph.end> a Channel fifty foot broad, in which <lb></lb>the derived water is to run waſte, ten foot deep, they think they <lb></lb>have diminiſhed the meaſure of the Water in the River five hun<lb></lb>dred feet, which thing doth not indeed ſo fall out; and the rea<lb></lb>ſon is plain; for that the Chanel being derived, the reſt of the <lb></lb>main River, diminiſheth in velocity, and therefore retains a grea<lb></lb>ter meaſure than it had at firſt before the derivation of the Cha<lb></lb>nel; and moreover, if the Chanel being derived, it ſhall not <lb></lb>conſerve the ſame velocity which it had at firſt in the main Ri<lb></lb>ver, but ſhall diminiſh it, it will be neceſſary, that it hath a grea<lb></lb>ter meaſure than it had before in the River; and therefore <lb></lb>to accompt aright, there ſhall not be ſo much water derived into <lb></lb>the Channel, as ſhall diminiſh the River, according to the quanti<lb></lb>ty of the water in the Channel, as is pretended.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XIII.</s></p><p type="main"> <s>This ſame conſideration giveth me occaſion to diſcover a moſt <lb></lb>ordinary errour, obſerved by me in the buſineſſe of the wa<lb></lb>ter of <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> when I was in thoſe parts, in ſervice of the moſt <lb></lb>Reverend and Illuſtrious Monfignor <emph type="italics"></emph>Corſini<emph.end type="italics"></emph.end>; the ſublime wit of <lb></lb>whom hath been a very great help to me in theſe contemplations; <lb></lb>its very true, I have been much perplexed, whether I ſhould <lb></lb>commit this particular to paper, or paſſe it over in ſilence, for <lb></lb>that I have ever doubted, that the opinion ſo common and <pb xlink:href="068/01/027.jpg" pagenum="13"></pb>moreover confirmed with a moſt manifeſt experiment, may not <lb></lb>onely make this my conjecture to be eſteemed far from true, <lb></lb>but alſo to diſcredit with the World the reſt of this my Treatiſe: <lb></lb>Nevertheleſſe I have at laſt reſolved not to be wanting to my <lb></lb>ſelf, and to truth in a matter of it ſelf, and for other conſe<lb></lb>quences moſt important; nor doth it ſeem to me requiſite in <lb></lb>difficult matters, ſuch as theſe we have in hand, to refigne our <lb></lb>ſelves to the common opinion, ſince it would be very ſtrange if <lb></lb>the multitude in ſuch matters ſhould hit on the truth, nor ought <lb></lb>that to be held difficult, in which even the vulgar do know the <lb></lb>truth and right; beſides that I hope morever to prove all in ſuch <lb></lb>ſort, that perſons of ſolid judgment, ſhall reſt fully perſwaded, <lb></lb>ſo that they but keep in mind the principal ground and foundation <lb></lb>of all this Treatiſe; and though that which I will propoſe, be a par<lb></lb>ticular, as I have ſaid, pertaining onely to the intereſts of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end>; <lb></lb>yet nevertheleſſe from this particular Doctrine well underſtood, <lb></lb>good judgement may be made of other the like caſes in general.</s></p><p type="main"> <s>I ſay then, for greater perſpecuity, and better underſtanding <lb></lb>of the whole, That about thirteen miles above <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> near to <lb></lb><emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> the main of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> branching it ſelf into two parts, with one <lb></lb>of its Arms it cometh cloſe to <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> retaining the name of the <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end>; and here again it divideth it ſelf into two other <lb></lb>branches, and that which continueth on the right hand, is called <lb></lb>the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Primaro<emph.end type="italics"></emph.end>; and that on the left the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>of <emph type="italics"></emph>Volana.<emph.end type="italics"></emph.end> But for that the bed of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being here<lb></lb>tofore augmented and raiſed, it followeth that it reſteth wholly <lb></lb>deprived of the Water of the great P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> except in the time of its <lb></lb>greater ſwelling; for in that caſe, this P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being re<lb></lb>ſtrained with a Bank near to <emph type="italics"></emph>Bondeno,<emph.end type="italics"></emph.end> would come alſo in the <lb></lb>overflowings of the main P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> to be free from its Waters: But the <lb></lb>Lords of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> are wont at ſuch time as the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> threateneth to <lb></lb>break out, to cut the bank; by which cutting, there diſ<lb></lb>gorgeth ſuch a Torrent of Water, that it is obſerved, that the <lb></lb>main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> in the ſpace of ſome few hours abateth near a foot, and <lb></lb>all perſons that I have ſpoken with hitherto, moved by this ex<lb></lb>periment, think that it is of great profit and benefit to keep ready <lb></lb>this Vent, and to make uſe of it in the time of its fullneſſe. </s> <s>And <lb></lb>indeed, the thing conſidered ſimply, and at the firſt appearance, <lb></lb>it ſeemeth that none can think otherwiſe; the rather, for that <lb></lb>many examining the matter narrowly, meaſure that body of <lb></lb>Water which runneth by the Channel, or Bed of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Fera<lb></lb>ra,<emph.end type="italics"></emph.end> and make account, that the body of the Water of the great <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> is diminiſhed the quantity of the body of the Water which <lb></lb>runneth by the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara.<emph.end type="italics"></emph.end> But if we well remember what <lb></lb>hath been ſaid in the beginning of the Treatiſe, and how much <pb xlink:href="068/01/028.jpg" pagenum="14"></pb>the variety of the velocities of the ſaid Water importeth, and the <lb></lb>knowledge of them is neceſſary to conclude the true quantity of <lb></lb>the running Water, we ſhall finde it manifeſt, that the benefit of <lb></lb>this Vent is far leſſe than it is generally thought: And mereover, <lb></lb>we ſhall finde, if I deceive not my ſelf, that there follow from <lb></lb>thence ſo many miſchiefs, that I could greatly incline to believe, <lb></lb>that it were more to the purpoſe wholly to ſtop it up, than to <lb></lb>maintain it open: yet I am not ſo wedded to my opinion, but <lb></lb>that I am ready to change my judgement upon ſtrength of better <lb></lb>reaſons; eſpecially of one that ſhall have firſt well underſtood <lb></lb>the beginning of this my diſcourſe, which I frequently inculcate, <lb></lb>becauſe its abſolutely impoſſible without this advertiſement to <lb></lb>treat of theſe matters, and not commit very great errours.</s></p><p type="main"> <s>I propoſe therefore to conſideration, that although it be true, <lb></lb>that whilſt the water of the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> is at its greateſt height, the <lb></lb>Bank and Dam then cut of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> and the ſuperior <lb></lb>waters having a very great fall into the Channel of <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> they <lb></lb>precipitate into the ſame with great violence and velocity, and <lb></lb>with the ſame in the beginning, or little leſſe, they run towards <lb></lb>the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Volana,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Argenta<emph.end type="italics"></emph.end> on the ſea coaſts; yet after the <lb></lb>ſpace of ſome few hours, the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being full, and the ſu<lb></lb>perior Waters not finding ſo great a diclivity there, as they had <lb></lb>at the beginning of the cutting, they fall not into the ſame with <lb></lb>the former velocity, but with far leſſe, and thereby a great deal <lb></lb>leſſe Water begins to iſſue from the great P<emph type="italics"></emph>o<emph.end type="italics"></emph.end>; and if we dili<lb></lb>gently compare the velocity at the firſt cutting, with the velocity <lb></lb>of the Water after the cutting made, and when the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end><lb></lb>ſhall be full of Water, we ſhall finde perhaps that to be fifteen or <lb></lb>twenty times greater than this, and conſequently the Water <lb></lb>which iſſues from the great P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> that firſt impetuoſity being paſt, <lb></lb>ſhall be onely the fifteenth or twentieth part of that which iſſued <lb></lb>at the beginning; and therefore the Waters of the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> will <lb></lb>return in a ſmall time almoſt to the firſt height. </s> <s>And here I will <lb></lb>pray thoſe who reſt not wholly ſatisfied with what hath been ſaid, <lb></lb>that for the love of truth, and the common good, they would <lb></lb>pleaſe to make diligent obſervation whether in the time of great <lb></lb>Floods, the ſaid Bank or Dam at <emph type="italics"></emph>Bondeno<emph.end type="italics"></emph.end> is cut, and that in few <lb></lb>hours the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> diminiſheth, as hath been ſaid about a foot in <lb></lb>its height; that they would obſerve I ſay, whether, a day or two <lb></lb>being paſt, the Waters of the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> return almoſt to their firſt <lb></lb>height; for if this ſhould follow, it would be very clear, that the <lb></lb>benefit which reſulteth from this diverſion or Vent, is not ſo great <lb></lb>as is univerſally preſumed; I ſay, it is not ſo great as is <lb></lb>preſumed; becauſe, though it be granted for true, that <lb></lb>the Waters of the main P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> abate at the beginning of <pb xlink:href="068/01/029.jpg" pagenum="17"></pb>the Vent, yet this benefit happens to be but temporary and for a <lb></lb>few hours: If the riſing of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> and the dangers of breaking forth <lb></lb>were of ſhort duration, as it ordinarily befalleth in the overflow<lb></lb>ings of Torrents, in ſuch a caſe the profit of the Vent would be <lb></lb>of ſome eſteem: But becauſe the ſwellings of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> continue for <lb></lb>thirty, or ſometimes for forty dayes, therefore the gain which <lb></lb>reſults from the Vent proveth to be inconſiderable. </s> <s>It remain<lb></lb>eth now to conſider the notable harms which follow the ſaid <lb></lb>Sluice or Vent, that ſo reflection being made, and the profit and <lb></lb>the detriment compared, one may rightly judge, and chooſe that <lb></lb>which ſhall be moſt convenient. </s> <s>The firſt prejudice therefore <lb></lb>which ariſeth from this Vent or Sluice, is; That the Channels of <lb></lb><emph type="italics"></emph>Ferara, Primaro,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Volana<emph.end type="italics"></emph.end> filling with Water, all thoſe parts <lb></lb>from <emph type="italics"></emph>Bondeno<emph.end type="italics"></emph.end> to the Sea ſide are allarmed and endangered <lb></lb>thereby. </s> <s>Secondly, The Waters of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro<emph.end type="italics"></emph.end> having <lb></lb>free ingreſſe into the upper Valleys, they fill them to the great <lb></lb>damage of the Fields adjacent, and obſtruct the courſe of the <lb></lb>ordinary Trenches in the ſame Valleys; inſomuch that all the <lb></lb>care, coſt, and labour about the draining, and freeing the upper <lb></lb>Valleys from Water, would alſo become vain and ineffectual. <lb></lb></s> <s>Thirdly, I conſider that theſe Waters of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being <lb></lb>paſſed downwards towards the Sea, at the time that the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>was in its greater excreſcences and heights, it is manifeſt by expe<lb></lb>rience, that when the great P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> diminiſheth, then theſe Waters <lb></lb>paſſed by the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> begin to retard in their courſe, and <lb></lb>finally come to turn the current upwards towards <emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> reſting <lb></lb>firſt iu the intermediate time, almoſt fixed and ſtanding, and <lb></lb>therefore depoſing the muddineſſe, they fill up the Channel of <lb></lb>the River or Current of <emph type="italics"></emph>Ferara.<emph.end type="italics"></emph.end> Fourthly and laſtly, There <lb></lb>followeth from this ſame diverſion another notable damage, and <lb></lb>it is like to that which followeth the breaches made by Rivers; <lb></lb>near to which breaches in the lower parts, namely below the <lb></lb>breach, there is begot in the Channel of the River, a certain ridge <lb></lb>or ſhelf, that is, the bottom of the River is raiſed, as if ſufficiently <lb></lb>manifeſt by experience; and thus juſt in the ſame manner cutting <lb></lb>the Bank at <emph type="italics"></emph>Bondeno,<emph.end type="italics"></emph.end> there is at it were a breach made, from which <lb></lb>followeth the riſing in the lower parts of the main P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> being paſt <lb></lb>the mouth of <emph type="italics"></emph>Pamaro<emph.end type="italics"></emph.end>; which thing, how pernitious it is, let any one <lb></lb>judge that underſtandeth theſe matters. </s> <s>And therefore both for <lb></lb>the ſmall benefit, and ſo many harms that enſue from maintain<lb></lb>ing this diverſion, I ſhould think it were more ſound advice to <lb></lb>keep that Bank alwaies whole at <emph type="italics"></emph>Bondeno,<emph.end type="italics"></emph.end> or in any other conve<lb></lb>nient place, and not to permit that the Water of the Grand P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>ſhould ever come near to <emph type="italics"></emph>Ferara.<emph.end type="italics"></emph.end></s></p><pb xlink:href="068/01/030.jpg" pagenum="16"></pb><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XIV.<lb></lb><arrow.to.target n="marg965"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg965"></margin.target>* <emph type="italics"></emph>Arteſia.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>In the Grand Rivers, which fall into the Sea, as here in <emph type="italics"></emph>Italy <lb></lb>Po, Adige,<emph.end type="italics"></emph.end>^{*} and <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> which are armed with Banks againſt their <lb></lb>excreſcencies, its obſerved that far from the Sea, they need <lb></lb>Banks of a notable height; which height goeth afterwards by <lb></lb>degrees diminiſhing, the more it approacheth to the Sea-coaſts: <lb></lb>in ſuch ſort, that the P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> diſtant from the Sea about fifty or ſixty <lb></lb>miles at <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> ſhall have Banks that be above twenty feet <lb></lb>higher than the ordinary Water marks; but ten or twelve miles <lb></lb>from the Sea, the Banks are not twelve feet higher than the ſaid <lb></lb>ordinary Water-marks, though the breadth of the River be the <lb></lb>ſame, ſo that the excreſcence of the ſame Innundation happens <lb></lb>to be far greater in meaſure remote from the Sea, then near; and <lb></lb>yet it ſhould ſeem, that the ſame quantity of Water paſſing by <lb></lb>every piace, the River ſhould need to have the ſame altitude of <lb></lb>Banks in all places: But we by our Principles and fundamentals <lb></lb>may be able to render the reaſon of that effect, and ſay; That <lb></lb>that exceſſe of quantity of Water, above the ordinary Water, <lb></lb>goeth alwaies acquiring greater velocity; the nearer it approach<lb></lb>eth the Sea, and therefore decreaſeth in meaſure, and conſequenly <lb></lb>in height. </s> <s>And this perhaps might have been the cauſe in great <lb></lb>part, why the <emph type="italics"></emph>Tyber<emph.end type="italics"></emph.end> in the Innundation <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1578. iſſued not <lb></lb>forth of its Channel below <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> towards the Sea.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XV.</s></p><p type="main"> <s>From the ſame Doctrine may be rendred a moſt manifeſt rea<lb></lb>ſon why the falling Waters go leſſening in their deſcent, ſo <lb></lb>that the ſame falling Water, meaſured at the beginning of <lb></lb>its fall, is greater, and bigger, and afterwards by degrees leſſeneth <lb></lb>in meaſure the more it is remote from the beginning of the fall. <lb></lb></s> <s>Which dependeth on no other, than on the acquiſition, which <lb></lb>it ſucceſſively makes of greater velocity; it being a moſt fami<lb></lb>liar concluſion among Philoſophers, that grave bodies falling, <lb></lb>the more they remove from the beginning of their motion, the <lb></lb>more they acquire of ſwiftneſſe; and therefore the Water, as a <lb></lb>grave body, falling, gradually velocitates, and therefore de<lb></lb>creaſeth in meaſure, and leſſeneth.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XVI.</s></p><p type="main"> <s>And on the contrary, the ſpirtings of a Fountain of Water, <lb></lb>which ſpring on high, work a contrary effect; namely <pb xlink:href="068/01/031.jpg" pagenum="17"></pb>in the beginning they are ſmall, and afterwards become greater <lb></lb>and bigge; and the reaſon is moſt manifeſt, becauſe in the be<lb></lb>ginning they are very ſwift, and afterwards gradually relent <lb></lb>their impetuoſity, and motion, ſo that in the beginning of the <lb></lb>excurſion that they make, they ought to be ſmall, and after<lb></lb>wards to grow bigger, as in the effect is ſeen.</s></p><p type="head"> <s>APPENDIX. I.</s></p><p type="main"> <s>Into the errour of not conſidering how much the different <lb></lb>velocities of the ſame running water in ſeveral places of <lb></lb>its current, are able to change the meaſure of the ſame <lb></lb>water, and to make it greater, or leſſe, I think, if I be not <lb></lb>deceived, that <emph type="italics"></emph>Ginlio Frontino<emph.end type="italics"></emph.end> a noble antient Writer, may <lb></lb>have faln in the Second Book which he writ, of the Aqueducts <lb></lb>of the City of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end>: Whilſt finding the meaſure of the Water <lb></lb>^{*}<emph type="italics"></emph>Commentaries<emph.end type="italics"></emph.end> leſſe than it was <emph type="italics"></emph>in erogatione 1263. Quinaries,<emph.end type="italics"></emph.end> he </s></p><p type="main"> <s><arrow.to.target n="marg966"></arrow.to.target><lb></lb>thought that ſo much difference might proceed from the negligence <lb></lb>of the Meaſures; and when afterwards with his own induſtry he <lb></lb>meaſured the ſame water at the beginnings of the Aqueducts, <lb></lb>finding it neer 10000. <emph type="italics"></emph>Quinaries<emph.end type="italics"></emph.end> bigger than it was <emph type="italics"></emph>in Commenta<lb></lb>riis<emph.end type="italics"></emph.end> he judged, that the overplus was imbeziled by Miniſters and <lb></lb>Partakers; which in part might be ſo, for it is but too true, that <lb></lb>the publique is almoſt alwayes defrauded; yet nevertheleſſe, I <lb></lb>verily believe withal, that beſides the frauds of theſe Officers, <lb></lb>the velocities of the water in the place wherein <emph type="italics"></emph>Frontino<emph.end type="italics"></emph.end> meaſu<lb></lb>red, it might be different from thoſe velocities, which are <lb></lb>found in other places before meaſured by others; and there<lb></lb>fore the meaſures of the waters might, yea ought necſſarily to <lb></lb>be diffcrent, it having been by us demonſtrated, that the mea<lb></lb>ſures of the ſame running water have reciprocal proportion to <lb></lb>their velocities. </s> <s>Which <emph type="italics"></emph>Frontino<emph.end type="italics"></emph.end> not well conſidering, and find<lb></lb>ing the water <emph type="italics"></emph>in Commentariis 12755. Quinaries in erogati<lb></lb>one<emph.end type="italics"></emph.end> 14018, and in his own meaſure <emph type="italics"></emph>ad capita ductuum,<emph.end type="italics"></emph.end> at the <lb></lb>head of the fountain 22755. <emph type="italics"></emph>Quinaries,<emph.end type="italics"></emph.end> or thereabouts, he <lb></lb>thought, that in all theſe places there paſt different quantities of <lb></lb>water; namely, greater at the fountain head then that which was <lb></lb><emph type="italics"></emph>in Erogatione,<emph.end type="italics"></emph.end> and this he judged greater than that which was <lb></lb><emph type="italics"></emph>in Commentariis.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg966"></margin.target>+ <emph type="italics"></emph>Commentarius<emph.end type="italics"></emph.end><lb></lb>beareth many ſen<lb></lb>ſes, but in this <lb></lb>place ſignifieth a <lb></lb>certain Regiſter of <lb></lb>the quantities of <lb></lb>the Waters in the <lb></lb>ſeveral publique A<lb></lb>qu ducts of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end>; <lb></lb>which word I find <lb></lb>frequently uſed in <lb></lb>the Law-books of <lb></lb>antient Civilians: <lb></lb>Andby errogation <lb></lb>we are to under<lb></lb>ſtand the diſtribu<lb></lb>tion or delivering <lb></lb>out of thoſe ſtores <lb></lb>of Water.</s></p><p type="head"> <s>APPENDIX II.</s></p><p type="main"> <s>Alike miſtake chanced lately in the Aqueduct of <emph type="italics"></emph>Acqua<lb></lb>Paola,<emph.end type="italics"></emph.end> which Water ſhould be 2000 Inches, and ſo many <lb></lb>effectively ought to be allowed; and it hath been given in <pb xlink:href="068/01/032.jpg" pagenum="18"></pb>ſo to be by the Signors of <emph type="italics"></emph>Bracciano<emph.end type="italics"></emph.end> to the <emph type="italics"></emph>Apoſtolick-Chamber<emph.end type="italics"></emph.end>; <lb></lb>and there was a meaſure thereof made at the beginning of the <lb></lb>Aqueduct; which meaſure proved afterwards much leſſe and <lb></lb>ſhort, conſidered and taken in <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> and thence followed diſ<lb></lb>contents and great diſorders, and all becauſe this property of <lb></lb>Running-Waters, of increaſing in meaſure, where the velocity <lb></lb>decreaſed; and of diminiſhing in meaſure, where the velocity <lb></lb>augmented, was not lookt into.</s></p><p type="head"> <s>APPENDIX III.</s></p><p type="main"> <s>Alike errour, in my judgement, hath beeen committed by <lb></lb>all thoſe learned men, which to prevent the diverſion of <lb></lb>the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> into P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> by the Channels, through <lb></lb>which it at preſent runneth, judged, that the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> being in its <lb></lb>greater excreſcence about 2000 feet, and the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> being near <lb></lb>1000 feet broad, they judged, I ſay, that letting the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> into <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> it would have raiſed the Water of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> two feet; from which <lb></lb>riſe, they concluded afterwards moſt exorbitant diſorders, either <lb></lb>of extraordinary Inundations, or elſe of immenſe and intolera<lb></lb>ble expences to the people in raiſing the Banks of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end><lb></lb>and with ſuch like weakneſſes, often vainly diſturbed the minds <lb></lb>of the perſons concerned: But now from the things demonſtra<lb></lb>ted, it is manifeſt, That the meaſure of the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> would <lb></lb>be different from the meaſure of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in P<emph type="italics"></emph>o<emph.end type="italics"></emph.end>; in caſe that the <lb></lb>velocity of the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> ſhould differ from the velocity <lb></lb>of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> as is more exactly determined in the fourth Pro<lb></lb>poſition.</s></p><p type="head"> <s>APPENDIX IV.</s></p><p type="main"> <s>No leſs likewiſe are thoſe Ingeneers and Artiſts deceived, <lb></lb>that have affirmed, That letting the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> there <lb></lb>would be no riſe at all in the Water of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end>: For the truth <lb></lb>is, That letting <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> there would alwaies be a riſing; but <lb></lb>ſometimes greater, ſometimes leſſe, as the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall have a ſwifter <lb></lb>or ſlower Current; ſo that if the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall be conſtituted in a great <lb></lb>velocity, the riſe will be very ſmall; and if the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall be <lb></lb>ſlow in its courſe, then the riſe will be notable.</s></p><p type="head"> <s>APPENDIX V.</s></p><p type="main"> <s>And here it will not be beſides the purpoſe to advertiſe, That <lb></lb>the meaſures, partments, and diſtributions of the Waters <lb></lb>of Fountains, cannot be made exactly, unleſs there be con<pb xlink:href="068/01/033.jpg" pagenum="19"></pb>fidered, beſides the meaſure, the velocity alſo of the Water; <lb></lb>which particular not being thorowly obſerved, is the cauſe of <lb></lb>continual miſcariages in ſuch like affairs.</s></p><p type="head"> <s>APPENDIX VI.</s></p><p type="main"> <s>Like conſideration ought to be had with the greater diligence, <lb></lb>for that an errour therein is more prejudicial; I ſay, ought to <lb></lb>be had by thoſe which part and divide Waters; for the <lb></lb>watering of fields, as is done in the Territories of <emph type="italics"></emph>Breſcia, Ber<lb></lb>gama, Crema, Pavia, Lodigiano, Cremona,<emph.end type="italics"></emph.end> and other places: <lb></lb>For if they have not regard to the moſt important point of the <lb></lb>variation of the velocity of the Water, but onely to the bare <lb></lb>Vulgar meaſure, there will alwaies very great diſorders and pre<lb></lb>judices enſue to the perſons concerned.</s></p><p type="head"> <s>APPENDIX VII.</s></p><p type="main"> <s>It ſeemeth that one may obſerve, that whilſt the Water run<lb></lb>neth along a Channel, Current, or Conduit, its velocity is <lb></lb>retarded, withheld, and impeded by its touching the Bank or <lb></lb>ſide of the ſaid Channel or Current; which, as immoveable, not <lb></lb>following the motion of the Water, interrupteth its velocity: <lb></lb>From which particular, being true, as I believe it to be moſt <lb></lb>true, and from our conſiderations, we have an occaſion of diſ<lb></lb>covering a very nice miſtake, into which thoſe commonly fall <lb></lb>who divide the Waters of Fountains. </s> <s>Which diviſion is wont <lb></lb>to be, by what I have ſeen here in <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> performed two wayes; <lb></lb>The firſt of which is with the meaſures of like figures, as Cir<lb></lb>cles, or Squares, having cut through a Plate of metal ſeveral <lb></lb>Circles or Squares, one of half an inch, another of one inch, <lb></lb>another of two, of three, of four, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> with which they after<lb></lb>wards adjuſt the Cocks to diſpence the Waters. </s> <s>The other <lb></lb>manner of dividing the Waters of Fountains, is with rectangle <lb></lb>paralellograms, of the ſame height, but of different Baſes, in ſuch <lb></lb>ſort likewiſe, that one paralellogram be of half an inch, another <lb></lb>of one, two, three, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> In which manner of meaſuring and <lb></lb>dividing the Water, it ſhould ſeem that the Cocks being placed <lb></lb>in one and the ſame plain, equidiſtant from the level, or ſuperior <lb></lb>ſuperficies of the water of the Well; and the ſaid meaſures be<lb></lb>ing moſt exactly made, the Water ought conſequently alſo to <lb></lb>be equally divided, and parted according to the proportion of <lb></lb>the meaſures. </s> <s>But if we well conſider every particular, we ſhall <lb></lb>finde, that the Cocks, as they ſucceſſively are greater, diſcharge <lb></lb>alwaies more Water than the juſt quantity, in compariſon of <pb xlink:href="068/01/034.jpg" pagenum="20"></pb>the leſſer; that is, to ſpeak more properly, The Water which <lb></lb>paſſeth through the greater Cock, hath alwaies a greater pro<lb></lb>portion to that which paſſeth through the leſſer, than the greater <lb></lb>Cock hath to the leſſer. </s> <s>All which I will declare by an exam<lb></lb>ple.</s></p><p type="main"> <s>Let there be ſuppoſed for more plainneſs two Squares; (the <lb></lb>ſame may be underſtood of Circles, and other like Figures) The <lb></lb>firſt Square is, as we will ſuppoſe, quadruple to the other, and <lb></lb>theſe Squares are the mouths of two Cocks.; one of four inches, <lb></lb>the other of one: Now its manifeſt by what hath been ſaid, that <lb></lb>the Water which paſſeth by the leſs Cock, findeth its velocity <lb></lb>impeded in the circumference of the Cock; which impediment <lb></lb><figure id="id.068.01.034.1.jpg" xlink:href="068/01/034/1.jpg"></figure><lb></lb>is meaſured by the ſaid circumfe<lb></lb>rence. </s> <s>Now it is to be conſider<lb></lb>ed, that if we would have the Wa<lb></lb>ter which paſſeth through the <lb></lb>greater Cock, to be onely qua<lb></lb>druple to that which paſſeth <lb></lb>through the leſſe, in equal ſpaces of time, it would be neceſſary, <lb></lb>that not onely the capacity and the meaſure of the greater Cock <lb></lb>be quadruple to the leſſer Cock, but that alſo the impediment be <lb></lb>quadrupled. </s> <s>Now in our caſe it is true, That the belly and <lb></lb>mouth of the Cock is quadrupled, and yet the impediment is not <lb></lb>quadrupled, but is onely doubled; ſeeing that the circumference <lb></lb>of the greater Square, is onely double to the circumference of <lb></lb>the leſier Square; for the greater circumference containeth eight <lb></lb>of thoſe parts, of which the leſſer containeth but four, as is ma<lb></lb>nifeſt by the deſcribed Figure; and for that cauſe there ſhall <lb></lb>paſs by the greater Cock, above four times as much Water, as <lb></lb>ſhall paſs by the leſſer Cock.</s></p><p type="main"> <s>The like errour occurreth alſo in the other manner of meaſu<lb></lb>ring the Water of a Fountain, as may eaſily be collected from <lb></lb>what hath been ſaid and obſerved above.</s></p><p type="head"> <s>APPENDIX VIII.</s></p><p type="main"> <s>The ſame contemplation diſcovereth the errour of thoſe <lb></lb>Architects, who being to erect a Bridge of ſundry Arches <lb></lb>over a River, conſider the ordinary breadth of the River; <lb></lb>which being <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> fourty fathom, and the Bridge being to conſiſt <lb></lb>of four Arches, it ſufficeth them, that the breadth of all the four <lb></lb>Arches taken together, be fourty fathom; not conſidering that <lb></lb>in the ordinary Channel of the River, the Water hath onely <lb></lb>two impediments which retard its velocity; namely, the touching <lb></lb>and gliding along the two ſides or ſhores of the River: but <pb xlink:href="068/01/035.jpg" pagenum="21"></pb>the ſame water in paſſing under the Bridge, in our caſe meeteth <lb></lb>with eight of the ſame impediments, bearing, and thruſting upon <lb></lb>two ſides of each Arch (to omit the impediment of the bottom, <lb></lb>for that it is the ſame in the River, and under the Bridge) from <lb></lb>which inadvertency ſometimes follow very great diſorders, as <lb></lb>quotidian practice ſhews us.</s></p><p type="head"> <s>APPENDIX IX.</s></p><p type="main"> <s>It is alſo worthy to conſider the great and admirable benefit <lb></lb>that thoſe fields receive, which are wont to drink up the Rain<lb></lb>water with difficulty, through the height of the water in the <lb></lb>principal Ditches; in which caſe the careful Husbandman cutteth <lb></lb>away the reeds and ruſhes in the Ditches, through which the <lb></lb>waters paſs; whereupon may be preſently ſeen, ſo ſoon as the <lb></lb>reeds and ruſhes are cut, a notable Ebb in the level of the water <lb></lb>in the Ditches; inſomuch that ſometimes it is obſerved, that the <lb></lb>water is abated after the ſaid cutting a third and more, of what it <lb></lb>was before the cutting. </s> <s>The which effect ſeemingly might de<lb></lb>pend on this, That, before thoſe weeds took up room in the <lb></lb>Ditch, and for that cauſe the water kept a higher level, and the <lb></lb>ſaid Plants being afterwards cut and removed, the water came to <lb></lb>abate, poſſeſſing the place that before was occupied by the <lb></lb>weeds: Which opinion, though probable, and at firſt ſight ſa<lb></lb>tisfactory, is nevertheleſs inſufficient to give the total reaſon of <lb></lb>that notable abatement which hath been ſpoken of: But it is ne<lb></lb>ceſſary to have recourſe to our confideration of the velocity in <lb></lb>the courſe of the water, the chiefeſt and true cauſe of the vari<lb></lb>ation of the meaſure of the ſame Running-Water; for, that <lb></lb>multitudes of reeds, weeds, and plants diſperſed through the cur<lb></lb>rent of the Ditch, do chance notably to retard the courſe of the <lb></lb>water, and therefore the meaſure of the water increaſeth; and <lb></lb>thoſe impediments removed, the ſame water gaineth velocity, <lb></lb>and therefore decreaſeth in meaſure, and conſequently in <lb></lb>height.</s></p><p type="main"> <s>And perhaps this point well underſtood, may be of great <lb></lb>profit to the fields adjacent to the <emph type="italics"></emph>Pontine<emph.end type="italics"></emph.end> Fens, and I doubt not <lb></lb>but if the River <emph type="italics"></emph>Ninfa,<emph.end type="italics"></emph.end> and the other principal Brooks of thoſe <lb></lb>Territories were kept well cleanſed from weeds, their waters <lb></lb>would be at a lower level, and conſequently the drains of the <lb></lb>fields would run into them more readily; it being alwayes to be <lb></lb>held for undoubted, that the meaſure of the water before the <lb></lb>cleanſing, hath the ſame proportion to the meaſure after clean<lb></lb>ſing, that the velocity after the cleanſing hath to the velocity <lb></lb>before the cleanſing: An dbecauſe thoſe weeds being cleanſed <pb xlink:href="068/01/036.jpg" pagenum="22"></pb>away, the courſe ef the water notably increaſeth, it is therefore <lb></lb>neceſſary that the ſaid water abate in meaſure, and become <lb></lb>lower.</s></p><p type="head"> <s>APPENDIX. X.</s></p><p type="main"> <s>We having above obſerved ſome errors that are commit<lb></lb>ted in diſtributing the waters of Fountains, and thoſe <lb></lb>that ſerve to water fields; it ſeemeth now fit, by way of <lb></lb>a cloſe to this diſcourſe, to advertiſe by what means theſe divi<lb></lb>ſions may be made juſtly and without error. </s> <s>I therefore think <lb></lb>that one might two ſeveral wayes exquiſitly divide the water of <lb></lb>Fountains; The firſt would be by diligently examining, Firſt, <lb></lb>how much water the whole Fountain diſchargeth in a determi<lb></lb>nate time, as for inſtance: How many Barrels, or Tuns it carri<lb></lb>eth in a ſet time; and in caſe you are afterwards to diſtribute <lb></lb>the water, diſtribute it at the rate of ſomany Barrels or Tuns, in <lb></lb>that ſame time; and in this caſe the participants would have <lb></lb>their punctual ſhares: Nor could it ever happen to ſend out more <lb></lb>water, than is reckoned to be in the principal Fountain; as befel <lb></lb><emph type="italics"></emph>Giulio Frontino,<emph.end type="italics"></emph.end> and as alſo it frequently happeneth in the Mo<lb></lb>dern Aqueducts, to the publick and private detriment.</s></p><p type="main"> <s>The other way of dividing the ſame waters of a Fountain, is <lb></lb>alſo ſufficiently exact and eaſie, and may be, by having one one<lb></lb>ly ſize for the Cock or Pipe, as ſuppoſe of an inch, or of half an <lb></lb>inch; and when the caſe requireth to diſpence two, three, and <lb></lb>more inches, take ſo many Cocks of the ſaid meaſure as do eva<lb></lb>cuate the water, which is to be emitted; and if we are to make <lb></lb>uſe onely of one greater Cock, we being to place one to diſ<lb></lb>charge for example four inches; and having the former ſole mea<lb></lb>ſure of an inch, we muſt make a Cock that is bigger, its true, than <lb></lb>the Cock of one inch; but not ſimply in a quadruple propor<lb></lb>tion, for that it would diſcharge more than juſt ſo much water, <lb></lb>as hath been ſaid above; but we ought to examine diligently <lb></lb>how much water the little Cock emitteth in an hour; and then <lb></lb>enlarge, and contract the greater Cock, ſo, that it may diſ<lb></lb>charge four times as much water as the leſſer in the ſame time; <lb></lb>and by this means we ſhall avoid the diſorder hinted in the <lb></lb>ſeventh Appendix. </s> <s>It would be neceſſary nevertheleſs, to ac<lb></lb>commodate the Cocks of the Ciſtern ſo, that the level of the <lb></lb>water in the Ciſtern may alwayes reſt at one determinate mark <lb></lb>above the Cock, otherwiſe the Cocks will emit ſometimes <lb></lb>greater, and ſometimes leſſe abundance of water: And becauſe <lb></lb>it may be that the ſame water of the Fountain may be ſometimes <lb></lb>more abundant, ſometimes leſs; in ſuch caſe it will be neceſſary <pb xlink:href="068/01/037.jpg" pagenum="23"></pb>to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa<lb></lb>ter, diſcharge into the publick Fountains, that ſo the particular <lb></lb>participants may have alwayes the ſame abundance of <lb></lb>water.</s></p><p type="head"> <s>APPENDIX XI.</s></p><p type="main"> <s>Much more difficult is the diviſion of the waters which <lb></lb>ſerve to water the fields, it not being poſſible to obſerve <lb></lb>ſo commodiouſly, what quantity of water the whole <lb></lb>Ditch ſends forth in one determinate time, as may be done in <lb></lb>Fountains: Yet nevertheleſs, if the ſecond propoſition by us a <lb></lb>little below demonſtrated, be well underſtood, there may be <lb></lb>thence taken a very ſafe and juſt way to diſtribute ſuch waters. <lb></lb></s> <s>The Propoſition therefore by us demonſtrated is this: If there <lb></lb>be two Sections, (namely two mouths of Rivers) the quantity of <lb></lb>the water which paſſeth by the firſt, hath a proportion to that <lb></lb>which paſſeth by the ſecond, compounded of the proportions of <lb></lb>the firſt Section to the ſecond, and of the velocity through <lb></lb>the firſt, to the velocity through the ſecond: As I will declare <lb></lb>for example by help of practice, that I may be underſtood by <lb></lb>all, in a matter ſo important. </s> <s>Let the two mouths of the <lb></lb>Rivers be A, and B, and let <lb></lb><figure id="id.068.01.037.1.jpg" xlink:href="068/01/037/1.jpg"></figure><lb></lb>the mouth A be in meaſure <lb></lb>and content thirty two feet, <lb></lb>and the mouth B, eight feet. <lb></lb></s> <s>Here you muſt take notice, <lb></lb>that it is not alwayes true, that <lb></lb>the Water which paſſeth by A, <lb></lb>hath the ſame proportion to that which paſſeth by B, that the <lb></lb>mouth A hath to the mouth B; but onely when the velocityes <lb></lb>by each of thoſe paſſages are equal: But if the velocityes ſhall <lb></lb>be unequal, it may be that the ſaid mouths may emit equal <lb></lb>quantity of Water in equal times, though their meaſure be un<lb></lb>equal; and it may be alſo, that the bigger doth diſcharge a great<lb></lb>er quantity of Water: And laſtly, it may be, that the leſs mouth <lb></lb>diſchargeth more Water than the greater; and all this is mani<lb></lb>feſt by the things noted in the beginning of this diſcourſe, and <lb></lb>by the ſaid ſecond Propoſition. </s> <s>Now to examine the propor<lb></lb>tion of the Water that paſſeth by one Ditch, to that which paſ<lb></lb>ſeth by another, that this being known, the ſame Waters and <lb></lb>mouths of Ditches may be then adjuſted; we are to keep ac<lb></lb>count not onely of the greatneſs of the mouths or paſſages of the <lb></lb>Water, but of the velocity alſo; which we will do, by firſt find<lb></lb>ing two numbers that have the ſame proportion between them<pb xlink:href="068/01/038.jpg" pagenum="24"></pb>ſelves, as have the mouths, which are the numbers 32 and 8 <lb></lb>in our example: Then this <lb></lb><figure id="id.068.01.038.1.jpg" xlink:href="068/01/038/1.jpg"></figure><lb></lb>being done, let the velocity <lb></lb>of the Water by the paſſa<lb></lb>ges A and B, be examined <lb></lb>(which may be done keeping <lb></lb>account what ſpace a piece <lb></lb>of Wood, or other body that <lb></lb>ſwimmeth, is carried by the ſtream in one determinate time; as <lb></lb>for inſtance in 50 pulſes) and then work by the golden Rule, as <lb></lb>the velocity by A, is to the velocity by B, ſo is the number 8, to <lb></lb>another number, which is 4. It is clear by what is demonſtra<lb></lb>ted in the ſaid ſecond Propoſition, that the quantity of water, <lb></lb>which paſſeth by the mouth A, ſhall have the ſame proportion of <lb></lb>that which paſſeth by the mouth B, that 8 hath to 1. Such pro<lb></lb>portion being compoſed of the proportions of 32 to 8, and of 8 to <lb></lb>4; namely, tothe greatneſs of the mouth A, to the greatneſs of the <lb></lb>mouth B, and of the velocity in A, to the velocity in B. </s> <s>This being <lb></lb>done, we muſt then contract the mouth which diſchargeth more <lb></lb>then its juſt quantity of water, or enlarge the other which diſchar<lb></lb>geth leſs, as ſhal be moſt commodious in practice, which to him that <lb></lb>hath underſtood this little that hath been delivered, will be very <lb></lb>afie.</s></p><p type="head"> <s>APPENDIX XII.</s></p><p type="main"> <s>Theſe opperations about Water, as I have hitherto on ſun<lb></lb>dry occaſions obſerved, are involved in ſo many difficul<lb></lb>ties, and ſuch a multiplicity of moſt extravagant accidents, <lb></lb>that it is no marvel if continually many, and very important er<lb></lb>rours be therein committed by many, and even by Ingeneers <lb></lb>themſelves, and Learned-men; and becauſe many times they <lb></lb>concern not onely the publique, but private intereſts: Hence it <lb></lb>is, that it not onely belongeth to Artiſts to treat thereof, but very <lb></lb>oft even the vulgar themſelves pretend to give their judgement <lb></lb>therein: And I have been troubled many times with a neceſſity <lb></lb>of treating, not onely with thoſe, which either by practice, or <lb></lb>particular ſtudy, underſtood ſomewhat in theſe matters; but alſo <lb></lb>with people wholly void of thoſe notions, which are neceſſary for <lb></lb>one that would on good grounds diſcourſe about this particular; <lb></lb>and thus many times have met with more difficulty in the thick <lb></lb>skulls of men, than in precipitous Torrents, and vaſt Fennes. <lb></lb></s> <s>And in particular, I had occafion ſome years paſt to go ſee the <lb></lb>Gave or Emiſſary of the Lake of <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> made many years agon <lb></lb>by <emph type="italics"></emph>Braccio Fortobraccio,<emph.end type="italics"></emph.end> but for that it was with great ruines by <lb></lb>Time decayed, and rendred unuſeful, it was repaired with in<pb xlink:href="068/01/039.jpg" pagenum="25"></pb>duſtry truly heroicall and admirable, by Monſignor <emph type="italics"></emph>Maffei Bar<lb></lb>herino,<emph.end type="italics"></emph.end> then Prefect for the Wayes, and now Pope. </s> <s>And being <lb></lb>neceſſitated, that I might be able to walk in the Cave, and for <lb></lb>other cauſes, I let down the Sluices of the ſaid Cave, at the mouth <lb></lb>of the Lake: No ſooner were they ſtopt, but a great many of the <lb></lb>people of the Towns and Villages coaſting upon the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ake <lb></lb>flocking thither, began to make grievous complaints, that if thoſe <lb></lb>Sluices were kept ſhut, not onely the Lake would want its due <lb></lb>Vent, but alſo the parts adjacent to the Lake would be over <lb></lb>flown to their very great detriment. </s> <s>And becauſe at firſt appea<lb></lb>rance their motion ſeemed very reaſonable, I found my ſelf hard <lb></lb>put to it, ſeeing no way to perſwade ſuch a multitude, that the <lb></lb>prejudice which they pretended I ſhould do them by keeping <lb></lb>the Sluices ſhut for two dayes, was abſolutely inſenſible; and that <lb></lb>by keeping them open, the Lake did not ebb in the ſame time ſo <lb></lb>much as the thickneſs of a ſheet of Paper: And therefore I was <lb></lb>neceſſitated to make uſe of the authority I had, and ſo followed <lb></lb>my buſineſs as cauſe required, without any regard to that Rab<lb></lb>ble tumultuouſly aſſembled. </s> <s>Now when I am not working with <lb></lb>Mattock or Spade, but with the Pen and Diſcourſe, I intend to <lb></lb>demonſtrate clearly to thoſe that are capable of reaſon, and that <lb></lb>have well underſtood the ground of this my Treatiſe, that the <lb></lb>fear was altogether vain which thoſe people conceited. </s> <s>And <lb></lb>therefore I ſay, that the Emiſſary or Sluice of the Lake of <emph type="italics"></emph>Peru<lb></lb>gia,<emph.end type="italics"></emph.end> ſtanding in the ſame mannner as at preſent, and the water <lb></lb>paſſing thorow it with the ſame velocity as now; to examine <lb></lb>how much the Lake may abate in two days ſpace, we ought to <lb></lb>conſider, what proportion the ſuperficies of the whole Lake hath <lb></lb>to the meaſure of the Section of the Emiſſary, and afterwards to <lb></lb>infer, that the velocity of the water by the Emiſſary or Sluice, <lb></lb>ſhall have the ſame proportion to the abatement of the Lake, <lb></lb>and to prove thorowly and clearly this diſcourſe, I intend to <lb></lb>demonſtrate the following Propoſition.</s></p><p type="main"> <s>Suppoſe a Veſſel of any bigneſſe, and that it hath an Emiſſary <lb></lb>or Cock, by which it diſchargeth its water. </s> <s>And look what pro<lb></lb>portion the ſuperſicies of the <lb></lb>veſſel hath to the meaſure of <lb></lb><figure id="id.068.01.039.1.jpg" xlink:href="068/01/039/1.jpg"></figure><lb></lb>the ſection of the cock, ſuch pro<lb></lb>portion ſhall the velocity of the <lb></lb>Water in the Cock have to the <lb></lb>abatement of the Lake Let the <lb></lb>Veſſel be A B C D, H I L B, through which the Water runneth, <lb></lb>the ſuperficies of the Water in the Veſſel A D, and the ſection <lb></lb>of the Cock H L: and let the Water in the Veſſel <lb></lb>be ſuppoſed to have falne in one determinate time from A to F. <pb xlink:href="068/01/040.jpg" pagenum="26"></pb>I ſay that the proportion of the ſuperficies of the Veſſel A D is <lb></lb>in proportion to the meaſure of the ſection of the Emiſſary <lb></lb>H L, as the velocity of the Emiſſary or Cock to the line A F; <lb></lb>which is manifeſt, for that the Water in the Veſsel moving by <lb></lb>the line A F; as far as F, and the whole maſs of Water A G <lb></lb>diſcharging it ſelf, and in the ſame time the ſame quantity of <lb></lb>Water being diſcharged by the ſection of the Emiſſary H L; it <lb></lb>is neceſſary by what I have demonſtrated in the third Propoſition, <lb></lb>and alſo explained in the beginning of this Treatiſe, that the ve<lb></lb>locity by the Emiſſary or Cock be in proportion to the velocity <lb></lb>of the abatement, as the ſuperficies of the Veſſel to the mea<lb></lb>ſure of the ſection of the Emiſſary, which was to be demon<lb></lb>ſtrated.</s></p><p type="main"> <s>That which hath been demonſtrated in the Veſſel, falls out ex<lb></lb>actly alſo in our Lake of <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> and its Emiſsary; and becauſe <lb></lb>the immenſity of the ſuperficies of the Lake is in proportion to <lb></lb>the ſuperficies of the Emiſsary or Sluice, as many millions to <lb></lb>one, as may be eaſily calculated; it is manifeſt, that ſuch abate<lb></lb>ment ſhall be imperceptible, and almoſt nothing, in two dayes <lb></lb>ſpace, nay in four or ſix: and all this will be true, when we <lb></lb>ſuppoſe that for that time there entreth no other Water into the <lb></lb>Lake from Ditches or Rivolets, which falling into the Lake would <lb></lb>render ſuch abatement yet leſs.</s></p><p type="main"> <s>Now we ſee, that it's neceſsary to examine ſuch abatements <lb></lb>and riſings, with excellent reaſons, or at leaſt, with accurate ex<lb></lb>periments, before we reſolve and conclude any thing; and how <lb></lb>farre the vulgar are diſtant from a right judgment in ſuch <lb></lb>matters.</s></p><p type="head"> <s>APPENDIX XIII.</s></p><p type="main"> <s>For greater confirmation of all this which I have ſaid, I <lb></lb>will inſtance in another like caſe, which alſo I met with here<lb></lb>tofore, wherein, for that the buſineſs was not rightly un<lb></lb>derſtood, many diſorders, vaſt expences, and conſiderable miſ<lb></lb>chiefs have followed. </s> <s>There was heretofore an Emiſsary or <lb></lb>Sluice made to drain the Waters, which from Rains, Springs, and <lb></lb>Rivolets fall into a Lake; to the end, the ſhores adjoyning on <lb></lb>the Lake, ſhould be free from the overflowing of the Waters; <lb></lb>but becauſe perhaps the enterprize was not well managed and <lb></lb>carried on, it fell out, that the Fields adjacent to the ſaid Chanel <lb></lb>could not drain, but continued under water; to which diſorders <lb></lb>a preſent remedy hath been uſed, namely, in a time convenient <lb></lb>to ſtop up the Sluice, by meanes of certain Floodgates kept on <lb></lb>purpoſe for that end; and thus abating the Level of the Water <pb xlink:href="068/01/041.jpg" pagenum="27"></pb>in the Emiſſary, in the ſpace of three or four dayes, the Fields <lb></lb>have been haply drained. </s> <s>But on the other part, the proprietors <lb></lb>bordering on the Lake oppoſed this, grievouſly complaining, that <lb></lb>whilſt the Floodgates are ſhut, and the courſe of the Water of <lb></lb>the Sluice hindered, the Lake overflowes the Lands adjacent, by <lb></lb>meanes of the Rivers that fell into it, to their very great damage; <lb></lb>and ſo continuing their ſuits, they got more of vexation than ſa<lb></lb>tisfaction. </s> <s>Now, being asked my opinion herein, I judged it <lb></lb>requiſite (ſince the point in controverſie was about the riſing <lb></lb>and falling of the Lake) that the ſaid abatement, when the <lb></lb>Floodgates are open, and increaſe when they are ſhut ſhould be <lb></lb>exactly meaſured, and told them, that it might be eaſily done at <lb></lb>a time when no extraordinary Waters fell into the Lake, neither <lb></lb>of Rain, or otherwiſe; and the Lake was undiſturbed by winds <lb></lb>that might drive the Water to any ſide, by planting neer to an <lb></lb>Iſlet, which is about the middle of the Lake, a thick poſt, on <lb></lb>which ſhould be made the marks of the Lakes riſing and falling <lb></lb>for two or three dayes. </s> <s>I would not, at that time, pawn, or re<lb></lb>ſolutely declare, my judgment, in regard I might be, by divers <lb></lb>accidents miſled. </s> <s>But this I told them, that (by what I have <lb></lb>demonſtrated, and particularly that which I have ſaid above <lb></lb>touching the Lake of <emph type="italics"></emph>Perugia<emph.end type="italics"></emph.end>) I inclined greatly to think, <lb></lb>that theſe riſings and fallings would prove imperceptible, and <lb></lb>inconſiderable; and therefore, that in caſe experience ſhould <lb></lb>make good my reaſon, it would be to no purpoſe for them to <lb></lb>continue diſputing and wrangling, which cauſeth, (according <lb></lb>to the Proverb) <emph type="italics"></emph>A great deal of cry,<emph.end type="italics"></emph.end> but produceth not much <lb></lb><emph type="italics"></emph>Wool.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Laſtly, it importing very much to know what a Rain conti<lb></lb>nued for many dayes can do in raiſing theſe Lakes, I will here in<lb></lb>ſert the Copy of a Letter, which I writ formerly to <emph type="italics"></emph>Signior Ga<lb></lb>lilæo Galilæi,<emph.end type="italics"></emph.end> chief Philoſopher to the Grand Duke of <emph type="italics"></emph>Tuſcany,<emph.end type="italics"></emph.end><lb></lb>wherein I have delivered one of my conceits in this buſineſſe, and <lb></lb>it may be, by this Letter, I may, more ſtrongly, confirm what I <lb></lb>have ſaid above.</s></p><pb xlink:href="068/01/042.jpg" pagenum="28"></pb><p type="main"> <s><emph type="italics"></emph>The Copy of a Letter to<emph.end type="italics"></emph.end> Signore GALILÆO <lb></lb>GALILÆI, <emph type="italics"></emph>Chief Philoſopher to the moſt Serene <lb></lb>Great Duke of TVSCANY.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Worthy and moſt Excellent<emph.end type="italics"></emph.end> SIR,</s></p><p type="main"> <s>In ſatisfaction of my promiſe, in my former Letters of <lb></lb>repreſenting unto you ſome of my Conſiderations <lb></lb>made upon the Lake <emph type="italics"></emph>Thraſimeno,<emph.end type="italics"></emph.end> I ſay, That in times <lb></lb>paſt, being in <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> where we held our General <lb></lb>Convention, having underſtood that the Lake <emph type="italics"></emph>Thraſimeno,<emph.end type="italics"></emph.end> by <lb></lb>the great drought of many Moneths was much abated, It came <lb></lb>into my head, to go privately and ſee this novelty, both for my <lb></lb>particular ſatisfaction, as alſo that might I be able to relate the <lb></lb>whole to my Patrons, upon the certitude of my own ſight of the <lb></lb>place. </s> <s>And ſo being come to the Emiſſary of the Lake, I found <lb></lb>that the Level of the Lakes ſurface was ebbed about five Ro<lb></lb>man Palmes of its wonted watermark, inſomuch that it was lower <lb></lb>than the tranſome of the mouth of the Emiſſary, by the length <lb></lb>of ----------------------------this deſcribed line, and there<lb></lb>fore no Water iſſued out of the Lake, to the great prejudice of <lb></lb>all the places and villages circumjacent, in regard that the Wa<lb></lb>ter which uſed to run from the ſaid Lake turned 22 Mills, which <lb></lb>not going, neceſſitated the inhabitants of thoſe parts to go a <lb></lb>dayes journey and more, to grinde upon the <emph type="italics"></emph>Tiber.<emph.end type="italics"></emph.end> Being retur<lb></lb>ned to <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> there followed a Rain, not very great, but con<lb></lb>ſtant, and even, which laſted for the ſpace of eight hours, or <lb></lb>thereabouts; and it came into my thoughts to examine, being <lb></lb>in <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> how much the Lake was increaſed and railed by this <lb></lb>Rain, ſuppoſing (as it was probable enough) that the Rain had <lb></lb>been univerſal over all the Lake; and like to that which fell in <lb></lb><emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> and to this purpoſe I took a Glaſſe formed like a Cy<lb></lb>linder, about a palme high, and half a palme broad; and having <lb></lb>put in water ſnfficient to cover the bottome of the Glaſſe, I no<lb></lb>ted diligently the mark of the height of the Water in the Glaſſe, <lb></lb>and afterwards expoſed it to the open weather, to receive the <lb></lb>Raine-water, which fell into it; and I let it ſtand for the <lb></lb>ſpace of an hour; and having obſerved that in that time the Wa<lb></lb>ter was riſen in the Veſſel the height of the following line---, <lb></lb>I conſidered that if I had expoſed to the ſame rain ſuch other veſ<lb></lb>ſels equal to that, the Water would have riſen in them all accor<lb></lb>ding to that meaſure: And thereupon concluded, that alſo in all <pb xlink:href="068/01/043.jpg" pagenum="29"></pb>the whole extent of the Lake, it was neceſſary the Water ſhould <lb></lb>be raiſed in the ſpace of an hour the ſame meaſure. </s> <s>Yet here I <lb></lb>conſidered two difficulties that might diſtutb and altar ſuch an <lb></lb>effect, or at leaſt render it inobſerveable, which afterwards well <lb></lb>weighed, and reſolved, left me (as I will tell you anon) in the <lb></lb>concluſion the more confirmed; that the Lake ought to be in<lb></lb>creaſed in the ſpace of eight hours, that the rain laſted eight <lb></lb>times that meaſure. </s> <s>And whilſt I again expoſed the Glaſs to re<lb></lb>peat the experiment, there came unto me an Ingeneer to talk <lb></lb>with me touching certain affairs of our Monaſtary of <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> and <lb></lb>diſcourſing with him, I ſhewed him the Glaſs out at my Cham<lb></lb>ber-window, expoſed in a Court-yard; and communicated to <lb></lb>him my fancy, relacing unto him all that I had done. </s> <s>But I <lb></lb>ſoon perceived that this brave fellow conceited me to be but of <lb></lb>a dull brain, for he ſmilling ſaid unto me; Sir, you deceive <lb></lb>your ſelf: I am of opinion that the Lake will not be increaſ<lb></lb>ed by this rain, ſo much as the thickneſſe of a ^{*} <emph type="italics"></emph>Julio.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg967"></arrow.to.target><lb></lb>Hearing him pronounce this his opinion with freeneſs and <lb></lb>confidence, I urged him to give me ſome reaſon for what he <lb></lb>ſaid, aſſuring him, that I would change my judgement, when I <lb></lb>ſaw the ſtrength of his Arguments: To which he anſwered, that <lb></lb>he had been very converſant about the Lake, and was every day <lb></lb>upon it, and was well aſſured that it was not at all increaſed. </s> <s>And <lb></lb>importuning him further, that he would give me ſome reaſon <lb></lb>for his ſo thinking, he propoſed to my conſideration the great <lb></lb>drought paſſed, and that that ſame rain was nothing for the <lb></lb>great parching: To which I anſwered, I believe Sir that the ſur<lb></lb>face of the Lake, on which the rain had fallen was moiſtned; and <lb></lb>therefore ſaw not how its drought, which was nothing at all, <lb></lb>could have drunk up any part of the rain. </s> <s>For all this he per<lb></lb>ſiſting in his conceit, without yielding in the leaſt to my allega<lb></lb>tion; he granted in the end (I believe in civility to me) that <lb></lb>my reaſon was plauſible and good, but that in practiſe it could <lb></lb>not hold. </s> <s>At laſt to clear up all, I made one be called, and <lb></lb>ſent him to the mouth of the Emiſſary of the Lake, with order <lb></lb>to bring me an exact account, how he found the water of the <lb></lb>Lake, in reſpect of the Tranſome of the Sluice. </s> <s>Now here, <lb></lb>Signore <emph type="italics"></emph>Galilo,<emph.end type="italics"></emph.end> I would not have you think that I had brought <lb></lb>the matter in hand to concern me in my honour; but believe me <lb></lb>(and there are witneſſes of the ſame ſtill living) that my meſſen<lb></lb>ger returning in the evening to <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> he brought me word, <lb></lb>that the water of the Lake began to run through the Cave; and <lb></lb>that it was riſen almoſt a fingers breadth above the Tranſome: <lb></lb>Inſomuch, that adding this meaſure, to that of the lowneſs of <lb></lb>the ſurface of the Lake, beneath the Tranſome before the rain, <pb xlink:href="068/01/044.jpg" pagenum="30"></pb>it was manifeſt that the riſing of the Lake cauſed by the rain, was <lb></lb>to a hair thoſe four fingers breadth that I had judged it to be. <lb></lb></s> <s>Two dayes after I had another bout with the Ingeneer, and re<lb></lb>lated to him the whole buſineſs, to which he knew not what to <lb></lb>anſwer.</s></p><p type="margin"> <s><margin.target id="marg967"></margin.target>* A Coyn of Pope <lb></lb><emph type="italics"></emph>Julius<emph.end type="italics"></emph.end> worth ſix <lb></lb>pence.</s></p><p type="main"> <s>Now the two difficulties which I thought of, able to impede <lb></lb>my concluſion, were theſe following: Firſt, I conſidered that <lb></lb>it might be, that the Wind blowing from the ſide where the <lb></lb>Sluice ſtood, to the Lake-ward; the mole and maſs of the Wa<lb></lb>ter of the Lake might be driven to the contrary ſhore; on which <lb></lb>the Water riſing, it might be fallen at the mouth of the Emiſſa<lb></lb>ry, and ſo the obſervation might be much obſcured. </s> <s>But this <lb></lb>difficulty wholly vaniſhed by reaſon of the Aires great tranqui<lb></lb>lity; which it kept at that time, for no Wind was ſtirring on any <lb></lb>ſide, neither whilſt it rained, nor afterwards.</s></p><p type="main"> <s>The ſecond difficulty which put the riſing in doubt, was, That <lb></lb>having obſerved in <emph type="italics"></emph>Florence,<emph.end type="italics"></emph.end> and elſewhere, thoſe Ponds into <lb></lb>which the rain-water, falling from the houſe, is conveyed <lb></lb>through the Common-ſhores: And that they are not thereby <lb></lb>ever filled, but that they ſwallow all that abundance of water, <lb></lb>that runs into them by thoſe conveyances which ſerve them with <lb></lb>water; inſomuch that thoſe conveyances which in time of <lb></lb>drought maintain the Pond, when there comes new abundance <lb></lb>of water into the Pond, they drink it up, and ſwallow it: A like <lb></lb>effect might alſo fall out in the Lake, in which there being many <lb></lb>veins (as it is very likely) that maintain and feed the Lake; theſe <lb></lb>veins might imbibe the new addition of the Rain-water, and ſo <lb></lb>by that means annuall the riſing; or elſe diminiſh it in ſuch ſort, as <lb></lb>to render it inobſervable. </s> <s>But this difficulty was eaſily reſolved <lb></lb>by conſidering my Treatiſe of the meaſure of Running-Waters; <lb></lb>foraſmuch as having demonſtrated, that the abatement of a Lake <lb></lb>beareth the reciprocal proportion to the velocity of the Emiſſa<lb></lb>ry, which the meaſure of the Section of the Emiſſary of the Lake, <lb></lb>hath to the meaſure of the ſurface of the Lake: making the <lb></lb>calculation and account, though in groſs; by ſuppoſing that its <lb></lb>veins were ſufficiently large, and that the velocity in them were <lb></lb>notable in drinking up the water of the Lake; yet I found never<lb></lb>theleſs, that many weeks and moneths would be ſpent in drink<lb></lb>ing up the new-come abundance of water by the rain, ſo that <lb></lb>I reſted ſure, that the riſing would enſue, as in effect it did.</s></p><p type="main"> <s>And becauſe many of accurate judgement, have again cauſed <lb></lb>me to queſtion this riſing, ſetting before me, that the Earth be<lb></lb>ing parched by the great drought, that had ſo long continued, it <lb></lb>might be, that that Bank of Earth which environed the brink of <lb></lb>the Lake, being dry, and imbibing great abundance of Water <pb xlink:href="068/01/045.jpg" pagenum="31"></pb>from the increaſing Lake, would not ſuffer it to increaſe in <lb></lb>height: I ſay therefore, that if we would rightly conſider this <lb></lb>doubt here propoſed, we ſhould, in the very conſideration of it, <lb></lb>ſee it reſolved; for, it being ſuppoſed that that liſt or border of <lb></lb>Banks which was to be occupied by the increaſe of the Lake, be <lb></lb>a Brace in breadth quite round the Lake, and that by reaſon of <lb></lb>its dryneſs it ſucks in water, and that by that means this propor<lb></lb>tion of water co-operates not in raiſing of the Lake: It is abſo<lb></lb>lutely neceſſary on the other hand, that we conſider, That the <lb></lb>Circuit of the water of the Lake being thirty miles, as its com<lb></lb>monly held, that is to ſay, Ninety thouſand Braces of <emph type="italics"></emph>Florence<emph.end type="italics"></emph.end><lb></lb>in compaſs; and therefore admitting for true, that each Brace of <lb></lb>this Bank drink two quarts of water, and that for the ſpieading <lb></lb>it require three quarts more, we ſhall finde, that the whole agre<lb></lb>gate of this portion of water, which is not imployed in the raiſing <lb></lb>of the Lake, will be four hundred and fifty thouſand Quarts of <lb></lb>water; and ſuppoſing that the Lake be ſixty ſquare miles, three <lb></lb>thouſand Braces long, we ſhall finde, that to diſpence the water <lb></lb>poſſeſt by the Bank about the Lake, above the total ſurface of <lb></lb>the Lake, it ought to be ſpread ſo thin, that one ſole quart of <lb></lb>water may over-ſpread ten thouſand ſquare Braces of ſurface: <lb></lb>ſuch a thinneſs, as muſt much exceed that of a leaf of beaten <lb></lb>Gold, and alſo leſs than that skin of water which covers the Bub<lb></lb>bles of it: and ſuch would that be, which thoſe men would have <lb></lb>ſubſtracted from the riſing of the Lake: But again, in the ſpace <lb></lb>of a quarter of an hour at the beginning of the rain, all that <lb></lb>Bank is ſoaked by the ſaid rain, ſo that we need not for the <lb></lb>moiſtning of it, imploy a drop of that water which falleth into <lb></lb>the Lake. </s> <s>Beſides we have not brought to account that abun<lb></lb>dance of water which runs in time of rain into the Lake, from <lb></lb>the ſteepneſs of the adjacent Hills and Mountains; which would <lb></lb>be enough to ſupply all our occaſions: So that, neither ought <lb></lb>we for this reaſon to queſtion our pretended riſing. </s> <s>And this <lb></lb>is what hath fallen in my way touching the conſideration of the <lb></lb><emph type="italics"></emph>Thraſimenian<emph.end type="italics"></emph.end> Lake.</s></p><p type="main"> <s>After which, perhaps ſomewhat raſhly, wandring beyond my <lb></lb>bounds, I proceeded to another contemplation, which I will re<lb></lb>late to you, hoping that you will receive it, as collected with <lb></lb>theſe cautions requiſite in ſuch like affairs; wherein we ought <lb></lb>not too poſitively to affirm any thing of our own heads for cer<lb></lb>tain, but ought to ſubmit all to the ſound and ſecure delibera<lb></lb>tion of the Holy Mother-Church, as I do this of mine, and all <lb></lb>others; moſt ready to change my judgement, and conform my <lb></lb>ſelf alwaies to the deliberations of my Superiors. </s> <s>Continu<pb xlink:href="068/01/046.jpg" pagenum="32"></pb>ing therefore my above-ſaid conceit about the riſing of the wa<lb></lb>ter in the glaſs tried before, it came into my minde, that the <lb></lb>forementioned rain having been very gentle, it might well be, <lb></lb>that if there ſhould have faln a Rain fifty, an hundred, or a thou<lb></lb>ſand times greater than this, and much more intenſe (which <lb></lb>would inſue as oft as thoſe falling drops were four, ſive or ten <lb></lb>times bigger than thoſe of the above-mentioned rain, keeping <lb></lb>the ſame number) in ſuch a caſe its manifeſt, that in the ſpace <lb></lb>of an hour the Water would riſe in our Glaſs, two, three, and <lb></lb>perhaps more Yards or Braces; and conſequently, if ſuch a <lb></lb>Raine ſhould fall upon a Lake, that the ſaid Lake would <lb></lb>riſe, according to the ſame rate: And likewiſe, if ſuch a <lb></lb>Rain were univerſall, over the whole Terreſtriall Globe, it <lb></lb>would neceſſarily, in the ſpace of an hour, make a ri<lb></lb>ſing of two, or three braces round about the ſaid Globe, <lb></lb>And becauſe we have from Sacred Records, that in the <lb></lb>time of the Deluge, it rained fourty dayes and fourty nights; <lb></lb>namely, for the ſpace of 960 houres; its clear, that if the ſaid <lb></lb>Rain had been ten times bigger than ours at <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> the riſing <lb></lb>of the Waters above the Terreſtrial Globe would reach and paſs <lb></lb>a mile higher than the tops of the Hills and Mountains that are <lb></lb>upon the ſuperficies of the Earth; and they alſo would concur <lb></lb>to increaſe the riſe. </s> <s>And therefore I conclude, that the riſe of <lb></lb>the Waters of the Deluge have a rational congruity with natural <lb></lb>Diſcourſes, of which I know very well that the eternal truths of <lb></lb>the Divine leaves have no need; but however I think ſo clear an <lb></lb>agreement is worthy of our conſideration, which gives us occa<lb></lb>ſion to adore and admire the greatneſſe of God in his mighty <lb></lb>Works, in that we are ſometimes able, in ſome ſort, to meaſure <lb></lb>them by the ſhort Standard of our Reaſon.</s></p><p type="main"> <s>Many Leſſons alſo may be deduced from the ſame Doctrine, <lb></lb>which I paſſe by, for that every man of himſelf may eaſily know <lb></lb>them, having once ſtabliſhed this Maxime; That it is not poſſi<lb></lb>ble to pronounce any thing, of a certainty, touching the quantity <lb></lb>of Running Waters, by conſidering only the ſingle vulgar mea<lb></lb>ſure of the Water wichout the velocity; and ſo on the contrary, <lb></lb>he that computes only the velocity, without the meaſure, ſhall <lb></lb>commit very great errours; for treating of the meaſure of Run<lb></lb>ning Waters, it is neceſſary, the water being a body, in handling <lb></lb>its quantity, to conſider in it all the three dimenſions of breadth, <lb></lb>depth, and length: the two firſt dimenſions are obſerved by all <lb></lb>in the common manner, and ordinary way of meaſuring Running <lb></lb>Waters; but the third dimenſion of length is omitted; and hap<lb></lb>ly ſuch an overſight is committed, by reaſon the length of Run<pb xlink:href="068/01/047.jpg" pagenum="33"></pb>ning Water is reputed in ſome ſenſe infinite, in that it never cea<lb></lb>ſeth to move away, and as infinite is judged incomprehenſible; <lb></lb>and ſuch as that there is no exact knowledge to be had thereof; <lb></lb>& ſo there comes to be no account made thereof; but if we ſhould <lb></lb>make ſtrict reflection upon our conſideration of the velocity of <lb></lb>Water, we ſhould find, that keeping account of the ſame, there <lb></lb>is a reckoning alſo made of the length; foraſmuch as whilſt we <lb></lb>ſay, the Water of ſuch a Spring runs with the velocity of paſſing <lb></lb>a thouſand or two thouſand paces an hour: this in ſubſtance is <lb></lb>no other than if we had ſaid, ſuch a Fountain diſchargeth in an <lb></lb>hour a Water of a thouſand or two thouſand paces long. </s> <s>So <lb></lb>that, albeit the total length of Running water be incomprehen<lb></lb>ſible, as being infinite, yet nevertheleſſe its rendered intelligible <lb></lb>by parts in its velocity. </s> <s>And ſo much ſufficeth to have hinted <lb></lb>about this matter, hoping to impart on ſome other occaſion other <lb></lb>more accurate Obſervations in this affair.</s></p><p type="head"> <s><emph type="italics"></emph>LAVS DEO.<emph.end type="italics"></emph.end></s></p><figure id="id.068.01.047.1.jpg" xlink:href="068/01/047/1.jpg"></figure><pb xlink:href="068/01/048.jpg"></pb><pb xlink:href="068/01/049.jpg"></pb><p type="head"> <s>GEOMETRICAL <lb></lb>DEMONSTRATIONS <lb></lb>OF THE <lb></lb>MEASURE <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s>BY <lb></lb>D. BENEDETTO CASTELLI, <lb></lb>Abbot of CASSINA, and Mathematician to <lb></lb>P. <emph type="italics"></emph>VRBAN. VIII.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>DEDICATED <lb></lb><emph type="italics"></emph>To the moſt Illuſtrious, and moſt Excellent Prince<emph.end type="italics"></emph.end></s></p><p type="head"> <s>DON THADDEO BARBERINI, <lb></lb>PRINCE OF <lb></lb>PALESTRINA, <lb></lb>AND <lb></lb>GENERAL of the HOLY CHURCH.</s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed <emph type="italics"></emph>Anno Domini,<emph.end type="italics"></emph.end> MDCLXI.</s></p><pb xlink:href="068/01/050.jpg"></pb><pb xlink:href="068/01/051.jpg" pagenum="37"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>Let it be ſuppoſed, that the banks of the Rivers of which <lb></lb>we ſpeak be erected perpendicular to the plane of the up<lb></lb>per ſuperficies of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>We ſuppoſe that the plane of the bottome of the River, of <lb></lb>which we ſpeak is at right angles with the banks.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>It is to be ſuppoſed, that we ſpeak of Rivers, when they are at <lb></lb>ebbe, in that ſtate of ſhallowneſſe, or at flowing in that ſtate <lb></lb>of deepneſſe, and not in their tranſition from the ebbe to the <lb></lb>flowing, or fr m the flowing to the ebbe.</s></p><p type="head"> <s><emph type="italics"></emph>Declaration of Termes.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>FIRST.</s></p><p type="main"> <s>If a River ſhall be cut by a Plane at right angles to the ſurface <lb></lb>of the water of the River, and to the banks of the River, <lb></lb>that ſame dividing Plane we call the Section of the River; and <lb></lb>this Section, by the Suppoſitions above, ſhall be a right angled <lb></lb>Parallelogram.</s></p><p type="head"> <s>SECOND.</s></p><p type="main"> <s>We call thoſe Sections equally Swift, by which the water runs <lb></lb>with equal velocity; and more ſwift and leſs ſwift that <lb></lb>Section of another, by which the water runs with greater or leſſe <lb></lb>velocity.</s></p><pb xlink:href="068/01/052.jpg" pagenum="38"></pb><p type="head"> <s>AXIOME I.</s></p><p type="main"> <s>Sections equal, and equally ſwift, diſcharge equal quantities <lb></lb>of Water in equal times.</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s>Sections equally ſwift, and that diſcharge equal quantity of <lb></lb>Water, in equal time, ſhall be equal.</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s>Sections equal, and that diſcharge equal quantities of Water <lb></lb>in equal times, ſhall be equally ſwift.</s></p><p type="head"> <s>AXIOME IV.</s></p><p type="main"> <s>When Sections are unequal, but equally ſwift, the quanti<lb></lb>ty of the Water that paſſeth through the firſt Section, <lb></lb>ſhall have the ſame proportion to the quantity that paſ<lb></lb>ſeth through the Second, that the firſt Section hath to the ſecond <lb></lb>Section. </s> <s>Which is manifeſt, becauſe the velocity being the <lb></lb>ſame, the difference of the Water that paſſeth ſhall be according <lb></lb>to the difference of the Sections.</s></p><p type="head"> <s>AXIOME V.</s></p><p type="main"> <s>If the Sections ſhall be equal, and of unequal velocity, the <lb></lb>quantity of the Water that paſſeth through the firſt, ſhall <lb></lb>have the ſame proportion to that which paſſeth through the <lb></lb>ſecond, that the velocity of the firſt Section, ſhall have to the <lb></lb>velocity of the ſecond Section. </s> <s>Which alſo is manifeſt, becauſe <lb></lb>the Sections being equal, the difference of the Water which <lb></lb>paſſeth, dependeth on the velocity.</s></p><p type="head"> <s><emph type="italics"></emph>PETITION.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>A Section of a River being given, we may ſuppoſe another <lb></lb>equal to the given, of different breadth, heigth, and ve<lb></lb>locity.</s></p><pb xlink:href="068/01/053.jpg" pagenum="37"></pb><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s><emph type="italics"></emph>The Sections of the ſame River diſcharge equal quan<lb></lb>tities of Water in equal times, although the Secti<lb></lb>ons themſelves he unequal.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the two Sections be A and B, in the River C, running <lb></lb>from A, towards B; I ſay, that they diſcharge equal quan<lb></lb>tity of Water in equal times; for if greater quantity of Wa<lb></lb>ter ſhould paſs through A, than paſſeth through B, it would <lb></lb><figure id="id.068.01.053.1.jpg" xlink:href="068/01/053/1.jpg"></figure><lb></lb>follow that the Water in the intermediate ſpace of the River C, <lb></lb>would increaſe continually, which is manifeſtly falſe, but if <lb></lb>more Water ſhould iſſue through the Section B, than entreth at <lb></lb>the Section A, the Water in the intermediate ſpace C, would <lb></lb>grow continually leſs, and alwaies ebb, which is likewiſe falſe; <lb></lb>therefore the quantity of Water that paſſeth through the Secti<lb></lb>on B, is equal to the quantity of Water which paſſeth through <lb></lb>the Section A, and therefore the Sections of the ſame River diſ<lb></lb>charge, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> Which w s to be demonſtrated.</s></p><p type="head"> <s>PROPOSITION II.</s></p><p type="main"> <s><emph type="italics"></emph>In two Sections of Rivers, the quantity of the Water <lb></lb>which paſſeth by one Section, is to that which paſ<lb></lb>ſeth by the ſecond, in a Proportion compounded of <lb></lb>the proportions of the firſt Section to the ſecond, and <lb></lb>of the velocitie through the first, to the velocitie <lb></lb>of the ſecond.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I Et A, and B be two Sections of a River; I ſay, that the <lb></lb>quantity of Water which paſſeth through A, is to that which <lb></lb>paſſeth through B, in a proportion compounded of the pro<lb></lb>portions of the firſt Section A, to the Section B; and of the velo<lb></lb>city through A, to the velocity through B: Let a Section be <pb xlink:href="068/01/054.jpg" pagenum="40"></pb>ſuppoſed equal to the Section A, in magnitude; but of velocity <lb></lb>equal to the Section B, and let it be G, and as the Section A is <lb></lb><figure id="id.068.01.054.1.jpg" xlink:href="068/01/054/1.jpg"></figure><lb></lb>to the Section B, ſo let the line F be to the line D; and as the <lb></lb>velocity A, is to the velocity by B, ſo let the line D be to the <lb></lb>line R: Therefore the Water which paſſeth thorow A, ſhall be <lb></lb>to that which paſſeth through G (in regard the Sections A and <lb></lb>G are of equal bigneſs, but of unequal velocity) as the velocity <lb></lb>through A, to the velocity through G; But as the velocity <lb></lb>through A, is to the velocity through G, ſo is the velocity through <lb></lb>A, to the velocity through B; namely, as the line D, to the <lb></lb>line R: therefore the quantity of the Water which paſſe the <lb></lb>through A, ſhall be to the quantity which paſſeth through G, as <lb></lb>the line D is to the line R; but the quantity which paſſeth <lb></lb>through G, is to that which paſſeth through B, (in regard the <lb></lb>Sections G, and B, are equally ſwift) as the Section G to the Se<lb></lb>ction B; that is, as the Section A, to the Section B; that is, as <lb></lb>the line F, to the line D: Therefore by the equal and perturbed <lb></lb>proportionality, the quantity of the Water which paſſeth through <lb></lb>A, hath the ſame proportion to that which paſſeth through B, <lb></lb>that the line F hath to the line R; but F to R, hath a proportion <lb></lb>compounded of the proportions of F to D, and of D to R; that <lb></lb>is, of the Section A to the Section B; and of the velocity through <lb></lb>A, to the velocity through B. </s> <s>Therefore alſo the quantity of <lb></lb>Water which paſſeth through the Section A, ſhall have a propor<lb></lb>tion to that which paſſeth through the Section B, compounded of <lb></lb>the proportions of the Section A, to the Section B; and of <lb></lb>the velocity through A, to the velocity through B: And <lb></lb>therefore in two Sections of Rivers, the quantity of Water which <lb></lb>paſſeth by the firſt, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which was to be demonſtrated.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The ſame followeth, though the quantity of the Water which <lb></lb>paſſeth through the Section A, be equal to the quantity of <lb></lb>Water which paſſeth through the Section B, as is manifeſt by the <lb></lb>ſame demonſtration.</s></p><pb xlink:href="068/01/055.jpg" pagenum="41"></pb><p type="head"> <s>PROPOSITION III.</s></p><p type="main"> <s><emph type="italics"></emph>In two Sections unequal, through which paſs equal <lb></lb>quantities of Water in equal times, the Sections <lb></lb>have to one another, reciprocal proportion to their <lb></lb>velocitie.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the two unequal Sections, by which paſs equal quantities <lb></lb>of Water in equal times be A, the greater; and B, the leſſer: <lb></lb>I ſay, that the Section A, ſhall have the ſame Proportion <lb></lb>to the Section B, that reciprocally the velocity through B, hath to <lb></lb>the velocity through A; for ſuppoſing that as the Water that <lb></lb>paſſeth through A, is to that which paſſeth through B, ſo is the <lb></lb><figure id="id.068.01.055.1.jpg" xlink:href="068/01/055/1.jpg"></figure><lb></lb>line E to the line F: therefore the quantity of water which paſ<lb></lb>ſeth through A, being equal to that which paſſeth through B, <lb></lb>the line E ſhall alſo be equal to the line F: Suppoſing moreover, <lb></lb>That as the Section A, is to the Section B, ſo is the line F, to the <lb></lb>line G; and becauſe the quantity of water which paſſeth <lb></lb>through the Section A, is to that which paſſeth through the <lb></lb>Section B, in a proportion compoſed of the proportions of the <lb></lb>Section A, to the Section B, and of the velocity through A, to the <lb></lb>velocity through B; therefore the line E, ſhall be the line to F, in <lb></lb>a proportion compounded of the ſame proportions; namely, of <lb></lb>the proportion of the Section A, to the Section B, and of the ve<lb></lb>locity through A, to the velocity through B; but the line E, hath <lb></lb>to the line G, the proportion of the Section A, to the Section B, <lb></lb>therefore the proportion remaining of the line G, to the line F, <lb></lb>ſhall be the proportion of the velocity through A, to the velocity <lb></lb>through B; therefore alſo the line G, ſhall be to the line E, as <lb></lb>the velocity by A, to the velocity by B: And converſly, the ve<lb></lb>locity through B, ſhall be to the velocity through A, as the line <lb></lb>E, to the line G; that is to ſay, as the Section A, to the Section B, <lb></lb>and therefore in two Sections, &c. </s> <s>which was to be demonſtrated.</s></p><pb xlink:href="068/01/056.jpg" pagenum="42"></pb><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Hence it is manifeſt, that Sections of the ſame River (which <lb></lb>are no other than the vulgar meaſures of the River) have <lb></lb>betwixt themſelves reciprocal proportions to their veloci<lb></lb>ties; for in the firſt Propoſition we have demonſtrated that the <lb></lb>Sections of the ſame River, diſcharge equal quantities of Water <lb></lb>in equal times; therefore, by what hath now been demonſtrated <lb></lb>the Sections of the ſame River ſhall have reciprocal proportion <lb></lb>to their velocities; And therefore the ſame running water chan<lb></lb>geth meaſure, when it changeth velocity; namely, increaſeth the <lb></lb>meaſure, when it decreaſeth the velocity, and decreaſeth the <lb></lb>meaſure, when it increaſeth the velocity.</s></p><p type="main"> <s>On which principally depends all that which hath been ſaid <lb></lb>above in the <emph type="italics"></emph>Diſcourſe,<emph.end type="italics"></emph.end> and obſerved in the <emph type="italics"></emph>Corollaries<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ap<lb></lb>pendixes<emph.end type="italics"></emph.end>; and therefore is worthy to be well underſtood and <lb></lb>heeded.</s></p><p type="head"> <s>PROPOSITION IV.</s></p><p type="main"> <s><emph type="italics"></emph>If a River fall into another River, the height of the <lb></lb>firſt in its own Chanel ſhall be to the height that it <lb></lb>ſhall make in the ſecond Chanel, in a proportion <lb></lb>compounded of the proportions of the breadth of <lb></lb>the Chanel of the ſecond, to the breadth of the <lb></lb>Chanel of the firſt, and of the velocitie acquired in <lb></lb>the Chanel of the ſecond, to that which it had in <lb></lb>its proper and first Chanel.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the River A B, whoſe height is A C, and breadth C B, <lb></lb>that is, whoſe Section is A C B; let it enter, I ſay, into a<lb></lb>nother River as broad as the line E F, and let it therein make <lb></lb>the riſe or height D E, that is to ſay, let it have its Section in <lb></lb>the River whereinto it falls D E F; I ſay, that the height A C <lb></lb>hath to the height D E the proportion compounded of the pro<lb></lb>portions of the breadth E F, to the breadth C B, and of the ve<lb></lb>locity through D F, to the velocity through A B. </s> <s>Let us ſup<lb></lb>poſe the Section G, equal in velocity to the Section A B, and in <lb></lb>breadth equal to E F, which carrieth a quantity of Water e<lb></lb>qual to that which the Section A B carrieth, in equal times, <lb></lb>and conſequently, equal to that which D F carrieth. </s> <s>Moreover, <lb></lb>as the breadth E F is to the breadth C B, ſo let the line H be to <pb xlink:href="068/01/057.jpg" pagenum="43"></pb>the line I; and as the velocity of D F is to the velocity of A B, <lb></lb>ſo let the line I be to the line L; becauſe therefore the two <lb></lb>Sections A B and G are equally ſwift, and diſcharge equal quan<lb></lb>tity of Water in equal times, they ſhall be equal Sections; and <lb></lb><figure id="id.068.01.057.1.jpg" xlink:href="068/01/057/1.jpg"></figure><lb></lb>therefore the height of A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> to the height of G, ſhall be as the <lb></lb>breadth of G, to the breadth of A <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> that is, as E F to C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end><lb></lb>that is, as the line H to the line I: but becauſe the Water which <lb></lb>paſſeth through G, is equal to that which paſſeth through D E F, <lb></lb>therefore the Section G, to the Section D E F, ſhall have the re<lb></lb>ciprocal proportion of the velocity through D E F, to the velo<lb></lb>city through G; but alſo the height of G, is to the height D E, <lb></lb>as the Section G, to the Section D E F: Therefore the height of <lb></lb>G, is to the height D E, as the velocity through D E F, is to the <lb></lb>velocity through G; that is, as the velocity through D E F, is to <lb></lb>the velocity through A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; That is, finally, as the line I, to the <lb></lb>line L; Therefore, by equal proportion, the height of <emph type="italics"></emph>A B,<emph.end type="italics"></emph.end> that <lb></lb>is, A C, ſhall be to the height D E; as H to L, that is, com<lb></lb>pounded of the proportions of the breadth E F, to the breadth <lb></lb>C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and of the velocity through D F, to the velocity through <lb></lb>A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>: So that if a River fall into another River, &c. </s> <s>which was <lb></lb>to be demonſtrated.</s></p><pb xlink:href="068/01/058.jpg" pagenum="44"></pb><p type="head"> <s>PROPOSITION V.</s></p><p type="main"> <s><emph type="italics"></emph>If a River diſcharge a certain quantitie of Water <lb></lb>in a certain time; and after that there come into it <lb></lb>a Flood, the quantity of Water which is diſchar<lb></lb>ged in as much time at the Flood, is to that which <lb></lb>was diſcharged before, whilſt the River was low, <lb></lb>in a proportion compounded of the proportions of <lb></lb>the velocity of the Flood, to the velocity of the first <lb></lb>Water, and of the height of the Flood, to the <lb></lb>height of the first Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Suppoſe a River, which whilſt it is low, runs by the Section <lb></lb>AF; and after a Flood cometh into the ſame, and runneth <lb></lb>through the Section D F, I ſay, that the quantity of the Wa<lb></lb>ter which is diſcharged through D F, is to that which is diſcharged <lb></lb><figure id="id.068.01.058.1.jpg" xlink:href="068/01/058/1.jpg"></figure><lb></lb>through A F, in a proportion compounded of the proportions of <lb></lb>the velocity through D F, to the velocity through A F, and of <lb></lb>the height D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> to the height A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; As the velocity through DF <lb></lb>is to the velocity through A F, ſo let the line R, to the line S; <lb></lb>and as the height D <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is to the height A <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> ſo let the line S, to <lb></lb>the line T; and let us ſuppoſe a Section L M N, equal to D F <lb></lb>in height and breadth; that is L M equal to D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and M N equal <lb></lb>to <emph type="italics"></emph>B F<emph.end type="italics"></emph.end>; but let it be in velocity equal to the Section A F, there<lb></lb>fore the quantity of Water which runneth through D F, ſhall be <lb></lb>to that which runneth through LN, as the velocity through DF, <lb></lb>is to the velocity through L N, that is, to the velocity through <lb></lb><emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; and the line R being to the line S, as the velocity through <lb></lb>D <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> to the velocity through <emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; therefore the quantity which <lb></lb>runneth through D <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> to that which runneth through L N, ſhall <lb></lb>have the proportion of R to S; but the quantity which runneth <lb></lb>through L N, to that which runneth through <emph type="italics"></emph>A F,<emph.end type="italics"></emph.end> (the Sections <pb xlink:href="068/01/059.jpg" pagenum="45"></pb>being equally ſwift) ſhall be in proportion as the Section <emph type="italics"></emph>L<emph.end type="italics"></emph.end> N, to <lb></lb>the Section A F; that is, as D B, to A B; that is as the line S, to <lb></lb>the line T: Therefore by equal proportion, the quantity of the <lb></lb>water which runneth through D F, ſhall be in proportion to that <lb></lb>which runneth through A F, as R is to T; that is, compounded of <lb></lb>the proportions of the height D B, to the height A B, and of the <lb></lb>velocity through <emph type="italics"></emph>D F,<emph.end type="italics"></emph.end> to the velocity through <emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; and therefore <lb></lb>if a River diſcharge a certain quantity, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which was to be de<lb></lb>monſtrated.</s></p><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>The ſame might have been demonſtrated by the ſecond <lb></lb>Propoſition above demonſtrated, as is manifeſt.</s></p><p type="head"> <s>PROPOSITION VI.</s></p><p type="main"> <s><emph type="italics"></emph>If two equal ſtreams of the ſame Torrent, fall into a <lb></lb>River at divers times, the heights made in the Ri<lb></lb>ver by the Torrent, ſhall have between them<lb></lb>ſelves the reciprocal proportion of the velocities <lb></lb>acquired in the River.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let A and B, be two equal ſtreams of the ſame Torrent, <lb></lb>which falling into a River at divers times, make the heights <lb></lb>C D, and F G; that is the ſtream A, maketh the height <lb></lb>C D, and the ſtream B, maketh the height F G; that is, Let <lb></lb>their Sections in the River, into which they are fallen, be C E, <lb></lb>and FH; I ſay, that the height C D, ſhall be to the height F G, <lb></lb>in reciprocal proportion, as the velocity through F H, to the ve<lb></lb>locity through C E; for the quantity of water which paſſeth <lb></lb>through A, being equal to the quantity which paſſeth through B, <lb></lb>in equal times; alſo the quantity which paſſeth through C E, ſhall <lb></lb><figure id="id.068.01.059.1.jpg" xlink:href="068/01/059/1.jpg"></figure><lb></lb>be equal to that which paſſeth through F H: And therefore the <lb></lb>proportion that the Section C E, hath to the Section F H; ſhall <lb></lb>be the ſame that the velocity through F H, hath to the velocity <lb></lb>through C E; But the Section C E, is to the Section F H, as <lb></lb>C D, to F G, by reaſon they are of the ſame breadth: Therefore <lb></lb>C D, ſhall be to F G, in reciprocal proportion, as the velocity <lb></lb>through F H, is to the velocity through C E, and therefore if two <lb></lb>equal ſtreams of the ſame Torrent, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which was to be de<lb></lb>monſtrated.</s></p><pb xlink:href="068/01/060.jpg"></pb><pb xlink:href="068/01/061.jpg" pagenum="47"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s><emph type="italics"></emph>Lib.<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>Having, in the cloſe of my Treatiſe of the <lb></lb>Menſuration of Running Waters promiſed <lb></lb>to declare upon another occaſion other par<lb></lb>ticulars more obſcure, and of very great <lb></lb>concern upon the ſame argumement: I now <lb></lb>do perform my promiſe on the occaſion <lb></lb>that I had the paſt year 1641. to propound <lb></lb>my thoughts touching the ſtate of the Lake <lb></lb>of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> a buſineſs certainly moſt important, as being the <lb></lb>concernment of that moſt noble and moſt admirable City; and <lb></lb>indeed of all <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> yea of all <emph type="italics"></emph>Europe, Aſia, & Africa<emph.end type="italics"></emph.end>; & one may <lb></lb>truly ſay of all the whole World. </s> <s>And being to proceed according <lb></lb>to the method neceſſary in Sciences, I wil propoſe, in the firſt place <lb></lb>certain Definitions of thoſe Terms whereof we are to make uſe <lb></lb>in our Diſcourſe: and then, laying down certain Principles we <lb></lb>will demonſtrate ſome Problemes and Theoremes neceſſary for <lb></lb>the underſtanding of thoſe things which we are to deliver; and <lb></lb>moreover, recounting ſundry caſes that have happened, we will <lb></lb>prove by practice, of what utility this contemplation of the <lb></lb>Meaſure of Running Waters is in the more important affairs both <lb></lb>Publique and Private.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s>Two Rivers are ſaid to move with equal velocity, when in e<lb></lb>qual times they paſſe ſpaces of equal length.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s>Rivers are ſaid to move with like velocity, when their propor<lb></lb>tional parts do move alike, that is, the upper parts alike to <lb></lb>the upper, and the lower to the lower; ſo that if the upper <lb></lb>part of one River ſhall be more ſwift than the upper part of ano<lb></lb>ther; then alſo the lower part of the former ſhall be more ſwift <lb></lb>than the part correſpondent to it in the ſecond, proportionally.</s></p><pb xlink:href="068/01/062.jpg" pagenum="48"></pb><p type="head"> <s>DEFINITON III.</s></p><p type="main"> <s>To meaſure a River, or running Water, is in our ſenſe to finde <lb></lb>out how many determinate meaſures, or weights of Water <lb></lb>in a given time paſſeth through the River, or Channel of the <lb></lb>Water that is to be meaſured.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s>If a Machine be made either of Brick, or of Stone, or of <lb></lb>Wood, ſo compoſed that two ſides of the ſaid Machine be <lb></lb>placed at right angles upon the ends of a third ſide, that is <lb></lb>ſuppoſed to be placed in the bottom of a River, parallel to the <lb></lb>Horizon, in ſuch a manner, that all the water which runneth <lb></lb>through the ſaid River, paſſeth thorow the ſaid Machine: And <lb></lb>if all the water coming to be diverted <lb></lb><figure id="id.068.01.062.1.jpg" xlink:href="068/01/062/1.jpg"></figure><lb></lb>that runneth through the ſaid River, the <lb></lb>upper ſuperficies of that third ſide placed <lb></lb>in the bottom do remain uncovered <lb></lb>and dry, and that the dead water be not <lb></lb>above it; This ſame Machine ſhall be <lb></lb><arrow.to.target n="marg968"></arrow.to.target><lb></lb>called by us ^{*} REGULATOR: And that third ſide of the <lb></lb>Machine which ſtandeth Horizontally is called the bottom of <lb></lb>the Regulator; and the other two ſides, are called the banks of <lb></lb>the Regulator; as is ſeen in this firſt Figure: A B C D, ſhall be <lb></lb>the Regulator; B C the bottom; and the other two ſides A B, <lb></lb>and C D are its banks.</s></p><p type="margin"> <s><margin.target id="marg968"></margin.target>* Or Sluice.</s></p><p type="head"> <s>DEFINITION V.</s></p><p type="main"> <s>By the quick height, we mean the Perpendicular from the upper <lb></lb>ſuperficies of the River, unto the upper ſuperficies of the bot<lb></lb>tom of the Regulator; as in the foregoing Figure the line. </s> <s>G H.</s></p><p type="head"> <s>DEFINITION VI.</s></p><p type="main"> <s>If the water of a <emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver be ſuppoſed to be marked by three <lb></lb>ſides of a Regulator, that Rightangled Parallelogram compre<lb></lb>hended between the banks of the Regulator, and the bottom, <lb></lb>and the ſuperficies of the Water is called a Section of the <lb></lb>River.</s></p><pb xlink:href="068/01/063.jpg" pagenum="49"></pb><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>Here it is to be noted, that the River it ſelf may have ſundry <lb></lb>and divers heights, in ſeveral parts of its Chanel, by reaſon of <lb></lb>the various velocities of the water, and its meaſures; as hath <lb></lb>been demonſtrated in the firſt book.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>It is ſuppoſed, that the Rivers equal in breadth, and quick <lb></lb>height, that have the ſame inclination of bed or bottom, ought <lb></lb>alſo to have equal velocities, the accidental impediments being <lb></lb>removed that are diſperſed throughout the courſe of the water, <lb></lb>and abſtracting alſo from the external windes, which may velo<lb></lb>citate, and retard the courſe of the water of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>Let us ſuppoſe alſo, that if there be two Rivers that are in <lb></lb>their beds of equal length, and of the ſame inclination, but of <lb></lb>quick heights unequal, they ought to move with like velocity, <lb></lb>according to the ſenſe explained in the ſecond definition.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>Becauſe it will often be requiſite to meaſure the time exactly <lb></lb>in the following Problems, we take that to be an excellent <lb></lb>way to meaſure the time, which was ſhewed me many years ſince <lb></lb>by <emph type="italics"></emph>Signore Galilæo Galilæi,<emph.end type="italics"></emph.end> which is as followeth.</s></p><p type="main"> <s>A ſtring is to be taken three Roman feet long, to the end of <lb></lb>which a Bullet of Lead is to be hanged, of about two or three <lb></lb>ounces; and holding it by the other end, the Plummet is to be <lb></lb>removed from its perpendicularity a Palm, more or leſs, and then <lb></lb>let go, which will make many ſwings to and again, paſſing and <lb></lb>repaſſing the Perpendicular, before that it ſtay in the ſame: Now <lb></lb>it being required to meaſure the time that is ſpent in any what<lb></lb>ſoever operation, thoſe vibrations are to be numbred, that are <lb></lb>made whilſt the work laſteth; and they ſhall be ſo many ſecond <lb></lb>minutes of an hour, if ſo be, that the ſtring be three Roman feet <lb></lb>long, but in ſhorter ſtrings, the vibrations are more frequent, and <lb></lb>in longer, leſs frequent; and all this ſtill followeth, whether the <lb></lb>Plummet be little or much removed from its Perpendicularity, or <lb></lb>whether the weight of the Lead be greater or leſſer.</s></p><p type="main"> <s>Theſe things being pre-ſuppoſed, we will lay down ſome fa<pb xlink:href="068/01/064.jpg" pagenum="50"></pb>miliar Problems, from which we ſhall paſs to the Notions and <lb></lb>queſtions more ſubtil and curious; which will alſo prove profi<lb></lb>table, and not to be ſleighted in this buſineſs of Waters.</s></p><p type="head"> <s>PROPOSITION I. PROBLEME I.</s></p><p type="main"> <s><emph type="italics"></emph>Achanel of Running-Water being given, the breadth <lb></lb>of which paſsing through a Regulator, is three <lb></lb>Palms; and the height one Palm, little more or <lb></lb>leſs, to meaſure what water paſſeth through the <lb></lb>Regulator in a time given.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt, we are to dam up the Chanel; ſo that there paſs not any <lb></lb>water below the Dam; then we muſt place in the ſide of the <lb></lb>Chanel, in the parts above the Regulator three, or four, or five <lb></lb>Bent-pipes, or Syphons, according to the quantity of the water <lb></lb>that runneth along the Chanel; in ſuch ſort, as that they may <lb></lb>drink up, or draw out of the Chanel all the water that the Cha<lb></lb>nel beareth (and then ſhall we know that the Syphons drink up <lb></lb>all the water, when we ſee that the water at the Dam doth nei<lb></lb>ther riſe higher, nor abate, but alwaies keepeth in the ſame Le<lb></lb>vel.) Theſe things being prepared, taking the Inſtrument to <lb></lb>meaſure the time, we will examine the quantity of the water that <lb></lb>iſſueth by one of thoſe Syphons in the ſpace of twenty vibrations, <lb></lb>and the like will we do one by one with the other Syphons; and <lb></lb>then collecting the whole ſumme, we will ſay, that ſo much is <lb></lb>the water that paſſeth and runneth thorow the Regulator or <lb></lb>Chanel (the Dam being taken away) in the ſpace of twenty ſe<lb></lb>cond minutes of an hour; and calculating, we may eaſily reduce <lb></lb>it to hours, dayes, months, and years: And it hath fallen to my <lb></lb>turn to meaſure this way the waters of Mills and Fountains, and I <lb></lb>have been well aſſured of its exactneſs, by often repeating the <lb></lb>ſame work.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>And this method muſt be made uſe of in meaſuring the waters, <lb></lb>that we are to bring into Conducts, and carry into Cities <lb></lb>and Caſtles, for Fountains; and that we may be able afterwards <lb></lb>to divide and ſhare them to particular perſons juſtly; which will <lb></lb>prevent infinite ſuits and controverſies that every day happen in <lb></lb>theſe matters..</s></p><pb xlink:href="068/01/065.jpg" pagenum="51"></pb><p type="head"> <s>PROPOSITION II. THEOREM I.</s></p><p type="main"> <s><emph type="italics"></emph>If a River moving with ſuch a certain velocitie <lb></lb>through its Regulator, ſhall have a given quick <lb></lb>height, and afterwards by new water ſhall increaſe <lb></lb>to be double, it ſhall alſo increaſe double in ve<lb></lb>locitie.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the quick height of a River in the Regulator A B C D, <lb></lb>be the perpendicular F B, and afterwards, by new water that <lb></lb>is added to the River, let the water be ſuppoſed to be raiſ<lb></lb>ed to G, ſo that G B may be double to E B. </s> <s>I ſay, that all the <lb></lb>water G C ſhall be double in velocity to <lb></lb><figure id="id.068.01.065.1.jpg" xlink:href="068/01/065/1.jpg"></figure><lb></lb>that of E C: For the water G F, having <lb></lb>for its bed the bottom E F, equally in<lb></lb>clined as the bed B C, and its quick <lb></lb>height G E being equal to the quick <lb></lb>height E C, and having the ſame breadth <lb></lb>B C, it ſhall have of it ſelf a velocity e<lb></lb>qual to the velocity of the firſt water <lb></lb>F C: but becauſe, beſides its own moti<lb></lb>on, which is imparted to it by the motion of the water E C, it <lb></lb>hath alſo over and above its own motion, the motion of E C. </s> <s>And <lb></lb>becauſe the two waters G C, and E C, are alike in velocity, by <lb></lb>the third Suppoſition; therefore the whole water G C ſhall be <lb></lb>double in velocity to the water E C; which was that which we <lb></lb>were to demonſtrate.</s></p><p type="main"> <s><emph type="italics"></emph>This demonſtration is not here inſerted, as perfect, the Authour ha<lb></lb>ving by ſeveral letters to his friends confeſſed himſelf unſatisfi<lb></lb>ed therewith; and that he intended not to publiſh the<emph.end type="italics"></emph.end> Theorem <lb></lb><emph type="italics"></emph>without a more ſolid demonſtration, which he was in hope to light <lb></lb>upon. </s> <s>But being overtaken by Death, he could not give the <lb></lb>finiſhing touch either to this, or to the rest of the ſecond Book. </s> <s>In <lb></lb>conſideration of which, it ſeemed good to the Publiſher of the <lb></lb>ſame, rather to omit it, than to do any thing contrary to the mind of <lb></lb>the Authour. </s> <s>And this he hints, by way of advertiſement, to <lb></lb>thoſe that have Manuſcript Copies of this Book, with the ſaid de<lb></lb>monſtration. </s> <s>For this time let the Reader content himſelf with <lb></lb>the knowledge of ſo ingenious and profitable a Concluſion; of the <lb></lb>truth of which he may, with ſmall expence and much pleaſure, be <lb></lb>aſſured by means of the experiment to be made in the ſame man<lb></lb>ner, with that which is laid down in the ſecond Corollary of<emph.end type="italics"></emph.end><pb xlink:href="068/01/066.jpg" pagenum="52"></pb><emph type="italics"></emph>the fourth<emph.end type="italics"></emph.end> Theorem <emph type="italics"></emph>of this, with its Table, and the uſe there<lb></lb>of annexed.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Hence it followeth, that when a River increaſeth in quick <lb></lb>height by the addition of new water, it alſo increaſeth in ve<lb></lb>locity; ſo that the velocity hath the ſame proportion to the velo<lb></lb>city that the quick height hath to the quick height; as may be <lb></lb>demonſtrated in the ſame manner.</s></p><p type="head"> <s>PROPOS. III. PROBLEME II.</s></p><p type="main"> <s><emph type="italics"></emph>Achanel of Water being given whoſe breadth exceeds not <lb></lb>twenty Palms, or thereabouts, and whoſe quick beight <lb></lb>is leſs than five Palms, to meaſure the quantity of the <lb></lb>Water that runneth thorow the Chanel in a time <lb></lb>given.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Place in the Chanel a Regulator, and obſerve the quick <lb></lb>height in the ſaid Regulator; then let the water be turned <lb></lb>away from the Chanel by a Chanellet of three or four Palms <lb></lb>in breadth, or thereabouts: And that being done, meaſure the <lb></lb>quantity of the water which paſſeth thorow the ſaid Chanellet, <lb></lb>as hath been taught in the ſecond Propoſition; and at the ſame <lb></lb>time obſerve exactly how much the quick height ſhall be abated <lb></lb>in the greater Chanel, by means of the diverſion of the Chancl<lb></lb>let; and all theſe particulars being performed, multiply the quick <lb></lb>height of the greater Chanel into it ſelf, and likewiſe multiply <lb></lb>into it ſelf the leſſer height of the ſaid bigger Chanel, and the <lb></lb>leſſer ſquare being taken, from the greater, the remainder ſhall <lb></lb>have the ſame proportion to the whole greater ſquare, as the wa<lb></lb>ter of the Chanellet diverted, hath to the water of the bigger <lb></lb>Chanel: And becauſe the water of the Chanellet is known by <lb></lb>the Method laid down in the firſt Theorem, and the terms of the <lb></lb>Theorem being alſo known, the quantity of the water which run<lb></lb>neth thorow the bigger Chanel, ſhall be alſo known by the Gol<lb></lb>den <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ule, which was that that was deſired to be known. </s> <s>We <lb></lb>will explain the whole buſineſs by an example.</s></p><p type="main"> <s>Let a Chanel be, for example, 15 Palms broad, its quick height <lb></lb>before its diverſion by the Chanellet ſhall be ſuppoſed to be 24 <lb></lb>inches; but after the diverſion, let the quick height of the Chanel <lb></lb>be onely 22 inches. </s> <s>Therefore the greater height to the leſſer, <lb></lb>is as the number 11. to 12. But the ſquare of 11. is 121, and the <lb></lb>ſquare of 12. is 144, the difference between the ſaid leſſer <pb xlink:href="068/01/067.jpg" pagenum="53"></pb>ſquare and the greater is 23. Therefore the diverted water, is <lb></lb>to the whole water, as 23. to 144: which is well near as 1 to <lb></lb>6 6/23: and that is the proportion that the quantity of the water <lb></lb>which runneth through the Chanellet ſhall have, to all the water <lb></lb>that runneth thorow the great Chanel. </s> <s>Now if we ſhould finde <lb></lb>by the Rule mentioned above in the firſt Propoſition, that the <lb></lb>quantity of the water that runneth through the Chanellet, is <lb></lb><emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> an hundred Barrels, in the ſpace of 15 ſecond minutes of <lb></lb>an hour, it is manifeſt, that the water which runneth through the <lb></lb>great Chanel in the ſaid time of 35 min. </s> <s>ſec. </s> <s>ſhall be about 600 <lb></lb>Barrels.</s></p><p type="head"> <s><emph type="italics"></emph>The ſame operation performed another way.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And becauſe very often in applying the Theory to Practice <lb></lb>it happeneth, that all the neceſſary particulars in the The<lb></lb>ory cannot ſo eaſily be put in execution; therefore we will <lb></lb>here add another way of performing the ſame Problem, if it ſhould <lb></lb>chance to happen that the Chanellet could not commodiouſly be <lb></lb>diverted from the great Chanel, but that it were eaſier for the <lb></lb>water of another ſmaller Chanel to be brought into the greater <lb></lb>Chanel; which water of the ſmaller Chanel might be eaſily mea<lb></lb>ſured, as hath been ſhewen in the firſt Probleme; or in caſe that <lb></lb>there did fall into a greater Chanel, a leſſer Chanel that might <lb></lb>be diverted and meaſured. </s> <s>Therefore I ſay in the firſt caſe, If <lb></lb>we would meaſure the quantity of the water that runneth in a <lb></lb>certain time thorow the greater Chanel, into which another leſſer <lb></lb>Chanel that is meaſurable may be brought, we muſt firſt exactly <lb></lb>meaſure the Chanellet, and then obſerve the quick height of the <lb></lb>greater Chanel, before the introduction of the leſſer; and having <lb></lb>brought in the ſaid Chanellet, we muſt agnin find the propor<lb></lb>tion that the water of the Chanellet hath to all the water of the <lb></lb>great Ghanel; for theſe terms of the proportion being known, as <lb></lb>alſo the quantity of the water of the Chanellet, we ſhall alſo <lb></lb>come to know the quantity of the water that runneth thorow <lb></lb>the great Chanel. </s> <s>It is likewiſe manifeſt, that we ſhall obtain <lb></lb>our intent, if the caſe were that there entered into the great <lb></lb>Chanel, another leſſer Chanel that was meaſurable, and that <lb></lb>might be diverted.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>It would be neceſſary to make uſe of this Doctrine in the di<lb></lb>ſtribution of the waters that are imploy'd to overflow the fields, <lb></lb>as is uſed in the <emph type="italics"></emph>Breſciau, Cremoneſe, Bergamaſe, Lodigian, Mila-<emph.end type="italics"></emph.end><pb xlink:href="068/01/068.jpg" pagenum="54"></pb><emph type="italics"></emph>neſe<emph.end type="italics"></emph.end> territories, and many other places, where very great ſuits <lb></lb>and differences ariſe, which not being to be determined with in<lb></lb>telligible reaſons, come oftentimes to be decided, by force of <lb></lb>armes; and inſtead of flowing their Grounds with Waters, they <lb></lb>cruelly flow them with the ſhedding of humane blood, impiouſly <lb></lb>inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders <lb></lb>and feuds, as that they are ſometimes accompanied with the ru<lb></lb>ine of whole Cities, or elſe unprofitably charge them with vain, <lb></lb>and ſometimes prejudicial expences.</s></p><p type="head"> <s>PROPOS. IV. THEOR. II.</s></p><p type="main"> <s><emph type="italics"></emph>If a River increaſe in quick height, the quantitie of <lb></lb>Water which the River diſchargeth after the in<lb></lb>creaſe, hath the Proportion compounded of the <lb></lb>Proportions of the Quick height to the Quick <lb></lb>height, and of the velocity to the velocity.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a River, which whilſt it is low, runneth thorow <lb></lb>the Regulator D F, with the Quick height A B, and after<lb></lb>wards let a Flood come; and then let it run with the height <lb></lb>D B, I ſay, that the quantity of the Water that is diſcharged <lb></lb>through D F, to that which diſchargeth through A F, hath the <lb></lb>proportion compounded of the proportions of the velocity <lb></lb>through D F to the velocity through A F, and of the height <lb></lb>D B to the height A B. </s> <s>As the velocity through D F is to the <lb></lb>velocity through A F, ſo let the line R be to the line S; and as <lb></lb>the height D B is to the height A B; ſo let the line S be to the <lb></lb><figure id="id.068.01.068.1.jpg" xlink:href="068/01/068/1.jpg"></figure><lb></lb>line T. </s> <s>And let a Section be ſuppoſed L M N equal to the <lb></lb>Section D F in height and length, but let it be in velocity equal <lb></lb>to the Section AF. </s> <s>Therefore the quantity of the Water that run<lb></lb>neth through D F to that which runneth through L N, ſhall be <pb xlink:href="068/01/069.jpg" pagenum="55"></pb>as the velocity through D F, to the velocity of L N, that is, to <lb></lb>the velocity through L N, that is, to the velocity through <emph type="italics"></emph>A F.<emph.end type="italics"></emph.end><lb></lb>therefore the quantity of Water which runneth through D <emph type="italics"></emph>F,<emph.end type="italics"></emph.end><lb></lb>to that which paſſeth through L N, ſhall have the proportion <lb></lb>that R hath to S; but the quantity of the Water that runneth <lb></lb>through L N, to that which runneth through <emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; (the Sections <lb></lb>being equally ſwift) ſhall have the proportion that the Section <lb></lb>L N hath to the Section A F, that is, that the height <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D hath to <lb></lb>the height <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A, that is, that S hath to T. Therefore, by equal <lb></lb>proportion, the quantity of the Water which runneth by D F, <lb></lb>to that which runneth by A F, ſhall have the proportion of R to <lb></lb>T, that is, ſhall be compounded of the proportions of the height <lb></lb>D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> to the height A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; and of the velocity through D F, to <lb></lb>the velocity through A F. </s> <s>And therefore if a River increaſe in <lb></lb>quick height, the quantity of the Water that runneth after the <lb></lb>increaſe, to that which runneth before the increaſe, hath the <lb></lb>proportion compounded, &c. </s> <s>Which was to be demonſtrated.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Hence it followeth, that we having ſhewn, that the quantity of <lb></lb>the Water which runneth, whilſt the River is high, to that <lb></lb>which ran, whilſt it was low, hath the proportion compounded <lb></lb>of the velocity to the velocity, and of the height to the height. <lb></lb></s> <s>And it having been demonſtrated, that the velocity to the velo<lb></lb>city is as the height to the height; it followeth, I ſay, that the <lb></lb>quantity of the Water that runneth, whilſt the River is high, to <lb></lb>that which runneth, whilſt it is low, hath duplicate proportion of <lb></lb>the height to the height, that is, the proportion that the ſquares <lb></lb>of the heights have.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE II.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Vpon which things dependeth the reaſon of that which I have <lb></lb>ſaid, in my ſecond Conſideration, that if by the diverſion of <lb></lb>5/9 of the Water that entereth by the Rivers into the Moor or <lb></lb>Fen, the Water be abated ſuch a meaſure, that ſame ſhall be <lb></lb>only one third of its whole height; but moreover diverting the 4/9, it <lb></lb>ſhall abate two other thirds, a moſt principal point; and ſuch, <lb></lb>that its not having been well underſtood, hath cauſed very great <lb></lb>diſorders, and there would now, more than ever, follow extream <lb></lb>dammage, if one ſhould put in execution the diverſion of the <emph type="italics"></emph>Sile<emph.end type="italics"></emph.end><lb></lb>and other Rivers; and it is manifeſt, that in the ſame manner, <lb></lb>wherewith it hath been demonſtrated, that the quantity of the <lb></lb>Water increaſing quadruple, the height would increaſe onely <pb xlink:href="068/01/070.jpg" pagenum="56"></pb>double, and the quantity increaſing nonuple, the height increa<lb></lb>ſeth triple; ſo that, by adding to units all the odde numbers, ac<lb></lb>cording to their Series, the heights increaſe according to the na<lb></lb>tural progreſſion of all the numbers, from units. </s> <s>As for exam<lb></lb>ple, there paſſing thorow a Regulator ſuch a certain quantity of <lb></lb>Water in one time; adding three of thoſe meaſures, the quick <lb></lb>height is two of thoſe parts, which at firſt was one; and con<lb></lb>tinuing to adde five of thoſe ſaid meaſures, the height is three of <lb></lb>thoſe parts which at firſt were one; and thus adding ſeven, and <lb></lb>then nine, and then 11. and then 13, &c. </s> <s>the heights ſhall be 4. <lb></lb>then 5, then 6. then 7, &c. </s> <s>And for the greater facility of the <lb></lb>Work, we have deſcribed the following Table, of which we will <lb></lb>declare the uſe: The Table is divided into three Series or Pro<lb></lb>greſſions of Numbers: the firſt Series containeth all the Num<lb></lb>bers in the Natural Progreſſion, beginning at a Unit, and is called <lb></lb>the Series of the Heights; the ſecond containeth all the odde <lb></lb>numbers, beginning at an unit, and is called the Series of the <lb></lb>Additions: the third containeth all the ſquare numbers, begin<lb></lb>ning at an unit, and is called the Series of Quantity.<lb></lb><arrow.to.target n="table73"></arrow.to.target></s></p><table><table.target id="table73"></table.target><row><cell>Heights.</cell><cell>1</cell><cell>2</cell><cell>3</cell><cell>4</cell><cell>5</cell><cell>6</cell><cell>7</cell><cell>8</cell><cell>9</cell><cell>10</cell><cell>11</cell></row><row><cell>Additions.</cell><cell>1</cell><cell>3</cell><cell>5</cell><cell>7</cell><cell>9</cell><cell>11</cell><cell>13</cell><cell>15</cell><cell>17</cell><cell>19</cell><cell>21</cell></row><row><cell>Quantities.</cell><cell>1</cell><cell>4</cell><cell>9</cell><cell>16</cell><cell>25</cell><cell>36</cell><cell>49</cell><cell>64</cell><cell>81</cell><cell>100</cell><cell>121</cell></row></table><p type="head"> <s><emph type="italics"></emph>The uſe of the afore-mentioned Table.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt, if we ſuppoſe the whole quick height of a River of Run<lb></lb>ning Water to be divided into any number of equal parts, at <lb></lb>pleaſure, and would abate the ſame one fift, by means of a divi<lb></lb>ſron; let there be found in the Table in the Series of heights the <lb></lb>number 5. the denominator of the part which the River is to a<lb></lb>bate, and take the number that is immediately under it in the <lb></lb>row of Additions, which is 9. which let be ſubſtracted from the <lb></lb>number 25. placed underneath the ſame in the row of Quanti<lb></lb>ties, the remainder 16. ſignifieth that of the 25. parts of Water <lb></lb>that ran in the River, whilſt it was 5 meaſures high, there do <lb></lb>onely run 16. parts; ſo that to make it abate 1/5 it is neceſſary to <lb></lb>take 9/25 from the Water that the whole River did carry; ſo that <lb></lb>with ſubſtracting ſomewhat more than one third of the Water of <lb></lb>the River, it is abated but only one fift.</s></p><p type="main"> <s>2. And thus, in the ſecond place, if on the contrary, one would <lb></lb>know how much water is to be added to the ſaid River to make <lb></lb>it increaſe one fift more in height, ſo as that it may run in the <pb xlink:href="068/01/071.jpg" pagenum="57"></pb>Regulator 6. of thoſe parts high; of which it ran before but 5. let <lb></lb>6 be found in the row of heights, and let the number 11. ſtand<lb></lb>ing under the ſame be taken and added to the number 25. <lb></lb>that is placed under the number 9. in the Additions, and 5. in <lb></lb>the heights, and you ſhall have 36; which is the quantity of the <lb></lb>water that runneth with the height of the River, when it is high <lb></lb>6 of thoſe parts, whereof it was before but 5.</s></p><p type="main"> <s>3. But if it ſhould be deſired, to know how much water it is <lb></lb>requiſite to add to make the River riſe ſo, as that it may run in <lb></lb>height 8. of thoſe parts of which before it ran but 5; one <lb></lb>ought to take the ſum of the number of the Series of Additions <lb></lb>ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39. <lb></lb>and this ſhall be the ſumme that muſt be added to 25: So that <lb></lb>to make the River to run 8. of thoſe parts in height, of which it <lb></lb>before did run 5, it will be neceſſary to add 39. of thoſe parts, <lb></lb>of which the River before was 25.</s></p><p type="main"> <s>4. Likewiſe the ſame Table giveth the quantity of water <lb></lb>that runneth from time to time through a River, that increaſeth <lb></lb>by the addition of new water to the ſame in one of its heights, the <lb></lb>quantity of its water be known. </s> <s>As for example: If we knew that <lb></lb>the River in one minute of an hour diſchargeth 2500. of thoſe mea<lb></lb>ſures of water, and runneth in height 5. parts in the Regulator, and <lb></lb>afterwards ſhould ſee that it runneth 8 Palms high, finding in the <lb></lb>row of quantity the number placed under 8. which is 64. we would <lb></lb>ſay that the River heightned, carrieth of water 64. of thoſe parts <lb></lb>whereof it carried before but 25; and becauſe before it carried <lb></lb>2500. meaſures, by the Golden Rule we will ſay, that the River <lb></lb>carrieth 6400. of thoſe meaſures, of which before it carried 2500.</s></p><p type="main"> <s>In this progreſs of Nature, is one thing really curious, and that <lb></lb>at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro<lb></lb>ceeding ordinately in the diverſions and additions, with additi<lb></lb>ons and diverſions ſo unequal, the abatings do notwithſtanding <lb></lb>alwaies prove equal, and ſo do the riſings: And who would ever <lb></lb>think that a River in height, <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> 10. Palms, running and carry<lb></lb>ing an hundred meaſures in a minute of an hour, is to abate but <lb></lb>one Palm, onely by the diverſion of 19. of thoſe meaſures; and <lb></lb>then again, that the buiſineſs cometh to that paſs, that it abateth <lb></lb>likewiſe a Palm by the diverſion of three onely of thoſe meaſures, <lb></lb>nay, by the diverſion of but one meaſure? </s> <s>and yet it is moſt <lb></lb>certain: And this truth meets with ſo manifeſt proofs in experi<lb></lb>ence, that it is very admirable! And for the full ſatisfaction of <lb></lb>thoſe, who not being able to comprehend ſubtil demonſtrati<lb></lb>ons, desire to be clearly inform'd by the matters of fact, and to <lb></lb>ſee with their bobily eyes, and touch with their hands, what their <lb></lb>underſtanding and reaſon cannot reach unto: I will hear add <lb></lb>another very eaſie way to reduce all to an experiment, the <pb xlink:href="068/01/072.jpg" pagenum="58"></pb>which may be made in little, in great, or in very great; of <lb></lb>which I make uſe frequently, to the admiration of ſuch as ſee it.</s></p><p type="main"> <s>I prepared an hundred Siphons, or, if you will, bowed Pipes, <lb></lb>all equal; and placed them at the brim of a Veſſel, wherein the <lb></lb>water is kept at one and the ſame level (whether all the Syphons <lb></lb>work, or but a certain number of them) the mouths by which <lb></lb>the water iſſueth being all placed in the ſame level, parallel to <lb></lb>the Horizon; but lower in level than the water in the Veſſel; and <lb></lb>gathered all the water falling from the Syphons into another <lb></lb>Veſſel ſtanding lower than the former, I made it to run away <lb></lb>thorow a Chanel, in ſuch manner inclined, that wanting water <lb></lb>from the Syphons, the ſaid Chanel remained quite dry.</s></p><p type="main"> <s>And this done, I meaſured the quick height of the Chanel <lb></lb>with care, and afterwards divided it exactly into 10 equal parts, <lb></lb>and cauſing 19. of thoſe Syphons to be taken away, ſo that the <lb></lb>Chanel did not run water, ſave onely with 81 of thoſe Syphons, <lb></lb>I again obſerved the quick height of the water in the ſame ſite <lb></lb>obſerved before, and found that its height was diminiſhed pre<lb></lb>ciſely the tenth part of all its firſt height; and thus continuing to <lb></lb>take away 17. other Syphons, the height was likewiſe diminiſh<lb></lb>ed 1/1. of all its firſt quick height; and trying to take away 15. <lb></lb>Syphons, then 13, then 11, then 9, then 7, then 5, and then 3. <lb></lb>alwaies in theſe diverſions, made in order as hath been ſaid, there <lb></lb>enſued ſtill an abatement of 1/1. of the whole height.</s></p><p type="main"> <s>And here was one thing worthy of obſervation, that the water <lb></lb>encreaſing in [<emph type="italics"></emph>or through<emph.end type="italics"></emph.end>] the Chanel, its quick height was diffe<lb></lb>rent in different ſites of the Chanel, that is ſtill leſſer, the more <lb></lb>one approached to the Out-let; notwithſtanding which the abate<lb></lb>ment followed in all places proportionably, that is in all its ſites <lb></lb>the firſt part of the height of that ſite diminiſhed: And more<lb></lb>over the water iſſued from the Chanel, and dilated into a broader <lb></lb>courſe, from which likewiſe having divers Out-lets and Mouths; <lb></lb>yet nevertheleſs in that breadth alſo the quick heights ſucceſſive<lb></lb>ly varied and altered in the ſame proportions. </s> <s>Nor did I here <lb></lb>deſiſt my obſervation, but the water being diminiſhed, that iſſu<lb></lb>ed from the Syphons, and there being but one of them left that <lb></lb>diſcharged water; I obſerved the quick height that it made in the <lb></lb>above-ſaid ſites, (the which was likewiſe 1/1. of all the firſt height) <lb></lb>there being added to the water of that Syphon, the water of <lb></lb>three other Syphons; ſo that all the water was of 4 Syphons, <lb></lb>and conſequently quadruple to the firſt Syphon; but the quick <lb></lb>height was onely double, and adding five Siphons, the quick <lb></lb>height became triple, and with adding ſeven Syphons, the height <lb></lb>increaſed quadruple; and ſo by adding of 9. it increaſed quin<lb></lb>tuple, and by adding of 11. it increaſed ſextuple, and by ad<pb xlink:href="068/01/073.jpg" pagenum="59"></pb>ding of 13. it increaſed ſeptuple, and by adding of 15. octuple, <lb></lb>and by adding of 17. nonuple, and laſtly by adding 19. Syphons; <lb></lb>ſo that all the water was centuple to the water of one Syphon, <lb></lb>yet nevertheleſs the quick height of all this water was onely de<lb></lb>cuple to the firſt height conjoyned by the water that iſſued from <lb></lb>one onely Syphon.</s></p><p type="main"> <s>For the more clear underſtanding of all which, I have made <lb></lb>the following Figure; in which we have the mouth A, that <lb></lb>maintaineth the water of the Veſſel B C in the ſame level; though <lb></lb>it continually run; to the brim of the Veſſel are put 25. Sy<lb></lb>phons (and there may be many more) divided into 5 Claſſes, <lb></lb>D E F G H, and the firſt D, are of one onely Syphon; the ſecond <lb></lb>E, of three Syphons; the third F, of five; the fourth G, of 7; the <lb></lb>fifth H, of 9; and one may ſuppoſe the ſixth of 11, the ſeventh <lb></lb>of 13 Syphons, and ſo of the other Claſſes, all containing in con<lb></lb>ſequent odd numbers ſucceſſively (we are content to repreſent in <lb></lb>the Figure no more but the five forenamed Claſſes to avoid con<lb></lb>fuſion) the gathered water D E F G H, which runneth thorow <lb></lb>the Chanel I K L, and falleth into the out-let M N O P; and ſo <lb></lb>much ſufficeth for the explanation of this experiment.</s></p><figure id="id.068.01.073.1.jpg" xlink:href="068/01/073/1.jpg"></figure><pb xlink:href="068/01/074.jpg" pagenum="60"></pb><p type="head"> <s>PROPOS. V. PROB. III.</s></p><p type="main"> <s><emph type="italics"></emph>Any River of any bigneſs, if being given to examine the <lb></lb>quantity of the Water that runneth thorow the River <lb></lb>in a time aſſigned.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By what we have ſaid already in the two preceding Pro<lb></lb>blems, we may alſo reſolve this that we have now before <lb></lb>us; and it is done, by diverting in the firſt place from the <lb></lb>great River a good big meaſurable Chanel, as is taught in the <lb></lb>ſecond Probleme, and obſerving the abatement of the River, <lb></lb>cauſed by the diverſion of the Chanel; and finding the proporti<lb></lb>on that the Water of the Chanel hath to that of the River, then <lb></lb>let the Water of the Chanel be meaſured by the ſecond Pro<lb></lb>bleme, and work as above, and you ſhall have your deſire.</s></p><p type="head"> <s>CONSIDERATION. I.</s></p><p type="main"> <s>And although it ſeemeth as if it might prove difficult, and <lb></lb>almoſt impoſſible to make uſe of the Regulator number, if <lb></lb>one be about to meaſure the water of ſome great River, <lb></lb>and conſequently would be impoſſible, or at leaſt very difficult <lb></lb>to reduce the Theory of the firſt Probleme into practice: Yet ne<lb></lb>vertheleſs, I could ſay that ſuch great conceits of meaſuring the <lb></lb>water of a great River, are not to come into the minds of any <lb></lb>but great Perſonages, and potent Princes; of whom it is expected <lb></lb>for their extraordinary concerns, that they will make theſe kinde <lb></lb>of enquiries; as if here in <emph type="italics"></emph>Italy<emph.end type="italics"></emph.end> it ſhould be of the Rivers <emph type="italics"></emph>Tyber, <lb></lb>Velino, Chiana, Arno, Serchio, Adice,<emph.end type="italics"></emph.end> in which it ſeemeth real<lb></lb>ly difficult to apply the <emph type="italics"></emph>R<emph.end type="italics"></emph.end>egulator, to finde exactly the quick <lb></lb>height of the <emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver: But becauſe in ſuch like caſes ſometimes <lb></lb>it would turn to account to be at ſome charge, to come to the <lb></lb>exact and true knowledge of the quantity of water which that <lb></lb><emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver carrieth, by knowledge whereof, other greater diſ<lb></lb>burſments might afterwards be avoided, that would oft times be <lb></lb>made in vain; and prevent the diſguſts, which ſometimes happen <lb></lb>amongſt Princes: Upon this ground I think it will be well to <lb></lb>ſhew alſo the way how to make uſe of the <emph type="italics"></emph>R<emph.end type="italics"></emph.end>egulator in theſe <lb></lb>great <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ivers; in which if we will but open our eyes, we ſhall meet <lb></lb>with good ones, and thoſe made without great coſt or labour, <lb></lb>which will ſerve our turn.</s></p><p type="main"> <s>For upon ſuch like <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ivers there are Wears, or Lockes made, <pb xlink:href="068/01/075.jpg" pagenum="61"></pb>to cauſe the Waters to riſe, and to turn them for the ſervice of <lb></lb>Mills, or the like. </s> <s>Now in theſe Caſes it is ſufficient, that one <lb></lb>erect upon the two extreames of the Weare two Pilaſters either <lb></lb>of Wood or Brick, which with the bottome of the Weare do <lb></lb>compoſe our Regulator, wherewith we may make our deſired <lb></lb>operation, yea the Chanel it ſelf diverted ſhall ſerve, without <lb></lb>making any other diverſion or union. </s> <s>And in brief, if the bu<lb></lb>fineſſes be but managed by a judicious perſon, there may wayes <lb></lb>and helps be made uſe of, according to occaſion, of which it <lb></lb>would be too tedious to ſpeak, and therefore this little that hath <lb></lb>been hinted ſhall ſuſſice.</s></p><p type="head"> <s>CONSIDERATION II.</s></p><p type="main"> <s>From what hath been declared, if it ſhall be well under<lb></lb>ſtood, may be deduced many benefits and conveniences, <lb></lb>not onely in dividing of Running Waters for infinite uſes <lb></lb>that they are put to in turning of Corne-Mills, Paper-Mills, <lb></lb>Gins, Powder-Mills, Rice-Mills, Iron Mills, Oil-Mills, Saw<lb></lb>ing-Mills, Mirtle-Mills, Felling-Mills, Fulling-Mills, Silk-Mills, <lb></lb>and ſuch other Machines; but alſo in ordering Navigable Cha<lb></lb>nels, diverting Rivers and Chanels of Waters, or terminating <lb></lb>and limiting the ſizes of Pipes for Fountains: In all which af<lb></lb>fairs there are great errours committed, to the loſſe of much <lb></lb>expence, the Chanels and Pipes that are made, ſometimes not <lb></lb>being ſufficient to carry the deſigned Waters, and ſometimes they <lb></lb>are made bigger than is neceſſary; which diſorders ſhall be <lb></lb>avoided, if the Engineer be adviſed of the things aboveſaid: and <lb></lb>in caſe that to theſe Notions there be added the knowledge of <lb></lb>Philoſophy and Mathematicks, agreeable to the ſublime Diſco<lb></lb>veries of <emph type="italics"></emph>Signore Galilæo,<emph.end type="italics"></emph.end> and the further improvement thereof <lb></lb>by <emph type="italics"></emph>Signore Evangeliſta Torricelli,<emph.end type="italics"></emph.end> Mathematician to the Grand <lb></lb><emph type="italics"></emph>Duke of Tuſcany,<emph.end type="italics"></emph.end> who hath ſubtilly and admirably handled this <lb></lb>whole buſineſſe of Motion, one ſhall then come to the know<lb></lb>ledge of particular notions of great curioſity in the Theoricks, <lb></lb>and of extraordinary benefit in the Practicks that daily occur in <lb></lb>theſe buſineſſes.</s></p><p type="main"> <s>And to ſhew, in effect, of what utility theſe Notions are, I <lb></lb>have thought fit to inſert, in this place, the Conſiderations by <lb></lb>me made upon the Lake of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> and to repreſent, <lb></lb>at large, by the experience of the laſt year 1641. the moſt Se<lb></lb>rene <emph type="italics"></emph>Erizzo,<emph.end type="italics"></emph.end> then Duke of the ſaid Republique. </s> <s>Being <lb></lb>therefore at <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> in the year aforeſaid, I was requeſted by the <lb></lb>moſt Illuſtrious and moſt Excellent <emph type="italics"></emph>Signore Giovanni Baſa-<emph.end type="italics"></emph.end><pb xlink:href="068/01/076.jpg" pagenum="62"></pb><emph type="italics"></emph>donna,<emph.end type="italics"></emph.end> a Senatour of great worth and merit, that I would inge<lb></lb>nuouſly deliver my opinion touching the ſtate of the Lake <lb></lb>of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; and after I had diſcourſed with his Honour ſeve<lb></lb>ral times, in the end I had order to ſet down the whole <lb></lb>buſineſſe in writing, who having afterwards read it privately, <lb></lb>the ſaid <emph type="italics"></emph>Signore<emph.end type="italics"></emph.end> imparted the ſame, with like privacy, to the <lb></lb>moſt Serene PRINCE, and I received order to repreſent the <lb></lb>ſame to the full <emph type="italics"></emph>Colledge,<emph.end type="italics"></emph.end> as accordingly I did in the Moneth <lb></lb>of <emph type="italics"></emph>May,<emph.end type="italics"></emph.end> the ſame year, and it was as followeth.</s></p><figure id="id.068.01.076.1.jpg" xlink:href="068/01/076/1.jpg"></figure><pb xlink:href="068/01/077.jpg" pagenum="63"></pb><p type="head"> <s>CONSIDER ATIONS <lb></lb>Concerning the <lb></lb>LAKE <lb></lb>OF <lb></lb>VENICE. <lb></lb>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, <lb></lb>Abbot of S. <emph type="italics"></emph>Benedetto Aloyſio,<emph.end type="italics"></emph.end> Mathematician to <lb></lb>Pope <emph type="italics"></emph>VR BAN VIII.<emph.end type="italics"></emph.end> and Profeſſor in <lb></lb>ROME.</s></p><p type="head"> <s><emph type="italics"></emph>CONSIDERATION I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Though the principal cauſe be but one <lb></lb>onely, that in my judgment threatneth <lb></lb>irreparable ruine to the Lake of <lb></lb><emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> in the preſent ſtate in which it <lb></lb>now ſtands; Yet nevertheleſſe, I think <lb></lb>that two Heads may be conſidered. <lb></lb></s> <s>And this Conſideration may peradven<lb></lb>ture ſerve us for to facilitate and explain <lb></lb>the opportune remedies, though not to <lb></lb>render the ſtate of things abſolutely unchangeable and eternal: <lb></lb>an enterprize impoſſible, and eſpecially in that which having had <lb></lb>ſome beginning, ought likewiſe neceſſarily to have its end; or <lb></lb>at leaſt to prevent the danger for many hundreds of years; and <lb></lb>poſſibly it may, in the mean time, by the mutation it ſelf be <lb></lb>brought into a better condition.</s></p><p type="main"> <s>I ſay therefore, that the preſent diſorder may be conſidered <lb></lb>under two Heads; One is the very notable diſcovery of Land <lb></lb>that is obſerved at the time of low Water, the which, beſides <lb></lb>the obſtructing of Navigation in the Lake and alſo in the <lb></lb>Chanels, doth likewiſe threaten another miſchief and diſorder <pb xlink:href="068/01/078.jpg" pagenum="64"></pb>worthy of very particular conſideration, which is, That the Sun <lb></lb>drying up that mudde, eſpecially in the times of hot Summers, <lb></lb>doth raiſe thence the putrified and pernicious vapours, fogs, and <lb></lb>exhalations that infect the Air, and may render the City unha<lb></lb>bitable.</s></p><p type="main"> <s>The ſecond Head is the great Stoppage that daily is grow<lb></lb>ing in the Ports, eſpecially of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> at <emph type="italics"></emph>Malamoco<emph.end type="italics"></emph.end>; concerning <lb></lb>which matters I will hint certain general points, and then <lb></lb>will proceed to the more particular and important affairs.</s></p><p type="main"> <s>And firſt, I ſay, that I hold it altogether impoſſible to effect <lb></lb>any thing, though never ſo profitable, which doth not bring with <lb></lb>it ſome miſchief; and therefore the good and the hurt ought to <lb></lb>be very well weighed, and then the leſſe harmful part to be im<lb></lb>braced.</s></p><p type="main"> <s>Secondly, I propoſe to conſideration, that the ſo notable diſ<lb></lb>covery of Earth & Mud, hath not been long obſerved, as I under<lb></lb>ſtand, from old perſons that can remember paſſages for fifty <lb></lb>years paſt; which thing being true, as to me it ſeemeth moſt <lb></lb>true, it ſhould appear that it could not but be good to reduce <lb></lb>matters to that paſſe that they were at formerly, (laying aſide <lb></lb>all affection or paſſion that ſelf-flattering minds have entertained <lb></lb>for their own conceits) or at leaſt it ſhall be neceſſary ſpeedily to <lb></lb>conſult the whole.</s></p><p type="main"> <s>Thirdly, I hold that it is neceſſary to weigh, whether from the <lb></lb>foreſaid diſcovery of Land, it followeth, that onely the Earth ri<lb></lb>ſeth, as it is commonly thought by all, without diſpute; or whe<lb></lb>ther the Waters are abated and faln away; or elſe whether it <lb></lb>proceedeth from both the one and other cauſe. </s> <s>And here it would <lb></lb>be ſeaſonable to enquire, what ſhare the ſaid cauſes may have, <lb></lb>each conſidered apart in the foreſaid effect. </s> <s>For, in the firſt <lb></lb>caſe, if the Earth have been raiſed, it would be neceſſary to <lb></lb>conſider of taking it down, and removing it: But if the Wa<lb></lb>ters have failed or abated, I believe that it would be extreamly ne<lb></lb>ceſſary to reſtore and raiſe them: And if both theſe reaſons have <lb></lb>conſpired in this effect, it will be neceſſary to remedy them each <lb></lb>apart. </s> <s>And I do, for my part, think, that the ſo notable appea<lb></lb>rance of Shelves at the time of low Water, proceeds principally <lb></lb>from the decreaſe and abatement of the Waters, which may <lb></lb>confidently be affirmed to need no other proof, in regard that the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> hath been actually diverted which did formerly diſcharge <lb></lb>its Water into the Lake.</s></p><p type="main"> <s>As to the other point of the great Stoppage of Ports, I hold, <lb></lb>that all proceedeth from the violence of the Sea, which being <lb></lb>ſometimes diſturbed by windes, eſpecially at the time of the wa<lb></lb>ters flowing, doth continually raiſe from its bottome immenſe <pb xlink:href="068/01/079.jpg" pagenum="65"></pb>heaps of ſand, carrying them by the tide; and force of the waves <lb></lb>into the Lake; it not having on its part any ſttength of current <lb></lb>that may raiſe and carry them away, they ſink to the bottom, and <lb></lb>ſo they choke up the Ports. </s> <s>And that this effect happeneth in <lb></lb>this manner, we have moſt frequent experiences thereof along the <lb></lb>Sea-coaſts: And I have obſerved in <emph type="italics"></emph>Tuſcany<emph.end type="italics"></emph.end> on the <emph type="italics"></emph>Roman<lb></lb>ſhores,<emph.end type="italics"></emph.end> and in the Kingdom of of <emph type="italics"></emph>Naples,<emph.end type="italics"></emph.end> that when a river fal<lb></lb>leth into the Sea, there is alwaies ſeen in the Sea it ſelf, at the place <lb></lb>of the rivets out-let, the reſemblance, as it were, of an half-Moon, <lb></lb>or a great ſhelf of ſettled ſand under water, much higher then the <lb></lb>reſt of the ſhore, and it is called in <emph type="italics"></emph>Tuſcany, il Cavallo<emph.end type="italics"></emph.end>; and here <lb></lb>in <emph type="italics"></emph>Venice, lo Scanto<emph.end type="italics"></emph.end>: the which cometh to be cut by the current <lb></lb>of the river, one while on the right ſide, another while on the <lb></lb>left, and ſometimes in the midſt, according as the Wind fits. </s> <s>And <lb></lb>a like effect I have obſerved in certain little Rillets of water, <lb></lb>along the Lake of <emph type="italics"></emph>Bolſena<emph.end type="italics"></emph.end>; with no other difference, ſave that of <lb></lb>ſmall and great.</s></p><p type="main"> <s>Now whoſo well conſidereth this effect, plainly ſeeth that it <lb></lb>proceeds from no other, than from the contrariety of the ſtream <lb></lb>of the River, to the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of the Sea waves; ſeeing that <lb></lb>great abundance of ſand which the Sea continually throws upon <lb></lb>the ſhore, cometh to be driven into the Sea by the ſtream of the <lb></lb>river; and in that place where thoſe two impediments meet <lb></lb>with equal force, the ſand ſetleth under water, and thereupon is <lb></lb>made that ſame Shelf or <emph type="italics"></emph>Cavallo<emph.end type="italics"></emph.end>; the which if the river carry <lb></lb>water, and that any conſiderable ſtore, it ſhall be thereby cut <lb></lb>and broken; one while in one place, and another while in ano<lb></lb>ther; as hath been ſaid, according as the Wind blows: And <lb></lb>through that Chanel it is that Veſſels fall down into the Sea, and <lb></lb>again make to the river, as into a Port. </s> <s>But if the Water of <lb></lb>the river ſhall not be continual or ſhall be weak, in that caſe the <lb></lb>force of the Sea-Wind ſhall drive ſuch a quantity of ſand into <lb></lb>the mouth of the Port, and of the river, as ſhall wholly choak it <lb></lb>up. </s> <s>And hereupon there are ſeen along the Sea-ſide, very many <lb></lb>Lakes and Meers, which at certain times of the year abound with <lb></lb>waters, and the Lakes bear down that encloſure, and run into <lb></lb>the Sea.</s></p><p type="main"> <s>Now it is neceſſary to make the like reflections on our Ports <lb></lb>of <emph type="italics"></emph>Venice, Malamocco, Bondolo,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Chiozza<emph.end type="italics"></emph.end>; which in a certain <lb></lb>ſenſe are no other than Creeks, mouths, and openings of the ſhore <lb></lb>that parts the Lake from the main Sea; and therefore I hold that <lb></lb>if the Waters in the Lake were plentiful, they would have <lb></lb>ſtrength to ſcowr the mouths of the Ports thorowly, & with great <lb></lb>force; but the Water in the Lake failing, the Sea will with<lb></lb>out any oppoſal, bring ſuch a drift of ſand into the Ports; that if <pb xlink:href="068/01/080.jpg" pagenum="66"></pb>it doth not wholly choke them up, it ſhall render them at leaſt <lb></lb>unprofitable, and impoſſible for Barks and great Veſſels.</s></p><p type="main"> <s>Many other conſiderations might be propounded concerning <lb></lb>theſe two heads of the ſtoppage of the Ports, and of the appea<lb></lb>rance of the Ouze and Mud in the Lakes, but ſo much ſhall ſuf<lb></lb>fice us to have hinted, to make way for diſcourſing of the opera<lb></lb>tions about the oportune remedies.</s></p><p type="main"> <s>Yet before that I propound my opinion, I ſay, That I know <lb></lb>very well that my propoſal, at firſt ſight, will ſeem abſurd and in<lb></lb>convenient; and therefore, as ſuch, will perhaps be rejected by <lb></lb>the moſt: and ſo much the rather, for that it will prove directly <lb></lb>contrary to what hath hitherto been, and as I hear, is intended to <lb></lb>be done. </s> <s>And I am not ſo wedded to my opinions, but that I <lb></lb>do conſider what others may judge thereof: But be it as it will, <lb></lb>I am obliged to ſpeak my thoughts freely, and that being done, <lb></lb>I will leawe it to wiſer men than my ſelf; when they ſhall have <lb></lb>well conſidered my reaſons, to judge and deliberate of the <emph type="italics"></emph>quid <lb></lb>agendum:<emph.end type="italics"></emph.end> And if the ſentence ſhall go againſt me, I appeal to the <lb></lb>moſt equitable and inexorable Tribunal of Nature, who not <lb></lb>caring in the leaſt to pleaſe either one party or another, will be <lb></lb>alwaies a punctual and inviolable executrix of her eternal De<lb></lb>crees, againſt which neither humane deliberations, nor our vain <lb></lb>deſires; ſhall ever have power to rebell. </s> <s>I added by word of <lb></lb>mouth that which followeth.</s></p><p type="main"> <s>Though your Highneſs intereſt your ſelf in this Noble Col<lb></lb>ledge, and cauſe it to be confirmed in the ^{*} Senate by univerſal <lb></lb><arrow.to.target n="marg969"></arrow.to.target><lb></lb>Vote, that the Winds do not blow, that the Sea doth not fluctuate, <lb></lb>that the Rivers do not run; yet ſhall the Winds be alwaies deaf, <lb></lb>the Sea ſhall be conſtant in its inconſtancy, and the Rivers moſt <lb></lb>obſtinate: And theſe ſhall be my Judges, and to their determi<lb></lb>nation I refer my ſelf.</s></p><p type="margin"> <s><margin.target id="marg969"></margin.target>* In <emph type="italics"></emph>Pregadi,<emph.end type="italics"></emph.end> a <lb></lb>particular Coun<lb></lb>cil, the Senators of <lb></lb>which have great <lb></lb>Authority.</s></p><p type="main"> <s>By what hath been ſaid, in my opinion, that is made very clear <lb></lb>and manifeſt, which in the beginning of this diſcourſe I glanced <lb></lb>at; namely, That the whole diſorder, although it be divided into <lb></lb>two heads, into the diſcovery of the Mud, and of the ſtoppage <lb></lb>Ports, yet nevertheleſs, by the application of one onely remedy, <lb></lb>and that in my eſteem very eaſie, the whole ſhall be removed: <lb></lb>And this it is; That there be reſtored into the Lake as much <lb></lb>Water as can be poſſible, and in particular from the upper parts <lb></lb>of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> taking care that the Water be as free from Mud as is <lb></lb>poſſible. </s> <s>And that this is the true and real remedy of the prece<lb></lb>dent diſorders, is manifeſt: For in the paſſage that this Water <lb></lb>ſhall make thorow the Lakes, it ſhall of it ſelf by degrees clear <lb></lb>the Chanels in ſundry parts of them, according to the currents <lb></lb>that it ſhall ſucceſſively acquire, and in this manner being diſ<pb xlink:href="068/01/081.jpg" pagenum="67"></pb>perſed thorow the Lake, it ſhall maintain the waters in the ſame, <lb></lb>and in the Chanels much higher, as I ſhall prove hereafter; a <lb></lb>thing that will make Navigation commodious; and that, which <lb></lb>moreover is of great moment in our buſineſſe; thoſe Shelves <lb></lb>of Mud which now diſcover themſelves at the time of Low<lb></lb>Waters ſhall be alwayes covered, ſo that the putrefaction of <lb></lb>the Air ſhall alſo be remedied.</s></p><p type="main"> <s>And laſtly, this abundance of Water being alwayes to diſ<lb></lb>charge it ſelf into the Sea by the Ports, I do not doubt, but that <lb></lb>their bottomes will be ſcoured. </s> <s>And that theſe effects muſt fol<lb></lb>low, Nature her ſelf ſeemeth to perſwade, there remaining onely <lb></lb>one great doubt, whether that abundance of Water that ſhall be <lb></lb>brought into the Lake may be really ſufficient to make the Wa<lb></lb>ters riſe ſo much as to keep the Shelves covered, and to facilitate <lb></lb>Navigation, which ought to be at leaſt half a ^{*} Brace, or there<lb></lb><arrow.to.target n="marg970"></arrow.to.target><lb></lb>abouts. </s> <s>And indeed it ſeemeth at firſt ſight to be impoſſible, <lb></lb>that the ſole Water of the ^{*} <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> let into the Lake, and diſ<lb></lb><arrow.to.target n="marg971"></arrow.to.target><lb></lb>perſed over the ſame, can occaſion ſo notable an height of water; <lb></lb>and the more to confirm the difficulties, one might ſay, reducing <lb></lb>the reaſon to calculation, that in caſe the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> were 40. Bra<lb></lb>ces broad, and two and an half high, and the breadth of the <lb></lb>Lake were 20000. Braces, it would ſeem neceſſary that the <lb></lb>height of the water of the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> dilated and diſtended thorow <lb></lb>the Lake would be but onely 1/200 of a Brace in height, which is <lb></lb>imperceptible, and would be of no avail to our purpoſe; nay <lb></lb>more, it being very certain that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> runneth very muddy <lb></lb>and foul, this would occaſion very great miſchief, filling and <lb></lb>contracting the Lake, and for that reaſon this remedy ought, as <lb></lb>pernicious, to be totally excluded and condemned.</s></p><p type="margin"> <s><margin.target id="marg970"></margin.target>* A <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> Brace <lb></lb>is 11/16 of our yard.</s></p><p type="margin"> <s><margin.target id="marg971"></margin.target>* A River of <lb></lb>that name.</s></p><p type="main"> <s>I here confeſſe that I am ſurprized at the forme of the Argu<lb></lb>ment, as if I were in a certain manner convinced, that I dare not <lb></lb>adventure to ſay more, or open my mouth in this matter; but <lb></lb>the ſtrength it ſelf of the Argument, as being founded upon <lb></lb>the means of Geometrical and Arithmetical Calculation, hath <lb></lb>opened me the way to diſcover a very crafty fraud that is couch<lb></lb>ed in the ſame Argument, which fraud I will make out to any <lb></lb>one that hath but any inſight in <emph type="italics"></emph>Geometry<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Arithmetick.<emph.end type="italics"></emph.end><lb></lb>And as it is impoſſible, that ſuch an argument ſhould be produced <lb></lb>by any but ſuch as have taſted of theſe, in ſuch affairs, moſt pro<lb></lb>fitable, and moſt neceſſary Sciences; ſo do not I pretend to make <lb></lb>my ſelf underſtood, ſave onely by ſuch, to whom I will evince <lb></lb>ſo clearly, as that more it cannot be deſired, the errour and fraud <lb></lb>wherein thoſe Ancients and Moderns have been, and alwayes <lb></lb>are intangled, that have in any way yet handled this matter of <lb></lb>conſidering the Meaſure and Quantity of the Waters that move. <pb xlink:href="068/01/082.jpg" pagenum="68"></pb>And ſo great is the eſteem that I have for that which I am now <lb></lb>about to ſay touching this particular, that I am content that all <lb></lb>the reſt of my Diſcourſe be rejected; provided, that that be per<lb></lb>fectly underſtood, which I am hereafter to propoſe, I holding <lb></lb>and knowing it to be a main Principle, upon which all that is <lb></lb>founded that can be ſaid either well or handſomely on this parti<lb></lb>cular. </s> <s>The other Diſcourſes may have an appearance of being <lb></lb>probable, but this hits the mark as full as can be deſired, arriving <lb></lb>at the higheſt degree of certainty.</s></p><p type="main"> <s>I have, ſeventeen years ſince, as I repreſented to the moſt Se<lb></lb>rene Prince, and to the Right Honourable the Preſident of the <lb></lb>Lords the Commiſſioners of the ^{*}Sewers, written a Treatiſe of the <lb></lb><arrow.to.target n="marg972"></arrow.to.target><lb></lb>Meaſure of the waters that move, in which I Geometrically de<lb></lb>monſtrate and declare this buſineſſe, and they who ſhall have <lb></lb>well underſtood the ground of my Diſcourſe, will reſt fully ſa<lb></lb>tisfied with that which I am now about to propoſe: But that all <lb></lb>may become rhe more eaſie, I will more briefly explicate and <lb></lb>declare ſo much thereof as I have demonſtrated in the Diſcourſe, <lb></lb>which will ſuffice for our purpoſe: And if that ſhould not be <lb></lb>enough, we have alwayes the experiment of a very eaſie and <lb></lb>cheap way to clear up the whole buſineſſe. </s> <s>And moreover I <lb></lb>will take the boldneſſe to affirm, that in caſe there ſhould not for <lb></lb>the preſent any deliberation be made concerning this affair, ac<lb></lb>cording to my opinion; yet nevertheleſſe it will be, at ſome <lb></lb>time or other; or if it be not, things will grow worſe and <lb></lb>worſe.</s></p><p type="margin"> <s><margin.target id="marg972"></margin.target>* <emph type="italics"></emph>I. </s> <s>Savii dell' <lb></lb>Acque,<emph.end type="italics"></emph.end> a particu<lb></lb>lar Council that <lb></lb>take care of the <lb></lb>Lakes and other <lb></lb>Aquatick affairs.</s></p><p type="main"> <s>For more clear underſtanding, therefore, it ought to be known, <lb></lb>that it being required, as it is generally uſed, to meaſure the wa<lb></lb>ters of a River, its breadth and its depth is taken, and theſe two <lb></lb>dimenſions being multiplied together, the product is affirmed to <lb></lb>be the quantity of that River: As for example, if a River ſhall <lb></lb>be 100. feet broad, and 20. feet high, it will be ſaid, that that <lb></lb>River is 2000 feet of Water, and ſo if a Ditch ſhall be 15. feet <lb></lb>broad, and 5. feet high, this ſame Ditch will be affirmed to be <lb></lb>75. feet of Water: And this manner of meaſuring Running <lb></lb>Water hath been uſed by the Ancients, and by Moderns, with <lb></lb>no other difference, ſave onely that ſome have made uſe of the <lb></lb>Foot, others of the Palme, others of the Brace, and others of <lb></lb>other meaſures.</s></p><p type="main"> <s>Now becauſe that in obſerving theſe Waters that move, I fre<lb></lb>quently found, that the ſame Water of the ſame River was in <lb></lb>ſome ſites of its Chanel pretty big, and in others much leſſe, <lb></lb>not arriving in ſome places to the twentieth, nor to the hundreth <lb></lb>part of that which it is ſeen to be in other places; therefore this <lb></lb>vulgar way of meaſuring the Waters that move, for that they did <pb xlink:href="068/01/083.jpg" pagenum="69"></pb>not give me a certain and ſtable meaſure and quantity of Water, <lb></lb>began deſervedly to be ſuſpected by me, as difficult and defective, <lb></lb>being alwayes various, and the meaſure, on the contrary, being <lb></lb>to be alwayes determinate, and the ſame; it is therefore written, <lb></lb>that <emph type="italics"></emph>Pondus & Pondus, Menſura & Menſura, utrumque abomi<lb></lb>nabile eſt apud Deum,<emph.end type="italics"></emph.end> Exod. </s> <s>I conſidered that in the Terri<lb></lb>tory of <emph type="italics"></emph>Breſcia,<emph.end type="italics"></emph.end> my native Countrey, and in other places, where <lb></lb>Waters are divided to overflow the Grounds, by the like way of <lb></lb>meaſuring them, there were committed grievous and moſt impor<lb></lb>tant errours, to the great prejudice of the Publique and of Pri<lb></lb>vate perſons, neither they that ſell, nor they that buy under<lb></lb>ſtanding the true quantity of that which is ſold and bought: In <lb></lb>regard that the ſame ſquare meaſure, as is accuſtomed in thoſe <lb></lb>parts, aſſigned one particular perſon, carried to ſometimes above <lb></lb>twice or thrice as much water, as did the ſame ſquare meaſure aſ<lb></lb>ſigned to another. </s> <s>Which thing proveth to be the ſame incon<lb></lb>venience, as if the meaſure wherewith Wine and Oil is bought <lb></lb>and ſold, ſhould hold twice or thrice as much Wine or Oil at one <lb></lb>time as at another. </s> <s>Now this Conſideration invited my minde <lb></lb>and curioſity to the finding out of the true meaſure of Running <lb></lb>Waters. </s> <s>And in the end, by occaſion of a moſt important bu<lb></lb>ſineſſe that I was imployed in ſome years ſince, with great in<lb></lb>tenſeneſſe of minde, and with the ſure direction of <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> I <lb></lb>have diſcovered the miſtake, which was, that we being upon the <lb></lb>buſineſſe of taking the meaſure of the Waters that move, do make <lb></lb>uſe of two dimenſions onely, namely, breadth and depth, keep<lb></lb>ing no account of the length. </s> <s>And yet the Water being, though <lb></lb>running, a Body, it is neceſſary in forming a conceit of its quan<lb></lb>tity, in relation to another, to keep account of all the three Di<lb></lb>menſions, that is of length, breadth, and depth.</s></p><p type="main"> <s>Here an objection hath been put to me, in behalf of the ordi<lb></lb>nary way of meaſuring Running Waters, in oppoſition to what <lb></lb>I have above conſidered and propoſed: and I was told, Its true, <lb></lb>that in meaſuring a Body that ſtands ſtill, one ought to take all <lb></lb>the three Dimenſions; but in meaſuring a Body that continually <lb></lb>moveth, as the Water, the caſe is not the ſame: For the length <lb></lb>is not to be had, the length of the water that moveth being infi<lb></lb>nite, as never finiſhing its running; and conſequently is incom<lb></lb>prehenſible by humane underſtanding, and therefore with reaſon, <lb></lb>nay upon neceſſity it cometh to be omitted.</s></p><p type="main"> <s>In anſwer to this, I ſay, that in the aboveſaid Diſcourſe, two <lb></lb>things are to be conſidered diſtinctly; Firſt, whether it be poſſible <lb></lb>to frame any conceit of the quantity of the Body of the Water <lb></lb>with two Dimenſions onely. </s> <s>And ſecondly, whether this length <lb></lb>be to be found. </s> <s>As to the firſt, I am very certain that no man, let <pb xlink:href="068/01/084.jpg" pagenum="70"></pb>him be never ſo great a Wit, can never promiſe to frame a con<lb></lb>ceit of the quantity of the Body of Water, without the third <lb></lb>Dimenſion of length: and hereupon I return to affirm, that the <lb></lb>vulgar Rule of meaſuring Running water is vain and erroneous. <lb></lb></s> <s>This point being agreed on, I come to the ſecond, which is, Whe<lb></lb>ther the third Dimenſion of length may be meaſured. </s> <s>And I ſay, <lb></lb>that if one would know the whole length of the water of a <lb></lb>Fountain or River, thereby to come to know the quantity of all <lb></lb>the Water, it would prove an impoſſible enterprize, nay the <lb></lb>knowing of it would not be uſeful. </s> <s>But if one would know how <lb></lb>much water a Fountain, or a River carrieth in a determinate time <lb></lb>of an hour, of a day, or of a moneth, &c. </s> <s>I ſay, that it is a very <lb></lb>poſſible and profitable enquiry, by reaſon of the innumerable <lb></lb>benefits that may be derived thence, it much importing to know <lb></lb>how much Water a Chanel carrieth in a time given; and I have <lb></lb>demonſtrated the ſame above in the beginning of this Book; and <lb></lb>of this we ſtand in need in the buſineſſe of the Lake, that ſo we <lb></lb>may be able to determine how much ſhall be the height of the <lb></lb><emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end> when it is ſpread all over the Lake: For the three dimen<lb></lb>ſions of a Body being given, the Body is known; and the quan<lb></lb>tity of a Body being given, if you have but two dimenſions, the <lb></lb>third ſhall be known. </s> <s>And thus diving farther and farther into <lb></lb>this Conſideration, I found that the Velocity of the courſe of the <lb></lb>water may be an hundred times greater or leſſer in one part of <lb></lb>its Chanel than in another. </s> <s>And therefore although there ſhould <lb></lb>be two mouths of Waters equal in bigneſſe; yet nevertheleſs it <lb></lb>might come to paſſe, that one might diſcharge an hundred or a <lb></lb>thouſand times more water than another: and this would be, if <lb></lb>the water in one of the mouths ſhould run with an hundred or a <lb></lb>thouſand times greater velocity, than the other; for that it <lb></lb>would be the ſame as to ſay, that the ſwifter was an hundred or <lb></lb>a thouſand times longer, than the ſlower: and in this manner I <lb></lb>diſcovered that to keep account of the velocity, was the keeping <lb></lb>account of the Length.</s></p><p type="main"> <s>And therefore it is manifeſt, that when two Mouths diſcharge <lb></lb>the ſame quantity of Wa r in an equal velocity, it is neceſſary <lb></lb>that the leſs ſwift Mouth be ſo much bigger than the more ſwift; <lb></lb>as the more ſwift exceedeth in velocity the leſs ſwift; as for <lb></lb>example.</s></p><p type="main"> <s>In caſe two Rivers ſhould carry equal quantity of water in <lb></lb>equal times, but that one of them ſhould be four times more <lb></lb>ſwift than the other, the more ſlow ſhould of neceſſity be four <lb></lb>times more large. </s> <s>And becauſe the ſame River in any part <lb></lb>thereof alwaies diſchargeth the ſame quantity of Water in equal <lb></lb>times (as is demonſtrated in the firſt Propoſition of the firſt <pb xlink:href="068/01/085.jpg" pagenum="71"></pb><arrow.to.target n="marg973"></arrow.to.target><lb></lb>Book^{*} of the meaſure of Running Watets;) but yet doth not <lb></lb>run thorowout with the ſame velocity: Hence it is, that the vul<lb></lb>gar meaſures of the ſaid River, in divers parts of its Chanel, are <lb></lb>alwaies divers; inſomuch, that if a River paſſing through its cha<lb></lb>nel had ſuch velocity, that it ran 100 Braces in the 1/60 of an hour<lb></lb>and afterwards the ſaid River ſhould be reduced to ſo much tardi, <lb></lb>ty of motion, as that in the ſame time it ſhould not run more than <lb></lb>one Brace, it would be neceſſary that that ſame River ſhould be<lb></lb>come 100. times bigger in that place where it was retarded; I <lb></lb>mean, 100. times bigger than it was in the place where it was <lb></lb>ſwifter. </s> <s>And let it be kept well in mind, that this point rightly <lb></lb>underſtood, will clear the underſtanding to diſcover very many <lb></lb>accidents worthy to be known. </s> <s>But for this time let it ſuffice, <lb></lb>that we have onely declared that which makes for our purpoſe, <lb></lb>referring apprehenſive and ſtudious Wits to the peruſal of my <lb></lb>aforenamed Treatiſe; for therein he ſhall finde profit and delight <lb></lb>both together.</s></p><p type="margin"> <s><margin.target id="marg973"></margin.target>* He here intends <lb></lb>the Demonſtrati<lb></lb>ons following, at <lb></lb>the end of the firſt <lb></lb>Book</s></p><p type="main"> <s>Now applying all to our principal intent, I ſay, That by what <lb></lb>hath been declared it is manifeſt, that if the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> were 40. Bra<lb></lb>ces broad, and 2 1/2 high, in ſome one part of its Chanel, that after<lb></lb>wards the ſame Water of the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> falling into the Lake, andpaſ<lb></lb>ſing thorow the ſame to the Sea, it ſhould loſe ſo much of its ve<lb></lb>locity, that it ſhould run but one Brace, in the time wherein <lb></lb>whilſt it was in its Chanel at the place aforeſaid, it ran 100. Bra<lb></lb>ces. </s> <s>It would be abſolutely neceſſary, that increaſing in mea<lb></lb>ſure, it ſhould become an hundred times ^{*} thicker; and therefore <lb></lb><arrow.to.target n="marg974"></arrow.to.target><lb></lb>if we ſhould ſuppoſe that the Lake were 20000. Braces, the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> that already hath been ſuppoſed in its Chanel 100. Braces, <lb></lb>being brought into the Lake, ſhould be 100. times 100. Brates; <lb></lb>that is, ſhall be 10000. Braces in thickneſs, and conſequently ſhall <lb></lb>be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a <lb></lb>Brace, as was concluded in the Argument.</s></p><p type="margin"> <s><margin.target id="marg974"></margin.target>* Deeper.</s></p><p type="main"> <s>Now one may ſee into what a groſs errour of 99. in 100. one <lb></lb>may fall through the not well underſtanding the true quantity <lb></lb>of Running Water, which being well underſtood, doth open a <lb></lb>direct way to our judging aright in this moſt conſiderable affair.</s></p><p type="main"> <s>And therefore admitting that wich hath been demonſtrated, <lb></lb>I fay, that I would (if it did concern me) greatly encline to con<lb></lb>ſult upon the returning of the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> again into the Lake: For it <lb></lb>being moſt evident, that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> in the Chanel of its mouth, is <lb></lb>much ſwifter than the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> being brought into the Lake, it will <lb></lb>certainly follow thereupon, that the thickneſs of the Water of <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> in the Lake, ſhall be ſo much greater than that of <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> in <lb></lb><emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end> by how much the <emph type="italics"></emph>Bront<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is ſwifter than thh <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end><lb></lb>in the Lake.</s></p><pb xlink:href="068/01/086.jpg" pagenum="72"></pb><p type="main"> <s>1. From which operation doth follow in the firſt place, that <lb></lb>the Lake being filled and increaſed by tbeſe Waters, ſhall be <lb></lb>more Navigable, and paſſible, than at preſent we ſee it to be.</s></p><p type="main"> <s>2. By the current of theſe Waters, the Chanels will be ſcour<lb></lb>ed, and will be kept clean from time to time.</s></p><p type="main"> <s>3. There will not appear at the times of low-waters ſo many <lb></lb>Shelves, and ſuch heaps of Mud, as do now appear.</s></p><p type="main"> <s>4. The Ayr will become more wholeſom, for that it ſhall not <lb></lb>be ſo infected by putrid vapours exhaled by the Sun, ſo long as <lb></lb>the Miery Ouze ſhall be covered by the Waters.</s></p><p type="main"> <s>5. Laſtly, in the current of theſe advantagious Waters,, which <lb></lb>muſt iſſue out of the Lake into the Sea, beſides thoſe of the Tyde, <lb></lb>the Ports will be kept ſcoured, and clear: And this is as much as <lb></lb>I ſhall offer for the preſent, touching this weighty buiſineſs; al<lb></lb>waies ſubmitting my ſelf to ſounder judgements.</s></p><p type="main"> <s>Of the above-ſaid Writing I preſented a Copy at <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> at a <lb></lb>full Colledge, in which I read it all, and it was hearkned to with <lb></lb>very great attention; and at laſt I preſented it to the Duke, and <lb></lb>left ſome Copies thereof with ſundry Senators, and went my way, <lb></lb>promiſing with all intenſeneſs to apply my pains with reiterated <lb></lb>ſtudies in the publick ſervice; and if any other things ſhould come <lb></lb>into my minde, I promiſed to declare them ſincerely, and ſo took <lb></lb>leave of <emph type="italics"></emph>His ſerenity,<emph.end type="italics"></emph.end> and that Noble Council. </s> <s>When I was <lb></lb>returned to <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> this buſineſs night and day continually run<lb></lb>ning in my mind, I hapned to think of another admirable and <lb></lb>moſt important conceit, which with effectual reaſons, confirmed <lb></lb>by exact operations, I with the Divine aſſiſtance, made clear and <lb></lb>manifeſt; and though the thing at firſt ſight ſeemed to me a moſt <lb></lb>extravagant Paradox, yet notwithſtanding, having ſatisfied my <lb></lb>ſelf of the whole buſineſs, I ſent it in writing to the moſt Illuſtri<lb></lb>ous and moſt Noble <emph type="italics"></emph>Signore Gio. </s> <s>Baſadonna<emph.end type="italics"></emph.end>; who after he had <lb></lb>well conſidered my Paper, carried it to the Council; and after <lb></lb>that thoſe Lords had for many months maturely conſidered <lb></lb>thereon, they in the end reſolved to ſuſpend the execution of the <lb></lb>diverſion which they had before conſulted to make of the River <lb></lb><emph type="italics"></emph>Sile,<emph.end type="italics"></emph.end> and of four other Rivers, which alſo fall into the Lake; a <lb></lb>thing by me blamed in this ſecond Paper, as moſt prejudicial, <lb></lb>and harmful. </s> <s>The writing ſpake as followeth.</s></p><pb xlink:href="068/01/087.jpg" pagenum="73"></pb><p type="head"> <s>CONSIDERATIONS <lb></lb>Concerning the <lb></lb>LAKE <lb></lb>OF <lb></lb>VENICE.</s></p><p type="head"> <s><emph type="italics"></emph>CONSIDERATION II.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If the diſcourſing well about the truth of <lb></lb>things, Moſt Serene Prince, were as the <lb></lb>carrying of Burdens, in which we ſee <lb></lb>that an hundred Horſes carry a greater <lb></lb>weight than one Horſe onely; it would <lb></lb>ſeem that one might make more account <lb></lb>of the opinion of many men, than of <lb></lb>one alone; But becauſe that diſcourſing <lb></lb>more reſembleth running, than carrying <lb></lb>Burdens, in which we ſee that one Barb alone runneth faſter <lb></lb>than an hundred heavy-heel'd Jades; therefore I have ever more <lb></lb>eſteemed one Concluſion well managed, and well conſidered by <lb></lb>one underſtanding man, although alone, than the common and <lb></lb>Vulgar opinions; eſpecially, when they concern abſtruce and <lb></lb>arduous points: Nay in ſuch caſes the opinions moulded and <lb></lb>framed by the moſt ignorant and ſtupid Vulgar, have been ever <lb></lb>ſuſpected by me as falſe, for that it would be a great wonder if <lb></lb>in difficult matters a common capacity ſhould hit upon that <lb></lb>which is handſom, good, and true. </s> <s>Hence I have, and do hold <lb></lb>in very great veneration the ſumme of the Government of the <lb></lb>moſt Serene, and eternal Republick of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; which although, <lb></lb>as being in nature a Common-wealth, it ought to be governed by <lb></lb>the greater part; yet nevertheleſs, in arduous affairs, it is alwaies <lb></lb>directed by the Grave Judgement of few, and not judged blindly <pb xlink:href="068/01/088.jpg" pagenum="74"></pb>by the <emph type="italics"></emph>Plebeian<emph.end type="italics"></emph.end> Rout. </s> <s>Tis true, that he that propoundeth Pro<lb></lb>poſitions far above the reach of common capacity, runneth a <lb></lb>great hazard of being very often condemned without further Pro<lb></lb>ceſs, or knowledge of the Cauſe; but yet for all that, the truth <lb></lb>is not to be deſerted in moſt weighty affairs, but ought rather to <lb></lb>be explained in due place and time with all poſſible perſpicuity; <lb></lb>that ſo being well underſtood, and conſidered, it may come after<lb></lb>wards for the Common good to be embraced.</s></p><p type="main"> <s>This which I ſpeak in general, hath often been my fortune in <lb></lb>very many particulars, not onely when I have kept within the <lb></lb>bounds of meer ſpeculation, but alſo when I have chanced to de<lb></lb>ſcend to Practice, and to Operations: and your Highneſs know<lb></lb>eth very well what befel me the laſt Summer 1641. when in obe<lb></lb>dience to your Soveraign Command, I did in full Colledge repre<lb></lb>ſent my thoughts touching the ſtate of the Lake of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; for <lb></lb>there not being ſuch wanting, who without ſo much as vouch<lb></lb>ſafing to underſtand me, but having onely had an inkling, and <lb></lb>bad apprehenſion of my opinion, fell furiouſly upon me, and by <lb></lb>violent means both with the Pen and Preſs, full of Gall, did abuſe <lb></lb>me in reward of the readineſs that I had expreſt to obey and <lb></lb>ſerve them: But I was above meaſure encouraged and pleaſed, to <lb></lb>ſee that thoſe few who vouchſafed to hear me, were all either <lb></lb>thorowly perſwaded that my opinion was well grounded, or at <lb></lb>leaſt ſuſpended their prudent verdict to more mature deliberati<lb></lb>on. </s> <s>And though at the firſt bout I chanced to propoſe a thing <lb></lb>that was totally contrary to the moſt received and antiquated <lb></lb>opinion, and to the reſolutions and conſultations taken above an <lb></lb>hundred years ago: Moved by theſe things, and to ſatisfie alſo <lb></lb>to the promiſe that I had made of tendering unto them what <lb></lb>ſhould farther offer it ſelf unto me touching the ſame buſineſs; I <lb></lb>have reſolved to preſent to the Throne of your Highneſs, another <lb></lb>Conſideration of no leſs importance, which perhaps at firſt ſight <lb></lb>will appear a ſtranger Paradox; but yet brought to the Teſt and <lb></lb>Touch-ſtone of experience, it ſhall prove moſt clear and evident. <lb></lb></s> <s>If it ſhall be accounted of, ſo that it ſucceedeth to the benefit of <lb></lb>your Highneſs, I ſhall have obtained my defire and intent: And <lb></lb>if not, I ſhall have ſatisfied my ſelf, and ſhall not have been <lb></lb>wanting to the Obligation of your moſt faithful Servant, and na<lb></lb>tive ſubject.</s></p><p type="main"> <s>That which I propounded in the Mouths paſs, touching the <lb></lb>moſt important buſineſs of the Lake, though it did onely expreſ<lb></lb>ly concern the point of the diverſion of the Mouth of the Lake, <lb></lb>already made and put in execution; yet it may be underſtood <lb></lb>and applyed alſo to the diverſion under debate, to be made of <lb></lb>the other five Rivers, and of the <emph type="italics"></emph>Sile<emph.end type="italics"></emph.end> in particular.</s></p><pb xlink:href="068/01/089.jpg" pagenum="75"></pb><p type="main"> <s>Now touching this, I had the fortune to offer an admirable <lb></lb>accident that we meet with when we come to the effect, which <lb></lb>I verily believe will be an utter ruine to the Lake of <emph type="italics"></emph>Ve<lb></lb>nice.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I ſay therefore, that by diverting theſe five Rivers that re<lb></lb>main, although their water that they diſcharge for the preſent in<lb></lb>to the Lake is not all taken together 4/5 parts of what the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end><lb></lb>alone did carry, yet nevertheleſſe the abatement of the water of <lb></lb>the Lake which ſhall enſue upon this laſt diverſion of four parts, <lb></lb>which was the whole water, ſhall prove double to that which hath <lb></lb>happened by the diverſion of <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> onely, although that the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> alone carried five parts of that water, of which the Rivers <lb></lb>that are to be diverted carry four: A wonder really great, and <lb></lb>altogether unlikely; for the reducing all this Propoſition to be <lb></lb>underſtood, is as if we ſhould ſay, that there being given us <lb></lb>three Rivers, of which the firſt diſchargeth five parts, the ſecond <lb></lb>three, and the third one, and that from the diverſion of the <lb></lb>firſt, there did follow ſuch a certain abatement or fall; from <lb></lb>the taking away of the ſecond there ought to follow alſo ſo <lb></lb>much more abatement; And laſtly, from the withdrawing of <lb></lb>the third the water ought to fall ſo much more, which is wholly <lb></lb>impoſſible: And yet it is moſt certain, and beſides the demon<lb></lb>ſtration that perſwades me to it, which I ſhall explain in due <lb></lb>time, I can ſet before your eyes ſuch an experiment as is not to <lb></lb>be denied by any one, although obſtinate: and I will make it <lb></lb>plainly ſeen and felt, that by taking away only four parts of the <lb></lb>five, which ſhall have been taken away, the abatement proveth <lb></lb>double to the abatement enſuing upon the diverting firſt of the <lb></lb>five onely; which thing being true, as moſt certainly it is, it <lb></lb>will give us to underſtand how pernicious this diverſion of five <lb></lb>Rivers is like to prove, if it ſhall be put in execution.</s></p><p type="main"> <s>By this little that I have hinted, and the much that I could <lb></lb>ſay, let your Highneſſe gather with what circumſpection this bu<lb></lb>ſineſſe ought to be managed, and with how great skill he ought <lb></lb>to be furniſhed who would behave himſelf well in theſe difficult <lb></lb>affairs.</s></p><p type="main"> <s>I have not at this time explained the demonſtration, nor have <lb></lb>I ſo much as propounded the way to make the Experiment, that <lb></lb>I am able to make in confirmation of what I have ſaid, that ſo <lb></lb>by ſome one or others miſ-apprehending the Demonſtration, <lb></lb>and maiming the Experiment, the truth may not happen to ſhine <lb></lb>with leſſe clarity than it doth, when all miſts of difficulty are re<lb></lb>moved: and if ſo be, no account ſhould be made of the Reaſons <lb></lb>by me alledged, and that men ſhould ſhut their eyes againſt the <lb></lb>Experiments that without coſt or charge may be made, I do de<pb xlink:href="068/01/090.jpg" pagenum="76"></pb>clare and proteſt that there ſhall follow very great dammages <lb></lb>to the Fields of the main Land, and extraordinary ſummes <lb></lb>ſhall be expended to no purpoſe. </s> <s>The Lake undoubtedly will <lb></lb>become almoſt dry, and will prove impaſſible for Navigation, <lb></lb>with a manifeſt danger of corrupting the Air: And in the laſt <lb></lb>place there will unavoidably enſue the choaking and ſtoppage of <lb></lb>the Ports of <emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Upon the 20th. </s> <s>of <emph type="italics"></emph>December,<emph.end type="italics"></emph.end> 1641. I imparted this my ſecond <lb></lb>Conſideration to the moſt Excellent <emph type="italics"></emph>Signore Baſadonna,<emph.end type="italics"></emph.end> preſen<lb></lb>ting him with a Copy thereof amongſt other Writings, which I <lb></lb>have thought good to inſert, although they ſeem not to belong <lb></lb>directly to our buſineſſe of the Lake.</s></p><p type="head"> <s>The way to examine the MUD and SAND <lb></lb>that entereth and remaineth in the <lb></lb>LAKE of <emph type="italics"></emph>VENICE.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>To the moſt Excellent<emph.end type="italics"></emph.end></s></p><p type="head"> <s>SIGNORE GIO. BASADONNA.</s></p><p type="main"> <s>Two very conſiderable Objections have been made a<lb></lb>gainſt my opinion concerning the Lake of <emph type="italics"></emph>Venice:<emph.end type="italics"></emph.end> One <lb></lb>was that, of which I have ſpoken at large in my firſt <lb></lb>Conſideration, namely, that the <emph type="italics"></emph>Brents<emph.end type="italics"></emph.end> having been taken out of <lb></lb>the Lake, cannot have been the occaſion of the notable fall of <lb></lb>the Waters in the Lake, as I pretend, and conſequently, that <lb></lb>the turning <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> into the Lake would be no conſiderable reme<lb></lb>dy, in regard that the water of <emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end> and the great expanſion <lb></lb>of the Lake over which the water of <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is to diffuſe and <lb></lb>ſpread being conſidered, it is found that the riſe proveth in<lb></lb>ſenſible.</s></p><p type="main"> <s>The ſecond Objection was, that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is very muddy, and <lb></lb>therefore if it ſhould fall muddy into the Lake, the Sand would <lb></lb>ſink and fill up the ſame.</s></p><p type="main"> <s>Touching the firſt Query, enough hath been ſaid in my firſt <lb></lb>Conſideration, where I have plainly diſcovered the deceipt of the <lb></lb>Argument, and ſhewn its fallacy; It remaineth now to examine <pb xlink:href="068/01/091.jpg" pagenum="77"></pb>the ſecond: to which in the firſt place I ſay, that one of the firſt <lb></lb>things that I propoſed in this affair was, that I held it impoſſible <lb></lb>to do any act, though never ſo beneficial, that was not alſo ac<lb></lb>companied by ſome inconvenience and miſchief; and therefore <lb></lb>we are to conſider well the profit, and the loſſe and prejudice; <lb></lb>and they both being weighed, we ſhall be able to chooſe the leſ<lb></lb>ſer evil: Secondly, I admit it to be moſt true, that <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is at ſome <lb></lb>times muddy, but it is alſo true, that for the greater part of the <lb></lb>year it is not muddy. </s> <s>Thirdly, I do not ſee nor underſtand <lb></lb>what ſtrength this objection hath, being taken ſo at large, and in <lb></lb>general; and methinks that it is not enough to ſay, that the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> runneth muddy, and to aſſert that it depoſeth its Muddi<lb></lb>neſſe in the Lake, but we ought moreover to proceed to particu<lb></lb>lars, and ſhew how much this Mud is, and in what time this <lb></lb>choaking up of the Ports may be effected. </s> <s>For the Reaſons are <lb></lb>but too apparent and particular, that conclude the ruine of the <lb></lb>Lake, and that in a very ſhort time, (for mention is made of <lb></lb>dayes) the Waters diverſion being made, and moreover we <lb></lb>have the circumſtance of an Experiment, the ſtate of things be<lb></lb>ing obſerved to have grown worſe ſince the ſaid diverſion. </s> <s>And <lb></lb>I have demonſtrated, that in caſe the Diverſion of the <emph type="italics"></emph>Sile<emph.end type="italics"></emph.end> and <lb></lb>the other Rivers ſhould be put in execution, the Lake would in a <lb></lb>few dayes become almoſt dry; and the Ports would be loſt, with <lb></lb>other miſchievous conſequences. </s> <s>But on the other ſide, al<lb></lb>though that we did grant the choaking of them, we may very <lb></lb>probably ſay, that it will not happen, ſave onely in the ſucceſſion <lb></lb>of many and many Centuries of years. </s> <s>Nor can I think it pru<lb></lb>dent counſel to take a reſolution and imbrace a Deſigne now, to <lb></lb>obtain a benefit very uncertain, and more than that, which only <lb></lb>ſhall concern thoſe who are to come very many Ages after us, <lb></lb>and thereby bring a certain inconvenience upon our ſelves, and <lb></lb>upon our children that are now alive and preſent.</s></p><p type="main"> <s>Let it be alledged therefore, (although I hold it falſe) that by <lb></lb>the diverſions of the Rivers the Lake may be kept in good con<lb></lb>dition for ſeveral years to come.</s></p><p type="main"> <s>But I ſay confidently, and hope to demonſtrate it; That the <lb></lb>Diverſions will bring the Lake, even in our dayes, to be almoſt <lb></lb>dry, and at leaſt will leave ſo little water in it, that it ſhall ceaſe <lb></lb>to be Navigable, and the Ports ſhall moſt infallibly be choaked <lb></lb>up. </s> <s>I will therefore ſay upon experience, in anſwer to this Ob<lb></lb>jection, that it is very neceſſary firſt well to diſcourſe, and ratio<lb></lb>nally to particularize and aſcertain the beſt that may be this <lb></lb>point of the quantity of this ſinking Mud or Sand.</s></p><p type="main"> <s>Now I fear I ſhall make my ſelf ridiculous to thoſe, who mea<lb></lb>ſuring the things of Nature with the ſhallowneſſe of their brains <pb xlink:href="068/01/092.jpg" pagenum="78"></pb>do think that it is abſolutely impoſſible to make this enquiry, and <lb></lb>will ſay unto me, <emph type="italics"></emph>Quis menſus eſt pugillo aquas, & terram palmo <lb></lb>ponderavit<emph.end type="italics"></emph.end>? </s> <s>Yet nevertheleſs I will propound a way whereby, <lb></lb>at leaſt in groſs, one may find out the ſame.</s></p><p type="main"> <s>Take a Veſſel of Cylindrical Figure, holding two barrels of <lb></lb>water, or thereabouts; and then fill it with the water of <emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end><lb></lb>at its Mouth or Fall into the Lake; but in the Lake at the time <lb></lb>that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> runneth muddy, and after it hath begun to run <lb></lb>muddy for eight or ten hours, to give the mud time to go as far <lb></lb>as S. <emph type="italics"></emph>Nicolo,<emph.end type="italics"></emph.end> to iſſue into the Sea; and at the ſame time take <lb></lb>another Veſſel, like, and equal to the firſt, and fill it with the wa<lb></lb>ter of the Lake towards S. <emph type="italics"></emph>Nicolo,<emph.end type="italics"></emph.end> (but take notice that this ope<lb></lb>ration ought to be made at the time when the waters go out, <lb></lb>and when the Sea is calm) and then, when the waters ſhall have <lb></lb>ſetled in the aforeſaid Veſſels, take out the clear water, and con<lb></lb>ſider the quantity of Sand that remains behind, and let it be ſet <lb></lb>down, or kept in mind: And I am eaſily induced to think, that <lb></lb>that ſhall be a greater quantity of Sand which ſhall be left in the <lb></lb>firſt Veſſel, than that left in the ſecond Veſſel. </s> <s>Afterwards <lb></lb>when the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> ſhall come to be clear, let both the operations be <lb></lb>repeated, and obſerve the quantity of Sand in the aforeſaid Veſ<lb></lb>ſels; for if the Sand in the firſt Veſſel ſhould be moſt, it would <lb></lb>be a ſign, that in the revolution of a year the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> would depoſe <lb></lb>Sand in the Lake: And in this manner one may calculate to a <lb></lb>ſmall matter what proportion the Sand that entreth into the Lake, <lb></lb>hath to that which remains: And by that proportion one may <lb></lb>judge how expedient it ſhall be for publick benefit. </s> <s>And if at <lb></lb>ſeveral times of the year you carefully repeat the ſame operati<lb></lb>ons, or rather obſervations, you would come to a more exact <lb></lb>knowledge in this buſineſs: And it would be good to make the <lb></lb>ſaid operations at thoſe times, when the Lake is diſturbed by <lb></lb>ſtrong high Winds, and made muddy by its own Mud, raiſed by <lb></lb>the commotion of the Waters.</s></p><p type="main"> <s>This notion would give us great light, if the ſame obſervations <lb></lb>ſhould be made towards the Mouth of <emph type="italics"></emph>Lio,<emph.end type="italics"></emph.end> at ſuch time as the <lb></lb>waters flow and ebb, in calm ſeaſons; for ſo one ſhould come to <lb></lb>know whether the waters of the Lake are more thick at the going <lb></lb>out, than at the entrance. </s> <s>I have propounded the foregoing <lb></lb>way of meaſuring Sands and Mud, to ſhew that we are not ſo <lb></lb>generally, and inconſiderately to pronounce any ſentence, but <lb></lb>proceed to ſtricter inquiries, and then deliberate what ſhall be <lb></lb>moſt expedient to be done. </s> <s>Others may propoſe more exqui<lb></lb>ſite examinations, but this ſhall ſerve me for the preſent.</s></p><p type="main"> <s>I will add onely, that if any one had greater curioſity (it would <lb></lb>be profitable to have it) in inveſtigating more exactly the quan<pb xlink:href="068/01/093.jpg" pagenum="79"></pb>tity of the Water that entereth into the Lake, by the means that <lb></lb>I have ſhewen in the beginning of this Book: When he ſhall <lb></lb>have found the proportion of the quantity of water to the quan<lb></lb>tity of Sand or Mud, he ſhall come to know how much Sand the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> ſhall leave in the Lake in the ſpace of a year. </s> <s>But to <lb></lb>perform theſe things, there are required perſons of diſcretion, and <lb></lb>fidelity, and that are imployed by publick Order; for there <lb></lb>would thence reſult eminent benefit and profit.</s></p><p type="main"> <s><emph type="italics"></emph>Here are wanting<emph.end type="italics"></emph.end> LETTERS <emph type="italics"></emph>from ſeveral perſons.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>To the Reverend Father, <emph type="italics"></emph>Franceſco di<emph.end type="italics"></emph.end></s></p><p type="head"> <s>S. GIUSEPPE.</s></p><p type="main"> <s>In execution of the command that you laid upon me in your <lb></lb>former Letters, by order from the moſt Serene, my Lord, <lb></lb><emph type="italics"></emph>Prince Leopold<emph.end type="italics"></emph.end>; that I ſhould ſpeak my judgment concern<lb></lb>ing the diſimboguement of the River called <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> whe<lb></lb>ther it ought to be let into the Sea, or into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; I ſay, that <lb></lb>I chanced 18. years ſince to be preſent, when the ſaid Mouth was <lb></lb>opened into the Sea, and that of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> ſtopt; which work was <lb></lb>done to remedy the great Innundation that was made in all that <lb></lb>Country, and Plain of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> that lyeth between the River <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end><lb></lb>and the Mountains of <emph type="italics"></emph>S. Giuliano,<emph.end type="italics"></emph.end> and the River <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; which <lb></lb>Plain continued long under water, inſomuch that not onely in the <lb></lb>Winter, but alſo for a great part of the Summer, thoſe fields <lb></lb>were overflowed; and when that the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> was <lb></lb>effectually opened into the Sea, the place was preſently freed from <lb></lb>the waters. </s> <s>and drained, to the great ſatisfaction of the Owners <lb></lb>of thoſe Grounds. </s> <s>And here I judge it worth your notice, that <lb></lb>for the generality of thoſe that poſſeſs eſtates in thoſe parts, they <lb></lb>deſired that the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> might ſtand open to the <lb></lb>Sea, and thoſe who would have it open into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> are perſons <lb></lb>that have no other concernment there, ſave the hopes of gaining <lb></lb>by having the diſpoſe of Commiſſions, and the like, &c,</s></p><p type="main"> <s>But for the more plain underſtanding of that which is to be <lb></lb>ſaid, it muſt be known, That the reſolution of opening the ſaid <lb></lb>Mouth into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> was taken in the time of the Great Duke <lb></lb><emph type="italics"></emph>Ferdinando<emph.end type="italics"></emph.end> the firſt, upon the ſame motives that are at this time <lb></lb>again propoſed, as your Letters tell me, Since that, it manifeſt<lb></lb>ly appearing, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> had, and hath its Mouth open to <lb></lb>the Sea, the Plain hathbeen kept dry; and it being alſo true, that <pb xlink:href="068/01/094.jpg" pagenum="80"></pb>the fury of the South, and South-Weſt-Winds carryed ſuch <lb></lb>abundance of ſand into the Mouth, or Out-let of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end><lb></lb>that it wholly ſtopt it up: eſpecially when the waters on <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end><lb></lb>ſide were low and ſhallow, And they think, that turning the <lb></lb>Lake of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> maintaining <lb></lb>continually its own Mouth with the force of its waters open to the <lb></lb>Sea, and conſequently alſo <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> they would have had the <lb></lb>Out-let clear and open; and in this manner they think, that the <lb></lb>Plain of <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> would have been freed from the waters. </s> <s>The bu<lb></lb>ſineſs paſſeth for current, at firſt ſight; but experience proveth <lb></lb>the contrary, and Reaſon confirmeth the ſame: For the height <lb></lb>of the water of thoſe Plains, was regulated by the height of the <lb></lb>waters in the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; that is, The waters at the <lb></lb>Mouth being high, the waters alſo do riſe in the fields; and when <lb></lb>the waters at the Mouth are low, the waters of the fields do like<lb></lb>wiſe abate: Nor is it enough to ſay, That the Out-let or Vent <lb></lb>of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is continual, but it muſt be very low: Now if <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> did determine in <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> it is manifeſt that it <lb></lb>would determine high; for <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> terminating in the Sea, when <lb></lb>ever it more and more aboundeth with water, and riſeth, it is ne<lb></lb>ceſlary that alſo <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> hath its level higher, and conſe<lb></lb>quently ſhall keep the waters in the Plains higher. </s> <s>Nay, it hath <lb></lb>happened ſometimes (and I ſpeak it upon my own ſight) that <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> hath reverſed its courſe upwards towards <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end>; <lb></lb>which caſe will ever happen, whenſoever the <emph type="italics"></emph>Piſan<emph.end type="italics"></emph.end> waters chance <lb></lb>to be lower than the level of thoſe of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; for in that caſe <lb></lb>the waters of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> return back upon the Plains thorow <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> in ſuch ſort, that the Muddineſſes, and the <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> have <lb></lb>been obſerved to be carried by this return as farr as the Walls of <lb></lb><emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end>; and then before ſuch time as ſo great waters can be aſ<lb></lb>ſwaged, which come in with great fury, and go out by little and <lb></lb>little, there do paſs very many days, and moneths, nay ſome<lb></lb>times one being never able to find the waters of <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end><lb></lb>when at the ſhalloweſt, ſo low as the Sea in level; (which is the <lb></lb>loweſt place of the waters) it thence doth follow, that the wa<lb></lb>ters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhould never at any time of the year, ſo long <lb></lb>as they determine in <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> be ſo low, as they come to be when <lb></lb>the ſame <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> determineth in the Sea. </s> <s>Tis true indeed, <lb></lb>that the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> opened into the Sea, is ſubject to <lb></lb>the inconvenience of being ſtopt up by the force of Winds: But <lb></lb>in this caſe, it is neceſſary to take ſome pains in opening it; which <lb></lb>may eaſily be done, by cutting that Sand a little which ſtayeth <lb></lb>in the Mouth, after that the Wind is laid; and it is enough if you <lb></lb>make a Trench little more than two Palms in breadth; for the <lb></lb>water once beginning to run into it, it will in a few hours carry <pb xlink:href="068/01/095.jpg" pagenum="81"></pb>that Sand away with it, and there will enſue a deep and broad <lb></lb>Trench that will drain away all the water of the Plains in very lit<lb></lb>tle time. </s> <s>And I have found by practice, that there having been <lb></lb>a great quantity of Sand driven back, by the fury of the South<lb></lb>Weſt-Wind, into the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> I having cauſed the <lb></lb>little gutter to be made in the Morning, ſomewhat before Noon, <lb></lb>a Mouth hath been opened of 40. Braces wide, and notably deep, <lb></lb>inſomuch that the water, which before had incommoded all the <lb></lb>Champian ran away in leſs than three dayes, and left the Coun<lb></lb>try free and dry, to the admiration of all men. </s> <s>There was pre<lb></lb>ſent upon the place, at this buſineſs, on the ſame day that I <lb></lb>opened the Mouth, the moſt Serene great Duke, the moſt Serene <lb></lb>Arch-Dutcheſs Mother, all the Commiſſioners of Sewers, with <lb></lb>many other Perſons and Peaſants of thoſe parts; and they all ſaw <lb></lb>very well, that it was never poſſible that a little Bark of eight <lb></lb>Oars, which was come from <emph type="italics"></emph>Legorn<emph.end type="italics"></emph.end> to wait upon the great <lb></lb>Duke, ſhould ever be able to maſter the Current, and to make <lb></lb>up into <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; and his Highneſs, who came with an intent <lb></lb>to cauſe the ſaid Mouth towards the Sea to be ſtopt; and that <lb></lb>into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> to be opened, changed his judgement, giving order <lb></lb>that it ſhould be left open towards the Sea, as it was done. </s> <s>And <lb></lb>if at this day it ſhall return into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> I am very certain that it <lb></lb>will be neceſſary to open it again into the Sea. </s> <s>And there was <lb></lb>alſo charge and order given to a perſon appointed for the pur<lb></lb>poſe, that he ſhould take care to open the ſaid Mouth, as hath <lb></lb>been ſaid upon occaſion. </s> <s>And thus things have ſucceeded very <lb></lb>well unto this very time. </s> <s>But from the middle of <emph type="italics"></emph>October,<emph.end type="italics"></emph.end> until <lb></lb>this firſt of <emph type="italics"></emph>February,<emph.end type="italics"></emph.end> there having continued high South, and <lb></lb>South-Weſt-Winds, with frequent and abundant Rains; it is no <lb></lb>wonder that ſome innundation hath happened; but yet I will <lb></lb>affirm, that greater miſchiefs would have followed, if the Mouth <lb></lb>had been opened into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> This which I have hitherto ſaid, <lb></lb>is very clear and intelligible to all ſuch as have but competent in<lb></lb>ſight, and indifferent skill in theſe affairs. </s> <s>But that which I am <lb></lb>now about to propoſe farther, will, I am very certain, be under<lb></lb>ſtood by your ſelf, but it will ſeem ſtrange and unlikely to many <lb></lb>others. </s> <s>The point is, that I ſay, That by raiſing the level of <lb></lb><emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> one half Brace, onely at its Mouth, (it will peni<lb></lb>penitrate into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> farther than it would into the Sea) it ſhall <lb></lb>cauſe the waters to riſe three, or perhaps more Braces upon the <lb></lb>fields towards <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and ſtill more by degrees as they ſhall recede <lb></lb>farther from the Sea-ſide; and thus there will follow very great <lb></lb>Innundations, and conſiderable miſchiefs. </s> <s>And to know that <lb></lb>this is true, you are to take notice of an accident, which I give <lb></lb>warning of in my diſcourſe of the Meaſure of Running Waters: <pb xlink:href="068/01/096.jpg" pagenum="82"></pb>where alſo I give the reaſon thereof, ^{*} <emph type="italics"></emph>Coroll.<emph.end type="italics"></emph.end> 14. The ac<lb></lb>cident is this, That there coming a Land-Flood, for example, <lb></lb>into <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> which maketh it to riſe above its ordinary Mouth <lb></lb>wthin <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> or a little above or below the City ſix or ſeven Bra<lb></lb>ces; this ſame height becometh alwaies leſſer and leſſer, the more <lb></lb>we approach towards the Sea-ſide; inſomuch, that near to the <lb></lb>Sea the ſaid River ſhall be raiſed hardly half a Brace: Whence <lb></lb>it followeth of neceſſary conſequence, that ſhould I again be at <lb></lb>the Sea-ſide, and knowing nothing of what hapneth, ſhould ſee <lb></lb>the River <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> raiſed by the acceſſion of a Land-flood, one third <lb></lb>of a Brace; I could certainly infer, that the ſame River was raiſed <lb></lb>in <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> thoſe ſame ſix or ſeven Braces. </s> <s>And that which I ſay of <lb></lb><emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> is true of all Rivers that fall into the Sea. </s> <s>Which thing <lb></lb>being true, it is neceſſary to make great account of every ſmall <lb></lb>riſing, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> maketh towards the Sea-ſide by fal<lb></lb>ling into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> For although the riſing of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> by <lb></lb>being to diſgorge its Waters into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> towards the Sea, were <lb></lb>onely a quarter of a Brace; we might very well be ſure, that fart <lb></lb>from the Sea, about <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and upon thoſe fields the riſe ſhall be <lb></lb>much greater, and ſhall become two or three Braces: And be<lb></lb>cauſe the Countrey lyeth low, that ſame riſe will cauſe a conti<lb></lb>nual Innundation of the Plains, like as it did before; I cauſed the <lb></lb>Mouth to be opened into the Sea. </s> <s>And therefore I conclude <lb></lb>that the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> ought by no means to be opened <lb></lb>into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; but ought to be continued into the Sea, uſing all <lb></lb>diligence to keep it open after the manner aforeſaid, ſo ſoon as <lb></lb>ever the Wind ſhall be laid. </s> <s>And if they ſhall do otherwiſe, I <lb></lb>confidently affirm, that there will daily follow greater damages; <lb></lb>not onely in the Plains, but alſo in the wholeſomneſs of the <lb></lb>Air; as hath been ſeen in times paſt. </s> <s>And again, It ought with <lb></lb>all care to be procured, that no waters do by any means run or <lb></lb>fall from the Trench of <emph type="italics"></emph>Libra,<emph.end type="italics"></emph.end> into the Plain of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> for theſe <lb></lb>Waters being to diſcharge into <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> they maintain it <lb></lb>much higher than is imagined, according to that which I have de<lb></lb>monſtrated in my conſideration upon the ſtate of the Lake of <lb></lb><emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> I have ſaid but little, but I ſpeak to you, who under<lb></lb>ſtandeth much, and I ſubmit all to the moſt refined judgment of <lb></lb>our moſt Serene Prince <emph type="italics"></emph>Leopold,<emph.end type="italics"></emph.end> whoſe hands I beſeech you in all <lb></lb>humility to kiſs in my name, and implore the continuance of his <lb></lb>Princely favour to me; and ſo deſiring your prayers to God for <lb></lb>me, I take my leave.</s></p><p type="main"> <s><emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> 1. Feb. <lb></lb></s> <s>1642.</s></p><p type="main"> <s><emph type="italics"></emph>Your moſt affectionate Servant,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>D. BENEDETTO CASTELLI.</s></p><pb xlink:href="068/01/097.jpg" pagenum="83"></pb><p type="head"> <s>The anſwer to a Letter written by BAR<lb></lb>TOLOTTI, touching the <lb></lb>difficultyes obſerved.</s></p><p type="head"> <s><emph type="italics"></emph>The former part of the Letter is omitted, and the diſcourſe <lb></lb>beginneth at the firſt Head.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And firſt I ſay, Whereas I ſuppoſe that the level of the <emph type="italics"></emph>Ser<lb></lb>chio<emph.end type="italics"></emph.end> is higher than that of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; this is moſt true, <lb></lb>at ſuch time as the waters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> are diſcharged in<lb></lb>to the Sea; but I did never ſay that things could never be brought <lb></lb>to that paſs, as that the level of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhould be higher than <lb></lb><emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>: and ſo I grant that it will follow, that the waters of <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhall go into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> and its very poſſible, that the <lb></lb>Drain of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> may be continuate; and I far<lb></lb>ther grant, that its poſſible, that the <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> doth never diſgorge <lb></lb>thorow <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> towards <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end>; Nay, I will yet farther grant <lb></lb>that it might have happened, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> might have had <lb></lb>ſuch a fall into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> as would have ſufficed to have turned <lb></lb>Mills: But then I add withall, that the Plains of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and the <lb></lb>City it ſelf muſt be a meer Lake.</s></p><p type="main"> <s>2. <emph type="italics"></emph>Signore Bartololti<emph.end type="italics"></emph.end> ſaith confidently, that when the Sea ſwel<lb></lb>leth by the South-Weſt, or other Winds, the level of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> in <lb></lb>the place marked A in the Platt, diſtant about 200. Braces, riſeth <lb></lb>very little: But that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> in D, and in E, many miles <lb></lb>more up into Land riſeth very much, and that certain Fiſhermen <lb></lb>confirm this, and ſhew him the ſignes of the riſing of the Water. <lb></lb></s> <s>I grant it to be very true, and I have ſeen it with my own eyes: <lb></lb>But this cometh to paſs, when the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is ſtopt <lb></lb>up by the Sea; as I ſhall ſhew by and by. </s> <s>And this riſing near <lb></lb>the Sea-ſide, is of no conſiderable prejudice to the fields. </s> <s>And <lb></lb>this is as much as I find to be true in the aſſertion of <emph type="italics"></emph>Signore Bar<lb></lb>tolotti,<emph.end type="italics"></emph.end> (without his confirming it by any other proof; as indeed <lb></lb>it needs none) That the level of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> riſeth in E, and ma<lb></lb>ny miles farther upwards it riſeth much; nor did I ever affirm the <lb></lb>contrary.</s></p><p type="main"> <s>3. Concerning the difficulty of opening the Mouth of <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> into the Sea, that which <emph type="italics"></emph>Il Caſtellano<emph.end type="italics"></emph.end> ſaith is moſt certain; <lb></lb>namely, That at the entrance upon the opening of the Mouth, it <lb></lb>is neceſſary to make a deep Trench: But I ſay, that at that time <lb></lb>it is difficult to open it, unleſs upon great occaſions; for that the <pb xlink:href="068/01/098.jpg" pagenum="84"></pb>difficulty proceedeth from the waters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> being low, <lb></lb>and the fields drained.</s></p><p type="main"> <s>4. As to the particular of the Cauſes that you tell me men <lb></lb>preſs ſo much unto the moſt <emph type="italics"></emph>Serene Grand Duke,<emph.end type="italics"></emph.end> and to the <lb></lb>Prince, I have not much to ſay, becauſe it is not my profeſſion; <lb></lb>nor have I conſidered of the ſame: Yet I believe, that when the <lb></lb>Prince and his Highneſſe ſee the benefit of his People and Sub<lb></lb>jects in one ſcale of the Ballance, and the accomodation of <lb></lb>Huntſmen in the other, his Highneſſe will incline to the profit <lb></lb>of his ſubjects; ſuch have I alwayes found his Clemency and <lb></lb>Nobleneſſe of minde. </s> <s>But if I were to put in my vote upon <lb></lb>this buſineſſe, I would ſay, that the points of Spears, and the <lb></lb>mouths of Guns, the yelping of Dogs, the wilyneſſe of Huntſ<lb></lb>men, who run thorow and narrowly ſearch all thoſe Woods, <lb></lb>Thickets and Heathes, are the true deſtroyers of Bucks and <lb></lb>Boares, and not a little Salt-water, which ſetleth at laſt in ſome <lb></lb>low places, and ſpreadeth not very far. </s> <s>Yet nevertheleſſe, I will <lb></lb>not enter upon any ſuch point, but confine my ſelf ſolely to the <lb></lb>buſineſſe before me.</s></p><p type="main"> <s>5. That Experiment of joyning together the water of <emph type="italics"></emph>Fiume <lb></lb>morto,<emph.end type="italics"></emph.end> and that of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> by a little trench to ſee what advan<lb></lb>tage the Level E hath upon the Level I, doth not give me full <lb></lb>ſatisfaction, taken ſo particularly, for it may come to paſſe, that <lb></lb>ſometimes E may be higher, and ſometimes A lower, and I do <lb></lb>not queſtion but that when <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> is low, and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> full <lb></lb>of Water, the level of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> will be higher than that of <lb></lb><emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> But <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> being full, and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſcant of Wa<lb></lb>ter, the contrary will follow, if the Mouth ſhall be opened to <lb></lb>the Sea. </s> <s>And here it ſhould ſeem to me, that it ought to be <lb></lb>conſidered, that there is as much advantage from E to the Sea <lb></lb>through the little Trench opened anew into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> as from E to <lb></lb>the Sea by the Mouth of <emph type="italics"></emph>Fiume morto.<emph.end type="italics"></emph.end> But the difficulty (which <lb></lb>is that we are to regard in our caſe) is, that the courſe of the <lb></lb>Waters thorow the Trench is three times longer than the courſe <lb></lb>of the Mouth of <emph type="italics"></emph>Fiums morto,<emph.end type="italics"></emph.end> as appeareth by the Draught or <lb></lb>Plat which you ſent me, which I know to be very exactly drawn, <lb></lb>for that the ſituation of thoſe places are freſh in my memory. <lb></lb></s> <s>Here I muſt give notice, that the waters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> determi<lb></lb>ning thorow the Trench in <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> (the waters of which <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> are, for certain, never ſo low as the Sea) their pendency or <lb></lb>declivity ſhall, for two cauſes, be leſſe than the pendency of thoſe <lb></lb>waters through the Mouth towards the Sea, that is, becauſe of <lb></lb>the length of the line through the Trench, and becauſe of the <lb></lb>height of their entrance into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> a thing which is of very <lb></lb>great import in diſcharging the waters which come ſuddenly, as <pb xlink:href="068/01/099.jpg" pagenum="85"></pb>he ſhall plainly ſee, who ſhall have underſtood my Book of the <lb></lb>Meaſure of Running Waters And this was the Reaſon why all <lb></lb>the Countrey did grow dry upon the opening of the Mouth into <lb></lb>the Sea. </s> <s>And here I propoſe to conſideration that which the Pea<lb></lb>ſants about <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> relate, namely, That the Water in the Fields <lb></lb>doth no conſiderable harm by continuing there five or ſix, yea, or <lb></lb>eight dayes. </s> <s>And therefore the work of the Countrey is to o<lb></lb>pen the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> in ſuch manner, that the Water <lb></lb>being come, they may have the Trench free and ready, when that <lb></lb>the Water cometh it may have a free drain, and may not ſtay <lb></lb>there above eight or nine dayes, for then the overflowings be<lb></lb>come hurtful. </s> <s>It is to be deſired alſo, that if any Propoſition is <lb></lb>produced touching theſe affairs, it might be propounded the moſt <lb></lb>diſtinctly that may be poſſible, and not conſiſt in generals, eſpe<lb></lb>cially when the Diſpute is of the riſings, of velocity, of tardity, <lb></lb>of much and little water; things that are all to be ſpecified by <lb></lb>meaſures.</s></p><p type="main"> <s>6. Your Letter ſaith, in the next place, that <emph type="italics"></emph>Signore Barto<lb></lb>lotti<emph.end type="italics"></emph.end> confeſſeth, that if the Mouth of the <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> might al<lb></lb>wayes be kept open, it would be better to let it continue as it is: <lb></lb>the which, that I may not yield to him in courteſie, I confeſſe, <lb></lb>for the keeping it ſtopt on all ſides would be a thing moſt per<lb></lb>nicious. </s> <s>But admitting of his confeſſion I again reply, that <emph type="italics"></emph>Fi<lb></lb>ume morto<emph.end type="italics"></emph.end> ought not to be let into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> but immediately in<lb></lb>to the Sea; becauſe although ſometimes the Mouth to Sea<lb></lb>wards be ſtopt up, yet for all that, the raiſing of the Bank above <lb></lb>the Plains (which is all the buſineſſe of importance) ſhall be ever <lb></lb>leſſer, if we make uſe of the Mouth leading to the Sea, than u<lb></lb>ſing that of <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>7. I will not omit to mention a kinde of ſcruple that I have <lb></lb>concerning the poſition of <emph type="italics"></emph>Sign. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> that is, where he ſaith <lb></lb>that the two Mouths A and D are equal to the like Mouths into <lb></lb>the Sea; Now it ſeems to me, that the Mouth A of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end><lb></lb>into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> is abſolutely within <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> nor can it be made low<lb></lb>er, and is regulated by the height of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>: But the Mouth <lb></lb>of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> terminates, and ought to be underſtood to ter<lb></lb>minate in the Sea it ſelf, the loweſt place. </s> <s>And this I believe <lb></lb>was very well peroeived by <emph type="italics"></emph>Sig. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> but I cannot tell why <lb></lb>he paſt it over without declaring it: and we ſee not that the <lb></lb>Mouth D falleth far from the Sea, which Mouth ought to be let <lb></lb>into the Sea it ſelf, and ſo the advantage of the <emph type="italics"></emph>M<emph.end type="italics"></emph.end>outh into the <lb></lb>Sea more clearly appeareth.</s></p><p type="main"> <s>8. That which <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> addeth, that when it is high <lb></lb>Waters, at ſuch time as the Waters are out, and when Winds <lb></lb>choak up <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> they not only retard it, but return the <pb xlink:href="068/01/100.jpg" pagenum="86"></pb>courſe of the Waters upwards very leaſurely, perſwadeth me <lb></lb>more readily to believe that <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> knoweth very well, <lb></lb>that the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> let into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> is hurtful: for <lb></lb>by this he acknowledgeth that the Mouth towards the Sea doth <lb></lb>in ſuch ſort drain the Countrey of the Waters, as that they be<lb></lb>come very low; and therefore upon every little <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> the wa<lb></lb>ters turn their courſe: And from the motions, being exceeding <lb></lb>ſlow, is inferred, that the abundance of Sea-water that com<lb></lb>eth into <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> is ſo much as is believed, and as <emph type="italics"></emph>Sig. </s> <s>Bat<lb></lb>tolotti<emph.end type="italics"></emph.end> affirmeth.</s></p><p type="main"> <s>9. After that <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> hath ſaid what he promiſeth a<lb></lb>bove, namely, that when the Windes blowing ſtrongly do ſtop <lb></lb>up <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> and not onely retard but turn the courſe up<lb></lb>wards, the time being Rainy, and the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhut <lb></lb>up, the Waves of the Sea paſſe over the Bank of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; at <lb></lb>that time, ſaith <emph type="italics"></emph>Signore Bartolotti,<emph.end type="italics"></emph.end> the Champain ſhall know the <lb></lb>benefit of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> diſcharged into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> and the mouth A <lb></lb>ſhall ſtand alwayes open; and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> may alwayes con<lb></lb>ſtantly run out, as alſo the Rains and Rain-waters, although the <lb></lb>hurtful Tempeſt ſhould laſt many dayes, &c. </s> <s>And I reply, that <lb></lb>all the Art conſiſts in this; for the benefit of thoſe Fields doth <lb></lb>not depend on, or conſiſt in ſaying, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is alwayes <lb></lb>open, and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> draineth continually; But all the buſi<lb></lb>neſſe of profit lyeth and conſiſteth in maintaining the Waters <lb></lb>low in thoſe Plaines, and thoſe Ditches, which ſhall never be ef<lb></lb>fected whilſt the World ſtands, if you let <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> into <emph type="italics"></emph>Ser<lb></lb>chio<emph.end type="italics"></emph.end>; but yet it may, by opening the mouth into the Sea: and <lb></lb>ſo much reaſon and nature proveth, and (which importeth) Ex<lb></lb>perience confirmeth.</s></p><p type="main"> <s>10. In the tenth place I come to conſider the anſwer that <lb></lb>was made to another Propoſition in the Letter which I writ to <lb></lb>Father <emph type="italics"></emph>Franceſco,<emph.end type="italics"></emph.end> which prudently of it ſelf alone might ſerve <lb></lb>to clear this whole buſineſſe. </s> <s>I ſaid in my Letter, That great <lb></lb>account is to be made of every ſmall riſing and ebbing of the <lb></lb>Waters neer to the Sea in <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> for that theſe riſings and <lb></lb>fallings, although that they be ſmall neer to the Sea-ſide, yet ne<lb></lb>vertheleſſe, they operate and are accompanied by notable riſings <lb></lb>and fallings within Land, and far from the Sea-ſide, and I have <lb></lb>declared by an example of <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> in which a Land-flood falling, <lb></lb>that made it increaſe above its ordinary height within <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> ſix or <lb></lb>ſeven Braces, that this height of the ſame Flood becometh ſtill <lb></lb>leſſer, the neerer we approach to the Sea-coaſts. </s> <s>Nor ſhall the <lb></lb>ſaid River be raiſed hardly half a Brace; whereupon it neceſſ<lb></lb>rily followeth, that if I ſhould return to the Sea-ſide, and not <lb></lb>knowing any think of that which happeneth at <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and ſeeing <pb xlink:href="068/01/101.jpg" pagenum="87"></pb>the River <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> raiſed by a Land-flood half a Brace, I might con<lb></lb>fidently affirm the ſaid River to be raiſed in <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> thoſe ſix or ſe<lb></lb>ven Braces, &c. </s> <s>From ſuch like accidents I conclude in the ſame <lb></lb>Letter, that it is neceſſary to make great account of every little <lb></lb>riſe that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhall make towards the Sea. </s> <s>Now cometh <lb></lb><emph type="italics"></emph>Bartolotti<emph.end type="italics"></emph.end> (and perhaps becauſe I knew not how to expreſs my <lb></lb>ſelf better, underſtandeth not my Propoſition) and ſpeaketh that <lb></lb>which indeed is true, but yet beſides our caſe: Nor have I ever <lb></lb>ſaid the contrary; and withall doth not apply it to his purpoſe. <lb></lb></s> <s>Nay I ſay, that if he had well applyed it, this alone had been a<lb></lb>ble to have made him change his opinion. </s> <s>And becauſe he ſaith, <lb></lb>that I ſaid, that it is true, when the abatement proceedeth from <lb></lb>ſome cauſe above, as namely by Rain, or opening of Lakes; <lb></lb>But when the cauſe is from below, that is, by ſome ſtop, as for <lb></lb>inſtance ſome Fiſhers Wears or Locks, or ſome impediment re<lb></lb>mote from the Sea, although at the Level it ſhall riſe ſome Braces <lb></lb>where the impediment is, yet that riſing ſhall go upwards; and <lb></lb>here he finiſheth his Diſcourſe, and concludeth not any thing <lb></lb>more. </s> <s>To which I ſay firſt, that I have alſo ſaid the ſame in the <lb></lb>Propoſition, namely, that a Flood coming (which maketh <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end><lb></lb>to riſe in <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> ſix or ſeven Braces (which I take to be a ſuperiour <lb></lb>cauſe whether it be Rain or the opening of Lakes, as beſt plea<lb></lb>ſeth <emph type="italics"></emph>Bartolotti<emph.end type="italics"></emph.end>) in ſuch a caſe I ſay, and in no other (for towards <lb></lb>the Sea-coaſts it ſhall not cauſe a riſing of full half a Brace; and <lb></lb>therefore ſeeing <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> at the Sea-ſide to be raiſed by a Flood, whe<lb></lb>ther of Rain, or of opening of Lakes half a Brace) it may be <lb></lb>inferred, that at <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> it ſhall be raiſed thoſe ſix or ſeven Braces; <lb></lb>which variety, well conſidered, explaineth all this affair in favour <lb></lb>of my opinion: For the riſing that is made by the impediment <lb></lb>placed below, of Fiſhing Weares and Locks, operateth at the be<lb></lb>ginning, raiſing the Waters that are neer to the impediment; <lb></lb>and afterwards leſs and leſs, as we retire upwards from the im<lb></lb>pediment: provided yet that we ſpeak not of a Flood that com<lb></lb>meth by acceſſion, but onely of the ordinary Water impeded. <lb></lb></s> <s>But there being a new acceſſion, as in our caſe, then the Water <lb></lb>of the Flood, I ſay, ſhall make a greater riſing in the parts ſuperi<lb></lb>our, far from the impediment; and theſe impediments ſhall <lb></lb>come to be thoſe that ſhall overflow the Plains, as happened <lb></lb>eighteen or nineteen years ago, before the opening of <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> into the Sea, The ſame will certainly follow, if <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> be let into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> Here I could alledge a very pretty <lb></lb>caſe that befell me in <emph type="italics"></emph>la ^{*} Campagna di Roma,<emph.end type="italics"></emph.end> neer to the Sea<lb></lb><arrow.to.target n="marg975"></arrow.to.target><lb></lb>ſide. </s> <s>where I drained a Bog or Fen, of the nature of the Wa<lb></lb>ters of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and I ſucceeded in the enterprize, the Waters in their <lb></lb>ſite towards the Sea abating only three Palmes, and yet in the <pb xlink:href="068/01/102.jpg" pagenum="88"></pb>Fen they fell more than fifteen Palmes. </s> <s>But the buſineſſe <lb></lb>would be long, and not ſo eaſily to be declared, and I am cer<lb></lb>tain that <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> having conſidered this, would alter his <lb></lb>judgment, and withall would know that remitting that impedi<lb></lb>ment anew, which I had left for leſſe than three Palmes towards <lb></lb>the Sea, the Waters in the Fen would return with the firſt Floods <lb></lb>and Raines to the ſame height as before, as likewiſe <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end><lb></lb>will do if it ſhall be let again into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg975"></margin.target>* The Countrey <lb></lb>or Province lying <lb></lb>round the City, <lb></lb>heretofore called <lb></lb><emph type="italics"></emph>Latium<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Here I intreat your Honour to do me the favour to importune <lb></lb><emph type="italics"></emph>P. Franceſco<emph.end type="italics"></emph.end> in my behalf, that he would be pleaſed to deelare <lb></lb>my meaning in the aforeſaid Letter to <emph type="italics"></emph>Sig. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> for I hope <lb></lb>that if he will underſtand this point, he will be no longer ſo te<lb></lb>nacious in his opinion.</s></p><p type="main"> <s>Next that theſe Lords in the Commiſſion of Sewers, with the <lb></lb>Right Honourable the Marqueſſe of S. <emph type="italics"></emph>Angelo,<emph.end type="italics"></emph.end> and your Honour <lb></lb>do approve of my judgment, doth very much rejoyce me; but <lb></lb>becauſe that I know that they do it not in deſign to complement <lb></lb>me, but onely to ſerve his Highneſs our Grand Duke, I freely <lb></lb>profeſs that I will pretend no farther obligations from them there<lb></lb>in, than I account my ſelf to owe to thoſe whoſe opinions are <lb></lb>contrary to mine, for that I know that they have the ſame end. <lb></lb></s> <s>The definitive ſentence of this whole buſineſs is, that they give <lb></lb>theſe Plains, theſe Draines, and theſe Waters farre fetcht ap<lb></lb>pellations.</s></p><p type="main"> <s>11. As to the quantity of the Water that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> diſ<lb></lb>chargeth into the Sea, there are very great diſputes about it, and <lb></lb>I have been preſent at ſome of them. </s> <s>But let your Honour be<lb></lb>lieve me, that as this is not continual, but only during a few <lb></lb>dayes, ſo it will never be of any great prejudice to theſe Fields; <lb></lb>and if your Lordſhip would be aſcertained thereof, you may <lb></lb>pleaſe to go to <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> at about a mile's diſtance from the <lb></lb>Sea, in the time of theſe ſtrong Windes, and obſerve the cur<lb></lb>rent from thence upwards, for you ſhall finde it extream ſlow, <lb></lb>and conſequently will know that the quantity of the Water that <lb></lb>is repuls'd is very ſmall. </s> <s>And this ſeems to be contradicted by the <lb></lb>rule of Riſings proceeding from cauſes below, which occaſion no <lb></lb>conſiderable alteration far from the Sea.</s></p><p type="main"> <s>I am neceſſitated to go to morrow out of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> with his Emi<lb></lb>nence Cardinal <emph type="italics"></emph>Gaetano<emph.end type="italics"></emph.end> about certain affairs touching Waters, <lb></lb>therefore I ſhall not farther inlarge, but for a cloſe to this tedious <lb></lb>Diſcourſe, I conclude in few words, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is by no <lb></lb>means to be let into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> nor are there any means intermedi<lb></lb>ate courſes to be taken, for they will alwayes be prejudicial; but <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is to be diſcharged immediately into the Sea. </s> <s>When <lb></lb>it is ſtopt up by the fury of the Sea waves, I affirm that it is a <pb xlink:href="068/01/103.jpg" pagenum="89"></pb>ſign that there is no need of opening it; and if there be any oc<lb></lb>caſion to open it, it is eaſily done. </s> <s>As for the reſt your Lordſhip <lb></lb>may pleaſe to keep account of all the particulars that occur, for <lb></lb>the memory of things paſt is our Tutreſſe in thoſe that are to <lb></lb>come. </s> <s>If occaſion ſhall offer, I intreat you to bow humbly in <lb></lb>my name to His Highneſs the Grand Duke, and the moſt Serene <lb></lb>Prince <emph type="italics"></emph>Leopold<emph.end type="italics"></emph.end>; and to attend the ſervice of Their Highneſſes, for <lb></lb>you ſerve I rinces of extraordinary merit; And to whom I my <lb></lb>ſelf am alſo exceedingly obliged. </s> <s>In the controverſies that ariſe <lb></lb>reſpect the pious end of ſpeaking the Truth, for then every <lb></lb>thing will ſucceed happily. </s> <s>I kiſs the hands of <emph type="italics"></emph>Padre Franceſco,<emph.end type="italics"></emph.end><lb></lb>of <emph type="italics"></emph>Sig. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> and of your Lordſhip.</s></p><p type="main"> <s><emph type="italics"></emph>Rome, 14. March<emph.end type="italics"></emph.end> 1642.</s></p><p type="main"> <s><emph type="italics"></emph>Your Honours<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>most Obliged Servant<emph.end type="italics"></emph.end></s></p><p type="main"> <s>D. <emph type="italics"></emph>BENEDETTO CASTELLI.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Vpon this occaſion I will here inſert a Diſcourſe that I made <lb></lb>upon the Draining and improvement of the <emph type="italics"></emph>Pontine Fens,<emph.end type="italics"></emph.end><lb></lb>for that I think that whatſoever may be done well and to pur<lb></lb>poſe in this matter hath abſolute dependance on the perfect know<lb></lb>ledge of that ſo important Propoſition, by me demonſtrated and <lb></lb>explained in my Treatiſe of the <emph type="italics"></emph>Menſuration<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Running Wa<lb></lb>ters,<emph.end type="italics"></emph.end> namely, That the ſame water of a River doth continually <lb></lb>change Meaſures, according as it altereth and changeth the ve<lb></lb>locity of its courſe; ſo that the meaſure of the thickneſſe of a <lb></lb>River in one Site, to the meaſure of the ſame River in another <lb></lb>Site, hath the ſame proportion reciprocally that the velocity in <lb></lb>this ſite hath to the velocity in the firſt ſite. </s> <s>And this is a Truth <lb></lb>ſo conſtant and unchangeable, that it altereth not in the leaſt <lb></lb>point on any occurrences of the Waters that change: and <lb></lb>being well underſtood, it openeth the way to the knowledge of <lb></lb>ſundry advertiſements in theſe matters, which are all reſolved by <lb></lb>this ſole Principle; and from it are derived very conſiderable be<lb></lb>nefits; and without theſe it is impoſſible to do any thing with <lb></lb>abſolute perfection</s></p><pb xlink:href="068/01/104.jpg"></pb><pb xlink:href="068/01/105.jpg" pagenum="91"></pb><p type="head"> <s>A <lb></lb>CONSIDERATION <lb></lb>Upon the <lb></lb>DRAINING <lb></lb>OF THE <lb></lb>Pontine Fenns. <lb></lb></s> <s>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, Abbot <lb></lb>of S. BENEDETTO ALOISIO, and Profeſſor <lb></lb>of the <emph type="italics"></emph>Mathematicks<emph.end type="italics"></emph.end> to P. <emph type="italics"></emph>Urban<emph.end type="italics"></emph.end> VIII. in the <lb></lb>Univerſity of <emph type="italics"></emph>ROME.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>CONSIDERATION<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>Amongſt the enterprizes by me eſteemed, if not ab<lb></lb>ſolutely impoſſible, , at leaſt exceeding difficult, <lb></lb>one was that famous one of Draining the <emph type="italics"></emph>Pontine <lb></lb>Fenns<emph.end type="italics"></emph.end>; and therefore I was thorowly reſolved <lb></lb>never to apply my minde thereunto, although <lb></lb>by my Patrons I ſhould be commanded to the <lb></lb>ſame: accounting that it was an occaſion rather of loſing repu<lb></lb>tation by the miſcarriage of the attempt, than of gaining fame by <lb></lb>reducing things to a better paſs then they now are at. </s> <s>Yet never<lb></lb>theleſs, having of late years obſerved the place, and ſailed through <lb></lb>thoſe Chanels, and thoſe Waters; after I had made ſome reflection <lb></lb>thereupon, I thought that the enterprize was not ſo difficult as <lb></lb>I had at firſt conceited it to be; and I am the more confirmed in <lb></lb>this opinion, upon the inducement of that which I have written <pb xlink:href="068/01/106.jpg" pagenum="92"></pb>Geometrically in my Treatiſe of the Menſuration of Running <lb></lb>Waters; ſo that talking with ſeveral perſons, I adventured to <lb></lb>affirm, in diſcoures, that this improvement might poſſibly be <lb></lb>brought into a good eſtate.</s></p><p type="main"> <s>Now I have reſolved to ſet down my thoughts in writing, and <lb></lb>to honour this my Paper with the Noble Name of your Lordſhip, <lb></lb>to render it the more credible and conſpicuous at the firſt view, <lb></lb>if it ſhould chance that the Subject I treat of, were not of ſuch <lb></lb>moment, as that it did deſerve to be valued for any other reaſon. <lb></lb></s> <s>Pardon me, Sir, if I have been too bold, and continue me in the <lb></lb>number of your Servants.</s></p><p type="main"> <s>The enterprize of Draining a great part of the Territories of <lb></lb>the <emph type="italics"></emph>Pontine Fenns,<emph.end type="italics"></emph.end> hath been undertaken both in the time of <lb></lb>the antient <emph type="italics"></emph>Romans,<emph.end type="italics"></emph.end> and laſt of all, in our days; yea in the late <lb></lb>times by <emph type="italics"></emph>Sixtus<emph.end type="italics"></emph.end> V. </s> <s>I do not doubt in the leaſt, but that it will <lb></lb>be poſſible yet to reduce things to a very good paſs; and if I be not <lb></lb>miſtaken, with a very ſmall charge in compariſon of the profit that <lb></lb>would be received from thoſe rich Grounds. </s> <s>This improvement <lb></lb>was of great expence in the time of <emph type="italics"></emph>Sixtus Quintus,<emph.end type="italics"></emph.end> but by rea<lb></lb>ſon the thing was not rightly underſtood, there were made many <lb></lb>Drains; a great part of which were unprofitable and vain: and <lb></lb>amongſt ſo many operations, there hapned ſome to be made that <lb></lb>ſucceeded, as was deſired; but not being underſtood, they were <lb></lb>held in no account; and thus the buſineſs being neglected, the <lb></lb>waters are returned into the ſame ſtate as they were at firſt, be<lb></lb>fore the improvement. </s> <s>Here I have by familiar diſcourſes <lb></lb>with my friends, explained this enterprize undertaken by <emph type="italics"></emph>Six<lb></lb>tus<emph.end type="italics"></emph.end> V. and haply alſo by ſome more antient, with the example of <lb></lb>the Fable of <emph type="italics"></emph>Orilo,<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Arioſto.<emph.end type="italics"></emph.end> This Monſter was made up with <lb></lb>ſuch enchantment, that men fought with him alwayes in vain; <lb></lb>for though in the Combate he were cut in pieces, thoſe divided <lb></lb>Members preſently re-united, and returned to the fight more <lb></lb>fierce then ever. </s> <s>But the <emph type="italics"></emph>Paladine Aſtolfo<emph.end type="italics"></emph.end> coming to undertake <lb></lb>him, after a long diſpute, at the end he cut his head ſheer off <lb></lb>from the ſhoulders at one blow; and nimbly alighting from his <lb></lb>Horſe, took the Monſtrous head, and mounting again, as he rid <lb></lb>away he fell to ſhave the Pole of that Monſter, and ſo he loſt <lb></lb>the Lock of Hair, in which alone the enchantment lay; and then <lb></lb>the horrible Head in an inſtant manifeſted ſigns of death, and the <lb></lb>trunk which ran, ſeeking to reunite to it anew, gave the laſt gaſp, <lb></lb>and in this manner the enchantment ended. </s> <s>The Book of Fate <lb></lb>ſerved admirably to the <emph type="italics"></emph>Paladine,<emph.end type="italics"></emph.end> whereby he came to under<lb></lb>ſtand that Charm; for by ſhaving his whole head, the enchanted <lb></lb>hairs came to be cut off amongſt the reſt: In the ſame manner, I <lb></lb>ſay, that it hath ſometimes happened in Draining thoſe Fields; <pb xlink:href="068/01/107.jpg" pagenum="93"></pb>for that amongſt ſo many tryals as have been made, that alſo <lb></lb>was light upon, on which the improvement and remedy to the <lb></lb>diſorder did depend. </s> <s>And to us my fore-named Treatiſe ſhall <lb></lb>ſerve for a Rule, which being well underſtood, ſhall make us to <lb></lb>know wherein conſiſteth, and whereon dependeth this miſcarri<lb></lb>age, and conſequently it will be eaſie to apply thereunto a ſeaſo<lb></lb>nable remedy.</s></p><p type="main"> <s>And firſt I ſay, That there is no doubt but that the waters <lb></lb>continue ſo high on thoſe Plains becauſe they are ſo high in the <lb></lb>principal River, which ought to receive them, and carry them <lb></lb>into the Sea. </s> <s>Now the Cauſes of the height of the River, may <lb></lb>in my judgement be reduced to one alone; which is that by me <lb></lb>ſo often mentioned for the moſt Potent one, and declared in my <lb></lb>afore-named Tractate; to wit, The tardity of the motion of the <lb></lb>waters, which doth alwayes infallibly, and preciſely cauſe the <lb></lb>ſelf ſame Running Water to change the meaſure of its thickneſs <lb></lb>at ſuch a rate, that the more it encreaſeth in velocity, the more <lb></lb>it decreaſeth in meaſure; and the more it decreaſeth in velocity, <lb></lb>the more it encreaſeth in meaſure: As for example; If a River <lb></lb>run in ſuch a place with the velocity of moving a mile in the <lb></lb>ſpace of an hour, and afterwards the ſame River in another place <lb></lb>doth encreaſe in velocity, ſo as to make three miles an hour; <lb></lb>that ſame River ſhall diminiſh in thickneſs two thirds: And on <lb></lb>the contrary, If it ſhall diminiſh in velocity ſo, as that it runneth <lb></lb>but half a mile in the ſame time, it ſhall encreaſe the double in <lb></lb>thickneſs and meaſure. </s> <s>And in a word, look what proportion <lb></lb>the velocity in the firſt place, hath to the velocity in the ſecond, <lb></lb>and ſuch hath reciprocally the meaſure of the thickneſs in the <lb></lb>ſecond place, to the meaſure in the firſt; as I have clearly demon<lb></lb>ſtrated in my Treatiſe: Which I repeat ſo frequently, that I <lb></lb>fear the Profeſſors of Polite Learning will charge me with Tua<lb></lb>tologie, and vain Repetition. </s> <s>But I am ſo deſirous in this moſt <lb></lb>important point to be well underſtood, becauſe it will then be <lb></lb>eaſie to comprehend all the reſt; and without this it is impoſſible <lb></lb>(I will not ſay difficult, but abſolutely impoſſible) to underſtand, <lb></lb>or ever to effect any thing to purpoſe. </s> <s>And the better to ex<lb></lb>plain the example, let it be ſuppoſed, <lb></lb><figure id="id.068.01.107.1.jpg" xlink:href="068/01/107/1.jpg"></figure><lb></lb>That the water of a River A D, <lb></lb>runneth high at the level of A F, <lb></lb>with ſuch a certain velocity; and let <lb></lb>it, by the ſame water, be velocitated <lb></lb>three times more; I ſay, that it will <lb></lb>abate 1/3, and ſhall ſtand at the level <lb></lb>in B E; and if it ſhall more veloci<lb></lb>tate, it will abate the more at the Sea; But if it ſhould retard <pb xlink:href="068/01/108.jpg" pagenum="94"></pb>more than it did at the level AF, it would riſe yet more above <lb></lb>the ſaid level A F; although that the ſelf ſame quantity of water <lb></lb>runneth all the while. </s> <s>By the above-named ſolid Principle I <lb></lb>reſolve extravagant Problems in my Treatiſe, and aſſign the Rea<lb></lb>ſons of admirable effects of Running Waters: But as for what <lb></lb>concerneth our purpoſe of the <emph type="italics"></emph>Pontine Fenns,<emph.end type="italics"></emph.end> we have the Cau<lb></lb>ſes very plain and clear; for which, by the trampling of Cattle <lb></lb>which paſs thorow the <emph type="italics"></emph>Draining River,<emph.end type="italics"></emph.end> the waters abate ſo nota<lb></lb>bly, that it is as it were a miracle for thoſe Reeds, Flags, and <lb></lb>Weeds that ſpring up, encreaſe, and ſpread all over the River, <lb></lb>ſtop and impede that velocity of the waters which they would <lb></lb>have by means of their declivity. </s> <s>But that paſſage of thoſe Beaſts, <lb></lb>treading down thoſe Weeds unto the bottom of the River, in ſuch <lb></lb>ſort, as that they no longer hinder the Current of the Water; <lb></lb>and the ſame Waters increaſing in their courſe, they do dimi<lb></lb>niſh in meaſure and height; and by this meanes the Ditches of the <lb></lb>Plains empty into the ſame ſucceſsfully, and leave them free <lb></lb>from Waters, and Drained. </s> <s>But theſe Weeds in a ſhort <lb></lb>time ſprouting up anew, and raiſing their ſtalkes thorow the <lb></lb>body of the Waters, they reduce things to the ſame evil <lb></lb>ſtate, as before, retarding the velocity of the Water, ma<lb></lb>king it to increaſe in height, and perhaps do occaſion grea<lb></lb>ter miſchiefs; ſeeing that thoſe many knots which each plant <lb></lb>ſhoots forth, begets a greater multitude of Stalks, which much <lb></lb>more incumbering the Water of the River, are a greater impe<lb></lb>diment unto its velocity, and conſequently make the height <lb></lb>of the waters to encreaſe ſo much the more, and do more miſchief <lb></lb>than before.</s></p><p type="main"> <s>Another head to which theſe harms may be reduced, but pro<lb></lb>ceeding from the ſame Root, which hath a great part in this <lb></lb>diſorder, is the impediment of thoſe Wears in the River which <lb></lb>are made by heightning the bed of the ſame, for placing of fiſh<lb></lb>ing-nets; of which <emph type="italics"></emph>Piſcaries<emph.end type="italics"></emph.end> I reckoned above ten, when I made <lb></lb>a voyage thorow thoſe waters to <emph type="italics"></emph>Sandolo.<emph.end type="italics"></emph.end> And theſe Fiſhing<lb></lb>Wears are ſuch impediments, that ſome one of them makes the <lb></lb>water of the River in the upper part to riſe half a Palm, and <lb></lb>ſometimes a whole Palm, and more; ſo that when they are all <lb></lb>gathered together, theſe impediments amount to more than ſeven, <lb></lb>or poſſibly than eight Palms.</s></p><p type="main"> <s>There concurreth for a third moſt Potent Cauſe of the waters <lb></lb>continuing high in the evacuating, or Draining Chanel, and con<lb></lb>ſequently on the Plains; The great abundance of water that iſſu<lb></lb>eth from <emph type="italics"></emph>Fiume Siſto,<emph.end type="italics"></emph.end> the waters of which do not keep within its <lb></lb>Banks when they are abundant; but encreaſing above its Chanel, <lb></lb>they unite with thoſe of the Evacuator, and diſperſing thorow <pb xlink:href="068/01/109.jpg" pagenum="95"></pb>the Fens are raiſed with great prejudice, and much grea<lb></lb>ter than is conceived, according to what hath been demon<lb></lb>ſtrated in the Second Conſideration upon the <emph type="italics"></emph>Lake of Venice.<emph.end type="italics"></emph.end><lb></lb>Nor is it to any purpoſe to ſay, that if we ſhould meaſure <lb></lb>all the Waters that disimbogue from <emph type="italics"></emph>Fiume Siſto,<emph.end type="italics"></emph.end> and gather <lb></lb>them into one ſumme, we ſhould not finde them to be ſuch, <lb></lb>as that they ſhall be able to make the Waters of the Fens <lb></lb>to increaſe, by reaſon of the great expanſion of them, over <lb></lb>which that body of water is to diſtend: for to this inſtance we <lb></lb>anſwer wich that which we have given notice of in the Firſt Con<lb></lb>ſideration touching the <emph type="italics"></emph>Lake of Venice,<emph.end type="italics"></emph.end> treating of the abate<lb></lb>ment that is cauſed by the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> let into the Lake. </s> <s>And more<lb></lb>over, if I ſhall adde thereto that which I write in the Second <lb></lb>Conſideration, it will be very apparent how greatly harmfull <lb></lb>and prejudicial theſe excurfions of Waters from <emph type="italics"></emph>Fiume Siſto<emph.end type="italics"></emph.end><lb></lb>may be, which are not kept under, and confined within the <lb></lb>River: Therefore, proceeding to the proviſions, and ope<lb></lb>rations that are to be accounted Principall, I reduce them to <lb></lb>three Heads.</s></p><p type="main"> <s>In the firſt place it is neceſſary to throw down thoſe Weares, <lb></lb>and to take the Piſciaries quite away, obſerving a Maxime, in <lb></lb>my judgment, infallible, that Fiſhing and Sowing are two things <lb></lb>that can never conſiſt together; Fiſhing being on the Water, and <lb></lb>Sowing on land.</s></p><p type="main"> <s>Secondly, it will be neceſſary to cut under Water in the bot<lb></lb>tome of the River thoſe Weeds and Plants that grow and in<lb></lb>creaſe in the River, and leave them to be carried into the Sea by <lb></lb>the Stream; for by this means theſe Reeds ſhall not ſpring up <lb></lb>and diſtend along the bottome of the River, by means of the <lb></lb>Beaſts treading upon them; And the ſame ought to be done <lb></lb>often, and with care, and muſt not be delaied till the miſ<lb></lb>chief increaſe, and the Champain Grounds be drowned, but <lb></lb>one ought to order matters ſo, as that they may not drown. <lb></lb></s> <s>And I will affirm, that otherwiſe this principal point would be<lb></lb>come a moſt conſiderable inconvenience.</s></p><p type="main"> <s>Thirdly, it is neceſſary to make good the Banks of <emph type="italics"></emph>Fiume Siſto<emph.end type="italics"></emph.end><lb></lb>on the left hand, and to procure that thoſe Waters may run in <lb></lb>the Chanel, and not break forth. </s> <s>And it is to be noted, that <lb></lb>it is not enough to do one or two of thoſe things, but we are to <lb></lb>put them all in execution; for omitting any thing, the whole <lb></lb>machine will be out of tune, and ſpoiled. </s> <s>But proceeding with <lb></lb>due care, you ſhall not only Drain the <emph type="italics"></emph>Pontine Fens,<emph.end type="italics"></emph.end> but by <lb></lb>means of this laſt particular the Current of <emph type="italics"></emph>Fiums Sisto<emph.end type="italics"></emph.end> ſhall <lb></lb>ſcowr its own Chanel of its ſelf, even to the carrying part of it <lb></lb>away: and haply with this abundance of water that it ſhall <pb xlink:href="068/01/110.jpg" pagenum="96"></pb>bear, the Mouth <emph type="italics"></emph>della Torre<emph.end type="italics"></emph.end> may be opened, and kept open <lb></lb>into the Sea. </s> <s>And it would, laſt of all, be of admirable bene<lb></lb>fit to cleanſe <emph type="italics"></emph>Fiume Sisto<emph.end type="italics"></emph.end> from many Trees and Buſhes where<lb></lb>with it is overgrown.</s></p><p type="main"> <s>And with this I conclude, that the Improvement or Drain <lb></lb>poſſible to be made conſiſteth in theſe three particulars. </s> <s>Firſt, <lb></lb>in taking away the Fiſhing Weares, leaving the Courſe <lb></lb>of the Waters free. </s> <s>Secondly, in keeping the Principal <lb></lb>Rivers clear from Weeds and Plants. </s> <s>Thirdly, in keeping <lb></lb>the water of <emph type="italics"></emph>Fiume Sisto<emph.end type="italics"></emph.end> in its own Chanel. </s> <s>All which are <lb></lb>things that may be done with very little charge, and to the <lb></lb>manifeſt benefit of the whole Country, and to the rendering <lb></lb>the Air wholſomer in all thoſe Places adjoyning to the <emph type="italics"></emph>Pon<lb></lb>tine Fens.<emph.end type="italics"></emph.end></s></p><figure id="id.068.01.110.1.jpg" xlink:href="068/01/110/1.jpg"></figure><pb xlink:href="068/01/111.jpg" pagenum="97"></pb><p type="head"> <s>A <lb></lb>CONSIDERATION <lb></lb>Upon the <lb></lb>DRAINING <lb></lb>Of the Territories of <lb></lb>Bologna, Ferrara, <lb></lb>AND <lb></lb>Romagna.</s></p><p type="head"> <s>BY <lb></lb>D. BENEDETTO CASTELLI, Abbot <lb></lb>of S. BENEDETTO ALOISIO, <emph type="italics"></emph>Mathematician<emph.end type="italics"></emph.end><lb></lb>to P. <emph type="italics"></emph>Vrban<emph.end type="italics"></emph.end> VIII. and Profeſſor in the <lb></lb>Univerſity of <emph type="italics"></emph>ROME.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The weghty buſineſſe of the Draining of <lb></lb>the Territories of <emph type="italics"></emph>Bologna, Ferrara,<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>Romagna<emph.end type="italics"></emph.end> having been punctually <lb></lb>handled and declared in writing from <lb></lb>the excellent memory of the Right Ho<lb></lb>nourable and Noble <emph type="italics"></emph>Monſignore Corſini,<emph.end type="italics"></emph.end><lb></lb>who was heretofore Deputed Commiſ<lb></lb>ſary General, and Viſitor of thoſe Wa<lb></lb>ters; I am not able to make ſuch ano<lb></lb>ther Diſcourſe upon the ſame Subject, but will only ſay ſome<lb></lb>what for farther confirmation of that which I have ſaid in this <lb></lb>Book upon the <emph type="italics"></emph>Lake of Venice,<emph.end type="italics"></emph.end> upon the <emph type="italics"></emph>Pontine Fens,<emph.end type="italics"></emph.end> and up<lb></lb>on the Draining of thoſe Plains of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> lying between the Ri<lb></lb>vers <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; whereby it is manifeſt, that in all the <pb xlink:href="068/01/112.jpg" pagenum="98"></pb>aforementioned Caſes, and in the preſent one that we are in hand <lb></lb>with, there have, in times paſt, very groſſe Errours been com<lb></lb>mitted, through the not having ever well underſtood the true <lb></lb>meaſure of Running waters; and here it is to be noted, that the <lb></lb>buſineſſe is, that in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> the diverſion of the waters of the <lb></lb>Lake, by diverting the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> was debated, and in part executed, <lb></lb>without conſideration had how great abatement of water might <lb></lb>follow in the Lake, if the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> were diverted, as I have ſhewn <lb></lb>in the firſt Conſideration upon this particular, from which act <lb></lb>there hath inſued very bad conſequences, not only the difficulty <lb></lb>of Navigation, but it hath infected the wholſomneſſe of the Air, <lb></lb>and cauſed the ſtoppage of the Ports of <emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> And on the <lb></lb>contrary, the ſame inadvertency of not conſidering what riſing of <lb></lb>the Water the <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and other Rivers being opened into the Val<lb></lb>leys of <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> might cauſe in the ſaid Valleys, is <lb></lb>the certain cauſe that ſo many rich and fertile Fields are drown<lb></lb>ed under water, converting the happy habitations and dwellings <lb></lb>of men into miſerable receptacles for Fiſhes: Things which <lb></lb>doubtleſſe would never have happened, if thoſe Rivers had been <lb></lb>kept at their height, and <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> had been turn'd into <emph type="italics"></emph>Main-Po,<emph.end type="italics"></emph.end><lb></lb>and the other Rivers into that of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Volano.<emph.end type="italics"></emph.end> Now <lb></lb>there having ſufficient been ſpoken by the above-named <emph type="italics"></emph>Monſig. <lb></lb></s> <s>Corſini<emph.end type="italics"></emph.end> in his Relation, I will only adde one conceit of my own, <lb></lb>which after the Rivers ſhould be regulated, as hath been ſaid, I <lb></lb>verily believe would be of extraordinary profit, I much doubt in<lb></lb>deed that I ſhall finde it a hard matter to perſwade men to be of <lb></lb>my mind, but yet nevertheleſs I will not queſtion, but that thoſe, <lb></lb>at leaſt, who ſhall have underſtood what I have ſaid and demon<lb></lb>ſtrated concerning the manners and proportions, according to <lb></lb>which the abatements and riſings of Running waters proceed, <lb></lb>that are made by the Diverſions and Introductions of Waters, <lb></lb>will apprehend that my conjecture is grounded upon Reaſon. <lb></lb></s> <s>And although I deſcend not to the exactneſſe of particulars, I <lb></lb>will open the way to others, who having obſerved the requiſite <lb></lb>Rules of conſidering the quantity of the waters that are intro<lb></lb>duced, or that happen to be diverted, ſhall be able with punctu<lb></lb>ality to examine the whole buſineſſe, and then reſolve on that <lb></lb>which ſhall be expedient to be done.</s></p><p type="main"> <s>Reflecting therefore upon the firſt Propoſition, that the <lb></lb>Riſings of a Running Water made by the acceſſion of new water <lb></lb>into the River, are to one another, as the Square-Roots of the <lb></lb>quantity of the water that runneth; and conſequently, that the <lb></lb>ſame cometh to paſs in the Diverſions: Inſomuch, that a River <lb></lb>running in height one ſuch a certain meaſure, to make it encreaſe <lb></lb>double in height, the water is to be encreaſed to three times as <pb xlink:href="068/01/113.jpg" pagenum="99"></pb>much as it ran before; ſo that when the water ſhall be quadru<lb></lb>ple, the height ſhall be double; and if the water were centuple, <lb></lb>the height would be decuple onely, and ſo from one quantity <lb></lb>to another: And on the contrary, in the Diverſions; If of the <lb></lb>100. parts of water that run thorow a River, there ſhall be di<lb></lb>verted 19/160, the height of the River diminiſheth onely 1/10, and con<lb></lb>tinuing to divert 17/100, the height of the River abateth likewiſe 1/10, <lb></lb>and ſo proceeding to divert 15/100 and then 13/100, and then 11/100, and <lb></lb>then 9/100, and then 7/100, and then 5/100, and then 3/106, alwaies by <lb></lb>each of theſe diverſions, the height of the Running Water di<lb></lb>miniſheth the tenth part: although that the diverſions be ſo une. <lb></lb></s> <s>qual. </s> <s>Reflecting I ſay upon this infallible Truth, I have had a <lb></lb>conceit, that though the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> and other Rivers were diverted <lb></lb>from the Valleyes, and there was onely left the <emph type="italics"></emph>Chanel of Navi<lb></lb>gation,<emph.end type="italics"></emph.end> which was onely the 1/20 part of the whole water that fal<lb></lb>leth into the Valleys; yet nevertheleſs, the water in thoſe ſame <lb></lb>Valleyes would retain a tenth part of that height that became <lb></lb>conjoyned by the concourſe of all the Rivers: And therefore I <lb></lb>ſhould think that it were the beſt reſolution to maintain the <emph type="italics"></emph>Gha<lb></lb>nel of Navigation<emph.end type="italics"></emph.end> (if it were poſſible) continuate unto the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <lb></lb><emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and from thence to carry it into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Volano<emph.end type="italics"></emph.end>; for <lb></lb>beſides that it would be of very great eaſe in the Navigation of <lb></lb><emph type="italics"></emph>Bologna,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> the ſaid water would render the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> oſ <lb></lb><emph type="italics"></emph>Volano<emph.end type="italics"></emph.end> navigable as far as to the very Walls of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and con<lb></lb>ſequently the Navigation would be continuate from <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> to <lb></lb>the Sea-ſide.</s></p><p type="main"> <s>But to manage this enterprize well, it is neceſſary to meaſure <lb></lb>the quantity of the Water that the Rivers diſcharge into the Val<lb></lb>leys, and that which the <emph type="italics"></emph>Chanel of Navigation<emph.end type="italics"></emph.end> carryeth, in man<lb></lb>ner as I have demonſtrated at the beginning of this Book; for this <lb></lb>once known, we ſhall alſo come to know, how profitable this di<lb></lb>verſion of the <emph type="italics"></emph>Chanel of Navigation<emph.end type="italics"></emph.end> from the Valleys is like to <lb></lb>prove; which yet would ſtill be unprofitable, if ſo be that all <lb></lb>the Rivers that diſcharge their waters into the Valleys, ſhould <lb></lb>not ſirſt be Drained, according to what hath been above ad<lb></lb>vertiſed.</s></p><p type="main"> <s>Abbot CASTELLI, <emph type="italics"></emph>in the preſent conſideration referring <lb></lb>himfelf to the Relation of<emph.end type="italics"></emph.end> Monſig. </s> <s>Corſini, <emph type="italics"></emph>grounded upon the Ob<lb></lb>ſervations and Precepts of the ſaid Abbot; as is ſeen in the pre<lb></lb>ſent Diſcourſe. </s> <s>I thought it convenient for the compleating of the <lb></lb>Work of our Aulhour, upon theſe ſubjects, to inſert it in this <lb></lb>place.<emph.end type="italics"></emph.end></s></p><pb xlink:href="068/01/114.jpg" pagenum="100"></pb><p type="head"> <s>A <lb></lb>Relation of the Waters in the Territories <lb></lb>of <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara.<emph.end type="italics"></emph.end><lb></lb>BY</s></p><p type="head"> <s>The Right Honourable and Illuſtrious, <emph type="italics"></emph>Monſig<lb></lb>nore<emph.end type="italics"></emph.end> CORSINI, a Native of <emph type="italics"></emph>Juſcany,<emph.end type="italics"></emph.end> Su<lb></lb>perintendent of the general DRAINS, <lb></lb>and Preſident of <emph type="italics"></emph>Romagna-<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The <emph type="italics"></emph>Rheno,<emph.end type="italics"></emph.end> and other Brooks of <emph type="italics"></emph>Romagna,<emph.end type="italics"></emph.end> were by the <lb></lb>advice of <emph type="italics"></emph>P. </s> <s>Agoſtino Spernazzati<emph.end type="italics"></emph.end> the Jeſuite, towards <lb></lb>the latter end of the time of <emph type="italics"></emph>Pope Clement<emph.end type="italics"></emph.end> VIII. notwith<lb></lb>ſtanding the oppoſition of the <emph type="italics"></emph>Bologneſi,<emph.end type="italics"></emph.end> and others concerned <lb></lb>therein, diverted from their Chanels, for the more commodious <lb></lb>cleanſing of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and of its two Branches of <emph type="italics"></emph>Prima<lb></lb>ro,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Volano<emph.end type="italics"></emph.end>; in order to the introducing the water of the <lb></lb><emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end> into them, to the end that their wonted Torrents being <lb></lb>reſtored, they might carry the Muddy-water thence into the Sea, <lb></lb>and reſtore to the City the Navigation which was laſt, as is ma<lb></lb>nifeſt by the Brief of the ſaid <emph type="italics"></emph>Pope Clement,<emph.end type="italics"></emph.end> directed to the <emph type="italics"></emph>Car<lb></lb>dinal San Clemence,<emph.end type="italics"></emph.end> bearing date the 22. of <emph type="italics"></emph>Auguſt,<emph.end type="italics"></emph.end> 1604.</s></p><p type="main"> <s>The work of the ſaid cleanſing, and introducing of the ſaid <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> either as being ſuch in it ſelf, or by the contention of the <lb></lb><emph type="italics"></emph>Cardinal Legates<emph.end type="italics"></emph.end> then in theſe parts; and the jarrings that hap<lb></lb>ned betwixt them, proved ſo difficult, that after the expence of <lb></lb>vaſt ſumms in the ſpace of 21. years, there hath been nothing <lb></lb>done, ſave the rendring of it the more difficult to be effected.</s></p><p type="main"> <s>Interim, the Torrents with their waters, both muddy and <lb></lb>clear, have damaged the Grounds lying on the right hand of the <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Rheno<emph.end type="italics"></emph.end> thoſe on its Banks; of which I <lb></lb>will ſpeak in the firſt place, as of that which is of greater impor<lb></lb>tance, and from which the principal cauſe of the miſchiefs that <lb></lb>reſult from the reſt doth proceed.<lb></lb><arrow.to.target n="marg976"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg976"></margin.target>* Or Lordſhip.</s></p><p type="main"> <s>This <emph type="italics"></emph>Rbeno<emph.end type="italics"></emph.end> having overflowed the ^{*} Tennency of <emph type="italics"></emph>Sanmartina,<emph.end type="italics"></emph.end><lb></lb>in circumference about fourteen miles given it before, and part <lb></lb>of that of <emph type="italics"></emph>Cominale<emph.end type="italics"></emph.end> given it afterwards, as it were, for a recepta<lb></lb>cle; from whence, having depoſed the matter of its muddineſs, <lb></lb>it iſſued clear by the Mouths of <emph type="italics"></emph>Maſi,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Lievaloro,<emph.end type="italics"></emph.end> into <lb></lb>the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Volano<emph.end type="italics"></emph.end>; did break down the encom<pb xlink:href="068/01/115.jpg" pagenum="101"></pb>paſſing Bank or Dam towards S. <emph type="italics"></emph>Martino,<emph.end type="italics"></emph.end> and that of its new <lb></lb>Chanel on the right hand neer to <emph type="italics"></emph>Torre del Fondo.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By the breaches on this ſide it ſtreamed out in great abun<lb></lb>dance from the upper part of <emph type="italics"></emph>Cominale,<emph.end type="italics"></emph.end> and in the parts about <lb></lb><emph type="italics"></emph>Raveda, Pioggio, Caprara, Chiare di Reno, Sant' Agoſtino, San <lb></lb>Proſpero, San Vincenzo,<emph.end type="italics"></emph.end> and others, and made them to become <lb></lb>incultivable: it made alſo thoſe places above but little fruitful, <lb></lb>by reaſon of the impediments that their Draines received, finding <lb></lb>the Conveyances called <emph type="italics"></emph>Riolo<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Scorſuro,<emph.end type="italics"></emph.end> not only filled by <emph type="italics"></emph>la <lb></lb>Motta<emph.end type="italics"></emph.end> and <emph type="italics"></emph>la Belletta,<emph.end type="italics"></emph.end> but that they turned backwards of them<lb></lb>ſelves.</s></p><p type="main"> <s>But by the Mouths in the incloſing Bank or Dam at <emph type="italics"></emph>Borgo di<emph.end type="italics"></emph.end><lb></lb>S. <emph type="italics"></emph>Martino<emph.end type="italics"></emph.end> iſſuing with violence, it firſt gave obſtruction to the <lb></lb>ancient Navigation of <emph type="italics"></emph>la Torre del la Foſſa,<emph.end type="italics"></emph.end> and afterwards to <lb></lb>the moderne of the mouth of <emph type="italics"></emph>Maſi,<emph.end type="italics"></emph.end> ſo that at preſent the Com<lb></lb>merce between <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> is loſt, nor can it ever be <lb></lb>in any durable way renewed, whilſt that this exceeds its due <lb></lb>bounds, and what ever moneys ſhall be imployed about the ſame <lb></lb>ſhall be without any equivalent benefit, and to the manifeſt </s></p><p type="main"> <s><arrow.to.target n="marg977"></arrow.to.target><lb></lb>and notable prejudice of the ^{*} Apoſtolick Chamber.</s></p><p type="margin"> <s><margin.target id="marg977"></margin.target>* The Popes <lb></lb>Exchequer.</s></p><p type="main"> <s>Thence paſſing into the Valley of <emph type="italics"></emph>Marzara,<emph.end type="italics"></emph.end> it ſwelleth high<lb></lb>er, not only by the riſing of the water, but by the raiſing of the <lb></lb>bottome, by reaſon of the matter ſunk thither after Land<lb></lb>floods, and dilateth ſo, that it covereth all the Meadows there<lb></lb>abouts, nor doth it receive with the wonted facility the Drains of <lb></lb>the upper Grounds, of which the next unto it lying under the wa<lb></lb>ters that return upwards by the Conveyances, and the more re<lb></lb>mote, not finding a paſſage for Rain-waters that ſettle, become <lb></lb>either altogether unproſitable or little better.</s></p><p type="main"> <s>From this Valley, by the Trench or Ditch of <emph type="italics"></emph>Marzara,<emph.end type="italics"></emph.end> or of <lb></lb><emph type="italics"></emph>la Duca<emph.end type="italics"></emph.end> by <emph type="italics"></emph>la Buova,<emph.end type="italics"></emph.end> or mouth of <emph type="italics"></emph>Caſtaldo de Roſſi,<emph.end type="italics"></emph.end> and by the <lb></lb>new paſſage it falleth into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> which being to re<lb></lb>ceive it clear, that ſo it may ſink farther therein, and receiving <lb></lb>it muddy, becauſe it hath acquired a quicker courſe, there will <lb></lb>ariſe a very contrary effect.</s></p><p type="main"> <s>Here therefore the ſuperficies of the water keeping high, until <lb></lb>it come to the Sea, hindereth the Valleys of <emph type="italics"></emph>Ravenna,<emph.end type="italics"></emph.end> where <lb></lb>the River <emph type="italics"></emph>Senio,<emph.end type="italics"></emph.end> thoſe of <emph type="italics"></emph>San Bernardino<emph.end type="italics"></emph.end> where <emph type="italics"></emph>Santerno<emph.end type="italics"></emph.end> was <lb></lb>turned, thoſe of <emph type="italics"></emph>Buon' acquiſto,<emph.end type="italics"></emph.end> and thoſe of <emph type="italics"></emph>Marmorto,<emph.end type="italics"></emph.end> where <lb></lb>the <emph type="italics"></emph>Idice, Quaderna, Sellero<emph.end type="italics"></emph.end> ſall in, from ſwallowing and taking <lb></lb>in their Waters by their uſual In-lets, yet many times, as I my <lb></lb>ſelf have ſeen in the <emph type="italics"></emph>Viſitation,<emph.end type="italics"></emph.end> they drink them up plentifully, <lb></lb>whereupon, being conjoyned with the muddineſſe of thoſe Ri<lb></lb>vers that fall into the ſame, they ſwell, and dilate, and overflow <lb></lb>ſome grounds, and deprive others of their Drains in like manner <pb xlink:href="068/01/116.jpg" pagenum="102"></pb>as hath been ſaid of that of <emph type="italics"></emph>Marrara,<emph.end type="italics"></emph.end> inſomuch that from the <lb></lb>Point of S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> as far as S. <emph type="italics"></emph>Alberto<emph.end type="italics"></emph.end> all thoſe that are between <lb></lb>the Valleys and P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> are ſpoiled, of thoſe that are between Valley <lb></lb>and Valley many are in a very bad condition, and thoſe that are <lb></lb>ſome conſiderable ſpace above not a little damnified.</s></p><p type="main"> <s>In fine, by raiſing the bottom or ſand of the Valleys, and the <lb></lb>bed of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and the too great repletion of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro<emph.end type="italics"></emph.end><lb></lb>with waters, the Valleys of <emph type="italics"></emph>Comacchio<emph.end type="italics"></emph.end> (on which ſide the Banks <lb></lb>are very bad) and ^{*} <emph type="italics"></emph>Poleſine di<emph.end type="italics"></emph.end> S. <emph type="italics"></emph>Giorgio<emph.end type="italics"></emph.end> are threatned with a <lb></lb><arrow.to.target n="marg978"></arrow.to.target><lb></lb>danger, that may in time, if it be not remedied, become irrepa<lb></lb>rable, and at preſent feeleth the incommodity of the Waters, <lb></lb>which penetrating thorow the pores of the Earth do ſpring up in <lb></lb>the ſame, which they call <emph type="italics"></emph>Purlings,<emph.end type="italics"></emph.end> which is all likely to redound <lb></lb>to the prejudice of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> ſo noble a City of <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> and ſo im<lb></lb>portant to the <emph type="italics"></emph>Eccleſtaſtick State.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg978"></margin.target>+ <emph type="italics"></emph>Poleſine<emph.end type="italics"></emph.end> is a <lb></lb>plat of Ground al<lb></lb>moſt ſurrounded <lb></lb>with Bogs or wa<lb></lb>ters, like an Iſland</s></p><p type="main"> <s>Which particulars all appear to be atteſted under the hand of <lb></lb>a Notary in the <emph type="italics"></emph>Viſitation<emph.end type="italics"></emph.end> which I made upon the command of <lb></lb>His Holineſſe, and are withall known to be true by the ^{*}<emph type="italics"></emph>Ferrareſt<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg979"></arrow.to.target><lb></lb>themſelves, of whom (beſides the requeſt of the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end>) the <lb></lb>greater part beg compaſſion with ſundry <emph type="italics"></emph>Memorials,<emph.end type="italics"></emph.end> and reme<lb></lb>dies, aſwell for the miſchiefs paſt, as alſo for thoſe in time to <lb></lb>come, from which I hold it a duty of Conſcience, and of Cha<lb></lb>rity to deliver them.</s></p><p type="margin"> <s><margin.target id="marg979"></margin.target>* People of <emph type="italics"></emph>Fer<lb></lb>rara.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Pope <emph type="italics"></emph>Clement<emph.end type="italics"></emph.end> judged, that the ſufficient means to effect this <lb></lb>was the ſaid Introduction of the <emph type="italics"></emph>Main Po<emph.end type="italics"></emph.end> into the Chancl of <lb></lb><emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end>; a reſolution truly Heroical, and of no leſſe beauty <lb></lb>than benefit to that City, of which I ſpeak not at preſent, be<lb></lb>cauſe I think that there is need of a readier and more acco<lb></lb>modate remedy.</s></p><p type="main"> <s>So that I ſee not how any other thing can be ſo much conſide<lb></lb>rable as the removal of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> omitting for this time to ſpeak of <lb></lb><arrow.to.target n="marg980"></arrow.to.target><lb></lb>^{*} incloſing it from Valley to Valley untill it come to the Sea, as <lb></lb>the Dukes of <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> did deſign, foraſmuch as all thoſe <emph type="italics"></emph>Ferra<lb></lb>reſi<emph.end type="italics"></emph.end> that have intereſt in the <emph type="italics"></emph>Poleſine di<emph.end type="italics"></emph.end> S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> and on the <lb></lb>right hand of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta<emph.end type="italics"></emph.end> do not deſire it, and do, but too <lb></lb>openly, proteſt againſt it; and becauſe that before the Chanel <lb></lb>were made as far as the Sea, many hundreds of years would be <lb></lb>ſpent, and yet would not remedy the dammages of thoſe who <lb></lb>now are agrieved, but would much increaſe them, in regard the <lb></lb>Valleys would continue ſubmerged, the Drains ſtopped, and the <lb></lb>other Brooks obſtructed, which would of neceſſity drown not a <lb></lb>few Lands that lie between Valley and Valley; and in fine, in <lb></lb>regard it hath not from <emph type="italics"></emph>San Martina<emph.end type="italics"></emph.end> to the Sea for a ſpace of ſif<lb></lb>ty miles a greater fall then 19, 8, 6, feet, it would want that force <lb></lb>which they themſelves who propound this project do require it to <pb xlink:href="068/01/117.jpg" pagenum="103"></pb>have, that ſo it may not depoſe the matter of the muddineſs when <lb></lb>it is intended to be let into <emph type="italics"></emph>Volana.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg980"></margin.target>* In Chanels <lb></lb>made by hand.</s></p><p type="main"> <s>So that making the Line of the bottome neer to <emph type="italics"></emph>Vigarano,<emph.end type="italics"></emph.end> it <lb></lb>would riſe to thoſe prodigious termes that they do make bigger, <lb></lb>and they may thence expect thoſe miſchiefs, for which they <lb></lb>will not admit of introducing it into the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Volana.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Amongſt the wayes therefore that I have thought of for effect<lb></lb>ing that ſame remotion, and which I have cauſed to be viewed by <lb></lb>skilful men that have taken a level thereof, (with the aſſiſtance of <lb></lb>the venerable Father, <emph type="italics"></emph>D. </s> <s>Benedetto Caſtelli<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Caſina,<emph.end type="italics"></emph.end> a man of <lb></lb>much fidelity and honeſty, and no leſs expert in ſuch like affairs <lb></lb>touching waters, than perfect in the <emph type="italics"></emph>Mathematick<emph.end type="italics"></emph.end> Diſciplines) two <lb></lb>onely, the reſt being either too tedious, or too dangerous to the <lb></lb>City, have ſeemed to me worthy, and one of them alſo more than <lb></lb>the other, to offer to your Lordſhip.</s></p><p type="main"> <s>The one is to remit it into the Chanel of <emph type="italics"></emph>Volana,<emph.end type="italics"></emph.end> thorow which <lb></lb>it goeth of its own accord to the Sea.</s></p><p type="main"> <s>The other is to turn it into <emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end> at <emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> for, as at other <lb></lb>times it hath done, it will carry it to the Sea happily.</s></p><p type="main"> <s>As to what concerns the making choice of the firſt way, that <lb></lb>which ſeemeth to perſwade us to it is, that we therein do nothing <lb></lb>that is new, in that it is but reſtored to the place whence it was <lb></lb>removed in the year 1522. in the time of Pope <emph type="italics"></emph>Adrian,<emph.end type="italics"></emph.end> by an <lb></lb>agreement made in way of contract, between <emph type="italics"></emph>Alfonſo,<emph.end type="italics"></emph.end> Duke of <lb></lb><emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end>; and that it was diverted for reaſons, <lb></lb>that are either out of date, or elſe have been too long time <lb></lb>deferred.</s></p><p type="main"> <s>In like manner the facility wherewith it may be effected, let<lb></lb>ting it run into the divided P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> whereby it will be turned to <emph type="italics"></emph>Fer<lb></lb>rara,<emph.end type="italics"></emph.end> or elſe carrying it by <emph type="italics"></emph>Torre del Fondo,<emph.end type="italics"></emph.end> to the mouth of <emph type="italics"></emph>Maſi,<emph.end type="italics"></emph.end><lb></lb>and from thence thorow the Trench made by the <emph type="italics"></emph>Ferrareſi,<emph.end type="italics"></emph.end><lb></lb>along by <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> where alſo finding an ample Bed, and high and <lb></lb>thick Banks, that will ſerve at other times for it, and for the wa<lb></lb>ters of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> there may a great expence be ſpared.</s></p><p type="main"> <s>That what ever its Fall be, it would maintain the ſame, not <lb></lb>having other Rivers, which with their Floods can hinder it; and <lb></lb>that running confined between good Banks, without doubt it <lb></lb>would not leave <emph type="italics"></emph>la Motto<emph.end type="italics"></emph.end> by the way; but eſpecially, that it <lb></lb>would be ſufficient if it came to <emph type="italics"></emph>Codigoro,<emph.end type="italics"></emph.end> where being aſſiſted by <lb></lb>the Ebbing and Flowing of the Sea, it would run no hazard of <lb></lb>having its Chanel filled up from thence downwards.</s></p><p type="main"> <s>That there might thence many benefits be derived to the City, <lb></lb>by means of the Running Waters, and alſo no mean Navigation <lb></lb>might be expected.</s></p><p type="main"> <s>On the contrary it is objected, That it is not convenient to <pb xlink:href="068/01/118.jpg" pagenum="104"></pb>think of returning this Torrent into the divided P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> by reaſon of <lb></lb>the peril that would thence redound to this City.</s></p><p type="main"> <s>And that going by <emph type="italics"></emph>Torre del Fondo,<emph.end type="italics"></emph.end> through <emph type="italics"></emph>Sanmartina<emph.end type="italics"></emph.end> to <lb></lb>the Mouth <emph type="italics"></emph>de Maſi<emph.end type="italics"></emph.end> by the Chappel of <emph type="italics"></emph>Vigarano<emph.end type="italics"></emph.end> unto the Sea, it is <lb></lb>by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, ſo <lb></lb>that it would come to fall but 4. inches & an half, or thereabouts <lb></lb>in a mile; whereas the common opinion of the skilfull (to the <lb></lb>end that the Torrents may not depoſe their ſand that they bring <lb></lb>with them in Land-Floods) requireth the twenty fourth part of <lb></lb>the hundredth part of their whole length, which in our caſe, <lb></lb>accounting according to the meaſure of theſe places, is 16. inches <lb></lb><arrow.to.target n="marg981"></arrow.to.target><lb></lb>a ^{*} mile; whereupon the ſinking of the Mud and Sand would <lb></lb>moſt certainly follow, and ſo an immenſe heightning of the Line <lb></lb>of the Bottom, and conſequently a neceſſity of raiſing the Banks, <lb></lb>the impoſſibility of maintaining them, the danger of breaches <lb></lb>and decayes, things very prejudicial to the <emph type="italics"></emph>Iſlets<emph.end type="italics"></emph.end> of this City, and <lb></lb>of <emph type="italics"></emph>San Giorgio,<emph.end type="italics"></emph.end> the obſtruction of the Drains, which from the <lb></lb>Tower of <emph type="italics"></emph>Tienne<emph.end type="italics"></emph.end> downwards, fall into the ſaid Chanel; to wit, <lb></lb>thoſe of the Sluices of <emph type="italics"></emph>Goro,<emph.end type="italics"></emph.end> and the Drains, of the Meadows of <lb></lb><emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end>: And moreover, the damages that would ariſe unto the <lb></lb>ſaid <emph type="italics"></emph>Iſlet<emph.end type="italics"></emph.end> of S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> and the Valleys of <emph type="italics"></emph>Comachio,<emph.end type="italics"></emph.end> by the wa<lb></lb>ters that ſhould enter into the <emph type="italics"></emph>Goro<emph.end type="italics"></emph.end> or Dam of the Mills of <emph type="italics"></emph>Belri<lb></lb>guardo,<emph.end type="italics"></emph.end> thorow the Trenches of <emph type="italics"></emph>Quadrea,<emph.end type="italics"></emph.end> which cannot be ſtopt, <lb></lb>becauſe they belong to the Duke of <emph type="italics"></emph>Modena,<emph.end type="italics"></emph.end> who hath right of <lb></lb>diverting the waters of that place at his pleaſure to the work of <lb></lb>turning Mills.</s></p><p type="margin"> <s><margin.target id="marg981"></margin.target>* The inch of <lb></lb>theſe places is <lb></lb>ſomewhat bigger <lb></lb>than ours.</s></p><p type="main"> <s>The greater part of which Objections, others pretend to prove <lb></lb>frivolous, by ſaying, that its running there till at the laſt it was <lb></lb>turned another way, is a ſign that it had made ſuch an elevation <lb></lb>of the Line, of its Bed as it required; denying that it needeth <lb></lb>ſo great a declivity as is mentioned above; and that for the fu<lb></lb>ture it would riſe no more.</s></p><p type="main"> <s>That the ſaid Dra ns and Ditches did empty into the ſame, <lb></lb>whilſt P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> was there; ſo that they muſt needs be more able to do <lb></lb>ſo when onely <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> runs that way.</s></p><p type="main"> <s>That there would no Breaches follow, or if they did, they <lb></lb>would be onely of the water of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> which in few hours might <lb></lb>be taken away (in thoſe parts they call damming up of Breaches, <lb></lb>and mending the Bank, <emph type="italics"></emph>taking away the Breaches<emph.end type="italics"></emph.end>) and its a que<lb></lb>ſtion whether they would procure more inconvenience than bene<lb></lb>fit, for that its Mud and Sand might in many places, by filling <lb></lb>them up, occaſion a ſeaſonable improvement.</s></p><p type="main"> <s>Now omitting to diſcourſe of the ſolidity of the reaſons on the <lb></lb>oneſide, or on the other, I will produce thoſe that move me to <lb></lb>ſuſpend my allowance of this deſign.</s></p><pb xlink:href="068/01/119.jpg" pagenum="105"></pb><p type="main"> <s>The firſt is, that although I dare not ſubſcribe to the opinion <lb></lb>of thoſe that require 16. inches Declivity in a mile to <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> to <lb></lb>prevent its depoſing of Mud; yet would I not be the Author that <lb></lb>ſhould make a trial of it with ſo much hazard, for having to ſa<lb></lb>tisfie my ſelf in ſome particulars cauſed a Level to be taken of <lb></lb>the Rivers <emph type="italics"></emph>L'amone, Senio,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Santerno,<emph.end type="italics"></emph.end> by <emph type="italics"></emph>Bernardino Aleotti,<emph.end type="italics"></emph.end><lb></lb>we found that they have more Declivity by much than Artiſts re<lb></lb>quire, as alſo the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> hath from <emph type="italics"></emph>la Botta de Ghiſlieri<emph.end type="italics"></emph.end> to the <lb></lb>Chappel of <emph type="italics"></emph>Vigarano,<emph.end type="italics"></emph.end> for in the ſpace of four miles its Bottom<lb></lb>Line falleth five feet and five inches. </s> <s>So that I hold it greater <lb></lb>prudence to depend upon that example, than to go contrary to a <lb></lb>common opinion, eſpecially ſince, that the effects cauſed by <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>it ſelf do confirm me in the ſame, for when it was forſaken by <lb></lb>the P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> after a few years, either becauſe it had choaked up its <lb></lb>Chanel with Sand, or becauſe its too long journey did increaſe <lb></lb>it, it alſo naturally turned aſide, and took the way of the ſaid <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> towards <emph type="italics"></emph>Stellata.<emph.end type="italics"></emph.end> Nay, in thoſe very years that it did run that <lb></lb>way, it only began (as relations ſay) to make Breaches, an evi<lb></lb>dent ſign that it doth depoſe Sand, and raiſe its Bed; which a<lb></lb>greeth with the teſtimony of ſome that were examined in the <lb></lb><emph type="italics"></emph>Viſitation<emph.end type="italics"></emph.end> of the Publique Notary, who found great benefit by <lb></lb>having Running Water, and ſome kind of paſſage for Boats, <lb></lb>and yet nevertheleſs affirm that it for want of Running Water <lb></lb>had made too high Stoppages and Shelfes of Sand; ſo that if <lb></lb>it ſhould be reſtored to the Courſe that it forſook, I much fear <lb></lb>that after a ſhort time, if not ſuddenly, it would leave it a<lb></lb>again.</s></p><p type="main"> <s>The ſecond I take from the obſervation of what happened to <lb></lb><emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> when with ſo great applauſe of the <emph type="italics"></emph>Ferareſi,<emph.end type="italics"></emph.end> it was <lb></lb>brought by Cardinal <emph type="italics"></emph>Serra<emph.end type="italics"></emph.end> into the ſaid Chanel of <emph type="italics"></emph>Volana<emph.end type="italics"></emph.end>; for <lb></lb>that notwithſtanding that it had Running Waters in much grea<lb></lb>ter abundance than <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end>; yet in the time that it continued in <lb></lb>that Chanel it raiſed its Bed well neer five feet, as is to be ſeen <lb></lb>below the Sluice made by Cardinal <emph type="italics"></emph>Capponi<emph.end type="italics"></emph.end> to his new Chanel; <lb></lb>yea, the ſaid Cardinal <emph type="italics"></emph>Serra<emph.end type="italics"></emph.end> who deſired that this his under taking <lb></lb>ſhould appear to have been of no danger nor damage, was con<lb></lb>ſtrained at its Overflowings, to give it Vent into <emph type="italics"></emph>Sanmartina,<emph.end type="italics"></emph.end> that <lb></lb>it might not break in upon, and prejudice the City; which dan<lb></lb>ger I ſhould more fear from <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> in regard it carrieth a greater <lb></lb>abundance of Water and Sand</s></p><p type="main"> <s>Thirdly, I am much troubled (in the uncertainty of the ſuc<lb></lb>ceſs of the affair) at the great expence thereto required; For in <lb></lb>regard I do not approve of letting it in, neer to the Fortreſſe, <lb></lb>for many reſpects, and carrying it by <emph type="italics"></emph>la Torre del Fondo<emph.end type="italics"></emph.end> to the <lb></lb>Month <emph type="italics"></emph>de Maſt,<emph.end type="italics"></emph.end> it will take up eight miles of double Banks, a <pb xlink:href="068/01/120.jpg" pagenum="106"></pb>thing not eaſie to be procured, by reaſon that the Grounds lie <lb></lb>under Water; but from the Mouth <emph type="italics"></emph>de Maſi<emph.end type="italics"></emph.end> unto <emph type="italics"></emph>Codigoro,<emph.end type="italics"></emph.end> it <lb></lb>would alſo be neceſſary to make new Scowrings of the Chanel; <lb></lb>to the end, that the Water approaching (by wearing and carry<lb></lb>ing away the Earth on both ſhores, might make a Bed ſufficient <lb></lb>for its Body, the depth made for <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> not ſerving the turn, as <lb></lb>I conceive; and if it ſhould ſuffice, when could the people of <lb></lb><emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> hope to be re-imburſed and ſatisfied for the charge <lb></lb>thereof?</s></p><p type="main"> <s>Fourthly, it ſerves as an Argument with me, to ſee that the <lb></lb>very individual perſons concerned in the Remotion or Diverſion <lb></lb>of the ſaid Torrent, namely, the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end> do not incline unto it, <lb></lb>and that the whole City of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> even thoſe very perſons who <lb></lb>at preſent receive damage by it, cannot indure to hear thereof. <lb></lb></s> <s>The reaſon that induceth theſe laſt named to be ſo averſe thereto, <lb></lb>is, either becauſe that this undertaking will render the introducti<lb></lb>on of the Water of <emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end> more difficult; or becauſe they fear <lb></lb>the danger thereof; The others decline the Project, either for <lb></lb>that they know that <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> cannot long continue in that Courſe, <lb></lb>or becauſe they fear that it is too much expoſed to thoſe mens re<lb></lb>vengeful Cutting of it who do not deſire it ſhould; and if a <lb></lb>man have any other wayes, he ought, in my opinion, to forbear <lb></lb>that, which to ſuch as ſtand in need of its Removal, is leſſe ſatiſ<lb></lb>factory, and to ſuch as oppoſe it, more prejudicial.</s></p><p type="main"> <s>To conclude, I exceedingly honour the judgment of Cardinal <lb></lb><emph type="italics"></emph>Capponi,<emph.end type="italics"></emph.end> who having to his Natural Ability and Prudence added <lb></lb>a particular Study, Obſervation, and Experience of theſe Wa<lb></lb>ters for the ſpace of three years together, doth not think that <lb></lb><emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> can go by <emph type="italics"></emph>Volana<emph.end type="italics"></emph.end>; to which agreeth the opinion of Car<lb></lb>dinal S. <emph type="italics"></emph>Marcello,<emph.end type="italics"></emph.end> Legate of this City, of whom, for his exqui<lb></lb>ſite underſtanding, we ought to make great account. </s> <s>But if e<lb></lb>ver this ſhould be reſolved on, it would be materially neceſſary <lb></lb>to unite the Quick and Running Waters of the little Chanel of <lb></lb><emph type="italics"></emph>Cento,<emph.end type="italics"></emph.end> of the Chanel <emph type="italics"></emph>Navilio,<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Guazzaloca,<emph.end type="italics"></emph.end> and at its very <lb></lb>beginning thoſe of <emph type="italics"></emph>Dardagna,<emph.end type="italics"></emph.end> which at preſent, is one of the <lb></lb>Springs or Heads of <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> that ſo they might aſſiſt it in carry<lb></lb>ing its Sand, and the matter of its Muddineſs into the Sea; and <lb></lb>then there would not fail to be a greater evacuation and ſcowr<lb></lb>ing; but withall the Proprietors in the Iſlet of <emph type="italics"></emph>San Giorgio<emph.end type="italics"></emph.end> and <lb></lb>of <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> muſt prepare themſelves to indure the inconveniences <lb></lb>of Purlings or Sewings of the Water from the River thorow <lb></lb>the Boggy Ground thereabouts.</s></p><p type="main"> <s>I ſhould more eaſily incline therefore to carry it into <emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end><lb></lb>at <emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> for the Reaſons that Cardinal <emph type="italics"></emph>Capponi<emph.end type="italics"></emph.end> moſt ingeni<lb></lb>ouſly enumerates in a ſhort, but well-grounded Tract of his: not <pb xlink:href="068/01/121.jpg" pagenum="107"></pb>becauſe that indeed it would not both by Purlings and by Brea<lb></lb>ches occaſion ſome inconvenience; eſpecially, in the beginning: <lb></lb>but becauſe I hold this for the incomodities of it, to be a far leſs <lb></lb>evil than any of the reſt; and becauſe that by this means there is <lb></lb>no occaſion given to them of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> to explain that they are <lb></lb>deprived of the hope of ever ſeeing the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> again under the Walls <lb></lb>of their City: To whom, where it may be done, it is but reaſon <lb></lb>that ſatisfaction ſhould be given.</s></p><p type="main"> <s>It is certain that P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> was placed by Nature in the midſt of this <lb></lb>great Valley made by the <emph type="italics"></emph>Appennine<emph.end type="italics"></emph.end> Hills, and by the Alps, to <lb></lb>carry, as the Maſter-Drain to the Sea, that is the grand receptacle <lb></lb>of all Waters; thoſe particular ſtreams which deſcend from <lb></lb>them.</s></p><p type="main"> <s>That the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> by all Geographers, <emph type="italics"></emph>Strabo, Pliuy, Solimas, <lb></lb>Mella,<emph.end type="italics"></emph.end> and others is enumerated among the Rivers that fall into <lb></lb>the ſaid P<emph type="italics"></emph>o.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>That although P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhould of it ſelf change its courſe, yet would <lb></lb><emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> go to look it out, if the works erected by humane ind uſtry <lb></lb>did not obſtruct its paſſage; ſo that it neither is, nor ought to <lb></lb>ſeem ſtrange, if one for the greater common good ſhould turn it <lb></lb>into the ſame.</s></p><p type="main"> <s>Now at <emph type="italics"></emph>Stellata<emph.end type="italics"></emph.end> it may go ſeveral waies into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> as appeareth <lb></lb>by the levels that were taken by my Order; of all which I ſhould <lb></lb>beſt like the turning of it to <emph type="italics"></emph>la Botta de' Ghiſlieri,<emph.end type="italics"></emph.end> carrying it <lb></lb>above <emph type="italics"></emph>Bondeno<emph.end type="italics"></emph.end> to the Church of <emph type="italics"></emph>Gambarone,<emph.end type="italics"></emph.end> or a little higher or <lb></lb>lower, as ſhall be judged leaſt prejudicial, when it cometh to the <lb></lb>execution, and this for two principal reaſons: The one becauſe <lb></lb>that then it will run along by the confines of the Church P tri<lb></lb>mony, without ſeparating <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> from the reſt of it; The other <lb></lb>is, Becauſe the Line is ſhorter, and conſequently the fall greater; <lb></lb>for that in a ſpace of ten miles and one third, it falleth twenty ſix <lb></lb>feet, more by much than is required by Artiſts; and would go <lb></lb>by places where it could do but little hurt, notwithſtanding that <lb></lb>the perſons interreſſed ſtudy to amplifie it incredibly.</s></p><p type="main"> <s>On the contrary, there are but onely two objections that are <lb></lb>worthy to be examined; One, That the Drains and Ditches of <lb></lb>S. <emph type="italics"></emph>Bianca,<emph.end type="italics"></emph.end> of the Chanel of <emph type="italics"></emph>Cento,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Burana,<emph.end type="italics"></emph.end> and all thoſe <lb></lb>others that enter into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> do hinder this diverſion of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> by the <lb></lb>encreaſing of the waters in the P<emph type="italics"></emph>o.<emph.end type="italics"></emph.end> The other is that P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> riſing <lb></lb>about the Tranſom of the <emph type="italics"></emph>Pilaſter<emph.end type="italics"></emph.end>-Sluice, very near 20 feet, the <lb></lb><emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> would have no fall into the ſame; whereupon it would riſe <lb></lb>to a terrible height, at which it would not be poſſible to make, or <lb></lb>keep the Banks made, ſo that it would break out and drown <lb></lb>the Meadowes, and cauſe miſchiefs, and damages unſpeakable <lb></lb>and irreparable; as is evident by the experiment made upon <pb xlink:href="068/01/122.jpg" pagenum="108"></pb><emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> which being confined between Banks, that it might go <lb></lb>into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> this not being neither in its greateſt excreſcenſe, it broke <lb></lb>out into the territories of <emph type="italics"></emph>Final,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Ferrara.<emph.end type="italics"></emph.end> And though <lb></lb>that might be done, it would thereupon enſue, that there being <lb></lb>let into the Chanel of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> 2800, ſquare feet of water (for ſo much <lb></lb>we account thoſe of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> taken together in their <lb></lb>greateſt heights) the ſuperficies of it would riſe at leaſt four feet, <lb></lb>inſomuch that either it would be requiſite to raiſe its Banks all the <lb></lb>way unto the Sea, to the ſame height, which the treaſures of the <lb></lb><emph type="italics"></emph>Indies<emph.end type="italics"></emph.end> would not ſuffice to effect; or elſe there would be a neceſ<lb></lb>ſity of enduring exceſſive Breaches. </s> <s>To theſe two Heads are the <lb></lb>Arguments reduced, which are largely amplified againſt our opi<lb></lb>nion; and I ſhall anſwer firſt to the laſt, as moſt material.</s></p><p type="main"> <s>I ſay therefore, that there are three caſes to be conſidered: <lb></lb>Firſt, P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> high, and <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> low. </s> <s>Secondly, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> high, and P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>low. </s> <s>Thirdly, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> and P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> both high together.</s></p><p type="main"> <s>As to the firſt and ſecond, there is no difficulty in them; for if <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall not be at its greateſt height, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> ſhall ever have a fall <lb></lb>into it, and there ſhall need no humane Artifice about the Banks: <lb></lb>And if <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> ſhall be low, P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall regurgitate and flow up into <lb></lb>the Chanel of it; and alſo from thence no inconvenience ſhall <lb></lb>follow. </s> <s>The third remains, from which there are expected ma<lb></lb>ny miſchiefs; but it is a moſt undoubted truth, that the excreſcen<lb></lb>cies of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> as coming from the adjacent <emph type="italics"></emph>Appennines<emph.end type="italics"></emph.end> and Rains, <lb></lb>are to continue but ſeven, or eight hours at moſt, and ſo would <lb></lb>never, or very rarely happen to be at the ſame time with thoſe of <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> cauſed by the melting of the ſnowes of the Alps, at leaſt 400. <lb></lb>miles diſtance from thence. </s> <s>But becauſe it ſometimes may hap<lb></lb>pen, I reply, that when it cometh to paſs, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> ſhall not go into <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> but it ſhall have allowed it one or two Vents; namely, into <lb></lb>the Chanel of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> as it hath ever had; and into <emph type="italics"></emph>Sanmartina,<emph.end type="italics"></emph.end><lb></lb>where it runneth at preſent, and wherewith there is no doubt, but <lb></lb>that the perſons concerned will be well pleaſed, it being a great <lb></lb>benefit to them, to have the water over-flow their grounds once <lb></lb>every four or five years, inſtead of ſeeing it anoy them continu<lb></lb>ally. </s> <s>Yea, the Vent may be regulated, reſerving for it the Cha<lb></lb>nel in which <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> at preſent runneth; and inſtead of turning it <lb></lb>by a Dam at <emph type="italics"></emph>la Betta de Chiſlieri,<emph.end type="italics"></emph.end> perhaps, to turn it by help of <lb></lb>ſtrong Sluices, that may upon all occaſions be opened and ſhut. <lb></lb></s> <s>And for my part, I do not queſtion but that the Proprietors <lb></lb>themſelves in <emph type="italics"></emph>Sanmartina<emph.end type="italics"></emph.end> would make a Chanel for it; which <lb></lb>receiving, and confining it in the time of the Vents, might carry <lb></lb>the Sand into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro:<emph.end type="italics"></emph.end> Nor need there thence be fear<lb></lb>ed any ſtoppage by Mud and Sand, ſince that it is ſuppoſed that <lb></lb>there will but very ſeldom be any neceſſity of uſing it; ſo that <pb xlink:href="068/01/123.jpg" pagenum="109"></pb>time would be allowed, upon occaſion, to ſcowr and cleanſe <lb></lb>it.</s></p><p type="main"> <s>And in this manner all thoſe Prodigies vaniſh that are raiſed <lb></lb>with ſo much fear from the enterance of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>ſwelled into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> when it is high, to which there needeth no other <lb></lb>anſwer; yet nevertheleſſe we do not take that quantity of Wa<lb></lb>ter, that is carried by <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and by <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> to be ſo great as is affir<lb></lb>med: For that P. D. <emph type="italics"></emph>Benedetto Caſtelli<emph.end type="italics"></emph.end> hath no leſſe accutely <lb></lb>than accurately obſerved the meaſures of this kind, noting that <lb></lb>the breadth and depth of a River is not enough to reſolve the <lb></lb>queſtion truly, but that there is reſpect to be had to the velocity <lb></lb>of the Waters, and the term of time, things hitherto not conſi<lb></lb>dered by the Skilful in theſe affairs; and therefore they are not <lb></lb>able to ſay what quantity of Waters the ſaid Rivers carry, nor <lb></lb>to conclude of the riſings that will follow thereupon. </s> <s>Nay, it <lb></lb>is moſt certain, that if all the Rivers that fall into <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> which are <lb></lb>above thirty, ſhould riſe at the rate that theſe compute <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> to <lb></lb>do, an hundred feet of Banks would not ſuffice, and yet they <lb></lb>have far fewer: So that this confirmes the Rule of R. P. D. <emph type="italics"></emph>Bene<lb></lb>detto,<emph.end type="italics"></emph.end> namely, that the proportion of the height of the Water <lb></lb>of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> to the height of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> is <lb></lb>compounded of the proportion of the breadth of the Chanel of <lb></lb><emph type="italics"></emph>Po<emph.end type="italics"></emph.end> to that of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and of the velocity of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>in <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> to the velccity of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end>; a manifeſt <lb></lb>argument that there cannot in it, by this new augmentation of <lb></lb>Waters follow any alteration that neceſſitates the raiſing of its <lb></lb>Banks, as appeareth by the example of <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> which hath been <lb></lb>ſo far from ſwelling P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> that it hath rather aſſwaged it, for it hath <lb></lb>carried away many Shelfs and many Iſlets that had grown in its <lb></lb>Bed, for want of Waters ſufficient to bear away the matter of <lb></lb>Land-floods in ſo broad a Chanel; and as is learnt by the trial <lb></lb>made by us in <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> with the Water of <emph type="italics"></emph>Burana<emph.end type="italics"></emph.end>; for erecting <lb></lb>in the River ſtanding marks, and ſhutting the ſaid Sluice, we could <lb></lb>ſee no ſenſible abatement, nor much leſs after we had opened it <lb></lb>ſenſible increaſment; by which we judge that the ſame is to ſuc<lb></lb>ceed to P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> by letting in of <emph type="italics"></emph>Reno, Burana<emph.end type="italics"></emph.end> having greater pro<lb></lb>portion to <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> than <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> to P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> conſidering the ſtate of thoſe <lb></lb>Rivers in which the Obſervation was made. </s> <s>So that there is no <lb></lb>longer any occaſion for thoſe great raiſings of Banks, and the <lb></lb>danger of the ruptures as well of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> as of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> do vaniſh, as al<lb></lb>ſo the fear leſt that the Sluices which empty into P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhould re<lb></lb>ceive obſtruction: which if they ſhould, yet it would be over in <lb></lb>a few hours. </s> <s>And as to the Breaches of <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> which happened <lb></lb>in 1623. I know not why, ſeeing that it is confeſſed that the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>was not, at that time, at its height, one ſhould rather charge it <pb xlink:href="068/01/124.jpg" pagenum="110"></pb>with the crime, than quit it thereof. </s> <s>The truth is, that the <lb></lb>Bank was not made of proof, ſince that the ſame now continu<lb></lb>eth whole and good, and <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> doth not break out; nay, there <lb></lb>was, when it brake more than a foot and half of its Banks above <lb></lb>the Water, and to ſpare; but it broke thorow by a Moles wor<lb></lb>king, or by the hole of a Water-Rat, or ſome ſuch vermine; <lb></lb>and by occaſion of the badneſs of the ſaid Banks, as I finde by <lb></lb>the teſtimony of ſome witneſſes examined by my command, that <lb></lb>I might know the truth thereof. </s> <s>Nor can I here forbear to ſay, <lb></lb>that it would be better, if in ſuch matters men were more candid <lb></lb>and ſincere. </s> <s>But to ſecure our ſelves nevertheleſſe, to the ut<lb></lb>moſt of our power, from ſuch like Breaches which may happen <lb></lb>at the firſt, by reaſon of the newneſſe of the Banks, I preſuppoſe <lb></lb>that from P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> unto the place whence <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> is cut, there ought to <lb></lb>be a high and thick Fence made with its Banks, ſo that there <lb></lb>would be no cauſe to fear any whatſoever acceſſions of Water, <lb></lb>although that concurrence of three Rivers, which was by ſome <lb></lb>more ingeniouſly aggravated than faithfully ſtated by that which <lb></lb>was ſaid above were true; to whom I think not my ſelf bound <lb></lb>to make any farther reply, neither to thoſe who ſay that <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> will <lb></lb>aſcend upwards into <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> ſince that theſe are the ſame perſons <lb></lb>who would introduce a ſmall branch of the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> into the <lb></lb>Chanel of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> that ſo it may conveigh to the Sea, not <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>onely, but alſo all the other Brooks of which we complained; <lb></lb>and becauſe that withal it is impoſſible, that a River ſo capacious <lb></lb>as <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> ſhould be incommoded by a Torrent, that, as I may ſay, <lb></lb>hath no proportion to it.</s></p><p type="main"> <s>I come now to the buſineſſe of the Ditches and Draines; and <lb></lb>as to the Conveyance of <emph type="italics"></emph>Burana,<emph.end type="italics"></emph.end> it hath heretofore been deba<lb></lb>ted to turn it into <emph type="italics"></emph>Main-Po,<emph.end type="italics"></emph.end> ſo that in this caſe it will receive no <lb></lb>harm, and though it were not removed, yet would it by a Trench <lb></lb>under ground purſue the courſe that it now holdeth, and alſo <lb></lb>would be able to diſ-imbogue again into the ſaid new Chanel of <lb></lb><emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> which conforming to the ſuperficies of the Water of <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end><lb></lb>would continue at a lower level than that which <emph type="italics"></emph>Panara<emph.end type="italics"></emph.end> had <lb></lb>when it came to <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> into which <emph type="italics"></emph>Burana<emph.end type="italics"></emph.end> did nevertheleſſe <lb></lb>empty it ſelf for ſome time.</s></p><p type="main"> <s>The Conveyance or Drain of <emph type="italics"></emph>Santa Bianca,<emph.end type="italics"></emph.end> and the little <lb></lb>Chanel of <emph type="italics"></emph>Cento<emph.end type="italics"></emph.end> may alſo empty themſelves by two ſubterranean <lb></lb>Trenches, without any prejudice where they run at preſent, or <lb></lb>without any more works of that nature, they may be turned into <lb></lb>the ſaid new Chanel, although with ſomewhat more of incon<lb></lb>venience; and withall, the Chanel of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> left dry, would <lb></lb>be a ſufficient receptacle for any other Sewer or Drain whatſoe<lb></lb>ver, that ſhould remain there.</s></p><pb xlink:href="068/01/125.jpg" pagenum="111"></pb><p type="main"> <s>All which Operations might be brought to perfection with <lb></lb>150. thouſand Crowns, well and faithfully laid out; which ſumm <lb></lb>the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end> will not be unwilling to provide; beſides that thoſe <lb></lb><emph type="italics"></emph>Ferrareſi<emph.end type="italics"></emph.end> ought to contribute to it, who ſhall partake of the <lb></lb>benefit.</s></p><p type="main"> <s>Let me be permitted in this place to propoſe a thing which I <lb></lb>have thought of, and which peradventure might occaſion two <lb></lb>benefits at once, although it be not wholly new. </s> <s>It was in the <lb></lb>time of <emph type="italics"></emph>Pope Paul<emph.end type="italics"></emph.end> V. propounded by one <emph type="italics"></emph>Creſcenzio<emph.end type="italics"></emph.end> an Ingi<lb></lb>neer, to cut the <emph type="italics"></emph>Main-Po,<emph.end type="italics"></emph.end> above <emph type="italics"></emph>le Papozze<emph.end type="italics"></emph.end>; and having made a <lb></lb>ſufficient evacuation to derive the water thereof into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <lb></lb><emph type="italics"></emph>Adriano,<emph.end type="italics"></emph.end> and ſo to procure it to be Navigable, which was not at <lb></lb>that time effected, either by reaſon of the oppoſitions of thoſe, <lb></lb>whoſe poſſeſſions were to be cut thorow, or by reaſon of the <lb></lb>great ſum of money that was neceſſary for the effecting of it: But <lb></lb>in viewing thoſe Rivers, we have obſerved, that the ſedge cutting <lb></lb>might eaſily be made below <emph type="italics"></emph>le Papozze,<emph.end type="italics"></emph.end> in digging thorow the <lb></lb>Bank called <emph type="italics"></emph>Santa Maria,<emph.end type="italics"></emph.end> & drawing a Trench of the bigneſs that <lb></lb>skilful Artiſts ſhall judge meet unto the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ^{*} of <emph type="italics"></emph>Ariano,<emph.end type="italics"></emph.end> below the <lb></lb><arrow.to.target n="marg982"></arrow.to.target><lb></lb><emph type="italics"></emph>Secche<emph.end type="italics"></emph.end> of the ſaid S. <emph type="italics"></emph>Maria<emph.end type="italics"></emph.end>; which as being a work of not <lb></lb>above 160. Perches in length, would be finiſhed with onely <lb></lb>12000. Crowns.</s></p><p type="margin"> <s><margin.target id="marg982"></margin.target>* Of <emph type="italics"></emph>Adriano.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt; it is to be believed, that the waters running that way, <lb></lb>would not fail to open that Mouth into the Sea, which at pre<lb></lb>ſent is almoſt choakt up by the Shelf of Sand, which the new <lb></lb>Mouth of <emph type="italics"></emph>Ponto Virro<emph.end type="italics"></emph.end> hath brought thither; and that it would <lb></lb>again bring into uſe the Port <emph type="italics"></emph>Goro,<emph.end type="italics"></emph.end> and its Navigation.</s></p><p type="main"> <s>And haply experience might teach us, that the ſuperficies of <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> might come to fall by this aſſwagement of Water, ſo that the <lb></lb>acceſſion of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> would queſtionleſs make no riſing in it: <lb></lb>Whereupon, if it ſhould ſo fall out, thoſe Princes would have <lb></lb>no reaſon to complain; who ſeem to queſtion, leſt by this new <lb></lb>acceſſion of water into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> the Sluices might be endangered. <lb></lb></s> <s>Which I thought not fit to omit to repreſent to your Lordſhip; <lb></lb>not, that I propoſe it to you as a thing abſolutely certain, but that <lb></lb>you might, if you ſo pleaſed, lay it before perſons whoſe judge<lb></lb>ments are approved in theſe affairs.</s></p><p type="main"> <s>I return now from where I degreſt, and affirm it as indubita<lb></lb>ble, that <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> neither can, nor ought to continue longer where <lb></lb>it at this day is; and that it cannot go into any other place but <lb></lb>that, whither <emph type="italics"></emph>Cardinal Capponi<emph.end type="italics"></emph.end> deſigned to carry it, and which <lb></lb>at preſent pleaſeth me better than any other; or into <emph type="italics"></emph>Volana,<emph.end type="italics"></emph.end><lb></lb>whence it was taken away; the vigilance of Men being able to <lb></lb>obviate part of thoſe miſchiefs, which it may do there.</s></p><p type="main"> <s>But from its Removal, beſides the alleviation of the harm <pb xlink:href="068/01/126.jpg" pagenum="112"></pb>which by it ſelf is cauſed, there would alſo reſult the diminution <lb></lb>of that which is occaſioned by the other Brooks, to the right hand <lb></lb>of the <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta<emph.end type="italics"></emph.end>; foraſmuch as the ſaid <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> wanting all the <lb></lb>water of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> it would of neceſſity come to ebb in ſuch man<lb></lb>ner, that the Valleys would have a greater Fall into the ſame, <lb></lb>and conſequently it would take in, and ſwallow greater abun<lb></lb>dance of water; and by this means the Ditches and Draines <lb></lb>of the Up-Lands would likewiſe more eaſily Fall into them; eſ<lb></lb>pecially if the ſcouring of <emph type="italics"></emph>Zenzalino<emph.end type="italics"></emph.end> were brought to perfection, <lb></lb>by which the waters of <emph type="italics"></emph>Marrara<emph.end type="italics"></emph.end> would fall into <emph type="italics"></emph>Marmorta<emph.end type="italics"></emph.end>: And <lb></lb>if alſo that of <emph type="italics"></emph>Baſtia<emph.end type="italics"></emph.end> were enlarged, and finiſhed, by which there <lb></lb>might enter as much water into the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> as is taken <lb></lb>from it by the removal of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end>; although that by that meanes <lb></lb>the water of the Valleys would aſſwage double: Nor would the <lb></lb>people of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> the Iſles of S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Comacchio<emph.end type="italics"></emph.end> have any <lb></lb>cauſe to complain; for that there would not be given to them <lb></lb>more water than was taken away: Nay ſometimes whereas they <lb></lb>had Muddy waters, they would have clear; nor need they to fear <lb></lb>any riſing: And furthermore, by this means a very great quan<lb></lb>tity of ground would be reſtored to culture; For the effecting of <lb></lb>all which, the ſumm of 50. thouſand Crowns would go very far, <lb></lb>and would ſerve the turn at preſent touching thoſe Brooks, car<lb></lb>rying them a little farther in the mean time, to fill up the greater <lb></lb>cavities of the Valleys, that we might not enter upon a vaſter <lb></lb>and harder work, that would bring with it the difficulties of other <lb></lb>operations, and ſo would hinder the benefit which theſe people <lb></lb>expect from the paternal charity of His Holineſs.</s></p><pb xlink:href="068/01/127.jpg" pagenum="113"></pb><p type="head"> <s>TO <lb></lb>The Right Honourable, <lb></lb>MONSIGNORE <lb></lb>D. </s> <s>Ferrante Ceſarini.</s></p><p type="main"> <s>My Treatiſe of the MENSURATION of RUN<lb></lb>NING WATERS, Right Honourable, and <lb></lb>moſt Noble Sir, hath not a greater Preroga<lb></lb>tive than its having been the production of the <lb></lb>command of Pope <emph type="italics"></emph>Vrban<emph.end type="italics"></emph.end> VIII. when His Ho<lb></lb>lineſs was pleaſed to enjoyn me to go with <lb></lb><emph type="italics"></emph>Monſignore Corſini,<emph.end type="italics"></emph.end> in the Viſitation that was <lb></lb>impoſed upon him in the year 1625. of the Waters of <emph type="italics"></emph>Ferrara, <lb></lb>Bologna, Romagna,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Romagnola<emph.end type="italics"></emph.end>; for that, on that occaſion <lb></lb>applying my whole Study to my ſervice and duty, I publiſhed in <lb></lb>that Treatiſe ſome particulars till then not rightly underſtood and <lb></lb>conſidered (that I knew) by any one; although they be in them<lb></lb>ſelves moſt important, and of extraordinary conſequence. </s> <s>Yet <lb></lb>I muſt render thanks to Your Lordſhip for the honour you have <lb></lb>done to that my Tract; but wiſh withal, that your Eſteem of it <lb></lb>may not prejudice the univerſal Eſteem that the World hath of <lb></lb>Your Honours moſt refined judgement.</s></p><p type="main"> <s>As to that Point which I touch upon in the Concluſion, name<lb></lb>ly, That the conſideration of the Velocity of Running Water ſup<lb></lb>plyeth the conſideration of the ^{*} Length omitted in the common <lb></lb><arrow.to.target n="marg983"></arrow.to.target><lb></lb>way of meaſuring Running Waters; Your Lordſhip having com<lb></lb>manded me that in favour of <emph type="italics"></emph>Practiſe,<emph.end type="italics"></emph.end> and for the perfect diſco<lb></lb>very of the diſorder that commonly happeneth now adayes in <lb></lb>the diſtribution of the Waters of Fountains, I ſhould demon<lb></lb>ſtrate that the knowledge of the Velocity ſerveth for the finding <lb></lb>of the Length: I have thought fit to ſatisfie your Command by <lb></lb>relating a Fable; which, if I do not deceive my ſelf, will make <lb></lb>out to us the truth thereof; inſomuch that the reſt of my Treatiſe <lb></lb>ſhall thereby alſo become more manifeſt and intelligible, even to <pb xlink:href="068/01/128.jpg" pagenum="432"></pb>thoſe who finde therein ſome kinde of obſcurity.</s></p><p type="margin"> <s><margin.target id="marg983"></margin.target>* Larghezza, but <lb></lb>miſprinted.</s></p><p type="main"> <s>In the dayes of yore, before that the admirable Art of Wea<lb></lb>ving was in uſe, there was found in <emph type="italics"></emph>Perſia<emph.end type="italics"></emph.end> a vaſtand unvaluable <lb></lb>Treaſure, which conſiſted in an huge multitude of pieces of Er<lb></lb>meſin, or Damask, I know not whether; which, as I take it, <lb></lb>amounted to near two thouſand pieces; which were of ſuch a <lb></lb>nature, that though their Breadth and Thickneſs were finite and <lb></lb>determinate, as they uſe to be at this day; yet nevertheleſs, their <lb></lb>Length was in a certain ſenſe infinite, for that thoſe two thouſand <lb></lb>pieces, day and night without ceaſing, iſſued out with their ends <lb></lb>at ſuch a rate, that of each piece there iſſued 100. Ells a day, from <lb></lb>a deep and dark Cave, conſecrated by the Superſtition of thoſe <lb></lb>people, to the fabulous <emph type="italics"></emph>Arachne.<emph.end type="italics"></emph.end> In thoſe innocent and early <lb></lb>times (I take it to have been, in that ſo much applauded and <lb></lb>deſired Golden age) it was left to the liberty of any one, to cut <lb></lb>off of thoſe pieces what quantity they pleaſed without any diffi<lb></lb>culty: But that felicity decaying and degenerating, which was <lb></lb>altogether ignorant of <emph type="italics"></emph>Meum<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Tuum<emph.end type="italics"></emph.end>; terms certainly moſt <lb></lb>pernicious, the Original of all evils, and cauſe of all diſcords; <lb></lb>there were by thoſe people ſtrong and vigilant Guards placed <lb></lb>upon the Cave, who reſolved to make merchandize of the Stuffes; <lb></lb>and in this manner they began to ſet a price upon that ineſtima<lb></lb>ble Treaſure, ſelling the propriety in thoſe pieces to divers Mer<lb></lb>chants; to ſome they ſold a right in one, to ſome in two, and to <lb></lb>ſome in more. </s> <s>But that which was the worſt of all, There was <lb></lb>found out by the inſatiable avarice of theſe men crafty inventions <lb></lb>to deceive the Merchants alſo; who came to buy the aforeſaid <lb></lb>commodity, and to make themſelves Maſters, ſome of one <lb></lb>ſome of two, and ſome of more ends of thoſe pieces of ſtuff; <lb></lb>and in particular, there were certain ingenuous Machines placed <lb></lb>in the more ſecret places of the Cave, with which at the pleaſure <lb></lb>of the Guards, they did retard the velocity of thoſe Stuffs, in <lb></lb>their iſſuing out of the Cave; inſomuch, that he who ought to have <lb></lb>had 100. Ells of Stuff in a day, had not above 50, and he who <lb></lb>ſhould have had 400, enjoyed the benefit of 50. onely; and ſo all <lb></lb>the reſt were defrauded of their Rights, the ſurpluſage being ſold, <lb></lb>appropriated, and ſhared at the will of the corrupt Officers: So <lb></lb>that the buſineſs was without all order or juſtice, inſomuch that <lb></lb>the Goddeſs <emph type="italics"></emph>Arachne<emph.end type="italics"></emph.end> being diſpleaſed at thoſe people, deprived <lb></lb>every one of their benefit, and with a dreadful Earthquake for <lb></lb>ever cloſing the mouth of the Cave, in puniſhment of ſo much <lb></lb>impiety and malice: Nor did it avail them to excuſe themſelves, <lb></lb>by ſaying that they allowed the Buyer the Breadth and Thick<lb></lb>neſs bargained for; and that of the Length, which was infinite, <pb xlink:href="068/01/129.jpg" pagenum="115"></pb>there could no account be kept: For the wiſe and prudent <lb></lb>Prieſt of the Sacred <emph type="italics"></emph>Grotto<emph.end type="italics"></emph.end> anſwered, That the deceit lay in the <lb></lb>length, which they were defrauded of, in that the velocity of the <lb></lb>ftuffe was retarded, as it iſſued out of the Cave: and although <lb></lb>the total length of the Piece was infinite, for that it never cea<lb></lb>ſed coming forth, and ſo was not to be computed; yet never<lb></lb>theleſs its length conſidered, part by part, as it came out of the <lb></lb>Cave, and was bargained for, continued ſtill finite, and might <lb></lb>be one while greater, and another while leſſer, according as the <lb></lb>Piece was conſtituted in greater or leſſer velocity; and he added <lb></lb>withall, that exact Juſtice required, that when they ſold a piece <lb></lb>of ſtuff, and the propriety or dominion therein, they ought not <lb></lb>only to have aſcertained the breadth and thickneſſe of the Piece, <lb></lb>but alſo to have determined the length, determining its ve<lb></lb>locity.</s></p><p type="main"> <s>The ſame diſorder and confuſion, that was repreſented in the <lb></lb>Fable, doth come to paſſe in the Hiſtory of the Diſtribution of <lb></lb>the Waters of Conduits and Fountains, ſeeing that they are ſold <lb></lb>and bought, having regard only to the two Dimenſions, I mean <lb></lb>of Breadth and Height of the Mouth that diſchargeth the Wa<lb></lb>ter; and to remedy ſuch an inconvenience, it is neceſſary to de<lb></lb>termine the length in the velocity; for never ſhall we be able to <lb></lb>make a gueſſe at the quantity of the Body of Running Water, <lb></lb>with the two Dimenſions only of Breadth and Height, without <lb></lb>Length.</s></p><p type="main"> <s>And to the end, that the whole buſineſs may be reduced <lb></lb>to a moſt eaſie practice, by which the waters of Aqueducts <lb></lb>may be bought and ſold juſtly, and with meaſures alwayes ex<lb></lb>act and conſtant.</s></p><p type="main"> <s>Firſt, the quantity of the Water ought diligently to be exa<lb></lb>mined, which the whole principal ^{*} Pipe diſchargeth in a time <lb></lb>certain, as for inſtance, in an hour, in half an hour, or in a leſſe <lb></lb>interval of time, (for knowing which I have a moſt exact and <lb></lb>eaſie Rule) and finding that the whole principal pipe diſchar<lb></lb>geth <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> a thouſand Tuns of Water in the ſpace of one or <lb></lb>more hours, in ſelling of this water, it ought not to be uttered by <lb></lb>the ordinary and falſe meaſure, but the diſtribution is to be <lb></lb>made with agreement to give and maintain to the buyer ten or <lb></lb>twenty, or a greater number of Tuns, as the bargain ſhall be <lb></lb>made, in the ſpace of an hour, or of ſome other ſet and deter<lb></lb>minate time. </s> <s>And here I adde, that if I were to undertake to <lb></lb>make ſuch an adjuſtment, I would make uſe of a way to divide <lb></lb>and meaſure the time with ſuch accurateneſſe, that the ſpace of <lb></lb>an hour ſhould be divided into four, ſix, or eight thouſand parts <pb xlink:href="068/01/130.jpg" pagenum="116"></pb>without the leaſt errour; which Rule was taught me by my <lb></lb>Maſter <emph type="italics"></emph>Sign. </s> <s>Galilæo Galilæi,<emph.end type="italics"></emph.end> Chief Philoſopher to the moſt Se<lb></lb>rene <emph type="italics"></emph>Grand Duke<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Tuſcany.<emph.end type="italics"></emph.end> And this way will ſerve eaſily and <lb></lb>admirably to our purpoſe and occaſion; ſo that we ſhall <lb></lb>thereby be able to know how many Quarts of Water an A<lb></lb>queduct will diſcharge in a given time of hours, moneths, or <lb></lb>years. </s> <s>And in this manner we may conſtitute a Cock that ſhall <lb></lb>diſcharge a certain and determinate quantity of water in a time <lb></lb>given.</s></p><p type="main"> <s>And becauſe daily experience ſhews us, that the Springs of A<lb></lb>queducts do not maintain them alwayes equally high, and full <lb></lb>of Water, but that ſometimes they increaſe, and ſometimes de<lb></lb>creaſe, which accident might poſſibly procure ſome difficulty in <lb></lb>our diſtribution: Therefore, to the end that all manner of ſcru<lb></lb>ple may be removed, I conceive that it would be convenient to <lb></lb>provide a Ciſtern, according to the occaſion, into which there <lb></lb>might alwayes fall one certain quantity of water, which ſhould <lb></lb>not be greater than that which the principal pipe diſchargeth in <lb></lb>times of drought, when the Springs are bare of water, that ſo in <lb></lb>this Ciſtern the water might alwayes keep at one conſtant height. <lb></lb></s> <s>Then to the Ciſtern ſo prepared we are to faſten the Cocks of <lb></lb>particular perſons, to whom the Water is ſold by the Reverend <lb></lb>Apoſtolique Chamber, according to what hath been obſerved <lb></lb>before; and that quantity of Water which remaineth over and <lb></lb>above, is to be diſcharged into another Ciſtern, in which the <lb></lb>Cocks of the Waters for publick ſervices, and of thoſe which <lb></lb>people buy upon particular occaſions are to be placed. </s> <s>And <lb></lb>when the buſineſſe ſhall have been brought to this paſſe, there <lb></lb>will likewiſe a remedy be found to the ſo many diſorders that <lb></lb>continually happen; of which, for brevity ſake, I will inſtance <lb></lb>in but four only, which concern both publique and private bene<lb></lb>fit, as being, in my judgment, the moſt enormous and intole<lb></lb>rable.</s></p><p type="main"> <s>The firſt inconvenience is, that in the common way of meaſu<lb></lb>ring, diſpenſing, and ſelling the Waters of Aqueducts, it is not <lb></lb>underſtood, neither by the Buyer nor Seller, what the quantity <lb></lb>truly is that is bought and ſold; nor could I ever meet with any <lb></lb>either Engineer or Architect, or Artiſt, or other that was able to <lb></lb>decypher to me, what one, or two, or ten inches of water was. <lb></lb></s> <s>But by our above declared Rule, for diſpenſing the Waters of <lb></lb>Aqueducts we may very eaſily know the true quantity of Water <lb></lb>that is bought or ſold, as that it is ſo many Tuns an hour, ſo ma<lb></lb>ny a day, ſo many in a year, &c.</s></p><p type="main"> <s>The ſecond diſorder that happeneth, at preſent, in the diſtri<pb xlink:href="068/01/131.jpg" pagenum="117"></pb>bution of Aqueducts is, that as the buſineſſe is now governed, it <lb></lb>lieth in the power of a ſordid Maſon to take unjuſtly from one, <lb></lb>and give undeſervedly to another more or leſſe Water than be<lb></lb>longeth to them of right: And I have ſeen it done, of my <lb></lb>own experience. </s> <s>But in our way of meaſuring and diſtri<lb></lb>buting Waters, there can no fraud be committed; and put<lb></lb>ting the caſe that they ſhould be committed, its an eaſie mat<lb></lb>ter to know it, and amend it, by repairing to the Tribunal <lb></lb>appointed.</s></p><p type="main"> <s>Thirdly, it happens very often, (and we have examples there<lb></lb>of both antient and modern) that in diſpenſing the Water after <lb></lb>the common and vulgar way; there is ſometimes more Water diſ<lb></lb>pended than there is in the Regiſter, in which there will be regi<lb></lb>ſtred, as they ſay, two hundred inches (for example) and there <lb></lb>will be diſpenſed two hundred and fifty inches, or more. </s> <s>Which <lb></lb>paſſage happened in the time of <emph type="italics"></emph>Nerva<emph.end type="italics"></emph.end> the Emperour, as <emph type="italics"></emph>Giulio <lb></lb>Frontino<emph.end type="italics"></emph.end> writes, in his 2. Book, <emph type="italics"></emph>De Aquaductibus Vrbis Romæ,<emph.end type="italics"></emph.end><lb></lb>where he obſerveth that they had <emph type="italics"></emph>in Commentariis 12755. Qui<lb></lb>naries<emph.end type="italics"></emph.end> of Water; and found that they diſpenſed 14018. <emph type="italics"></emph>Qui<lb></lb>naries.<emph.end type="italics"></emph.end> And the like Errour hath continued, and is in uſe alſo <lb></lb>modernly until our times. </s> <s>But if our Rule ſhall be obſerved, <lb></lb>we ſhall incur no ſuch diſorder, nay there will alwayes be given <lb></lb>to every one his ſhare, according to the holy end of exact juſtice, <lb></lb>which <emph type="italics"></emph>dat unicuique quod ſuum eſt.<emph.end type="italics"></emph.end> As on the contrary, it is <lb></lb>manifeſt, that His Divine Majeſty hateth and abominateth <emph type="italics"></emph>Pon<lb></lb>dus & pondus, Menſura & menſura,<emph.end type="italics"></emph.end> as the Holy Ghoſt ſpeak<lb></lb>eth by the mouth of <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> in the <emph type="italics"></emph>Proverbs, Chap. </s> <s>20. Pondus <lb></lb>& Pondus, Menſura & Menſura, utrumque abominabile eſt apud <lb></lb>Deum.<emph.end type="italics"></emph.end> And therefore who is it that ſeeth not that the way of <lb></lb>dividing and meaſuring of Waters, commonly uſed, is expreſly <lb></lb>againſt the Law of God. </s> <s>Since that thereby the ſame meaſure <lb></lb>is made ſometimes greater, and ſometimes leſſer; A diſorder ſo <lb></lb>enormous and execrable, that I ſhall take the boldneſs to ſay, that <lb></lb>for this ſole reſpect it ought to be condemned and prohibited like<lb></lb>wiſe by human Law, which ſhould Enact that in this buſineſs there <lb></lb>ſhould be imployed either this our Rule, or ſome other that <lb></lb>is more exquiſite and practicable, whereby the meaſure <lb></lb>might keep one conſtant and determinate tenor, as we make it, <lb></lb>and not, as it is now, to make <emph type="italics"></emph>Pondus & Pondus, Menſur a & <lb></lb>Menſura.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this is all that I had to offer to Your moſt Illuſtrious <lb></lb>Lordſhip, in obedience to your commands, reſerving to my ſelf <lb></lb>the giving of a more exact account of this my invention, when <lb></lb>the occaſion ſhall offer, of reducing to practice ſo holy, juſt, and <pb xlink:href="068/01/132.jpg" pagenum="118"></pb>neceſſary a reformation of the Meaſure of Running Waters and <lb></lb>of Aqueducts in particular: which Rule may alſo be of great <lb></lb>benefit in the diviſion of the greater Waters to over-flow <lb></lb>Grounds, and for other uſes: I humbly bow,</s></p><p type="main"> <s><emph type="italics"></emph>Your Most Devoted,<emph.end type="italics"></emph.end><lb></lb>and <lb></lb><emph type="italics"></emph>Moſt Obliged Servant,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>D. </s> <s>Benedetto Caſtelli, <emph type="italics"></emph>Abb. </s> <s>Caſin.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>FINIS.</s></p><pb xlink:href="068/01/133.jpg"></pb><p type="head"> <s>A TABLE</s></p><p type="head"> <s>Of the moſt obſervable matters in this Treatiſe of the <lb></lb>MENSURATION of RUNNING <lb></lb>WATERS.<lb></lb><arrow.to.target n="table74"></arrow.to.target></s></p><table><table.target id="table74"></table.target><row><cell>A</cell><cell></cell></row><row><cell>Abatements <emph type="italics"></emph>of a River in different and unequal Diverſions, is alwaies equal, which is proved with<emph.end type="italics"></emph.end> 100. Syphons.</cell><cell><emph type="italics"></emph>Page<emph.end type="italics"></emph.end> 75</cell></row><row><cell>Arno <emph type="italics"></emph>River when it riſeth upon a Land-Flood near the Sea one third of a Brace, it riſeth about<emph.end type="italics"></emph.end> Piſa 6. <emph type="italics"></emph>or 7. Braces.<emph.end type="italics"></emph.end></cell><cell>82</cell></row><row><cell>B</cell><cell></cell></row><row><cell><emph type="italics"></emph>Banks near to the Sea lower, than far from thence. Corollary<emph.end type="italics"></emph.end> XIV.</cell><cell>16</cell></row><row><cell>Brent <emph type="italics"></emph>River diverted from the Lake o<emph.end type="italics"></emph.end>f Venice, <emph type="italics"></emph>and its effects.<emph.end type="italics"></emph.end></cell><cell>64</cell></row><row><cell>Brent <emph type="italics"></emph>ſuppoſed inſufficient to remedy the inconveniences of the Lake, and the falſity of that ſuppoſition.<emph.end type="italics"></emph.end></cell><cell>67</cell></row><row><cell>Brent, <emph type="italics"></emph>and its benefits in the Lake.<emph.end type="italics"></emph.end></cell><cell>70</cell></row><row><cell><emph type="italics"></emph>Its Depoſition of Sand in the Lake, bow great it is.<emph.end type="italics"></emph.end></cell><cell>78, 79</cell></row><row><cell><emph type="italics"></emph>Bridges over Rivers, and how they are to be made. Appendix<emph.end type="italics"></emph.end> VIII.</cell><cell>20</cell></row><row><cell>Burana <emph type="italics"></emph>River, its riſing, and falling in<emph.end type="italics"></emph.end> Panaro.</cell><cell>110</cell></row><row><cell>C</cell><cell></cell></row><row><cell>Caſtelli <emph type="italics"></emph>applyed himſelf to this Study by Order of<emph.end type="italics"></emph.end> Urban VIII.</cell><cell>2</cell></row><row><cell>Chanel of Navigation <emph type="italics"></emph>in the Valleys of<emph.end type="italics"></emph.end> Bologna, <emph type="italics"></emph>and its inconveniences.<emph.end type="italics"></emph.end></cell><cell>99</cell></row><row><cell><emph type="italics"></emph>Carried into the<emph.end type="italics"></emph.end> Po <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>and its benefits<emph.end type="italics"></emph.end></cell><cell>ibid.</cell></row><row><cell>Ciampoli <emph type="italics"></emph>alover of theſe Obſervations of Waters.<emph.end type="italics"></emph.end></cell><cell>3</cell></row><row><cell>D</cell><cell></cell></row><row><cell><emph type="italics"></emph>Difficulty of this buſineſs of Meaſuring Waters.<emph.end type="italics"></emph.end></cell><cell>2</cell></row><row><cell><emph type="italics"></emph>Diſorders that happen in the diſtribution of the Waters of Aqueducts, and their re-medies.<emph.end type="italics"></emph.end></cell><cell>113</cell></row><row><cell><emph type="italics"></emph>Diſtribution of the Waters of Fountains, and Aqueducts. Appendix<emph.end type="italics"></emph.end> X.</cell><cell>22</cell></row><row><cell><emph type="italics"></emph>Diſtribution of Water to over-flow Grounds. Appendix<emph.end type="italics"></emph.end> XI.</cell><cell>23, 69, 70</cell></row><row><cell><emph type="italics"></emph>Diverſion of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>and other Brooks of<emph.end type="italics"></emph.end> Romagna, <emph type="italics"></emph>adviſed by<emph.end type="italics"></emph.end> P. Spernazzati <emph type="italics"></emph>to what end it was.<emph.end type="italics"></emph.end></cell><cell>100</cell></row><row><cell><emph type="italics"></emph>Drains and Ditches, the benefit they receive by cutting away the Weeds and Reeds. Appendix<emph.end type="italics"></emph.end> IX.</cell><cell>21</cell></row><row><cell><emph type="italics"></emph>Drains and Sewers obſtructed, in the Diverſion of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into<emph.end type="italics"></emph.end> Main Po, <emph type="italics"></emph>and a remedy for the ſame.<emph.end type="italics"></emph.end></cell><cell>110</cell></row><row><cell>E</cell><cell></cell></row><row><cell><emph type="italics"></emph>Engineers unverſ'd in the matters of Waters.<emph.end type="italics"></emph.end></cell><cell>2</cell></row><row><cell><emph type="italics"></emph>Erour found in the common way of Meaſuring Running Waters.<emph.end type="italics"></emph.end></cell><cell>68, 69</cell></row><row><cell><emph type="italics"></emph>Errour in deriving the Water of<emph.end type="italics"></emph.end> Acqua Paola. <emph type="italics"></emph>Appendix<emph.end type="italics"></emph.end> II.</cell><cell>17, 18</cell></row><pb xlink:href="068/01/134.jpg"></pb><row><cell><emph type="italics"></emph>Errour of<emph.end type="italics"></emph.end> Bartolotti.</cell><cell>86, 87</cell></row><row><cell><emph type="italics"></emph>Errours of Engineers in the Derivation of Chenels. Corollary<emph.end type="italics"></emph.end> XII.</cell><cell>12</cell></row><row><cell><emph type="italics"></emph>Errour of Engineers in Meaſuring of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>in<emph.end type="italics"></emph.end> Po. <emph type="italics"></emph>Appendix<emph.end type="italics"></emph.end> III.</cell><cell>ibid.</cell></row><row><cell><emph type="italics"></emph>Errour of other Engineers, contrary to the precedent. Appendix<emph.end type="italics"></emph.end> IV.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Errour of<emph.end type="italics"></emph.end> Giovanni Fontana <emph type="italics"></emph>in Meaſuring Waters, Corollary<emph.end type="italics"></emph.end> XI.</cell><cell>9</cell></row><row><cell><emph type="italics"></emph>Errour of<emph.end type="italics"></emph.end> Giulio Frontino <emph type="italics"></emph>in Meaſuring the Waters of Aqueducts. Appen-dix<emph.end type="italics"></emph.end> I.</cell><cell>17</cell></row><row><cell><emph type="italics"></emph>Errours committed in cutting the Bank at<emph.end type="italics"></emph.end> Bondeno, <emph type="italics"></emph>in the ſwellings of<emph.end type="italics"></emph.end> Po: <emph type="italics"></emph>Corollary<emph.end type="italics"></emph.end>XIII.</cell><cell>81</cell></row><row><cell>F</cell><cell></cell></row><row><cell><emph type="italics"></emph>Fenns<emph.end type="italics"></emph.end> Pontine, <emph type="italics"></emph>Drained by Pope<emph.end type="italics"></emph.end> Sixtus Quintus, <emph type="italics"></emph>with vaſt expence.<emph.end type="italics"></emph.end></cell><cell>92</cell></row><row><cell><emph type="italics"></emph>The ruine and miſcarriage thereof.<emph.end type="italics"></emph.end></cell><cell>93</cell></row><row><cell><emph type="italics"></emph>Tardity of the principal Chanel that Drains them, cauſe of the Drowning.<emph.end type="italics"></emph.end></cell><cell>ibid.</cell></row><row><cell><emph type="italics"></emph>They are obſtructed by the Fiſhing-Wears, which ſuell the River.<emph.end type="italics"></emph.end></cell><cell>94</cell></row><row><cell><emph type="italics"></emph>Waters of<emph.end type="italics"></emph.end> Fiume Siſto, <emph type="italics"></emph>which flow in great abundance into the<emph.end type="italics"></emph.end> Evacuator <emph type="italics"></emph>of the ſaid Fenns.<emph.end type="italics"></emph.end></cell><cell>94, 95</cell></row><row><cell><emph type="italics"></emph>Remedies to the diſorders of thoſe Fenns.<emph.end type="italics"></emph.end></cell><cell>95, 96</cell></row><row><cell>Fontana Giovanni, <emph type="italics"></emph>his errours in Meaſuring Waters. Corollary<emph.end type="italics"></emph.end> XI.</cell><cell>9</cell></row><row><cell>Fiume Morto, <emph type="italics"></emph>whether it ought to fall into the Sea, or into<emph.end type="italics"></emph.end> Serchio,</cell><cell>79</cell></row><row><cell><emph type="italics"></emph>Let into<emph.end type="italics"></emph.end> Serchio <emph type="italics"></emph>and its inconveniences.<emph.end type="italics"></emph.end></cell><cell>79, 80</cell></row><row><cell><emph type="italics"></emph>The dangerous riſing of its Waters, when to be expected.<emph.end type="italics"></emph.end></cell><cell>81</cell></row><row><cell><emph type="italics"></emph>Its inconveniences when it is higher in level than<emph.end type="italics"></emph.end> Serchio, <emph type="italics"></emph>and why it riſeth moſt On the Sea-coaſts, at ſuch time as the Winds make the Sea to ſuell.<emph.end type="italics"></emph.end></cell><cell>83</cell></row><row><cell>G</cell><cell></cell></row><row><cell>Galilæo Galilæi. <emph type="italics"></emph>hoxourably mentioned.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>Page<emph.end type="italics"></emph.end> 2, 28</cell></row><row><cell><emph type="italics"></emph>His Rule for meaſuring the time.<emph.end type="italics"></emph.end></cell><cell>49</cell></row><row><cell>H</cell><cell></cell></row><row><cell><emph type="italics"></emph>Height,<emph.end type="italics"></emph.end> vide <emph type="italics"></emph>Quick<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Heights different, made by the ſame ſtream of a Brock or Torrent, according to the divers Velocities in the entrance of the River. Corollary<emph.end type="italics"></emph.end> I.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Heights different, made by the Torrent in the River, according to the different heights of the River. Corollary<emph.end type="italics"></emph.end> II.</cell><cell>ibid.</cell></row><row><cell>K</cell><cell></cell></row><row><cell><emph type="italics"></emph>Knowledge of Motion how much it importeth.<emph.end type="italics"></emph.end></cell><cell>1</cell></row><row><cell>L</cell><cell></cell></row><row><cell><emph type="italics"></emph>t<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Lake of<emph.end type="italics"></emph.end> Perugia, <emph type="italics"></emph>and, he Obſervation made on it. Appendix<emph.end type="italics"></emph.end> XII.</cell><cell>42</cell></row><row><cell><emph type="italics"></emph>Lake of<emph.end type="italics"></emph.end> Thraſimenus <emph type="italics"></emph>and Conſiderations upon it, a Letter written to<emph.end type="italics"></emph.end> Sig. Galilæo Galilæi.</cell><cell>28</cell></row><row><cell><emph type="italics"></emph>Lake of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>and Conſiderations upon it.<emph.end type="italics"></emph.end></cell><cell>63, 73</cell></row><row><cell><emph type="italics"></emph>Low Waters which let the bottom of it be diſcovered.<emph.end type="italics"></emph.end></cell><cell>64</cell></row><row><cell><emph type="italics"></emph>The ſtoppage and choaking of the Ports, a main cauſe of the diſorders of the Lake, and the grand remedy to thoſe diſorders what it is.<emph.end type="italics"></emph.end></cell><cell>66</cell></row><row><cell><emph type="italics"></emph>Lakes and Metrs along the Sea-coaſts, and the cauſes thereof.<emph.end type="italics"></emph.end></cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Length of Waters, how it is to be Meaſured.<emph.end type="italics"></emph.end></cell><cell>70</cell></row><row><cell>M</cell><cell></cell></row><row><cell><emph type="italics"></emph>Meaſure and Diſtributions of Waters. Appendix<emph.end type="italics"></emph.end> V.</cell><cell>18</cell></row><pb xlink:href="068/01/135.jpg"></pb><row><cell><emph type="italics"></emph>Meaſure of Rivers that fall into others difficult. Coroll.<emph.end type="italics"></emph.end> X:</cell><cell>9</cell></row><row><cell><emph type="italics"></emph>Meaſure of the Running Water of a Chanel of an height known by a<emph.end type="italics"></emph.end> Regulator <emph type="italics"></emph>of a Mea-ſure given, in a time aſſigned. Propoſition<emph.end type="italics"></emph.end> I. <emph type="italics"></emph>Problem<emph.end type="italics"></emph.end> I.</cell><cell>50</cell></row><row><cell><emph type="italics"></emph>Meaſure of the Water of any River, of any greatneſs, in a time given. Propoſition<emph.end type="italics"></emph.end> V. <emph type="italics"></emph>Problem<emph.end type="italics"></emph.end> III.</cell><cell>60</cell></row><row><cell><emph type="italics"></emph>Meaſure that ſhewes how much Water a River diſchargeth in a time given.<emph.end type="italics"></emph.end></cell><cell>48</cell></row><row><cell><emph type="italics"></emph>Mole-holes,<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Motion the principal ſubject of Philoſophy.<emph.end type="italics"></emph.end></cell><cell>1</cell></row><row><cell><emph type="italics"></emph>Mud.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Sand.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>N</cell><cell></cell></row><row><cell><emph type="italics"></emph>Navigation from<emph.end type="italics"></emph.end> Bologna <emph type="italics"></emph>to<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>is become impoſſible, till ſuch time as<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>be diverted.<emph.end type="italics"></emph.end></cell><cell>101</cell></row><row><cell><emph type="italics"></emph>Navigation in the Lake of<emph.end type="italics"></emph.end> Venice <emph type="italics"></emph>endangered, and how restored.<emph.end type="italics"></emph.end></cell><cell>65, 70</cell></row><row><cell>P</cell><cell></cell></row><row><cell><emph type="italics"></emph>Perpendicularity of the Banks of the River, to the upper ſuperficies of it.<emph.end type="italics"></emph.end></cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Perpendicularity of the Banks to the bottom.<emph.end type="italics"></emph.end></cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Perugia.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Lake.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Pontine.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Fenns.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Ports of<emph.end type="italics"></emph.end> Venice, Malamocco, Bondolo, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Chiozza, <emph type="italics"></emph>choaked up for want of Water in the Lake.<emph.end type="italics"></emph.end></cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Proportions of unequal Sections of equal Velocity, and of equal Sections of unequal Velo-city. Axiome<emph.end type="italics"></emph.end> IV. <emph type="italics"></emph>and<emph.end type="italics"></emph.end> V.</cell><cell>38</cell></row><row><cell><emph type="italics"></emph>Proportions of equal and unequal quantities of Water, which paſs by the Sections of dif-ferent Rivers. Propoſition<emph.end type="italics"></emph.end> II.</cell><cell>39</cell></row><row><cell><emph type="italics"></emph>Proportions of unequal Sections that in equal times diſcharge equal quantities of Water. Propoſition<emph.end type="italics"></emph.end> III.</cell><cell>41</cell></row><row><cell><emph type="italics"></emph>Proportion wherewith one River falling into another, varieth in height. Propo-ſition<emph.end type="italics"></emph.end> IV.</cell><cell>44</cell></row><row><cell><emph type="italics"></emph>Proportion of the Water diſcharged by a River in the time of Flood, to the Water diſcharged in an equal time by the ſaid River, before or after the Flood. Propoſition<emph.end type="italics"></emph.end> V.</cell><cell>44</cell></row><row><cell><emph type="italics"></emph>Proportion of the Heights made by two equal Brooks or Streams falling into the ſame River. Propoſition<emph.end type="italics"></emph.end> VI.</cell><cell>45</cell></row><row><cell><emph type="italics"></emph>Proportion of the Water which a River diſchargeth encreaſing in Quick-height by the ad-dition of new Water, to that which it diſchargeth after the encreaſe is made. Propo-ſition<emph.end type="italics"></emph.end> IV. <emph type="italics"></emph>Theor.<emph.end type="italics"></emph.end> II.</cell><cell>54</cell></row><row><cell><emph type="italics"></emph>Proportion of a River when high, to it ſelf when low. Coroll.<emph.end type="italics"></emph.end> I.</cell><cell>55</cell></row><row><cell>Q</cell><cell></cell></row><row><cell><emph type="italics"></emph>Quantity of Running Waters is never certain, if with the Vulgar way of Meaſuring them, their Velocities be not conſidered.<emph.end type="italics"></emph.end></cell><cell>32</cell></row><row><cell><emph type="italics"></emph>Quantities of Waters which are diſcharged by a River, anſwer in equality to the Velocities and times in which they are diſcharged. Axiome<emph.end type="italics"></emph.end> I, II, III.</cell><cell>38</cell></row><row><cell>Quick-Height <emph type="italics"></emph>of a River, what it is. Definition<emph.end type="italics"></emph.end> V.</cell><cell>48</cell></row><row><cell>R</cell><cell></cell></row><row><cell><emph type="italics"></emph>Reaſon of the Proverb,<emph.end type="italics"></emph.end> Take heed of the ſtill Waters. <emph type="italics"></emph>Coroll.<emph.end type="italics"></emph.end> VI.</cell><cell>7</cell></row><row><cell><emph type="italics"></emph>Reaſons of<emph.end type="italics"></emph.end> Monſignore Corſini <emph type="italics"></emph>againſt the diverſion of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into the<emph.end type="italics"></emph.end> Po <emph type="italics"></emph>of<emph.end type="italics"></emph.end>Volano.</cell><cell>105</cell></row><row><cell><emph type="italics"></emph>Reaſons of<emph.end type="italics"></emph.end> Cardinal Capponi <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Monſig. Corſini, <emph type="italics"></emph>for the turning of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into Main<emph.end type="italics"></emph.end> Po.</cell><cell>106</cell></row><pb xlink:href="068/01/136.jpg"></pb><row><cell><emph type="italics"></emph>Two objections on the contrary, and anſwers to them.<emph.end type="italics"></emph.end></cell><cell>104 <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 105</cell></row><row><cell><emph type="italics"></emph>What ought to be the proportion of the Heights of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>in<emph.end type="italics"></emph.end> Reno, <emph type="italics"></emph>and of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>in<emph.end type="italics"></emph.end>Po.</cell><cell>110</cell></row><row><cell><emph type="italics"></emph>Regulator what it is. Definition<emph.end type="italics"></emph.end> IV.</cell><cell>48</cell></row><row><cell><emph type="italics"></emph>Relation of the Waters of<emph.end type="italics"></emph.end> Bologna <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>by<emph.end type="italics"></emph.end> Monſignore Corſini</cell><cell>100</cell></row><row><cell>Reno <emph type="italics"></emph>in the Valleys, and its bad effects.<emph.end type="italics"></emph.end></cell><cell>100, 101</cell></row><row><cell><emph type="italics"></emph>Two wayes to divert it.<emph.end type="italics"></emph.end></cell><cell>103</cell></row><row><cell><emph type="italics"></emph>The facility and utility of thoſe wayes.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>The difficulties objected.<emph.end type="italics"></emph.end></cell><cell>104</cell></row><row><cell><emph type="italics"></emph>Reply to<emph.end type="italics"></emph.end> Bartolotti <emph type="italics"></emph>touching the dangers of turning<emph.end type="italics"></emph.end> Fiume Morto <emph type="italics"></emph>into<emph.end type="italics"></emph.end> Serchio.</cell><cell>83</cell></row><row><cell><emph type="italics"></emph>Retardment of the courſe of a River cauſed by its Banks. Appendix<emph.end type="italics"></emph.end> VII.</cell><cell>19</cell></row><row><cell><emph type="italics"></emph>Riſings made by Flood-Gates but ſmall. Appendix<emph.end type="italics"></emph.end> XIII.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Rivers that are ſhallow ſwell much upon ſmall ſhowers, ſuch as are deep riſe but little upon great Floods. Corollary<emph.end type="italics"></emph.end> III.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Rivers the higher they are, the ſwifter.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Rivers the higher they are, theleſſe they encreaſe upon Floods.<emph.end type="italics"></emph.end></cell><cell>49</cell></row><row><cell><emph type="italics"></emph>Rivers when they are to have equal and when like Velocity.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Rivers in falling into the Sea, form a Shelf of Sand called<emph.end type="italics"></emph.end> Cavallo.</cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Five Rivers to be diverted from the Lake of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>and the inconveniences that would enſue thereupon.<emph.end type="italics"></emph.end></cell><cell>74, 75</cell></row><row><cell><emph type="italics"></emph>A River of Quick-height, and Velocity in its Regulator being given, if the Height be redoubled by new Water, it redoubleth alſo in Velocity. Propoſition<emph.end type="italics"></emph.end> II. <emph type="italics"></emph>The-orem<emph.end type="italics"></emph.end> I.</cell><cell>51</cell></row><row><cell><emph type="italics"></emph>Keepeth the proportion of the heights, to the Velocities. Corollary<emph.end type="italics"></emph.end></cell><cell>52</cell></row><row><cell>S</cell><cell></cell></row><row><cell><emph type="italics"></emph>Sand and Mud that entereth into the Lake of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>and the way to examine it.<emph.end type="italics"></emph.end></cell><cell>76</cell></row><row><cell><emph type="italics"></emph>Seas agitated and driven by the Winds ſtop up the Ports.<emph.end type="italics"></emph.end></cell><cell>64, 65</cell></row><row><cell><emph type="italics"></emph>Sections of a River what they are. Definition<emph.end type="italics"></emph.end> I.</cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Sections equally ſwift what they are. Definition<emph.end type="italics"></emph.end> II.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Sections of a River being given, to conceive others equal to them, of different breadth, height and Velocity. Petition.<emph.end type="italics"></emph.end></cell><cell>38</cell></row><row><cell><emph type="italics"></emph>Sections of the ſame River, and their Proportions to their Velocities. Coroll.<emph.end type="italics"></emph.end> I.</cell><cell>42</cell></row><row><cell><emph type="italics"></emph>Sections of a River diſcharge in any whatſoever place of the ſaid River, equal quantities of Water in equal times. Propoſition<emph.end type="italics"></emph.end> I.</cell><cell>39</cell></row><row><cell>Sile <emph type="italics"></emph>River what miſchiefes it threatneth, diverted from the Lake.<emph.end type="italics"></emph.end></cell><cell>74</cell></row><row><cell><emph type="italics"></emph>Spirtings of Waters grow bigger the higher they go. Coroll.<emph.end type="italics"></emph.end> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"></emph>Sreams of Rivers how they encreaſe and vary. Coroll.<emph.end type="italics"></emph.end> I.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Streams retarded, and the effects thereof. Coroll.<emph.end type="italics"></emph.end> IX.</cell><cell>8</cell></row><row><cell>T</cell><cell></cell></row><row><cell><emph type="italics"></emph>Table of the Heights, Additions, and Quantities of Waters, and its uſe.<emph.end type="italics"></emph.end></cell><cell>56</cell></row><row><cell><emph type="italics"></emph>Thraſimenus.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Lake.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Time how its meaſured in theſe Operations of the Waters.<emph.end type="italics"></emph.end></cell><cell>49</cell></row><row><cell><emph type="italics"></emph>Torrents encreaſe at the encreaſing of a River, though they carry no more Water than before: Coroll.<emph.end type="italics"></emph.end> IV.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Torrents when they depoſe and carry away the Sand. Coroll.<emph.end type="italics"></emph.end> V.</cell><cell>7</cell></row><row><cell><emph type="italics"></emph>Torrents and their effects in a River.<emph.end type="italics"></emph.end></cell><cell>6, 7</cell></row><row><cell><emph type="italics"></emph>Torrents that fall into the Valleys, or into<emph.end type="italics"></emph.end> Po <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Volano, <emph type="italics"></emph>and their miſchiefs prevent-ed, by the diverting of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into<emph.end type="italics"></emph.end> Main Po.</cell><cell>100</cell></row><row><cell><emph type="italics"></emph>Tyber and the cauſes of its inundations. Coroll.<emph.end type="italics"></emph.end> VIII.</cell><cell>8</cell></row><pb xlink:href="068/01/137.jpg"></pb><row><cell>V</cell><cell></cell></row><row><cell><emph type="italics"></emph>Valleys of<emph.end type="italics"></emph.end> Bologna <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>their inundations and diſorders, whence they pro-ceed.<emph.end type="italics"></emph.end></cell><cell>97</cell></row><row><cell><emph type="italics"></emph>Velocity of the Water ſhewn by ſeveral Examples.<emph.end type="italics"></emph.end></cell><cell>3</cell></row><row><cell><emph type="italics"></emph>Its proportion to the Meaſure.<emph.end type="italics"></emph.end></cell><cell>5</cell></row><row><cell><emph type="italics"></emph>Velocities equal, what they are.<emph.end type="italics"></emph.end></cell><cell>47</cell></row><row><cell><emph type="italics"></emph>Velocities like, what they are.<emph.end type="italics"></emph.end></cell><cell>47, 48</cell></row><row><cell><emph type="italics"></emph>Velocities of Water known, how they help us in finding the Lengths.<emph.end type="italics"></emph.end></cell><cell>113</cell></row><row><cell><emph type="italics"></emph>A Fable to explain the truth thereof.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Lake.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Vſe of the<emph.end type="italics"></emph.end> Regulator <emph type="italics"></emph>in meaſuring great Rivers. Conſideration I.<emph.end type="italics"></emph.end></cell><cell>60</cell></row><row><cell>W</cell><cell></cell></row><row><cell><emph type="italics"></emph>Waters falling, why they diſgroß. Coroll.<emph.end type="italics"></emph.end> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"></emph>Waters, how the Length of them is Meaſured.<emph.end type="italics"></emph.end></cell><cell>70</cell></row><row><cell><emph type="italics"></emph>Waters that are imployed to flow Grounds, how they are to be diſtributed.<emph.end type="italics"></emph.end></cell><cell>19, 53, 54</cell></row><row><cell><emph type="italics"></emph>Waters to be carryed in Pipes, to ſerve Aquaducts and Conduits, how they are to be Mea-ſured.<emph.end type="italics"></emph.end></cell><cell>115, 116</cell></row><row><cell><emph type="italics"></emph>Way to know the riſing of Lakes by Raines.<emph.end type="italics"></emph.end></cell><cell>28</cell></row><row><cell><emph type="italics"></emph>Way of the Vulgar to Meaſure the Waters of Rivers.<emph.end type="italics"></emph.end></cell><cell>68</cell></row><row><cell><emph type="italics"></emph>Wind Gun, and Tortable Fountain of<emph.end type="italics"></emph.end> Vincenzo Vincenti <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Urbin.</cell><cell>11</cell></row><row><cell><emph type="italics"></emph>Windes contrary, retard, and make Rivers encreaſe. Coroll.<emph.end type="italics"></emph.end> VII.</cell><cell>8</cell></row></table><p type="head"> <s>The END of the TABLE of the Second Part <lb></lb>of the Firſt TOME.</s></p> </chap> </body> <back></back> </text></archimedes>