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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"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Salusbury, Thomas</author> <title>Mathematical collections and translations</title> <date>1667</date> <place>London</place> <translator></translator> <lang>en</lang> <cvs_file>salus_mathe_040_en_1667.xml</cvs_file> <cvs_version></cvs_version> <locator>040.xml</locator> </info> <text> <front> <section> <pb xlink:href="040/01/001.jpg"/><p type="head"> <s>MATHEMATICAL <lb/>Collections <emph type="italics"/>and<emph.end type="italics"/> Tran&longs;lations: <lb/><emph type="italics"/>In two<emph.end type="italics"/><lb/>TOMES.</s></p><pb xlink:href="040/01/002.jpg"/><pb xlink:href="040/01/003.jpg"/><p type="head"> <s>MATHEMATICAL <lb/>COLLECTIONS <lb/>AND <lb/>TRANSLATIONS: <lb/>THE FIRST <lb/>TOME. <lb/><emph type="italics"/>IN TWO PARTS.<emph.end type="italics"/></s></p><p type="head"> <s>THE FIRST PART;</s></p><p type="head"> <s>Containing,</s></p><p type="main"> <s><emph type="italics"/>I.<emph.end type="italics"/> GALILEUS GALILEUS <emph type="italics"/>His SYSTEM of the <lb/>WORLD.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>II.<emph.end type="italics"/> GALILEUS <emph type="italics"/>His EPISTLE to the GRAND <lb/>DUTCHESSE MOTHER, concerning the Au­<lb/>thority of Holy SCRIPTURE in Philo&longs;ophical <lb/>Controver&longs;ies.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>III.<emph.end type="italics"/> JOHANNES KEPLERUS <emph type="italics"/>His Reconcilings of SCRI­<lb/>PTURE Texts, &c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>IV.<emph.end type="italics"/> DIDACUS à STUNICA <emph type="italics"/>His Reconcilings of SCRI­<lb/>PTURE Texts, &c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>V.<emph.end type="italics"/> P. A. FOSCARINUS <emph type="italics"/>His Epi&longs;tle to Father FANTONUS, <lb/>reconciling the Authority of SCRIPTURE, and Judg­<lb/>ments of Divines alledged again&longs;t this SYSTEM.<emph.end type="italics"/></s></p><p type="head"> <s>By <emph type="italics"/>THOMAS SALUSBURY, <expan abbr="E&longs;q.">E&longs;que</expan><emph.end type="italics"/></s></p><p type="head"> <s>LONDON, <lb/>Printed by WILLIAM LEYBOURN, MDCLXI.</s></p><pb xlink:href="040/01/004.jpg"/><pb xlink:href="040/01/005.jpg"/></section><section><p type="head"> <s>To the Noble and mo&longs;t perfectly Accompli&longs;hed <lb/>S^{t.} JOHN DENHAM <lb/>Knight of the Noble Order of the <lb/>BATH, <lb/>And Surveyor General of his Ma^{ties} Works, &c.</s></p><p type="main"> <s>SIR,</s></p><p type="main"> <s>I humbly begge your Pardon for <lb/>bringing this Book under your Pro­<lb/>tection. </s> <s>Were it a Work of my <lb/>own, or I any thing but the Tran&longs;la­<lb/>tour, I should ma&longs;ter my Thoughts to a meaner <lb/>Dedication; But being a Collection of &longs;ome of <lb/>the greate&longs;t Ma&longs;ters in the World, and never <lb/>made English till now, I conceived I might <lb/>&longs;ooner procure their Welcome to a per&longs;on &longs;o <lb/>eminent for Noble Candor, as well as for all <lb/>tho&longs;e Intellectual Excellencies wherewith <lb/>Your Rich Soulis known to be furnished. </s> <s>I <lb/>re&longs;olv'd to be as kind to this Book as I could, <pb xlink:href="040/01/006.jpg"/>and &longs;eriou&longs;ly con&longs;idering which way to effect <lb/>it, I at la&longs;t concluded to prefix Your Name, <lb/>whom His Maje&longs;ty and all his Subjects, (who <lb/>have a higher Sen&longs;e and Judgement of Excel­<lb/>lent Parts) know be&longs;t able to defend my Im­<lb/>perfections. </s> <s>And yet I confe&longs;s there's one <lb/>thing makes again&longs;t me, which is your eminent <lb/>Integrity and great Affection to Truth, where­<lb/>by my Lap&longs;esin a Work of this Nature might <lb/>ju&longs;tly de&longs;pair of Shelter, but that the Excel­<lb/>lency of Your Native Candor &longs;trives for Pre­<lb/>dominancy over all Your great Abilities. </s> <s>For <lb/>'tis all-mo&longs;t impo&longs;&longs;ible to think what Your <lb/>Matchle&longs;s Wit is not able to Conquer, would <lb/>Your known Mode&longs;ty but give leave: there­<lb/>fore <emph type="italics"/>Galileus, Kepler,<emph.end type="italics"/> and tho&longs;e other worthies <lb/>in Learning are now brought before You in <lb/>English Habit, having chang'd their Latine, <lb/>Italian and French, whereby they were almo&longs;t <lb/>Strangers to our Nation, unle&longs;s to &longs;uch as You, <lb/>who &longs;o perfectly ma&longs;ter the Originals. </s> <s>I know <lb/>you have &longs;o much and great imployment for <lb/>His Maje&longs;ty, and his good Subjects that I shall <lb/>not robb you of another Minutes lo&longs;s; be&longs;ides <lb/>the liberty of &longs;ub&longs;cribing my Self;</s></p><p type="main"> <s>SIR,</s></p><p type="main"> <s><emph type="italics"/>Your Honours<emph.end type="italics"/></s></p><p type="main"> <s>Mo&longs;t Humble <lb/>and <lb/>Mo&longs;t obedient Servant</s></p><p type="main"> <s>THOMAS SALUSBURY.</s></p><pb xlink:href="040/01/007.jpg"/></section><section><p type="main"> <s>READER,</s></p><p type="main"> <s>Mathematical Learning <emph type="italics"/>(to &longs;peak nothing touching the nece&longs;sity & delight thereof) hath bin &longs;o &longs;paring­<lb/>ly imparted to our Countrymen in their native Engli&longs;h, e&longs;pecially the nobler and &longs;ublimer part, <lb/>that in Compliance with the<emph.end type="italics"/> Solicitations <emph type="italics"/>of &longs;everal of my noble and learned Friends, and the<emph.end type="italics"/> Incli­<lb/>nations <emph type="italics"/>of &longs;uch as are Mathematically di&longs;po&longs;ed, more e&longs;pecially tho&longs;e, who either want Time or <lb/>Patience to look into the vulgar and un&longs;tudied Languages, I did adventure upon this Work of Collecting & Tran&longs;­<lb/>lating from among&longs;t the excellent Pieces that are &longs;o abounding in the Italian and French Tongues, &longs;ome of tho&longs;e <lb/>that my own ob&longs;ervation and the intimation of Friends were mo&longs;t u&longs;efull and de&longs;ired, and with all mo&longs;t wanting <lb/>in their Own.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>I was, indeed, at fir&longs;t &longs;eriou&longs;ly Con&longs;cious, and am now, by experience, fully convinced how di&longs;proportionate the <lb/>weight of the Enterprize is to the weakne&longs;s of the Vndertaker, but yet the Pa&longs;sion I ever had to be &longs;ub&longs;ervient to <lb/>my Friends and Compatriots in their Inqui&longs;ition after the&longs;e Sublime Studies, and a Patience which I owe to the <lb/>Flegme that is predominant in my Con&longs;titution, joyned with a nine-years conver&longs;ence in the&longs;e Languages, as al&longs;o an <lb/>unhappy and long Vacation that the per&longs;ecutions of the late Tyrants gave me from more advantagious employ­<lb/>ments &longs;o prevailed with me, that I re&longs;olved to improve even my very Confinement to &longs;erve tho&longs;e Friends, whom, as <lb/>the Times then &longs;tood, I could not &longs;ee.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The Book being for Subject and De&longs;ign intended chiefly for Gentlemen, I have hin as carele&longs;s of u&longs;ing a &longs;tudied <lb/>Pedantry in my Style; as careful in contriving a plea&longs;ant and beautiful Impre&longs;&longs;ion. </s> <s>And when I had con&longs;idered <lb/>the hazard, and computed the charge of the undertaking, I found it to exceed the ability of a private Pur&longs;e, e&longs;pe­<lb/>cially of mine, that had bin &longs;o lately emptied by the hand of violent enemies, and perfidious friends; not to <lb/>make mention here of the Sums that a Loyal Reflexion upon my Princes Affairs had at the &longs;ame time drawn <lb/>from me; and judg'd that the most &longs;afe, ea&longs;y, and rea&longs;onable way was to invite tho&longs;e Per&longs;ons who had appeared <lb/>de&longs;irous of the Book, to be contributary to their own Contentment, by &longs;ub&longs;cribing towards the charge of this Pu­<lb/>blication.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And for the better management of the Work, I joyned to my &longs;elf a Printer, who&longs;e Genius having rendered <lb/>him Mathematical, and my overtures of profit having intere&longs;&longs;ed his diligence, I was induced to promi&longs;e my &longs;elf a <lb/>more than common A&longs;&longs;i&longs;tance from him: and at his door I with rea&longs;on lay all mi&longs;carriages that concerns his <lb/>Profe&longs;&longs;ion in the Bu&longs;ine&longs;s.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>In this Work I found more than ordinary Encouragement from that publick &longs;pirited Per&longs;on the Reverend and <lb/>Learned Dr.<emph.end type="italics"/> Thomas Barlow, <emph type="italics"/>Provo&longs;t of Queens Colledge Oxford, and<emph.end type="italics"/> Margaret <emph type="italics"/>Profe&longs;&longs;or in that Vniver­<lb/>&longs;ity, as al&longs;o from tho&longs;e two able Mathematicians and my Reall Friends Major<emph.end type="italics"/> Miles Symner, <emph type="italics"/>and Mr.<emph.end type="italics"/> Robert <lb/>Wood <emph type="italics"/>of Trinity Colledge<emph.end type="italics"/> Dublin, <emph type="italics"/>and &longs;ome few others who&longs;e Mode&longs;ty hath expre&longs;ly enjoin'd me a concealment <lb/>of their Names.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Well, at length I have got to the end of my fir&longs;t Stage; and if I have not rid Po&longs;t, let my excu&longs;e be that my long <lb/>&longs;tay for my Warrant cau&longs;ed me to &longs;et out late; and being ill mounted, and in a road full of rubbs, I could not with <lb/>any &longs;afety go fa&longs;ter; but hope to get it up in the next Stage, for in that I intend to &longs;hift my Hor&longs;es.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The names of tho&longs;e Authors and Treatices which I judged would mo&longs;t grace our Language, and gratify Stu­<lb/>dents, are particularly expre&longs;t in the General Title of the two Tomes. </s> <s>Di&longs;tinct Tomes they are as con&longs;i&longs;ting of <lb/>&longs;everat Pieces: Collections I call them, becau&longs;e they have bin &longs;o publi&longs;hed, di&longs;per&longs;t, and worn out of Print, that <lb/>they very rarely meet in one hand: and Tran&longs;lations I own them to be, as not pretending to any thing more than <lb/>the di&longs;po&longs;ure and conver&longs;ion of them: tho&longs;e Tracts only excepted which compo&longs;e the &longs;econd Part of the &longs;econd <lb/>Tome.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The fir&longs;t Book which offers it &longs;elf to your view in this Tome is that &longs;ingular and unimitable Piece of Rea&longs;on <lb/>and Demon&longs;tration the Sy&longs;teme of<emph.end type="italics"/> Galilco. <emph type="italics"/>The &longs;ubject of it is a new and Noble port of A&longs;tronomy, to wit the <lb/>Doctrine and Hypothe&longs;is of the Mobility of the carth and the Stability of the Sun; the Hi&longs;tory whereof I &longs;hall <lb/>hereafter give you at large in the Life of that famous Man. </s> <s>Only this by the by; that the Reader may not wonder <lb/>why the&longs;e Dialogues found &longs;o various entertainment in Italy (for he cannot but have heard that though they have <lb/>been with all veneration valued, read & applauded by the Iudicious yet they were with much dete&longs;tation per&longs;ecuted, <lb/>&longs;uppre&longs;&longs;ed & exploded by the Super&longs;titious) I am to tell him that our Author having a&longs;&longs;igned his intimate Friends<emph.end type="italics"/><lb/>Salviati <emph type="italics"/>and<emph.end type="italics"/> Sagredo <emph type="italics"/>the more &longs;ucceßfull Parts of the Challenger, and Moderater, he made the famous Commen­<lb/>tator<emph.end type="italics"/> Simplicius <emph type="italics"/>to per&longs;onate the Peripatetick. </s> <s>The Book coming out, and Pope<emph.end type="italics"/> Urban <emph type="italics"/>the<emph.end type="italics"/> VIII. <emph type="italics"/>taking his Ho­<lb/>nour to be concern'd as having in his private Capacity bin very po&longs;itive in declaiming against the Samian Philo­<lb/>&longs;ophy, and now (as he &longs;uppo&longs;ed) being ill delt with by<emph.end type="italics"/> Galilco <emph type="italics"/>who had &longs;ummed up all his Arguments, and pur <lb/>them into the mouth of<emph.end type="italics"/> Simplicius; <emph type="italics"/>his Holine&longs;s thereupon conceived an implacable Di&longs;plea&longs;ure against our Au­<lb/>thor, and thinking no other revenge &longs;ufficient, he employed his Apo&longs;tolical Authority, and deals with the Con&longs;i&longs;tory <lb/>to condemn him and pro&longs;cribe his Book as Heretical; pro&longs;tituting the Cen&longs;ure of the Church to his private revenge. <lb/></s> <s>This was<emph.end type="italics"/> Galilco's <emph type="italics"/>fortune in<emph.end type="italics"/> Italy: <emph type="italics"/>but had I not rea&longs;on to hope that the Engli&longs;h will be more ho&longs;pitable, on the <lb/>account of that Principle which induceth them to be civil to (I &longs;ay not to dote on) Strangers, I &longs;hould fear to be <lb/>charged with imprudence for appearing an Interpreter to that great Philo&longs;opher. </s> <s>And in this confidence I &longs;hall <lb/>forbear to make any large Exordium concerning him or his Book: & the rather in regard that &longs;uch kind of Gau­<lb/>deries become not the Gravity of the Subject; as al&longs;o knowing how much (coming from me) they must fall &longs;hort of <lb/>the Merits of it, or him: but principally becau&longs;e I court only per&longs;ons of Judgement & Candor, that can di&longs;tingui&longs;h <lb/>between a Native Beauty, and &longs;purious Verni&longs;h. </s> <s>This only let me premi&longs;e, though more to excu&longs;e my weakne&longs;s in <lb/>the menaging, than to in&longs;inuate my ability in accompli&longs;hing this &longs;o arduous a Task, that the&longs;e profound Dialogues <lb/>have bin found &longs;o unea&longs;y to Tran&longs;late, that neither affectation of Novelty could induce the French, nor the <lb/>Tran&longs;lating humour per&longs;wade the Germans to undertake them. </s> <s>This difficulty, as I conceived, was charged either <lb/>upon the Intricacy of this manner of Writing, or upon the &longs;ingular Elegance in the &longs;tile of<emph.end type="italics"/> Galilco, <emph type="italics"/>or el&longs;e upon the<emph.end type="italics"/><pb xlink:href="040/01/008.jpg"/><emph type="italics"/>mi&longs;carriage of the unfortunate<emph.end type="italics"/> Mathias Berneggeius <emph type="italics"/>who fir&longs;t attempted to turn them into Latine for the benefit <lb/>of the Learned World.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>I &longs;hall not pre&longs;ume to Cen&longs;ure the Cen&longs;ure which the Church of Rome pa&longs;t upon this Doctrine and its A&longs;&longs;ectors. <lb/></s> <s>But, on the contrary, my Author having bin indefinite in his di&longs;cour&longs;e, I &longs;hall forbear to exa&longs;perate, and attempt <lb/>to reconcile &longs;uch per&longs;ons to this Hypothe&longs;is as devout e&longs;teem for Holy Scripture, and dutifull Re&longs;pect to Canonical <lb/>Injunctions hath made to &longs;tand off from this Opinion: and therefore for their &longs;akes I have at the end of the Dia­<lb/>logues by way of &longs;upplement added an Epi&longs;tle of<emph.end type="italics"/> Galilco <emph type="italics"/>to Her Most Serene Highne&longs;s<emph.end type="italics"/> Chri&longs;tina Lotharinga <emph type="italics"/>the <lb/>Grand Dutche&longs;&longs;e Mother of<emph.end type="italics"/> Tu&longs;cany; <emph type="italics"/>as al&longs;o certain Ab&longs;tracts of<emph.end type="italics"/> John Kepler, <emph type="italics"/>Mathematician to two Empe­<lb/>rours, and<emph.end type="italics"/> Didacus à Stunica <emph type="italics"/>a famous Divine of Salamanca, with an Epi&longs;tle of<emph.end type="italics"/> Paulo Antonio Fo&longs;carini <emph type="italics"/>a learn­<lb/>ed Carmelite of Naples, that &longs;hew the Authority of Sacred Scripture in determining of Philo&longs;ophical and Natu­<lb/>ral Controver&longs;ies: hoping that the ingenious & impartial Reader will meet with full &longs;atisfaction in the &longs;ame. <lb/></s> <s>And lea&longs;t what I have &longs;poken of the prohibiting of the&longs;e Pieces by the Inqui&longs;ition may deterre any &longs;crupulous <lb/>per&longs;on from reading of them, I have purpo&longs;ely in&longs;erted the Imprimatur by which that Office licenced them. </s> <s>And <lb/>for a larger account of the Book or Author, I refer you to the Relation of his Life, which &longs;hall bring up the Reare <lb/>in the Second Tome.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>What remains of this, is that Excellent Di&longs;cour&longs;e of D.<emph.end type="italics"/> Benedetto Ca&longs;telli Abbate di San Benedetto Aloy&longs;io, <lb/><emph type="italics"/>concerning the Men&longs;uration of Running waters, with other Treati&longs;es of that Learned Prelate, & of the Superin­<lb/>tendent<emph.end type="italics"/> Cor&longs;ini. <emph type="italics"/>Some may alledge, and I doe confe&longs;s that I promi&longs;ed to publi&longs;h the Life of<emph.end type="italics"/> Galilco <emph type="italics"/>in this place: <lb/>But the great mi&longs;carriages of Letters from &longs;ome Friends in Italy and el&longs;e where, to whom I am a Debtor for &longs;e­<lb/>veral Remarques, & from whom I daily expect yet greater Helps concerning the Hi&longs;tory of that famous Per&longs;onage: <lb/>the&longs;e di&longs;appointments, I &longs;ay, joyned with the undeniable Reque&longs;t of &longs;ome Friends, who were impatient to &longs;ee<emph.end type="italics"/> Ca&longs;telli <lb/><emph type="italics"/>in Engli&longs;h, together with a con&longs;ideration of the di&longs;proportionate Bulk that would otherwi&longs;e have bin betwixt the <lb/>two Volumes, per&longs;waded me to this exchange. </s> <s>This deviation from my Promi&longs;e I hope is Venial, and for the ex­<lb/>plating of it I plead Supererrogation: having in each Tome made &longs;o large Aditions (though to my great ex­<lb/>pen&longs;e) that they make neer a third part more than I &longs;tood by promi&longs;e bound to Publi&longs;h. </s> <s>That this is &longs;o will appearby <lb/>comparing the Contents I here prefix with the Adverti&longs;ment I formerly Printed. </s> <s>For not to mention tho&longs;e Epitomes <lb/>of<emph.end type="italics"/> Kepler <emph type="italics"/>and<emph.end type="italics"/> à Stunica, <emph type="italics"/>the whole &longs;econd and following Books of<emph.end type="italics"/> Ca&longs;tclli, <emph type="italics"/>were not come to my hands at the time of <lb/>my penning that Paper; yet knowing how imperfect the Volume would be without them, they being partly a &longs;up­<lb/>plement to the Theoremes and Problemes which the Abbot had formerly Printed, and partly experiments that <lb/>had procured him and his Doctrine a very great Reputation, knowing this I &longs;ay, I apprehended a nece&longs;&longs;ity of pu­<lb/>bli&longs;hing them with the re&longs;t: and hope that if you think not the &longs;ervice I have done therein worth your acknowledge­<lb/>ment, you will yet at lea&longs;t account the encrea&longs;e of my expence a &longs;ufficient extenuation of the Tre&longs;pa&longs;s that tho&longs;e <lb/>Additions have forced me to commit upon your Patience in point of Time.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>As for the &longs;econd Tome, I have only this to a&longs;&longs;ure the Generous Readers; 1 that I am very confident I &longs;hall <lb/>be much more punctual in publi&longs;hing that, than (for the rea&longs;ons above related.) I was able to be in &longs;etting forth <lb/>this: 2 that they &longs;hall not be abu&longs;ed in advancing of their moneys, (as hath bin u&longs;ed in the like ca&longs;e) by &longs;elling <lb/>the remaining Copyes at an under rate; and 2 that I have a very great care that no di&longs;e&longs;teem may by my means a­<lb/>ri&longs;e unto this way of publi&longs;hing Books, for that it is of excellent u&longs;e in u&longs;hering Great and Co&longs;tly Volumes into <lb/>the World.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>To &longs;ay nothing of the di&longs;advantages of Tran&longs;lations in general, this of mine doubtle&longs;s is not without it's Er­<lb/>rours, and over&longs;ights: but tho&longs;e of the Printer di&longs;counted, I hope the re&longs;t may be allowed me upon the &longs;core of<emph.end type="italics"/> Hu­<lb/>man Imbecilitic. <emph type="italics"/>The truth is, I have a&longs;&longs;umed the Liberty to note the Mi&longs;takes in the Florid Ver&longs;ion of<emph.end type="italics"/> Bernegge­<lb/>rus <emph type="italics"/>in the Margent, not &longs;o much to reproach him, as to convince tho&longs;e who told me that they accounted my pains <lb/>needle&longs;s, having his Latine Tran&longs;lation by them. </s> <s>The like they &longs;aid of the whole two Tomes: but they thereby cau&longs;ed <lb/>me to question their Under&longs;tanding or Veracity. </s> <s>For &longs;ome of the Books were yet never extant: As for in&longs;tance; <lb/>the Mcchanicks of Mon&longs;ieur<emph.end type="italics"/> Des Cartes, <emph type="italics"/>a Manu&longs;cript which I found among&longs;t the many other Rarities that en­<lb/>rich the well-cho&longs;en Library of my Learned and Worthy Friend Dr.<emph.end type="italics"/> Charles Scarburgh; <emph type="italics"/>the Experiments of Gra­<lb/>vity, and the Life of<emph.end type="italics"/> Galileo, <emph type="italics"/>both my own: Others were included in Volumes of great price, or &longs;o di&longs;per&longs;ed that <lb/>they were not to be purcha&longs;ed for any money; as tho&longs;e of<emph.end type="italics"/> Kepler, à Stunica, Archimedes, Tartaglia, <emph type="italics"/>and the Mecha­<lb/>nicks of<emph.end type="italics"/> Galileo: <emph type="italics"/>And the remainder, though ea&longs;yer to procure, were harder to be under&longs;tood; as<emph.end type="italics"/> Tartaglia <emph type="italics"/>his notes <lb/>on<emph.end type="italics"/> Archimedes, Torricellio <emph type="italics"/>his Doctrine of Projects,<emph.end type="italics"/> Galileo <emph type="italics"/>his Epi&longs;tle to the Dutche&longs;&longs;e of<emph.end type="italics"/> Tu&longs;cany, <emph type="italics"/>and above all <lb/>his Dialogues<emph.end type="italics"/> de Motu; <emph type="italics"/>(never till now done into any Language) which were &longs;o intermixt of Latine and Italian, <lb/>that the difficulty of the Stile, joyned with the intricatne&longs;&longs;e of the Subject rendered them Unplea&longs;ant, if not wholly <lb/>Vnintelligible, to &longs;uch as were not ab&longs;olute Ma&longs;ters of both the Tongues.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>To conclude; according to the entertainment that you plea&longs;e to afford the&longs;e Collections, I &longs;hall be encouraged to <lb/>proceed with the Publication of a large Body of Hydrography; declaring the Hi&longs;tory, Art, Lawes, and Apendages <lb/>of that Princely Study of Navigation, wherein I have omitted nothing of note that can be found either in<emph.end type="italics"/> Dud­<lb/>ley, Fournier, Aurigarius, Nonius, Snellus, Mar&longs;ennus, Bay&longs;ius, Mori&longs;etus, Blondus, Wagoner, <emph type="italics"/>abroad, or learnt <lb/>amongst our Mariners at home, touching the Office of an Admiral, Commander, Pilot, Modelli&longs;t, Shipwright, <lb/>Gunner, &c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>But order requiring that I &longs;hould di&longs;charge my fir&longs;t Obligation before I contract a &longs;econd; I &longs;hall detein you no <lb/>longer in the Portall, but put you into po&longs;&longs;e&longs;&longs;ion of the Premi&longs;es,<emph.end type="italics"/></s></p><p type="main"> <s>Novemb. </s> <s>20, 1661.</s></p><p type="main"> <s><emph type="italics"/>T. S.<emph.end type="italics"/></s></p><pb xlink:href="040/01/009.jpg"/></section><section><p type="head"> <s>The CONTENTS of the FIRST <lb/>TOME.</s></p><p type="head"> <s>PART THE FIRST.</s></p><p type="main"> <s><arrow.to.target n="marg1"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1"></margin.target><emph type="italics"/>Treati&longs;e<emph.end type="italics"/></s></p><p type="main"> <s>I. GALILEUS GALILEUS, his SYSIEME of the WORLD: in Four DIALOGUES.</s></p><p type="main"> <s>II. HIS EPISTLE to her SERENE HIGHNESSE CHRISTIANA LOTHERINGA <lb/>GRAND DUTCHESSE of TUSCANY, touching the Ancient and Modern <lb/>DOCTRINE of HOLY FATHERS, and JUDICIOUS DIVINES, concerning <lb/>the AUTHORITY of SACRED SCRIPTURE in PHYLOSOPHICAL <lb/>CONTROVERSIES.</s></p><p type="main"> <s>III. JOHANNES KEPLERUS, his RECONCILINGS of TEXTS of SACRED <lb/>SCRIPTURE that &longs;eem to oppo&longs;e the DOCTRINE of the EARTHS MOBILI­<lb/>TY: ab&longs;tracted from his INTRODUCTION unto his LEARNED COMMEN­<lb/>TARIES upon the PLANET MARS.</s></p><p type="main"> <s>IV. DIDACUS A STUNICA, a learned SPANISH DIVINE, his RECONCILINGS of <lb/>the &longs;aid DOCTRINE with the TEXTS of SACRED SCRIPTURE; ab&longs;tracted <lb/>from his COMMENTARIE upon JOB.</s></p><p type="main"> <s>V. PAULUS ANTONIUS FOSCARINUS, a CARMELITE, his EPISTLE to <lb/>SEBASTIANUS FANTONUS, the GENERAL of his ORDER, concerning <lb/>the PYTHAGOREAN and COPERNICAN OPINION of the MOBILITY OF <lb/>THE EARTH, and STABILITY OF THE SUN; and of the NEW SYSTEME <lb/>or CONSTITUTION of the WORLD: in which he reconcileth the TEXTS <lb/>OF SACRED SCRIPTURE, and ASSERTIONS of DIVINES, commonly <lb/>alledged against this OPINION.</s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/> Table <emph type="italics"/>of the most ob&longs;ervable<emph.end type="italics"/> Per&longs;ons <emph type="italics"/>and<emph.end type="italics"/> Matters <emph type="italics"/>mentioned in the<emph.end type="italics"/> Fir&longs;t Part.</s></p><p type="head"> <s>PART THE SECOND.</s></p><p type="main"> <s>I. D. BENEDICTUS CASTELLUS, ABBOT OF S. BENEDICTUS ALOYSIUS, his <lb/>DISCOURSE of the MENSURATION OF RUNNING WATERS: The Fir&longs;t <lb/>BOOK.</s></p><p type="main"> <s>II. HIS LETTER to GALILEUS, repre&longs;enting the &longs;tate of the Lake of PERUGIA in <lb/>TUSCANY.</s></p><p type="main"> <s>III. HIS GEOMETRICAL DEMONSTRATIONS of the MEASURE of RUNNING <lb/>WATERS.</s></p><p type="main"> <s>IV. HIS DISCOURSE of the MENSURATION OF RUNNING WATERS: The Second <lb/>BOOK.</s></p><p type="main"> <s>V. HIS CONSIDERATIONS concerning the LAKE OF VENICE. </s> <s>In two DISCOURSES.</s></p><p type="main"> <s>VI. HIS RULE for computing the quantity of MUD and SAND that LAND-FLOODS bring <lb/>down to, and leave in the LAKE of VENICE.</s></p><p type="main"> <s>VII. HIS LETTER to Father FRANCESCO DI S. GIVSEPPE, wherein, at the in&longs;tance <lb/>of PRINCE LEOPALDO, he delivereth his judgment concerning the turning <lb/>FIUME MORTO (a River near PISA in TUSCANY) into the SEA, and into <lb/>the River SERCHIO.</s></p><p type="main"> <s>VIII. HIS &longs;econd LETTER in anfwer to certain OBJECTIONS propo&longs;ed, and DIFFICUL­<lb/>TIES ob&longs;erved by SIGNORE BARTOLOTTI, in that affair of the <lb/>DIVERSION of FIUME MORTO.</s></p><p type="main"> <s>IX. HIS CONSIDERATION upon the DRAINING of the PONTINE FENNS in CALA­<lb/>BRIA.</s></p><p type="main"> <s>X. HIS CONSIDERATION upon the DRAINING of the TERRITORIES of BOLOG­<lb/>NA, FERRARA, and ROMAGNA.</s></p><p type="main"> <s>XI. HIS LETTER to D. FERRANTE CESARINI, applying his DOCTRINE to the <lb/>MENSURATION of the LENGTH, and DISTRIBUTION of the QUANTITY <lb/>of the WATERS of RIVERS, SPRINGS, AQUEDUCTS, &c.</s></p><p type="main"> <s>XII. D. CORSINUS, SUPERINTENDENT of the GENERAL DRAINS and PRESIDENT <lb/>of ROMAGNA, his RELATION of the &longs;tate of the WATERS in the <lb/>TERRITORIES of BOLOGNA and FERRARA.</s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/> Table <emph type="italics"/>of the mo&longs;t ob&longs;ervable<emph.end type="italics"/> Per&longs;ons <emph type="italics"/>and<emph.end type="italics"/> Matters <emph type="italics"/>mentioned in the<emph.end type="italics"/> Second Part.</s></p><pb xlink:href="040/01/010.jpg"/><p type="head"> <s>The CONTENTS of the SECOND <lb/>TOME,</s></p><p type="head"> <s>PART THE FIRST.</s></p><p type="main"> <s><arrow.to.target n="marg2"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg2"></margin.target><emph type="italics"/>Treati&longs;e<emph.end type="italics"/></s></p><p type="main"> <s>I. GALILEUS GALILEUS, his MATHEMATICAL DISCOURSES and DEMON­<lb/>STRATIOMS touching two NEVV SCIENCES, pertaining to the MECHA­<lb/>NICKS, and LOCAL MOTION: with an APPENDIX of the CENTRE of <lb/>GRAVITY of &longs;ome SOLIDS in Four DIALOGUES.</s></p><p type="main"> <s>II. HIS MECHANICKS; a New PEICE.</s></p><p type="main"> <s>III. RHENATUS DES CARTES, his MECHANICKS; tran&longs;lated from his FRENCM <lb/>MANUSCRIPT; a New PEICE.</s></p><p type="main"> <s>IV. ARCHIMEDES, his Tract DE INSIDENTIBUS HUMIDO; with the NOTES and <lb/>DEMONSTRASIONS of NICOLAUS TARTALEUS, in Two BOOKS.</s></p><p type="main"> <s>V. GALILEUS his DISCOURSE of the things that move in or upon the WATER.</s></p><p type="main"> <s>VI. NICOLAUS TARTALEUS his INVENTIONS for DIVING UNDER WATER, <lb/>RAISING OF SHIPS SUNK, &c. </s> <s>in Two BOOKS.</s></p><p type="head"> <s>PART THE SECOND.</s></p><p type="main"> <s>I. EVANGELISTA TORRICELLIUS, his DOCTRINE OF PROJECTS, and TABLES <lb/>of the RANGES of GREAT GUNNS of all &longs;orts; wherein he detects &longs;undry <lb/>ERRORS in GUNNERY: An EPITOME.</s></p><p type="main"> <s>II T. S. his EXPERIMENTS of the COMPARATIVE GRAVITY OF BODIES in the <lb/>AIRE and WATER.</s></p><p type="main"> <s>III. GALILEUS GALILEUS, his LIFE: in Five BOOKS,</s></p><p type="main"> <s>BOOK I. </s> <s>Containing Five Chapters.</s></p><p type="main"> <s><emph type="italics"/>Chap.<emph.end type="italics"/> 1. His Country.</s></p><p type="main"> <s>2. His Parents and Extraction.</s></p><p type="main"> <s>3. His time of Birth.</s></p><p type="main"> <s>4. His fir&longs;t Education.</s></p><p type="main"> <s>5. His Ma&longs;ters.</s></p><p type="main"> <s>II. </s> <s>Containing Three Chapters.</s></p><p type="main"> <s><emph type="italics"/>Chap.<emph.end type="italics"/> 1. His judgment in &longs;everal Learnings.</s></p><p type="main"> <s>2. His Opinions and Doctrine.</s></p><p type="main"> <s>3. His Auditors and Scholars.</s></p><p type="main"> <s>III. </s> <s>Containing Four Chapters.</s></p><p type="main"> <s><emph type="italics"/>Chap.<emph.end type="italics"/> 1. His behaviour in Civil Affairs.</s></p><p type="main"> <s>2. His manner of Living.</s></p><p type="main"> <s>3. His morall Virtues.</s></p><p type="main"> <s>4. His misfortunes and troubles.</s></p><p type="main"> <s>IV. </s> <s>Containing Four Chapters.</s></p><p type="main"> <s><emph type="italics"/>Chap.<emph.end type="italics"/> 1. His per&longs;on de&longs;cribed.</s></p><p type="main"> <s>2. His Will and Death.</s></p><p type="main"> <s>3. His Inventions.</s></p><p type="main"> <s>4. His Writings.</s></p><p type="main"> <s>5. His Dialogues of the Sy&longs;teme in particular, containing <emph type="italics"/>Nine Sections.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Section<emph.end type="italics"/> 1. Of A&longs;tronomy in General; its Definition, Prai&longs;e, Original.</s></p><p type="main"> <s>2. Of A&longs;tronomers: a Chronological Catalogue of the <lb/>mo&longs;t famous of them.</s></p><p type="main"> <s>3. Of the Doctrine of the Earths Mobility, <emph type="italics"/>&c.<emph.end type="italics"/> its Antiquity, <lb/>and Progre&longs;&longs;e from <emph type="italics"/>Pythagoras<emph.end type="italics"/> to the time of <emph type="italics"/>Copernicus.<emph.end type="italics"/></s></p><p type="main"> <s>4. Of the Followers of <emph type="italics"/>Copernicus,<emph.end type="italics"/> unto the time of <emph type="italics"/>Galileus.<emph.end type="italics"/></s></p><p type="main"> <s>5. Of the &longs;everall Sy&longs;temes among&longs;t A&longs;tronomers.</s></p><p type="main"> <s>6. Of the Allegations again&longs;t the <emph type="italics"/>Copern.<emph.end type="italics"/> Sy&longs;teme, in 77 <lb/>Arguments taken out of <emph type="italics"/>Ricciolo,<emph.end type="italics"/> with An&longs;wers to them.</s></p><p type="main"> <s>7. Of the Allegations for the <emph type="italics"/>Copern.<emph.end type="italics"/> Sy&longs;teme in so Arguments.</s></p><p type="main"> <s>8. Of the Scriptures Authorities produced again&longs;t and for the <lb/>Earths mobility.</s></p><p type="main"> <s>9. The Conclu&longs;ion of the whole Chapter.</s></p><p type="main"> <s>V. </s> <s>Containing Four Chapters.</s></p><p type="main"> <s><emph type="italics"/>Chap.<emph.end type="italics"/> 1. His Patrons, Friends, and Emulators.</s></p><p type="main"> <s>2. Authors judgments of him.</s></p><p type="main"> <s>3. Authors that have writ for, or again&longs;t him.</s></p><p type="main"> <s>4. A Conclu&longs;ion in certain Reflections upon his whole Life.</s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/> Table <emph type="italics"/>of the whole<emph.end type="italics"/> Second TOME.</s></p> </section> </front> <pb xlink:href="040/01/011.jpg"/> <body> <chap> <p type="head"> <s>THE <lb/> SYSTEME <lb/>OF THE <lb/>WORLD: <lb/>IN FOUR <lb/>DIALOGUES. <lb/></s><s>Wherein the Two <lb/>GRAND SYSTEMES</s></p><p type="head"><s>Of <emph type="italics"/>PTOLOMY<emph.end type="italics"/> and <emph type="italics"/>COPERNICUS<emph.end type="italics"/> <lb/>are largely di&longs;cour&longs;ed of:</s></p><p type="head"><s>And the <emph type="italics"/>REASONS,<emph.end type="italics"/> both <emph type="italics"/>Phylo&longs;ophical<emph.end type="italics"/> and <emph type="italics"/>Phy&longs;ical,<emph.end type="italics"/> <lb/>as well on the one &longs;ide as the other, <emph type="italics"/>impartially<emph.end type="italics"/> <lb/>and <emph type="italics"/>indefinitely<emph.end type="italics"/> propounded:</s></p><p type="head"><s>By <emph type="italics"/>GALILEUS GALILEUS LINCEUS,<emph.end type="italics"/> <lb/>A <emph type="italics"/>Gentleman<emph.end type="italics"/> of <emph type="italics"/>FLORENCE:<emph.end type="italics"/> Extraordinary <emph type="italics"/>Profe&longs;&longs;or<emph.end type="italics"/> of <lb/>the <emph type="italics"/>Mathematicks<emph.end type="italics"/> in the UNIVERSITY of <emph type="italics"/>PISA<emph.end type="italics"/>; and <lb/>Chief <emph type="italics"/>Mathematician<emph.end type="italics"/> to the GRAND DUKE of <emph type="italics"/>TVSCANY.<emph.end type="italics"/></s></p><p type="head"><s><emph type="italics"/>Ingli&longs;hed from the<emph.end type="italics"/> Original <emph type="italics"/>Italián<emph.end type="italics"/> Copy, <emph type="italics"/>by<emph.end type="italics"/> THOMAS SALUSBURY.</s></p><p type="head"><s>ALCINOUS, <lb/><foreign lang="greek">*dei_ d) e)leuge/rion ei)_nai th_| gnwmh_| r\n me/llonta filosofei_n.</foreign></s></p><p type="head"><s>SENECA, <lb/><emph type="italics"/>Inter nullos magis quam inter PHILOSOPHOS e&longs;&longs;e debet aqua LIBERTAS.<emph.end type="italics"/></s></p><p type="head"><s><emph type="italics"/>LONDON,<emph.end type="italics"/> <lb/>Printed by WILLIAM LEYBOURNE. MDCLXI.</s></p><pb xlink:href="040/01/012.jpg"/><pb xlink:href="040/01/013.jpg"/></chap><chap><p type="head"><s>To the mo&longs;t Serene Grand DUKE <lb/>OF <lb/>TUSCANY.</s></p><p type="main"><s>Though the difference between Men and other <lb/>living Creatures be very great, yet happly he that <lb/>&longs;hould &longs;ay that he could &longs;hew little le&longs;s between <lb/>Man and Man would not &longs;peak more than he <lb/>might prove. </s><s>What proportion doth one bear to <lb/>athou&longs;and? </s><s>and yet it is a common Proverb, <emph type="italics"/>One Man is <lb/>worth athou&longs;and, when as a thou&longs;and are not worth one.<emph.end type="italics"/> This difference <lb/>hath dependence upon the different abilities of their Intelle­ <lb/>ctuals; which I reduce to the being, or not being a Philo&longs;o­ <lb/>pher; in regard that Philo&longs;ophy as being the proper food of <lb/>&longs;uch as live by it, di&longs;tingui&longs;heth a Man from the common E&longs;­ <lb/>&longs;ence of the Vulgar in a more or le&longs;s honourable degree accord­ <lb/>ing to the variety of that diet. </s><s>In this &longs;ence he that hath the <lb/>highe&longs;t looks, is of highe&longs;t quality; and the turning over of <lb/>the great Volume of Nature, which is the proper Object of <lb/>Philo&longs;ophy is the way to make one look high: in which Book, <lb/>although what&longs;oever we read, as being the Work of Al­ <lb/>mighty God, is therefore mo&longs;t proportionate; yet notwith­ <lb/>&longs;tanding that is more ab&longs;olute and noble wherein we more <lb/>plainly de&longs;erne his art and skill. </s><s>The <emph type="italics"/>Con&longs;titution<emph.end type="italics"/> of the <emph type="italics"/>Vnivers,<emph.end type="italics"/> <lb/>among all Phy&longs;ical points that fall within Humane Compre­ <lb/>hen&longs;ion, may, in my opinion, be preferred to the Precedency: <lb/>for if that in regard of univer&longs;al extent it excell all others, it <lb/>ought as the Rule and Standard of the re&longs;t to goe before <lb/>them in Nobility. </s><s>Now if ever any per&longs;ons might challenge <lb/>to be &longs;ignally di&longs;tingui&longs;hed for Intellectuals from other men; <pb xlink:href="040/01/014.jpg"/><emph type="italics"/>Ptolomey<emph.end type="italics"/> and <emph type="italics"/>Copernicus<emph.end type="italics"/> were they that have had the honour to <lb/>&longs;ee farthe&longs;t into, and di&longs;cour&longs;e mo&longs;t profoundly of the <emph type="italics"/>Worlds <lb/>Sy&longs;teme.<emph.end type="italics"/> About the Works of which famous Men the&longs;e Dia­ <lb/>lous being chiefly conver&longs;ant, I conceived it my duty to De­ <lb/>dicate them only to <emph type="italics"/>Your Highne&longs;s.<emph.end type="italics"/> For laying all the weight <lb/>upon the&longs;e two, whom I hold to be the Able&longs;t Wits that <lb/>have left us their Works upon the&longs;e Subjects; to avoid a Sole­ <lb/>ci&longs;mein Manners, I was obliged to addre&longs;s them to Him, who <lb/>with me, is the Greate&longs;t of all Men, from whom they can re­ <lb/>ceive either Glory or Patrociny. </s><s>And if the&longs;e two per&longs;ons <lb/>have &longs;o farre illuminated my Under&longs;tanding as that this my <lb/>Book may in a great part be confe&longs;&longs;ed to belong to them, well <lb/>may it al&longs;o be acknowledged to belong to <emph type="italics"/>Your Highne&longs;s,<emph.end type="italics"/> unto <lb/>who&longs;e Bounteous Magnificence I owe the time and lea&longs;ure I <lb/>had to write it, as al&longs;o unto Your Powerful A&longs;&longs;i&longs;tance, (never <lb/>weary of honouring me) the means that at length I have had <lb/>to publi&longs;h it. </s><s>May <emph type="italics"/>Your Highne&longs;s<emph.end type="italics"/> therefore be plea&longs;ed to accept <lb/>of it according to Your accu&longs;tomed Goodne&longs;s; and if any <lb/>thing &longs;hall be found therein, that may be &longs;ub&longs;ervient towards <lb/>the information or &longs;atisfaction of tho&longs;e that are Lovers of <lb/>Truth; let them acknowledge it to be due to <emph type="italics"/>Your Self,<emph.end type="italics"/> who are <lb/>&longs;o expert in doing good, that Your Happy Dominion cannot <lb/>&longs;hew the man that is concerned in any of tho&longs;e general Cala­ <lb/>mities that di&longs;turb the World; &longs;o that Praying for Your Pro&longs;pe­ <lb/>rity, and continuance in this Your Pious and Laudable Cu­ <lb/>&longs;tome, I humbly ki&longs;s Your Hands;</s></p><p type="main"><s><emph type="italics"/>Your Mo&longs;t Serene Highne&longs;&longs;es<emph.end type="italics"/></s></p><p type="main"><s>Mo&longs;t Humble and mo&longs;t devoted</s></p><p type="main"><s>Servant and Subject</s></p><p type="main"><s>GALILEO GALILEI.</s></p></chap><chap><pb xlink:href="040/01/015.jpg"/><p type="head"><s>THE AUTHOR'S <lb/>INTRODUCTION.</s></p><p type="main"><s>Judicious Reader,</s></p><p type="main"><emph type="italics"/><s>There was publi&longs;hed &longs;ome years &longs;ince in<emph.end type="italics"/> Rome <emph type="italics"/>a &longs;alutiferous Edict, that, for <lb/>the obviating of the dangerous Scandals of the pre&longs;ent Age, impo&longs;ed a &longs;ea­ <lb/>&longs;onable Silence upon the Pythagorean Opinion of the Mobility of the Earth. <lb/></s><s>There want not &longs;uch as unadvi&longs;edly affirm, that that Decree was not the produ­ <lb/>ction of a &longs;ober Scrutiny, but of an ill informed Pa&longs;sion; & one may hear &longs;ome mut­ <lb/>ter that Con&longs;ultors altogether ignorant of A&longs;tronomical Ob&longs;ervations ought not <lb/>to clipp the Wings of Speculative Wits with ra&longs;h Prohibitions. </s><s>My zeale can­ <lb/>not keep &longs;ilence when I hear the&longs;e incon&longs;iderate complaints. </s><s>I thought fit, as being thoroughly ac­ <lb/>quainted with that prudent Determination, to appear openly upon the Theatre of the World as a Wit­ <lb/>ne&longs;s of the naked Truth. </s><s>I was at that time in<emph.end type="italics"/> Rome; <emph type="italics"/>and had not only the audiences, but applauds of <lb/>the mo&longs;t Eminent Prelates of that Court; nor was that Decree Publi&longs;hed without Previous Notice given <lb/>me thereof. </s><s>Therefore it is my re&longs;olution in the pre&longs;ent ca&longs;e to give Foraign Nations to &longs;ee that this <lb/>point is as well under stood in<emph.end type="italics"/> Italy, <emph type="italics"/>and particularly in<emph.end type="italics"/> Rome, <emph type="italics"/>as Tran&longs;alpine Diligence can imagine <lb/>it to be: and collecting together all the proper Speculations that concern the<emph.end type="italics"/> Copernican Sy&longs;teme, <lb/><emph type="italics"/>to let them know, that the notice of all preceded the Cen&longs;ure of the<emph.end type="italics"/> Roman Court; <emph type="italics"/>and that there <lb/>proceed from this Climate not only Doctrines for the health of the Soul, but al&longs;o ingenious Di&longs;coveries <lb/>for the recreating of the Mind.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>To this end I have per&longs;onated the<emph.end type="italics"/> Copernican <emph type="italics"/>in this Di&longs;cour&longs;e; proceeding upon an Hypothe&longs;is <lb/>purely Mathematical; &longs;triving by all artificial wayes to repre&longs;ent it Superiour, not to that of the Im­ <lb/>mobility of the Earth ab&longs;olutely, but according as it is mentioned by &longs;ome, that retein no more, but the <lb/>name of<emph.end type="italics"/> Peripateticks, <emph type="italics"/>and are content, without going farther, to adore Shadows, not philo&longs;ophizing <lb/>with requi&longs;it caution, but with the &longs;ole remembrance of four<emph.end type="italics"/> Principles, <emph type="italics"/>but badly under &longs;tood.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>We &longs;hall treat of three principall heads. </s><s>Fir&longs;t I will endeavour to &longs;hew that all Experiments that can <lb/>be made upon the Earth are in&longs;ufficient means to conclude it's Mobility, but are indifferently applicable <lb/>to the Earth moveable or immoveable: and I hope that on this occa&longs;ion we &longs;hall di&longs;cover many ob&longs;er­ <lb/>vable pa&longs;&longs;ages unknown to the Ancients. </s><s>Secondly we will examine the Cœle&longs;tiall<emph.end type="italics"/> Phœnomena <lb/><emph type="italics"/>that make for the<emph.end type="italics"/> Copernican Hypothe&longs;is, <emph type="italics"/>as if it were to prove ab&longs;olutely victorious; adding by the <lb/>way certain new Ob&longs;ervations, which yet &longs;erve only for the A&longs;tronomical Facility, not for Natural <lb/>Neceßity. </s><s>In the third place I will propo&longs;e an ingenuous Fancy. </s><s>I remember that I have &longs;aid many <lb/>years &longs;ince, that the unknown Probleme of the Tide might receive &longs;ome light, admitting the Earths <lb/>Motion. </s><s>This Po&longs;ition of mine pa&longs;sing from one to another had found charitable Fathers that <lb/>adopted it for the I&longs;&longs;ue of their own wit. </s><s>Now, becau&longs;e no &longs;tranger may ever appear that defending him­ <lb/>&longs;elf with our armes &longs;hall charge us with want of caution in &longs;o principal an Accident, I have thought <lb/>good to lay down tho&longs;e probabilities that would render it credible, admitting that the Earth did <lb/>move. </s><s>I hope, that by the&longs;e Con&longs;ider ations the World will come to know, that if other Nations have <lb/>Navigated more than we, we have not &longs;tudied le&longs;s than they; & that our returning to a&longs;&longs;ert the Earths <lb/>Stability, and to take the contrary only for a Mathematical<emph.end type="italics"/> Capriccio, <emph type="italics"/>proceeds not from inadvertency <lb/>of what others have thought thereof, but (had we no other inducements) from tho&longs;e Rea&longs;ons that Pic­ <lb/>ty, Religion, the Knowledge of the Divine Omnipotency, and a con&longs;ciou&longs;ne&longs;s of the incapacity of mans <lb/>Vnder&longs;tanding dictate unto us.<emph.end type="italics"/></s></p><pb xlink:href="040/01/016.jpg"/><p type="main"><s><emph type="italics"/>With all I conceived it very proper to expre&longs;s the&longs;e conceits by way of Dialogue, which, as not being <lb/>bound up to the riggid ob&longs;ervance of Mathematical Laws, gives place al&longs;o to Digre&longs;sions that are <lb/>&longs;ometimes no le&longs;s curious than the principal Argument.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>I chanced to be &longs;everal years &longs;ince, at &longs;everal times, in the Stupendious Citty of<emph.end type="italics"/> Venice, <emph type="italics"/>where I <lb/>conver&longs;ed with<emph.end type="italics"/> Signore Giovan France&longs;co Sagredo <emph type="italics"/>of a Noble Extraction, and piercing wit. </s><s>There <lb/>came thither from<emph.end type="italics"/> Florence <emph type="italics"/>at the &longs;ame time<emph.end type="italics"/> Signore Filippo Salviati, <emph type="italics"/>who&longs;e lea&longs;t glory was the Emi­ <lb/>nence of his Blood, and Magnificence of his E&longs;tate: a &longs;ublime Wit that fed not more hungerly upon <lb/>any plea&longs;ure than on elevated Speculations. </s><s>In the company of the&longs;e two I often di&longs;cour&longs;ed of the&longs;e <lb/>matters before a certain Peripatetick Philo&longs;opher who &longs;eemed to have no geater ob&longs;tacle in under&longs;tand­ <lb/>ing of the Truth, than the Fame he had acquired by Ari&longs;totelical Interpretations.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>Now, &longs;eeing that inexorable Death hath deprived<emph.end type="italics"/> Venice <emph type="italics"/>and<emph.end type="italics"/> Florence <emph type="italics"/>of tho&longs;e two great Lights in <lb/>the very Meridian of their years, I did re&longs;olve, as far as my poor ability would permit, to perpetuate <lb/>their lives to their honour in the&longs;e leaves, bringing them in as Interlocutors in the pre&longs;ent Controver&longs;y. <lb/></s><s>Nor &longs;hall the Honest Peripatetick want his place, to whom for his exce&longs;sive affection to wards the Com­ <lb/>mentaries of<emph.end type="italics"/> Simplicius, <emph type="italics"/>I thought fit, without mentioning his own Name, to leave that of the Author <lb/>he &longs;o much re&longs;pected. </s><s>Let tho&longs;e two great Souls, ever venerable to my heart, plea&longs;e to accept this pu­ <lb/>blick Monument of my never dying Love; and let the remembr ance of their Eloquence a&longs;si&longs;t me in <lb/>delivering to Po&longs;terity the Con&longs;ider ations that I have promi&longs;ed.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>There ca&longs;ually happened (as was u&longs;uall) &longs;everal di&longs;cour&longs;es at times between the&longs;e Gentlemen, the <lb/>which had rather inflamed than &longs;atisfied in their wits the thir&longs;t they had to be learning; whereupon <lb/>they took a di&longs;creet re&longs;olution to meet together for certain dayes, in which all other bu&longs;ine&longs;s &longs;et a&longs;ide, <lb/>they might betake them&longs;elves more methodically to contemplate the Wonders of God in Heaven, and in <lb/>the Earth: the place appointed for their meeting being in the Palace of the Noble<emph.end type="italics"/> Sagredo, <emph type="italics"/>after the <lb/>due, but very &longs;hort complements<emph.end type="italics"/>; Signore Salviati <emph type="italics"/>began in this manner.<emph.end type="italics"/></s></p></chap> <chap> <pb xlink:href="040/01/017.jpg" pagenum="1"/><p type="head"><s>GALILÆUS <lb/>Galilæus Lyncæus, <lb/>HIS <lb/>SYSTEME <lb/>OF THE <lb/>WORLD.</s></p> <p type="head"><s>The Fir&longs;t Dialogue.</s></p><p type="head"><s><emph type="italics"/>INTERLOCVTORS.<emph.end type="italics"/></s></p><p type="head"><s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="head"><s>SALVIATUS.</s></p><p type="main"><s>It was our ye&longs;terdayes re&longs;olution, and a­ <lb/>greement, that we &longs;hould to day di&longs;cour&longs;e <lb/>the mo&longs;t di&longs;tinctly, and particularly we <lb/>could po&longs;&longs;ible, of the natural rea&longs;ons, and <lb/>their efficacy that have been hitherto al­ <lb/>ledged on the one or other part, by the <lb/>maintainers of the Po&longs;itions, <emph type="italics"/>Aristotelian,<emph.end type="italics"/> <lb/>and <emph type="italics"/>Ptolomaique<emph.end type="italics"/>; and by the followers </s></p><p type="main"><s><arrow.to.target n="marg3"></arrow.to.target> <lb/>of the <emph type="italics"/>Copernican Sy&longs;teme<emph.end type="italics"/>: And becau&longs;e <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> placing the Earth among the moveable Bodies of Hea­ <lb/>ven, comes to con&longs;titute a Globe for the &longs;ame like to a Planet; it <lb/>would be good that we began our di&longs;putation with the examina­ <lb/>tion of what, and how great the energy of the <emph type="italics"/>Peripateticks<emph.end type="italics"/> ar­ <lb/>guments is, when they demon&longs;trate, that this <emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> is impo&longs;­ <pb xlink:href="040/01/018.jpg" pagenum="2"/>&longs;ible: Since that it is nece&longs;&longs;ary to introduce in Nature, &longs;ub&longs;tances <lb/><arrow.to.target n="marg4"></arrow.to.target> <lb/>different betwixt them&longs;elves, that is, the Cœle&longs;tial, and Elementa­ <lb/>ry; that impa&longs;&longs;ible and immortal, this alterable and corruptible. <lb/></s><s>Which argument <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> handleth in his book <emph type="italics"/>De Cœlo,<emph.end type="italics"/> in&longs;inu­ <lb/>ating it fir&longs;t, by &longs;ome di&longs;cour&longs;es dependent on certain general a&longs;­ <lb/>&longs;umptions, and afterwards confirming it with experiments and per­ <lb/>ticular demon&longs;trations: following the &longs;ame method, I will pro­ <lb/>pound, and freely &longs;peak my judgement, &longs;ubmitting my &longs;elf to <lb/>your cen&longs;ure, and particularly to <emph type="italics"/>Simplicius,<emph.end type="italics"/> a Stout Champion <lb/>and contender for the <emph type="italics"/>Ari&longs;totelian<emph.end type="italics"/> Doctrine. <lb/><arrow.to.target n="marg5"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg3"></margin.target>Copernicus <emph type="italics"/>repu­ <lb/>teth the earth œ <lb/>Globe like to a Pla­ <lb/>net.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg4"></margin.target><emph type="italics"/>Cœle&longs;tial &longs;ub&longs;tan­ <lb/>ces that are inalte­ <lb/>rable, and Elemen­ <lb/>tary that be alte­ <lb/>rable, are nece&longs;&longs;ary <lb/>in the opinion of<emph.end type="italics"/> <lb/>Ari&longs;totle.</s></p><p type="margin"><s><margin.target id="marg5"></margin.target>Ari&longs;totle <emph type="italics"/>maketh <lb/>the World perfect, <lb/>becau&longs;e it hath the <lb/>threefold demen&longs;i­ <lb/>on.<emph.end type="italics"/></s></p><p type="main"><s>And the fir&longs;t Step of the <emph type="italics"/>Peripatetick<emph.end type="italics"/> arguments is that, where <emph type="italics"/>A­ <lb/>ri&longs;totle<emph.end type="italics"/> proveth the integrity and perfection of the World, telling <lb/>us, that it is not a &longs;imple line, nor a bare &longs;uperficies, but a body <lb/>adorned with Longitude, Latitude, and Profundity; and becau&longs;e <lb/>there are no more dimen&longs;ions but the&longs;e three; The World having <lb/>them, hath all, and having all, is to be concluded perfect. </s><s>And <lb/>again, that by &longs;imple length, that magnitude is con&longs;tituted, which <lb/>is called a Line, to which adding breadth, there is framed the Su­ <lb/>perficies, and yet further adding the altitude or profoundity, there <lb/>re&longs;ults the Body, and after the&longs;e three dimen&longs;ions there is no <lb/>pa&longs;&longs;ing farther, &longs;o that in the&longs;e three the integrity, and to &longs;o &longs;peak, <lb/>totality is terminated, which I might but with ju&longs;tice have requi­ <lb/>red <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> to have proved to me by nece&longs;&longs;ary con&longs;equences, the <lb/>rather in regard he was able to do it very plainly, and &longs;peedily.</s></p><p type="main"><s>SIMPL. </s><s>What &longs;ay you to the excellent demon&longs;trations in the </s></p><p type="main"><s><arrow.to.target n="marg6"></arrow.to.target> <lb/>2. 3. and 4. Texts, after the definition of <emph type="italics"/>Continual<emph.end type="italics"/>? </s><s>have you it <lb/>not fir&longs;t there proved, that there is no more but three dimen&longs;ions, <lb/>for that tho&longs;e three are all things, and that they are every where? <lb/></s><s>And is not this confirmed by the Doctrine and Authority of the <lb/><arrow.to.target n="marg7"></arrow.to.target> <lb/><emph type="italics"/>Pythagorians,<emph.end type="italics"/> who &longs;ay that all things are determined by three, be­ <lb/>ginning, middle, and end, which is the number of All? </s><s>And where <lb/>leave you that rea&longs;on, namely, that as it were by the law of Na­ <lb/>ture, this number is u&longs;ed in the &longs;acrifices of the Gods? </s><s>And why <lb/>being &longs;o dictated by nature, do we atribute to tho&longs;e things that <lb/>are three, and not to le&longs;&longs;e, the title of all? </s><s>why of two is it &longs;aid <lb/>both, and not all, unle&longs;s they be three? </s><s>And all this Doctrine you <lb/>have in the &longs;econd Text. </s><s>Afterwards in the third, <emph type="italics"/>Ad pleniorem<emph.end type="italics"/> <lb/><arrow.to.target n="marg8"></arrow.to.target> <lb/><emph type="italics"/>&longs;cientiam,<emph.end type="italics"/> we read that <emph type="italics"/>All,<emph.end type="italics"/> the <emph type="italics"/>Whole,<emph.end type="italics"/> and <emph type="italics"/>Perfect,<emph.end type="italics"/> are formally <lb/>one and the &longs;ame; and that therefore onely the <emph type="italics"/>Body,<emph.end type="italics"/> among&longs;t <lb/>magnitudes is perfect: becau&longs;e it is determined by three, which is <lb/>All, and being divi&longs;ible three manner of waies, it is every way di­ <lb/>vi&longs;ible; but of the others, &longs;ome are dividible in one manner, and <lb/>&longs;ome in two, becau&longs;e according to the number a&longs;&longs;ixed, they have <lb/>their divi&longs;ion and continuity, and thus one magnitude is continu­ <lb/><arrow.to.target n="marg9"></arrow.to.target> <lb/>ate one way, another two, a third, namely the Body, every way. <pb xlink:href="040/01/019.jpg" pagenum="3"/>Moreover in the fourth Text; doth he not after &longs;ome other Do­ <lb/>ctrines, prove it by another demon&longs;tration? <emph type="italics"/>Scilicet,<emph.end type="italics"/> That no tran­ <lb/>&longs;ition is made but according to &longs;ome defect (and &longs;o there is a tran­ <lb/>&longs;ition or pa&longs;&longs;ing from the line to the &longs;uperficies, becau&longs;e the line is <lb/>defective in breadth) and that it is impo&longs;&longs;ible for the perfect to <lb/>want any thing, it being every way &longs;o; therefore there is no tran­ <lb/>&longs;ition from the Solid or Body to any other magnitude. </s><s>Now <lb/>think you not that by all the&longs;e places he hath &longs;ufficiently proved, <lb/>how that there's no going beyond the three dimen&longs;ions, Length, <lb/>Breadth, and Thickne&longs;s, and that therefore the body or &longs;olid, <lb/>which hath them all, is perfect?</s></p><p type="margin"><s><margin.target id="marg6"></margin.target>Ari&longs;totles <emph type="italics"/>demon­ <lb/>&longs;trations to prove <lb/>the dimen&longs;ions to be <lb/>three and no more.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg7"></margin.target><emph type="italics"/>The number three <lb/>celebrated among &longs;t <lb/>the<emph.end type="italics"/> Pythagorians</s></p><p type="margin"><s><margin.target id="marg8"></margin.target>Omne, Totum & <lb/>Perfectum.</s></p><p type="margin"><s><margin.target id="marg9"></margin.target>Or Solid.</s></p><p type="main"><s>SALV. </s><s>To tell you true, I think not my &longs;elf bound by all the&longs;e <lb/>rea&longs;ons to grant any more but onely this, That that which hath <lb/>beginning, middle, and end, may, and ought to be called perfect: But <lb/>that then, becau&longs;e beginning, middle, and end, are Three, the num­ <lb/>ber Three is a perfect number, and hath a faculty of conferring <lb/><emph type="italics"/>Perfection<emph.end type="italics"/> on tho&longs;e things that have the &longs;ame, I find no inducement <lb/>to grant; neither do I under&longs;tand, nor believe that, for example, <lb/>of feet, the number three is more perfect then four or two, nor do <lb/>I conceive the number four to be any imperfection to the Ele­ <lb/>ments: and that they would be more perfect if they were three. <lb/></s><s>Better therefore it had been to have left the&longs;e &longs;ubtleties to the <lb/><emph type="italics"/>Rhetoricians,<emph.end type="italics"/> and to have proved his intent, by nece&longs;&longs;ary demon&longs;tra­ <lb/>tion; for &longs;o it behoves to do in demon&longs;trative &longs;ciences.</s></p><p type="main"><s>SIMPL. </s><s>You &longs;eem to &longs;corn the&longs;e rea&longs;ons, and yet it is all the <lb/>Doctrine of the <emph type="italics"/>Pythagorians,<emph.end type="italics"/> who attribute &longs;o much to numbers; <lb/>and you that be a <emph type="italics"/>Mathematician,<emph.end type="italics"/> and believe many opinions in <lb/>the <emph type="italics"/>Pythagorick<emph.end type="italics"/> Philo&longs;ophy, &longs;eem now to contemn their My­ <lb/>&longs;teries.</s></p><p type="main"><s>SALV. </s><s>That the <emph type="italics"/>Pythagorians<emph.end type="italics"/> had the &longs;cience of numbers in <lb/>high e&longs;teem, and that <emph type="italics"/>Plato<emph.end type="italics"/> him&longs;elf admired humane under&longs;tand­ <lb/>ing, and thought that it pertook of Divinity, for that it under­ <lb/><arrow.to.target n="marg10"></arrow.to.target> <lb/>&longs;tood the nature of numbers, I know very well, nor &longs;hould I be <lb/>far from being of the &longs;ame opinion: But that the My&longs;teries for <lb/>which <emph type="italics"/>Pythagoras<emph.end type="italics"/> and his &longs;ect, had the Science of numbers in &longs;uch <lb/>veneration, are the follies that abound in the mouths and writings <lb/><arrow.to.target n="marg11"></arrow.to.target> <lb/>of the vulgar, I no waies credit: but rather becau&longs;e I know that they, <lb/>to the end admirable things might not be expo&longs;ed to the con­ <lb/>tempt, and &longs;corne of the vulgar, cen&longs;ured as &longs;acrilegious, the pub­ <lb/><arrow.to.target n="marg12"></arrow.to.target> <lb/>li&longs;hing of the ab&longs;truce properties of Numbers, and incommen­ <lb/>&longs;urable and irrational quantities, by them inve&longs;tigated; and di­ <lb/>vulged, that he who di&longs;covered them, was tormented in the other <lb/>World: I believe that &longs;ome one of them to deter the common <lb/>&longs;ort, and free him&longs;elf from their inqui&longs;itivene&longs;s, told them that the <lb/>my&longs;teries of numbers were tho&longs;e trifles, which afterwards did &longs;o <pb xlink:href="040/01/020.jpg" pagenum="4"/>&longs;pread among&longs;t the vulgar; and this with a di&longs;cretion and &longs;ubtlety <lb/>re&longs;embling that of the prudent young man, that to be freed <lb/>from the importunity of his inqui&longs;itive Mother or Wife, I know <lb/>not whether, who pre&longs;&longs;ed him to impart the &longs;ecrets of the Senate, <lb/>contrived that &longs;tory, which afterwards brought her and many o­ <lb/>ther women to be derided and laught at by the &longs;ame Senate.</s></p><p type="margin"><s><margin.target id="marg10"></margin.target>Plato <emph type="italics"/>held that <lb/>humane under­ <lb/>&longs;tanding partook <lb/>of divinity, becau&longs;e <lb/>it understood num­ <lb/>bers.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg11"></margin.target><emph type="italics"/>The My&longs;tery of<emph.end type="italics"/> <lb/>Pythagorick <emph type="italics"/>num­ <lb/>bers fabulous.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg12"></margin.target>De Papyrio præ­ <lb/>textato, <emph type="italics"/>Gellius<emph.end type="italics"/> I: <lb/>2. 3.</s></p><p type="main"><s>SIMPL. </s><s>I will not be of the number of tho&longs;e who are over curi­ <lb/>ous about the <emph type="italics"/>Pythagorick<emph.end type="italics"/> my&longs;teries; but adhering to the point <lb/>in hand; I reply, that the rea&longs;ons produced by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> to prove <lb/>the dimen&longs;ions to be no more than three, &longs;eem to me conclu­ <lb/>dent, and I believe, That had there been any more evident demon­ <lb/>&longs;trations thereof, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> would not have omitted them.</s></p><p type="main"><s>SAGR. </s><s>Put in at lea&longs;t, if he had known, or remembred any more. <lb/></s><s>But you <emph type="italics"/>Salviatus<emph.end type="italics"/> would do me a great plea&longs;ure to alledge unto <lb/>me &longs;ome arguments that may be evident, and clear enough for me <lb/>to comprehend.</s></p><p type="main"><s>SALV. </s><s>I will; and they &longs;hall be &longs;uch as are not onely to be ap­ <lb/>prehended by you, but even by <emph type="italics"/>Simplicius<emph.end type="italics"/> him&longs;elf: nor onely <lb/>to be comprehended, but are al&longs;o already known, although hap­ <lb/>ly unob&longs;erved; and for the more ea&longs;ie under&longs;tanding thereof, <lb/>we will take this Pen and Ink, which I &longs;ee already prepared for <lb/><arrow.to.target n="marg13"></arrow.to.target> <lb/>&longs;uch occa&longs;ions, and de&longs;cribe a few figures. </s><s>And fir&longs;t we will note <lb/>[Fig. </s><s>1. <emph type="italics"/>at the end of this Dialog.<emph.end type="italics"/>] the&longs;e two points AB, and draw <lb/>from the one to the other the curved lines, ACB, and ADB, and the <lb/>right line A B, I demand of you which of them, in your mind, is <lb/>that which determines the di&longs;tance between the terms AB, & why?</s></p><p type="margin"><s><margin.target id="marg13"></margin.target><emph type="italics"/>A Geometrical de­ <lb/>mon&longs;tration of the <lb/>triple dimen&longs;ion.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>S<emph.end type="italics"/>AGR. </s><s>I &longs;hould &longs;ay the right line, and not the crooked, as well <lb/>becau&longs;e the right is &longs;horter, as becau&longs;e it is one, &longs;ole, and deter­ <lb/>minate, whereas the others are infinit, unequal, and longer; and my <lb/>determination is grounded upon that, That it is one, and certain.</s></p><p type="main"><s>SALV. </s><s>We have then the right line to determine the length be­ <lb/>tween the two terms; let us add another right line and parallel to <lb/>AB, which let be CD, [<emph type="italics"/>Fig.<emph.end type="italics"/> 2.] &longs;o that there is put between them a <lb/>&longs;uperficies, of which I de&longs;ire you to a&longs;&longs;ign me the breadth, therefore <lb/>departing from the point A, tell me how, and which way you will <lb/>go, to end in the line C D, and &longs;o to point me out the breadth com­ <lb/>prehended between tho&longs;e lines; let me know whether you will <lb/>terminate it according to the quantity of the curved line A E, or <lb/>the right line A F, or any other.</s></p><p type="main"><s>SIMPL. </s><s>According to the right A F, and not according to the <lb/>crooked, that being already excluded from &longs;uch an u&longs;e.</s></p><p type="main"><s>SAGR. </s><s>But I would take neither of them, &longs;eeing the right line <lb/>A F runs obliquely; But would draw a line, perpendicular to C <lb/>D, for this &longs;hould &longs;eem to me the &longs;horte&longs;t, and the propere&longs;t of <lb/>infinite that are greater, and unequal to one another, which may be <pb xlink:href="040/01/021.jpg" pagenum="5"/>produced from the term A to any other part of the oppo&longs;ite line <lb/>C D.</s></p><p type="main"><s>SALV. </s><s>Your choice, and the rea&longs;on you bring for it in my judg­ <lb/>ment is mo&longs;t excellent; &longs;o that by this time we have proved that <lb/>the fir&longs;t dimen&longs;ion is determined by a right line, the &longs;econd name­ <lb/>ly the breadth with another line right al&longs;o, and not onely right, <lb/>but withall, at right-angles to the other that determineth the <lb/>length, and thus we have the two dimen&longs;ions of length and <lb/>breadth, definite and certain. </s><s>But were you to bound or termi­ <lb/>nate a height, as for example, how high this Roof is from the pave­ <lb/>ment, that we tread on, being that from any point in the Roof, <lb/>we may draw infinite lines, both curved, and right, and all of di­ <lb/>ver&longs;e lengths to infinite points of the pavement, which of all the&longs;e <lb/>lines would you make u&longs;e of?</s></p><p type="main"><s>SAGR. </s><s>I would fa&longs;ten a line to the Seeling, and with a plummet <lb/>that &longs;hould hang at it, would let it freely di&longs;tend it &longs;elf till it <lb/>&longs;hould reach well near to the pavement, and the length of &longs;uch a <lb/>thread being the &longs;treighte&longs;t and &longs;horte&longs;t of all the lines, that could <lb/>po&longs;sibly be drawn from the &longs;ame point to the pavement, I would <lb/>&longs;ay was the true height of this Room.</s></p><p type="main"><s>SALV. </s><s>Very well, And when from the point noted in the pave­ <lb/>ment by this pendent thread (taking the pavement to be levell <lb/>and not declining) you &longs;hould produce two other right lines, one <lb/>for the length, and the other for the breadth of the &longs;uperficies of <lb/>the&longs;aid pavement, what angles &longs;hould they make with the &longs;aid <lb/>thread?</s></p><p type="main"><s>SAGR. </s><s>They would doubtle&longs;s meet at right angles, the &longs;aid <lb/>lines falling perpendicular, and the pavement being very plain and <lb/>levell.</s></p><p type="main"><s>SALV. </s><s>Therefore if you a&longs;&longs;ign any point, for the term from whence <lb/>to begin your mea&longs;ure; and from thence do draw a right line, as <lb/>the terminator of the fir&longs;t mea&longs;ure, namely of the length, it will <lb/>follow of nece&longs;&longs;ity, that that which is to de&longs;ign out the largene&longs;s <lb/>or breadth, toucheth the fir&longs;t at right-angles, and that that which is <lb/>to denote the altitude, which is the third dimen&longs;ion, going from the <lb/>&longs;ame point formeth al&longs;o with the other two, not oblique but right <lb/>angles, and thus by the three perpendiculars, as by three lines, one, <lb/>certain, and as &longs;hort as is po&longs;&longs;ible, you have the three dimen&longs;ions <lb/>A B length, A C breadth, and A D height; and becau&longs;e, clear it <lb/>is, that there cannot concurre any more lines in the &longs;aid point, &longs;o <lb/>as to make therewith right-angles, and the dimen&longs;ions ought to <lb/>be determined by the &longs;ole right lines, which make between them­ <lb/>&longs;elves right-angles; therefore the dimen&longs;ions are no more but <lb/>three, and that which hath three hath all, and that which hath all, <lb/>is divi&longs;ible on all &longs;ides, and that which is &longs;o, is perfect, <emph type="italics"/>&c.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/022.jpg" pagenum="6"/><p type="main"><s>SIMPL. </s><s>And who &longs;aith that I cannot draw other lines? </s><s>why <lb/>may not I protract another line underneath, unto the point A, <lb/>that may be perpendicular to the re&longs;t?</s></p><p type="main"><s>SALV. </s><s>You can doubtle&longs;s, at one and the &longs;ame point, make no <lb/>more than three right lines concurre, that con&longs;titute right angles <lb/>between them&longs;elves.</s></p><p type="main"><s>SAGR. </s><s>I &longs;ee what <emph type="italics"/>Simplicius<emph.end type="italics"/> means, namely, that &longs;hould the <lb/>&longs;aid D A be prolonged downward, then by that means there might <lb/>be drawn two others, but they would be the &longs;ame with the fir&longs;t <lb/>three, differing onely in this, that whereas now they onely touch, <lb/>then they would inter&longs;ect, but not produce new dimen&longs;ions. <lb/><arrow.to.target n="marg14"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg14"></margin.target><emph type="italics"/>In phyfical proofs <lb/>geometrical exact­ <lb/>ne&longs;s is not nece&longs;&longs;a­ <lb/>ry.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I will not &longs;ay that this your argument may not be con­ <lb/>cludent; but yet this I &longs;ay with <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that in things natural <lb/>it is not alwaies nece&longs;&longs;ary, to bring <emph type="italics"/>Mathematical<emph.end type="italics"/> demon&longs;trations.</s></p><p type="main"><s>SAGR. </s><s>Grant that it were &longs;o where &longs;uch proofs cannot be had, <lb/>yet if this ca&longs;e admit of them, why do not you u&longs;e them? </s><s>But it <lb/>would be good we &longs;pent no more words on this particular, for I <lb/>think that <emph type="italics"/>Salviatus<emph.end type="italics"/> will yield, both to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and you, with­ <lb/>out farther demon&longs;tration, that the World is a body, and perfect, <lb/>yea mo&longs;t perfect, as being the greate&longs;t work of God.</s></p><p type="main"><s>SALV. </s><s>So really it is, therefore leaving the general contempla­</s></p><p type="main"><s><arrow.to.target n="marg15"></arrow.to.target> <lb/>tion of the whole, let us de&longs;cend to the con&longs;ideration of its parts, <lb/>which <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> in his fir&longs;t divi&longs;ion, makes two, and they very diffe­ <lb/>rent and almo&longs;t contrary to one another; namely the Cœle&longs;tial, <lb/>and Elementary: that ingenerable, incorruptible, unalterable, un­ <lb/>pa&longs;&longs;ible, &c. </s><s>and this expo&longs;ed to a continual alteration, mutati­ <lb/>on, &c. </s><s>Which difference, as from its original principle, he de­ <lb/>rives from the diver&longs;ity of local motions, and in this method he <lb/>proceeds.</s></p><p type="margin"><s><margin.target id="marg15"></margin.target><emph type="italics"/>Parts of the world <lb/>are two, according <lb/>to<emph.end type="italics"/> Ari&longs;totle, <emph type="italics"/>Cœle­ <lb/>&longs;tial and Elemen­ <lb/>tary contrary to <lb/>one another.<emph.end type="italics"/></s></p><p type="main"><s>Leaving the &longs;en&longs;ible, if I may &longs;o &longs;peak, and retiring into the <lb/>Ideal world, he begins Architectonically to con&longs;ider that nature <lb/>being the principle of motion, it followeth that natural bodies be <lb/><arrow.to.target n="marg16"></arrow.to.target> <lb/>indued with local motion. </s><s>Next he declares local motion to be <lb/>of three kinds, namely, circular, right, and mixt of right and cir­ <lb/>cular: and the two fir&longs;t he calleth &longs;imple, for that of all lines the <lb/><arrow.to.target n="marg17"></arrow.to.target> <lb/>circular, and right are onely &longs;imple; and here &longs;omewhat re­ <lb/>&longs;training him&longs;elf, he defineth anew, of &longs;imple motions, one to be <lb/>circular, namely that which is made about the <emph type="italics"/>medium,<emph.end type="italics"/> and the <lb/>other namely the right, upwards, and downwards; upwards, that <lb/>which moveth from the <emph type="italics"/>medium<emph.end type="italics"/>; downwards, that which goeth to­ <lb/>wards the <emph type="italics"/>medium.<emph.end type="italics"/> And from hence he infers, as he may by and ne­ <lb/><arrow.to.target n="marg18"></arrow.to.target> <lb/>ce&longs;&longs;ary con&longs;equence, that all &longs;imple motions are confined to the&longs;e <lb/>three kinds, namely, to the <emph type="italics"/>medium,<emph.end type="italics"/> from the <emph type="italics"/>medium,<emph.end type="italics"/> and about <lb/>the <emph type="italics"/>medium<emph.end type="italics"/>; the which corre&longs;ponds &longs;aith he, with what hath been <lb/>&longs;aid before of a body, that it al&longs;o is perfected by three things, and &longs;o <pb xlink:href="040/01/023.jpg" pagenum="7"/>is its motion. </s><s>Having confirmed the&longs;e motions, he proceeds &longs;aying, <lb/>that of natural bodies &longs;ome being &longs;imple, and &longs;ome compo&longs;ed of <lb/>them (and he calleth &longs;imple bodies tho&longs;e, that have a principle <lb/>of motion from nature, as the Fire and Earth) it follows that <lb/>&longs;imple motions belong to &longs;imple bodies, and mixt to the com­ <lb/>pound; yet in &longs;uch &longs;ort, that the compounded incline to the part <lb/>predominant in the compo&longs;ition.</s></p><p type="margin"><s><margin.target id="marg16"></margin.target><emph type="italics"/>Local motion of <lb/>three kinds, right, <lb/>circular, & mixt.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg17"></margin.target><emph type="italics"/>Circular, and <lb/>&longs;treight motions <lb/>are &longs;imple, as pro­ <lb/>ceeding by &longs;imple <lb/>lines.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg18"></margin.target><emph type="italics"/>Ad medium, à me­ <lb/>dio, & circa medi­ <lb/>um.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Pray you hold a little <emph type="italics"/>Salviatus,<emph.end type="italics"/> for I find &longs;o many <lb/>doubts to &longs;pring up on all &longs;ides in this di&longs;cour&longs;e, that I &longs;hall be <lb/>con&longs;trained, either to communicate them if I would attentively <lb/>hearken to what you &longs;hall add, or to take off my attention from <lb/>the things &longs;poken, if I would remember objections.</s></p><p type="main"><s>SALV. </s><s>I will very willingly &longs;tay, for that I al&longs;o run the &longs;ame <lb/>hazard, and am ready at every &longs;tep to lo&longs;e my &longs;elf whil&longs;t I &longs;ail be­ <lb/>tween Rocks, and boi&longs;terous Waves, that make me, as they &longs;ay, to <lb/>lo&longs;e my <emph type="italics"/>Compa&longs;s<emph.end type="italics"/>; therefore before I make them more, propound <lb/>your difficulties. <lb/><arrow.to.target n="marg19"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg19"></margin.target><emph type="italics"/>The definition of <lb/>Nature, either im­ <lb/>perfect, or un&longs;ea&longs;o­ <lb/>nable, produced by<emph.end type="italics"/> <lb/>Ari&longs;totle.</s></p><p type="main"><s>SAGR. </s><s>You and <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> together would at fir&longs;t take me a <lb/>little out of the &longs;en&longs;ible World, to tell me of the <emph type="italics"/>Architecture,<emph.end type="italics"/> <lb/>wherewith it ought to be fabricated; and very appo&longs;itly begin to <lb/>tell me, that a natural body is by nature moveable, nature being <lb/>(as el&longs;ewhere it is defined) the principle of motion. </s><s>But here I <lb/>am &longs;omewhat doubtfull why <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aid not that of natural bo­ <lb/>dies, &longs;ome are moveable by nature, and others immoveable, for <lb/>that in the definition, nature is &longs;aid to be the principle of Motion, <lb/>and Re&longs;t; for if natural bodies have all a principle of motion, <lb/>either he might have omitted the mention of Re&longs;t, in the definiti­ <lb/>on of nature: or not have introduced &longs;uch a definition in this place. <lb/></s><s>Next, as to the declaration of what <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> intends by &longs;imple <lb/>motions, and how by Spaces he determines them, calling tho&longs;e &longs;im­ <lb/>ple, that are made by &longs;imple lines, which are onely the right, and </s></p><p type="main"><s><arrow.to.target n="marg20"></arrow.to.target> <lb/>circular, I entertain it willingly; nor do I de&longs;ire to tenter the <lb/>in&longs;tance of the Helix, about the Cylinder; which in that it is in e­ <lb/>very part like to it &longs;elf, might &longs;eemingly be numbred among &longs;im­ <lb/>ple lines. </s><s>But herein I cannot concurre, that he &longs;hould &longs;o re­ <lb/>&longs;train &longs;imple motions (whil&longs;t he &longs;eems to go about to repeat the <lb/>&longs;ame definition in other words) as to call one of them the motion <lb/>about the <emph type="italics"/>medium,<emph.end type="italics"/> the others <emph type="italics"/>Sur&longs;um & Deor&longs;um,<emph.end type="italics"/> namely up­ <lb/>wards and downward; which terms are not to be u&longs;ed, out of the <lb/>World fabricated, but imply it not onely made, but already in­ <lb/>habited by us; for if the right motion be &longs;imple, by the &longs;implicity <lb/>of the right line, and if the &longs;imple motion be natural, it is made on <lb/>every &longs;ide, to wit, upwards, downwards, backwards, forwards, to <lb/>the right, to the left, and if any other way can be imagined, pro­ <lb/>vided it be &longs;traight, it &longs;hall agree to any &longs;imple natural body; or <pb xlink:href="040/01/024.jpg" pagenum="8"/>if not &longs;o, then the &longs;uppo&longs;ion of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> is defective. </s><s>It appears <lb/><arrow.to.target n="marg21"></arrow.to.target> <lb/>moreover that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hinteth but one circular motion alone to <lb/>be in the World, and con&longs;equently but one onely Center, to <lb/>which alone the motions of upwards and downwards, refer. </s><s>All <lb/>which are apparent proofs, that <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> aim is, to make white <lb/>black, and to accommodate <emph type="italics"/>Architectur<emph.end type="italics"/> to the building, and not <lb/>to modle the building according to the precepts of <emph type="italics"/>Arthitecture:<emph.end type="italics"/> <lb/>for if I &longs;hould &longs;ay that Nature in Univer&longs;al may have a thou­ <lb/>&longs;and Circular Motions, and by con&longs;equence a thou&longs;and Cen­ <lb/>ters, there would be al&longs;o a thou&longs;and motions upwards, and <lb/>downwards. </s><s>Again he makes as hath been &longs;aid, a &longs;imple motion, <lb/>and a mixt motion, calling &longs;imple, the circular and right; and <lb/>mixt, the compound of them two: of natural bodies he calls &longs;ome <lb/>&longs;imple (namely tho&longs;e that have a natural principle to &longs;imple mo­ <lb/>tion) and others compound: and &longs;imple motions he attributes <lb/>to &longs;imple bodies, and the compounded to the compound; but by <lb/>compound motion he doth no longer under&longs;tand the mixt of right <lb/>and circular, which may be in the World; but introduceth a mixt <lb/>motion as impo&longs;&longs;ible, as it is impo&longs;&longs;ible to mixe oppo&longs;ite motions <lb/>made in the &longs;ame right line, &longs;o as to produce from them a motion <lb/>partly upwards, partly downwards; and, to moderate &longs;uch an ab­ <lb/>&longs;urdity, and impo&longs;&longs;ibility, he a&longs;&longs;erts that &longs;uch mixt bodies move <lb/><arrow.to.target n="marg22"></arrow.to.target> <lb/>according to the &longs;imple part predominant: which nece&longs;&longs;itates <lb/>others to &longs;ay, that even the motion made by the &longs;ame right line is <lb/>&longs;ometimes &longs;imple, and &longs;ometimes al&longs;o compound: &longs;o that the &longs;im­ <lb/>plicity of the motion, is no longer dependent onely on the &longs;im­ <lb/>plicity of the line.</s></p><p type="margin"><s><margin.target id="marg20"></margin.target><emph type="italics"/>The Helix about <lb/>the Cylinder may <lb/>be &longs;aid to be a &longs;im­ <lb/>ple line.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg21"></margin.target>Ari&longs;totle <emph type="italics"/>accom­ <lb/>modates the rules of<emph.end type="italics"/> <lb/>Architecture <emph type="italics"/>to <lb/>the frame of the <lb/>World, and not the <lb/>frame to the rules.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg22"></margin.target><emph type="italics"/>Right motion, &longs;ome­ <lb/>times &longs;imple, ard <lb/>&longs;ometimes mixt ac­ <lb/>cording to<emph.end type="italics"/> Ari&longs;t.</s></p><p type="main"><s>SIMPL. How? </s><s>Is it not difference &longs;ufficient, that the &longs;imple and <lb/>ab&longs;olute are more &longs;wift than that which proceeds from predomi­ <lb/>nion? </s><s>and how much fa&longs;ter doth a piece of pure Earth de&longs;cend, <lb/>than a piece of Wood?</s></p><p type="main"><s>SAGR. Well, <emph type="italics"/>Simplicius<emph.end type="italics"/>; But put ca&longs;e the &longs;implicity for this <lb/>cau&longs;e was changed, be&longs;ides that there would be a hundred thou­ <lb/>&longs;and mixt motions, you would not be able to determine the &longs;im­ <lb/>ple; nay farther, if the greater or le&longs;&longs;e velocity be able to alter <lb/>the &longs;implicity of the motion, no &longs;imple body &longs;hould move with a <lb/>&longs;imple motion; &longs;ince that in all natural right motions, the veloci­ <lb/>ty is ever encrea&longs;ing, and by con&longs;equence &longs;till changing the &longs;impli­ <lb/>city, which as it is &longs;implicity, ought of con&longs;equence to be immu­ <lb/>table, and that which more importeth, you charge <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> with <lb/>another thing, that in the definition of motions compounded, he <lb/>hath not made mention of tardity nor velocity, which you now <lb/>in&longs;ert for a nece&longs;&longs;ary and e&longs;&longs;ential point. </s><s>Again you can draw <lb/>no advantage from this rule, for that there will be among&longs;t the <lb/>mixt bodies &longs;ome, (and that not a few) that will move &longs;wiftly, <pb xlink:href="040/01/025.jpg" pagenum="9"/>and others more &longs;lowly than the &longs;imple; as for example, Lead, and <lb/>Wood, in compari&longs;on of earth; and therefore among&longs;t the&longs;e mo­ <lb/>tions, which call you the &longs;imple, and which the mixt?</s></p><p type="main"><s>SIMPL. </s><s>I would call that &longs;imple motion, which is made by a <lb/>&longs;imple body, and mixt, that of a compound body.</s></p><p type="main"><s>SAGR. </s><s>Very well, and yet <emph type="italics"/>Simplicius<emph.end type="italics"/> a little before you &longs;aid, <lb/>that the &longs;imple, and compound motions, di&longs;covered which were <lb/>mixt, and which were &longs;imple bodies; now you will have me by <lb/>&longs;imple and mixt bodies, come to know which is the &longs;imple, and <lb/>which is the compound motion: an excellent way to keep us igno­ <lb/>rant, both of motions and bodies. </s><s>Moreover you have al&longs;o a little <lb/>above declared, how that a greater velocity did not &longs;uffice, but <lb/>you &longs;eek a third condition for the definement of &longs;imple motion, for <lb/>which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> contented him&longs;elf with one alone, namely, of the <lb/>&longs;implicity of the Space, or <emph type="italics"/>Medium<emph.end type="italics"/>: But now according to you, <lb/>the &longs;imple motion, &longs;hall be that which is made upon a &longs;imple line, <lb/>with a certain determinate velocity, by a body &longs;imply moveable. <lb/></s><s>Now be it as you plea&longs;e, and let us return to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who defi­ <lb/>neth the mixt motion to be that compounded of the right, and cir­ <lb/>cular, but produceth not any body, which naturally moveth with <lb/>&longs;uch a motion.</s></p><p type="main"><s>SALV. </s><s>I come again to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who having very well, and <lb/>Methodically begun his di&longs;cour&longs;e, but having a greater aim to <lb/>re&longs;t at, and hit a marke, predefigned in his minde, then that to <lb/>which his method lead him, digre&longs;&longs;ing from the purpo&longs;e, he comes <lb/>to a&longs;&longs;ert, as a thing known and manife&longs;t, that as to the motions <lb/>directly upwards or downwards, they naturally agree to Fire, and <lb/>Earth; and that therefore it is nece&longs;&longs;ary, that be&longs;ides the&longs;e bodies, <lb/>which are neer unto us, there mu&longs;t be in nature another, to which <lb/>the circular motion may agree: which &longs;hall be &longs;o much the more <lb/>excellent by how much the circular motion is more perfect, then the <lb/>&longs;treight, but how much more perfect that is than this, he deter­ <lb/>mines from the greatne&longs;s of the circular lines perfection above the <lb/><arrow.to.target n="marg23"></arrow.to.target> <lb/>right line; calling that perfect, and this imperfect; imperfect, be­ <lb/>cau&longs;e if infinite it wanteth a termination, and end: and if it be fi­ <lb/>nite, there is yet &longs;omething beyond which it may be prolonged. <lb/></s><s>This is the ba&longs;is, ground work, and ma&longs;ter-&longs;tone of all the Fabrick <lb/>of the <emph type="italics"/>Aristotelian<emph.end type="italics"/> World, upon which they &longs;uper&longs;truct all their <lb/>other properties, of neither heavy nor light, of ingenerable incor­ <lb/>ruptible, exemption from all motions, &longs;ome onely the local, &c. <lb/></s><s>And all the&longs;e pa&longs;&longs;ions he affirmeth to be proper to a &longs;imple body <lb/>that is moved circularly; and the contrary qualities of gravity, <lb/>levity, corruptibility, &c. </s><s>he a&longs;&longs;igns to bodies naturally moveable <lb/>in a &longs;treight line, for that if we have already di&longs;covered defects in <lb/>the foundation, we may rationally que&longs;tion what &longs;oever may far­ <pb xlink:href="040/01/026.jpg" pagenum="10"/>ther built thereon. </s><s>I deny not, that this which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hitherto <lb/>hath introduced, with a general di&longs;cour&longs;e dependent upon univer­ <lb/>&longs;al primary principles, hathbeen &longs;ince in proce&longs;s of time, re-inforced <lb/>with particular rea&longs;ons, and experiments; all which it would be <lb/>nece&longs;&longs;ary di&longs;tinctly to con&longs;ider and weigh; but becau&longs;e what hath <lb/>been &longs;aid hitherto pre&longs;ents to &longs;uch as con&longs;ider the &longs;ame many and <lb/>no &longs;mall difficulties, (and yet it would be nece&longs;&longs;ary, that the pri­ <lb/>mary principles and fundamentals, were certain, firm, and e&longs;tabli&longs;h­ <lb/>ed, that &longs;o they might with more confidence be built upon) it <lb/>would not be ami&longs;s, before we farther multiply doubts, to &longs;ee if <lb/>haply (as I conjecture) betaking our &longs;elves to other waies, we may <lb/>not light upon a more direct and &longs;ecure method; and with better <lb/>con&longs;idered principles of Architecture lay our primary fundamen­ <lb/>tals. </s><s>Therefore &longs;u&longs;pending for the pre&longs;ent the method of <emph type="italics"/>Ari&longs;to­ <lb/>tle,<emph.end type="italics"/> (which we will re-a&longs;&longs;ume again in its proper place, and parti­ <lb/>cularly examine;) I &longs;ay, that in the things hitherto affirmed by <lb/><arrow.to.target n="marg24"></arrow.to.target> <lb/>him, I agree with him, and admit that the World is a body enjoy­ <lb/>ing all dimen&longs;ions, and therefore mo&longs;t perfect; and I add, that as <lb/>&longs;uch, it is nece&longs;&longs;arily mo&longs;t ordinate, that is, having parts between <lb/>them&longs;elves, with exqui&longs;ite and mo&longs;t perfect order di&longs;po&longs;ed; which <lb/>a&longs;&longs;umption I think is not to be denied, neither by you or any <lb/>other.</s></p><p type="margin"><s><margin.target id="marg23"></margin.target><emph type="italics"/>The circular line <lb/>perfect, according <lb/>to<emph.end type="italics"/> Ari&longs;totle, <emph type="italics"/>and <lb/>but the right im­ <lb/>perfect, and why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg24"></margin.target><emph type="italics"/>The world is &longs;up­ <lb/>po&longs;ed by the Au­ <lb/>thor to be perfectly <lb/>ordinate.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>Who can deny it? </s><s>the fir&longs;t particular (of the worlds <lb/>dimen&longs;ions) is taken from <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf, and its denominati­ <lb/>on of ordinate &longs;eems onely to be a&longs;&longs;umed from the order which it <lb/>mo&longs;t exactly keeps. <lb/><arrow.to.target n="marg25"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg25"></margin.target><emph type="italics"/>Streight motion <lb/>impo&longs;&longs;ible in the <lb/>world exactly or­ <lb/>dinate.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>This principle then e&longs;tabli&longs;hed, one may immediately <lb/>conclude, that if the entire parts of the World &longs;hould be by their <lb/>nature moveable, it is impo&longs;&longs;ible that their motions &longs;hould be <lb/>right, or other than circular; and the rea&longs;on is &longs;ufficiently ea&longs;ie, <lb/>and manife&longs;t; for that what&longs;oever moveth with a right motion, <lb/>changeth place; and continuing to move, doth by degrees more <lb/>and more remove from the term from whence it departed, and <lb/>from all the places thorow which it &longs;ucce&longs;&longs;ively pa&longs;&longs;ed; and if <lb/>&longs;uch motion naturally &longs;uited with it, then it was not at the be­ <lb/>ginning in its proper place; and &longs;o the parts of the World were <lb/>not di&longs;po&longs;ed with perfect order. </s><s>But we &longs;uppo&longs;e them to be per­ <lb/>fectly ordinate, therefore as &longs;uch, it is impo&longs;&longs;ible that they &longs;hould <lb/>by nature change place, and con&longs;equently move in a right moti­</s></p><p type="main"><s><arrow.to.target n="marg26"></arrow.to.target> <lb/>on. </s><s>Again, the right motion being by nature infinite, for that <lb/>the right line is infinite and indeterminate, it is impo&longs;&longs;ible that <lb/><arrow.to.target n="marg27"></arrow.to.target> <lb/>any moveable can have a natural principle of moving in a right <lb/>line; namely toward the place whither it is impo&longs;&longs;ible to arrive, <lb/><arrow.to.target n="marg28"></arrow.to.target> <lb/>there being no præ-&longs;inite term; and nature, as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf <lb/>&longs;aith well, never attempts to do that which can never be done, <pb xlink:href="040/01/027.jpg" pagenum="11"/>nor e&longs;&longs;aies to move whither it is impo&longs;&longs;ible to arrive. </s><s>And if any <lb/>one &longs;hould yet object, that albeit the right line, and con&longs;equent­ <lb/>ly the motion by it is producible <emph type="italics"/>in infinitum,<emph.end type="italics"/> that is to &longs;ay, is in­ <lb/>terminate; yet neverthele&longs;s Nature, as one may &longs;ay, arbitrarily <lb/>hath a&longs;&longs;igned them &longs;ome terms, and given natural in&longs;tincts to <lb/>its natural bodies to move unto the &longs;ame; I will reply, that this <lb/><arrow.to.target n="marg29"></arrow.to.target> <lb/>might perhaps be fabled to have come to pa&longs;s in the fir&longs;t Chaos, <lb/>where indi&longs;tinct matters confu&longs;edly and inordinately wandered; <lb/>to regulate which, Nature very appo&longs;itely made u&longs;e of right mo­ <lb/><arrow.to.target n="marg30"></arrow.to.target> <lb/>tions, by which, like as the well-con&longs;tituted, moving, di&longs;dorder <lb/>them&longs;elves, &longs;o were they which were before depravedly di&longs;po&longs;ed <lb/>by this motion ranged in order: but after their exqui&longs;ite di&longs;tribu­ <lb/>tion and collocation, it is impo&longs;&longs;ible that there &longs;hould remain na­ <lb/>tural inclinations in them of longer moving in a right motion, <lb/>from which now would en&longs;ue their removal from their proper and <lb/>natural place, that is to &longs;ay, their di&longs;ordination; we may there­ <lb/>fore &longs;ay that the right motion &longs;erves to conduct the matter to erect <lb/>the work; but once erected, that it is to re&longs;t immoveable, or if <lb/><arrow.to.target n="marg31"></arrow.to.target> <lb/>moveable, to move it &longs;elf onely circularly. </s><s>Unle&longs;s we will &longs;ay <lb/>with <emph type="italics"/>Plato,<emph.end type="italics"/> that the&longs;e mundane bodies, after they had been made <lb/>and fini&longs;hed, were for a certain time moved by their Maker, in a <lb/>right motion, but that after their attainment to certain and de­ <lb/>terminate places, they were revolved one by one in Spheres, pa&longs;­ <lb/>&longs;ing from the right to the circular motion, wherein they have <lb/>been ever &longs;ince kept and maintained. </s><s>A &longs;ublime conceipt, and <lb/><arrow.to.target n="marg32"></arrow.to.target> <lb/>worthy indeed of <emph type="italics"/>Plato<emph.end type="italics"/>: upon which, I remember to have heard <lb/>our common friend the ^{*}<emph type="italics"/>Lyncean Academick<emph.end type="italics"/> di&longs;cour&longs;e in this man­ <lb/>ner, if I have not forgot it. </s><s>Every body for any rea&longs;on con&longs;titu­ <lb/>ted in a &longs;tate of re&longs;t, but which is by nature moveable, being &longs;et <lb/><arrow.to.target n="marg33"></arrow.to.target> <lb/>at liberty doth move; provided withal, that it have an inclina­ <lb/>tion to &longs;ome particular place; for &longs;hould it &longs;tand indifferently af­ <lb/>fected to all, it would remain in its re&longs;t, not having greater in­ <lb/>ducement to move one way than another. </s><s>From the having of <lb/>this inclination nece&longs;&longs;arily proceeds, that it in its moving &longs;hall con­ <lb/><arrow.to.target n="marg34"></arrow.to.target> <lb/>tinually increa&longs;e its acceleration, and beginning with a mo&longs;t &longs;low <lb/>motion, it &longs;hall not acquire any degree of velocity, before it <lb/>&longs;hall have pa&longs;&longs;ed thorow all the degrees of le&longs;s velocity, or grea­ <lb/>ter tardity: for pa&longs;&longs;ing from the &longs;tate of quiet (which is the in­ <lb/><arrow.to.target n="marg35"></arrow.to.target> <lb/>finite degree of tardity of motion) there is no rea&longs;on by which <lb/>it &longs;hould enter into &longs;uch a determinate degree of velocity, before <lb/>it &longs;hall have entred into a le&longs;s, and into yet a le&longs;s, before it entred <lb/>into that: but rather it &longs;tands with rea&longs;on, to pa&longs;s fir&longs;t by tho&longs;e <lb/>degrees neare&longs;t to that from which it departed, and from tho&longs;e to <lb/>the more remote; but the degree from whence the moveable <lb/><arrow.to.target n="marg36"></arrow.to.target> <lb/>began to move, is that of extreme tardity, namely of re&longs;t. <pb xlink:href="040/01/028.jpg" pagenum="12"/><arrow.to.target n="marg37"></arrow.to.target> <lb/>Now this acceleration of motion is never made, but when the <lb/>moveable in moving acquireth it; nor is its acqui&longs;t other than an <lb/>approaching to the place de&longs;ired, to wit, whither its natural in­ <lb/>clination attracts it, and thither it tendeth by the &longs;horte&longs;t way; <lb/>namely, by a right line. </s><s>We may upon good grounds therefore <lb/>&longs;ay, That Nature, to confer upon a moveable fir&longs;t con&longs;tituted in <lb/>re&longs;t a determinate velocity, u&longs;eth to make it move according to <lb/><arrow.to.target n="marg38"></arrow.to.target> <lb/>a certain time and &longs;pace with a right motion. </s><s>This pre&longs;uppo&longs;ed, <lb/>let us imagine God to have created the Orb <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> of <emph type="italics"/>Jupiter,<emph.end type="italics"/> on <lb/>which he had determined to confer &longs;uch a certain velocity, which <lb/>it ought afterwards to retain perpetually uniform; we may with <lb/><emph type="italics"/>Plato<emph.end type="italics"/> &longs;ay, that he gave it at the beginning a right and accelerate <lb/>motion, and that it afterwards being arrived to that intended de­ <lb/><arrow.to.target n="marg39"></arrow.to.target> <lb/>gree of velocity, he converted its right, into a circular motion, <lb/>the velocity of which came afterwards naturally to be uniform.</s></p><p type="margin"><s><margin.target id="marg26"></margin.target><emph type="italics"/>Right motion by <lb/>nature infinite.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg27"></margin.target><emph type="italics"/>Motion by a right <lb/>line naturally im­ <lb/>po&longs;&longs;ible.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg28"></margin.target><emph type="italics"/>Nature attempts <lb/>not things impo&longs;&longs;i­ <lb/>ble to be effected.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg29"></margin.target><emph type="italics"/>Right motion might <lb/>perhaps be in the <lb/>fir&longs;t Chaos.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg30"></margin.target><emph type="italics"/>Right motion is <lb/>commodious to <lb/>range in order, <lb/>things ous of or­ <lb/>der.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg31"></margin.target><emph type="italics"/>Mundane bodies <lb/>moved in the be­ <lb/>ginning in a right <lb/>line, and after­ <lb/>wards circularly? <lb/></s><s>according to<emph.end type="italics"/> Plato.</s></p><p type="margin"><s><margin.target id="marg32"></margin.target>* Thus doth he co­ <lb/>vertly and mode&longs;t­ <lb/>ly &longs;tile him&longs;elfe <lb/>throughout this <lb/>work.</s></p><p type="margin"><s><margin.target id="marg33"></margin.target><emph type="italics"/>A moveable be­ <lb/>ing in a &longs;tate of <lb/>re&longs;t, &longs;hall not move <lb/>unle&longs;s it have an <lb/>inclination to &longs;ome <lb/>particular place.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg34"></margin.target><emph type="italics"/>The moveable ac­ <lb/>celerates its moti­ <lb/>on, going towards <lb/>the place whither <lb/>it hath an inclina­ <lb/>tion.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg35"></margin.target><emph type="italics"/>The moveable pa&longs;­ <lb/>&longs;ing from re&longs;t, go­ <lb/>eth thorow all the <lb/>degrees of tardity.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg36"></margin.target><emph type="italics"/>Re&longs;t the in&longs;inioe <lb/>degree of tardity.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg37"></margin.target><emph type="italics"/>The moveable doth <lb/>not accelerate, &longs;ave <lb/>only as it approach­ <lb/>eth nearer to its <lb/>term.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg38"></margin.target><emph type="italics"/>Nature, to intro­ <lb/>duce in the move­ <lb/>able a certain de­ <lb/>gree of velocity, <lb/>made it move in a <lb/>right line.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg39"></margin.target><emph type="italics"/>Vniform velocity <lb/>convenient to the <lb/>circular motion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I hearken to this Di&longs;cour&longs;e with great delight; and I <lb/>believe the content I take therein will be greater, when you have <lb/>&longs;atisfied me in a doubt: that is, (which I do not very well com­ <lb/>prehend) how it of nece&longs;&longs;ity en&longs;ues, that a moveable departing <lb/><arrow.to.target n="marg40"></arrow.to.target> <lb/>from its re&longs;t, and entring into a motion to which it had a natural <lb/>inclination, it pa&longs;&longs;eth thorow all the precedent degrees o&longs; tardity, <lb/>comprehended between any a&longs;&longs;igned degree of velocity, and the <lb/>&longs;tate of re&longs;t, which degrees are infinite? </s><s>&longs;o that Nature was not <lb/>able to confer them upon the body of <emph type="italics"/>Jupiter,<emph.end type="italics"/> his circular moti­ <lb/>on being in&longs;tantly created with &longs;uch and &longs;uch velocity. <lb/><arrow.to.target n="marg41"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg40"></margin.target><emph type="italics"/>Betwixt re&longs;t, and <lb/>any a&longs;&longs;igned degree <lb/>of velocity, infinite <lb/>degrees of le&longs;s ve­ <lb/>locity interpo&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg41"></margin.target><emph type="italics"/>Nature doth not <lb/>immediately con­ <lb/>fer a determinate <lb/>degree of velocity, <lb/>howbeit &longs;he could.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I neither did, nor dare &longs;ay, that it was impo&longs;&longs;ible for <lb/>God or Nature to confer that velocity which you &longs;peak of, imme­ <lb/>diately; but this I &longs;ay, that <emph type="italics"/>de facto<emph.end type="italics"/> &longs;he did not doit; &longs;o that the <lb/>doing it would be a work extra-natural, and by confequence mi­ <lb/>raculous.</s></p><p type="main"><s>SAGR. </s><s>Then you believe, that a &longs;tone leaving its re&longs;t, and en­ <lb/>tring into its natural motion towards the centre of the Earth, pa&longs;­ <lb/>&longs;eth thorow all the degrees of tardity inferiour to any degree of <lb/>velocity?</s></p><p type="main"><s>SALV. </s><s>I do believe it, nay am certain of it; and &longs;o certain, <lb/>that I am able to make you al&longs;o very well &longs;atisfied with the truth <lb/>thereof.</s></p><p type="main"><s>SAGR. </s><s>Though by all this daies di&longs;cour&longs;e I &longs;hould gain no <lb/>more but &longs;uch a knowledge, I &longs;hould think my time very well <lb/>be&longs;towed.</s></p><p type="main"><s>SALV. </s><s>By what I collect from our di&longs;cour&longs;e, a great part of <lb/>your &longs;cruple lieth in that it &longs;hould in a time, and that very &longs;hort, <lb/>pa&longs;s thorow tho&longs;e infinite degrees of tardity precedent to any ve­ <lb/>locity, acquired by the moveable in that time: and therefore be­ <lb/>fore we go any farther, I will &longs;eek to remove this difficulty, which <pb xlink:href="040/01/029.jpg" pagenum="13"/>&longs;hall be an ea&longs;ie task; for I reply, that the moveable pa&longs;&longs;eth by <lb/>the afore&longs;aid degrees, but the pa&longs;&longs;age is made without &longs;taying in </s></p><p type="main"><s><arrow.to.target n="marg42"></arrow.to.target> <lb/>any of them; &longs;o that the pa&longs;&longs;age requiring but one &longs;ole in&longs;tant <lb/>of time, and every &longs;mall time containing infinite in&longs;tants, we &longs;hall <lb/>not want enough of them to a&longs;&longs;ign its own to each of the infinite <lb/>degrees of tardity; although the time were never &longs;o &longs;hort.</s></p><p type="margin"><s><margin.target id="marg42"></margin.target><emph type="italics"/>The moveable de­ <lb/>parting from re&longs;v <lb/>pa&longs;&longs;eth thorow all <lb/>degrees of velocity <lb/>without &longs;taying in <lb/>any.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Hitherto I apprehend you; neverthele&longs;s it is very much <lb/>that that Ball &longs;hot from a Cannon (for &longs;uch I conceive the ca­ <lb/>dent moveable) which yet we &longs;ee to fall with &longs;uch a precipice, <lb/>that in le&longs;s than ten pul&longs;es it will pa&longs;s two hundred yards of al­ <lb/>titude; &longs;hould in its motion be found conjoyned with &longs;o &longs;mall a <lb/>degree of velocity, that, &longs;hould it have continued to have moved <lb/>at that rate without farther acceleration, it would not have pa&longs;t <lb/>the &longs;ame in a day.</s></p><p type="main"><s>SALV. </s><s>You may &longs;ay, nor yet in a year, nor in ten, no nor in a <lb/>thou&longs;and; as I will endeavour to &longs;hew you, and al&longs;o happily with­ <lb/>out your contradiction, to &longs;ome &longs;ufficiently &longs;imple que&longs;tions that <lb/>I will propound to you. </s><s>Therefore tell me if you make any que­ <lb/>&longs;tion of granting that, that that ball in de&longs;cending goeth increa­ <lb/>&longs;ing its <emph type="italics"/>impetus<emph.end type="italics"/> and velocity.</s></p><p type="main"><s>SAGR. </s><s>I am mo&longs;t certain it doth.</s></p><p type="main"><s>SALV. </s><s>And if I &longs;hould &longs;ay that the <emph type="italics"/>impetus<emph.end type="italics"/> acquired in any <lb/>place of its motion, is &longs;o much, that it would &longs;uffice to re-carry <lb/>it to that place from which it came, would you grant it?</s></p><p type="main"><s>SAGR. </s><s>I &longs;hould con&longs;ent to it without contradiction, provided al­ <lb/>waies, that it might imploy without impediment its whole <emph type="italics"/>impetus<emph.end type="italics"/> <lb/>in that &longs;ole work of re-conducting it &longs;elf, or another equal toit, to <lb/><arrow.to.target n="marg43"></arrow.to.target> <lb/>that &longs;elf-&longs;ame height as it would do, in ca&longs;e the Earth were bored <lb/>thorow the centre, and the Bullet fell a thou&longs;and yards from the <lb/>&longs;aid centre, for I verily believe it would pa&longs;s beyond the centre, <lb/>a&longs;cending as much as it had de&longs;cended; and this I &longs;ee plainly in <lb/>the experiment of a plummet hanging at a line, which removed <lb/>from the perpendicular, which is its &longs;tate of re&longs;t, and afterwards <lb/>let go, falleth towards the &longs;aid perpendicular, and goes as far be­ <lb/>yond it; or onely &longs;o much le&longs;s, as the oppo&longs;ition of the air, and <lb/>line, or other accidents have hindred it. </s><s>The like I &longs;ee in the wa­ <lb/>ter, which de&longs;cending thorow a pipe, re-mounts as much as it had <lb/>de&longs;cended.</s></p><p type="margin"><s><margin.target id="marg43"></margin.target><emph type="italics"/>The ponderous mo­ <lb/>ver de&longs;cending ac­ <lb/>quireth<emph.end type="italics"/> impetus <lb/><emph type="italics"/>&longs;ufficient to re­ <lb/>carry it to the like <lb/>height.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You argue very well. </s><s>And for that I know you will not <lb/>&longs;cruple to grant that the acqui&longs;t of the <emph type="italics"/>impetus<emph.end type="italics"/> is by means of the <lb/>receding from the term whence the moveable departed, and its ap­ <lb/>proach to the centre, whither its motion tendeth; will you &longs;tick <lb/>to yeeld, that two equal moveables, though de&longs;cending by divers <lb/>lines, without any impediment, acquire equal <emph type="italics"/>impetus,<emph.end type="italics"/> provided <lb/>that the approaches to the centre be equal?</s></p> <pb xlink:href="040/01/030.jpg" pagenum="14"/><p type="main"><s>SAGR. </s><s>I do not very well under&longs;tand the que&longs;tion.</s></p><p type="main"><s>SALV. </s><s>I will expre&longs;s it better by drawing a Figure: therefore <lb/>I will &longs;uppo&longs;e the line A B [in <emph type="italics"/>Fig.<emph.end type="italics"/> 3.] parallel to the Horizon, <lb/>and upon the point B, I will erect a perpendicular B C; and after <lb/>that I adde this &longs;launt line C A. </s><s>Under&longs;tanding now the line C <lb/>A to be an inclining plain exqui&longs;itely poli&longs;hed, and hard, upon <lb/>which de&longs;cendeth a ball perfectly round and of very hard matter, <lb/>and &longs;uch another I &longs;uppo&longs;e freely to de&longs;cend by the perpendicular <lb/>C B: will you now confe&longs;s that the <emph type="italics"/>impetus<emph.end type="italics"/> of that which de­ <lb/>&longs;cends by the plain C A, being arrived to the point A, may be <lb/>equal to the <emph type="italics"/>impetus<emph.end type="italics"/> acquired by the other in the point B, after <lb/>the de&longs;cent by the perpendicular C B? <lb/><arrow.to.target n="marg44"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg44"></margin.target><emph type="italics"/>The impetuo&longs;ity of <lb/>moveables equally <lb/>approaching to the <lb/>centre, are equal.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I re&longs;olutely believe &longs;o: for in effect they have both the <lb/>&longs;ame proximity to the centre, and by that, which I have already <lb/>granted, their impetuo&longs;ities would be equally &longs;ufficient to re-carry <lb/>them to the &longs;ame height.</s></p><p type="main"><s>SALV. </s><s>Tell me now what you believe the &longs;ame ball would do <lb/>put upon the Horizontal plane A B?</s></p><p type="main"><s><arrow.to.target n="marg45"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg45"></margin.target><emph type="italics"/>Vpon an horizon­ <lb/>tall plane the move­ <lb/>able lieth &longs;till.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>It would lie &longs;till, the &longs;aid plane having no declination.</s></p><p type="main"><s>SALV. </s><s>But on the inclining plane C A it would de&longs;cend, but <lb/>with a gentler motion than by the perpendicular C B?</s></p><p type="main"><s>SAGR. </s><s>I may confidently an&longs;wer in the affirmative, it &longs;eem­ <lb/>ing to me nece&longs;&longs;ary that the motion by the perpendicular C B <lb/>&longs;hould be more &longs;wift, than by the inclining plane C A; yet ne­ <lb/>verthele&longs;s, i&longs; this be, how can the Cadent by the inclination ar­ <lb/>rived to the point A, have as much <emph type="italics"/>impetus,<emph.end type="italics"/> that is, the &longs;ame de­ <lb/>gree of velocity, that the Cadent by the perpendicular &longs;hall have <lb/>in the point B? the&longs;e two Propo&longs;itions &longs;eem contradictory.</s></p><p type="main"><s><arrow.to.target n="marg46"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg46"></margin.target><emph type="italics"/>The veloeity by the <lb/>inclining plane e­ <lb/>qual to the veloci­ <lb/>ty by the perpendi­ <lb/>oular, and the mo­ <lb/>tion by the perpen­ <lb/>dicular &longs;wifter <lb/>than by the incli­ <lb/>nation.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Then you would think it much more fal&longs;e, &longs;hould I <lb/>&longs;ay, that the velocity of the Cadents by the perpendicular, and <lb/>inclination, are ab&longs;olutely equal: and yet this is a Propo&longs;ition <lb/>mo&longs;t true, as is al&longs;o this that the Cadent moveth more &longs;wiftly by <lb/>the perpendicular, than by the inclination.</s></p><p type="main"><s>SAGR. </s><s>The&longs;e Propo&longs;itions to my ears &longs;ound very har&longs;h: and <lb/>I believe to yours <emph type="italics"/>Simplicius<emph.end type="italics"/>?</s></p><p type="main"><s>SIMPL. </s><s>I have the &longs;ame &longs;en&longs;e of them.</s></p><p type="main"><s>SALV. </s><s>I conceit you je&longs;t with me, pretending not to compre­ <lb/>hend what you know better than my &longs;elf: therefore tell me <emph type="italics"/>Sim­ <lb/>plicius,<emph.end type="italics"/> when you imagine a moveable more &longs;wift than ano­ <lb/>ther, what conceit do you fancy in your mind?</s></p><p type="main"><s>SIMPL. </s><s>I fancie one to pa&longs;s in the &longs;ame time a greater &longs;pace <lb/>than the other, or to move equal &longs;paces, but in le&longs;&longs;er time.</s></p><p type="main"><s>SALV. </s><s>Very well: and for moveables equally &longs;wift, what's <lb/>your conceit of them?</s></p><p type="main"><s>SIMPL. </s><s>I fancie that they pa&longs;s equal &longs;paces in equal times.</s></p> <pb xlink:href="040/01/031.jpg" pagenum="15"/><p type="main"><s>SALV. </s><s>And have you no other conceit thereof than this?</s></p><p type="main"><s>SIMPL. </s><s>This I think to be the proper definition of equal mo­ <lb/>tions.</s></p><p type="main"><s><arrow.to.target n="marg47"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg47"></margin.target><emph type="italics"/>Velocities are &longs;aid <lb/>to be equal, when <lb/>the &longs;paces pa&longs;&longs;ed <lb/>are proportionate to <lb/>their time.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>We will add moreover this other: and call that equal <lb/>velocity, when the &longs;paces pa&longs;&longs;ed have the &longs;ame proportion, as the <lb/>times wherein they are pa&longs;t, and it is a more univer&longs;al definition.</s></p><p type="main"><s>SALV. </s><s>It is &longs;o: for it comprehendeth the equal &longs;paces pa&longs;t in <lb/>equal times, and al&longs;o the unequal pa&longs;t in times unequal, but pro­ <lb/>portionate to tho&longs;e &longs;paces. </s><s>Take now the &longs;ame Figure, and apply­ <lb/>ing the conceipt that you had of the more ha&longs;tie motion, tell me <lb/>why you think the velocity of the Cadent by C B, is greater <lb/>than the velocity of the De&longs;cendent by C A?</s></p><p type="main"><s>SIMPL. </s><s>I think &longs;o; becau&longs;e in the &longs;ame time that the Cadent <lb/>&longs;hall pa&longs;s all C B, the De&longs;cendent &longs;hall pa&longs;s in C A, a part le&longs;s <lb/>than C B.</s></p><p type="main"><s>SALV. True; and thus it is proved, that the moveable moves <lb/>more &longs;wiftly by the perpendicular, than by the inclination. </s><s>Now <lb/>con&longs;ider, if in this &longs;ame Figure one may any way evince the o­ <lb/>ther conceipt, and finde that the moveables were equally &longs;wift <lb/>by both the lines C A and C B.</s></p><p type="main"><s>SIMPL. </s><s>I &longs;ee no &longs;uch thing; nay rather it &longs;eems to contradict <lb/>what was &longs;aid before.</s></p><p type="main"><s>SALV. </s><s>And what &longs;ay you, <emph type="italics"/>Sagredus<emph.end type="italics"/>? </s><s>I would not teach you <lb/>what you knew before, and that of which but ju&longs;t now you pro­ <lb/>duced me the definition.</s></p><p type="main"><s>SAGR. </s><s>The definition I gave you, was, that moveables may <lb/>be called equally &longs;wift, when the &longs;paces pa&longs;&longs;ed are proportional <lb/>to the times in which they pa&longs;&longs;ed; therefore to apply the defini­ <lb/>tion to the pre&longs;ent ca&longs;e, it will be requi&longs;ite, that the time of de­ <lb/>&longs;cent by C A, to the time of falling by C B, &longs;hould have the <lb/>&longs;ame proportion that the line C A hath to the line C B; but I <lb/>under&longs;tand not how that can be, for that the motion by C B is <lb/>&longs;wifter than by C A.</s></p><p type="main"><s>SALV. </s><s>And yet you mu&longs;t of nece&longs;&longs;ity know it. </s><s>Tell me a little, <lb/>do not the&longs;e motions go continually accelerating?</s></p><p type="main"><s>SAGR. </s><s>They do; but more in the perpendicular than in the <lb/>inclination.</s></p><p type="main"><s>SALV. </s><s>But this acceleration in the perpendicular, is it yet not­ <lb/>with&longs;tanding &longs;uch in compari&longs;on of that of the inclined, that <lb/>two equal parts being taken in any place of the &longs;aid perpendicu­ <lb/>lar and inclining lines, the motion in the parts of the perpendicu­ <lb/>lar is alwaies more &longs;wift, than in the part of the inclination?</s></p><p type="main"><s>SAGR. </s><s>I &longs;ay not &longs;o: but I could take a &longs;pace in the inclinati­ <lb/>on, in which the velocity &longs;hall be far greater than in the like &longs;pace <lb/>taken in the perpendicular; and this &longs;hall be, if the &longs;pace in the <pb xlink:href="040/01/032.jpg" pagenum="16"/>perpendicular &longs;hould be taken near to the end C, and in the in­ <lb/>clination, far from it.</s></p><p type="main"><s>SALV. </s><s>You &longs;ee then, that the Propo&longs;ition which &longs;aith, that <lb/>the motion by the perpendicular is more &longs;wift than by the incli­ <lb/>nation, holds not true univer&longs;ally, but onely of the motions, <lb/>which begin from the extremity, namely from the point of re&longs;t: <lb/>without which re&longs;triction, the Propo&longs;ition would be &longs;o deficient, <lb/>that its very direct contrary might be true; namely, that the mo­ <lb/>tion in the inclining plane is &longs;wifter than in the perpendicular: <lb/>for it is certain, that in the &longs;aid inclination, we may take a &longs;pace <lb/>pa&longs;t by the moveable in le&longs;s time, than the like &longs;pace pa&longs;t in the <lb/>perpendicular. </s><s>Now becau&longs;e the motion in the inclination is in <lb/>&longs;ome places more, in &longs;ome le&longs;s, than in the perpendicular; there­ <lb/>fore in &longs;ome places of the inclination, the time of motion of the <lb/>moveable, &longs;hall have a greater proportion to the time of the motion <lb/>of the moveable, by &longs;ome places of the perpendicular, than the <lb/>&longs;pace pa&longs;&longs;ed, to the &longs;pace pa&longs;&longs;ed: and in other places, the pro­ <lb/>portion of the time to the time, &longs;hall be le&longs;s than that of the <lb/>&longs;pace to the &longs;pace. </s><s>As for example: two moveables departing <lb/>from their quie&longs;cence, namely, from the point C, one by the per­ <lb/>pendicular C B, [in <emph type="italics"/>Fig.<emph.end type="italics"/> 4.] and the other by the inclination C A, <lb/>in the time that, in the perpendicular, the moveable &longs;hall have <lb/>pa&longs;t all C B, the other &longs;hall have pa&longs;t C T le&longs;&longs;er. </s><s>And therefore <lb/>the time by C T, to the time by C B (which is equal) &longs;hall have <lb/>a greater proportion than the line C T to C B, being that the <lb/><emph type="italics"/>&longs;ame<emph.end type="italics"/> to the <emph type="italics"/>le&longs;s,<emph.end type="italics"/> hath a greater proportion than to the <emph type="italics"/>greater.<emph.end type="italics"/> <lb/>And on the contrary, if in C A, prolonged as much as is requi­ <lb/>&longs;ite, one &longs;hould take a part equal to C B, but pa&longs;t in a &longs;horter <lb/>time; the time in the inclination &longs;hall have a le&longs;s proportion to <lb/>the time in the perpendicular, than the &longs;pace to the &longs;pace. </s><s>If <lb/>therefore in the inclination and perpendicular, we may &longs;uppo&longs;e <lb/>&longs;uch &longs;paces and velocities, that the proportion between the &longs;aid <lb/>&longs;paces be greater and le&longs;s than the proportion of the times; we <lb/>may ea&longs;ily grant, that there are al&longs;o &longs;paces, by which the times <lb/>of the motions retain the &longs;ame proportion as the &longs;paces.</s></p><p type="main"><s>SAGR. </s><s>I am already freed from my greate&longs;t doubt, and con­ <lb/>ceive that to be not onely po&longs;&longs;ible, but nece&longs;&longs;ary, which I but <lb/>now thought a contradiction: but neverthele&longs;s I under&longs;tand not <lb/>as yet, that this whereof we now are &longs;peaking, is one of the&longs;e <lb/>po&longs;&longs;ible or nece&longs;&longs;ary ca&longs;es; &longs;o as that it &longs;hould be true, that the <lb/>time of de&longs;cent by C A, to the time of the fall by C B, hath the <lb/>&longs;ame proportion that the line C A hath to C B; whence it may <lb/>without contradiction be affirmed, that the velocity by the incli­ <lb/>nation C A, and by the perpendicular C B, are equal.</s></p><p type="main"><s>SALV. </s><s>Content your &longs;elf for this time, that I have removed <pb xlink:href="040/01/033.jpg" pagenum="17"/>your incredulity; but for the knowledge of this, expect it at <lb/>&longs;ome other time, namely, when you &longs;hall &longs;ee the matters concer­ <lb/>ning local motion demon&longs;trated by our <emph type="italics"/>Academick<emph.end type="italics"/>; at which <lb/>time you &longs;hall find it proved, that in the time that the one movea­ <lb/>ble falls all the &longs;pace C B, the other de&longs;cendeth by C A as far <lb/>as the point T, in which falls the perpendicular drawn from the <lb/>point B: and to find where the &longs;ame Cadent by the perpendi­ <lb/>cular would be when the other arriveth at the point A, draw from <lb/>A the perpendicular unto C A, continuing it, and C B unto the <lb/>interfection, and that &longs;hall be the point &longs;ought. </s><s>Whereby you <lb/>&longs;ee how it is true, that the motion by C B is &longs;wifter than by the <lb/>inclination C A (&longs;uppo&longs;ing the term C for the beginning of the <lb/>motions compared) becau&longs;e the line C B is greater than C T, <lb/>and the other from C unto the inter&longs;ection of the perpendicular <lb/>drawn from A, unto the line C A, is greater than C A, and <lb/>therefore the motion by it is &longs;wifter than by C A But when we <lb/>compare the motion made by all C A, not with all the motion <lb/>made in the &longs;ame time by the perpendicular continued, but with <lb/>that made in part of the time, by the &longs;ole part C B, it hinders <lb/>not, that the motion by C A, continuing to de&longs;cend beyond, may <lb/>arrive to A in &longs;uch a time as is in proportion to the other time, <lb/>as the line C A is to the line C B. </s><s>Now returning to our fir&longs;t <lb/>purpo&longs;e; which was to &longs;hew, that the grave moveable leaving <lb/>its quie&longs;cence, pa&longs;&longs;eth defcending by all the degrees of tardity, <lb/>precedent to any what&longs;oever degree of velocity that it aequireth, <lb/>re-a&longs;&longs;uming the &longs;ame Figure which we u&longs;ed before, let us remem­ <lb/>ber that we did agree, that the De&longs;cendent by the inclination C <lb/>A, and the Cadent by the perpendicular C B, were found to have <lb/>acquired equal degrees of velocity in the terms B and A: now to <lb/>proceed, I &longs;uppo&longs;e you will not &longs;cruple to grant, that upon ano­ <lb/>ther plane le&longs;s &longs;teep than A C; as for example, A D [in <emph type="italics"/>Fig.<emph.end type="italics"/> 5.] <lb/>the motion of the de&longs;cendent would be yet more &longs;low than in the <lb/>plane A C. </s><s>So that it is not any whit dubitable, but that there <lb/>may be planes &longs;o little elevated above the Horizon A B, that the <lb/>moveable, namely the &longs;ame ball, in any the longe&longs;t time may <lb/>reach the point A, which being to move by the plane A B, an infi­ <lb/>nite time would not &longs;uffice: and the motion is made always more <lb/>&longs;lowly, by how much the declination is le&longs;s. </s><s>It mu&longs;t be therefore <lb/>confe&longs;t, that there may be a point taken upon the term B, &longs;o near <lb/>to the &longs;aid B, that drawing from thence to the point A a plane, <lb/>the ball would not pa&longs;s it in a whole year. </s><s>It is requi&longs;ite next <lb/>for you to know, that the <emph type="italics"/>impetus,<emph.end type="italics"/> namely the degree of velo­ <lb/>city the ball is found to have acquired when it arriveth at the <lb/>point A, is &longs;uch, that &longs;hould it continue to move with this &longs;elf-&longs;ame <lb/>degree uniformly, that is to &longs;ay, without accelerating or retarding; <pb xlink:href="040/01/034.jpg" pagenum="18"/>in as much more time as it was in coming by the inclining plane, it <lb/>would pa&longs;s double the &longs;pace of the plane inclined: namely (for <lb/>example) if the ball had pa&longs;t the plane D A in an hour, con­ <lb/>tinuing to move uniformly with that degree of velocity which it <lb/>is found to have in its arriving at the term A, it &longs;hall pa&longs;s in an <lb/>hour a &longs;pace double the length D A; and becau&longs;e (as we have <lb/>&longs;aid) the degrees of velocity acquired in the points B and A, by <lb/>the moveables that depart from any point taken in the perpendicu­ <lb/>lar C B, and that de&longs;cend, the one by the inclined plane, the o­ <lb/>ther by the &longs;aid perpendicular, are always equal: therefore the <lb/>cadent by the perpendicular may depart from a term &longs;o near to B, <lb/>that the degree of velocity acquired in B, would not &longs;uffice (&longs;till <lb/>maintaining the &longs;ame) to conduct the moveable by a &longs;pace dou­ <lb/>ble the length of the plane inclined in a year, nor in ten, no nor <lb/>in a hundred. </s><s>We may therefore conclude, that if it be true, <lb/>that according to the ordinary cour&longs;e of nature a moveable, all <lb/>external and accidental impediments removed, moves upon an in­ <lb/>clining plane with greater and greater tardity, according as the <lb/>inclination &longs;hall be le&longs;s; &longs;o that in the end the tardity comes to be <lb/>infinite, which is, when the inclination concludeth in, and joyneth <lb/>to the horizontal plane; and if it be true likewi&longs;e, that the de­ <lb/>gree of velocity acquired in &longs;ome point of the inclined plane, is <lb/>equal to that degree of velocity which is found to be in the move­ <lb/>able that de&longs;cends by the perpendicular, in the point cut by a <lb/>parallel to the Horizon, which pa&longs;&longs;eth by that point of the incli­ <lb/>ning plane; it mu&longs;t of nece&longs;&longs;ity be granted, that the cadent de­ <lb/>parting from re&longs;t, pa&longs;&longs;eth thorow all the infinite degrees of tar­ <lb/>dity, and that con&longs;equently, to acquire a determinate degree of <lb/>velocity, it is nece&longs;&longs;ary that it move fir&longs;t by right lines, de&longs;cend­ <lb/>ing by a &longs;hort or long &longs;pace, according as the velocity to be acqui­ <lb/>red, ought to be either le&longs;s or greater, and according as the plane <lb/>on which it de&longs;cendeth is more or le&longs;s inclined; &longs;o that a plane <lb/>may be given with &longs;o &longs;mall inclination, that to acquire in it the <lb/>a&longs;&longs;igned degree of velocity, it mu&longs;t fir&longs;t move in a very great &longs;pace, <lb/>and take a very long time; whereupon in the horizontal plane, any <lb/>how little &longs;oever velocity, would never be naturally acquired, <lb/>&longs;ince that the moveable in this ca&longs;e will never move: but the </s></p><p type="main"><s><arrow.to.target n="marg48"></arrow.to.target> <lb/>motion by the horizontal line, which is neither declined or incli­ <lb/>ned, is a circular motion about the centre: therefore the circu­ <lb/>lar motion is never acquired naturally, without the right motion <lb/>precede it; but being once acquired, it will continue perpetually <lb/>with uniform velocity. </s><s>I could with other di&longs;cour&longs;es evince and <lb/>demon&longs;trate the &longs;ame truth, but I will not by &longs;o great a digre&longs;­ <lb/>fion interrupt our principal argument: but rather will return to <lb/>it upon &longs;ome other occa&longs;ion; e&longs;pecially &longs;ince we now a&longs;&longs;umed the <pb xlink:href="040/01/035.jpg" pagenum="19"/>&longs;ame, not to &longs;erve for a nece&longs;&longs;ary demon&longs;tration, but to adorn a <lb/><emph type="italics"/>Platonick<emph.end type="italics"/> Conceit; to which I will add another particular ob&longs;er­ <lb/>vation of our <emph type="italics"/>Academick,<emph.end type="italics"/> which hath in it &longs;omething of admira­ <lb/>ble. </s><s>Let us &longs;uppo&longs;e among&longs;t the decrees of the divine <emph type="italics"/>Architect,<emph.end type="italics"/> <lb/>a purpo&longs;e of creating in the World the&longs;e Globes, which we be­ <lb/>hold continually moving round, and of a&longs;&longs;igning the centre of <lb/>their conver&longs;ions; and that in it he had placed the Sun immoveable, <lb/>and had afterwards made all the &longs;aid Globes in the &longs;ame place, <lb/>and with the intended inclinations of moving towards the Centre, <lb/>till they had acquired tho&longs;e degrees of velocity, which at fir&longs;t &longs;ee­ <lb/>med good to the &longs;ame Divine Minde; the which being acquired, <lb/>we la&longs;tly &longs;uppo&longs;e that they were turned round, each in his Sphere <lb/>retaining the &longs;aid acquired velocity: it is now demanded, in <lb/>what altitude and di&longs;tance from the Sun the place was where the <lb/>&longs;aid Orbs were primarily created; and whether it be po&longs;&longs;ible that <lb/>they might all be created in the &longs;ame place? </s><s>To make this inve­ <lb/>&longs;tigation, we mu&longs;t take from the mo&longs;t skilfull A&longs;tronomers the <lb/>magnitude of the Spheres in which the Planets revolve, and like­ <lb/>wi&longs;e the time of their revolutions: from which two cognitions is <lb/>gathered how much (for example) <emph type="italics"/>Jupiter<emph.end type="italics"/> is &longs;wifter than <emph type="italics"/>Sa­ <lb/>turne<emph.end type="italics"/>; and being found (as indeed it is) that <emph type="italics"/>Jupiter<emph.end type="italics"/> moves more <lb/>&longs;wiftly, it is requi&longs;ite, that departing from the &longs;ame altitude, <emph type="italics"/>Ju­ <lb/>piter<emph.end type="italics"/> be de&longs;cended more than <emph type="italics"/>Saturne,<emph.end type="italics"/> as we really know it is, its <lb/>Orbe being inferiour to that of <emph type="italics"/>Saturne.<emph.end type="italics"/> But by proceeding for­ <lb/>wards, from the proportions of the two velocities of <emph type="italics"/>Jupiter<emph.end type="italics"/> and <lb/><emph type="italics"/>Saturne,<emph.end type="italics"/> and from the di&longs;tance between their Orbs, and from the <lb/>proportion of acceleration of natural motion, one may finde in <lb/>what altitude and di&longs;tance from the centre of their revolutions, <lb/><arrow.to.target n="marg49"></arrow.to.target> <lb/>was the place from whence they fir&longs;t departed. </s><s>This found out, <lb/>and agreed upon, it is to be &longs;ought, whether <emph type="italics"/>Mars<emph.end type="italics"/> de&longs;cending <lb/>from thence to his Orb, the magnitude of the Orb, and the ve­ <lb/>locity of the motion, agree with that which is found by calcula­ <lb/>tion; and let the like be done of the <emph type="italics"/>Eartb,<emph.end type="italics"/> of <emph type="italics"/>Venus,<emph.end type="italics"/> and of <lb/><emph type="italics"/>Mercury<emph.end type="italics"/>; the greatne&longs;s of which Spheres, and the velocity of <lb/>their motions, agree &longs;o nearly to what computation gives, that it <lb/>is very admirable.</s></p><p type="margin"><s><margin.target id="marg48"></margin.target><emph type="italics"/>The circular mo­ <lb/>tion is never ac­ <lb/>quired naturally, <lb/>without right mo­ <lb/>tion precede it. <lb/></s><s>Circular motion <lb/>perpetually uni­ <lb/>form.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg49"></margin.target><emph type="italics"/>The magnitude of <lb/>the Orbs, and the <lb/>velocity of the mo­ <lb/>tion of the Planets, <lb/>an&longs;wer proportion­ <lb/>ably, as if de&longs;cend­ <lb/>ed from the &longs;ame <lb/>place.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I have hearkened to this conceit with extreme delight; <lb/>and, but that I believe the making of the&longs;e calculations truly <lb/>would be a long and painfull task, and perhaps too hard for me <lb/>to comprehend, I would make a trial of them.</s></p><p type="main"><s>SALV. </s><s>The operation indeed is long and difficult; nor could <lb/>I be certain to finde it &longs;o readily; therefore we &longs;hall refer it to an­ <lb/>other time, and for the pre&longs;ent we will return to our fir&longs;t propo­ <lb/>&longs;al, going on there where we made digre&longs;&longs;ion; which, if I well <lb/>remember, was about the proving the motion by a right line of no <pb xlink:href="040/01/036.jpg" pagenum="20"/>u&longs;e, in the ordinate parts of the World; and we did proceed to <lb/>&longs;ay, that it was not &longs;o in circular motions, of which that which is <lb/>made by the moveable in it &longs;elf, &longs;till retains it in the &longs;ame place, <lb/><arrow.to.target n="marg50"></arrow.to.target> <lb/>and that which carrieth the moveable by the circumference of a <lb/>circle about its fixed centre, neither puts it &longs;elf, nor tho&longs;e about it <lb/>in di&longs;order; for that &longs;uch a motion primarily is finite and terminate <lb/>(though not yet fini&longs;hed and determined) but there is no point <lb/><arrow.to.target n="marg51"></arrow.to.target> <lb/>in the circumference, that is not the fir&longs;t and la&longs;t term in the cir­ <lb/>culation; and continuing it in the circumference a&longs;&longs;igned it, it <lb/>leaveth all the re&longs;t, within and without that, free for the u&longs;e of <lb/>others, without ever impeding or di&longs;ordering them. </s><s>This being <lb/>a motion that makes the moveable continually leave, and con­ <lb/><arrow.to.target n="marg52"></arrow.to.target> <lb/>tinually arrive at the end; it alone therefore can primarily be u­ <lb/>niform; for that acceleration of motion is made in the moveable, <lb/>when it goeth towards the term, to which it hath inclination; <lb/>and the retardation happens by the repugnance that it hath to <lb/>leave and part from the &longs;ame term; and becau&longs;e in circular mo­ <lb/>tion, the moveable continually leaves the natural term, and con­ <lb/>tinually moveth towards the &longs;ame, therefore, in it, the repug­ <lb/>nance and inclination are always of equal force: from which e­ <lb/>quality re&longs;ults a velocity, neither retarded nor accelerated, <emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> an <lb/>uniformity in motion. </s><s>From this conformity, and from the being <lb/><arrow.to.target n="marg53"></arrow.to.target> <lb/>terminate, may follow the perpetual continuation by &longs;ucce&longs;&longs;ively <lb/>reiterating the circulations; which in an undeterminated line, <lb/>and in a motion continually retarded or accelerated, cannot na­ <lb/><arrow.to.target n="marg54"></arrow.to.target> <lb/>turally be. </s><s>I &longs;ay, naturally; becau&longs;e the right motion which is <lb/>retarded, is the violent, which cannot be perpetual; and the ac­ <lb/>celerate arriveth nece&longs;&longs;arily at the term, if one there be; and if <lb/>there be none, it cannot be moved to it, becau&longs;e nature moves <lb/>not whether it is impo&longs;&longs;ible to attain. </s><s>I conclude therefore, that <lb/>the circular motion can onely naturally con&longs;i&longs;t with natural bo­ <lb/>dies, parts of the univer&longs;e, and con&longs;tituted in an excellent di&longs;po­ <lb/>&longs;ure; and that the right, at the mo&longs;t that can be &longs;aid for it, is <lb/><arrow.to.target n="marg55"></arrow.to.target> <lb/>a&longs;&longs;igned by nature to its bodies, and their parts, at &longs;uch time as <lb/>they &longs;hall be out of their proper places, con&longs;tituted in a depraved <lb/>di&longs;po&longs;ition, and for that cau&longs;e needing to be redured by the &longs;hort­ <lb/>e&longs;t way to their natural &longs;tate. </s><s>Hence, me thinks, it may ratio­ <lb/>nally be concluded, that for maintenance of perfect order among &longs;t <lb/>the parts of the World, it is nece&longs;&longs;ary to &longs;ay, that moveables are <lb/>moveable onely circularly; and if there be any that move not <lb/><arrow.to.target n="marg56"></arrow.to.target> <lb/>circularly, the&longs;e of nece&longs;&longs;ity are immoveable: there being no­ <lb/>thing but re&longs;t and circular motion apt to the con&longs;ervation of or­ <lb/>der. </s><s>And I do not a little wonder with my &longs;elf, that <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>who held that the Terre&longs;trial globe was placed in the centre of <lb/>the World, and there remained immoveable, &longs;hould not &longs;ay, that <pb xlink:href="040/01/037.jpg" pagenum="21"/>of natural bodies &longs;ome are moveable by nature, and others immo­ <lb/>veable; e&longs;pecially having before defined Nature, to be the prin­ <lb/>ciple of Motion and Re&longs;t.</s></p><p type="margin"><s><margin.target id="marg50"></margin.target><emph type="italics"/>Finite and termi­ <lb/>nate circular mo­ <lb/>tions di&longs;order not <lb/>the parts of the <lb/>World.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg51"></margin.target><emph type="italics"/>In the circular mo­ <lb/>tion, every point in <lb/>the circumference <lb/>is the begining and <lb/>end.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg52"></margin.target><emph type="italics"/>Circular motion <lb/>onely is uniform.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg53"></margin.target><emph type="italics"/>Circular motion <lb/>may be continued <lb/>perpetually.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg54"></margin.target><emph type="italics"/>Right motion can­ <lb/>not naturally be <lb/>perpetual.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg55"></margin.target><emph type="italics"/>Right motion a&longs;­ <lb/>&longs;igned to natural <lb/>bodies, to reduce <lb/>them to perfect or­ <lb/>der, when removed <lb/>from their places.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg56"></margin.target><emph type="italics"/>Re&longs;t onely, and <lb/>circular motion are <lb/>apt to con&longs;erve or­ <lb/>der.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> though of a very per&longs;picacious wit, would <lb/>not &longs;train it further than needed: holding in all his argumen­ <lb/><arrow.to.target n="marg57"></arrow.to.target> <lb/>tations, that &longs;en&longs;ible experiments were to be preferred before <lb/>any rea&longs;ons founded upon &longs;trength of wit, and &longs;aid tho&longs;e which <lb/>&longs;hould deny the te&longs;timony of &longs;en&longs;e de&longs;erved to be puni&longs;hed with <lb/><arrow.to.target n="marg58"></arrow.to.target> <lb/>the lo&longs;s of that &longs;en&longs;e; now who is &longs;o blind, that &longs;ees not the <lb/>parts of the Earth and Water to move, as being grave, natural­ <lb/>ly downwards, namely, towards the centre of the Univer&longs;e, a&longs;­ <lb/>&longs;igned by nature her &longs;elf for the end and term of right motion <lb/><emph type="italics"/>deor&longs;ùm<emph.end type="italics"/>; and doth not likewi&longs;e &longs;ee the Fire and Air to move <lb/>right upwards towards the Concave of the Lunar Orb, as to the <lb/>natural end of motion <emph type="italics"/>&longs;ur&longs;ùm<emph.end type="italics"/>? </s><s>And this being &longs;o manife&longs;tly &longs;een, <lb/>and we being certain, that <emph type="italics"/>eadem est ratio totius & partium,<emph.end type="italics"/> why <lb/>may we not a&longs;&longs;ert it for a true and manife&longs;t propo&longs;ition, that the <lb/>natural motion of the Earth is the right motion <emph type="italics"/>ad medium,<emph.end type="italics"/> and <lb/>that of the Fire, the right <emph type="italics"/>à medio<emph.end type="italics"/>?</s></p><p type="margin"><s><margin.target id="marg57"></margin.target><emph type="italics"/>Sen&longs;ible experi­ <lb/>ments are to be pre­ <lb/>ferred before hu­ <lb/>mane argument a­ <lb/>tions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg58"></margin.target><emph type="italics"/>He who denies <lb/>&longs;en&longs;e, de&longs;erves to <lb/>be deprived of it. <lb/></s><s>Sen&longs;e &longs;heweth that <lb/>things grave move <lb/>to the<emph.end type="italics"/> medium, <emph type="italics"/>and <lb/>the light to the <lb/>concave.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The mo&longs;t that you can pretend from this your Di&longs;­ <lb/>cour&longs;e, were it granted to be true, is that, like as the parts of the <lb/>Earth removed from the whole, namely, from the place where <lb/>they naturally re&longs;t, that is in &longs;hort reduced to a depraved and di&longs;­ <lb/>ordered di&longs;po&longs;ure, return to their place &longs;pontaneou&longs;ly, and there­ <lb/>fore naturally in a right motion, (it being granted, that <emph type="italics"/>eadem <lb/>&longs;it ratio totius & partium<emph.end type="italics"/>) &longs;o it may be inferred, that the <lb/>Terre&longs;trial Globe removed violently from the place a&longs;&longs;igned <lb/><arrow.to.target n="marg59"></arrow.to.target> <lb/>it by nature, it would return by a right line. </s><s>This, as I have <lb/>&longs;aid, is the mo&longs;t that can be granted you, and that onely for want <lb/>of examination; but he that &longs;hall with exactne&longs;s revi&longs;e the&longs;e <lb/>things, will fir&longs;t deny, that the parts of the Earth, in returning to <lb/>its whole, move in a right line, and not by a circular or mixt; and <lb/>really you would have enough to do to demon&longs;trate the contra­ <lb/>ry, as you &longs;hall plainly &longs;ee in the an&longs;wers to the particular rea&longs;ons <lb/>and experiments alledged by <emph type="italics"/>Ptolomey<emph.end type="italics"/> and <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/> Secondly, <lb/>If another &longs;hould &longs;ay that the <emph type="italics"/>parts<emph.end type="italics"/> of the Earth, go not in their <lb/>motion towards the Centre of the World, but to unite with its <lb/><emph type="italics"/>Whole,<emph.end type="italics"/> and that for that rea&longs;on they naturally incline towards the <lb/>centre of the Terre&longs;trial Globe, by which inclination they con­ <lb/>&longs;pire to form and pre&longs;erve it, what other <emph type="italics"/>All,<emph.end type="italics"/> or what other Centre <lb/>would you find for the World, to which the whole Terrene <lb/><arrow.to.target n="marg60"></arrow.to.target> <lb/>Globe, being thence removed, would &longs;eek to return, that &longs;o the <lb/>rea&longs;on of the <emph type="italics"/>Whole<emph.end type="italics"/> might be like to that of its <emph type="italics"/>parts<emph.end type="italics"/>? </s><s>It may be <lb/>added, That neither <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> nor you can ever prove, that the <lb/>Earth <emph type="italics"/>de facto<emph.end type="italics"/> is in the centre of the Univer&longs;e; but if any Centre <pb xlink:href="040/01/038.jpg" pagenum="22"/><arrow.to.target n="marg61"></arrow.to.target> <lb/>may be a&longs;ligned to the Univer&longs;e, we &longs;hall rather find the Sun <lb/>placed in it, as by the &longs;equel you &longs;hall under&longs;tand.</s></p><p type="margin"><s><margin.target id="marg59"></margin.target><emph type="italics"/>It is que&longs;tionable <lb/>whether de&longs;cending <lb/>weights move in a <lb/>right line.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg60"></margin.target><emph type="italics"/>The Earth speri­ <lb/>cal by the con&longs;pi­ <lb/>ration of its parts <lb/>to its Centre.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg61"></margin.target><emph type="italics"/>The Sun more pro­ <lb/>bably in the centre <lb/>of the Vniver&longs;e, <lb/>than the Earth.<emph.end type="italics"/></s></p><p type="main"><s>Now, like as from the con&longs;entaneous con&longs;piration of all the <lb/>parts of the Earth to form its whole, doth follow, that they with <lb/><arrow.to.target n="marg62"></arrow.to.target> <lb/>equal inclination concurr thither from all parts; and to unite <lb/>them&longs;elves as much as is po&longs;&longs;ible together, they there &longs;phelically <lb/>adapt them&longs;elves; why may we not believe that the Sun, Moon, <lb/>and other mundane Bodies, be al&longs;o of a round figure, not by o­ <lb/>ther than a concordant in&longs;tinct, and natural concour&longs;e of all the <lb/>parts compo&longs;ing them? </s><s>Of which, if any, at any time, by any <lb/>violence were &longs;eparated from the whole, is it not rea&longs;onable to <lb/>think, that they would &longs;pontaneou&longs;ly and by natural in&longs;tinct re­ <lb/>turn? </s><s>and in this manner to infer, that the right motion agreeth <lb/>with all mundane bodies alike.</s></p><p type="margin"><s><margin.target id="marg62"></margin.target><emph type="italics"/>Natural inclina­ <lb/>tion of the parts of <lb/>all the globes of <lb/>the World to go to <lb/>their centre.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. Certainly, if you in this manner deny not onely the <lb/>Principles of Sciences, but manife&longs;t Experience, and the Sen&longs;es <lb/>them&longs;elves, you can never be convinced or removed from any o­ <lb/>pinion which you once conceit, therefore I will choo&longs;e rather to <lb/>be &longs;ilent (for, <emph type="italics"/>contra negantes principia non e&longs;t di&longs;putandum<emph.end type="italics"/>) <lb/>than contend with you. </s><s>And in&longs;i&longs;ting on the things alledged by <lb/>you even now (&longs;ince you que&longs;tion &longs;o much as whether grave move­ <lb/>ables have a right motion or no) how can you ever rationally de­ <lb/><arrow.to.target n="marg63"></arrow.to.target> <lb/>ny, that the parts of the Earth; or, if you will, that ponderous <lb/>matters de&longs;cend towards the Centre, with a right motion; when­ <lb/>as, if from a very high Tower, who&longs;e walls are vcry upright and <lb/>perpendicular, you let them fall, they &longs;hall de&longs;cend gliding and <lb/>&longs;liding by the Tower to the Earth, exactly in that very place <lb/>where a plummet would fall, being hanged by a line fa&longs;tned above, <lb/>ju&longs;t there, whence the &longs;aid weights were let fall? </s><s>is not this a <lb/>more than evident argument of the motions being right, and to­ <lb/><arrow.to.target n="marg64"></arrow.to.target> <lb/>wards the Centre? </s><s>In the &longs;econd place you call in doubt, whe­ <lb/>ther the parts of the Earth are moved, as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> affirms, to­ <lb/>wards the Centre of the World; as if he had not rationally de­ <lb/>mon&longs;trated it by contrary motions, whil&longs;t he thus argueth; The <lb/>motion of heavie bodies is contrary to that of the light: but the <lb/>motion of the light is manife&longs;t to be directly upwards, namely, <lb/>towards the circumference of the World, therefore the motion of <lb/>the heavie is directly towards the Centre of the World: and it <lb/><arrow.to.target n="marg65"></arrow.to.target> <lb/>happens <emph type="italics"/>per accidens,<emph.end type="italics"/> that it be towards the centre of the Earth, <lb/>for that this &longs;triveth to be united to that. </s><s>The &longs;eeking in the <lb/>next place, what a part of the Globe of the Sun or Moon would <lb/>do, were it &longs;eparated from its whole, is vanity; becau&longs;e that there­ <lb/><arrow.to.target n="marg66"></arrow.to.target> <lb/>by that is &longs;ought, which would be the con&longs;equence of an impo&longs;&longs;i­ <lb/>bility; in regard that, as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> al&longs;o demon&longs;trates, the cœle&longs;tial <lb/>bodies are impa&longs;&longs;ible, impenetrable, and infrangible; &longs;o that &longs;uch <pb xlink:href="040/01/039.jpg" pagenum="23"/>a ca&longs;e can never happen: and though it &longs;hould, and that the &longs;e­ <lb/><arrow.to.target n="marg67"></arrow.to.target> <lb/>parated part &longs;hould return to its whole, it would not return as <lb/>grave or light, for that the &longs;ame <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> proveth, that the Cœ­ <lb/>le&longs;tial Bodies are neither heavie nor light.</s></p><p type="margin"><s><margin.target id="marg63"></margin.target><emph type="italics"/>The right motion <lb/>of grave bodies <lb/>manife&longs;t to &longs;en&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg64"></margin.target><emph type="italics"/>Arguments of<emph.end type="italics"/> A­ <lb/>ri&longs;totle, <emph type="italics"/>to prove <lb/>that grave bodies <lb/>move with an in­ <lb/>clination to arrive <lb/>at the centre of the <lb/>Vniver&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg65"></margin.target><emph type="italics"/>Heavie bodies <lb/>move towards the <lb/>centre of the Earth<emph.end type="italics"/> <lb/>per accidens.</s></p><p type="margin"><s><margin.target id="marg66"></margin.target><emph type="italics"/>To &longs;eek what <lb/>would follow upon <lb/>an impo&longs;&longs;ibility, is <lb/>folly.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg67"></margin.target><emph type="italics"/>Cœle&longs;tial bodies <lb/>neither heavie nor <lb/>light, according to<emph.end type="italics"/> <lb/>Ari&longs;totle.</s></p><p type="main"><s>SALV. </s><s>With what rea&longs;on I doubt, whether grave bodies move <lb/>by a right and perpendicular line, you &longs;hall hear, as I &longs;aid be­ <lb/>fore, when I &longs;hall examine this particular argument. </s><s>Touching <lb/>the &longs;econd point, I wonder that you &longs;hould need to di&longs;cover the <lb/><emph type="italics"/>Paralogi&longs;m<emph.end type="italics"/> of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> being of it &longs;elf &longs;o manife&longs;t; and that <lb/>you perceive not, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;uppo&longs;eth that which is in que&longs;ti­ <lb/>on: therefore take notice.</s></p><p type="main"><s>SIMPL. </s><s>Pray <emph type="italics"/>Salviatus<emph.end type="italics"/> &longs;peak with more re&longs;pect of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>: <lb/>for who can you ever per&longs;wade, that he who was the fir&longs;t, only, <lb/>and admirable explainer of the <emph type="italics"/>Syllogi&longs;tick<emph.end type="italics"/> forms of demon&longs;tration, <lb/><arrow.to.target n="marg68"></arrow.to.target> <lb/>of <emph type="italics"/>Elenchs,<emph.end type="italics"/> of the manner of di&longs;covering <emph type="italics"/>Sophi&longs;ms, Paralogi&longs;ms,<emph.end type="italics"/> and <lb/>in &longs;hort, of all the parts of <emph type="italics"/>Logick,<emph.end type="italics"/> &longs;hould afterwards &longs;o notoriou&longs;ly <lb/>equivocate in impo&longs;ing that for known, which is in que&longs;tion? </s><s>It <lb/>would be better, my Ma&longs;ters, fir&longs;t perfectly to under&longs;tand him, <lb/>and then to try, if you have a minde, to oppo&longs;e him.</s></p><p type="margin"><s><margin.target id="marg68"></margin.target>Ari&longs;totle <emph type="italics"/>cannot e­ <lb/>quivocate, being <lb/>the inventer of<emph.end type="italics"/> Lo­ <lb/>gick.</s></p><p type="main"><s>SALV. <emph type="italics"/>Simplicius,<emph.end type="italics"/> we are here familiarly di&longs;cour&longs;ing among <lb/>our &longs;elves, to inve&longs;tigate &longs;ome truth; I &longs;hall not be di&longs;plea&longs;ed <lb/>that you di&longs;cover my errors; and if I do not follow the mind of <lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> freely reprehend me, and I &longs;hall take it in good part. <lb/></s><s>Onely give me leave to expound my doubts, and to reply &longs;ome­ <lb/>thing to your la&longs;t words, telling you, that <emph type="italics"/>Logick,<emph.end type="italics"/> as it is well <lb/>under&longs;tood, is the Organe with which we philo&longs;ophate; but as it <lb/>may be po&longs;&longs;ible, that an Arti&longs;t may be excellent in making Or­ <lb/>gans, but unlearned in playing on them, thus he might be a great <lb/>Logician, but unexpert in making u&longs;e of <emph type="italics"/>Logick<emph.end type="italics"/>; like as we have <lb/>many that theorically under&longs;tand the whole Art of Poetry, and <lb/>yet are unfortunate in compo&longs;ing but meer four Ver&longs;es; others <lb/><arrow.to.target n="marg69"></arrow.to.target> <lb/>enjoy all the precepts of <emph type="italics"/>Vinci<emph.end type="italics"/>^{*}, and yet know not how to paint <lb/>a Stoole. </s><s>The playing on the Organs is not taught by them who <lb/>know how to make Organs, but by him that knows how to play <lb/>on them: Poetry is learnt by continual reading of Poets: Limn­ <lb/>ing is learnt by continual painting and de&longs;igning: Demon&longs;tration <lb/>from the reading of Books full of demon&longs;trations, which are the <lb/>Mathematical onely, and not the Logical. </s><s>Now returning to our <lb/>purpo&longs;e, I &longs;ay, that that which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;eeth of the motion of <lb/>light bodies, is the departing of the Fire from any part of the <lb/>Superficies of the Terre&longs;trial Globe, and directly retreating from <lb/>it, mounting upwards; and this indeed is to move towards a <lb/>circumference greater than that of the Earth; yea, the &longs;ame <emph type="italics"/>A­ <lb/>ri&longs;totle<emph.end type="italics"/> makes it to move to the concave of the Moon, but that <lb/>this circumference is that of the World, or concentrick to it, &longs;o <pb xlink:href="040/01/040.jpg" pagenum="24"/>that to move towards this, is a moving towards that of the World, <lb/>that he cannot affirm, unle&longs;s he &longs;uppo&longs;eth, That the Centre of the <lb/><arrow.to.target n="marg70"></arrow.to.target> <lb/>Earth, from which we &longs;ee the&longs;e light a&longs;cendent bodies to depart, <lb/>be the &longs;ame with the Centre of the World; which is as much as <lb/>to &longs;ay, that the terre&longs;trial Globe is con&longs;tituted in the mid&longs;t of the <lb/>World: which is yet that of which we were in doubt, and which <lb/><emph type="italics"/>Aristotle<emph.end type="italics"/> intended to prove. </s><s>And do you &longs;ay that this is not a <lb/><arrow.to.target n="marg71"></arrow.to.target> <lb/>manife&longs;t <emph type="italics"/>Paralogi&longs;m<emph.end type="italics"/>?</s></p><p type="margin"><s><margin.target id="marg69"></margin.target>* A famous <emph type="italics"/>Italian<emph.end type="italics"/> <lb/>Painter.</s></p><p type="margin"><s><margin.target id="marg70"></margin.target><emph type="italics"/>Paralogi&longs;m of<emph.end type="italics"/> A­ <lb/>ri&longs;totle, <emph type="italics"/>in proving <lb/>the Earth to be in <lb/>the Centre of the <lb/>World.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg71"></margin.target><emph type="italics"/>The Paralogi&longs;me <lb/>of<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>another <lb/>way di&longs;covered.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This Argument of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> appeared to me deficient <lb/>al&longs;o, and <emph type="italics"/>non<emph.end type="italics"/>-concludent for another re&longs;pect; though it were <lb/>granted, that that Circumference, to which the Fire directly mo­ <lb/>veth, be that which includeth the World: for that in a circle, <lb/>not onely the centre, but any other point being taken, every move­ <lb/>able which departing thence, &longs;hall move in a right line, and to­ <lb/>wards any what&longs;oever part, &longs;hall without any doubt go towards <lb/>the circumference, and continuing the motion, &longs;hall al&longs;o arrive <lb/>thither; &longs;o that we may truly &longs;ay, that it moveth towards the <lb/>circumference: but yet it doth not follow, that that which mo­ <lb/>veth by the &longs;ame line with a contrary motion, would go towards <lb/>the centre, unle&longs;s when the point taken were the centre it &longs;elf, <lb/>or that the motion were made by that onely line, which produced <lb/>from the point a&longs;&longs;igned, pa&longs;&longs;eth thorow the centre. </s><s>So that to <lb/>&longs;ay, that Fire moving in a right line, goeth towards the circumfe­ <lb/>rence of the World, therefore the parts of the Earth which by <lb/>the &longs;ame lines move with a contrary motion, go towards the cen­ <lb/>tre of the World, concludeth not, unle&longs;s then when it is pre­ <lb/>&longs;uppo&longs;ed, that the lines of the Fire prolonged pa&longs;s by the centre <lb/>of the World; and becau&longs;e we know certainly of them, that they <lb/>pa&longs;s by the centre of the Terre&longs;trial Globe (being perpendicu­ <lb/>lar to its &longs;uperficies, and not inclined) therefore to conclude, it <lb/>mu&longs;t be &longs;uppo&longs;ed, that the centre of the Earth is the &longs;ame with <lb/>the centre of the World; or at lea&longs;t, that the parts of the Fire <lb/>and Earth de&longs;cend not, &longs;ave onely by one &longs;ole line which pa&longs;&longs;eth <lb/>by the centre of the World. </s><s>Which neverthele&longs;s is fal&longs;e, and re­ <lb/>pugnant to experience, which &longs;heweth us, that the parts of <lb/>Fire, not by one line onely, but by infinite, produced from the <lb/>centre of the Earth towards all the parts of the World, a&longs;cend <lb/>always by lines perpendicular to the Superficies of the Terre&longs;tri­ <lb/>al Globe.</s></p><p type="main"><s>SALV. </s><s>You do very ingeniou&longs;ly lead <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> to the &longs;ame in­ <lb/>convenience, <emph type="italics"/>Sagredus,<emph.end type="italics"/> &longs;hewing his manife&longs;t equivoke; but <lb/>withal you add another incon&longs;i&longs;tency. </s><s>We &longs;ee the Earth to be <lb/>&longs;pherical, and therefore are certain that it hath its centre, to which <lb/>we &longs;ee all its parts are moved; for &longs;o we mu&longs;t &longs;ay, whil&longs;t their <lb/>motions are all perpendicular to the Superficies of the Earth; we <pb xlink:href="040/01/041.jpg" pagenum="25"/>mean, that as they move to the centre of the Earth, they move to <lb/>their <emph type="italics"/>Whole,<emph.end type="italics"/> and to their Univer&longs;al Mother: and we are &longs;till far­ <lb/>ther &longs;o free, that we will &longs;uffer our &longs;elves to be per&longs;waded, that <lb/><arrow.to.target n="marg72"></arrow.to.target> <lb/>their natural in&longs;tinct is, not to go towards the centre of the Earth, <lb/>but towards that of the Univer&longs;e; which we know not where to <lb/>find, or whether it be or no; and were it granted to be, it is but <lb/>an imaginary point, and a nothing without any quality. </s><s>As to <lb/>what <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;aid la&longs;t, that the contending whether the parts <lb/>of the Sun, Moon, or other cœle&longs;tial Body, &longs;eparated from their <lb/><emph type="italics"/>Whole,<emph.end type="italics"/> &longs;hould naturally return to it, is a vanity, for that the ca&longs;e <lb/>is impo&longs;&longs;ible; it being clear by the Demon&longs;trations of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>that the cœle&longs;tial Bodies are impa&longs;&longs;ible, impenetrable, unparta­ <lb/><arrow.to.target n="marg73"></arrow.to.target> <lb/>ble, <emph type="italics"/>&c.<emph.end type="italics"/> I an&longs;wer, that none of the conditions, whereby <emph type="italics"/>Aristo­ <lb/>tle<emph.end type="italics"/> di&longs;tingui&longs;heth the Cœle&longs;tial Bodies from Elementary, hath o­ <lb/>ther foundation than what he deduceth from the diver&longs;ity of the <lb/>natural motion of tho&longs;e and the&longs;e; in&longs;omuch that it being deni­ <lb/>ed, that the circular motion is peculiar to Cœle&longs;tial Bodies, and <lb/>affirmed, that it is agreeable to all Bodies naturally moveable, it <lb/>is behoofull upon nece&longs;&longs;ary con&longs;equence to &longs;ay, either that the <lb/>attributes of generable, or ingenerable, alterable, or unalterable, <lb/>partable, or unpartable, <emph type="italics"/>&c.<emph.end type="italics"/> equally and commonly agree with <lb/>all worldly bodies, namely, as well to the Cœle&longs;tial as to the E­ <lb/>lementary; or that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath badly and erroneou&longs;ly dedu­ <lb/>ced tho&longs;e from the circular motion, which he hath a&longs;&longs;igned to Cœ­ <lb/>le&longs;tial Bodies.</s></p><p type="margin"><s><margin.target id="marg72"></margin.target><emph type="italics"/>Grave bodies may <lb/>more rationally be <lb/>affirmed to tend to <lb/>the Centre of the <lb/>Earth, than of the <lb/>Vniver&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg73"></margin.target><emph type="italics"/>The conditions and <lb/>attributes which <lb/>differ the cœle&longs;tial <lb/>bodies from Ele­ <lb/>mentary, depend on <lb/>the motions a&longs;&longs;ign­ <lb/>ed them by<emph.end type="italics"/> Ari&longs;t.</s></p><p type="main"><s>SIMPL. </s><s>This manner of argumentation tends to the &longs;ubver&longs;i­ <lb/>on of all Natural Philo&longs;ophy, and to the di&longs;order and &longs;ubver&longs;ion <lb/>of Heaven and Earth, and the whole Univer&longs;e; but I believe the <lb/>Fundamentals of the <emph type="italics"/>Peripateticks<emph.end type="italics"/> are &longs;uch, that we need not <lb/>fear that new Sciences can be erected upon their ruines.</s></p><p type="main"><s>SALV. </s><s>Take no thought in this place for Heaven or the Earth, <lb/>neither fear their &longs;ubver&longs;ion, or the ruine of Philo&longs;ophy. </s><s>As to <lb/>Heaven, your fears are vain for that which you your &longs;elf hold <lb/>unalterable and impa&longs;&longs;ible; as for the Earth, we &longs;trive to enoble <lb/>and perfect it, whil&longs;t we make it like to the Cœle&longs;tial Bodies, <lb/>and as it were place it in Heaven, whence your Philo&longs;ophers have <lb/>exiled it. </s><s>Philo&longs;ophy it &longs;elf cannot but receive benefit from our <lb/><arrow.to.target n="marg74"></arrow.to.target> <lb/>Di&longs;putes, for if our conceptions prove true, new Di&longs;coveries will <lb/>be made; if fal&longs;e, the fir&longs;t Doctrine will be more confirmed. <lb/></s><s>Rather be&longs;tow your care upon &longs;ome Philo&longs;ophers, and help and <lb/>defend them; for as to the Science it &longs;elf, it cannot but improve. <lb/></s><s>And that we may return to our purpo&longs;e, be plea&longs;ed freely to pro­ <lb/>duce what pre&longs;ents it &longs;elf to you in confirmation of that great dif­ <lb/>ference which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> puts between the Cœle&longs;tial Bodies, and <lb/>the Elementary parts of the World, in making tho&longs;e ingenerable, <pb xlink:href="040/01/042.jpg" pagenum="26"/>incorruptible, unalterable, <emph type="italics"/>&c.<emph.end type="italics"/> and this corruptible, alterable, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg74"></margin.target><emph type="italics"/>The di&longs;putes and <lb/>contradictions of <lb/>Philo&longs;ophers may <lb/>conduce to the <lb/>benefit of Philo&longs;o­ <lb/>phy.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I &longs;ee not yet any need that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath of help, <lb/>&longs;tanding as he doth &longs;toutly and &longs;trongly on his feet; yea not be­ <lb/>ing yet a&longs;&longs;aulted, much le&longs;s foiled by you. </s><s>And what ward will <lb/>you choo&longs;e in this combate for this fir&longs;t blow? <emph type="italics"/>Aristotle<emph.end type="italics"/> writeth, <lb/><arrow.to.target n="marg75"></arrow.to.target> <lb/>that whatever is generated, is made out of a contrary in &longs;ome <lb/>&longs;ubject, and likewi&longs;e is corrupted in &longs;ome certain &longs;ubject from a <lb/><arrow.to.target n="marg76"></arrow.to.target> <lb/>contrary into a contrary; &longs;o that (ob&longs;erve) corruption and ge­ <lb/>neration is never but onely in contraries; If therefore to a Cœ­ <lb/>le&longs;tial Body no contrary can be a&longs;&longs;igned, for that to the circular <lb/><arrow.to.target n="marg77"></arrow.to.target> <lb/>motion no other motion is contrary, then Nature hath done very <lb/>well to make that exempt from contraries, which was to be in­ <lb/>generable and incorruptible, This fundamental fir&longs;t confirmed, <lb/>it immediately followeth of con&longs;equence, that it is inaugmenta­ <lb/>ble, inalterable, impa&longs;&longs;ible, and finally eternal, and a propor­ <lb/><arrow.to.target n="marg78"></arrow.to.target> <lb/>tionate habitation to the immortal Deities, conformable to the <lb/>opinion even of all men that have any conceit of the Gods. </s><s>He <lb/><arrow.to.target n="marg79"></arrow.to.target> <lb/>afterwards confirmeth the &longs;ame by &longs;en&longs;e; in regard, that in all <lb/>times pa&longs;t, according to memory or tradition, we &longs;ee nothing re­ <lb/>moved, according to the whole outward Heaven, nor any of its <lb/><arrow.to.target n="marg80"></arrow.to.target> <lb/>proper parts. </s><s>Next, as to the circular motion, that no other is <lb/>contrary to it, <emph type="italics"/>Aristotle<emph.end type="italics"/> proveth many ways; but without reci­ <lb/>ting them all, it is &longs;ufficiently demon&longs;trated, &longs;ince fimple motions <lb/>are but three, to the <emph type="italics"/>medium,<emph.end type="italics"/> from the <emph type="italics"/>medium,<emph.end type="italics"/> and about the <lb/><emph type="italics"/>medium,<emph.end type="italics"/> of which the two right, <emph type="italics"/>&longs;ur&longs;um<emph.end type="italics"/> and <emph type="italics"/>deor&longs;um,<emph.end type="italics"/> are mani­ <lb/>fe&longs;tly contrary; and becau&longs;e one onely hath onely one for con­ <lb/>trary, therefore there re&longs;ts no other motion which may be contra­ <lb/>ry to the circular. </s><s>You &longs;ee the &longs;ubtle and mo&longs;t concluding di&longs;­ <lb/>cour&longs;e of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> whereby he proveth the incorruptibility of <lb/>Heaven.</s></p><p type="margin"><s><margin.target id="marg75"></margin.target>Ari&longs;totles <emph type="italics"/>di&longs;cour&longs;e <lb/>to prove the incor­ <lb/>ruptibility of Hea­ <lb/>ven.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg76"></margin.target><emph type="italics"/>Generation & cor­ <lb/>ruption is onely a­ <lb/>mong&longs;t contraries, <lb/>according to<emph.end type="italics"/> Ari&longs;t.</s></p><p type="margin"><s><margin.target id="marg77"></margin.target><emph type="italics"/>To the circular <lb/>motion no other <lb/>motion is contrary.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg78"></margin.target><emph type="italics"/>Heaven an habi­ <lb/>tation for the imm­ <lb/>ortal Gods.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg79"></margin.target><emph type="italics"/>Immutability of <lb/>Heaven evident to <lb/>&longs;ex&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg80"></margin.target><emph type="italics"/>He proveth that <lb/>the circular motion <lb/>hath no contrary.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>This is nothing more, &longs;ave the pure progre&longs;s of <emph type="italics"/>Ari&longs;to­ <lb/>tle,<emph.end type="italics"/> by me hinted before; wherein, be&longs;ides that I affirm, that the <lb/>motion which you attribute to the Cœle&longs;tial Bodies agreeth al&longs;o <lb/>to the Earth, its illation proves nothing. </s><s>I tell you therefore, <lb/>that that circular motion which you a&longs;&longs;ign to Cœle&longs;tial Bodies, <lb/>&longs;uiteth al&longs;o to the Earth, from which, &longs;uppo&longs;ing that the re&longs;t of <lb/>your di&longs;cour&longs;e were concludent, will follow one of the&longs;e three <lb/>things, as I told you a little before, and &longs;hall repeat; namely, <lb/>either that the Earth it &longs;elf is al&longs;o ingenerable, and incorruptible, <lb/>as the Cœle&longs;tial bodies; or that the Cœle&longs;tial bodies are, like as <lb/>the Elementary generable, alterable &c. </s><s>or that this difference of <lb/>motion hath nothing to do with Generation and Corruption. <lb/></s><s>The di&longs;cour&longs;e of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and yours al&longs;o contain many Propo&longs;i­ <lb/>tions not to be lightly admitted, and the better to examine them, <lb/>it will be convenient to reduce them to the mo&longs;t ab&longs;tracted and <pb xlink:href="040/01/043.jpg" pagenum="27"/>di&longs;tinct that can be po&longs;&longs;ible; and excu&longs;e me <emph type="italics"/>Sagredus,<emph.end type="italics"/> if haply <lb/>with &longs;ome tediou&longs;ne&longs;s you hear me oft repeat the &longs;ame things, <lb/>and fancie that you &longs;ee me rea&longs;&longs;ume my argument in the pub­ <lb/>lick circle of Di&longs;putations. </s><s>You &longs;ay Generation and Corrupti­ <lb/>on are onely made where there are contraries; contraries <lb/>are onely among&longs;t &longs;imple natural bodies, moveable with contrary <lb/>motions; contrary motions are onely tho&longs;e which are made by <lb/>a right line between contrary terms; and the&longs;e are onely two, <lb/>that is to &longs;ay, from the <emph type="italics"/>medium,<emph.end type="italics"/> and towards the <emph type="italics"/>medium<emph.end type="italics"/>; and <lb/>&longs;uch motions belong to no other natural bodies, but to the <emph type="italics"/>Earth,<emph.end type="italics"/> <lb/>the <emph type="italics"/>Fire,<emph.end type="italics"/> and the other two Elements: therefore Generation <lb/>and Corruption is onely among&longs;t the Elements. </s><s>And becau&longs;e <lb/>the third &longs;imple motion, namely, the circular about the <emph type="italics"/>medium,<emph.end type="italics"/> <lb/>hath no contrary, (for that the other two are contraries, and one <lb/>onely, hath but onely one contrary) therefore that natural body <lb/>with which &longs;uch motion agreeth, wants a contrary; and having <lb/>no contrary is ingenerable and incorruptible, &c. </s><s>Becau&longs;e where <lb/>there is no contrariety, there is no generation or corruption, <emph type="italics"/>&c.<emph.end type="italics"/> <lb/>But &longs;uch motion agreeth onely with the Cœle&longs;tial bodies; there­ <lb/><arrow.to.target n="marg81"></arrow.to.target> <lb/>fore onely the&longs;e are ingenerable, incorruptible, <emph type="italics"/>&c.<emph.end type="italics"/> And to <lb/>begin, I think it a more ea&longs;ie thing, and &longs;ooner done to re&longs;olve, <lb/>whether the Earth (a mo&longs;t va&longs;t Body, and for its vicinity to us, <lb/>mo&longs;t tractable) moveth with a &longs;peedy motion, &longs;uch as its revo­ <lb/>lution about its own axis in twenty four hours would be, than it <lb/>is to under&longs;tand and re&longs;olve, whether Generation and Corruption <lb/>ari&longs;eth from contrariety, or el&longs;e whether there be &longs;uch things as <lb/>generation, corruption and contrariety in nature. </s><s>And if you, <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> can tell me what method Nature ob&longs;erves in working, <lb/>when &longs;he in a very &longs;hort time begets an infinite number of flies <lb/>from a little vapour of the Mu&longs;t of wine, and can &longs;hew me which <lb/>are there the contraries you &longs;peak of, what it is that corrupteth, <lb/>and how; I &longs;hould think you would do more than I can; for I <lb/>profe&longs;s I cannot comprehend the&longs;e things. </s><s>Be&longs;ides, I would ve­ <lb/>ry gladly under&longs;tand how, and why the&longs;e corruptive contraries are <lb/>&longs;o favourable to Daws, and &longs;o cruel to Doves; &longs;o indulgent to <lb/>Stags, and &longs;o ha&longs;ty to Hor&longs;es, that they do grant to them many <lb/>more years of life, that is, of incorruptibility, than weeks to the&longs;e. <lb/></s><s>Peaches and Olives are planted in the &longs;ame &longs;oil, expo&longs;ed to the <lb/>&longs;ame heat and cold, to the &longs;ame wind and rains, and, in a word, <lb/>to the &longs;ame contrarieties; and yet tho&longs;e decay in a &longs;hort time, <lb/>and the&longs;e live many hundred years. </s><s>Furthermore, I never was <lb/>thorowly &longs;atisfied about this &longs;ub&longs;tantial tran&longs;mutation (&longs;till keep­ <lb/>ing within pure natural bounds) whereby a matter becometh &longs;o <lb/>transform'd, that it &longs;hould be nece&longs;&longs;arily &longs;aid to be de&longs;troy'd, &longs;o <lb/>that nothing remaineth of its fir&longs;t being, and that another body <pb xlink:href="040/01/044.jpg" pagenum="28"/><arrow.to.target n="marg82"></arrow.to.target> <lb/>quite differing there-from &longs;hould be thence produced; and if I <lb/>fancy to my &longs;elf a body under one a&longs;pect, and by and by under <lb/>another very different, I cannot think it impo&longs;&longs;ible but that it may <lb/>happen by a &longs;imple tran&longs;po&longs;ition of parts, without corrupting or <lb/>ingendring any thing a-new; for we &longs;ee &longs;uch kinds of Metamor­ <lb/>pho&longs;es dayly: &longs;o that to return to my purpo&longs;e, I an&longs;wer you, <lb/>that ina&longs;much as you go about to per&longs;wade me that the Earth can <lb/>not move circularly by way of corruptibility and generability, <lb/>you have undertook a much harder task than I, that with argu­ <lb/>ments more difficult indeed, but no le&longs;s concluding, will prove <lb/>the contrary.</s></p><p type="margin"><s><margin.target id="marg81"></margin.target><emph type="italics"/>Its ea&longs;ier to prove <lb/>the Earth to move, <lb/>than that corrupti­ <lb/>on is made by con­ <lb/>traries.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg82"></margin.target><emph type="italics"/>Bare tran&longs;po&longs;ition <lb/>of parts may repre­ <lb/>&longs;ent bodies under <lb/>diver&longs;e asp cts.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Pardon me, <emph type="italics"/>Salviatus,<emph.end type="italics"/> if I interrupt your di&longs;cour&longs;e, <lb/>which, as it delights me much, for that I al&longs;o am gravel'd with <lb/>the &longs;ame doubts; &longs;o I fear that you can never conclude the &longs;ame, <lb/>without altogether digre&longs;&longs;ing from your chief de&longs;ign: therefore <lb/>if it be permitted to proceed in our fir&longs;t argument, I &longs;hould think <lb/>that it were convenient to remit this que&longs;tion of generation and <lb/>corruption to another di&longs;tinct and &longs;ingle conference; as al&longs;o, if <lb/>it &longs;hall plea&longs;e you and <emph type="italics"/>Simplicius,<emph.end type="italics"/> we may do by other particular <lb/>que&longs;tions which may fall in the way of our di&longs;cour&longs;e; which I <lb/>will keep in my mind to propo&longs;e, and exactly di&longs;cu&longs;s them &longs;ome <lb/>other time. </s><s>Now as for the pre&longs;ent, &longs;ince you &longs;ay, that if <emph type="italics"/>Ari­ <lb/>&longs;totle<emph.end type="italics"/> deny circular motion to the Earth in common with other <lb/>bodies Cœle&longs;tial, it chence will follow, that the &longs;ame which be­ <lb/>falleth the Earth, as to its being generable, alterable, <emph type="italics"/>&c.<emph.end type="italics"/> will <lb/>hold al&longs;o of Heaven, let us enquire no further if there be &longs;uch <lb/>things in nature, as generation and corruption, or not; but let <lb/>us return to enquire what the Globe of the Earth doth.</s></p><p type="main"><s>SIMPL. </s><s>I cannot &longs;uffer my ears to hear it que&longs;tion'd, whether <lb/>generation and corruption be in <emph type="italics"/>rerum naturà,<emph.end type="italics"/> it being a thing <lb/>which we have continually before our eyes, and whereof <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/><arrow.to.target n="marg83"></arrow.to.target> <lb/>hath written two whole Books. </s><s>But if you go about to deny the <lb/>Principles of Sciences, and que&longs;tion things mo&longs;t manife&longs;t, who <lb/>knows not, but that you may prove what you will, and maintain <lb/>any <emph type="italics"/>Paradox<emph.end type="italics"/>? </s><s>And if you do not dayly &longs;ee herbs, plants, ani­ <lb/>mals to generate and corrupt, what is it that you do &longs;ee? </s><s>Al&longs;o, <lb/>do you not continually behold contrarieties contend together, <lb/>and the Earth change into Water, the Water turn to Air, the <lb/>Air into Fire, and again the Air to conden&longs;e into Clouds, Rains, <lb/>Hails and Storms?</s></p><p type="margin"><s><margin.target id="marg83"></margin.target><emph type="italics"/>By denying Prin­ <lb/>ciples in the Scien­ <lb/>ces, any Paradox <lb/>may be maintain­ <lb/>ed.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. Yes, we &longs;ee the&longs;e things indeed, and therefore will <lb/>grant you the di&longs;cour&longs;e of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> as to this part of generation <lb/>and corruption made by contraries; but if I &longs;hall conclude by <lb/>virtue of the &longs;ame propo&longs;itions which are granted to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>that the Cœle&longs;tial bodies them&longs;elves are al&longs;o generable and cor­ <pb xlink:href="040/01/045.jpg" pagenum="29"/>ruptible, a&longs;well as the Elementary, what will you &longs;ay then?</s></p><p type="main"><s>SIMPL. </s><s>I will &longs;ay you have done that which is impo&longs;&longs;ible to <lb/>be done.</s></p><p type="main"><s>SAGR. </s><s>Go to; tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> are not the&longs;e affections <lb/>contrary to one another?</s></p><p type="main"><s>SIMPL. Which?</s></p><p type="main"><s>SAGR. </s><s>Why the&longs;e; Alterable, unalterable; pa&longs;&longs;ible, ^{*} impa&longs;­ <lb/><arrow.to.target n="marg84"></arrow.to.target> <lb/>&longs;ible; generable, ingenerable; corruptible, incorruptible?</s></p><p type="margin"><s><margin.target id="marg84"></margin.target>* <emph type="italics"/>Or,<emph.end type="italics"/> Impatible.</s></p><p type="main"><s>SIMPL. </s><s>They are mo&longs;t contrary.</s></p><p type="main"><s>SAGR. </s><s>Well then, if this be true, and it be al&longs;o granted, <lb/>that Cœle&longs;tial Bodies are ingenerable and incorruptible; I prove <lb/>that of nece&longs;&longs;ity Cœle&longs;tial Bodies mu&longs;t be generable and corru­ <lb/>ptible.</s></p><p type="main"><s>SIMPL. </s><s>This mu&longs;t needs be a <emph type="italics"/>Sophi&longs;m.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Hear my Argument, and then cen&longs;ure and re&longs;olve it. <lb/><arrow.to.target n="marg85"></arrow.to.target> <lb/>Cœle&longs;tial Bodies, for that they are ingenerable and incorruptible, <lb/>have in Nature their contraries, which are tho&longs;e Bodies that be <lb/>generable and corruptible; but where there is contrariety, there <lb/>is al&longs;o generation and corruption; therefore Cœle&longs;tial Bodies are <lb/>generable and corruptible.</s></p><p type="margin"><s><margin.target id="marg85"></margin.target><emph type="italics"/>Cœlestial Bodies <lb/>are generable and <lb/>corruptible, be­ <lb/>cau&longs;e they are in­ <lb/>generable and in­ <lb/>corruptible.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>Did I not &longs;ay it could be no other than a <emph type="italics"/>Sophi&longs;m<emph.end type="italics"/>? <lb/></s><s>This is one of tho&longs;e forked Arguments called <emph type="italics"/>Soritæ<emph.end type="italics"/>: like that <lb/><arrow.to.target n="marg86"></arrow.to.target> <lb/>of the <emph type="italics"/>Cretan,<emph.end type="italics"/> who &longs;aid that all <emph type="italics"/>Cretans<emph.end type="italics"/> were lyars; but he as <lb/>being a <emph type="italics"/>Cretan,<emph.end type="italics"/> had told a lye, in &longs;aying that the <emph type="italics"/>Cretans<emph.end type="italics"/> were ly­ <lb/>ars; it followed therefore, that the <emph type="italics"/>Cretans<emph.end type="italics"/> were no lyars, and <lb/>con&longs;equently that he, as being a <emph type="italics"/>Cretan,<emph.end type="italics"/> had &longs;poke truth: And <lb/>yet in &longs;aying the <emph type="italics"/>Cretans<emph.end type="italics"/> were lyars, he had &longs;aid true, and com­ <lb/>prehending him&longs;elf as a <emph type="italics"/>Cretan,<emph.end type="italics"/> he mu&longs;t con&longs;equently be a lyar. <lb/></s><s>And thus in the&longs;e kinds of <emph type="italics"/>Sophi&longs;ms<emph.end type="italics"/> a man may dwell to eternity, <lb/>and never come to any conclu&longs;ion.</s></p><p type="margin"><s><margin.target id="marg86"></margin.target><emph type="italics"/>The forked Syllo­ <lb/>gi&longs;m cal'd<emph.end type="italics"/> <foreign lang="greek">*cwri/ths.</foreign></s></p><p type="main"><s>SAGR. </s><s>You have hitherto cen&longs;ured it, it remaineth now that <lb/>you an&longs;wer it, &longs;hewing the fallacie.</s></p><p type="main"><s>SIMPL. </s><s>As to the re&longs;olving of it, and finding out its fallacie, <lb/>do you not in the fir&longs;t place &longs;ee a manife&longs;t contradiction in it? <lb/></s><s>Cœle&longs;tial Bodies are ingenerable and incorruptible; <emph type="italics"/>Ergo,<emph.end type="italics"/> Cœle­ <lb/>&longs;tial Bodies are generable and corruptible. </s><s>And again, the con­ <lb/><arrow.to.target n="marg87"></arrow.to.target> <lb/>trariety is not betwixt the Cœle&longs;tial Bodies, but betwixt the E­ <lb/>lements, which have the contrariety of the Motions, <emph type="italics"/>&longs;ur&longs;ùm<emph.end type="italics"/> and <lb/><emph type="italics"/>deor&longs;ùm,<emph.end type="italics"/> and of levity and gravity; But the Heavens which move <lb/>circularly, to which motion no other motion is contrary, want <lb/>contrariety, and therefore they are incorruptible.</s></p><p type="margin"><s><margin.target id="marg87"></margin.target><emph type="italics"/>Among&longs;t Cœle&longs;tial <lb/>Bodies there is no <lb/>contrariety.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Fair and &longs;oftly, <emph type="italics"/>Simplicius<emph.end type="italics"/>; this contrariety whereby <lb/>you &longs;ay &longs;ome &longs;imple Bodies become corruptible, re&longs;ides it in the <lb/>&longs;ame Body which is corrupted, or el&longs;e hath it relation to &longs;ome o­ <lb/>other? </s><s>I &longs;ay, for example, the humidity by which a piece of Earth <pb xlink:href="040/01/046.jpg" pagenum="30"/>is corrupted, re&longs;ides it in the &longs;ame Earth or in &longs;ome other bodie, <lb/>which mu&longs;t either be the Air or Water? </s><s>I believe you will grant, <lb/>that like as the Motions upwards and downwards, and gravity <lb/>and levity, which you make the fir&longs;t contraries, cannot be in the <lb/>&longs;ame Subject, &longs;o neither can moi&longs;t and dry, hot and cold: you <lb/>mu&longs;t therefore con&longs;equently acknowledg that when a bodie cor­ <lb/><arrow.to.target n="marg88"></arrow.to.target> <lb/>rupteth, it is occa&longs;ioned by &longs;ome quality re&longs;iding in another con­ <lb/>trary to its own: therefore to make the Cœle&longs;tial Body become <lb/>corruptible, it &longs;ufficeth that there are in Nature, bodies that have <lb/>a contrariety to that Cœle&longs;tial body; and &longs;uch are the Elements, <lb/>if it be true that corruptibility be contrary to incorruptibility.</s></p><p type="margin"><s><margin.target id="marg88"></margin.target><emph type="italics"/>Contraries which <lb/>are the cau&longs;es of <lb/>corruption, re&longs;ide <lb/>not in the &longs;ame bo­ <lb/>dy that corrupteth.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>This &longs;ufficeth not, Sir; The Elements alter and cor­ <lb/>rupt, becau&longs;e they are intermixed, and are joyn'd to one another, <lb/><arrow.to.target n="marg89"></arrow.to.target> <lb/>and &longs;o may exerci&longs;e their contrariety; but Cœle&longs;tial bodies are <lb/>&longs;eparated from the Elements, by which they are not &longs;o much as <lb/>toucht, though indeed they have an influence upon the Elements. <lb/></s><s>It is requi&longs;ite, if you will prove generation and corruption in Cœ­ <lb/>le&longs;tial bodies, that you &longs;hew, that there re&longs;ides contrarieties be­ <lb/>tween them.</s></p><p type="margin"><s><margin.target id="marg89"></margin.target><emph type="italics"/>Cœle&longs;tial Bodies <lb/>touch, but are not <lb/>touched by the E­ <lb/>lements.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>See how I will find tho&longs;e contrarieties between them. <lb/></s><s>The fir&longs;t fountain from whence you derive the contrariety of the <lb/>Elements, is the contrariety of their motions upwards and down­ <lb/>wards: it therefore is nece&longs;&longs;ary that tho&longs;e Principles be in like <lb/><arrow.to.target n="marg90"></arrow.to.target> <lb/>manner contraries to each other, upon which tho&longs;e motions de­ <lb/>pend. </s><s>and becau&longs;e that is moveable upwards by lightne&longs;s, <lb/>and this downwards by gravitv, it is nece&longs;&longs;ary that lightne&longs;s and <lb/>gravity are contrary to each other: no le&longs;s are we to believe tho&longs;e <lb/>other Principles to be contraries, which are the cau&longs;es that this is <lb/>heavy, and that light: but by your own confe&longs;&longs;ion, levity and <lb/>gravity follow as con&longs;equents of rarity and den&longs;ity; therefore <lb/><arrow.to.target n="marg91"></arrow.to.target> <lb/>rarity and den&longs;ity &longs;hall be contraries: the which conditions or <lb/>affections are &longs;o amply found in Cœle&longs;tial bodies, that you e­ <lb/>&longs;teem the &longs;tars to be onely more den&longs;e parts of their Heaven: <lb/>and if this be &longs;o, it followeth that the den&longs;ity of the &longs;tars exceeds <lb/>that of the re&longs;t of Heaven, by almo&longs;t infinite degrees: <lb/>which is manife&longs;t, in that Heaven is infinitely tran&longs;parent, and <lb/>the &longs;tars extremely opacous; and for that there are there above <lb/>no other qualities, but more and le&longs;s den&longs;ity and rarity, which <lb/>may be cau&longs;es of the greater or le&longs;s tran&longs;parency. </s><s>There being <lb/>then &longs;uch contrariety between the Cœleftial bodies, it is nece&longs;&longs;ary <lb/>that they al&longs;o be generable and corruptible, in the &longs;ame manner <lb/>as the Elementary bodies are; or el&longs;e that contrariety is not the <lb/><arrow.to.target n="marg92"></arrow.to.target> <lb/>cau&longs;e of corruptibility, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg90"></margin.target><emph type="italics"/>Gravity & levity, <lb/>varity and den&longs;ity, <lb/>are contrary qua­ <lb/>lities.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg91"></margin.target><emph type="italics"/>The &longs;tars infinitely <lb/>&longs;urpa&longs;s the &longs;ub­ <lb/>&longs;tance of the re&longs;t of <lb/>Heaven in den&longs;ity.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg92"></margin.target><emph type="italics"/>Rarity & den&longs;ity <lb/>in Cœle&longs;tial bodies, <lb/>is different from <lb/>the rarity & den­ <lb/>&longs;ity of the elements.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>There is no nece&longs;&longs;ity either of one or the other, for <lb/>that den&longs;ity and rarity in Cœle&longs;tial bodies, are not contraries to <pb xlink:href="040/01/047.jpg" pagenum="31"/>each other, as in Elementary bodies; for that they depend not <lb/>on the primary qualities, cold and heat, which are contraries; but <lb/>on the more or le&longs;s matter in proportion to quantity: now much <lb/>and little, &longs;peak onely a relative oppo&longs;ition, that is, the lea&longs;t of <lb/>oppo&longs;itions, and which hath nothing to do with generation and <lb/>corruption.</s></p><p type="main"><s>SAGR. </s><s>Therefore affirming, that den&longs;ity and rarity, which a­ <lb/>mong&longs;t the Elements &longs;hould be the cau&longs;e of gravity and levity, <lb/>which may be the cau&longs;es of contrary motions <emph type="italics"/>&longs;ur&longs;ùm<emph.end type="italics"/> and <emph type="italics"/>deor­ <lb/>&longs;ùm,<emph.end type="italics"/> on which, again, dependeth the contrarieties for generation <lb/>and corruption; it &longs;ufficeth not that they be tho&longs;e den&longs;ne&longs;&longs;es and <lb/>rarene&longs;&longs;es which under the &longs;ame quantity, or (if you will) ma&longs;s <lb/>contain much or little matter, but it is nece&longs;&longs;ary that they be den&longs;­ <lb/>ne&longs;&longs;es and rarene&longs;&longs;es cau&longs;ed by the primary qualities, hot and <lb/>cold, otherwi&longs;e they would operate nothing at all: but if this be <lb/>&longs;o, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath deceived us, for that he &longs;hould have told it us at <lb/><arrow.to.target n="marg93"></arrow.to.target> <lb/>fir&longs;t, and &longs;o have left written that tho&longs;e &longs;imple bodies are gene­ <lb/>rable and corruptible, that are moveable with &longs;imple motions <lb/>upwards and downwards, dependent on levity and gravity, cau­ <lb/>&longs;ed by rarity and den&longs;ity, made by much or little matter, by <lb/>rea&longs;on of heat and cold; and not to have &longs;taid at the &longs;imple mo­ <lb/>tion <emph type="italics"/>&longs;ur&longs;ùm<emph.end type="italics"/> and <emph type="italics"/>deor&longs;ùm<emph.end type="italics"/>: for I a&longs;&longs;ure you that to the making <lb/>of bodies heavy or light, whereby they come to be moved with <lb/>contrary motions, any kind of den&longs;ity and rarity &longs;ufficeth, whe­ <lb/>ther it proceed from heat and cold, or what el&longs;e you plea&longs;e; for <lb/>heat and cold have nothing to do in this affair: and you &longs;hall <lb/>upon experiment find, that a red hot iron, which you mu&longs;t grant <lb/>to have heat, weigheth as much, and moves in the &longs;ame manner <lb/>as when it is cold. </s><s>But to overpa&longs;s this al&longs;o, how know you but <lb/>that Cœle&longs;tial rarity and den&longs;ity depend on heat and cold?</s></p><p type="margin"><s><margin.target id="marg93"></margin.target>Ari&longs;totle <emph type="italics"/>defective <lb/>in a&longs;&longs;igning the <lb/>cau&longs;es why the ele­ <lb/>ments are genera­ <lb/>ble & corruptible.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I know it, becau&longs;e tho&longs;e qualities are not among&longs;t <lb/>Cœle&longs;tial bodies, which are neither hot nor cold.</s></p><p type="main"><s>SALV. </s><s>I &longs;ee we are again going about to engulph our &longs;elves in <lb/>a bottomle&longs;s ocean, where there is no getting to &longs;hore; for this <lb/>is a Navigation without Compa&longs;s, Stars, Oars or Rudder: &longs;o that <lb/>it will follow either that we be forced to pa&longs;s from Shelf to Shelf, <lb/>or run on ground, or to &longs;ail continually in danger of being lo&longs;t. <lb/></s><s>Therefore, if according to your advice we &longs;hall proceed in our <lb/>main de&longs;ign, we mu&longs;t of nece&longs;&longs;ity for the pre&longs;ent overpa&longs;s this <lb/>general con&longs;ideration, whether direct motion be nece&longs;&longs;ary in Na­ <lb/>ture, and agree with &longs;ome bodies; and come to the particular <lb/>demon&longs;trations, ob&longs;ervations and experiments; propounding in <lb/>the fir&longs;t place all tho&longs;e that have been hitherto alledged by <emph type="italics"/>Ari­ <lb/>&longs;totle, Ptolomey,<emph.end type="italics"/> and others, to prove the &longs;tability of the Earth, en­ <lb/>deavouring in the next place to an&longs;wer them: and producing in <pb xlink:href="040/01/048.jpg" pagenum="32"/>the la&longs;t place, tho&longs;e, by which others may be per&longs;waded, that the <lb/>Earth is no le&longs;s than the Moon, or any other Planet to be num­ <lb/>bered among&longs;t natural bodies that move circularly.</s></p><p type="main"><s>SAGR. </s><s>I &longs;hall the more willingly incline to this, in that I am <lb/>better &longs;atisfied with your Architectonical and general di&longs;cour&longs;e, <lb/>than with that of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> for yours convinceth me without the <lb/>lea&longs;t &longs;cruple, and the other at every &longs;tep cro&longs;&longs;eth my way with <lb/>&longs;ome block. </s><s>And I &longs;ee no rea&longs;on why <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;hould not be <lb/>pre&longs;ently &longs;atisfied with the Argument you alledg, to prove that <lb/>there can be no &longs;uch thing in nature as a motion by a right line, <lb/>if we do but pre&longs;uppo&longs;e that the parts of the Univer&longs;e are di&longs;po­ <lb/>&longs;ed in an excellent con&longs;titution and perfect order.</s></p><p type="main"><s>SALV. </s><s>Stay a little, good <emph type="italics"/>Sagredus,<emph.end type="italics"/> for ju&longs;t now a way comes <lb/>into my mind, how I may give <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;atisfaction, provided <lb/>that he will not be &longs;o &longs;trictly wedded to every expre&longs;&longs;ion of <emph type="italics"/>A­ <lb/>ri&longs;totle,<emph.end type="italics"/> as to hold it here&longs;ie to recede in any thing from him. </s><s>Nor <lb/>is there any que&longs;tion to be made, but that if we grant the excel­ <lb/>lent di&longs;po&longs;ition and perfect order of the parts of the Univer&longs;e, <lb/>as to local &longs;cituation, that then there is no other but the circular <lb/>motion, and re&longs;t; for as to the motion by a right line, I &longs;ee not <lb/>how it can be of u&longs;e for any thing, but to reduce to their natural <lb/>con&longs;titution, &longs;ome integral bodies, that by &longs;ome accident were re­ <lb/>mov'd and &longs;eparated from their whole, as we &longs;aid above.</s></p><p type="main"><s>Let us now con&longs;ider the whole Terre&longs;trial Globe, and enquire <lb/>the be&longs;t we can, whether it, and the other Mundane bodies are to <lb/>con&longs;erve them&longs;elves in their perfect and natural di&longs;po&longs;ition. </s><s>It <lb/>is nece&longs;&longs;ary to &longs;ay, either that it re&longs;ts and keeps perpetually im­ <lb/>moveable in its place; or el&longs;e that continuing always in its place, <lb/>it revolves in its &longs;elf; or that it turneth about a Centre, moving <lb/><arrow.to.target n="marg94"></arrow.to.target> <lb/>by the circumference of a circle. </s><s>Of which accidents, both <emph type="italics"/>Ari­ <lb/>&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomey,<emph.end type="italics"/> and all their followers &longs;ay, that it hath ever <lb/>ob&longs;erved, and &longs;hall continually keep the fir&longs;t, that is, a perpetual <lb/><arrow.to.target n="marg95"></arrow.to.target> <lb/>re&longs;t in the &longs;ame place. </s><s>Now, why, I pray you, ought they not <lb/>to have &longs;aid, that its natural affection is to re&longs;t immoveable, ra­ <lb/>ther than to make natural unto it the motion ^{*} downwards, with <lb/>which motion it never did or &longs;hall move? </s><s>And as to the motion <lb/><arrow.to.target n="marg96"></arrow.to.target> <lb/>by a right line, they mu&longs;t grant us that Nature maketh u&longs;e of it <lb/>to reduce the &longs;mall parts of the Earth, Water, Air, Fire, and every <lb/>other integral Mundane body to their <emph type="italics"/>Whole,<emph.end type="italics"/> when any of them <lb/>by chance are &longs;eparated, and &longs;o tran&longs;ported out of their proper <lb/>place; if al&longs;o haply, &longs;ome circular motion might not be found <lb/>to be more convenient to make this re&longs;titution. </s><s>In my judg­ <lb/>ment, this primary po&longs;ition an&longs;wers much better, even according <lb/>to <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> own method, to all the other con&longs;equences, than <lb/>to attribute the &longs;traight motion to be an intrin&longs;ick and natural <pb xlink:href="040/01/049.jpg" pagenum="33"/>principle of the Elements. </s><s>Which is manife&longs;t, for that if I aske <lb/>the <emph type="italics"/>Peripatetick,<emph.end type="italics"/> if, being of opinion that Cœle&longs;tial bodies are <lb/>incorruptibe and eternal, he believeth that the Terre&longs;tial Globe <lb/>is not &longs;o, but corruptible and mortal, &longs;o that there &longs;hall come a <lb/>time, when the Sun and Moon and other Stars, continuing their <lb/>beings and operations, the Earth &longs;hall not be found in the <lb/>World, but &longs;hall with the re&longs;t of the Elements be de&longs;troyed <lb/>and annihilated, I am certain that he would an&longs;wer me, no: <lb/><arrow.to.target n="marg97"></arrow.to.target> <lb/>therefore generation and corruption is in the parts and not in the <lb/>whole; and in the parts very &longs;mall and &longs;uperficial, which are, <lb/>as it were, incen&longs;ible in compari&longs;on of the whole ma&longs;&longs;e. </s><s>And <lb/>becau&longs;e <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> deduceth generation and corruption from the <lb/>contrariety of &longs;treight motions, let us remit &longs;uch motions to the <lb/>parts, which onely change and decay, and to the whole Globe <lb/>and Sphere of the Elements, let us a&longs;cribe either the circular mo­ <lb/>tion, or a perpetual con&longs;i&longs;tance in its proper place: the only <lb/>affections apt for perpetuation, and maintaining of perfect order. <lb/></s><s>This which is &longs;poken of the Earth, may be &longs;aid with the &longs;ame <lb/>rea&longs;on of Fire, and of the greate&longs;t part of the Air; to which <lb/><arrow.to.target n="marg98"></arrow.to.target> <lb/>Elements, the <emph type="italics"/>Peripateticks<emph.end type="italics"/> are forced to a&longs;cribe for intrin&longs;ical <lb/>and natural, a motion wherewith they were never yet moved, <lb/>nor never &longs;hall be; and to call that motion preternatural to them, <lb/>wherewith, if they move at all, they do and ever &longs;hall move. <lb/></s><s>This I &longs;ay, becau&longs;e they a&longs;&longs;ign to the Air aud Fire the motion <lb/>upwards, wherewith tho&longs;e Elements were never moved, but <lb/>only &longs;ome parts of them, and tho&longs;e were &longs;o moved onely in or­ <lb/>der to the recovery of their perfect con&longs;titution, when they were <lb/>out of their natural places; and on the contrary they call the <lb/>circular motion preternatural to them, though they are thereby <lb/>ince&longs;&longs;antly moved: forgeting, as it &longs;eemeth, what <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> oft in­ <lb/>culcateth, that nothing violent can be permanent.</s></p><p type="margin"><s><margin.target id="marg94"></margin.target>Ari&longs;t. <emph type="italics"/>&<emph.end type="italics"/> Ptolomey <lb/><emph type="italics"/>make the Terre­ <lb/>strial Globe immo­ <lb/>veable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg95"></margin.target><emph type="italics"/>It is better to &longs;ay, <lb/>that the Terre&longs;tri­ <lb/>al Globe naturally <lb/>resteth, than that <lb/>it moveth directly <lb/>downwards.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg96"></margin.target>*The word is, <emph type="italics"/>all' <lb/>ingiù,<emph.end type="italics"/> which the <lb/>Latine ver&longs;ion ren­ <lb/>dreth <emph type="italics"/>&longs;ur&longs;ùm,<emph.end type="italics"/> <lb/>which is quite con­ <lb/>trary to the Au­ <lb/>thors &longs;en&longs;e.</s></p><p type="margin"><s><margin.target id="marg97"></margin.target><emph type="italics"/>Right Motion <lb/>with more rea&longs;on <lb/>attributed to the <lb/>parts, than to the <lb/>whole Elements.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg98"></margin.target><emph type="italics"/>The Peripateticks <lb/>improperly a&longs;&longs;ign <lb/>tho&longs;e motious to <lb/>the Elements for <lb/>Natural, with <lb/>which they never <lb/>were moved, and <lb/>tho&longs;e for Preter­ <lb/>natural with which <lb/>they alwayes are <lb/>moved.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>To all the&longs;e we have very pertinent an&longs;wers, which <lb/><arrow.to.target n="marg99"></arrow.to.target> <lb/>I for this time omit, that we may come to the more particular <lb/>rea&longs;ons, and &longs;en&longs;ible experiments, which ought in conclu&longs;ion to <lb/>be oppo&longs;ed, as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aitn well, to whatever humane rea&longs;on <lb/>can pre&longs;ent us with.</s></p><p type="margin"><s><margin.target id="marg99"></margin.target><emph type="italics"/>Sen&longs;ible experi­ <lb/>ments to be prefer­ <lb/>red to humane <lb/>Arguments.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>What hath been &longs;poken hitherto, &longs;erves to clear up <lb/>unto us which of the two general di&longs;cour&longs;es carrieth with it mo&longs;t <lb/>of probability, I mean that of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> which would per&longs;wade <lb/>us, that the &longs;ublunary bodies are by nature generable, and corru­ <lb/>ptible, <emph type="italics"/>&c.<emph.end type="italics"/> and therefore mo&longs;t different from the e&longs;&longs;ence of Cœ­ <lb/>leftial bodies, which are impa&longs;&longs;ible, ingenerable, incorruptible, <lb/><emph type="italics"/>&c.<emph.end type="italics"/> drawn from the diver&longs;ity of &longs;imple motions; or el&longs;e this of <lb/><emph type="italics"/>Salviatus,<emph.end type="italics"/> who &longs;uppo&longs;ing the integral parts of the World to be <lb/>di&longs;po&longs;ed in a perfect con&longs;titution, excludes by nece&longs;&longs;ary confe­ <pb xlink:href="040/01/050.jpg" pagenum="34"/>quence the right or &longs;traight motion of &longs;imple natural bodies, as <lb/>being of no u&longs;e in nature, and e&longs;teems the Earth it &longs;elf al&longs;o to <lb/>be one of the Cœle&longs;tial bodies adorn'd with all the prerogatives <lb/>that agree with them; which la&longs;t di&longs;cour&longs;e is hitherto much <lb/>more likely, in my judgment, than that other. </s><s>Therefore re­ <lb/>&longs;olve, <emph type="italics"/>Simplicius,<emph.end type="italics"/> to produce all the particular rea&longs;ons, experi­ <lb/>ments and ob&longs;ervations, as well Natural as A&longs;tronomical, that <lb/>may &longs;erve to per&longs;wade us that the Earth differeth from the Cœ­ <lb/>le&longs;tial bodies, is immoveable, and &longs;ituated in the Centre of the <lb/>World, and what ever el&longs;e excludes its moving like to the Planets, <lb/>as <emph type="italics"/>Jupiter<emph.end type="italics"/> or the <emph type="italics"/>Moon, &c.<emph.end type="italics"/> And <emph type="italics"/>Salviatus<emph.end type="italics"/> will be plea&longs;ed to <lb/>be &longs;o civil as to an&longs;wer to them one by one.</s></p><p type="main"><s>SIMPL. </s><s>See here for a beginning, two mo&longs;t convincing Argu­ <lb/>ments to demon&longs;trate the Earth to be mo&longs;t different from the <lb/>Cœle&longs;tial bodies. </s><s>Fir&longs;t, the bodies that are generable, corru­ <lb/>ptible, alterable, <emph type="italics"/>&c.<emph.end type="italics"/> are quite different from tho&longs;e that are in­ <lb/>generable, incorruptible, unalterable, <emph type="italics"/>&c.<emph.end type="italics"/> But the Earth is ge­ <lb/>nerable, corruptible, alterable, <emph type="italics"/>&c.<emph.end type="italics"/> and the Cœle&longs;tial bodies in­ <lb/>generable, incorruptible, unalterable, <emph type="italics"/>&c.<emph.end type="italics"/> Therefore the Earth <lb/>is quite different from the Cœle&longs;tial bodies.</s></p><p type="main"><s>SAGR. </s><s>By your fir&longs;t Argument you &longs;pread the Table with the <lb/>&longs;ame Viands, which but ju&longs;t now with much adoe were voided.</s></p><p type="main"><s>SIMPL. </s><s>Hold a little, Sir, and take the re&longs;t along with you, <lb/>and then tell me if this be not different from what you had be­ <lb/>fore. </s><s>In the former, the <emph type="italics"/>Minor<emph.end type="italics"/> was proved <emph type="italics"/>à priori,<emph.end type="italics"/> & now you &longs;ee <lb/>it proved <emph type="italics"/>à po&longs;teriori:<emph.end type="italics"/> Judg then if it be the &longs;ame. </s><s>I prove the <lb/><emph type="italics"/>Minor,<emph.end type="italics"/> therefore (the <emph type="italics"/>Major<emph.end type="italics"/> being mo&longs;t manife&longs;t) by &longs;en&longs;ible ex­ <lb/>perience, which &longs;hews us that in the Earth there are made conti­ <lb/>nual generations, corruptions, alterations, <emph type="italics"/>&c.<emph.end type="italics"/> which neither our <lb/>&longs;en&longs;es, nor the traditions or memories of our Ance&longs;tors, ever &longs;aw <lb/>an in&longs;tance of in Heaven; therefore Heaven is unalterable, <emph type="italics"/>&c.<emph.end type="italics"/> <lb/><arrow.to.target n="marg100"></arrow.to.target> <lb/>and the Earth alterable, <emph type="italics"/>&c.<emph.end type="italics"/> and therefore different from Hea­ <lb/>ven. </s><s>I take my &longs;econd Argument from a principal and e&longs;&longs;ential <lb/>accident, and it is this. </s><s>That body which is by its nature ob­ <lb/><arrow.to.target n="marg101"></arrow.to.target> <lb/>&longs;cure and deprived of light, is divers from the luminous and &longs;hi­ <lb/>ning bodies; but the Earth is ob&longs;cure and void of light, and the <lb/>Cœle&longs;tial bodies &longs;plendid, and full of light; <emph type="italics"/>Ergo, &c.<emph.end type="italics"/> An&longs;wer <lb/>to the&longs;e Arguments fir&longs;t, that we may not heap up too many, <lb/>and then I will alledge others.</s></p><p type="margin"><s><margin.target id="marg100"></margin.target><emph type="italics"/>Heaven immuta­ <lb/>ble, becau&longs;e there <lb/>never was any mu­ <lb/>tation &longs;een in it.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg101"></margin.target><emph type="italics"/>Bodies naturally <lb/>lucid, are different <lb/>from tho&longs;e which <lb/>are by nature ob­ <lb/>&longs;cure.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>As to the fir&longs;t, the &longs;tre&longs;&longs;e whereof you lay upon ex­ <lb/>perience, I de&longs;ire that you would a little more di&longs;tinctly produce <lb/>me the alteration which you &longs;ee made in the Earth, and not in <lb/>Heaven; upon which you call the Earth alterable, and the Hea­ <lb/>vens not &longs;o.</s></p><p type="main"><s>SIMPL. </s><s>I &longs;ee in the Earth, plants and animals continually ge­ <pb xlink:href="040/01/051.jpg" pagenum="35"/>nerating and decaying; winds, rains, tempe&longs;ts, &longs;torms ari&longs;ing; and <lb/>in a word, the a&longs;pect of the Earth to be perpetually metamorpho­ <lb/>&longs;ing; none of which mutations are to be di&longs;cern'd in the Cœle&longs;tial <lb/>bodies; the con&longs;titution and figuration of which is mo&longs;t punctu­ <lb/>ally conformable to that they ever were time out of mind; without <lb/>the generation of any thing that is new, or corruption of any thing <lb/>that was old.</s></p><p type="main"><s>SALV. </s><s>But if you content your &longs;elf with the&longs;e vi&longs;ible, or to <lb/>&longs;ay better, &longs;een experiments, you mu&longs;t con&longs;equently account <lb/><emph type="italics"/>China<emph.end type="italics"/> and <emph type="italics"/>America<emph.end type="italics"/> Cœle&longs;tial bodies, for doubtle&longs;&longs;e you never <lb/>beheld in them the&longs;e alterations which you &longs;ee here in <emph type="italics"/>Italy,<emph.end type="italics"/> and <lb/>that therefore according to your apprehen&longs;ion they are inal­ <lb/>terable.</s></p><p type="main"><s>SIMPL. </s><s>Though I never did &longs;ee the&longs;e alterations &longs;enfibly in <lb/>tho&longs;e places, the relations of them are not to be que&longs;tioned; <lb/>be&longs;ides that, <emph type="italics"/>cum eadem &longs;it ratio totius, & partium,<emph.end type="italics"/> tho&longs;e <lb/>Countreys being a part of the Earth, as well as ours, they <lb/>mu&longs;t of nece&longs;&longs;ity be alterable as the&longs;e are.</s></p><p type="main"><s>SALV. </s><s>And why have you not, without being put to believe <lb/>other mens relations, examined and ob&longs;erved tho&longs;e alterations <lb/>with your own eyes?</s></p><p type="main"><s>SIMPL. </s><s>Becau&longs;e tho&longs;e places, be&longs;ides that they are not ex­ <lb/>po&longs;ed to our eyes, are &longs;o remote, that our &longs;ight cannot reach <lb/>to comprehend therein &longs;uch like mutations.</s></p><p type="main"><s>SALV. </s><s>See now, how you have unawares di&longs;covered the falla­ <lb/>cy of your Argument; for, if you &longs;ay that the alterations that <lb/>are &longs;een on the Earth neer at hand, cannot, by rea&longs;on of the too <lb/>great di&longs;tance, be &longs;een in <emph type="italics"/>America,<emph.end type="italics"/> much le&longs;&longs;e can you &longs;ee them <lb/>in the Moon, which is &longs;o many hundred times more remote: <lb/>And if you believe the alterations in <emph type="italics"/>Mexico<emph.end type="italics"/> upon the report of <lb/>tho&longs;e that come from thence, what intelligence have you from <lb/>the Moon, to a&longs;&longs;ure you that there is no &longs;uch alterations in it? <lb/></s><s>Therefore, from your not &longs;eeing any alterations in Heaven, <lb/>whereas, if there were any &longs;uch, you could not &longs;ee them by rea­ <lb/>&longs;on of their too great di&longs;tance, and from your not having intel­ <lb/>ligence thereof, in regard that it cannot be had, you ought not <lb/>to argue, that there are no &longs;uch alterations; howbeit, from the <lb/>&longs;eeing and ob&longs;erving of them on Earth, you well argue that <lb/>therein &longs;uch there are.</s></p><p type="main"><s>SIMPL. </s><s>I will &longs;hew &longs;o great mutations that have befaln on <lb/>the Earth; that if any &longs;uch had happened in the Moon, they <lb/>might very well have been ob&longs;erved here below. </s><s>We find in <lb/><arrow.to.target n="marg102"></arrow.to.target> <lb/>very antient records, that heretofore at the Streights of <emph type="italics"/>Gibraltar,<emph.end type="italics"/> <lb/>the two great Mountains <emph type="italics"/>Abila,<emph.end type="italics"/> and <emph type="italics"/>Calpen,<emph.end type="italics"/> were continued to­ <lb/>gether by certain other le&longs;&longs;e Mountains which there gave check <pb xlink:href="040/01/052.jpg" pagenum="36"/>to the Ocean: but tho&longs;e Hills, being by &longs;ome cau&longs;e or other &longs;e­ <lb/>parated, and a way being opened to the Sea to break in, it made <lb/>&longs;uch an inundation, that it gave occa&longs;ion to the calling of it &longs;ince <lb/>the Mid-land Sea: the greatne&longs;s whereof con&longs;idered, and the di­ <lb/>vers a&longs;pect the &longs;urface of the Water and Earth then made, had it <lb/>been beheld afar off, there is no doubt but &longs;o great a change <lb/>might have been di&longs;cerned by one that was then in the Moon; <lb/>as al&longs;o to us inhabitants of the Earth, the like alterations would <lb/>be perceived in the Moon; but we find not in antiquity, that e­ <lb/>ver there was &longs;uch a thing &longs;een; therefore we have no cau&longs;e to <lb/>&longs;ay, that any of the Cœle&longs;tial bodies are alterable, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg102"></margin.target><emph type="italics"/>The Mediterr ani­ <lb/>an Sea made by the <lb/>&longs;eparation of<emph.end type="italics"/> Abi­ <lb/>la <emph type="italics"/>and<emph.end type="italics"/> Calpen.</s></p><p type="main"><s>SALV. </s><s>That &longs;o great alterations have hapned in the Moon, I <lb/>dare not &longs;ay, but for all that, I am not yet certain but that &longs;uch <lb/>changes might occur; and becau&longs;e &longs;uch a mutation could onely <lb/>repre&longs;ent unto us &longs;ome kind of variation between the more clear, <lb/>and more ob&longs;cure parts of the Moon, I know not whether we <lb/>have had on Earth ob&longs;ervant Selenographers, who have for any <lb/>con&longs;iderable number of years, in&longs;tructed us with &longs;o exact Seleno­ <lb/>graphy, as that we &longs;hould confidently conclude, that there hath <lb/>no &longs;uch change hapned in the face of the Moon; of the figura­ <lb/>tion of which I find no more particular de&longs;cription, than the &longs;ay­ <lb/>ing of &longs;ome, that it repre&longs;ents an humane face; of others, that <lb/>it is like the muzzle of a lyon; and of others, that it is <emph type="italics"/>Cain<emph.end type="italics"/> with <lb/>a bundle of thorns on his back: therefore, to &longs;ay Heaven is un­ <lb/>alterable, becau&longs;e that in the Moon, or other Cœle&longs;tial bodies, no <lb/>&longs;uch alterations are &longs;een, as di&longs;cover them&longs;elves on Earth, is a bad <lb/>illation, and concludeth nothing.</s></p><p type="main"><s>SAGR. </s><s>And there is another odd kind of &longs;cruple in this Argu­ <lb/>ment of <emph type="italics"/>Simplicius,<emph.end type="italics"/> running in my mind, which I would gladly <lb/>have an&longs;wered; therefore I demand of him, whether the Earth <lb/>before the Mediterranian inundation was generable and corrupti­ <lb/>ble, or el&longs;e began then &longs;o to be?</s></p><p type="main"><s>SIMPL. </s><s>It was doubtle&longs;s generable and corruptible al&longs;o be­ <lb/>fore that time; but that was &longs;o va&longs;t a mutation, that it might <lb/>have been ob&longs;erved as far as the Moon.</s></p><p type="main"><s>SAGR. </s><s>Go to; if the Earth was generable and corruptible <lb/>before that Inundation, why may not the Moon be &longs;o like­ <lb/>wi&longs;e without &longs;uch a change? </s><s>Or why &longs;hould that be nece&longs;&longs;ary <lb/>in the Moon, which importeth nothing on Earth?</s></p><p type="main"><s>SALV. </s><s>It is a &longs;hrewd que&longs;tion: But I am doubtfull that <emph type="italics"/>Sim­ <lb/>plicius<emph.end type="italics"/> a little altereth the Text of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and the other <emph type="italics"/>Peri­ <lb/>patelicks,<emph.end type="italics"/> who &longs;ay, they hold the Heavens unalterable, for that <lb/>they &longs;ee therein no one &longs;tar generate or corrupt, which is proba­ <lb/>bly a le&longs;s part of Heaven, than a City is of the Earth, and yet <lb/>innumerable of the&longs;e have been de&longs;troyed, &longs;o as that no mark of <lb/>them hath remain'd.</s></p> <pb xlink:href="040/01/053.jpg" pagenum="37"/><p type="main"><s>SAGR. </s><s>I verily believed otherwi&longs;e, and conceited that <emph type="italics"/>Sim­ <lb/>plicius<emph.end type="italics"/> di&longs;&longs;embled this expo&longs;ition of the Text, that he might not <lb/>charge his Ma&longs;ter and Con&longs;ectators, with a notion more ab&longs;urd <lb/>than the former. </s><s>And what a folly it is to &longs;ay the Cœle&longs;tial <lb/>part is unalterable, becau&longs;e no &longs;tars do generate or corrupt there­ <lb/>in? </s><s>What then? </s><s>hath any &longs;een a Terre&longs;trial Globe corrupt, and <lb/>another regenerate in its place? </s><s>And yet is it not on all hands <lb/>granted by Philo&longs;ophers, that there are very few &longs;tars in Heaven <lb/>le&longs;s than the Earth, but very many that are much bigger? </s><s>So <lb/><arrow.to.target n="marg103"></arrow.to.target> <lb/>that for a &longs;tar in Heaven to corrupt, would be no le&longs;s than if the <lb/>whole Terre&longs;trial Globe &longs;hould be de&longs;troy'd. </s><s>Therefore, if for <lb/>the true proof of generation and corruption in the Univer&longs;e, it be <lb/>nece&longs;&longs;ary that &longs;o va&longs;t bodies as a &longs;tar, mu&longs;t corrupt and regene­ <lb/>rate, you may &longs;atisfie your &longs;elf and cea&longs;e your opinion; for I <lb/>a&longs;&longs;ure you, that you &longs;hall never &longs;ee the Terre&longs;trial Globe or any <lb/>other integral body of the World, to corrupt or decay &longs;o, that <lb/>having been beheld by us for &longs;o many years pa&longs;t, they &longs;hould &longs;o <lb/>di&longs;&longs;olve, as not to leave any foot&longs;teps of them.</s></p><p type="margin"><s><margin.target id="marg103"></margin.target><emph type="italics"/>Its no le&longs;s impo&longs;&longs;i­ <lb/>ble for a &longs;tar to <lb/>corrupt, than for <lb/>the whole Terre­ <lb/>&longs;trial Globe.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>But to give <emph type="italics"/>Simplicius<emph.end type="italics"/> yet fuller &longs;atisfaction, and to <lb/>reclaim him, if po&longs;&longs;ible, from his error; I affirm, that we have in <lb/><arrow.to.target n="marg104"></arrow.to.target> <lb/>our age new accidents and ob&longs;ervations, and &longs;uch, that I que&longs;tion <lb/>not in the lea&longs;t, but if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> were now alive, they would make <lb/>him change his opinion; which may be ea&longs;ily collected from the <lb/>very manner of his di&longs;cour&longs;ing: For when he writeth that he e­ <lb/>&longs;teemeth the Heavens inalterable, &c. </s><s>becau&longs;e no new thing was <lb/>&longs;een to be begot therein, or any old to be di&longs;&longs;olved, he &longs;eems im­ <lb/>plicitely to hint unto us, that when he &longs;hould &longs;ee any &longs;uch acci­ <lb/>dent, he would hold the contrary; and confront, as indeed it is <lb/>meet, &longs;en&longs;ible experiments to natural rea&longs;on: for had he not <lb/>made any reckoning of the &longs;en&longs;es, he would not then from the <lb/>not &longs;eeing of any &longs;en&longs;ible mutation, have argued immutability.</s></p><p type="margin"><s><margin.target id="marg104"></margin.target>Ari&longs;totle <emph type="italics"/>would <lb/>change his opinion, <lb/>did he &longs;ee the no­ <lb/>velties of our age.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> deduceth his principal Argument <emph type="italics"/>à priori,<emph.end type="italics"/> <lb/>&longs;hewing the nece&longs;&longs;ity of the inalterability of Heaven by natural, <lb/>manife&longs;t and clear principles; and then &longs;tabli&longs;heth the &longs;ame <emph type="italics"/>à po­ <lb/>&longs;teriori,<emph.end type="italics"/> by &longs;en&longs;e, and the traditions of the antients.</s></p><p type="main"><s>SALV. </s><s>This you &longs;peak of is the Method he hath ob&longs;erved in <lb/>delivering his Doctrine, but I do not bethink it yet to be that <lb/>wherewith he invented it; for I do believe for certain, that he <lb/>fir&longs;t procured by help of the &longs;en&longs;es, &longs;uch experiments and ob&longs;er­ <lb/>vations as he could, to a&longs;&longs;ure him as much as it was po&longs;&longs;ible, of the <lb/><arrow.to.target n="marg105"></arrow.to.target> <lb/>conclu&longs;ion, and that he afterwards &longs;ought out the means how to <lb/>demon&longs;trate it: For this, the u&longs;ual cour&longs;e in demon&longs;trative Scien­ <lb/>ces, and the rea&longs;on thereof is, becau&longs;e when the conclu&longs;ion is <lb/>true, by help of re&longs;olutive Method, one may hit upon &longs;ome pro­ <lb/>po&longs;ition before demon&longs;trated, or come to &longs;ome principle known <pb xlink:href="040/01/054.jpg" pagenum="38"/><emph type="italics"/>per &longs;e<emph.end type="italics"/>; but if the conclu&longs;ion be fal&longs;e, a man may proceed <emph type="italics"/>in in­ <lb/>finitum,<emph.end type="italics"/> and never meet with any truth already known; but ve­ <lb/>ry oft he &longs;hall meet with &longs;ome impo&longs;&longs;ibility or manife&longs;t ab&longs;urdi­ <lb/><arrow.to.target n="marg106"></arrow.to.target> <lb/>ty. </s><s>Nor need you que&longs;tion but that <emph type="italics"/>Pythagoras<emph.end type="italics"/> along time be­ <lb/>fore he found the demon&longs;tration for which he offered the Heca­ <lb/>tomb, had been certain, that the &longs;quare of the &longs;ide &longs;ubtending <lb/>the right angle in a rectangle triangle, was equal to the &longs;quare of <lb/>the other two &longs;ides: and the certainty of the conclu&longs;ion condu­ <lb/>ced not a little to the inve&longs;tigating of the demon&longs;tration, un­ <lb/>der&longs;tanding me alwayes to mean in demon&longs;trative Sciences. </s><s>But <lb/>what ever was the method of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and whether his arguing <emph type="italics"/>à <lb/>priori<emph.end type="italics"/> preceded &longs;en&longs;e <emph type="italics"/>à po&longs;teriori,<emph.end type="italics"/> or the contrary; it &longs;ufficeth that <lb/>the &longs;ame <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> preferreth (as hath been oft &longs;aid) &longs;en&longs;ible ex­ <lb/>periments before all di&longs;cour&longs;es; be&longs;ides, as to the Arugments <emph type="italics"/>à <lb/>priori<emph.end type="italics"/> their force hath been already examined. </s><s>Now returning <lb/>to my purpo&longs;ed matter, I &longs;ay, that the things in our times di&longs;­ <lb/>covered in the Heavens, are, and have been &longs;uch, that they may <lb/>give ab&longs;olute &longs;atisfaction to all Philo&longs;ophers; fora&longs;much as in <lb/>the particular bodies, and in the univer&longs;al expan&longs;ion of Heaven, <lb/>there have been, and are continually, &longs;een ju&longs;t &longs;uch accidents as <lb/>we call generations and corruptions, being that excellent A­ <lb/>&longs;tronomers have ob&longs;erved many Comets generated and di&longs;&longs;olved <lb/>in parts higher than the Lunar Orb, be&longs;ides the two new Stars, <lb/><arrow.to.target n="marg107"></arrow.to.target> <lb/><emph type="italics"/>Anuo<emph.end type="italics"/> 1572, and <emph type="italics"/>Anno<emph.end type="italics"/> 1604, without contradiction much higher <lb/>than all the Planets; and in the face of the Sun it &longs;elf, by help <lb/><arrow.to.target n="marg108"></arrow.to.target> <lb/>of the <emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/> certain den&longs;e and ob&longs;cure &longs;ub&longs;tances, in &longs;em­ <lb/>blance very like to the foggs about the Earth, are &longs;een to be <lb/>produced and di&longs;&longs;olved; and many of the&longs;e are &longs;o va&longs;t, that <lb/>they far exceed not only the Mediterranian Streight, but all <lb/><arrow.to.target n="marg109"></arrow.to.target> <lb/><emph type="italics"/>Affrica<emph.end type="italics"/> and <emph type="italics"/>A&longs;ia<emph.end type="italics"/> al&longs;o. </s><s>Now if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had &longs;een the&longs;e things, <lb/>what think you he would have &longs;aid, and done <emph type="italics"/>Simplicius?<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg105"></margin.target><emph type="italics"/>The certaixty of <lb/>the conclu&longs;ion hel­ <lb/>peth by are&longs;olutive <lb/>method to &longs;ind the <lb/>demonstration.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg106"></margin.target>Pythagoras <emph type="italics"/>offered <lb/>an Hecatomb for <lb/>a Geometrical de­ <lb/>mon&longs;tration which <lb/>he found.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg107"></margin.target><emph type="italics"/>New &longs;tars di&longs;co­ <lb/>vered in Heaven.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg108"></margin.target><emph type="italics"/>Spots generate and <lb/>di&longs;&longs;olve in the face <lb/>of the Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg109"></margin.target><emph type="italics"/>Solar spots are <lb/>bigger than all<emph.end type="italics"/> A­ <lb/>&longs;ia <emph type="italics"/>and<emph.end type="italics"/> Affrick.</s></p><p type="main"><s>SIMPL. </s><s>I know not what <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> would have done or &longs;aid, <lb/>that was the great Ma&longs;ter of all the Sciences, but yet I know in <lb/>part, what his Sectators do and &longs;ay, and ought to do and &longs;ay, <lb/>unle&longs;&longs;e they would deprive them&longs;elves of their guide, leader, and <lb/>Prince in Philo&longs;ophy. </s><s>As to the Comets, are not tho&longs;e Modern <lb/>A&longs;tronomers, who would make them Cœle&longs;tial, convinced by <lb/><arrow.to.target n="marg110"></arrow.to.target> <lb/>the ^{*}<emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> yea, and overcome with their own weapons, I <lb/>mean by way of Paralaxes and Calculations, every way tryed, <lb/>concluding at the la&longs;t in favour of <emph type="italics"/>Aristotle,<emph.end type="italics"/> that they are all <lb/>Elementary? </s><s>And this being overthrown, which was as it were <lb/>their foundation, have the&longs;e Novelli&longs;ts any thing more where­ <lb/>with to maintain their a&longs;&longs;ertion?</s></p><p type="margin"><s><margin.target id="marg110"></margin.target>* <emph type="italics"/>A&longs;tronomers con­ <lb/>futed by<emph.end type="italics"/> Anti-Ty­ <lb/>cho.</s></p><p type="main"><s>SALV. </s><s>Hold a little, good <emph type="italics"/>Simplicius,<emph.end type="italics"/> this modern Author, <lb/>what &longs;aith he to the new Stars, <emph type="italics"/>Anno<emph.end type="italics"/> 1572, and 1604, and to <pb xlink:href="040/01/055.jpg" pagenum="39"/>the Solar &longs;pots? </s><s>for as to the Comets, I for my own particular <lb/>little care to make them generated under or above the Moon; <lb/>nor did I ever put much &longs;tre&longs;&longs;e on the loquacity of <emph type="italics"/>Tycho<emph.end type="italics"/>; nor <lb/>am I hard to believe that their matter is Elementary, and that <lb/>they may elevate (&longs;ublimate) them&longs;elves at their plea&longs;ure, with­ <lb/>out meeting with any ob&longs;tacle from the impenetrability of the <lb/><emph type="italics"/>Peripatetick<emph.end type="italics"/> Heaven, which I hold to be far more thin, yielding, <lb/>and &longs;ubtil than our Air; and as to the calculations of the Pa­ <lb/>rallaxes, fir&longs;t, the uncertainty whether Comets are &longs;ubject to <lb/>&longs;uch accidents, and next, the incon&longs;tancy of the ob&longs;ervations, <lb/>upon which the computations are made, make me equally &longs;u&longs;­ <lb/>pect both tho&longs;e opinions: and the rather, for that I &longs;ee him <lb/><arrow.to.target n="marg111"></arrow.to.target> <lb/>you call <emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> &longs;ometimes &longs;tretch to his purpo&longs;e, or el&longs;e <lb/>reject tho&longs;e ob&longs;ervations which interfere with his de&longs;ign.</s></p><p type="margin"><s><margin.target id="marg111"></margin.target>Anti-Tycho <emph type="italics"/>wre­ <lb/>&longs;teth A&longs;tronomical <lb/>ob&longs;ervations to his <lb/>own parpo&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>As to the new Stars, <emph type="italics"/>Anti-Tycho<emph.end type="italics"/> extricates him&longs;elf <lb/>finely in three or four words; &longs;aying, That tho&longs;e mo­ <lb/>dern new Stars are no certain parts of the Cœle&longs;tial bodies, and <lb/>that the adver&longs;aries, if they will prove alteration and genera­ <lb/>tion in tho&longs;e &longs;uperior bodies, mu&longs;t &longs;hew &longs;ome mutations that <lb/>have been made in the Stars de&longs;cribed &longs;o many ages pa&longs;t, of <lb/>which there is no doubt but that they be Cœle&longs;tial bodies, <lb/>which they can never be able to do: Next, as to tho&longs;e mat­ <lb/>ters which &longs;ome affirm, to generate and di&longs;&longs;ipate in the face of <lb/>the Sun, he makes no mention thereof; wherefore I conclude, <lb/>that he believed them fictious, or the illu&longs;ions of the Tube, or <lb/>at mo&longs;t, &longs;ome petty effecs cau&longs;ed by the Air, and in brief, any <lb/>thing rather than matters Cœle&longs;tial.</s></p><p type="main"><s>SALV. </s><s>But you, <emph type="italics"/>Simplicius,<emph.end type="italics"/> what an&longs;wer could you give to <lb/>the oppo&longs;ition of the&longs;e importunate &longs;pots which are &longs;tarted up <lb/>to di&longs;turb the Heavens, and more than that, the <emph type="italics"/>Peripatetick<emph.end type="italics"/> <lb/>Philo&longs;ophy? </s><s>It cannot be but that you, who are &longs;o re&longs;olute a <lb/>Champion of it, have found &longs;ome reply or &longs;olution for the <lb/>&longs;ame, of which you ought not to deprive us.</s></p><p type="main"><s>SIMPL. </s><s>I have heard &longs;undry opinions about this particular. <lb/></s><s>One &longs;aith: “They are Stars which in their proper Orbs, like as <lb/><arrow.to.target n="marg112"></arrow.to.target> <lb/><emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mervury,<emph.end type="italics"/> revolve about the Sun, and in pa&longs;&longs;ing un­ <lb/>der it, repre&longs;ent them&longs;elves to us ob&longs;cure; and for that they <lb/>are many, they oft happen to aggregate their parts together, <lb/>and afterwards &longs;eperate again. </s><s>Others believe them to be <lb/>aerial impre&longs;&longs;ions; others, the illu&longs;ions of the chry&longs;tals; and o­ <lb/>thers, other things: But I incline to think, yea am verily per­ <lb/>&longs;waded, That they are an aggregate of many &longs;everal opacous <lb/>bodies, as it were ca&longs;ually concurrent among them&longs;elves. </s><s>And <lb/>therefore we often &longs;ee, that in one of tho&longs;e &longs;pots one may <lb/>number ten or more &longs;uch &longs;mall bodies, which are of irregu­ <pb xlink:href="040/01/056.jpg" pagenum="40"/>lar figures, and &longs;eem to us like flakes of &longs;now, or flocks of <lb/>wooll, or moaths flying: they vary &longs;ite among&longs;t them&longs;elves, <lb/>and one while &longs;ever, another while meet, and mo&longs;t of all be­ <lb/>neath the Sun, about which, as about their Centre, they con­ <lb/>tinually move. </s><s>But yet, mu&longs;t we not therefore grant, that <lb/>they are generated or di&longs;&longs;olved, but that at &longs;ometimes they are <lb/>hid behind the body of the Sun, and at other times, though <lb/>remote from it, yet are they not &longs;een for the vicinity of the <lb/>immea&longs;urable light of the Sun; in regard that in the eccentrick <lb/>Orb of the Sun, there is con&longs;tituted, as it were, an Onion, com­ <lb/>po&longs;ed of many folds one within another, each of which, being <lb/><arrow.to.target n="marg113"></arrow.to.target> <lb/>^{*}&longs;tudded with certain &longs;mall &longs;pots, doth move; and albeit their <lb/>motion at fir&longs;t &longs;eemeth incon&longs;tant and irregular, yet neverthe­ <lb/>le&longs;&longs;e, it is &longs;aid at la&longs;t, to be ob&longs;erved that the very &longs;ame &longs;pots, <lb/>as before,” do within a determinate time return again. </s><s>This <lb/>&longs;eemeth to me the fitte&longs;t an&longs;wer that hath been found to a&longs;&longs;igne <lb/>a rea&longs;on of that &longs;ame appearance, and withal to maintain the <lb/>incorruptability and ingenerability of the Heavens; and if this <lb/>doth not &longs;uffice; there wants not more elevated wits, which will <lb/>give you other, more convincing.</s></p><p type="margin"><s><margin.target id="marg112"></margin.target><emph type="italics"/>Sundry opinions <lb/>touching the Solar <lb/>&longs;pots.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg113"></margin.target>* The Original <lb/>&longs;aith [<emph type="italics"/>tempe&longs;tata &longs;i <lb/>muove<emph.end type="italics"/>] which the <lb/>Latine Tran&longs;lati­ <lb/>on, (Mi&longs;taking <lb/><emph type="italics"/>Tempectata,<emph.end type="italics"/> aword <lb/>in Heraldry, for <lb/><emph type="italics"/>Tempe&longs;tato,<emph.end type="italics"/>) ren­ <lb/>dereth [<emph type="italics"/>incitata <lb/>movetur<emph.end type="italics"/>] which <lb/>&longs;ignifieth a violent <lb/>tran&longs;portmeut, as <lb/>in a &longs;torm, that of <lb/>a Ship.</s></p><p type="main"><s>SALV. </s><s>If this of which we di&longs;pute, were &longs;ome point of Law, <lb/><arrow.to.target n="marg114"></arrow.to.target> <lb/>or other part of the Studies called <emph type="italics"/>Humanity,<emph.end type="italics"/> wherein there is <lb/>neither truth nor fal&longs;hood, if we will give &longs;ufficient credit to <lb/>the acutene&longs;&longs;e of the wit, readine&longs;&longs;e of an&longs;wers, and the gene­ <lb/>ral practice of Writers, then he who mo&longs;t aboundeth in the&longs;e, <lb/>makes his rea&longs;on more probable and plau&longs;ible; but in Natural <lb/>Sciences, the conclu&longs;ions of which are true and nece&longs;&longs;ary, and <lb/>wherewith the judgment of men hath nothing to do, one is to <lb/>be more cautious how he goeth about to maintain any thing that <lb/>is fal&longs;e; for a man but of an ordinary wit, if it be his good for­ <lb/>tune to be of the right &longs;ide, may lay a thou&longs;and <emph type="italics"/>Demo&longs;thenes<emph.end type="italics"/> and <lb/>a thou&longs;and <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> at his feet. </s><s>Therefore reject tho&longs;e hopes <lb/>and conceits, wherewith you flatter your &longs;elf, that there can be <lb/>any men &longs;o much more learned, read, and ver&longs;ed in Authors, <lb/>than we, that in de&longs;pite of nature, they &longs;hould be able to <lb/>make that become true, which is fal&longs;e. </s><s>And &longs;eeing that of all <lb/>the opinions that have been hitherto alledged touching the e&longs;­ <lb/>&longs;ence of the&longs;e Solar &longs;pots, this in&longs;tanced in by you, is in your <lb/>judgment the true&longs;t, it followeth (if this be &longs;o) that all the re&longs;t <lb/>are fal&longs;e; and to deliver you from this al&longs;o, which doubtle&longs;&longs;e is a <lb/>mo&longs;t fal&longs;e <emph type="italics"/>Chimœra,<emph.end type="italics"/> over-pa&longs;&longs;ing infinite other improbabilities <lb/>that are therein, I &longs;hall propo&longs;e again&longs;t it onely two experiments; <lb/><arrow.to.target n="marg115"></arrow.to.target> <lb/>one is, that many of tho&longs;e &longs;pots are &longs;een to ari&longs;e in the mid&longs;t of <lb/>the Solar ring, and many likewi&longs;e to di&longs;&longs;olve and vani&longs;h at a great <lb/>di&longs;tance from the circumference of the Sun; a nece&longs;&longs;ary Argu­ <pb xlink:href="040/01/057.jpg" pagenum="41"/>ment that they generate and di&longs;&longs;olve; for if without generating <lb/>or corrrupting, they &longs;hould appear there by onely local motion, <lb/>they would all be &longs;een to enter, and pa&longs;s out by the extreme cir­ <lb/><arrow.to.target n="marg116"></arrow.to.target> <lb/>cumference. </s><s>The other ob&longs;ervation to &longs;uch as are not &longs;ituate in <lb/>the lowe&longs;t degree of ignorance in Per&longs;pective, by the mutation <lb/>of the appearing figures, and by the apparent mutations of the <lb/>velocity of motion is nece&longs;&longs;arily concluding, that the &longs;pots are <lb/>contiguous to the body of the Sun, and that touching its &longs;uperfi­ <lb/>cies, they move either with it or upon it, and that they in no wi&longs;e <lb/>move in circles remote from the &longs;ame. </s><s>The motion proves <lb/><arrow.to.target n="marg117"></arrow.to.target> <lb/>it, which towards the circumference of the Solar Circle, <lb/>appeareth very &longs;low, and towards the mid&longs;t, more &longs;wift; the fi­ <lb/>gures of the &longs;pots confirmeth it, which towards the circumference <lb/><arrow.to.target n="marg118"></arrow.to.target> <lb/>appear exceeding narrow in compari&longs;on of that which they &longs;eem <lb/>to be in the parts nearer the middle; and this becau&longs;e in the <lb/>mid&longs;t they are &longs;een in their full lu&longs;ter, and as they truly be; and <lb/>towards the circumference by rea&longs;on of the convexity of the glo­ <lb/>bous &longs;uperficies, they &longs;eem more compre&longs;&longs;'d: And both the&longs;e <lb/>diminutions of figure and motion, to &longs;uch as know how to ob&longs;erve <lb/>and calculate them exactly, preci&longs;ely an&longs;wer to that which &longs;hould <lb/>appear, the &longs;pots being contiguous to the Sun, and differ irrecon­ <lb/>cileably from a motion in circles remote, though but for &longs;mal <lb/>intervalls from the body of the Sun; as hath been diffu&longs;ely de­ <lb/><arrow.to.target n="marg119"></arrow.to.target> <lb/>mon&longs;trated by our ^{*} Friend, in his Letters about the Solar &longs;pots, <lb/>to <emph type="italics"/>Marcus Vel&longs;erus.<emph.end type="italics"/> It may be gathered from the &longs;ame muta­ <lb/>tion of figure, that none of them are &longs;tars, or other bodies of <lb/>&longs;pherical figure; for that among&longs;t all figures the &longs;phere never <lb/>appeareth compre&longs;&longs;ed, nor can ever be repre&longs;ented but onely per­ <lb/>fectly round; and thus in ca&longs;e any particular &longs;pot were a round <lb/>body, as all the &longs;tars are held to be, the &longs;aid roundne&longs;s would as <lb/>well appear in the mid&longs;t of the Solar ring, as when the &longs;pot is near <lb/>the extreme: whereas, its &longs;o great compre&longs;&longs;ion, and &longs;hewing its <lb/>&longs;elf &longs;o &longs;mall towards the extreme, and contrariwi&longs;e, &longs;patious and <lb/>large towards the middle, a&longs;&longs;ureth us, that the&longs;e &longs;pots are flat <lb/><arrow.to.target n="marg120"></arrow.to.target> <lb/>plates of &longs;mall thickne&longs;s or depth, in compari&longs;on of their length <lb/>and breadth. </s><s>La&longs;tly, whereas you &longs;ay that the &longs;pots after their <lb/>determinate periods are ob&longs;erved to return to their former a&longs;pect, <lb/>believe it not, <emph type="italics"/>Simplicius,<emph.end type="italics"/> for he that told you &longs;o, will deceive <lb/>you; and that I &longs;peak the truth, you may ob&longs;erve them to be hid <lb/>in the face of the Sun far from the circumference; nor hath your <lb/>Ob&longs;ervator told you a word of that compre&longs;&longs;ion, which nece&longs;&longs;a­ <lb/>rily argueth them to be contiguous to the Sun. </s><s>That which he <lb/>tells you of the return of the &longs;aid &longs;pots, is nothing el&longs;e but what <lb/>is read in the forementioned Letters, namely, that &longs;ome of them <lb/>may &longs;ometimes &longs;o happen that are of &longs;o long a duration, that <pb xlink:href="040/01/058.jpg" pagenum="42"/>they cannot be di&longs;&longs;ipated by one &longs;ole conver&longs;ion about the Sun, <lb/>which is accompli&longs;hed in le&longs;s than a moneth.</s></p><p type="margin"><s><margin.target id="marg114"></margin.target><emph type="italics"/>In natural Sci­ <lb/>ences, the art of <lb/>Oratory is of no <lb/>force.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg115"></margin.target><emph type="italics"/>An Argument <lb/>that nece&longs;&longs;arily <lb/>proveth the Solar <lb/>&longs;pots to generate <lb/>and di&longs;&longs;olwe.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg116"></margin.target><emph type="italics"/>A conclu&longs;ive de­ <lb/>mon&longs;tration, that <lb/>the &longs;pots are conti­ <lb/>guous to the body <lb/>of the Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg117"></margin.target><emph type="italics"/>The motion of the <lb/>spots towards the <lb/>circumference of <lb/>the Sun appears <lb/>&longs;low.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg118"></margin.target><emph type="italics"/>The figure of the <lb/>spots appears nar­ <lb/>row towards the <lb/>circumference of <lb/>the Suns<emph.end type="italics"/> di&longs;cus, <emph type="italics"/>& <lb/>why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg119"></margin.target>* Under this word <lb/><emph type="italics"/>Friend,<emph.end type="italics"/> as al&longs;o that <lb/>of <emph type="italics"/>Academick, & <lb/>Common Friend, <lb/>Galilœus<emph.end type="italics"/> mode&longs;tly <lb/>conceals him&longs;elf <lb/>throughout the&longs;e <lb/>Dialogues.</s></p><p type="margin"><s><margin.target id="marg120"></margin.target><emph type="italics"/>The Solar spots <lb/>are not &longs;pherical, <lb/>but flat like thin <lb/>plates.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. I, for my part, have not made either &longs;o long, or &longs;o <lb/>exact ob&longs;ervations, as to enable me to boa&longs;t my &longs;elf Ma&longs;ter of the <lb/><emph type="italics"/>Quod ect<emph.end type="italics"/> of this matter: but I will more accurately con&longs;ider the <lb/>&longs;ame, and make tryal my &longs;elf for my own &longs;atisfaction, whether I <lb/>can reconcile that which experience &longs;hews us, with that which <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> teacheth us; for it's a certain Maxim, that two Truths <lb/>cannot be contrary to one another.</s></p><p type="main"><s>SALV. </s><s>If you would reconcile that which &longs;en&longs;e &longs;heweth you, <lb/><arrow.to.target n="marg121"></arrow.to.target> <lb/>with the &longs;olider Doctrines of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> you will find no great dif­ <lb/>ficulty in the undertaking; and that &longs;o it is, doth not <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>&longs;ay, that one cannot treat confidently of the things of Heaven, <lb/>by rea&longs;on of their great remotene&longs;s?</s></p><p type="margin"><s><margin.target id="marg121"></margin.target><emph type="italics"/>One cannot<emph.end type="italics"/> (<emph type="italics"/>&longs;aith<emph.end type="italics"/> <lb/>Ari&longs;totle) <emph type="italics"/>&longs;peak <lb/>confidently of Hea­ <lb/>ven, by rea&longs;on of <lb/>its great di&longs;tance.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>He expre&longs;ly &longs;aith &longs;o. <lb/><arrow.to.target n="marg122"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg122"></margin.target>Ari&longs;totle <emph type="italics"/>prefers <lb/>&longs;en&longs;e before ratio­ <lb/>cination.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>And doth he not likewi&longs;e affirm, that we ought to pre­ <lb/>fer that which &longs;en&longs;e demon&longs;trates, before all Arguments, though <lb/>in appearance never &longs;o well grounded? </s><s>and &longs;aith he not this <lb/>without the lea&longs;t doubt or hæ&longs;itation?</s></p><p type="main"><s>SIMPL. </s><s>He doth &longs;o.</s></p><p type="main"><s>SALV. </s><s>Why then, the &longs;econd of the&longs;e propo&longs;itions, which are <lb/>both the doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that &longs;aith, that &longs;en&longs;e is to take </s></p><p type="main"><s><arrow.to.target n="marg123"></arrow.to.target> <lb/>place of Logick, is a doctrine much more &longs;olid and undoubted, <lb/>than that other which holdeth the Heavens to be unalterable; and <lb/>therefore you &longs;hall argue more <emph type="italics"/>Ari&longs;totelically,<emph.end type="italics"/> &longs;aying, the Hea­ <lb/>vens are alterable, for that &longs;o my &longs;en&longs;e telleth me, than if you <lb/>&longs;hould &longs;ay, the Heavens are u alterable, for that Logick &longs;o per&longs;wa­ <lb/>ded <emph type="italics"/>Aristotle.<emph.end type="italics"/> Furthermore, we may di&longs;cour&longs;e of Cœle&longs;tial mat­ <lb/><arrow.to.target n="marg124"></arrow.to.target> <lb/>ters much better than <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; becau&longs;e, he confe&longs;&longs;ing the know­ <lb/>ledg thereof to be difficult to him, by rea&longs;on of their remotene&longs;s <lb/>from the &longs;en&longs;es, he thereby acknowledgeth, that one to whom <lb/>the &longs;en&longs;es can better repre&longs;ent the &longs;ame, may philo&longs;ophate upon <lb/>them with more certainty. </s><s>Now we by help of the Tele&longs;cope, <lb/>are brought thirty or forty times nearer to the Heavens, than ever <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> came; &longs;o that we may di&longs;cover in them an hundred <lb/>things, which he could not &longs;ee, and among&longs;t the re&longs;t, the&longs;e &longs;pots <lb/>in the Sun, which were to him ab&longs;olutely invi&longs;ible; therefore <lb/>we may di&longs;cour&longs;e of the Heavens and Sun, with more certainty <lb/>than <emph type="italics"/>Ari&longs;tolte.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg123"></margin.target><emph type="italics"/>Its a doctrine more <lb/>agreeing with<emph.end type="italics"/> A­ <lb/>ri&longs;totle, <emph type="italics"/>to &longs;ay the <lb/>Heavens are alter­ <lb/>able, than that <lb/>which affirms <lb/>them inalterable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg124"></margin.target><emph type="italics"/>We may by help of <lb/>the<emph.end type="italics"/> Tele&longs;cope <emph type="italics"/>di&longs;­ <lb/>cour&longs;e better of cœ­ <lb/>le&longs;tial matters, <lb/>than<emph.end type="italics"/> Ari&longs;tot. <emph type="italics"/>him­ <lb/>&longs;elf.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I &longs;ee into the heart of <emph type="italics"/>Simplicius,<emph.end type="italics"/> and know that he is <lb/>much moved at the &longs;trength of the&longs;e &longs;o convincing Arguments; <lb/>but on the other &longs;ide, when he con&longs;idereth the great authority <lb/>which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath won with all men, and remembreth the great <lb/>number of famous Interpreters, which have made it their bu&longs;ine&longs;s <lb/>to explain his &longs;en&longs;e; and &longs;eeth other Sciences, &longs;o nece&longs;&longs;ary and <pb xlink:href="040/01/059.jpg" pagenum="43"/>profitable to the publick, to build a great part of their e&longs;teem <lb/>and reputation on the credit of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> he is much puzzled and <lb/>perplexed: and methinks I hear him &longs;ay, To whom then &longs;hould <lb/><arrow.to.target n="marg125"></arrow.to.target> <lb/>we repair for the deci&longs;ion of our controver&longs;ies, if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> were <lb/>removed from the chair? </s><s>What other Author &longs;hould we follow <lb/>in the Schools, Academies and Studies? </s><s>What Philo&longs;opher hath <lb/>writ all the parts of Natural Philo&longs;ophy, and that &longs;o methodically <lb/>without omitting &longs;o much as one &longs;ingle conclu&longs;ion? </s><s>Shall we then <lb/>overthrow that Fabrick under which &longs;o many pa&longs;&longs;engers find <lb/>&longs;helter? </s><s>Shall we de&longs;troy that <emph type="italics"/>A&longs;ylum,<emph.end type="italics"/> that <emph type="italics"/>Prytaneum,<emph.end type="italics"/> where­ <lb/>in &longs;o many Students meet with commodious harbour, where <lb/>without expo&longs;ing them&longs;elves to the injuries of the air, with the <lb/>onely turning over of a few leaves, one may learn all the &longs;e­ <lb/>crets of Nature? </s><s>Shall we di&longs;mantle that fort in which we are <lb/>&longs;afe from all ho&longs;tile a&longs;&longs;aults? </s><s>But I pitie him no more than I do <lb/>that Gentleman who with great expence of time and trea&longs;ure, <lb/>and the help of many hundred arti&longs;ts, erects a very &longs;umptu­ <lb/>ous Pallace, and afterwards beholds it ready to fall, by rea&longs;on <lb/>of the bad foundation; but being extremely unwilling to &longs;ee <lb/>the Walls &longs;tript which are adorned with &longs;o many beautifull <lb/>Pictures; or to &longs;uffer the columns to fall, that uphold the &longs;tate­ <lb/>ly Galleries; or the gilded roofs, chimney-pieces, the freizes, <lb/>the corni&longs;hes of marble, with &longs;o much co&longs;t erected, to be rui­ <lb/>ned; goeth about with girders, props, &longs;hoars, buttera&longs;&longs;es, to pre­ <lb/>vent their &longs;ubver&longs;ion.</s></p><p type="margin"><s><margin.target id="marg125"></margin.target><emph type="italics"/>The Declamation <lb/>of<emph.end type="italics"/> Simplicius.</s></p><p type="main"><s>SALV. </s><s>But ala&longs;s, <emph type="italics"/>Simplicius<emph.end type="italics"/> as yet fears no &longs;uch fall, and <lb/>I would undertake to &longs;ecure him from that mi&longs;chief at a far <lb/>le&longs;s charge. </s><s>There is no danger that &longs;o great a multitude of <lb/><arrow.to.target n="marg126"></arrow.to.target> <lb/>&longs;ubtle and wi&longs;e Philo&longs;ophers, &longs;hould &longs;uffer them&longs;elves to be <lb/><emph type="italics"/>Hector'd<emph.end type="italics"/> by one or two, who make a little blu&longs;tering; nay, <lb/>they will rather, without ever turning the points of their pens <lb/>again&longs;t them, by their &longs;ilence onely render them the object of <lb/>univer&longs;al &longs;corn and contempt. </s><s>It is a fond conceit for any one <lb/>to think to introduce new Philo&longs;ophy, by reproving this or that <lb/>Author: it will be fir&longs;t nece&longs;&longs;ary to new-mold the brains of <lb/>men, and make them apt to di&longs;tingui&longs;h truth from fal&longs;hood. </s><s>A <lb/>thing which onely God can do. </s><s>But from one di&longs;cour&longs;e to another <lb/>whither are we &longs;tray'd? </s><s>your memory mu&longs;t help to guide me into <lb/>the way again.</s></p><p type="margin"><s><margin.target id="marg126"></margin.target><emph type="italics"/>Peripatetick Phi­ <lb/>lo&longs;ophy unchange­ <lb/>able.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I remember very well where we left. </s><s>We were <lb/>upon the an&longs;wer of <emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> to the objections again&longs;t the <lb/>immutability of the Heavens, among which you in&longs;erted this <lb/>of the Solar fpots, not &longs;poke of by him; and I believe you <lb/>intended to examine his an&longs;wer to the in&longs;tance of the New <lb/>Stars.</s></p> <pb xlink:href="040/01/060.jpg" pagenum="44"/><p type="main"><s>SALV. </s><s>Now I remember the re&longs;t, and to proceed, Methinks <lb/>there are &longs;ome things in the an&longs;wer of <emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> worthy of <lb/>reprehen&longs;ion. </s><s>And fir&longs;t, if the two New Stars, which he can do <lb/>no le&longs;s than place in the uppermo&longs;t parts of the Heavens, and <lb/>which were of a long duration, but finally vani&longs;hed, give him no <lb/>ob&longs;truction in maintaining the inalterability of Heaven, in that <lb/>they were not certain parts thereof, nor mutations made in the <lb/>antient Stars, why doth he &longs;et him&longs;elf &longs;o vigorou&longs;ly and earne&longs;tly <lb/>again&longs;t the Comets, to bani&longs;h them by all ways from the Cœle­ <lb/>&longs;tial Regions? </s><s>Was it not enough that he could &longs;ay of them <lb/>the &longs;ame which he &longs;poke of the New &longs;tars? </s><s>to wit, that in re­ <lb/>gard they were no certain parts of Heaven, nor mutations made <lb/>in any of the Stars, they could no wi&longs;e prejudice either Heaven, <lb/>or the Doctrine of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>? </s><s>Secondly, I am not very well &longs;atis­ <lb/>fied of his meaning; when he &longs;aith that the alterations that &longs;hould <lb/>be granted to be made in the Stars, would be de&longs;tructive to the <lb/>prerogative of Heaven; namely, its incorruptibility, <emph type="italics"/>&c.<emph.end type="italics"/> and <lb/>this, becau&longs;e the Stars are Cœle&longs;tial &longs;ub&longs;tances, as is manife&longs;t <lb/>by the con&longs;ent of every one; and yet is nothing troubled that <lb/><arrow.to.target n="marg127"></arrow.to.target> <lb/>the &longs;ame alterations &longs;hould be made ^{*} without the Stars in the re&longs;t <lb/>of the Cœle&longs;tial expan&longs;ion. </s><s>Doth he think that Heaven is no <lb/>Cœle&longs;tial &longs;ub&longs;tance? </s><s>I, for my part, did believe that the Stars <lb/>were called Cœle&longs;tial bodies, by rea&longs;on that they were in Hea­ <lb/>ven, or for that they were made of the &longs;ub&longs;tance of Heaven; <lb/>and yet I thought that Heaven was more Cœle&longs;tial than they; in <lb/>like &longs;ort, as nothing can be &longs;aid to be more Terre&longs;trial, or more <lb/>fiery than the Earth or Fire them&longs;elves. </s><s>And again, in that he ne­ <lb/>ver made any mention of the Solar &longs;pots, which have been evi­ <lb/>dently demon&longs;trated to be produced, and di&longs;&longs;olved, and to be <lb/>neer the Sun, and to turn either with, or about the &longs;ame, I have <lb/>rea&longs;on to think that this Author probably did write more for others <lb/>plea&longs;ure, than for his own &longs;atisfaction; and this I affirm, fora&longs;­ <lb/>much as he having &longs;hewn him&longs;elf to be skilful in the Mathema­ <lb/>ticks, it is impo&longs;&longs;ible but that he &longs;hould have been convinced by <lb/>Demon&longs;trations, that tho&longs;e &longs;ub&longs;tances are of nece&longs;&longs;ity contigu­ <lb/>ous with the body of the Sun, and are &longs;o great generations and <lb/>corruptions, that none comparable to them, ever happen in the <lb/>Earth: And if &longs;uch, &longs;o many, and &longs;o frequent be made in the <lb/>very Globe of the Sun, which may with rea&longs;on be held one of the <lb/>noble&longs;t parts of Heaven, what &longs;hould make us think that others <lb/>may not happen in the other Orbs? <lb/><arrow.to.target n="marg128"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg127"></margin.target>* Ex tra Stellas.</s></p><p type="margin"><s><margin.target id="marg128"></margin.target><emph type="italics"/>Generability and <lb/>alteration is a <lb/>greater perfection <lb/>in the Worlds bo­ <lb/>dies than the con­ <lb/>trary qualities.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I cannot without great admiration, nay more, deni­ <lb/>al of my under&longs;tanding, hear it to be attributed to natural bodies, <lb/>for a great honour and perfection that they are ^{*} impa&longs;&longs;ible, im­ <lb/>mutable, inalterable, <emph type="italics"/>&c.<emph.end type="italics"/> And on the contrary, to hear it to </s></p><p type="main"><s><arrow.to.target n="marg129"></arrow.to.target> <pb xlink:href="040/01/061.jpg" pagenum="45"/>be e&longs;teemed a great imperfection to be alterable, generable, mu­ <lb/>table, <emph type="italics"/>&c.<emph.end type="italics"/> It is my opinion that the Earth is very noble and ad­ <lb/><arrow.to.target n="marg130"></arrow.to.target> <lb/>mirable, by rea&longs;on of &longs;o many and &longs;o different alterations, mu­ <lb/>tations, generations, <emph type="italics"/>&c.<emph.end type="italics"/> which are ince&longs;&longs;antly made therein; <lb/>and if without being &longs;ubject to any alteration, it had been all <lb/>one va&longs;t heap of &longs;and, or a ma&longs;&longs;e of <emph type="italics"/>Ja&longs;per,<emph.end type="italics"/> or that in the time <lb/>of the Deluge, the waters freezing which covered it, it had <lb/>continued an immen&longs;e Globe of Chri&longs;tal, wherein nothing had <lb/><arrow.to.target n="marg131"></arrow.to.target> <lb/>ever grown, altered, or changed, I &longs;hould have e&longs;teemed it a <lb/>lump of no benefit to the World, full of idlene&longs;&longs;e, and in a <lb/>word &longs;uperfluous, and as if it had never been in nature; and <lb/>&longs;hould make the &longs;ame difference in it, as between a living and <lb/>dead creature: The like I &longs;ay of the <emph type="italics"/>Moon, Jupiter,<emph.end type="italics"/> and all the <lb/>other Globes of the World. </s><s>But the more I dive into the con­ <lb/>&longs;ideration of the vanity of popular di&longs;cour&longs;es, the more empty <lb/>and &longs;imple I find them. </s><s>And what greater folly can there be <lb/>imagined, than to call Jems, Silver and Gold pretious; and Earth <lb/>and dirt vile? </s><s>For do not the&longs;e per&longs;ons con&longs;ider, that if there <lb/><arrow.to.target n="marg132"></arrow.to.target> <lb/>&longs;hould be as great a &longs;carcity of Earth, as there is of Jewels and <lb/>pretious metals, there would be no Prince, but would gladly give <lb/>a heap of Diamonds and Rubies, and many Wedges of Gold, <lb/>to purcha&longs;e onely &longs;o much Earth as &longs;hould &longs;uffice to plant a Ge&longs;&longs;e­ <lb/>mine in a little pot, or to &longs;et therein a <emph type="italics"/>China Orange,<emph.end type="italics"/> that he might <lb/>&longs;ee it &longs;prout, grow up, and bring forth &longs;o goodly leaves, &longs;o odi­ <lb/>riferous flowers, and &longs;o delicate fruit? </s><s>It is therefore &longs;carcity and <lb/><arrow.to.target n="marg133"></arrow.to.target> <lb/>plenty that make things e&longs;teemed and contemned by the vulgar; <lb/>who will &longs;ay that &longs;ame is a mo&longs;t beautiful Diamond, for that it <lb/>re&longs;embleth a cleer water, and yet will not part with it for ten <lb/>Tun of water: The&longs;e men that &longs;o extol incorruptibility, inalte­ <lb/><arrow.to.target n="marg134"></arrow.to.target> <lb/>rability, <emph type="italics"/>&c.<emph.end type="italics"/> &longs;peak thus I believe out of the great de&longs;ire they <lb/>have to live long, and for fear of death; not confidering, that <lb/>if men had been immortal, they &longs;hould have had nothing to do <lb/>in the World. </s><s>The&longs;e de&longs;erve to meet with a <emph type="italics"/>Medu&longs;a<emph.end type="italics"/>'s head, <lb/><arrow.to.target n="marg135"></arrow.to.target> <lb/>that would transform them into Statues of <emph type="italics"/>Dimond<emph.end type="italics"/> and <emph type="italics"/>Ja&longs;per,<emph.end type="italics"/> <lb/>that &longs;o they might become more perfect than they are.</s></p><p type="margin"><s><margin.target id="marg129"></margin.target>* Impatible.</s></p><p type="margin"><s><margin.target id="marg130"></margin.target><emph type="italics"/>The Earth very <lb/>noble, by rea&longs;on of <lb/>the many mutati­ <lb/>ons made therein.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg131"></margin.target><emph type="italics"/>The carth unpro­ <lb/>&longs;itable and full of <lb/>idlene&longs;&longs;e, its alte­ <lb/>rations taken away<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg132"></margin.target><emph type="italics"/>The Earth more <lb/>noble than Gold <lb/>and Jewels.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg133"></margin.target><emph type="italics"/>Scarcity and plen­ <lb/>ty enhan&longs;e and de­ <lb/>ba&longs;e the price of <lb/>things.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg134"></margin.target><emph type="italics"/>Incorruptibility e­ <lb/>&longs;teemed by the vul­ <lb/>gar out of their <lb/>fear of death.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg135"></margin.target><emph type="italics"/>The di&longs;paragers of <lb/>corraptibility de­ <lb/>&longs;erve to be turned <lb/>into Statua's.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>And it may be &longs;uch a <emph type="italics"/>Metamorpho&longs;is<emph.end type="italics"/> would not be al­ <lb/>together unprofitable to them; for I am of opinion that it is bet­ <lb/>ter not to di&longs;cour&longs;e at all, than to argue erroniou&longs;ly.</s></p><p type="main"><s>SIMPL. </s><s>There is not the lea&longs;t que&longs;tion to be made, but that <lb/>the Earth is much more perfect, being as it is alterable, mutable, <lb/><emph type="italics"/>&c.<emph.end type="italics"/> than if it had been a ma&longs;&longs;e of &longs;tone; yea although it were <lb/>one entire Diamond, mo&longs;t hard and impa&longs;&longs;ile. </s><s>But look how mueh <lb/><arrow.to.target n="marg136"></arrow.to.target> <lb/>the&longs;e qualifications enoble the Earth, they render the Heavenly <lb/>bodies again on the other &longs;ide &longs;o much the more imperfect, in <lb/>which, &longs;uch conditions would be &longs;uperfluous; in regard that the <pb xlink:href="040/01/062.jpg" pagenum="46"/>Cœle&longs;tial bodies, namely, the Sun, Moon, and the other Stars, <lb/>which are ordained for no other u&longs;e but to &longs;erve the Earth, need <lb/>no other qualities for attaining of that end, &longs;ave onely tho&longs;e of <lb/>light and motion.</s></p><p type="margin"><s><margin.target id="marg136"></margin.target><emph type="italics"/>The Cœle&longs;tial bo­ <lb/>dies de&longs;igned to <lb/>&longs;erve the Earth, <lb/>need no more but <lb/>motion and light.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. How? </s><s>Will you affirm that nature hath produced and <lb/>de&longs;igned &longs;o many va&longs;t perfect and noble Cœle&longs;tial bodies, impa&longs;­ <lb/>&longs;ible, immortal, and divine, to no other u&longs;e but to &longs;erve the pa&longs;­ <lb/>&longs;ible, frail, and mortal Earth? </s><s>to &longs;erve that which you call the <lb/>dro&longs;&longs;e of the World, and &longs;ink of all uncleanne&longs;&longs;e? </s><s>To what <lb/>purpo&longs;e were the Cœle&longs;tial bodies made immortal, <emph type="italics"/>&c.<emph.end type="italics"/> to &longs;erve a <lb/>frail, <emph type="italics"/>&c.<emph.end type="italics"/> Take away this &longs;ub&longs;erviency to the Earth, and the in­ <lb/>numerable multitude of Cœle&longs;tial bodies become wholly unu&longs;e­ <lb/><arrow.to.target n="marg137"></arrow.to.target> <lb/>ful, and &longs;uperfluous, &longs;ince they neither have nor can have any <lb/>mutual operation betwixt them&longs;elves; becau&longs;e they are all unal­ <lb/>terable, immutable, impa&longs;&longs;ible: For if, for Example, the Moon <lb/>be impa&longs;&longs;ible, what influence can the Sun or any other Star have <lb/>upon her? </s><s>it would doubtle&longs;&longs;e have far le&longs;&longs;e effect upon her, than <lb/>that of one who would with his looks or imagination, lignifie a <lb/>piece of Gold. </s><s>Moreover, it &longs;eemeth to me, that whil&longs;t the Cœ­ <lb/>le&longs;tial bodies concurre to the generation and alteration of the <lb/>Earth, they them&longs;elves are al&longs;o of nece&longs;&longs;ity alterable; for other­ <lb/>wi&longs;e I cannot under&longs;tand how the application of the Sun or Moon <lb/>to the Earth, to effect production, &longs;hould be any other than to lay <lb/>a marble Statue by a Womans &longs;ide, and from that conjunction to <lb/>expect children. <lb/><arrow.to.target n="marg138"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg137"></margin.target><emph type="italics"/>Celestial bodies <lb/>want an inter­ <lb/>changeable opera­ <lb/>tion upon each o­ <lb/>ther.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg138"></margin.target><emph type="italics"/>Alterability, &c. <lb/></s><s>are not in the whole <lb/>Terre&longs;trial Globe, <lb/>but in &longs;ome of its <lb/>parts.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. Corruptibility, alteration, mutation, <emph type="italics"/>&c.<emph.end type="italics"/> are not in <lb/>the whole Terre&longs;trial Globe, which as to its whole, is no le&longs;&longs;e eter­ <lb/>nal than the Sun or Moon, but it is generable and corruptible as to <lb/>its external parts; but yet it is al&longs;o true that likewi&longs;e in them ge­ <lb/>neration and corruption are perpetual, and as &longs;uch require the <lb/>heavenly eternal operations; and therefore it is nece&longs;&longs;ary that <lb/>the Cœle&longs;tial bodies be eternal.</s></p><p type="main"><s>SAGR. </s><s>All this is right; but if the corruptibility of the &longs;uper­ <lb/>ficial parts of the Earth be nowi&longs;e prejudicial to the eternity of <lb/>its whole Globe, yea, if their being generable, corruptible, alter­ <lb/>able, <emph type="italics"/>&c.<emph.end type="italics"/> gain them great ornament and perfection; why can­</s></p><p type="main"><s><arrow.to.target n="marg139"></arrow.to.target> <lb/>not, and ought not you to admit alteration, generation, <emph type="italics"/>&c.<emph.end type="italics"/> like­ <lb/>wi&longs;e in the external parts of the Cœle&longs;tial Globes, adding to <lb/>them ornament, without taking from them perfection, or berea­ <lb/>ving them of action; yea rather encrea&longs;ing their effects, by grant­ <lb/>ing not onely that they all operate on the Earth, but that they mu­ <lb/>tually operate upon each other, and the Earth al&longs;o upon them <lb/>all?</s></p><p type="margin"><s><margin.target id="marg139"></margin.target><emph type="italics"/>Cœle&longs;tial bodies <lb/>alterable in their <lb/>outward parts.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>This cannot be, becau&longs;e the generations, mutations, <lb/><emph type="italics"/>&c.<emph.end type="italics"/> which we &longs;hould &longs;uppo&longs;e <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> in the Moon; would be vain <lb/>and u&longs;ele&longs;&longs;e, <emph type="italics"/>& natura nihil fru&longs;tra facit.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/063.jpg" pagenum="47"/><p type="main"><s>SAGR. </s><s>And why &longs;hould they be vain and u&longs;ele&longs;&longs;e?</s></p><p type="main"><s>SIMPL. </s><s>Becau&longs;e we cleerly &longs;ee, and feel with our hands, that <lb/><arrow.to.target n="marg140"></arrow.to.target> <lb/>all generations, corruptions, <emph type="italics"/>&c.<emph.end type="italics"/> made in the Earth, are all ei­ <lb/>ther mediately or immediately directed to the u&longs;e, convenience, <lb/>and benefit of man; for the u&longs;e of man are hor&longs;es brought forth, <lb/>for the feeding of hor&longs;es, the Earth produceth gra&longs;&longs;e, and the <lb/>Clouds water it; for the u&longs;e and nouri&longs;hment of man, herbs, corn, <lb/>fruits, bea&longs;ts, birds, fi&longs;hes, are brought forth; and in &longs;um, if <lb/>we &longs;hould one by one dilligently examine and re&longs;olve all the&longs;e <lb/>things, we &longs;hould find the end to which they are all directed, to be <lb/>the nece&longs;&longs;ity, u&longs;e, convenience, and delight of man. </s><s>Now of what <lb/>u&longs;e could the generations which we &longs;uppo&longs;e to be made in the <lb/>Moon or other Planets, ever be to mankind? </s><s>unle&longs;&longs;e you &longs;hould <lb/>&longs;ay that there were al&longs;o men in the Moon, that might enjoy the <lb/>benefit thereof; a conceit either fabulous or impious.</s></p><p type="margin"><s><margin.target id="marg140"></margin.target><emph type="italics"/>The generations & <lb/>mutations happen­ <lb/>ing in the Earth, <lb/>are all for the good <lb/>of Man.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>That in the Moon or other Planets, there are genera­ <lb/><arrow.to.target n="marg141"></arrow.to.target> <lb/>ted either herbs, or plants, or animals, like to ours, or that there <lb/>are rains, winds, or thunders there, as about the Earth, I nei­ <lb/>ther know, nor believe, and much le&longs;&longs;e, that it is inhabited by <lb/>men: but yet I under&longs;tand not, becau&longs;e there are not genera­ <lb/>ted things like to ours, that therefore it nece&longs;&longs;arily followeth, <lb/>that no alteration is wrought therein, or that there may not be <lb/>other things that change, generate, and di&longs;&longs;olve, which are not <lb/><arrow.to.target n="marg142"></arrow.to.target> <lb/>onely different from ours, but exceedingly beyond our imagina­ <lb/>tion, and in a word, not to be thought of by us. </s><s>And if, as I <lb/>am certain, that one born and brought up in a &longs;patious Forre&longs;t, <lb/>among&longs;t bea&longs;ts and birds, and that hath no knowledg at all of the <lb/>Element of Water, could never come to imagine another World <lb/><arrow.to.target n="marg143"></arrow.to.target> <lb/>to be in Nature, different from the Eatth, full of living crea­ <lb/>tures, which without legs or wings &longs;wiftly move, and not upon <lb/>the &longs;urface onely, as bea&longs;ts do upon the Earth, but in the very <lb/>bowels thereof; and not onely move, but al&longs;o &longs;tay them&longs;elves <lb/>and cea&longs;e to move at their plea&longs;ure, which birds cannot do in the <lb/>air; and that moreover men live therein, and build Palaces and <lb/>Cities, and have &longs;o great convenience in travailing, that without <lb/>the lea&longs;t trouble, they can go with their Family, Hou&longs;e, and <lb/>whole Cities, to places far remote, like as I &longs;ay, I am certain, <lb/>&longs;uch a per&longs;on, though of never &longs;o piercing an imagination, could <lb/>never fancy to him&longs;elf Fi&longs;hes, the Ocean, Ships, Fleets, <emph type="italics"/>Arma­ <lb/>do's<emph.end type="italics"/> at Sea; thus, and much more ea&longs;ily, may it happn, that in <lb/>the Moon, remote from us by &longs;o great a &longs;pace, and of a &longs;ub­ <lb/>&longs;tance perchance very different from the Earth, there may be mat­ <lb/>ters, and operations, not only wide off, but altogether beyond <lb/>all our imaginations, as being &longs;uch as have no re&longs;emblance to <lb/>ours, and therefore wholly inexcogitable, in regard, that what we <pb xlink:href="040/01/064.jpg" pagenum="48"/>imagine to our &longs;elves, mu&longs;t nece&longs;&longs;arily be either a thing already <lb/>&longs;een, or a compo&longs;ition of things, or parts of things &longs;een at ano­ <lb/>ther time; for &longs;uch are the <emph type="italics"/>Sphinxes, Sirenes, Chimœra's, Cen­ <lb/>taurs,<emph.end type="italics"/> &c.</s></p><p type="margin"><s><margin.target id="marg141"></margin.target><emph type="italics"/>The Moon hath <lb/>no generatings of <lb/>things, like as we <lb/>have, nor is it in­ <lb/>habited by men.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg142"></margin.target><emph type="italics"/>In the Moon may <lb/>be a generation of <lb/>things different <lb/>from ours.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg143"></margin.target><emph type="italics"/>He that had not <lb/>heard of the Ele­ <lb/>ment of Water, <lb/>could never fancy <lb/>to him&longs;elf Ships <lb/>and Fi&longs;hes.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I have very often let my fancy ruminate upon the&longs;e &longs;pe­ <lb/>culations, and in the end, have thought that I had found &longs;ome <lb/>things that neither are nor can be in the Moon; but yet I <lb/>have not found therein any of tho&longs;e which I believe are, and may <lb/>be there, &longs;ave onely in a very general acceptation, namely, things <lb/>that adorn it by operating, moving and living; and perhaps in a way <lb/><arrow.to.target n="marg144"></arrow.to.target> <lb/>very different from ours; beholding and admiring the greatne&longs;s and <lb/>beauty of the World, and of its Maker and Ruler, and with <lb/>continual <emph type="italics"/>Encomiums<emph.end type="italics"/> &longs;inging his pray&longs;es; and in &longs;umme (which is <lb/>that which I intend) doing what &longs;acred Writers &longs;o frequently af­ <lb/>firm, to wit, all the creatures making it their perpetual imploy­ <lb/>ment to laud God.</s></p><p type="margin"><s><margin.target id="marg144"></margin.target><emph type="italics"/>There may be &longs;ub­ <lb/>&longs;tances in the <lb/>Moon very diffe­ <lb/>rent from ours.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The&longs;e are the things, which &longs;peaking in general terms, <lb/>may be there; but I would gladly hear you in&longs;tance in &longs;uch as you <lb/>believe neither are nor can be there; which perchance may be <lb/>more particularly named.</s></p><p type="main"><s>SALV. </s><s>Take notice <emph type="italics"/>Sagredus<emph.end type="italics"/> that this will be the third time <lb/>that we have unawares by running from one thing to another, lo&longs;t <lb/>our principal &longs;ubject; and if we continue the&longs;e digre&longs;&longs;ions, it <lb/>will be longere we come to a conclu&longs;ion of our di&longs;cour&longs;e; there­ <lb/>fore I &longs;hould judg it better to remit this, as al&longs;o &longs;uch other points, <lb/>to be decided on a particular occa&longs;ion.</s></p><p type="main"><s>SAGR. </s><s>Since we are now got into the Moon, if you plea&longs;e, let <lb/>us di&longs;patch &longs;uch things as concern her, that &longs;o we be not forced to <lb/>&longs;uch another tedious journey.</s></p><p type="main"><s>SALV. </s><s>It &longs;hall be as you would have it. </s><s>And to begin with <lb/>things more general, I believe that the Lunar Globe is far diffe­ <lb/>rent from the Terre&longs;trial, though in &longs;ome things they agree. </s><s>I will <lb/>recount fir&longs;t their re&longs;emblances, and next their differences. </s><s>The <lb/><arrow.to.target n="marg145"></arrow.to.target> <lb/>Moon is manife&longs;tly like to the Earth in figure, which undoubtedly <lb/>is &longs;pherical, as may be nece&longs;&longs;arily concluded from the a&longs;pect of its <lb/>&longs;urface, which is perfectly Orbicular, and the manner of its re­ <lb/>ceiving the light of the Sun, from which, if its &longs;urface were flat, <lb/>it would come to be all in one and the &longs;ame time illuminated, and <lb/>likewi&longs;e again in another in&longs;tant of time ob&longs;cured, and not tho&longs;e <lb/>parts fir&longs;t, which are &longs;ituate towards the Sun, and the re&longs;t &longs;ucce&longs;­ <lb/>&longs;ively, &longs;o that in its oppo&longs;ition, and not till then, its whole <lb/>apparent circumference is enlightned; which would happen quite <lb/>contrary, if the vi&longs;ible &longs;urface were concave; namely, the illu­ <lb/><arrow.to.target n="marg146"></arrow.to.target> <lb/>mination would begin from the parts oppo&longs;ite or aver&longs;e to the Sun. <lb/></s><s>Secondly &longs;he is as the Earth, in her &longs;elf ob&longs;cure and opacous, by <lb/>which opacity it is enabled to receive, and reflect the light of the <pb xlink:href="040/01/065.jpg" pagenum="49"/>Sun; which were it not &longs;o, it could not do. </s><s>Thirdly, I hold its <lb/><arrow.to.target n="marg147"></arrow.to.target> <lb/>matter to be mo&longs;t den&longs;e and &longs;olid as the Earth is, which I clearly <lb/>argue from the unevenne&longs;s of its &longs;uperficies in mo&longs;t places, by means <lb/>of the many eminencies and cavities di&longs;covered therein by help of <lb/>the <emph type="italics"/>&longs;ele&longs;cope<emph.end type="italics"/>: of which eminencies there are many all over it, di­ <lb/>rectly re&longs;embling our mo&longs;t &longs;harp and craggy mountains, of which <lb/>you &longs;hall there perceive &longs;ome extend and run in ledges of an hun­ <lb/>dred miles long; others are contracted into rounder forms; and <lb/>there are al&longs;o many craggy, &longs;olitary, &longs;teep and cliffy rocks. </s><s>But <lb/>that of which there are frequente&longs;t appearances, are certain Banks <lb/>(I u&longs;e this word, becau&longs;e I cannot thing of another that better ex­ <lb/>pre&longs;&longs;eth them) pretty high rai&longs;ed, which environ and inclo&longs;e fields <lb/>of &longs;everal bigne&longs;&longs;es, and form &longs;undry figures, but for the mo&longs;t part <lb/>circular; many of which have in the mid&longs;t a mount rai&longs;ed pretty <lb/>high, and &longs;ome few are repleni&longs;hed with a matter &longs;omewhat ob­ <lb/>&longs;cure, to wit, like to the great &longs;pots di&longs;cerned by the bare eye, and <lb/>the&longs;e are of the greate&longs;t magnitude; the number moreover of tho&longs;e <lb/>that are le&longs;&longs;er and le&longs;&longs;er is very great, and yet almo&longs;t all circular. <lb/><arrow.to.target n="marg148"></arrow.to.target> <lb/>Fourthly, like as the &longs;urface of our Globe is di&longs;tingui&longs;hed into two <lb/>principal parts, namely, into the Terre&longs;trial and Aquatick: &longs;o in <lb/>the Lunar &longs;urface we di&longs;cern a great di&longs;tinction of &longs;ome great fields <lb/>more re&longs;plendant, and &longs;ome le&longs;s: who&longs;e a&longs;pect makes me believe, <lb/>that that of the Earth would &longs;eem very like it, beheld by any one <lb/>from the Moon, or any other the like di&longs;tance, to be illuminated <lb/><arrow.to.target n="marg149"></arrow.to.target> <lb/>by the Sun: and the &longs;urface of the &longs;ea would appear more ob­ <lb/>&longs;cure, and that of the Earth more bright. </s><s>Fifthly, like as we from <lb/>the Earth behold the Moon, one while all illuminated, another <lb/><arrow.to.target n="marg150"></arrow.to.target> <lb/>while half; &longs;ometimes more, &longs;ometimes le&longs;s; &longs;ometimes horned, <lb/>&longs;ometimes wholly invi&longs;ibly; namely, when its ju&longs;t under the Sun <lb/>beams; &longs;o that the parts which look towards the Earth are dark: <lb/>Thus in every re&longs;pect, one &longs;tanding in the Moon would &longs;ee the <lb/>illumination of the Earths &longs;urface by the Sun, with the &longs;ame <lb/>periods to an hair, and under the &longs;ame changes of figures. <lb/></s><s>Sixtly, -----</s></p><p type="margin"><s><margin.target id="marg145"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Fir&longs;t <emph type="italics"/>re&longs;em­ <lb/>blance between the <lb/>Moon and Earth; <lb/>which is that of <lb/>figure; is proved by <lb/>the manner of be­ <lb/>ing illuminated by <lb/>the Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg146"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Second <emph type="italics"/>con­ <lb/>formity is the <lb/>Moons being opa­ <lb/>cous as the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg147"></margin.target><emph type="italics"/>Thirdly, The mat­ <lb/>ter of the Moon is <lb/>den&longs;e and mo ita­ <lb/>nous as the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg148"></margin.target><emph type="italics"/>Fourthly, The <lb/>Moon is di&longs;tin­ <lb/>gui&longs;hed into two <lb/>different parts for <lb/>clarity and ob&longs;cu­ <lb/>rity, as the Terre­ <lb/>strial Globe into <lb/>Sea and Land.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg149"></margin.target><emph type="italics"/>The &longs;urface of the <lb/>Sea would &longs;hew at <lb/>a di&longs;tance more ob­ <lb/>&longs;oure than that of <lb/>the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg150"></margin.target><emph type="italics"/>Fiftly, Muta­ <lb/>tion of &longs;igures in <lb/>the Earth, like to <lb/>tho&longs;e of the Moon, <lb/>and made with the <lb/>&longs;ame periods.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Stay a little, <emph type="italics"/>Salviatus<emph.end type="italics"/>; That the illumination of <lb/>the Earth, as to the &longs;everal figures, would repre&longs;ent it &longs;elf to a per&longs;on <lb/>placed in the Moon, like in all things to that which we di&longs;cover in <lb/>the Moon, I under&longs;tand very well, but yet I cannot conceive how <lb/>it &longs;hall appear to be done in the &longs;ame period; &longs;eeing that that <lb/>which the Suns illumination doth in the Lunar &longs;uperficies in a <lb/>month, it doth in the Terre&longs;trial in twenty four hours.</s></p><p type="main"><s>SALV. </s><s>Its true, the effect of the Sun about the illuminating <lb/>the&longs;e two bodies, and repleni&longs;hing with its &longs;plendor their whole <lb/>&longs;urfaces, is di&longs;patch'd in the Earth in a Natural day, and in the <lb/>Moon in a Month; but the variation of the figures in which the <pb xlink:href="040/01/066.jpg" pagenum="50"/>illuminated parts of the Terre&longs;trial &longs;uperficies appear beheld from <lb/>the Moon, depends not on this alone, but on the divers a&longs;pects <lb/>which the Moon is &longs;till changing with the Sun; &longs;o that, if for in­ <lb/>&longs;tance, the Moon punctually followed the motion of the Sun, and <lb/>&longs;tood, for example, always in a direct line between it and the <lb/>Earth, in that a&longs;pect which we call Conjunction, it looking always <lb/>to the &longs;ame Hemi&longs;phere of the Earth which the Sun looks unto, <lb/>&longs;he would behold the &longs;ame all light: as on the contrary, if it &longs;hould <lb/>always &longs;tay in Oppo&longs;ition to the Sun, it would never behold the <lb/>Earth, of which the dark part would be continually turn'd towards <lb/>the Moon, and therefore invi&longs;ible. </s><s>But when the Moon is in <lb/>Quadrature of the Sun, that half of the Terre&longs;trial Hemi&longs;phere ex­ <lb/>po&longs;ed to the &longs;ight of the Moon which is towards the Sun, is lumi­ <lb/>nous; and the other towards the contrary is ob&longs;cure: and there­ <lb/>fore the illuminated part of the Earth would repre&longs;ent it &longs;elf to the <lb/>Moon in a &longs;emi-circular figure.</s></p><p type="main"><s>SAGR. </s><s>I clearly perceive all this, and under&longs;tand very well, <lb/>that the Moon departing from its Oppo&longs;ition to the Sun, where it <lb/>&longs;aw no part of the illumination of the Terre&longs;trial &longs;uperficies, and <lb/>approaching day by day nearer the Sun, &longs;he begins by little and <lb/>little to di&longs;cover &longs;ome part of the face of the illuminated Earth; <lb/>and that which appeareth of it &longs;hall re&longs;emble a thin &longs;ickle, in regard <lb/>the figure of the Earth is round: and the Moon thus acquiring by <lb/>its motion day by day greater proximity to the Sun, &longs;ucce&longs;&longs;ively <lb/>di&longs;covers more and more of the Terre&longs;trial Hemi&longs;phere enlightned, <lb/>&longs;o that at the Quadrature there is ju&longs;t half of it vi&longs;ible, in&longs;omuch <lb/>that we may &longs;ee the other part of her: continuing next to proceed <lb/>towards the Conjunction, it &longs;ucce&longs;&longs;ively di&longs;covers more and more <lb/>of its &longs;urface to be illuminated, and in fine, at the time of Conjun­ <lb/>ction &longs;eeth the whole Hemi&longs;phere enlightned. </s><s>And in &longs;hort, I <lb/>very well conceive, that what befalls the Inhabitants of the Earth, <lb/>in beholding the changes of the Moon, would happen to him that <lb/>from the Moon &longs;hould ob&longs;erve the Earth; but in a contrary order, <lb/>namely, that when the Moon is to us at her full, and in Oppo&longs;ition <lb/>to the Sun, then the Earth would be in Conjunction with the Sun, <lb/>and wholly ob&longs;cure and invi&longs;ible; on the contrary, that po&longs;ition <lb/>which is to us a Conjunction of the Moon with the Sun, and for <lb/>that cau&longs;e a <emph type="italics"/>M<emph.end type="italics"/>oon &longs;ilent and un&longs;een, would be there an Oppo&longs;ition <lb/>of the Earth to the Sun, and, to &longs;o &longs;peak, <emph type="italics"/>Full Earth,<emph.end type="italics"/> to wit, all <lb/>enlightned. </s><s>And la&longs;tly, look what part of the Lunar &longs;urface ap­ <lb/>pears to us from time to time illuminated, &longs;o much of the Earth <lb/>in the &longs;ame time &longs;hall you behold from the Moon to be ob&longs;cured: <lb/>and look how much of the Moon is to us deprived of light, &longs;o much <lb/>of the Earth is to the Moon illuminated. </s><s>In one thing yet the&longs;e <lb/>mutual operations in my judgment &longs;eem to differ, and it is, that it <pb xlink:href="040/01/067.jpg" pagenum="51"/>being &longs;uppo&longs;ed, and not granted, that &longs;ome one being placed in the <lb/>Moon to ob&longs;erve the Earth, he would every day &longs;ee the whole <lb/>Terre&longs;trial &longs;uperficies, by means of the Moons going about the <lb/>Earth in twenty four or twenty five hours; but we never &longs;ee but <lb/>half of the Moon, &longs;ince it revolves not in it &longs;elf, as it mu&longs;t do to <lb/>be &longs;een in every part of it.</s></p><p type="main"><s>SALV. </s><s>So that this, befals not contrarily, namely, that her re­ <lb/>volving in her &longs;elf, is the cau&longs;e that we &longs;ee not the other half of <lb/>her, for &longs;o it would be nece&longs;&longs;ary it &longs;hould be, if &longs;he had the Epicy­ <lb/>cle. </s><s>But what other difference have you behind, to exchange for <lb/>this which you have named?</s></p><p type="main"><s>SAGR. </s><s>Let me &longs;ee; Well for the pre&longs;ent I cannot think of <lb/>any other.</s></p><p type="main"><s>SALV. </s><s>And what if the Earth (as you have well noted) &longs;eeth <lb/><arrow.to.target n="marg151"></arrow.to.target> <lb/>no more than half the Moon, whereas from the Moon one may &longs;ee <lb/>all the Earth; and on the contrary, all the Earth &longs;eeth the Moon, and <lb/>but onely half of it &longs;eeth the Earth? </s><s>For the inhabitants, to &longs;o &longs;peak, <lb/>of the &longs;uperior Hemi&longs;phere of the Moon, which is to us invi&longs;ible, <lb/>are deprived of the &longs;ight of the Earth: and the&longs;e haply are the <lb/><emph type="italics"/>Anticthones.<emph.end type="italics"/> But here I remember a particular accident, newly <lb/>ob&longs;erved by our <emph type="italics"/>Academian,<emph.end type="italics"/> in the Moon, from whch are gathered <lb/><arrow.to.target n="marg152"></arrow.to.target> <lb/>two nece&longs;&longs;ary con&longs;equences; one is, that we &longs;ee &longs;omewhat more <lb/>than half of the Moon; and the other is, that the motion of the <lb/>Moon hath exact concentricity with the Earth: and thus he finds <lb/>the <emph type="italics"/>Phœnomenon<emph.end type="italics"/> and ob&longs;ervation. </s><s>When the Moon hath a cor­ <lb/>re&longs;pondence and natural &longs;ympathy with the Earth, towards which <lb/>it hath its a&longs;pect in &longs;uch a determinate part, it is nece&longs;&longs;ary that the <lb/>right line which conjoyns their centers, do pa&longs;&longs;e ever by the &longs;ame <lb/>point of the Moons &longs;uperficies; &longs;o that, who &longs;o &longs;hall from the cen­ <lb/>ter of the Earth behold the &longs;ame, &longs;hall alwayes &longs;ee the &longs;ame <lb/><emph type="italics"/>Di&longs;cus<emph.end type="italics"/> or Face of the Moon punctually determined by one and <lb/>the &longs;ame circumference; But if a man be placed upon the Terre­ <lb/>&longs;trial &longs;urface, the ray which from his eye pa&longs;&longs;eth to the centre of the <lb/>Lunar Globe, will not pa&longs;s by the &longs;ame point of its &longs;uperficies, by <lb/>which the line pa&longs;&longs;eth that is drawn from the centre of the Earth <lb/>to that of the Moon, &longs;ave onely when it is vertical to him: but <lb/>the Moon being placed in the Ea&longs;t, or in the We&longs;t, the point of <lb/>incidence of the vi&longs;ual ray, is higher than that of the line which <lb/>conjoyns the centres; and therefore the ob&longs;erver may di&longs;cern <lb/>&longs;ome part of the Lunar Hemi&longs;phere towards the upper circumfe­ <lb/>rence, and alike part of the other is invi&longs;ible: they are di&longs;cerna­ <lb/>ble and undi&longs;cernable, in re&longs;pect of the Hemi&longs;phere beheld from <lb/>the true centre of the Earth: and becau&longs;e the part of the Moons <lb/>circumference, which is &longs;uperiour in its ri&longs;ing, is nethermo&longs;t in its <lb/>&longs;etting; therefore the difference of the &longs;aid &longs;uperiour and inferi­ <pb xlink:href="040/01/068.jpg" pagenum="52"/>our parts mu&longs;t needs be very ob&longs;ervable; certain &longs;pots and other <lb/>notable things in tho&longs;e parts, being one while di&longs;cernable, and <lb/>another while not. </s><s>A like variation may al&longs;o be ob&longs;erved towards <lb/>the North and South extremities of the &longs;ame <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> (or Surface) <lb/>according as the Moons po&longs;ition is in one or the other Section of <lb/>its Dragon; For, if it be North, &longs;ome of its parts towards the <lb/>North are hid, and &longs;ome of tho&longs;e parts towards the South are <lb/>di&longs;covered, and &longs;o on the contrary. </s><s>Now that the&longs;e con&longs;equen­ <lb/><arrow.to.target n="marg153"></arrow.to.target> <lb/>ces are really true, is verified by the <emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/> for there be in <lb/>the Moon two remarkable &longs;pots, one of which, when the Moon <lb/>is in the meridian, is &longs;ituate to the Northwe&longs;t, and the other is <lb/>almo&longs;t diametrically oppo&longs;ite unto it; and the fir&longs;t of the&longs;e is vi­ <lb/>&longs;ible even without the <emph type="italics"/>Tele&longs;cope<emph.end type="italics"/>; but the other is not. </s><s>That to­ <lb/>wards the Northwe&longs;t is a rea&longs;onable great &longs;pot of oval figure, &longs;e­ <lb/>parated from the other great ones; the oppo&longs;ite one is le&longs;&longs;e, and <lb/>al&longs;o &longs;evered from the bigge&longs;t, and &longs;ituate in a very cleer field; in <lb/>both the&longs;e we may manife&longs;tly di&longs;cern the fore&longs;aid variations, and <lb/>&longs;ee them one after another; now neer the edge or limb of the <lb/>Lunar <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> and anon remote, with &longs;o great difference that <lb/>the di&longs;tance betwixt the Northwe&longs;t and the circumference of the <lb/><emph type="italics"/>Di&longs;cus<emph.end type="italics"/> is more than twice as great at one time, as at the other; <lb/>and as to the &longs;econd &longs;pot (becau&longs;e it is neerer to the circumfe­ <lb/>rence) &longs;uch mutation importeth more, than twice &longs;o much in the <lb/>former. </s><s>Hence its manife&longs;t, that the Moon, as if it were drawn <lb/>by a magnetick vertue, con&longs;tantly beholds the Terre&longs;trial Globe <lb/>with one and the &longs;ame a&longs;pect, never deviating from the &longs;ame.</s></p><p type="margin"><s><margin.target id="marg151"></margin.target><emph type="italics"/>All the Earth <lb/>&longs;eeth half onely of <lb/>the Moon, & the <lb/>half onely of the <lb/>Moon &longs;eeth all the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg152"></margin.target><emph type="italics"/>From the Earth <lb/>we &longs;ee more than <lb/>half the Lunar <lb/>Globe.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg153"></margin.target><emph type="italics"/>Two &longs;pots in the <lb/>Moon, by which it <lb/>is perceived that <lb/>&longs;he hath respect to <lb/>the centre of the <lb/>Earth in her mo­ <lb/>tion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. Oh! when will there be an end put to the new ob­ <lb/>&longs;ervations aud di&longs;coveries of this admirable In&longs;trument?</s></p><p type="main"><s>SALV. </s><s>If this &longs;ucceed according to the progre&longs;&longs;e of other great <lb/>inventions, it is to be hoped, that in proce&longs;&longs;e of time, one may <lb/>arrive to the &longs;ight of things, to us at pre&longs;ent not to be imagined. <lb/><arrow.to.target n="marg154"></arrow.to.target> <lb/>But returning to our fir&longs;t di&longs;cour&longs;e, I &longs;ay for the &longs;ixth re&longs;emblance <lb/>betwixt the Moon and Earth, that as the Moon for a great part <lb/>of time, &longs;upplies the want of the Suns light, and makes the <lb/>nights, by the reflection of its own, rea&longs;onable clear; &longs;o the <lb/>Earth, in recompence, affordeth it when it &longs;tands in mo&longs;t need, <lb/>by reflecting the Solar rayes, a very cleer illumination, and &longs;o <lb/>much, in my opinion, greater than that which cometh from her to <lb/>us, by how much the &longs;uperficies of the Earth is greater than that <lb/>of the Moon.</s></p><p type="margin"><s><margin.target id="marg154"></margin.target><emph type="italics"/>Sixthly, The <lb/>Earth and Moon <lb/>interchangeably do <lb/>illuminate.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Hold there, <emph type="italics"/>Salviatus<emph.end type="italics"/> hold there, and permit me the <lb/>plea&longs;ure of relating to you, how at this fir&longs;t hint I have penetrated <lb/>the cau&longs;e of an accident, which I have a thou&longs;and times thought <lb/><arrow.to.target n="marg155"></arrow.to.target> <lb/>upon, but could never find out. </s><s>You would &longs;ay, that the imper­ <lb/>fect light which is &longs;een in the Moon, e&longs;pecially when it is horned, <pb xlink:href="040/01/069.jpg" pagenum="53"/>comes from the reflection of the light of the Sun on the Superfi­ <lb/>cies of the Earth and Sea; and that light is more clear, by how <lb/>much the horns are le&longs;&longs;e, for then the luminous part of the Earth, <lb/>beheld by the Moon, is greater, according to that which was <lb/>a little before proved; to wit, that the luminous part of the Earth, <lb/>expo&longs;ed to the Moon, is alway as great as the ob&longs;cure part of <lb/>the Moon, that is vi&longs;ible to the Earth; whereupon, at &longs;uch time <lb/>as the Moon is &longs;harp-forked, and con&longs;equently its tenebrous part <lb/>great, great al&longs;o is the illuminated part of the Earth beheld from <lb/>the Moon, and its reflection of light &longs;o much the more potent.</s></p><p type="margin"><s><margin.target id="marg155"></margin.target><emph type="italics"/>Light reflected <lb/>from the Earth in­ <lb/>to the Moon.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>This is exactly the &longs;ame with what I was about to &longs;ay. <lb/></s><s>In a word, it is a great plea&longs;ure to &longs;peak with per&longs;ons judicious <lb/>and apprehen&longs;ive, and the rather to me, for that while&longs;t others <lb/>conver&longs;e and di&longs;cour&longs;e touching Axiomatical truths, I have ma­ <lb/>ny times creeping into my brain &longs;uch arduous Paradoxes, that <lb/>though I have a thou&longs;and times rehear&longs;ed this which you at the ve­ <lb/>ry fir&longs;t, have of your &longs;elf apprehended, yet could I never beat <lb/>it into mens brains.</s></p><p type="main"><s>SIMPL. </s><s>If you mean by your not being able to per&longs;wade them <lb/>to it, that you could not make them under&longs;tand the &longs;ame, I <lb/>much wonder thereat, and am very confident that if they did <lb/>not under&longs;tand it by your demon&longs;tration (your way of expre&longs;&longs;ion, <lb/>being, in my judgment, very plain) they would very hardly have <lb/>apprehended it upon the explication of any other man; but if <lb/>you mean you have not per&longs;waded them, &longs;o as to make them be­ <lb/>lieve it, I wonder not, in the lea&longs;t, at this; for I confe&longs;&longs;e my <lb/>&longs;elf to be one of tho&longs;e who under&longs;tand your di&longs;cour&longs;es, but <lb/>am not &longs;atisfied therewith; for there are in this, and &longs;ome of <lb/>the other &longs;ix congruities, or re&longs;emblances, many difficulties, <lb/>which I &longs;hall in&longs;tance in, when you have gone through them <lb/>all.</s></p><p type="main"><s>SALV. </s><s>The de&longs;ire I have to find out any truth, in the acqui&longs;t <lb/>whereof the objections of intelligent per&longs;ons (&longs;uch as your &longs;elf) <lb/>may much a&longs;&longs;i&longs;t me, will cau&longs;e me to be very brief in di&longs;patching <lb/>that which remains. </s><s>For a &longs;eventh conformity, take their reci­ <lb/><arrow.to.target n="marg156"></arrow.to.target> <lb/>procal re&longs;pon&longs;ion as well to injuries, as favours; whereby the <lb/>Moon, which very often in the height of its illumination, by the <lb/>interpo&longs;ure of the Earth betwixt it and the Sun, is deprived of <lb/>light, and eclip&longs;ed, doth by way of revenge; in like manner, in­ <lb/>terpo&longs;e it &longs;elf between the Earth and the Sun, and with its &longs;hadow <lb/>ob&longs;cureth the Earth; and although the revenge be not an&longs;wer­ <lb/>able to the injury, for that the Moon often continueth, and <lb/>that for a rea&longs;onable long time, wholly immer&longs;ed in the Earths <lb/>&longs;hadow, but never was the Earth wholly, nor for any long time, <lb/>eclip&longs;ed by the Moon; yet, neverthele&longs;&longs;e, having re&longs;pect to the <pb xlink:href="040/01/070.jpg" pagenum="54"/>&longs;malne&longs;&longs;e of the body of this, in compari&longs;on to the magnitude <lb/>of the other, it cannot be denied but that the <emph type="italics"/>will<emph.end type="italics"/> and as it <lb/>were <emph type="italics"/>valour<emph.end type="italics"/> of this, is very great. </s><s>Thus much for their con­ <lb/>gruities or re&longs;emblances. </s><s>It &longs;hould next follow that we di&longs;cour&longs;e <lb/>touching their di&longs;parity; but becau&longs;e <emph type="italics"/>Simplicius<emph.end type="italics"/> will favour us <lb/>with his objections again&longs;t the former, its nece&longs;&longs;ary that we hear <lb/>and examine them, before we proceed any farther.</s></p><p type="margin"><s><margin.target id="marg156"></margin.target><emph type="italics"/>Seventhly, The <lb/>Earth and Moon <lb/>do mutually eclip&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>And the rather, becau&longs;e it is to be &longs;uppo&longs;ed that <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> will not any wayes oppo&longs;e the di&longs;parities, and incon­ <lb/>gruities betwixt the Earth and Moon, &longs;ince that he accounts their <lb/>&longs;ub&longs;tances extremely different.</s></p><p type="main"><s>SIMPL. </s><s>Among&longs;t the re&longs;emblances by you recited, in the pa­ <lb/>rallel you make betwixt the Earth and Moon, I find that I can <lb/>admit none confidently &longs;ave onely the fir&longs;t, and two others; I <lb/>grant the fir&longs;t, namely, the &longs;pherical figure; howbeit, even in <lb/>this there is &longs;ome kind of difference, for that I hold that of the <lb/>Moon to be very &longs;mooth and even, as a looking-gla&longs;&longs;e, where­ <lb/>as, we find and feel this of the Earth to be extraordinary montu­ <lb/>ous and rugged; but this belonging to the inequality of &longs;uperfi­ <lb/>cies, it &longs;hall be anon con&longs;idered, in another of tho&longs;e Re&longs;emblan­ <lb/>ces by you alledged; I &longs;hall therefore re&longs;erve what I have to &longs;ay <lb/>thereof, till I come to the con&longs;ideration of that. </s><s>Of what you <lb/>affirm next, that the Moon &longs;eemeth, as you &longs;ay in your &longs;econd <lb/>Re&longs;emblance, opacous and ob&longs;cure in its &longs;elf, like the Earth; I <lb/>admit not any more than the fir&longs;t attribute of opacity, of which <lb/>the Eclip&longs;es of the Sun a&longs;&longs;ure me. </s><s>For were the Moon tran&longs;pa­ <lb/>rent, the air in the total ob&longs;curation of the Sun, would not be­ <lb/>come &longs;o duski&longs;h, as at &longs;uch a time it is, but by means of the <lb/>tran&longs;parency of the body of the Moon, a refracted light would <lb/>pa&longs;&longs;e through it, as we &longs;ee it doth through the thicke&longs;t clouds. </s><s>But <lb/>as to the ob&longs;curity, I believe not that the Moon is wholly depri­ <lb/>ved of light, as the Earth; nay, that clarity which is &longs;een in the <lb/>remainder of its <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> over and above the &longs;mall cre&longs;cent en­ <lb/>lightened by the Sun, I repute to be its proper and natural light, <lb/><arrow.to.target n="marg157"></arrow.to.target> <lb/>and not a reflection of the Earth, which I e&longs;teem unable, by <lb/>rea&longs;on of its a&longs;perity (craggine&longs;&longs;e) and ob&longs;curity, to reflect the <lb/>raies of the Sun. </s><s>In the third Parallel I a&longs;&longs;ent unto you in one <lb/><arrow.to.target n="marg158"></arrow.to.target> <lb/>part, and di&longs;&longs;ent in another: I agree in judging the body of the <lb/>Moon to be mo&longs;t &longs;olid and hard, like the Earth, yea much more; <lb/><arrow.to.target n="marg159"></arrow.to.target> <lb/>for if from <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> we receive that the Heavens are impenetrable, <lb/>and the Stars the mo&longs;t den&longs;e parts of Heaven, it mu&longs;t nece&longs;&longs;arily <lb/>follow, that they are mo&longs;t &longs;olid and mo&longs;t impenetrable.</s></p><p type="margin"><s><margin.target id="marg157"></margin.target><emph type="italics"/>The &longs;econd clarity <lb/>of the Moon e­ <lb/>&longs;teemed to be its <lb/>native light.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg158"></margin.target><emph type="italics"/>The Earth unable <lb/>to reflect the Suns <lb/>raies.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg159"></margin.target><emph type="italics"/>The &longs;ub&longs;tance of <lb/>the Heavens impe­ <lb/>netrable, accord­ <lb/>ing to<emph.end type="italics"/> Ari&longs;totle.</s></p><p type="main"><s>SAGR. </s><s>What excellent matter would the Heavens afford us for <lb/>to make Pallaces of, if we could procure a &longs;ub&longs;tance &longs;o hard and &longs;o <lb/>tran&longs;parent?</s></p> <pb xlink:href="040/01/071.jpg" pagenum="55"/><p type="main"><s>SALV. </s><s>Rather how improper, for being by its tran&longs;parence, <lb/>wholly invi&longs;ible, a man would not be able without &longs;tumbling at <lb/>the thre&longs;holds, and breaking his head again&longs;t the Walls, to pa&longs;s <lb/>from room to room.</s></p><p type="main"><s>SAGR. </s><s>This danger would not befall him, if it be true, as &longs;ome <lb/><arrow.to.target n="marg160"></arrow.to.target> <lb/><emph type="italics"/>Peripateticks<emph.end type="italics"/> &longs;ay, that it is intangible: and if one cannot <lb/>touch it, much le&longs;s can it hurt him.</s></p><p type="margin"><s><margin.target id="marg160"></margin.target><emph type="italics"/>The &longs;ubstance of <lb/>Heaven intangi­ <lb/>ble.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>This would not &longs;erve the turn, for though the matter <lb/>of the Heavens cannot be toucht, as wanting tangible qualities: <lb/>yet may it ea&longs;ily touch the elementary bodies; and to offend us <lb/>it is as &longs;ufficient that it &longs;trike us, nay wor&longs;e, than if we &longs;hould <lb/>&longs;trike it. </s><s>But let us leave the&longs;e <emph type="italics"/>Pallaces,<emph.end type="italics"/> or, to &longs;ay better, the&longs;e <lb/><emph type="italics"/>Ca&longs;tles<emph.end type="italics"/> in the air, and not interrupt <emph type="italics"/>Simplicius.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>The que&longs;tion which you have &longs;o ca&longs;ually &longs;tarted, is one <lb/>of the mo&longs;t difficulty that is di&longs;puted in Philo&longs;ophy; and I have <lb/>on that &longs;ubject mo&longs;t excellent conceits of a very learned Doctor <lb/>of <emph type="italics"/>Padoua,<emph.end type="italics"/> but it is not now time to enter upon them. </s><s>Therefore <lb/>returning to our purpo&longs;e, I &longs;ay that the Moon, in my opinion, is <lb/>much more &longs;olid than the Earth, but do not infer the &longs;ame, as you <lb/>do, from the craggine&longs;s and montuo&longs;ity of its &longs;uperficies; but <lb/><arrow.to.target n="marg161"></arrow.to.target> <lb/>rather from the contrary, namely, from its aptitude to receive (as <lb/>we &longs;ee it experimented in the harde&longs;t &longs;tones) a poli&longs;h and lu&longs;tre <lb/>exceeding that of the &longs;moothe&longs;t gla&longs;s, for &longs;uch nece&longs;&longs;arily mu&longs;t <lb/>its &longs;uperficies be, to render it apt to make &longs;o lively reflection of <lb/>the Suns rays. </s><s>And for tho&longs;e appearances which you mention, <lb/>of Mountains, Cliffs, Hills, Valleys, <emph type="italics"/>&c.<emph.end type="italics"/> they are all illu&longs;ions: <lb/>and I have been pre&longs;ent at certain publick di&longs;putes, where I have <lb/>heard it &longs;trongly maintained again&longs;t the&longs;e introducers of novelties, <lb/><arrow.to.target n="marg162"></arrow.to.target> <lb/>that &longs;uch appearances proceed from nothing el&longs;e, but from the un­ <lb/>equal di&longs;tribution of the opacous and per&longs;picuous parts, of which <lb/>the Moon is inwardly and outwardly compo&longs;ed: as we &longs;ee it <lb/>often fall out in chry&longs;tal, amber, and many other precious &longs;tones <lb/>of perfect lu&longs;tre; in which by rea&longs;on of the opacity of &longs;ome parts, <lb/>and the tran&longs;parency of others, there doth appear &longs;everal conca­ <lb/>vities and prominencies. </s><s>In the fourth re&longs;emblance, I grant, that <lb/>the &longs;uperficies of Terre&longs;trial Globe beheld from afar, would make <lb/>two different appearances, namely, one more clear, the other more <lb/>dark; but I believe that &longs;uch diver&longs;ity would &longs;ucceed quite con­ <lb/>trary to what you &longs;ay; that is, I hold that the &longs;urface of the wa­ <lb/>ter would appear lucid, becau&longs;e that it is &longs;mooth and tran&longs;parent; <lb/>and that of the Earth would appear ob&longs;cure, by rea&longs;on of its o­ <lb/>pacity and &longs;cabro&longs;ity, ill accommodated for reflecting the light of <lb/>the Sun. </s><s>Concernïng the fifth compari&longs;on, I grant it wholly, and <lb/>am able, in ca&longs;e the Earth did &longs;hine as the Moon, to &longs;how the <lb/>&longs;ame to any one that &longs;hould from thence above behold it, repre­ <pb xlink:href="040/01/072.jpg" pagenum="56"/>&longs;ented by figures an&longs;werable to tho&longs;e which we &longs;ee in the Moon: <lb/>I comprehend al&longs;o, how the period of its illumination and varia­ <lb/>tion of figure, would be monthly, albeit the Sun revolves round <lb/>about it in twenty four hours: and la&longs;tly, I do not &longs;cruple to <lb/>admit, that the half onely of the Moon &longs;eeth all the Earth, and <lb/>that all the Earth &longs;eeth but onely half of the Moon. </s><s>For what <lb/>remains, I repute it mo&longs;t fal&longs;e, that the Moon can receive light <lb/>from the Earth, which is mo&longs;t ob&longs;cure, opacous, and utterly un­ <lb/>apt to reflect the Suns light, as the Moon doth reflect it to us: and <lb/>as I have &longs;aid, I hold that that light which we &longs;ee in the remain­ <lb/>der of the Moons face (the &longs;plendid cre&longs;cents &longs;ubducted) by the <lb/>illumination, is the proper and natural light of the Moon, and no <lb/>ea&longs;ie matter would induce me to believe otherwi&longs;e. </s><s>The &longs;eventh, <lb/>touching the mutual Eclip&longs;es, may be al&longs;o admitted; howbeit <lb/>that is wont to be called the eclip&longs;e of the Sun, which you are <lb/>plea&longs;ed to phra&longs;e the eclip&longs;e of the Earth. </s><s>And this is what <emph type="italics"/>I<emph.end type="italics"/> <lb/>have at this time to &longs;ay in oppo&longs;ition to your &longs;even congruities <lb/>or re&longs;emblances, to which objections, if you are minded to make <lb/>any reply, <emph type="italics"/>I<emph.end type="italics"/> &longs;hall willingly hear you.</s></p><p type="margin"><s><margin.target id="marg161"></margin.target><emph type="italics"/>The &longs;uperficies of <lb/>the Moon more <lb/>&longs;leek than any <lb/>Looking-glaß.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg162"></margin.target><emph type="italics"/>The eminencies <lb/>and cavities in the <lb/>Moon are illu&longs;ions <lb/>of its opacous and <lb/>perspicuous parts.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>If I have well apprehended what you have an&longs;wered, it <lb/>&longs;eems to me, that there &longs;till remains in controver&longs;ie between us, cer­ <lb/>tain conditions, which I made common betwixt the Moon & Earth, <lb/>and they are the&longs;e; You e&longs;teem the Moon to be &longs;mooth and poli&longs;ht, <lb/>as a Looking-gla&longs;s, and as &longs;uch, able to reflect the Suns light; and <lb/>contrarily, the Earth, by rea&longs;on of its montuo&longs;ity, unable to make <lb/>&longs;uch reflection: You yield the Moon to be &longs;olid and hard, and that <lb/>you argue from its being &longs;mooth and polite, and not from its being <lb/>montuous; and for its appearing montuous, you a&longs;&longs;ign as the <lb/>cau&longs;e, that it con&longs;i&longs;ts of parts more and le&longs;s opacous and per&longs;pi­ <lb/>cuous. </s><s>And la&longs;tly, you e&longs;teem that &longs;econdary light, to be proper <lb/>to the <emph type="italics"/>M<emph.end type="italics"/>oon, and not reflected from the Earth; howbeit you <lb/>&longs;eem not to deny the &longs;ea, as being of a &longs;mooth &longs;urface, &longs;ome <lb/>kind of reflection. </s><s>As to the convincing you of that error, that <lb/>the reflection of the <emph type="italics"/>M<emph.end type="italics"/>oon is made, as it were, like that of a <lb/>Looking-gla&longs;s, <emph type="italics"/>I<emph.end type="italics"/> have &longs;mall hope, whil&longs;t <emph type="italics"/>I<emph.end type="italics"/> &longs;ee, that what hath <lb/><arrow.to.target n="marg163"></arrow.to.target> <lb/>been read in the ^{*} <emph type="italics"/>Saggiator<emph.end type="italics"/> and in the <emph type="italics"/>Solar Letters<emph.end type="italics"/> of our <emph type="italics"/>Com­ <lb/>mon Friend,<emph.end type="italics"/> hath profited nothing in your judgment, if haply <lb/>you have attentively read what he hath there written on this &longs;ub­ <lb/>ject.</s></p><p type="margin"><s><margin.target id="marg163"></margin.target>* <emph type="italics"/>Il Saggiatore, & <lb/>Lettere Solari,<emph.end type="italics"/> <lb/>two Treati&longs;es of <lb/><emph type="italics"/>Galilæus.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. <emph type="italics"/>I<emph.end type="italics"/> have peru&longs;ed the &longs;ame &longs;o &longs;uperficially, according to <lb/>the &longs;mall time of lea&longs;ure allowed me from more &longs;olid &longs;tudies; <lb/>therefore, if you think you can, either by repeating &longs;ome of tho&longs;e <lb/>rea&longs;ons, or by alledging others, re&longs;olve me the&longs;e doubts, <emph type="italics"/>I<emph.end type="italics"/> will <lb/>hearken to them attentively.</s></p><p type="main"><s>SALV. <emph type="italics"/>I<emph.end type="italics"/> will tell you what comes into my mind upon the <pb xlink:href="040/01/073.jpg" pagenum="57"/>in&longs;tant, and its po&longs;&longs;ible it may be a commixtion of my own con­ <lb/>ceipts; and tho&longs;e which I have &longs;ometime read in the fore-&longs;aid <lb/>Books, by which I well remember, that I was then perfectly <lb/>&longs;atisfied, although the conclu&longs;ions, at fir&longs;t &longs;ight &longs;eem'd unto me <lb/>&longs;trange Paradoxes. </s><s>We enquire <emph type="italics"/>Simplicius,<emph.end type="italics"/> whether to the ma­ <lb/>king a reflection of light, like that which we receive from the <lb/>Moon, it be nece&longs;&longs;ary that the &longs;uperficies from whence the refle­ <lb/>ction commeth, be &longs;o &longs;mooth and polite, as the face of a Looking­ <lb/>Gla&longs;&longs;e, or whether a &longs;uperficies not &longs;mooth or poli&longs;ht, but rough <lb/>and uneven, be more apt for &longs;uch a purpo&longs;e. </s><s>Now &longs;uppo&longs;ing <lb/>two reflections &longs;hould come unto us, one more bright, the other <lb/>le&longs;&longs;e, from two &longs;uperficies oppo&longs;ite unto us, I demand of you, <lb/>which of the two &longs;uperficies you think would repre&longs;ent it &longs;elf to <lb/>our &longs;ight, to be the cleare&longs;t, and which the ob&longs;cure&longs;t.</s></p><p type="main"><s>SIMPL. </s><s>I am very confident, that that &longs;ame, which mo&longs;t for­ <lb/>cibly reflected the light upon me, would &longs;hew its &longs;elf in its a&longs;pect <lb/>the clearer, and the other darker.</s></p><p type="main"><s>SALV. </s><s>Be plea&longs;ed to take that Gla&longs;&longs;e which hangs on yonder <lb/><arrow.to.target n="marg164"></arrow.to.target> <lb/>Wall, and let us go out into the Court-yard. </s><s>Come <emph type="italics"/>Sagredus.<emph.end type="italics"/> <lb/>Now hang the gla&longs;&longs;e yonder, again&longs;t that &longs;ame Wall, on which <lb/>the Sun &longs;hines, and now let us with-draw our &longs;elves into the &longs;hade. <lb/></s><s>See yonder two &longs;uperficies beaten by the Sun, namely, the Wall <lb/>and the Gla&longs;&longs;e. </s><s>Tell me now which appears cleare&longs;t unto you, <lb/>that of the Wall or that of the Gla&longs;&longs;e? </s><s>Why do you not an&longs;wer <lb/>me?</s></p><p type="margin"><s><margin.target id="marg164"></margin.target><emph type="italics"/>It is proved at <lb/>large that the <lb/>Moons &longs;urface is <lb/>&longs;harp.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I leave the reply to <emph type="italics"/>Simplicius,<emph.end type="italics"/> who made the que&longs;ti­ <lb/>on; but I, for my own part, am per&longs;waded upon this &longs;mall be­ <lb/>ginning of the experiment, that the Moon mu&longs;t be of a very un­ <lb/>poli&longs;ht &longs;urface.</s></p><p type="main"><s>SALV. </s><s>What &longs;ay you <emph type="italics"/>Simplicius,<emph.end type="italics"/> if you were to depaint that <lb/>Wall, and that Gla&longs;&longs;e fa&longs;tened unto it, where would you u&longs;e <lb/>your darke&longs;t colours, in de&longs;igning the Wall, or el&longs;e in painting <lb/>the Looking-Gla&longs;&longs;e.</s></p><p type="main"><s>SIMPL. </s><s>Much the darker in depainting the Gla&longs;&longs;e.</s></p><p type="main"><s>SALV. </s><s>Now if from the &longs;uperficies, which repre&longs;ents it &longs;elf <lb/>more clear, there proceedeth a more powerful reflection of light, <lb/>the Wall will more forcibly reflect the raies of the Sun, than the <lb/>Gla&longs;&longs;e.</s></p><p type="main"><s>SIMPL. </s><s>Very well, Sir, have you ever a better experiment <lb/>than this? </s><s>you have placed us where the Gla&longs;&longs;e doth not rever­ <lb/>berate upon us; but come along with me a little this way; how, <lb/>will you not &longs;tir?</s></p><p type="main"><s>SAGR. </s><s>You perhaps &longs;eek the place of the reflection, which the <lb/>Gla&longs;&longs;e makth.</s></p><p type="main"><s>SIMPL. </s><s>I do &longs;o.</s></p> <pb xlink:href="040/01/074.jpg" pagenum="58"/><p type="main"><s>SAGR. </s><s>Why look you, there it is upon the oppo&longs;ite Wall, ju&longs;t <lb/>as big as the Gla&longs;&longs;e, and little le&longs;&longs;e bright than if the Sun had <lb/>directly &longs;hined upon it.</s></p><p type="main"><s>SIMPL. </s><s>Come hither therefore, and &longs;ee from hence the &longs;ur­ <lb/>face of the Gla&longs;&longs;e, and tell me whether you think it more ob­ <lb/>&longs;cure than that of the Wall.</s></p><p type="main"><s>SAGR. </s><s>Look on it your &longs;elf, for I have no mind at this time, <lb/>to dazle my eyes; and I know very well, without &longs;eeing it, <lb/>that it there appears as &longs;plendid and bright as the Sun it &longs;elf, or <lb/>little le&longs;&longs;e.</s></p><p type="main"><s>SIMPL. </s><s>What &longs;ay you therefore, is the reflection of a Gla&longs;&longs;e <lb/>le&longs;&longs;e powerful than that of a Wall? </s><s>I &longs;ee, that in this oppo&longs;ite <lb/>Wall, where the reflection of the other illuminated Wall comes, <lb/>together with that of the Gla&longs;&longs;e, this of the Gla&longs;&longs;e is much <lb/>clearer; and I &longs;ee likewi&longs;e, that, from this place where I &longs;tand, <lb/>the gla&longs;&longs;e it &longs;elf appears with much more lu&longs;tre than the Wall.</s></p><p type="main"><s>SALV. </s><s>You have prevented me with your &longs;ubtlety; for I &longs;tood <lb/>in need of this very ob&longs;ervation to demon&longs;trate what remains. <lb/></s><s>You &longs;ee then the difference which happens betwixt the two refle­ <lb/>ctions made by the two &longs;uperficies of the Wall and Gla&longs;&longs;e, per­ <lb/>cu'&longs;t in the &longs;elf-&longs;ame manner, by the rayes of the Sun; and you <lb/>&longs;ee, how the reflection which comes from the Wall, diffu&longs;eth it <lb/>&longs;elf towards all the parts oppo&longs;ite to it, but that of the Gla&longs;&longs;e <lb/>goeth towards one part onely, not at all bigger than the Gla&longs;&longs;e <lb/>it &longs;elf: you &longs;ee likewi&longs;e, how the &longs;uperficies of the Wall, beheld <lb/>from what part &longs;oever, alwayes &longs;hews it &longs;elf of one and the &longs;ame <lb/>cleerne&longs;&longs;e, and every way, much clearer than that of the Gla&longs;&longs;e, <lb/>excepting only in that little place, on which the Gla&longs;&longs;es reflection <lb/>reverberates, for from thence indeed the Gla&longs;&longs;e appears much more <lb/>lucid than the Wall. </s><s>By the&longs;e &longs;o &longs;en&longs;ible, and palpable experi­ <lb/>ments, my thinks one may &longs;oon come to know, whether the <lb/>reflection which the Moon &longs;ends upon us, proceed as from a <lb/>Gla&longs;&longs;e, or el&longs;e, as from a Wall, that is, from a &longs;mooth &longs;uperfi­ <lb/>cies, or a rugged.</s></p><p type="main"><s>SAGR. </s><s>If I were in the Moon it &longs;elf, I think I could not with <lb/>my hands more plainly feel the unevenne&longs;&longs;e of its &longs;uperficies, than <lb/>I do now perceive it, by apprehending your di&longs;cour&longs;e. </s><s>The Moon <lb/>beheld in any po&longs;ture, in re&longs;pect of the Sun and us, &longs;heweth us <lb/>its &longs;uperficies, touch't by the Suns rayes, alwayes equally clear; <lb/>an effect, which an&longs;wers to an hair that of the Wall, which be­ <lb/>held from what place &longs;oever, appeareth equally bright, and dif­ <lb/>fereth from the Gla&longs;&longs;e, which from one place onely appeareth lu­ <lb/>cid, and from all others ob&longs;cure. </s><s>Moreover, the light which <lb/>cometh to me from the reflection of the Wall, is tollerable, <lb/>and weak, in compari&longs;on of that of the Gla&longs;&longs;e, which is little <pb xlink:href="040/01/075.jpg" pagenum="59"/>le&longs;&longs;e forcible and offen&longs;ive to the &longs;ight, than that primary and <lb/>direct light of the Sun. </s><s>And thus without trouble do we behold <lb/>the face of the Moon; which were it as a Gla&longs;&longs;e, it appearing to <lb/>us by rea&longs;on of its vicinity, as big as the Sun it &longs;elf, its &longs;plendor <lb/>would be ab&longs;olutely intollerable, and would &longs;eem as if we beheld <lb/>another Sun.</s></p><p type="main"><s>SALV. </s><s>A&longs;cribe not, I be&longs;eech you <emph type="italics"/>Sagredus,<emph.end type="italics"/> more to my de­ <lb/>mon&longs;tration, than it produceth. </s><s>I will oppo&longs;e you with an in&longs;tance, <lb/>which I &longs;ee not well how you can ea&longs;ily re&longs;olve. </s><s>You in&longs;i&longs;t upon it <lb/>as a grand difference between the Moon and Gla&longs;&longs;e, that it emits <lb/>its reflection towards all parts equally, as doth the Wall; where­ <lb/>as the Gla&longs;&longs;e ca&longs;ts it upon one onely determinate place; and from <lb/>hence you conclude the Moon to be like to the Wall, and not to <lb/>the Gla&longs;&longs;e: But I mu&longs;t tell you, that that &longs;ame Gla&longs;&longs;e ca&longs;ts its <lb/><arrow.to.target n="marg165"></arrow.to.target> <lb/>reflection on one place onely, becau&longs;e its &longs;urface is flat, and the <lb/>reflex rayes being to depart at angles equal to tho&longs;e of the rayes <lb/>of incidence, it mu&longs;t follow that from a plane or flat &longs;uperficies, <lb/>they do depart unitedly towards the &longs;ame place; but in regard <lb/>that the &longs;uperficies of the Moon is not plain, but &longs;pherical, and <lb/>the incident rayes upon &longs;uch a &longs;uperficies, being to reflect them­ <lb/>&longs;elves at angles equal to tho&longs;e of the incidence towards all parts, <lb/>by means of the infinity of the inclinations which compo&longs;e the <lb/>&longs;pherical &longs;uperficies, therefore the Moon may &longs;end forth its reflecti­ <lb/>on every way; and there is no nece&longs;&longs;ity for its repercu&longs;&longs;ion upon one <lb/>place onely, as that Gla&longs;&longs;e which is flat.</s></p><p type="margin"><s><margin.target id="marg165"></margin.target><emph type="italics"/>Flat Looking­ <lb/>gla&longs;&longs;es ca&longs;t forth <lb/>the reflection to­ <lb/>wards but one <lb/>place, but the <lb/>&longs;pherical every <lb/>way.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>This is one of the very &longs;ame objections, which I in­ <lb/>tended to have made again&longs;t him.</s></p><p type="main"><s>SAGR. </s><s>If this be one, you had need have more of them; yet <lb/>I tell you, that as to this fir&longs;t, it &longs;eems to me to make more a­ <lb/>gain&longs;t you, than for you.</s></p><p type="main"><s>SIMPL. </s><s>You have pronounced as a thing manife&longs;t, that the refle­ <lb/>ction made by that Wall, is as cleer and lucid as that which the <lb/>Moon &longs;ends forth, and I e&longs;teem it nothing in compari&longs;on thereto. <lb/></s><s>“For, in this bu&longs;ine&longs;&longs;e of the illumination, its requi&longs;ite to re&longs;pect, <lb/>and to di&longs;tingui&longs;h the <emph type="italics"/>Sphere<emph.end type="italics"/> of <emph type="italics"/>Activity<emph.end type="italics"/>; and who que&longs;tions <lb/><arrow.to.target n="marg166"></arrow.to.target> <lb/>but the Cœle&longs;tial bodies have greater Spheres of activity, than <lb/>the&longs;e our elementary, frail, and mortal ones? </s><s>and that Wall, <lb/>finally, what el&longs;e is it but a little ob&longs;cure Earth, unapt to <lb/>&longs;hine?”</s></p><p type="margin"><s><margin.target id="marg166"></margin.target><emph type="italics"/>The &longs;phere of <lb/>Activity greater <lb/>in the Cœle&longs;tial <lb/>bodies than in Ele­ <lb/>mentary.<emph.end type="italics"/></s></p><p type="main"><s><emph type="italics"/>S<emph.end type="italics"/>AGR. </s><s>And here al&longs;o I believe, that you very much deceive your <lb/>felf. </s><s>But I come to the fir&longs;t objection moved by <emph type="italics"/>Salviatus<emph.end type="italics"/>; and <lb/>I con&longs;ider, that to make a body appear unto us luminous, it &longs;uf­ <lb/>ficeth not that the rayes of the illuminating body fall upon it, <lb/>but it is moreover requi&longs;ite that the reflex rayes arrive to our <lb/>eye; as is manife&longs;tly &longs;een in the example of that Gla&longs;&longs;e, upon <pb xlink:href="040/01/076.jpg" pagenum="60"/>which, without que&longs;tion, the illuminating rayes of the Sun do <lb/>come; yet neverthele&longs;&longs;e, it appears not to us bright and &longs;hining, <lb/>unle&longs;&longs;e we &longs;et our eye in that particular place, where the refle­ <lb/>ction arriveth. </s><s>Now let us con&longs;ider what would &longs;ucceed, were <lb/>the gla&longs;&longs;e of a &longs;pherical figure; for without doubt, we &longs;hould <lb/>find, that of the reflection made by the whole &longs;urface illumina­ <lb/>ted, that to be but a very &longs;mall part, which arriveth to the eye <lb/>of a particular beholder; by rea&longs;on that that is but an incon&longs;ide­ <lb/>rable particle of the whole &longs;pherical &longs;uperficies, the inclination <lb/>of which ca&longs;ts the ray to the particular place of the eye; whence <lb/>the part of the &longs;pherical &longs;uperficies, which &longs;hews it &longs;elf &longs;hining <lb/>to the eye, mu&longs;t needs be very &longs;mall; all the re&longs;t being repre­ <lb/>&longs;ented ob&longs;cure. </s><s>So that were the Moon &longs;mooth, as a Looking­ <lb/><arrow.to.target n="marg167"></arrow.to.target> <lb/>gla&longs;&longs;e, a very &longs;mall part would be &longs;een by any particular eye to <lb/>be illu&longs;trated by the Sun, although its whole Hemi&longs;phere were ex­ <lb/>po&longs;ed to the Suns rayes; and the re&longs;t would appear to the eye of <lb/>the beholder as not illuminated, and therefore invi&longs;ible; and <lb/>finally, the whole Moon would be likewi&longs;e invi&longs;ible, for &longs;o much <lb/>as that particle, whence the reflection &longs;hould come, by rea&longs;on of <lb/>its &longs;malne&longs;&longs;e and remotene&longs;&longs;e, would be lo&longs;t. </s><s>And as it would be <lb/>invi&longs;ible to the eye, &longs;o would it not afford any light; for it is al­ <lb/>together impo&longs;&longs;ible, that a bright body &longs;hould take away our <lb/>darkne&longs;&longs;e by its &longs;plendor, and we not to &longs;ee it.</s></p><p type="margin"><s><margin.target id="marg167"></margin.target><emph type="italics"/>The Moon if it <lb/>were &longs;mooth, like a <lb/>&longs;pherical gla&longs;&longs;e, <lb/>would be invi&longs;ible.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Stay good <emph type="italics"/>Sagredus,<emph.end type="italics"/> for I &longs;ee &longs;ome emotions in <lb/>the face and eyes of <emph type="italics"/>Simplicius,<emph.end type="italics"/> which are to me as indices that <lb/>he is not either very apprehen&longs;ive of, or &longs;atisfied with this which <lb/>you, with admirable proof, and ab&longs;olute truth have &longs;poken. <lb/></s><s>And yet I now call to mind, that I can by another experiment <lb/>remove all &longs;cruple. </s><s>I have &longs;een above in a Chamber, a great <lb/>&longs;pherical Looking-gla&longs;&longs;e; let us &longs;end for it hither, and while&longs;t it <lb/>is in bringing, let <emph type="italics"/>Simplicius<emph.end type="italics"/> return to con&longs;ider, how great the <lb/>clarity is which cometh to the Wall here, under the penthou&longs;e, <lb/>from the reflection of the flat gla&longs;&longs;e.</s></p><p type="main"><s>SIMPL. </s><s>I &longs;ee it is little le&longs;&longs;e &longs;hining, than if the Sun had di­ <lb/>rectly beat upon it.</s></p><p type="main"><s>SALV. </s><s>So indeed it is. </s><s>Now tell me, if taking away that &longs;mall <lb/>flat gla&longs;&longs;e, we &longs;hould put that great &longs;pherical one in the &longs;ame <lb/>place, what effect (think you) would its reflection have upon the <lb/>&longs;ame Wall?</s></p><p type="main"><s><emph type="italics"/>S<emph.end type="italics"/>IMPL. </s><s>I believe that it would eject upon it a far greater and <lb/>more diffu&longs;ed light.</s></p><p type="main"><s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s><s>But if the illumination &longs;hould be nothing, or &longs;o <lb/>&longs;mall, that you would &longs;car&longs;e di&longs;cern it, what would you &longs;ay <lb/>then?</s></p><p type="main"><s><emph type="italics"/>S<emph.end type="italics"/>IMPL. </s><s>When I have &longs;een the effect, I will bethink my &longs;elf <lb/>of an an&longs;wer.</s></p> <pb xlink:href="040/01/077.jpg" pagenum="61"/><p type="main"><s>SALV. </s><s>See here is the gla&longs;&longs;e, which I would have to be placed <lb/>clo&longs;e to the other. </s><s>But fir&longs;t let us go yonder towards the reflection <lb/>of that flat one, and attentively ob&longs;erve its clarity; &longs;ee how <lb/>bright it is here where it &longs;hines, and how di&longs;tinctly one may di&longs;cern <lb/>the&longs;e &longs;mall unevenne&longs;&longs;es in the Wall.</s></p><p type="main"><s>SIMPL. </s><s>I have &longs;een and very well ob&longs;erved the &longs;ame, now place <lb/>the other gla&longs;&longs;e by the &longs;ide of the fir&longs;t.</s></p><p type="main"><s>SALV. </s><s>See where it is. </s><s>It was placed there a&longs;&longs;oon as you be­ <lb/>gan to look upon the Walls &longs;mall unevenne&longs;&longs;es, and you percei­ <lb/>ved it not, &longs;o great was the encrea&longs;e of the light all over the re&longs;t of <lb/>the Wall. </s><s>Now take away the flat gla&longs;&longs;e. </s><s>Behold now all refle­ <lb/>ction removed, though the great convex gla&longs;&longs;e &longs;till remaineth. <lb/></s><s>Remove this al&longs;o, and place it there again if you plea&longs;e, and you <lb/>&longs;hall &longs;ee no alteration of light in all the Wall. </s><s>See here then de­ <lb/>mon&longs;trated to &longs;en&longs;e, that the reflection of the Sun, made upon a <lb/>&longs;pherical convex gla&longs;&longs;e, doth not &longs;en&longs;ibly illuminate the places neer <lb/>unto it. </s><s>Now what &longs;ay you to this experiment?</s></p><p type="main"><s>SIMPL. </s><s>I am afraid that there may be &longs;ome <emph type="italics"/>Leigerdemain,<emph.end type="italics"/> <lb/>u&longs;ed in this affair; yet in beholding that gla&longs;&longs;e I &longs;ee it dart forth <lb/>a great &longs;plendor, which dazleth my eyes; and that which im­ <lb/>ports mo&longs;t of all, I &longs;ee it from what place &longs;oever I look upon it; <lb/>and I &longs;ee it go changing &longs;ituation upon the &longs;uperficies of the gla&longs;&longs;e, <lb/>which way &longs;oever I place my &longs;elf to look upon it; a nece&longs;&longs;ary ar­ <lb/>gument, that the light is livelily reflected towards every &longs;ide, and <lb/>con&longs;equently, as &longs;trongly upon all that Wall, as upon my eye.</s></p><p type="main"><s>SALV. </s><s>Now you &longs;ee how cautiou&longs;ly and re&longs;ervedly you ought <lb/>to proceed in lending your a&longs;&longs;ent to that, which di&longs;cour&longs;e alone re­ <lb/>pre&longs;enteth to you. </s><s>There is no doubt but that this which you &longs;ay, <lb/>carrieth with it probability enough, yet you may &longs;ee, how &longs;en&longs;i­ <lb/>ble experience proves the contrary.</s></p><p type="main"><s>SIMPL. </s><s>How then doth this come to pa&longs;s?</s></p><p type="main"><s>SALV. </s><s>I will deliver you my thoughts thereof, but I cannot <lb/>tell how you may be plea&longs;'d therewith. </s><s>And fir&longs;t, that lively <lb/>&longs;plendor which you &longs;ee upon the gla&longs;s, and which you think occu­ <lb/>pieth a good part thereof, is nothing near &longs;o great, nay is very ex­ <lb/>ceeding &longs;mall; but its liveline&longs;s occa&longs;ioneth in your eye, (by means <lb/>of the reflection made on the humidity of the extream parts of the <lb/>eye-brows, which di&longs;tendeth upon the pupil) an adventitious irradi­ <lb/>ation, like to that blaze which we think we &longs;ee about the flame of <lb/>a candle placed at &longs;ome di&longs;tance; or if you will, you may <lb/>re&longs;emble it to the adventitious &longs;plendor of a &longs;tar; for if you &longs;hould <lb/><arrow.to.target n="marg168"></arrow.to.target> <lb/>compare the &longs;mall body <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> of the <emph type="italics"/>Canicula,<emph.end type="italics"/> &longs;een in the day time <lb/>with the <emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/> when it is &longs;een without &longs;uch irradiation, with <lb/>the &longs;ame &longs;een by night by the eye it &longs;elf, you will doubtle&longs;s com­ <lb/>prehend that being irradiated, it appeareth above a thou&longs;and <pb xlink:href="040/01/078.jpg" pagenum="62"/>times bigger than the naked and real body: and a like or greater <lb/>augmentation doth the image of the Sun make, which you &longs;ee in <lb/>that gla&longs;s. </s><s>I &longs;ay greater, for that it is more lively than the &longs;tar, <lb/>as is manife&longs;t from our being able to behold the &longs;tar with much <lb/>le&longs;s offence, than this reflection of the gla&longs;s. </s><s>The reverberation <lb/>therefore which is to di&longs;pere it &longs;elf all over this wall, cometh from <lb/>a &longs;mall part of that gla&longs;s, and that which even now came from <lb/>the whole flat gla&longs;s di&longs;per&longs;ed and re&longs;train'd it &longs;elf to a very &longs;mall <lb/>part of the &longs;aid wall. </s><s>What wonder is it then, that the fir&longs;t re­ <lb/>flection very lively illuminates, and that this other is almo&longs;t im­ <lb/>perceptible?</s></p><p type="margin"><s><margin.target id="marg168"></margin.target><emph type="italics"/>The &longs;mall body of <lb/>the &longs;tars fringed <lb/>round about with <lb/>rays, appeareth ve­ <lb/>ry much biggerthan <lb/>plain and naked, <lb/>and in its native <lb/>clarity.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I find my &longs;elf more perplexed than ever, and there <lb/>pre&longs;ents it &longs;elf unto me the other difficulty, how it can be that <lb/>that wall, being of a matter &longs;o ob&longs;cure, and of a &longs;uperficies &longs;o un­ <lb/>poli&longs;h'd, &longs;hould be able to dart from it greater light, than a gla&longs;s <lb/>very &longs;mooth and polite.</s></p><p type="main"><s>SALV. </s><s>Greater light it is not, but more univer&longs;al; for as to <lb/>the degree of brightne&longs;s, you &longs;ee that the reflection of that &longs;mall <lb/>flat gla&longs;s, where it beamed forth yonder under the &longs;hadow of the <lb/>penthou&longs;e, illuminateth very much; and the re&longs;t of the wall which <lb/>receiveth the reflection of the wall on which the gla&longs;s is placed, <lb/>is not in any great mea&longs;ure illuminated, as was the &longs;mall part on <lb/>which the reflection of the gla&longs;s fell. </s><s>And if you would under­ <lb/>&longs;tand the whole of this bu&longs;ine&longs;s, you mu&longs;t con&longs;ider that the &longs;uper­ <lb/><arrow.to.target n="marg169"></arrow.to.target> <lb/>ficies of that wall's being rough, is the &longs;ame as if it were compo­ <lb/>&longs;ed of innumerable &longs;mall &longs;uperficies, di&longs;po&longs;ed according to in­ <lb/>numerable diver&longs;ities of inclinations: among&longs;t which it nece&longs;&longs;a­ <lb/>rily happens, that there are many di&longs;po&longs;ed to &longs;end forth their <lb/>reflex rays from them into &longs;uch a place, many others into another: <lb/>and in &longs;um, there is not any place to which there comes not very <lb/>many rays, reflected from very many &longs;mall &longs;uperficies, di&longs;per&longs;ed <lb/>throughout the whole &longs;uperficies of the rugged body, upon which <lb/>the rays of the Sun fall. </s><s>From which it nece&longs;&longs;arily follow­ <lb/>eth, That upon any, what&longs;oever, part of any &longs;uperficies, <lb/>oppo&longs;ed to that which receiveth the primary incident rays, <lb/>there is produced reflex rays, and con&longs;equently illumi­ <lb/>nation. </s><s>There doth al&longs;o follow thereupon, That the &longs;ame <lb/>body upon which the illuminating rays fall, beheld from <lb/>what&longs;oever place, appeareth all illuminated and &longs;hining: and <lb/>therefore the Moon, as being of a &longs;uperficies rugged and <lb/><arrow.to.target n="marg170"></arrow.to.target> <lb/>not &longs;mooth, beameth forth the light of the Sun on every <lb/>&longs;ide, and to all beholders appeareth equally lucid. </s><s>But if <lb/>the &longs;urface of it, being &longs;pherical, were al&longs;o &longs;mooth as a gla&longs;s, it <lb/>would become wholly invi&longs;ible; fora&longs;much as that &longs;mall part, <lb/>from which the image of the Sun &longs;hould be reflected unto the eye <pb xlink:href="040/01/079.jpg" pagenum="63"/>of a particular per&longs;on, by rea&longs;on of its great di&longs;tance would be in­ <lb/>vi&longs;ible, as I have &longs;aid before.</s></p><p type="margin"><s><margin.target id="marg169"></margin.target><emph type="italics"/>The reflex light <lb/>of uneven bodies, is <lb/>more univer&longs;al <lb/>than that of the <lb/>&longs;mooth, & why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg170"></margin.target><emph type="italics"/>The Moon, if it <lb/>were &longs;mooth and <lb/>&longs;leek, would be in­ <lb/>vi&longs;ible.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I am very apprehen&longs;ive of your di&longs;cour&longs;e; yet me­ <lb/>thinks I am able to re&longs;olve the &longs;ame with very little trouble; and <lb/>ea&longs;ily to maintain, that the Moon is rotund and polite, and that it <lb/>reflects the Suns light unto us in manner of a gla&longs;s; nor there­ <lb/>fore ought the image of the Sun to be &longs;een in the middle of it, “for­ <lb/>a&longs;much as the &longs;pecies of the Sun it &longs;elf admits not its &longs;mall figure <lb/>to be &longs;een at &longs;o great a di&longs;tance, but the light produced by the <lb/>Sun may help us to conceive that it illuminateth the whole Lu­ <lb/>nar Body: a like effect we may &longs;ee in a plate gilded and well <lb/>polli&longs;h'd, which touch't by a luminous body, appeareth to him <lb/>that beholds it at &longs;ome di&longs;tance to be all &longs;hining; and onely near <lb/>at hand one may di&longs;cover in the middle of it the &longs;mall image of <lb/>the luminous body.”</s></p><p type="main"><s>SALV. </s><s>Ingenuou&longs;ly confe&longs;&longs;ing my dullne&longs;s of apprehen&longs;ion, <lb/>I mu&longs;t tell you, that I under&longs;tand not any thing of this your di&longs;­ <lb/>cour&longs;e, &longs;ave onely what concerns the gilt plate: and if you permit <lb/>me to &longs;peak freely, I have a great conceit that you al&longs;o under&longs;tand <lb/>not the &longs;ame, but have learnt by heart tho&longs;e words written by &longs;ome <lb/>one out of a de&longs;ire of contradiction, and to &longs;hew him&longs;elf more intel­ <lb/>ligent than his adver&longs;ary; but it mu&longs;t be to tho&longs;e, which to appear <lb/>al&longs;o more wi&longs;e, applaud that which they do not under&longs;tand, and <lb/>entertain a greater conceit of per&longs;ons, the le&longs;s they are by them <lb/>under&longs;tood: and the writer him&longs;elf may be one of tho&longs;e (of which <lb/>there are many) who write what they do not under&longs;tand, and <lb/><arrow.to.target n="marg171"></arrow.to.target> <lb/>con&longs;equently under&longs;tand not what they write. </s><s>Therefore, o­ <lb/>mitting the re&longs;t, I reply, as to the gilt plate, that if it be flat and <lb/>not very big, it may appear at a di&longs;tance very bright, whil&longs;t a great <lb/>light beameth upon it, but yet it mu&longs;t be when the eye is in a de­ <lb/>terminate line, namely in that of the reflex rays: and it will ap­ <lb/>pear the more &longs;hining, if it were <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> of &longs;ilver, by means of its <lb/>being burni&longs;hed, and apt through the great den&longs;ity of the metal, <lb/>to receive a perfect poli&longs;h. </s><s>And though its &longs;uperficies, being very <lb/>well brightned, were not exactly plain, but &longs;hould have various in­ <lb/>clinations, yet then al&longs;o would its &longs;plendor be &longs;een many ways; <lb/>namely, from as many places as the various reflections, made by <lb/>the &longs;everal &longs;uperficies, do reach: for therefore are Diamonds <lb/><arrow.to.target n="marg172"></arrow.to.target> <lb/>ground to many &longs;ides, that &longs;o their plea&longs;ing lu&longs;tre might be beheld <lb/>from many places. </s><s>But if the Plate were very big, though it &longs;hould <lb/>be all plain, yet would it not at a di&longs;tance appear all over &longs;hining: <lb/>and the better to expre&longs;s my &longs;elf, Let us &longs;uppo&longs;e a very large gilt <lb/>plate expo&longs;ed to the Sun, it will &longs;hew to an eye far di&longs;tant, the <lb/>image of the Sun, to occupy no more but a certain part of the &longs;aid <lb/>plate; to wit, that from whence the reflection of the incident <pb xlink:href="040/01/080.jpg" pagenum="64"/>&longs;olar rays come: but it is true that by the vivacity of the light, the <lb/>&longs;aid image will appear fringed about with many rays, and &longs;o will <lb/>&longs;eem to occupie a far greater part of the plate, than really it doth. <lb/></s><s>And to &longs;hew that this is true, when you have noted the particular <lb/>place of the plate from whence the reflection cometh, and concei­ <lb/>ved likewi&longs;e how great the &longs;hining place appeared to you, cover the <lb/>greater part of that &longs;ame &longs;pace, leaving it only vi&longs;ible about the <lb/>mid&longs;t; and all this &longs;hall not any whit dimini&longs;h the apparent &longs;plen­ <lb/>dor to one that beholds it from afar; but you &longs;hall &longs;ee it largely <lb/>di&longs;pers'd upon the cloth or other matter, wherewith you covered <lb/>it. </s><s>If therefore any one, by &longs;eeing from a good di&longs;tance a &longs;mall <lb/>gilt plate to be all over &longs;hining, &longs;hould imagine that the &longs;ame <lb/>would al&longs;o even in a plate as broad as the Moon, he is no le&longs;s de­ <lb/>ceived, than if he &longs;hould believe the Moon to be no bigger than <lb/>the bottom of a tub. </s><s>If again the plate were turn'd into a &longs;phe­ <lb/>rical &longs;uperficies, the reflection would be &longs;een &longs;trong in but one &longs;ole <lb/>particle of it; but yet by rea&longs;on of its liveline&longs;s, it will appear <lb/>fringed about with many glittering rays: the re&longs;t of the Ball would <lb/>appear according as it was burni&longs;hed; and this al&longs;o onely then <lb/><arrow.to.target n="marg173"></arrow.to.target> <lb/>when it was not very much poli&longs;hed, for &longs;hould it be perfectly <lb/>brightned, it would appear ob&longs;cure. </s><s>An example of this we <lb/>have dayly before our eyes in &longs;ilver ve&longs;&longs;els, which whil&longs;t they are <lb/>only boyl'd in the <emph type="italics"/>Argol<emph.end type="italics"/> and <emph type="italics"/>Salt,<emph.end type="italics"/> they are all as white as &longs;now, and <lb/>do not reflect any image; but if they be in any part burni&longs;h'd, they <lb/>become in that place pre&longs;ently ob&longs;cure: and in them one may &longs;ee the <lb/>repre&longs;entation of any thing as in Looking-gla&longs;&longs;es. </s><s>And that chan­ <lb/>to ob&longs;curity, proceeds from nothing el&longs;e but the &longs;moothing and <lb/>plaining of a fine grain, which made the &longs;uperficies of the &longs;ilver <lb/>rough, and yet &longs;uch, as that it reflected the light into all parts, <lb/>whereby it &longs;eemed from all parts equally illuminated: which <lb/>&longs;mall unevenne&longs;&longs;es, when they come to be exqui&longs;itely plained by <lb/>the burni&longs;h, &longs;o that the reflection of the rays of incidence are all <lb/>directed unto one determinate place; then, from that &longs;ame place, <lb/>the burni&longs;h'd part &longs;hall &longs;hew much more bright and &longs;hining than <lb/>the re&longs;t which is onely whitened by boyling; but from all other <lb/>places it looks very ob&longs;cure. </s><s>And note, that the diver&longs;ity of <lb/><arrow.to.target n="marg174"></arrow.to.target> <lb/>&longs;ights of looking upon burni&longs;h'd &longs;uperficies, occa&longs;ioneth &longs;uch <lb/>difference in appearances, that to imitate and repre&longs;ent in picture, <lb/><emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> a poli&longs;h'd Cuirace, one mu&longs;t couple black plains with white, <lb/>one &longs;ideways to the other, in tho&longs;e parts of the arms where the <lb/>light falleth equally.</s></p><p type="margin"><s><margin.target id="marg171"></margin.target><emph type="italics"/>Some write what <lb/>they under&longs;tand <lb/>not, and therefore <lb/>under&longs;tand not <lb/>what they write.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg172"></margin.target><emph type="italics"/>Diamonds ground <lb/>to divers &longs;ides, & <lb/>why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg173"></margin.target><emph type="italics"/>Silver burni&longs;hed <lb/>appears more ob­ <lb/>&longs;cuee, than the not <lb/>burni&longs;hed, & why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg174"></margin.target><emph type="italics"/>Burni&longs;h'd Steel <lb/>beheld from one <lb/>place appears very <lb/>bright, and from <lb/>another, very ob­ <lb/>&longs;cure.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>If therefore the&longs;e great Philo&longs;ophers would acquie&longs;e <lb/>in granting, that the Moon, <emph type="italics"/>Venus<emph.end type="italics"/> and the other Planets, were not <lb/>of &longs;o bright and &longs;mooth a &longs;urface as a Looking-gla&longs;s, but wanted <lb/>&longs;ome &longs;mall matter of it, namely, were as a &longs;ilver plate, onely boyled <pb xlink:href="040/01/081.jpg" pagenum="65"/>white, but not burni&longs;hed; would this yet &longs;uffice to the making <lb/>of it vi&longs;ible, and apt for darting forth the light of the Sun?</s></p><p type="main"><s>SALV. </s><s>It would &longs;uffice in part; but would not give a light &longs;o <lb/>&longs;trong, as it doth being mountainous, and in &longs;um, full of <lb/>eminencies and great cavities. </s><s>But the&longs;e Philo&longs;ophers will never <lb/>yield it to be le&longs;&longs;e polite than a gla&longs;&longs;e; but far more, if more it <lb/>can be imagined; for they e&longs;teeming that to perfect bodies perfect <lb/>figures are mo&longs;t &longs;utable; it is nece&longs;&longs;ary, that the &longs;phericity of tho&longs;e <lb/>Cœle&longs;tial Globes be mo&longs;t exact; be&longs;ides, that if they &longs;hould <lb/>grant me &longs;ome inequality, though never &longs;o &longs;mall, I would not <lb/>&longs;cruple to take any other greater; for that &longs;uch perfection con&longs;i&longs;t­ <lb/>ing in indivi&longs;ibles, an hair doth as much detract from its perfection <lb/>as a mountain.</s></p><p type="main"><s>SAGR. </s><s>Here I meet with two difficulties, one is to know the <lb/>rea&longs;on why the greater inequality of &longs;uperficies maketh the &longs;tron­ <lb/>ger reflection of light; the other is, why the&longs;e <emph type="italics"/>Peripatetick<emph.end type="italics"/> Gen­ <lb/>tlemen are for this exact figure.</s></p><p type="main"><s>SALV. </s><s>I will an&longs;wer to the fir&longs;t; and leave to <emph type="italics"/>Simplieius<emph.end type="italics"/> the <lb/><arrow.to.target n="marg175"></arrow.to.target> <lb/>care of making reply to the &longs;econd. </s><s>You mu&longs;t know therefore, <lb/>that the &longs;ame &longs;uperficies happen to be by the &longs;ame light more or le&longs;s <lb/>illuminated, according as the rayes of illumination fall upon them <lb/><arrow.to.target n="marg176"></arrow.to.target> <lb/>more or le&longs;&longs;e obliquely; &longs;o that the greate&longs;t illumination is where <lb/>the rayes are perpendicular. </s><s>And &longs;ee, how I will prove it to your <lb/>&longs;en&longs;e. </s><s>I bend this paper, &longs;o, that one part of it makes an angle <lb/>upon the other: and expo&longs;ing both the&longs;e parts to the reflection of <lb/>the light of that oppo&longs;ite Wall, you &longs;ee how this &longs;ide which re­ <lb/>ceiveth the rayes obliquely, is le&longs;&longs;e &longs;hining than this other, where <lb/>the reflection fals at right angles; and ob&longs;erve, that as I by <lb/>degrees receive the illumination more obliquely, it groweth <lb/>weaker.</s></p><p type="margin"><s><margin.target id="marg175"></margin.target><emph type="italics"/>The more rough <lb/>&longs;uperficies make <lb/>greater reflection <lb/>of light, than the <lb/>le&longs;s rough.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg176"></margin.target><emph type="italics"/>Perpendicular <lb/>rays illuminate <lb/>more than the ob­ <lb/>lique, and why.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I &longs;ee the effect, but comprehend not the cau&longs;e.</s></p><p type="main"><s>SALV. </s><s>If you thought upon it but a minute of an hour, you <lb/>would find it; but that I may not wa&longs;te the time, &longs;ee a kind of <lb/>demon&longs;tration thereof in <emph type="italics"/>Fig.<emph.end type="italics"/> 7.</s></p><p type="main"><s>SAGR. </s><s>The bare &longs;ight of this Figure hath fully &longs;atisfied me, <lb/>therefore proceed.</s></p><p type="main"><s>SIMPL. </s><s>Pray you let me hear you out, for I am not of &longs;o <lb/>quick an apprehen&longs;ion.</s></p><p type="main"><s>SALV. </s><s>Fancie to your &longs;elf, that all the paralel lines, which you <lb/>&longs;ee to depart from the terms A. B. are the rays which fall upon the <lb/><arrow.to.target n="marg177"></arrow.to.target> <lb/>line C. D. at right angles: then incline the &longs;aid C. D. till it hang <lb/>as D. O. now do not you &longs;ee that a great part of tho&longs;e rays which <lb/>peirce C. D. pa&longs;s by without touching D. O? </s><s>If therefore D. O. <lb/>be illuminated by fewer rays, it is very rea&longs;onable, that the light <lb/>received by it be more weak. </s><s>Let us return now to the Moon, <pb xlink:href="040/01/082.jpg" pagenum="66"/>which being of a &longs;pherical figure, if its &longs;uperficies were &longs;mooth, as <lb/>this paper, the parts of its hemi&longs;phere illuminated by the Sun, <lb/>which are towards its extremity, would receive much le&longs;s light, <lb/>than the middle parts; the rays falling upon them mo&longs;t obliquely, <lb/>and upon the&longs;e at right angles; whereupon at the time of full <lb/>Moon, when we &longs;ee almo&longs;t its whole Hemi&longs;phere illuminated, the <lb/>parts towards the mid&longs;t, would &longs;hew them&longs;elves to us with more <lb/>&longs;plendor, than tho&longs;e others towards the circumference: which is <lb/>not &longs;o in effect. </s><s>Now the face of the Moon being repre&longs;ented <lb/>to me full of indifferent high mountains, do not you &longs;ee how their <lb/>tops and continuate ridges, being elevated above the convexity of <lb/>the perfect &longs;pherical &longs;uperficies, come to be expo&longs;ed to the view <lb/>of the Sun, and accommodated to receive its rays much le&longs;s ob­ <lb/>liquely, and con&longs;equently to appear as luminous as the re&longs;t?</s></p><p type="margin"><s><margin.target id="marg177"></margin.target><emph type="italics"/>The more oblique <lb/>Rayes illuminate <lb/>leß, and why.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>All this I well perceive: and if there are &longs;uch moun­ <lb/>tains, its true, the Sun will dart upon them much more directly <lb/>than it would do upon the inclination of a polite &longs;uperficies: but <lb/>it is al&longs;o true, that betwixt tho&longs;e mountains all the valleys would <lb/>become ob&longs;cure, by rea&longs;on of the va&longs;t &longs;hadows, which in that <lb/>time would be ca&longs;t from the mountains, whereas the parts towards <lb/>the middle, though full of valleys and hills, by rea&longs;on they have <lb/>the Sun elevated, would appear without &longs;hadow, and therefore <lb/>more lucid by far than the extreme parts, which are no le&longs;s diffu­ <lb/>&longs;ed with &longs;hadow than light, and yet we can perceive no &longs;uch diffe­ <lb/>rence.</s></p><p type="main"><s>SIMPL. </s><s>I was ruminating upon the like difficulty.</s></p><p type="main"><s>SALV. </s><s>How much readier is <emph type="italics"/>Simplicius<emph.end type="italics"/> to apprehend the ob­ <lb/>jections which favour the opinions of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> than their &longs;oluti­ <lb/>ons? </s><s>I have a kind of &longs;u&longs;pition, that he &longs;trives al&longs;o &longs;ometimes to <lb/>di&longs;&longs;emble them; and in the pre&longs;ent ca&longs;e, he being of him&longs;elf able <lb/>to hit upon the doubt, which yet is very ingenious, I cannot be­ <lb/>lieve but that he al&longs;o was advi&longs;'d of the an&longs;wer; wherefore I will <lb/>attempt to wre&longs;t the &longs;ame (as they &longs;ay) out of his mouth. </s><s>There­ <lb/>fore tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> do you think there can be any &longs;hadow, <lb/>where the rays of the Sun do &longs;hine?</s></p><p type="main"><s>SIMPL. </s><s>I believe, nay I am certain that there cannot; for that <lb/>it being the grand luminary, which with its rays driveth away dark­ <lb/>ne&longs;s, it is impo&longs;&longs;ible any tenebro&longs;ity &longs;hould remain where it com­ <lb/>eth; moreover, we have the definition, that <emph type="italics"/>Tenebræ &longs;unt priva­ <lb/>tio luminis.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Therefore the Sun, beholding the Earth, Moon or o­ <lb/>ther opacous body, never &longs;eeth any of its &longs;hady parts, it not ha­ <lb/>ving any other eyes to &longs;ee with, &longs;ave its rays, the conveyers of <lb/>light: and con&longs;equently, one &longs;tanding in the Sun would never <lb/>&longs;ee any thing of umbrage, fora&longs;much as his vi&longs;ive rays would ever <pb xlink:href="040/01/083.jpg" pagenum="67"/>go accompanied with tho&longs;e illuminating beams of the Sun.</s></p><p type="main"><s>SIMPL. </s><s>This is true, without any contradiction.</s></p><p type="main"><s>SALV. </s><s>But when the Moon is oppo&longs;ite to the Sun, what dif­ <lb/>ference is there between the tract of the rayes of your &longs;ight, and <lb/>that motion which the Suns rayes make?</s></p><p type="main"><s>SIMPL. </s><s>Now I under&longs;tand you; for you would &longs;ay, that the <lb/>rayes of the &longs;ight and tho&longs;e of the Sun, moving by the &longs;ame lines, <lb/>we cannot perceive any of the ob&longs;cure valleys of the Moon. </s><s>Be <lb/>plea&longs;ed to change this your opinion, that I have either &longs;imulation <lb/>or di&longs;&longs;imulation in me; for I prote&longs;t unto you, as I am a Gentle­ <lb/>man, that I did not gue&longs;&longs;e at this &longs;olution, nor &longs;hould I have <lb/>thought upon it, without your help, or without long &longs;tudy.</s></p><p type="main"><s>SAGR. </s><s>The re&longs;olutions, which between you two have been <lb/>alledged touching this la&longs;t doubt, hath, to &longs;peak the truth, &longs;atisfi­ <lb/>ed me al&longs;o. </s><s>But at the &longs;ame time this con&longs;ideration of the vi­ <lb/>fible rayes accompanying the rayes of the Sun, hath begotten in me <lb/>another &longs;cruple, about the other part, but I know not whether I <lb/>can expre&longs;&longs;e it right, or no: for it but ju&longs;t now comming into my <lb/>mind, I have not yet methodized it to my mind: but let us &longs;ee if <lb/>we can, all together, make it intelligible. </s><s>There is no que&longs;tion, <lb/>but that the parts towards the circumference of that poli&longs;h't, but not <lb/>burni&longs;h't Hemi&longs;phere, which is illuminated by the Sun, receiving the <lb/>rayes obliquely, receive much fewer thereof, than the middle­ <lb/>mo&longs;t parts, which receive them directly. </s><s>And its po&longs;&longs;ible, that a <lb/>tract or &longs;pace of <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> twenty degrees in breadth, and which is to­ <lb/>wards the extremity of the Hemi&longs;phere, may not receive more rays <lb/>than another towards the middle parts, of but four degree broad: <lb/>&longs;o that that doubtle&longs;s will be much more ob&longs;cure than this; and <lb/>&longs;uch it will appear to whoever &longs;hall behold them both in the face, <lb/>or (as I may &longs;ay) in their full magnitude. </s><s>But if the eye of the <lb/>beholder were con&longs;tituted in &longs;uch a place, that the breadth of the <lb/>twenty degrees of the ob&longs;cure &longs;pace, appeared not to it longer <lb/>than one of four degrees, placed in the mid&longs;t of the Hemi&longs;phere, <lb/>I hold it not impo&longs;&longs;ible for it to appear to the &longs;aid beholder e­ <lb/>qually clear and lucid with the other; becau&longs;e, finally, between <lb/>two equal angles, to wit, of four degrees apiece, there come to <lb/>the eye the reflections of two equal numbers of rayes: namely, <lb/>tho&longs;e which are reflected from the middlemo&longs;t &longs;pace, four degrees <lb/>in breadth, and tho&longs;e reflected from the other of twenty degrees, <lb/>but &longs;een by compre&longs;&longs;ion, under the quantity of four degrees: and <lb/>&longs;uch a &longs;ituation &longs;hall the eye obtain, when it is placed between the <lb/>&longs;aid Hemi&longs;phere, and the body which illuminates it; for then the <lb/>&longs;ight and rayes move in the &longs;ame lines. </s><s>It &longs;eemeth not impo&longs;&longs;ible <lb/>therefore, but that the Moon may be of a very equal &longs;uperficies; <lb/>and that neverthele&longs;&longs;e, it may appear when it is at the full, no le&longs;s <pb xlink:href="040/01/084.jpg" pagenum="68"/>light in the extremities, than in the middle parts.</s></p><p type="main"><s>SALV. </s><s>The doubt is ingenious and worthy of con&longs;ideration; <lb/>and as it but ju&longs;t now came into your mind unawares, &longs;o I will <lb/>like wi&longs;e an&longs;wer with what fir&longs;t comes into my thoughts, and it may <lb/>happily fall out, that by thinking more upon it, I may &longs;tumble <lb/>upon a better reply. </s><s>But before, that I labyrinth my &longs;elf any far­ <lb/>ther, it would be nece&longs;&longs;ary, that we a&longs;&longs;ure our &longs;elves by &longs;ome ex­ <lb/>periment, whether your objection prove in effect, what it &longs;eemeth <lb/>to conclude in appearance; and therefore taking once more the <lb/>&longs;ame paper, and making it to incline, by bending a little part <lb/>thereof upon the remainder, let us try whether expo&longs;ing it to the <lb/>Sun, &longs;o that the rayes of light fall upon the le&longs;&longs;er part directly, <lb/>and upon the other obliquely; this which receiveth the rayes direct­ <lb/>ly appeareth more lucid; and &longs;ee here by manife&longs;t experience, <lb/>that it is notably more clear. </s><s>Now if your objection be conclu&longs;ive, <lb/>it will follow, that &longs;tooping with our eye &longs;o, that in beholding <lb/>the other greater part, le&longs;s illuminated, in compre&longs;&longs;ion or fore­ <lb/>&longs;hortning, it appear unto us no bigger than the other, more &longs;hining; <lb/>and that con&longs;equently, it be not beheld at a greater angle than <lb/>that; it will nece&longs;&longs;arily en&longs;ue, I &longs;ay, that its light be encrea&longs;ed, &longs;o <lb/>that it do &longs;eem to us as bright as the other. </s><s>See how I behold, and <lb/>look upon it &longs;o obliquely, that it appeareth to me narrower than <lb/>the other; but yet, notwith&longs;tanding its ob&longs;curity, doth not to <lb/>my perceiving, at all grow clearer. </s><s>Try now if the &longs;ame &longs;ucceed <lb/>to you.</s></p><p type="main"><s>SAGR. </s><s>I have look't upon it, and though I have &longs;tooped with <lb/>my eye, yet cannot I &longs;ee the &longs;aid &longs;uperficies encrea&longs;e in light or <lb/>clarity; nay me thinks it rather grows more dusky.</s></p><p type="main"><s>SALV. </s><s>We are hitherto confident of the invalidity of the ob­ <lb/>jection; In the next place, as to the &longs;olution, I believe, that, by <lb/>rea&longs;on the Superficies of this paper is little le&longs;&longs;e than &longs;mooth, the <lb/>rayes are very few, which be reflected towards the point of inci­ <lb/>dence, in compari&longs;on of the multitude, which are reflected to­ <lb/>wards the oppo&longs;ite parts; and that of tho&longs;e few more and more <lb/>are lo&longs;t, the nearer the vi&longs;ive rayes approach to tho&longs;e lucid rayes <lb/>of incidence; and becau&longs;e it is not the incident rayes, but tho&longs;e <lb/>which are reflected to the eye, that make the object appear lu­ <lb/>minous; therefore, in &longs;tooping the eye, there is more lo&longs;t than got, <lb/>as you your &longs;elf confe&longs;&longs;e to have &longs;een in looking upon the ob&longs;cu­ <lb/>rer part of the paper.</s></p><p type="main"><s>SAGR. </s><s>I re&longs;t &longs;atisfied with this experiment and rea&longs;on: It re­ <lb/>mains now, that <emph type="italics"/>Simplicius<emph.end type="italics"/> an&longs;wer to my other que&longs;tion, and tell <lb/>me what moves the <emph type="italics"/>Peripateticks<emph.end type="italics"/> to require this &longs;o exact rotundity <lb/>in the Cœle&longs;tial bodies.</s></p><p type="main"><s>SIMPL. </s><s>The Cœle&longs;tial bodies being ingenerable, inalterable, im­ <pb xlink:href="040/01/085.jpg" pagenum="69"/>pa&longs;&longs;ible, immortal, <emph type="italics"/>&c.<emph.end type="italics"/> they mu&longs;t needs be ab&longs;olutely perfect; and <lb/><arrow.to.target n="marg178"></arrow.to.target> <lb/>their being ab&longs;olute perfect, nece&longs;&longs;arily implies that there is in them <lb/>all kinds of perfection; and con&longs;equently, that their figure be al&longs;o <lb/>perfect, that is to &longs;ay, &longs;pherical; and ab&longs;olutely and perfectly <lb/>&longs;pherical, and not rough and irregular.</s></p><p type="margin"><s><margin.target id="marg178"></margin.target><emph type="italics"/>Perfect &longs;phericity <lb/>why a&longs;cribed to <lb/>Cœlestial bodies, <lb/>by the<emph.end type="italics"/> Peripate­ <lb/>ticks.</s></p><p type="main"><s>SALV. </s><s>And this incorruptibility, from whence do you prove <lb/>it?</s></p><p type="main"><s>SIMPL. </s><s>Immediately by its freedom from contraries, and me­ <lb/>diately, by its &longs;imple circular motion.</s></p><p type="main"><s>SALV. </s><s>So that; by what I gather from your di&longs;cour&longs;e, in ma­ <lb/><arrow.to.target n="marg179"></arrow.to.target> <lb/>king the e&longs;&longs;ence of the Cœle&longs;tial bodies to be incorruptible, inal­ <lb/>terable, <emph type="italics"/>&c,<emph.end type="italics"/> there is no need of rotundity as a cau&longs;e, or requi­ <lb/>&longs;ite; for if this &longs;hould cau&longs;e inalterability, we might at our plea­ <lb/>&longs;ure make wood, wax, and other Elementary matters, incorrup­ <lb/>tible, by reducing them to a &longs;pherical figure.</s></p><p type="margin"><s><margin.target id="marg179"></margin.target><emph type="italics"/>The Figure is not <lb/>the cau&longs;e of incor­ <lb/>ruptibility, but of <lb/>longer duration.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>And is it not manife&longs;t that a ball of Wood will better <lb/>and longer be preferved, than an oblong, or other angular fi­ <lb/>gure, made of a like quantity of the &longs;ame wood.</s></p><p type="main"><s>SALV. </s><s>This is mo&longs;t certain, but yet it doth not of corruptible <lb/>become incorruptible, but &longs;till remains corruptible, though of a <lb/>much longer duration. </s><s>Therefore you mu&longs;t note, that a thing cor­ <lb/><arrow.to.target n="marg180"></arrow.to.target> <lb/>ruptible, is capable of being more or le&longs;&longs;e &longs;uch, and we may <lb/>properly &longs;ay this is le&longs;&longs;e corruptible than that; as for example, the <lb/><emph type="italics"/>Ja&longs;per,<emph.end type="italics"/> than the <emph type="italics"/>Pietra Sirena<emph.end type="italics"/>; but incorruptibility admits not <lb/>of more, or le&longs;&longs;e, &longs;o as that it may be &longs;aid this is more incorrupti­ <lb/>ble than that, if both be incorruptible and eternal. </s><s>The diver­ <lb/><arrow.to.target n="marg181"></arrow.to.target> <lb/>&longs;ity of figure therefore cannot operate: &longs;ave onely in matters ca­ <lb/>pable of more or le&longs;&longs;e duration; but in the eternal, which can­ <lb/>not be other than equally eternal, the operation of figure cea&longs;eth. <lb/></s><s>And therefore, &longs;ince the Cœle&longs;tial matter is not incorruptible by <lb/>figure, but otherwayes no man needs to be &longs;o &longs;olicitous for this <lb/>perfect &longs;phericity; for if the matter be incorruptible, let it have <lb/>what figure it will, it &longs;hall be alwayes &longs;uch.</s></p><p type="margin"><s><margin.target id="marg180"></margin.target><emph type="italics"/>Corruptibility ad­ <lb/>mits of more or <lb/>le&longs;&longs;e; &longs;o doth noe <lb/>incorruptibiliiy.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg181"></margin.target><emph type="italics"/>The perfection of <lb/>figure, operateth <lb/>in corruptible bo­ <lb/>dies, but not in the <lb/>eternal.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>But I am con&longs;idering another thing, and &longs;ay, that if <lb/><arrow.to.target n="marg182"></arrow.to.target> <lb/>we &longs;hould grant the &longs;pherical figure a faculty of conferring incor­ <lb/>ruptibility, all bodies of what&longs;oever figure, would be incorrupti­ <lb/>ble; fora&longs;much as if the rotund body be incorruptible, corrupti­ <lb/>bility would then &longs;ub&longs;i&longs;t in tho&longs;e parts which alter the perfect ro­ <lb/>tundity; as for in&longs;tance, there is in a <emph type="italics"/>Die<emph.end type="italics"/> a body perfectly round, <lb/>and, as &longs;uch, incorruptible; therefore it remaineth that tho&longs;e an­ <lb/>gles be corruptible which cover and hide the rotundity; &longs;o that <lb/>the mo&longs;t that could happen, would be, that tho&longs;e angles, and <lb/>(to &longs;o &longs;peak) excre&longs;cencies, would corrupt. </s><s>But if we proceed to a <lb/>more inward con&longs;ideration, that in tho&longs;e parts al&longs;o towards the <lb/>angles, there are compri&longs;ed other le&longs;&longs;er bals of the &longs;ame matter; <pb xlink:href="040/01/086.jpg" pagenum="70"/>and therefore they al&longs;o, as being round, mu&longs;t be al&longs;o incorrup­ <lb/>tible; and likewife in the remainders, which environ the&longs;e eight <lb/>le&longs;&longs;er Spheres, a man may under&longs;tand that there are others: &longs;o <lb/>that in the end, re&longs;olving the whole <emph type="italics"/>Die<emph.end type="italics"/> into innumerable balls, <lb/>it mu&longs;t nece&longs;&longs;arily be granted incorruptible. </s><s>And the &longs;ame di&longs;­ <lb/>cour&longs;e and re&longs;olution may be made in all other figures.</s></p><p type="margin"><s><margin.target id="marg182"></margin.target><emph type="italics"/>If the &longs;pherical fi­ <lb/>gure conferreth e­ <lb/>ternity, all bodies <lb/>would be eternal.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Your method in making the conclu&longs;ion, for if <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> a <lb/>round Chry&longs;tal were, by rea&longs;on of its figure, incorruptible; namely, <lb/>received from thence a faculy of re&longs;i&longs;ting all internal and external <lb/>alterations, we &longs;hould not find, that the joyning to it other Chry­ <lb/>&longs;tal, and reducing it <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> into a Cube, would any whit alter it <lb/>within, or without; &longs;o as that it would thereupon become le&longs;&longs;e <lb/>apt to re&longs;i&longs;t the new ambient, made of the &longs;ame matter, than it <lb/>was to re&longs;i&longs;t the other, of a matter different; and e&longs;pecially, if <lb/>it be true, that corruption is generated by contraries, as <emph type="italics"/>Ari­ <lb/>&longs;totle<emph.end type="italics"/> &longs;aith; and with what can you enclo&longs;e that ball of Cry&longs;tal, <lb/>that is le&longs;&longs;e contrary to it, than Cry&longs;tal it &longs;elf? </s><s>But we are not a­ <lb/>ware how time flies away; and it will be too late before we come <lb/>to an end of our di&longs;pute, if we &longs;hould make &longs;o long di&longs;cour&longs;es, <lb/>upon every particular; be&longs;ides our memories are &longs;o confounded <lb/>in the multiplicity of notions, that I can very hardly recal to <lb/>mind the Propot&longs;iions, which I propo&longs;ed in order to <emph type="italics"/>Simplicius,<emph.end type="italics"/> <lb/>for our con&longs;ideration.</s></p><p type="main"><s>SIMPL. </s><s>I very well remember them: And as to this particular <lb/>que&longs;tion of the montuo&longs;ity of the Moon, there yet remains un­ <lb/>an&longs;wered that which I have alledged, as the cau&longs;e, (and which <lb/>may very well &longs;erve for a &longs;olution) of that <emph type="italics"/>Phænomenon,<emph.end type="italics"/> &longs;aying, <lb/>that it is an illu&longs;ion proceeding from the parts of the Moon, be­ <lb/>ing unequally opacous, and per&longs;picuous.</s></p><p type="main"><s>SAGR. </s><s>Even now, when <emph type="italics"/>Simplicius<emph.end type="italics"/> a&longs;cribed the apparent Pro­ <lb/>tnberancies or unevenne&longs;&longs;es of the Moon (according to the opinion <lb/>of a certain <emph type="italics"/>Peripatetick<emph.end type="italics"/> his friend) to the diver&longs;ly opacous, and <lb/><arrow.to.target n="marg183"></arrow.to.target> <lb/>per&longs;picuous parts of the &longs;aid Moon, conformable to which the like <lb/>illu&longs;ions are &longs;een in Cry&longs;tal, and Jems of divers kinds, I bethought <lb/>my &longs;elf of a matter much more commodious for the repre&longs;enting <lb/>&longs;uch effects; which is &longs;uch, that I verily believe, that that Philo&longs;o­ <lb/>pher would give any price for it; and it is the mother of Pearl, which <lb/>is wrought into divers figures, and though it be brought to an ex­ <lb/>treme evenne&longs;&longs;e, yet it &longs;eemeth to the eye in &longs;everal parts, &longs;o vari­ <lb/>ou&longs;ly hollow and knotty, that we can &longs;carce credit our feeling of <lb/>their evenne&longs;&longs;e.</s></p><p type="margin"><s><margin.target id="marg183"></margin.target><emph type="italics"/>Mother of Pearl <lb/>accommodated to <lb/>imitate the appa­ <lb/>rent unevenne&longs;&longs;es <lb/>of the Moons &longs;ur­ <lb/>face.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>This invention is truly ingenious; and that which hath <lb/>not been done already, may be done in time to come; and if <lb/>there have been produced other Jems, and Cry&longs;tals, which have <lb/>nothing to do with the illu&longs;ions of the mother of Pearl, the&longs;e may <pb xlink:href="040/01/087.jpg" pagenum="71"/>be produced al&longs;o; in the mean time, that I may not prevent any <lb/>one, I will &longs;uppre&longs;&longs;e the an&longs;wer which might be given, and onely <lb/>for this time betake my &longs;elf to &longs;atisfie the objections brought by <lb/><emph type="italics"/>Simplicius.<emph.end type="italics"/> I &longs;ay therefore, that this rea&longs;on of yours is too ge­ <lb/>neral, and as you apply it not to all the appearances one by one; <lb/>which are &longs;een in the Moon, and for which my &longs;elf and others <lb/>are induced to hold it mountainous, I believe you will not find <lb/>any one that will be &longs;atisfied with &longs;uch a doctrine; nor can I think, <lb/>that either you, or the Author him&longs;elf, find in it any greater <lb/>quietude, than in any other thing wide from the purpo&longs;e. </s><s>Of the <lb/><arrow.to.target n="marg184"></arrow.to.target> <lb/>very many &longs;everal appearances which are &longs;een night by night in <lb/>the cour&longs;e of Moon, you cannot imitate &longs;o much as one, by making <lb/>a Ball at your choice, more or le&longs;s opacous and per&longs;picuous, and <lb/>that is of a polite &longs;uperficies; whereas on the contrary, one may <lb/><arrow.to.target n="marg185"></arrow.to.target> <lb/>make Balls of any &longs;olid matter what&longs;oever, that is not tran&longs;parent, <lb/>which onely with eminencies and cavities, and by receiving the il­ <lb/>lumination &longs;everal ways, &longs;hall repre&longs;ent the &longs;ame appearances and <lb/>mutations to an hair, which from hour to hour are di&longs;covered in <lb/><arrow.to.target n="marg186"></arrow.to.target> <lb/>the Moon. </s><s>In them you &longs;hall &longs;ee the ledges of Hills expo&longs;ed to <lb/>the Suns light, to be very &longs;hining, and after them the projections <lb/>of their &longs;hadows very ob&longs;cure; you &longs;hall &longs;ee them greater and le&longs;s, <lb/>according as the &longs;aid eminencies &longs;hall be more or le&longs;s di&longs;tant from <lb/>the confines which di&longs;tingui&longs;h the parts of the Moon illuminated, <lb/>from the ob&longs;cure: you &longs;hall &longs;ee the &longs;ame term and confine, not <lb/>equally diftended, as it would be if the Ball were poli&longs;h'd, but <lb/>craggie and rugged. </s><s>You &longs;hall &longs;ee beyond the &longs;ame term, in the <lb/>dark parts of the Moon many bright prominencies, and di&longs;tinct <lb/>from the re&longs;t of the illuminations: you &longs;hall &longs;ee the &longs;hadows a­ <lb/>fore&longs;aid, according as the illumination gradually ri&longs;eth, to demi­ <lb/>ni&longs;h by degrees, till they wholly di&longs;appear; nor are there any of <lb/>them to be &longs;een when the whole Hemi&longs;phere is enlightned. </s><s>A­ <lb/>gain on the contrary, in the lights pa&longs;&longs;age towards the other He­ <lb/>mi&longs;phere of the Moon, you &longs;hall again ob&longs;erve the &longs;ame eminen­ <lb/>cies that were marked, and you &longs;hall &longs;ee the projections of their <lb/>&longs;hadows to be made a contrary way, and to decrea&longs;e by degrees: <lb/>of which things, once more I &longs;ay, you cannot &longs;hew me &longs;o much as <lb/>one in yours that are opacous and per&longs;picuous.</s></p><p type="margin"><s><margin.target id="marg184"></margin.target><emph type="italics"/>The apparent un­ <lb/>evenne&longs;&longs;es of the <lb/>Moon cannot be i­ <lb/>mitated by way of <lb/>more and le&longs;s opa­ <lb/>city & per&longs;picuity.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg185"></margin.target><emph type="italics"/>The various a­ <lb/>&longs;pects of the Moon, <lb/>imitable with any <lb/>opacous matter.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg186"></margin.target><emph type="italics"/>Various appear an­ <lb/>ces from which the <lb/>Moons montuo&longs;ity <lb/>is argued.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>One of them certainly he may imitate, namely, that of <lb/>the Full-Moon, when by rea&longs;on of its being all illuminated, there <lb/>is not to be &longs;een either &longs;hadow, or other thing, which receiveth <lb/>any alteration from its eminencies and cavities. </s><s>But I be&longs;eech <lb/>you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> let us &longs;pend no more time on this Argument, for <lb/>a per&longs;on that hath had but the patience to make ob&longs;ervation of but <lb/>one or two Lunations, and is not &longs;atisfied with this mo&longs;t &longs;en&longs;ible <lb/>truth, may well be adjudged void of all judgment; and upon <pb xlink:href="040/01/088.jpg" pagenum="72"/>&longs;uch why &longs;hould we throw away our time and breath in vain?</s></p><p type="main"><s>SIMPI. </s><s>I mu&longs;t confe&longs;s I have not made the ob&longs;ervations, for <lb/>that I never had &longs;o much curio&longs;ity, or the In&longs;truments proper for <lb/>the bu&longs;ine&longs;s; but I will not fail to do it. </s><s>In the mean time, we <lb/>may leave this que&longs;tion in &longs;u&longs;pen&longs;e, and pa&longs;s to that point which <lb/>follows, producing the motives inducing you to think that the <lb/>Earth may reflect the light of the Sun no le&longs;s forceably than the <lb/>Moon, for it &longs;eems to me &longs;o ob&longs;cure and opacous, that I judg &longs;uch <lb/>an effect altogether impo&longs;&longs;ible.</s></p><p type="main"><s>SALV. </s><s>The cau&longs;e for which you repute the Earth unapt for <lb/>illumination, may rather evince the contrary: And would it not <lb/>be &longs;trange, <emph type="italics"/>Simplicius,<emph.end type="italics"/> if I &longs;hould apprehend your di&longs;cour&longs;es bet­ <lb/>ter than you your &longs;elf?</s></p><p type="main"><s>SIMPL. </s><s>Whether I argue well or ill, it may be, that you may <lb/>better under&longs;tand the &longs;ame than I; but be it ill or well that I <lb/>di&longs;cour&longs;e, I &longs;hall never believe that you can penetrate what I mean <lb/>better than I my &longs;elf.</s></p><p type="main"><s>SALV. Well, I will make you believe the &longs;ame pre&longs;ently. </s><s>Tell <lb/>me a little, when the Moon is near the Full, &longs;o that it may be &longs;een <lb/>by day, and al&longs;o at midnight, at what do you think it more &longs;plen­ <lb/>did, by day or by night?</s></p><p type="main"><s>SIMPL. </s><s>By night, without all compari&longs;on. </s><s>And methinks <lb/><arrow.to.target n="marg187"></arrow.to.target> <lb/>the Moon re&longs;embleth that pillar of Clouds and pillar of Fire, <lb/>which guided the <emph type="italics"/>I&longs;raelites<emph.end type="italics"/>; which at the pre&longs;ence of the Sun, <lb/>appeared like a Cloud, but in the night was very glorious. </s><s>Thus <lb/><arrow.to.target n="marg188"></arrow.to.target> <lb/>I have by day ob&longs;erved the Moon amid&longs;t certain &longs;mall Clouds, <lb/>ju&longs;t as if one of them had been coloured white, but by night it <lb/>&longs;hines with much &longs;plendor.</s></p><p type="margin"><s><margin.target id="marg187"></margin.target><emph type="italics"/>The Moon ap­ <lb/>pears brighter by <lb/>night than by day.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg188"></margin.target><emph type="italics"/>The Moon be­ <lb/>held in the day <lb/>time, is like to a <lb/>little cloud.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>So that if you had never happened to &longs;ee the Moon, <lb/>&longs;ave onely in the day time, you would not have thought it more <lb/>&longs;hining than one of tho&longs;e Clouds.</s></p><p type="main"><s>SIMPL. </s><s>I verily believe I &longs;hould not.</s></p><p type="main"><s>SALV. </s><s>Tell me now; do you believe that the Moon is really <lb/>more &longs;hining in the night than day, or that by &longs;ome accident it <lb/>&longs;eemeth &longs;o?</s></p><p type="main"><s>SIMPL. </s><s>I am of opinion, that it re&longs;plends in it &longs;elf as much in <lb/>the day as night, but that its light appears greater by night, be­ <lb/>cau&longs;e we behold it in the dark mantle of Heaven; and in the day <lb/>time, the whole Atmo&longs;phere being very clear, &longs;o that &longs;he little <lb/>exceedeth it in lu&longs;tre, &longs;he &longs;eems to us much le&longs;s bright.</s></p><p type="main"><s>SALV. </s><s>Now tell me; have you ever at midnight &longs;een the Ter­ <lb/>re&longs;trial Globe illuminated by the Sun?</s></p><p type="main"><s>SIMPL. </s><s>This &longs;eemeth to me a que&longs;tion not to be ask'd, unle&longs;s <lb/>in je&longs;t, or of &longs;ome per&longs;on known to be altogether void of &longs;en&longs;e.</s></p><p type="main"><s>SALV. No, no; I e&longs;teem you to be a very rational man, and <pb xlink:href="040/01/089.jpg" pagenum="73"/>do ask the que&longs;tion &longs;eriou&longs;ly; and therefore an&longs;wer me: and if <lb/>afterwards you &longs;hall think that I &longs;peak impertinently, I will be <lb/>content to be the &longs;en&longs;ele&longs;s man: for he is much more a fool who <lb/>interrogates &longs;imply, than he to whom the que&longs;tion is put.</s></p><p type="main"><s>SIMPL. </s><s>If then you do not think me altogether &longs;imple, take <lb/>it for granted that I have an&longs;wered you already, and &longs;aid, that it <lb/>is impo&longs;&longs;ible, that one that is upon the Earth, as we are, &longs;hould &longs;ee <lb/>by night that part of the Earth where it is day, namely, that is il­ <lb/>luminated by the Sun.</s></p><p type="main"><s>SALV. </s><s>Therefore you have never &longs;een the Earth enlightned, <lb/>&longs;ave onely by day; but you &longs;ee the Moon to &longs;hine al&longs;o in the <lb/>dead of night. </s><s>And this is the cau&longs;e, <emph type="italics"/>Simplicius,<emph.end type="italics"/> which makes <lb/>you believe that the Earth doth not &longs;hine like the Moon; but if <lb/>you could &longs;ee the Earth illuminated, whil&longs;t you were in &longs;ome dark <lb/>place, like our night, you would &longs;ee it &longs;hine brighter than the <lb/>Moon. </s><s>Now if you de&longs;ire that the compari&longs;on may proceed <lb/>well, you mu&longs;t compare the light of the Earth, with that of the <lb/>Moon &longs;een in the day time, and not with the &longs;ame by night: for <lb/>it is not in our power to &longs;ee the Earth illuminated, &longs;ave onely in <lb/>the day. </s><s>Is it not &longs;o?</s></p><p type="main"><s>SIMPL. </s><s>So it ought to be.</s></p><p type="main"><s>SALV. </s><s>And fora&longs;much as you your &longs;elf have already confe&longs;&longs;ed <lb/>to have &longs;een the Moon by day among &longs;ome little white Clouds, <lb/>and very nearly, as to its a&longs;pect, re&longs;embling one of them; you did <lb/><arrow.to.target n="marg189"></arrow.to.target> <lb/>thereby grant, that tho&longs;e Clouds, which yet are Elementary <lb/>matters, are as apt to receive illumination, as the Moon, yea <lb/>more, if you will but call to mind that you have &longs;ometimes &longs;een <lb/>&longs;ome Clouds of va&longs;t greatne&longs;s, and as perfect white as the Snow; <lb/>and there is no que&longs;tion, but that if &longs;uch a Cloud could be con­ <lb/>tinued &longs;o luminous in the deep of night, it would illuminate the <lb/>places near about it, more than an hundred Moons. </s><s>If therefore <lb/>we were a&longs;&longs;ured that the Earth is illuminated by the Sun, like one <lb/>of tho&longs;e Clouds, it would be undubitable, but that it would be no <lb/>le&longs;s &longs;hining than the Moon. </s><s>But of this there is no que&longs;tion to <lb/>be made, in regard we &longs;ee tho&longs;e very Clouds in the ab&longs;ence of <lb/>the Sun, to remain by night, as ob&longs;cure as the Earth: and that <lb/>which is more, there is not any one of us, but hath &longs;een many <lb/>times &longs;ome &longs;uch Clouds low, and far off, and que&longs;tioned whether <lb/>they were Clouds or Mountains: an evident &longs;ign that the Moun­ <lb/>tains are no le&longs;s luminous than tho&longs;e Clouds. <lb/><arrow.to.target n="marg190"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg189"></margin.target><emph type="italics"/>Clouds are no le&longs;s <lb/>apt than the Moon <lb/>to be illuminated <lb/>by the Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg190"></margin.target><emph type="italics"/>A wall illumina­ <lb/>ted by the Sun, <lb/>compared to the <lb/>Moon &longs;hineth no <lb/>le&longs;s than it.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>But what needs more di&longs;cour&longs;e? </s><s>See yonder the Moon <lb/>is ri&longs;en, and more than half of it illuminated; &longs;ee there that wall, <lb/>on which the Sun &longs;hineth; retire a little this way, &longs;o that you &longs;ee <lb/>the Moon &longs;ideways with the wall: look now; which of them <lb/>&longs;hews more lucid? </s><s>Do not you &longs;ee, that if there is any advantage, <pb xlink:href="040/01/090.jpg" pagenum="74"/>the wall hath it? </s><s>The Sun &longs;hineth on that wall; from thence it </s></p><p type="main"><s><arrow.to.target n="marg191"></arrow.to.target> <lb/>is reverberated upon the wall of the Hall, from thence it's refle­ <lb/>cted upon that chamber, &longs;o that it falls on it at the third reflection: <lb/>and I am very certain, that there is in that place more light, than <lb/>if the Moons light had directly faln upon it.</s></p><p type="margin"><s><margin.target id="marg191"></margin.target><emph type="italics"/>The third re&longs;le­ <lb/>ction of a Wall illu­ <lb/>minates more than <lb/>the fir&longs;t of the <lb/>Moon.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>But this I cannot believe; for the illumination of the <lb/>Moon, e&longs;pecially when it is at the full, is very great.</s></p><p type="main"><s>SAGR. </s><s>It &longs;eemeth great by rea&longs;on of the circumjacent dark <lb/><arrow.to.target n="marg192"></arrow.to.target> <lb/>places; but ab&longs;olutely it is not much, and is le&longs;s than that of the <lb/>twilight half an hour after the Sun is &longs;et; which is manife&longs;t, be­ <lb/>cau&longs;e you &longs;ee not the &longs;hadows of the bodies illuminated by the <lb/>Moon till then, to begin to be di&longs;tingui&longs;hed on the Earth. </s><s>Whe­ <lb/>ther, again, that third reflection upon that chamber, illuminates <lb/>more than the fir&longs;t of the Moon, may be known by going thether, <lb/>and reading a Book, and afterwards &longs;tanding there in the night <lb/>by the Moons light, which will &longs;hew by which of them lights one <lb/>may read more or le&longs;s plainly, but I believe without further tryal, <lb/>that one &longs;hould &longs;ee le&longs;s di&longs;tinctly by this later.</s></p><p type="margin"><s><margin.target id="marg192"></margin.target><emph type="italics"/>The light of the <lb/>Moon weaker than <lb/>that of the twi­ <lb/>light.<emph.end type="italics"/></s></p><p type="main"><s>SALV. Now, <emph type="italics"/>Simplicius,<emph.end type="italics"/> (if haply you be &longs;atisfied) you may <lb/>conceive, as you your &longs;elf know very well, that the Earth doth <lb/>&longs;hine no le&longs;s than the Moon; and the only remembring you of &longs;ome <lb/>things, which you knew of your &longs;elf, and learn'd not of me, hath <lb/>a&longs;&longs;ured you thereof: for I taught you not that the Moon &longs;hews <lb/>lighter by night than by day, but you under&longs;tood it of your &longs;elf; <lb/>as al&longs;o you could tell me that a little Cloud appeareth as lucid as <lb/>the Moon: you knew al&longs;o, that the illumination of the Earth can­ <lb/>not be &longs;een by night; and in a word, you knew all this, without <lb/>knowing that you knew it. </s><s>So that you have no rea&longs;on to be &longs;cru­ <lb/>pulous of granting, that the dark part of the Earth may illuminate <lb/>the dark part of the Moon, with no le&longs;s a light than that where­ <lb/>with the Moon illuminates the ob&longs;curities of the night, yea rather <lb/>&longs;o much the greater, ina&longs;much as the Earth is forty times bigger <lb/>than the Moon.</s></p><p type="main"><s>SIMPL. </s><s>I mu&longs;t confe&longs;s that I did believe, that that &longs;econdary <lb/>light had been the natural light of the Moon.</s></p><p type="main"><s>SALV. </s><s>And this al&longs;o you know of your &longs;elf, and perceive not <lb/>that you know it. </s><s>Tell me, do not you know without teaching, <lb/>that the Moon &longs;hews it &longs;elf more bright by night than by day, in <lb/><arrow.to.target n="marg193"></arrow.to.target> <lb/>re&longs;pect of the ob&longs;curity of the &longs;pace of the ambient? </s><s>and con&longs;e­ <lb/>quently, do you not know <emph type="italics"/>in genere,<emph.end type="italics"/> that every bright body &longs;hews <lb/>the clearer, by how much the ambient is ob&longs;curer?</s></p><p type="margin"><s><margin.target id="marg193"></margin.target><emph type="italics"/>Luminous bodies <lb/>appear the brighter <lb/>in an ob&longs;curer<emph.end type="italics"/> am­ <lb/>bient.</s></p><p type="main"><s>SIMPL. </s><s>This I know very well.</s></p><p type="main"><s>SALV. </s><s>When the Moon is horned, and that &longs;econdary light <lb/>&longs;eemeth to you very bright, is it not ever nigh the Sun, and con­ <lb/>&longs;equently, in the light of the <emph type="italics"/>crepu&longs;culum,<emph.end type="italics"/> (twilight?)</s></p> <pb xlink:href="040/01/091.jpg" pagenum="75"/><p type="main"><s>SIMPL. </s><s>It is &longs;o; and I have oftentimes wi&longs;h'd that the Air <lb/>would grow thicker, that I might be able to &longs;ee that &longs;ame light <lb/>more plainly; but it ever di&longs;appeared before dark night.</s></p><p type="main"><s>SALV. </s><s>You know then very certainly, that in the depth of <lb/>night, that light would be more con&longs;picuous.</s></p><p type="main"><s>SIMPL. </s><s>I do &longs;o; and al&longs;o more than that, if one could but <lb/>take away the great light of the cre&longs;cent illuminated by the Sun, <lb/>the pre&longs;ence of which much ob&longs;cureth the other le&longs;&longs;er.</s></p><p type="main"><s>SALV. Why, doth it not &longs;ometimes come to pa&longs;s, that one may <lb/>in a very dark night &longs;ee the whole face of the Moon, without be­ <lb/>ing at all illuminated by the Sun?</s></p><p type="main"><s>SIMPL. </s><s>I know not whether this ever happeneth, &longs;ave onely <lb/>in the total Ecclip&longs;es of the Moon.</s></p><p type="main"><s>SALV. Why, at that time this its light would appear very <lb/>clear, being in a mo&longs;t ob&longs;cure <emph type="italics"/>medium,<emph.end type="italics"/> and not darkned by the <lb/>clarity of the luminous cre&longs;cents: but in that po&longs;ition, how light <lb/>did it appear to you?</s></p><p type="main"><s>SIMPL. </s><s>I have &longs;ometimes &longs;een it of the colour of bra&longs;s, and a <lb/>little whiti&longs;h; but at other times it hath been &longs;o ob&longs;cure, that I <lb/>have wholly lo&longs;t the &longs;ight of it.</s></p><p type="main"><s>SALV. </s><s>How then can that light be &longs;o natural, which you &longs;ee &longs;o <lb/>cleer in the clo&longs;e of the twilight, notwith&longs;tanding the impediment <lb/>of the great and contiguous &longs;plendor of the cre&longs;cents; and which <lb/>again, in the more ob&longs;cure time of night, all other light removed, <lb/>appears not at all?</s></p><p type="main"><s>SIMPL. </s><s>I have heard of &longs;ome that believed that &longs;ame light to <lb/>be participated to the&longs;e cre&longs;cents from the other Stars, and in par­ <lb/>ticular from <emph type="italics"/>Venus,<emph.end type="italics"/> the Moons neighbour.</s></p><p type="main"><s>SALV. </s><s>And this likewi&longs;e is a vanity; becau&longs;e in the time of <lb/>its total ob&longs;curation, it ought to appear more &longs;hining than ever; <lb/>for you cannot &longs;ay, that the &longs;hadow of the Earth intercepts the <lb/>&longs;ight of <emph type="italics"/>Venus,<emph.end type="italics"/> or the other Stars. </s><s>But to &longs;ay true, it is not at <lb/>that in&longs;tant wholly deprived thereof, for that the Terre&longs;trial He­ <lb/>mi&longs;phere, which in that time looketh towards the Moon, is that <lb/>where it is night, that is, an intire privation of the light of the Sun. <lb/></s><s>And if you but diligently ob&longs;erve, you will very &longs;en&longs;ibly perceive, <lb/>that like as the Moon, when it is &longs;harp-horned, doth give very little <lb/>light to the Earth; and according as in her the parts illumi­ <lb/>nated by the Suns light do encrea&longs;e: &longs;o likewi&longs;e the &longs;plendor to <lb/>our &longs;eeming encrea&longs;eth, which from her is reflected towards us; <lb/>thus the Moon, whil&longs;t it is &longs;harp-forked, and that by being between <lb/>the Sun and the Earth, it di&longs;covereth a very great part of the Ter­ <lb/><arrow.to.target n="marg194"></arrow.to.target> <lb/>re&longs;trial Hemi&longs;phere illuminated, appeareth very clear: and depart­ <lb/>ing from the Sun, and pa&longs;&longs;ing towards the ^{*}Quadrature, you <lb/>may &longs;ee the &longs;aid light by degrees to grow dim; and after the <pb xlink:href="040/01/092.jpg" pagenum="76"/>Quadrature, the &longs;ame appears very weak, becau&longs;e it continually <lb/>lo&longs;eth more and more of the view of the luminous part of the <lb/>Earth: and yet it &longs;hould &longs;ucceed quite contrary, if that light were <lb/>its own, or communicated to it from the Stars; for then we &longs;hould <lb/>&longs;ee it in the depth of night, and in &longs;o very dark an ambient.</s></p><p type="margin"><s><margin.target id="marg194"></margin.target>*<emph type="italics"/>By the Moons two<emph.end type="italics"/> <lb/>Quadratures <emph type="italics"/>you <lb/>are to under&longs;tand <lb/>its fir&longs;t and last <lb/>quarters, as A­ <lb/>&longs;trologers call them<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>Stay a little; for I ju&longs;t now remember, that I have <lb/>read in a little modern tract, full of many novelties; “That this <lb/>&longs;econdary light is not derived from the Stars, nor innate in the <lb/>Moon, and lea&longs;t of all communicated by the Earth, but that it is <lb/><arrow.to.target n="marg195"></arrow.to.target> <lb/>received from the &longs;ame illumination of the Sun, which, the &longs;ub­ <lb/>&longs;tance of the Lunar Globe being &longs;omewhat tran&longs;parent, pene­ <lb/>trateth thorow all its body; but more livelily illuminateth the <lb/>&longs;uperficies of the Hemi&longs;phere expo&longs;ed to the rays of the Sun: <lb/>and its pro&longs;undity imbuing, and (as I may &longs;ay) &longs;wallowing that <lb/>light, after the manner of a cloud or chry&longs;tal, tran&longs;mits it, and <lb/>renders it vi&longs;ibly lucid. </s><s>And this (if I remember aright) he <lb/>proveth by Authority, Experience and Rea&longs;on; citing <emph type="italics"/>Cleomedes, <lb/>Vitellion, Macrobius,<emph.end type="italics"/> and a certain other modern Author: and <lb/>adding, That it is &longs;een by experience to &longs;hine mo&longs;t in the days <lb/>neare&longs;t the Conjunction, that is, when it is horned, and is chiefly <lb/>bright about its limb. </s><s>And he farther writes, That in the Solar <lb/>Ecclip&longs;es, when it is under the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> of the Sun, it may be &longs;een <lb/>tran&longs;lucid, and more e&longs;pecially towards its utmo&longs;t Circle. </s><s>And <lb/>in the next place, for Arguments, as I think, he &longs;aith, That it not <lb/>being able to derive that light either from the Earth, or from the <lb/>Stars, or from it &longs;elf, it nece&longs;&longs;arily follows, that it cometh from <lb/>the Sun. </s><s>Be&longs;ides that, if you do but grant this &longs;uppo&longs;ition, one <lb/>may ea&longs;ily give convenient rea&longs;ons for all the particulars that <lb/>occur. </s><s>For the rea&longs;on why that &longs;ecundary light &longs;hews more <lb/>lively towards the outmo&longs;t limb, is, the &longs;hortne&longs;s of the &longs;pace <lb/>that the Suns rays hath to penetrate, in regard that of the lines <lb/>which pa&longs;s through a circle, the greate&longs;t is that which pa&longs;&longs;eth <lb/>through the centre, and of the re&longs;t, tho&longs;e which are farthe&longs;t from <lb/>it, are always le&longs;s than tho&longs;e that are nearer. </s><s>From the &longs;ame <lb/>principle, he &longs;aith, may be &longs;hewn why the &longs;aid light doth not <lb/>much dimini&longs;h. </s><s>And la&longs;tly, by this way the cau&longs;e is a&longs;&longs;igned <lb/>whence it comes, that that &longs;ame more &longs;hining circle about the <lb/>utmo&longs;t edge of the Moon, is &longs;een at the time of the Solar Ec­ <lb/>clip&longs;e, in that part which lyeth ju&longs;t under the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> of the Sun, <lb/>but not in that which is be&longs;ide the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/>: which happeneth <lb/>becau&longs;e the rays of the Sun pa&longs;s directly to our eye, through the <lb/>parts of the Moon underneath: but as for the parts which are <lb/>be&longs;ides it, they fall be&longs;ides the eye.”</s></p><p type="margin"><s><margin.target id="marg195"></margin.target><emph type="italics"/>The &longs;econdary <lb/>light of the Moon <lb/>cau&longs;ed by the Sun, <lb/>according to &longs;ome.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>If this Philo&longs;opher had been the fir&longs;t Author of this o­ <lb/>pinion, I would not wonder that he &longs;hould be &longs;o affectionate to it, <pb xlink:href="040/01/093.jpg" pagenum="77"/>as to have received it for truth; but borrowing it from others, I <lb/>cannot find any rea&longs;on &longs;ufficient to excu&longs;e him for not perceiving <lb/>its fallacies; and e&longs;pecially after he had heard the true cau&longs;e of <lb/>that effect, and had it in his power to &longs;atisfie him&longs;elf by a thou&longs;and <lb/>experiments, and manife&longs;t circum&longs;tances, that the &longs;ame proceeded <lb/>from the reflection of the Earth, and from nothing el&longs;e: and the more <lb/>this &longs;peculation makes &longs;omething to be de&longs;ired, in the judgment of <lb/>this Author, and of all tho&longs;e who give no credit to it: &longs;o much the <lb/>more doth their not having under&longs;tood and remembred it, excu&longs;e <lb/>tho&longs;e more rece&longs;s Antients, who, I am very certain, did they now <lb/>under&longs;tand it, would without the lea&longs;t repugnance admit thereof. <lb/></s><s>And if I may freely tell you what I think, I cannot believe but <lb/>that this <emph type="italics"/>Modern<emph.end type="italics"/> doth in his heart believe it; but I rather think, <lb/>that the conceit he &longs;hould not be the fir&longs;t Author thereof, did a <lb/>little move him to endeavour to &longs;uppre&longs;&longs;e it, or to di&longs;parage it at <lb/>lea&longs;t among&longs;t the &longs;imple, who&longs;e number we know to be very <lb/>great; and many there are, who much more affect the nume­ <lb/>rous applauds of the people, than the approbation of a few not <lb/>vulgar judgments.</s></p><p type="main"><s>SAGR. </s><s>Hold good <emph type="italics"/>Salviatus,<emph.end type="italics"/> for me thinks, I &longs;ee that you <lb/>go not the way to hit the true mark in this your di&longs;cour&longs;e, for the&longs;e <lb/>that ^{*} confound all propriety, know al&longs;o how to make them&longs;elves <lb/><arrow.to.target n="marg196"></arrow.to.target> <lb/>Authors of others inventions, provided they be not &longs;o &longs;tale, <lb/>and publick in the Schools and Market-places, as that they are more <lb/>then notorious to every one.</s></p><p type="margin"><s><margin.target id="marg196"></margin.target>* Tendono le pare­ <lb/>te al commune.</s></p><p type="main"><s>SALV. Ha! well aimed, you blame me for roving from the <lb/>point in hand; but what have you to do with Schools and Mar­ <lb/><arrow.to.target n="marg197"></arrow.to.target> <lb/>kets? </s><s>Is it not all one whether opinions and inventions be new to <lb/>men, or the men new to them? </s><s>If you ^{*} contend about the e­ <lb/>&longs;teem of the Founders of Sciences, which in all times do &longs;tart up, <lb/><arrow.to.target n="marg198"></arrow.to.target> <lb/>you may make your &longs;elf their inventor, even to the Alphabet it <lb/>&longs;elf, and &longs;o gain admiration among&longs;t that illiterate rabble; and <lb/>though in proce&longs;&longs;e of time your craft &longs;hould be perceived, that <lb/>would but little prejudice your de&longs;igne; for that others would <lb/>&longs;ucceed them in maintaining the number of your fautors; but let <lb/>us return to prove to <emph type="italics"/>Simplicius<emph.end type="italics"/> the invalidity of the rea&longs;ons of his <lb/>modern Author, in which there are &longs;everal fal&longs;ities, incon&longs;equen­ <lb/><arrow.to.target n="marg199"></arrow.to.target> <lb/>cies, and incredible Paradoxes. </s><s>And fir&longs;t, it is fal&longs;e that this &longs;e­ <lb/>condary light is clearer about the utmo&longs;t limb than in the middle <lb/>parts, &longs;o as to form, as it were, a ring or circle more bright than <lb/>the re&longs;t of its &longs;pace or contence. </s><s>True it is, indeed, that looking <lb/>on the Moon at the time of twilight, at fir&longs;t &longs;ight there is the re­ <lb/>&longs;emblance of &longs;uch a circle, but by an illu&longs;ion ari&longs;ing from the di­ <lb/>ver&longs;ity of confines that bound the Moons <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> which are con­ <lb/>fu&longs;ed by means of this &longs;econdary light; fora&longs;much as on the part <pb xlink:href="040/01/094.jpg" pagenum="78"/>towards the Sun it is bounded by the lucid horns of the Moon, <lb/>and on the other part, its confining term is the ob&longs;cure tract of the <lb/>twilight; who&longs;e relation makes us think the candor of the Moons <lb/><emph type="italics"/>Di&longs;cus<emph.end type="italics"/> to be &longs;o much the clearer; the which happens to be ob­ <lb/>fu&longs;cated in the oppo&longs;ite part, by the greater clarity of the cre&longs;­ <lb/>cents; but if this modern Author had e&longs;&longs;aied to make an inter­ <lb/><arrow.to.target n="marg200"></arrow.to.target> <lb/>po&longs;ition between the eye and the primary &longs;plendor, by the ridg of <lb/>&longs;ome hou&longs;e, or &longs;ome other &longs;creen, &longs;o as to have left vi&longs;ible only <lb/>the gro&longs;e of the Moon, the horns excluded, he might have &longs;een <lb/>it all alike luminous.</s></p><p type="margin"><s><margin.target id="marg197"></margin.target><emph type="italics"/>Its all one whe­ <lb/>ther opinions be <lb/>new to men, or men <lb/>new to opinions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg198"></margin.target>* <emph type="italics"/>Conte&longs;tare<emph.end type="italics"/> fal&longs;ly <lb/>rendered in the <lb/>Latine Tran&longs;lation <lb/><emph type="italics"/>content are.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg199"></margin.target><emph type="italics"/>The &longs;econdary <lb/>light of the Moon <lb/>appears in form of <lb/>a Ring, that is to <lb/>&longs;ay, bright in the <lb/>extreme circumfe­ <lb/>rence, and not in <lb/>the mid&longs;t, and why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg200"></margin.target><emph type="italics"/>The may to ob­ <lb/>&longs;erve the &longs;econda­ <lb/>ry light of the <lb/>Moon.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL, I think, now I remember, that he writes of his <lb/>making u&longs;e of &longs;uch another Artifice, to hide from us the fal&longs;e <lb/><emph type="italics"/>Incidum.<emph.end type="italics"/></s></p><p type="main"><s>SALV. Oh! how is this (as I believed) inadvertency of his, <lb/>changed into a lie, bordering on ra&longs;hne&longs;&longs;e; for that every one <lb/>may frequently make proof of the contrary. </s><s>That in the next <lb/><arrow.to.target n="marg201"></arrow.to.target> <lb/>place, at the Suns Eclip&longs;e, the Moons <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> is &longs;een otherwayes <lb/>than by privation, I much doubt, and &longs;pecially when the E­ <lb/>clip&longs;e is not total, as tho&longs;e mu&longs;t nece&longs;&longs;arily have been, which <lb/>were ob&longs;erved by the Author; but if al&longs;o he &longs;hould have di&longs;cove­ <lb/>red &longs;omewhat of light, this contradicts not, rather favoureth our <lb/>opinion; for that at &longs;uch a time, the whole Terre&longs;trial Hemi­ <lb/>&longs;phere illuminated by the Sun, is oppo&longs;ite to the Moon, &longs;o that <lb/>although the Moons &longs;hadow doth ob&longs;cure a part thereof, yet this <lb/>is very &longs;mall in compari&longs;on of that which remains illuminated. <lb/></s><s>That which he farther adds, that in this ca&longs;e, the part of the <lb/>limb, lying under the Sun, doth appear very lucid, but that <lb/>which lyeth be&longs;ides it, not &longs;o; and that to proceed from the co­ <lb/>ming of the &longs;olar rayes directly through that part to the eye, but <lb/>not through this, is really one of tho&longs;e fopperies, which di&longs;co <lb/>ver the other fictions, of him which relates them: For if it be <lb/>requi&longs;ite to the making a &longs;econdary light vi&longs;ible in the lunar <emph type="italics"/>Di&longs;­ <lb/>cus,<emph.end type="italics"/> that the rayes of the Sun came directly through it to our <lb/>eyes, doth not this pitiful Philo&longs;opher perceive, that we &longs;hould ne­ <lb/>ver &longs;ee this &longs;ame &longs;econdary light, &longs;ave onely at the Eclip&longs;e of the <lb/>Sun? </s><s>And if a part onely of the Moon, far le&longs;&longs;e than half a de­ <lb/>gree, by being remote from the Suns <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> can deflect or de­ <lb/>viate the rayes of the Sun, &longs;o that they arrive not at our eye; <lb/>what &longs;hall it do when it is di&longs;tant twenty or thirty degrees, as it is <lb/>at its fir&longs;t apparition? </s><s>and what cour&longs;e &longs;hall the rayes of the Sun <lb/>keep, which are to pa&longs;&longs;e thorow the body of the Moon, that <lb/><arrow.to.target n="marg202"></arrow.to.target> <lb/>they may find out our eye? </s><s>This man doth go &longs;ucce&longs;&longs;ively con&longs;i­ <lb/>dering what things ought to be, that they may &longs;erve his purpo&longs;e, <lb/>but doth not gradually proceed, accommodating his conceits to <lb/>the things, as really they are. </s><s>As for in&longs;tance, to make the light <pb xlink:href="040/01/095.jpg" pagenum="79"/>of the Sun capable to penetrate the &longs;ub&longs;tance of the Moon, he <lb/>makes her in part diaphanous, as is <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> the tran&longs;parence of a cloud, <lb/>or cry&longs;tal: but I know not what he would think of &longs;uch a tran­ <lb/>&longs;parency, in ca&longs;e the &longs;olar rayes were to pa&longs;&longs;e a depth of clouds <lb/>of above two thou&longs;and miles; but let it be &longs;uppo&longs;ed that he <lb/>&longs;hould boldly an&longs;wer, that might well be in the Cœle&longs;tial, which <lb/>are quite other things from the&longs;e our Elementary, impure, and <lb/>feculent bodies; and let us convict his error by &longs;uch wayes, as <lb/>admit him no reply, or (to &longs;ay better) &longs;ubter-fuge. </s><s>If he will <lb/>maintain, that the &longs;ub&longs;tance of the Moon is diaphanous, he <lb/>mu&longs;t &longs;ay that it is &longs;o, while&longs;t that the rayes of the Sun are to pe­ <lb/>netrate its whole profundity, that is, more than two thou&longs;and <lb/>miles; but that if you oppo&longs;e unto them onely one mile, or <lb/>le&longs;&longs;e, they &longs;hould no more penetrate that, than they penetrate <lb/>one of our mountains.</s></p><p type="margin"><s><margin.target id="marg201"></margin.target><emph type="italics"/>The Moons<emph.end type="italics"/> Dif­ <lb/>cus <emph type="italics"/>in a &longs;olar E­ <lb/>clip&longs;e can be &longs;een <lb/>onely by privation.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg202"></margin.target><emph type="italics"/>The Author of the <lb/>Book of conclu&longs;i­ <lb/>ons, accommodates <lb/>the things to his <lb/>purpo&longs;es, and not <lb/>his purpo&longs;es to the <lb/>things.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>You put me in mind of a man, who would have &longs;old <lb/><arrow.to.target n="marg203"></arrow.to.target> <lb/>me a &longs;ecret how to corre&longs;pond, by means of a certain &longs;ympathy of <lb/>magnetick needles, with one, that &longs;hould be two or three thou­ <lb/>&longs;and miles di&longs;tant; and I telling him, that I would willingly buy <lb/>the &longs;ame, but that I de&longs;ired fir&longs;t to &longs;ee the experiment thereof, <lb/>and that it did &longs;uffice me to make it, I being in one Chamber, and <lb/>he in the next, he an&longs;wered me, that in &longs;o &longs;mall a di&longs;tance one <lb/>could not &longs;o well perceive the operation; whereupon I turn'd him <lb/>going, telling him, that I had no mind, at that time, to take a <lb/>journey unto <emph type="italics"/>Grand Cairo,<emph.end type="italics"/> or to <emph type="italics"/>Mu&longs;covy,<emph.end type="italics"/> to make the experi­ <lb/>ment; but that, if he would go him&longs;elf, I would perform the <lb/>other part, &longs;taying in <emph type="italics"/>Venice.<emph.end type="italics"/> But let us hear whither the dedu­ <lb/>ction of our Author tendeth, and what nece&longs;&longs;ity there is, that he <lb/>mu&longs;t grant the matter of the Moon to be mo&longs;t perforable by the <lb/>rayes of the Sun, in a depth of two thou&longs;and miles, but more <lb/>opacous than one of our mountains, in a thickne&longs;&longs;e of one mile <lb/>onely.</s></p><p type="margin"><s><margin.target id="marg203"></margin.target><emph type="italics"/>A je&longs;t put upon one <lb/>that would &longs;ell a <lb/>certain &longs;ecret for <lb/>holding corre&longs;pon­ <lb/>dency with a per&longs;on <lb/>a thou&longs;and miles <lb/>off<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The very mountains of the Moon them&longs;elves are a <lb/>proof thereof, which percu&longs;&longs;ed on one &longs;ide of the Sun, do ca&longs;t <lb/>on the contrary &longs;ide very dark &longs;hadows, terminate, and more di­ <lb/>&longs;tinct by much, than the &longs;hadows of ours; but had the&longs;e moun­ <lb/>tains been diaphanous, we could never have come to the know­ <lb/>ledg of any unevenne&longs;&longs;e in the &longs;uperficies of the Moon, nor have <lb/>&longs;een tho&longs;e luminous montuo&longs;ities di&longs;tingui&longs;hed by the terms which <lb/>&longs;eparate the lucid parts from the dark: much le&longs;&longs;e, &longs;hould we &longs;ee <lb/>this &longs;ame term &longs;o di&longs;tinct, if it were true, that the Suns light did <lb/>penetrate the whole thickne&longs;&longs;e of the Moon; yea rather, accord­ <lb/>ing to the Authors own words, we &longs;hould of nece&longs;&longs;ity di&longs;cern the <lb/>pa&longs;&longs;age, and confine, between the part of the Sun &longs;een, and the <lb/>part not &longs;een, to be very confu&longs;ed, and mixt with light and <pb xlink:href="040/01/096.jpg" pagenum="80"/>darkne&longs;&longs;e; for that that matter which admits the pa&longs;&longs;age of the <lb/>Suns rayes thorow a &longs;pace of two thou&longs;and miles, mu&longs;t needs be <lb/>&longs;o tran&longs;parent, that it would very weakly re&longs;i&longs;t them in a hun­ <lb/>dredth, or le&longs;&longs;er part of that thickne&longs;&longs;e; neverthele&longs;&longs;e, the term <lb/>which &longs;eparateth the part illuminated from the ob&longs;cure, is inci­ <lb/>dent, and as di&longs;tinct, as white is di&longs;tinct from black; and e­ <lb/>&longs;pecially where the Section pa&longs;&longs;eth through the part of the Moon, <lb/>that is naturally more clear and montanous; but where the old <lb/>&longs;pots do part, which are certain plains, that by means of their <lb/>&longs;pherical inclination, receive the rayes of the Sun obliquely, <lb/>there the term is not &longs;o di&longs;tinct, by rea&longs;on of the more dimme il­ <lb/>lumination. </s><s>That, la&longs;tly, which he &longs;aith, how that the &longs;econdary <lb/>light doth not dimini&longs;h and langui&longs;h, according as the Moon en­ <lb/>crea&longs;eth, but con&longs;erveth it &longs;elf continually in the &longs;ame efficacy; <lb/>is mo&longs;t fal&longs;e; nay it is hardly &longs;een in the quadrature, when, on <lb/>the contrary, it &longs;hould appear more &longs;plendid, and be vi&longs;ible after <lb/>the <emph type="italics"/>crepu&longs;culum<emph.end type="italics"/> in the dark of night. </s><s>Let us conclude therefore, <lb/>that the Earths reflection is very &longs;trong upon the Moon; and that, <lb/>which you ought more to e&longs;teem, we may deduce from thence an­ <lb/>other admirable congruity between the Moon and Earth; name­ <lb/><arrow.to.target n="marg204"></arrow.to.target> <lb/>ly, that if it be true, the Planets operate upon the Earth by their <lb/>motion and light, the Earth may probably be no le&longs;&longs;e potent in <lb/>operating reciprocally upon them with the &longs;ame light, and perad­ <lb/>venture, motion al&longs;o. </s><s>And though it &longs;hould not move, yet may <lb/>it retain the &longs;ame operation; becau&longs;e, as it hath been proved al­ <lb/>ready, the action of the light is the &longs;elf &longs;ame, I mean of the light <lb/>of the Sun reflected; and motion doth nothing, &longs;ave only vary <lb/>the a&longs;pects, which fall out in the &longs;ame manner, whether we make <lb/>the Earth move, and the Sun &longs;tand &longs;till, or the contrary.</s></p><p type="margin"><s><margin.target id="marg204"></margin.target><emph type="italics"/>The Earth may re­ <lb/>ciprocally operate <lb/>upon Cœle&longs;tial bo­ <lb/>dies, with its light.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>None of the Philo&longs;ophers are found to have &longs;aid, that <lb/>the&longs;e inferiour bodies operate on the Cœle&longs;tial, nay, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> af­ <lb/>firmes the direct contrary.</s></p><p type="main"><s>SALV. <emph type="italics"/>Aristotle<emph.end type="italics"/> and the re&longs;t, who knew not that the Earth and <lb/>Moon mutually illuminated each other, are to be excu&longs;ed; but <lb/>they would ju&longs;tly de&longs;erve our cen&longs;ure, if while&longs;t they de&longs;ire that <lb/>we &longs;hould grant and believe with them, that the Moon operateth <lb/>upon the Earth with light, they &longs;hould deny to us, who have <lb/>taught them that the Earth illuminates the Moon, the operation <lb/>the Earth hath on the Moon.</s></p><p type="main"><s>SIMPL. </s><s>In &longs;hort, I find in my &longs;elf a great unwillingne&longs;&longs;e to <lb/>admit this commerce, which you would per&longs;wade me to be be­ <lb/>twixt the Earth and Moon, placing it, as we &longs;ay, among&longs;t the <lb/>number of the Stars; for if there were nothing el&longs;e, the great <lb/>&longs;eparation and di&longs;tance between it and the Cœle&longs;tial bodies, doth <lb/>in my opinion nece&longs;&longs;arily conclude a va&longs;t di&longs;parity between them.</s></p> <pb xlink:href="040/01/097.jpg" pagenum="81"/><p type="main"><s>SALV. </s><s>See <emph type="italics"/>Simplicius<emph.end type="italics"/> what an inveterate affection and radica­ <lb/>ted opinion can do, &longs;ince it is &longs;o powerful, that it makes you think <lb/>that tho&longs;e very things favour you, which you produce again&longs;t <lb/>your &longs;elf. </s><s>For if &longs;eparation and di&longs;tance are accidents &longs;ufficient to <lb/>per&longs;wade with you a great diver&longs;ity of natures, it mn&longs;t follow that <lb/><arrow.to.target n="marg205"></arrow.to.target> <lb/>proximity and contiguity import &longs;imilitude. </s><s>Now how much more <lb/>neerer is the Moon to the Earth, than to any other of the Cœle&longs;tial <lb/>Orbs? </s><s>You mu&longs;t acknowledg therefore, according to your own con­ <lb/>ce&longs;&longs;ion (and you &longs;hall have other Philo&longs;ophers bear you company) <lb/>that there is a very great affinity betwixt the Earth and Moon. <lb/></s><s>Now let us proceed, and &longs;ee whether any thing remains to be con­ <lb/>&longs;idered, touching tho&longs;e objections which you made again&longs;t the re­ <lb/>&longs;emblances that are between the&longs;e two bodies.</s></p><p type="margin"><s><margin.target id="marg205"></margin.target><emph type="italics"/>Affinity between <lb/>he Earth & Moon <lb/>in re&longs;pect of their <lb/>vicinity.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>It re&longs;ts, that we &longs;ay &longs;omething touching the &longs;olidity of <lb/>the Moon, which I argued from its being exqui&longs;ite &longs;mooth and <lb/>polite, and you from its montuo&longs;ity. </s><s>There is another &longs;cruple al­ <lb/>&longs;o comes into my mind, from an opinion which I have, that the <lb/>Seas reflection ought by the equality of its &longs;urface, to be rendered <lb/>&longs;tronger than that of the Earth, who&longs;e &longs;uperficies is &longs;o rough and <lb/>opacous.</s></p><p type="main"><s>SALV. </s><s>As to the fir&longs;t objection; I &longs;ay, that like as among the <lb/>parts of the Earth, which all by their gravity &longs;trive to approach the <lb/><arrow.to.target n="marg206"></arrow.to.target> <lb/>neare&longs;t they can po&longs;&longs;ible to the center, &longs;ome of them alwayes are <lb/>more remote from it than the re&longs;t, as the mountains more than <lb/>the valleys, and that by rea&longs;on of their &longs;olidity and firmne&longs;&longs;e <lb/>(for if they were of fluid, they would be even) &longs;o the &longs;eeing &longs;ome <lb/>parts of the Moon to be elevated above the &longs;phericity of the low­ <lb/>er parts, argueth their hardne&longs;&longs;e; for it is probable that the mat­ <lb/>ter of the Moon is reduced into a &longs;pherical form by the harmoni­ <lb/>ous con&longs;piration of all its parts to the &longs;ame &longs;enten&longs;e. </s><s>Touching <lb/>the &longs;econd doubt, my thinks that the particulars already ob&longs;erved <lb/>to happen in the Looking-gla&longs;&longs;es, may very well a&longs;&longs;ure us, that the <lb/>reflection of light comming from the Sea, is far weaker than that <lb/><arrow.to.target n="marg207"></arrow.to.target> <lb/>which cometh from Land; under&longs;tanding it alwayes of the <lb/>univer&longs;al reflection; for as to that particular, on which the wa­ <lb/>ter being calm, ca&longs;teth upon a determinate place, there is no <lb/>doubt, but that he who &longs;hall &longs;tand in that place, &longs;hall &longs;ee a very <lb/>great reflection in the water, but every way el&longs;e he &longs;hall &longs;ee the <lb/>&longs;urface of the Water more ob&longs;cure than that of the Land; and to <lb/><arrow.to.target n="marg208"></arrow.to.target> <lb/>prove it to your &longs;en&longs;es, let us go into yonder Hall, and power <lb/>forth a little water upon the Pavement. </s><s>Tell me now, doth not <lb/>this wet brick &longs;hew more dull than the other dry ones? </s><s>Doubt­ <lb/>le&longs;&longs;e it doth, and will &longs;o appear, from what place &longs;oever you be­ <lb/>hold it, except one onely, and this is that way which the light <lb/>cometh, that entereth in at yonder window; go backwards <lb/>therefore by a little and a little.</s></p> <pb xlink:href="040/01/098.jpg" pagenum="82"/><p type="margin"><s><margin.target id="marg206"></margin.target><emph type="italics"/>Solidity of the <lb/>Lunar Globe argu­ <lb/>ed from its being <lb/>montainous.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg207"></margin.target><emph type="italics"/>The Seas refle­ <lb/>ction of light much <lb/>weaker than that <lb/>of the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg208"></margin.target><emph type="italics"/>An experiment <lb/>to prove the refle­ <lb/>ction of the Water <lb/>le&longs;&longs;e clear than <lb/>that of the Land.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>Here I &longs;ee the we&longs;t part &longs;hine more than all the re&longs;t of <lb/>the pavement, and I &longs;ee that it &longs;o hapneth, becau&longs;e the refle­ <lb/>ction of the light which entereth in at the window, cometh to­ <lb/>wards me.</s></p><p type="main"><s>SALV. </s><s>That moi&longs;ture hath done no more but filled tho&longs;e little <lb/>cavities which are in the brick with water, and reduced its &longs;uper­ <lb/>ficies to an exact evene&longs;&longs;e; whereupon the reflex rayes i&longs;&longs;ue <lb/>unitedly towards one and the &longs;ame place; but the re&longs;t of the <lb/>pavement which is dry, hath its protuberances, that is, an innu­ <lb/>merable variety of inclinations in its &longs;malle&longs;t particles; whereup­ <lb/>on the reflections of the light &longs;catter towards all parts, but more <lb/>weakly than if they had gone all united together; and therefore, <lb/>the &longs;ame &longs;heweth almo&longs;t all alike, beheld &longs;everal wayes, but far <lb/>le&longs;&longs;e clear than the moi&longs;tned brick. </s><s>I conclude therefore, that the <lb/>&longs;urface of the Sea, beheld from the Moon, in like manner, as it <lb/>would appear mo&longs;t equal, (the I&longs;lands and Rocks deducted) &longs;o it <lb/>would &longs;hew le&longs;&longs;e clear than that of the Earth, which is montanous <lb/>and uneven. </s><s>And but that I would not &longs;eem, as the &longs;aying is, <lb/>to harp too much on one &longs;tring, I could tell you that I have ob­ <lb/>&longs;erved in the Moon that &longs;econdary light which I told you came to <lb/>her from the reflection of the Terre&longs;trial Globe, to be notably <lb/><arrow.to.target n="marg209"></arrow.to.target> <lb/>more clear two or three dayes before the conjunction, than after, <lb/>that is, when we &longs;ee it before break of day in the Ea&longs;t, than <lb/>when it is &longs;een at night after Sun-&longs;et in the We&longs;t; of which dif­ <lb/>ference the cau&longs;e is, that the Terre&longs;trial Hemi&longs;phere, which looks <lb/>towards the Ea&longs;tern Moon, hath little Sea, and much Land, to <lb/>wit, all <emph type="italics"/>A&longs;ia,<emph.end type="italics"/> whereas, when it is in the We&longs;t, it beholds very <lb/>great Seas, that is, the whole <emph type="italics"/>Atlantick<emph.end type="italics"/> Ocean as far as <emph type="italics"/>America:<emph.end type="italics"/> <lb/>An Argument &longs;ufficiently probable that the &longs;urface of the water <lb/>appears le&longs;&longs;e &longs;plendid than that of the Earth.</s></p><p type="margin"><s><margin.target id="marg209"></margin.target><emph type="italics"/>The &longs;econdary <lb/>light of the Moon <lb/>clearer before the <lb/>conjunction, than <lb/>after.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>So that perhaps you believe, tho&longs;e great &longs;pots di&longs;co­ <lb/>vered in the face of the Moon, to be Seas, and the other clearer <lb/>parts to be Land, or &longs;ome &longs;uch thing?</s></p><p type="main"><s>SALV. </s><s>This which you ask me, is the beginning of tho&longs;e in­ <lb/>congruities which I e&longs;teem to be between the Moon and the <lb/>Earth, out of which it is time to di&longs;-ingage our &longs;elves, for we <lb/>have &longs;tayed too long in the Moon. </s><s>I &longs;ay therefore, that if there <lb/>were in nature but one way onely, to make two &longs;uperficies illu&longs;tra­ <lb/>ted by the Sun, to appear one more clear than the other, and <lb/>that this were by the being of the one Earth, and the other Wa­ <lb/>ter; it would be nece&longs;&longs;ary to &longs;ay that the &longs;urface of the Moon <lb/>were part earthy and part aquatick; but becau&longs;e we know many <lb/>wayes to produce the &longs;ame effect (and others there may be which <lb/>we know not of;) therefore I dare not affirm the Moon to con­ <lb/>&longs;i&longs;t of one thing more than another: It hath been &longs;een already <pb xlink:href="040/01/099.jpg" pagenum="83"/>that a &longs;ilver plate boiled, being toucht with the Burni&longs;her, be­ <lb/>cometh of white ob&longs;cure; that the moi&longs;t part of the Earth &longs;hews <lb/>more ob&longs;cure than the dry; that in the tops of Hills, the woody <lb/>parts appear more gloomy than the naked and barren; which <lb/>hapneth becau&longs;e there falleth very much &longs;hadow among the Trees, <lb/>but the open places are illuminated all over by the Sun. </s><s>And this <lb/>mixtion of &longs;hadow hath &longs;uch operation, that in tu&longs;ted velvet, the <lb/>&longs;ilk which is cut, is of a far darker colour than that which is not <lb/>cut, by means of the &longs;hadows diffu&longs;ed betwixt thred and thred, <lb/>and a plain velvet &longs;hews much blacker than a Taffata, made of the <lb/>&longs;ame &longs;ilk. </s><s>So that if there were in the Moon things which &longs;hould <lb/>look like great Woods, their a&longs;pect might repre&longs;ent unto us the <lb/>&longs;pots which we di&longs;cover; alike difference would be occa&longs;ioned, if <lb/>there were Seas in her: and la&longs;tly, nothing hindreth, but that tho&longs;e <lb/>&longs;pots may really be of an ob&longs;curer colour than the re&longs;t; for thus <lb/>the &longs;now makes the mountains &longs;hew brighter. </s><s>That which is plain­ <lb/><arrow.to.target n="marg210"></arrow.to.target> <lb/>ly ob&longs;erved in the Moon is, that its mo&longs;t ob&longs;cure parts are all <lb/>plains, with few ri&longs;es and bancks in them; though &longs;ome there be; <lb/>the re&longs;t which is of a brighter colour, is all full of rocks, moun­ <lb/>tains, hillocks of &longs;pherical and other figures; and in particular, round <lb/>about the &longs;pots are very great ledges of mountains. </s><s>That the <lb/><arrow.to.target n="marg211"></arrow.to.target> <lb/>&longs;pots be plain &longs;uperficies, we have a&longs;&longs;uredproof, in that we &longs;ee, <lb/>how that the term which di&longs;tingui&longs;heth the part illuminated from <lb/>the ob&longs;cure, in cro&longs;&longs;ing the &longs;pots makes the inter&longs;ection even, but <lb/>in the clear parts it &longs;hews all craggy and &longs;hagged. </s><s>But I know not <lb/>as yet whether this evenne&longs;&longs;e of &longs;uperficies may be &longs;ufficient of it <lb/>&longs;elf alone, to make the ob&longs;curity appear, and I rather think not. <lb/></s><s>Be&longs;ides, I account the Moon exceeding different from the Earth; <lb/>for although I imagine to my &longs;elf that tho&longs;e are not idle and dead <lb/>Regions, yet I affirm not, that there are in them motion and life, <lb/><arrow.to.target n="marg212"></arrow.to.target> <lb/>much le&longs;s that there are bred plants, animals or other things like <lb/>to ours; but, if &longs;uch there be, they &longs;hould neverthele&longs;s be very <lb/>different, and remote from our imagination. </s><s>And I am induced &longs;o <lb/>to think, becau&longs;e in the fir&longs;t place, I e&longs;teem that the matter of the <lb/>Lunar Globe con&longs;i&longs;ts not of Earth and Water; and this alone <lb/>&longs;ufficeth to take away the generations and alterations re&longs;embling <lb/>ours: but now &longs;uppo&longs;ing that there were in the Moon, Water and <lb/><arrow.to.target n="marg213"></arrow.to.target> <lb/>Earth, yet would they not produce plants and animals like to <lb/>ours; and this for two principal rea&longs;ons: The fir&longs;t is, that unto our <lb/><arrow.to.target n="marg214"></arrow.to.target> <lb/>productions there are required &longs;o many variable a&longs;pects of the Sun, <lb/>that without them they would all mi&longs;carry: now the habitudes of <lb/>the Sun towards the Earth are far different from tho&longs;e towards <lb/>the Moon. </s><s>We as to the diurnal illumination, have, in the greater <lb/>part of the Earth, every twenty four hours part day, and part <lb/>night, which effect in the Moon is monethly: and that annual decli­ <pb xlink:href="040/01/100.jpg" pagenum="84"/>nation and elevation of the Sun in the Zodiack, by which it pro­ <lb/><arrow.to.target n="marg215"></arrow.to.target> <lb/>duceth diver&longs;ity of Sea&longs;ons, and inequality of dayes and nights, <lb/>are fini&longs;hed in the Moon in a moneth; and whereas the Sun to us <lb/><arrow.to.target n="marg216"></arrow.to.target> <lb/>ri&longs;eth and declineth &longs;o much, that from the greate&longs;t to the lea&longs;t al­ <lb/>titude, there is a difference of almo&longs;t 47 degrees, for &longs;o much is <lb/>the di&longs;tance from one to the other Tropick; this is in the Moon <lb/>but ten degrees only, or little more; namely, as much as the grea­ <lb/>te&longs;t Latitudes of the Dragon on each &longs;ide the Ecliptick. </s><s>Now <lb/>con&longs;ider what effect the Sun would have in the torrid Zone, &longs;hould <lb/>it continually for fifteen dayes together beam forth its Rayes upon <lb/>it; which without all que&longs;tion would de&longs;troy plants, herbs, <lb/>and living creatures: and if it &longs;hould chance that there were any <lb/>production, it would be of herbs, plants, and creatures very diffe­ <lb/><arrow.to.target n="marg217"></arrow.to.target> <lb/>rent from tho&longs;e which are now there. </s><s>Secondly, I verily believe <lb/>that in the Moon there are no rains, for if Clouds &longs;hould gather <lb/>in any part thereof, as they do about the Earth, they would there­ <lb/>upon hide from our &longs;ight &longs;ome of tho&longs;e things, which we with the <lb/><emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> behold in the Moon, and in a word, would &longs;ome way or <lb/>other change its <emph type="italics"/>Phœnomenon,<emph.end type="italics"/> an effect which I could never by long <lb/>and diligent ob&longs;ervations di&longs;cover; but alwayes beheld it in a <lb/>even and pure &longs;erenity.</s></p><p type="margin"><s><margin.target id="marg210"></margin.target><emph type="italics"/>The ob&longs;curer <lb/>parts of the Moon <lb/>are plains, and the <lb/>more bright moun­ <lb/>tainous.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg211"></margin.target><emph type="italics"/>Long ledges of <lb/>mountaixs about <lb/>the &longs;pots of the <lb/>Moon.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg212"></margin.target><emph type="italics"/>There are not <lb/>generated in the <lb/>Moon things like <lb/>to ours, but if <lb/>there be any pro­ <lb/>ductions, they are <lb/>very different.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg213"></margin.target><emph type="italics"/>The Moon not <lb/>compo&longs;ed of Water <lb/>and Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg214"></margin.target><emph type="italics"/>Tho&longs;e a&longs;pects of <lb/>the Sun nece&longs;&longs;ary <lb/>for our generati­ <lb/>ons, are not &longs;o in <lb/>the Moon.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg215"></margin.target><emph type="italics"/>Natural dayas <lb/>in the Moon are of <lb/>a Moneth long.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg216"></margin.target><emph type="italics"/>To the Moon <lb/>the Sun a&longs;eondeth <lb/>and declineth with <lb/>a difference of ten <lb/>degrees, and to the <lb/>Earth of forty &longs;e­ <lb/>ven degrees.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg217"></margin.target><emph type="italics"/>There are no <lb/>rains in the Moon.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>To this may be an&longs;wered, either that there might be <lb/>great mi&longs;ts, or that it might rain in the time of their night, that is, <lb/>when the Sun doth not illuminate it.</s></p><p type="main"><s>SALV. </s><s>If other pa&longs;&longs;ages did but a&longs;&longs;ure us, that there were ge­ <lb/>nerations in it like to ours, and that there was onely wanting the <lb/>concour&longs;e of rains, we might find out this, or &longs;ome other tempe­ <lb/>rament to &longs;erve in&longs;tead thereof, as it happens in <emph type="italics"/>Egypt<emph.end type="italics"/> by the in­ <lb/>undation of <emph type="italics"/>Nile:<emph.end type="italics"/> but not meeting with any accident, which cor­ <lb/>re&longs;ponds with ours, of many that have been &longs;ought out for the pro­ <lb/>duction of the like effects, we need not trouble our &longs;elves to intro­ <lb/>duce one alone; and that al&longs;o, not becau&longs;e we have certain ob&longs;er­ <lb/>vation of it, but for a bare non-repugnance that we find therein. <lb/></s><s>Moreover, if I was demanded what my fir&longs;t apprehen&longs;ion, and pure <lb/>natural rea&longs;on dictated to me concerning the production of things <lb/>like or unlike there above, I would alwayes reply, that they are <lb/>mo&longs;t different, and to us altogether unimaginable, for &longs;o me thinks <lb/>the riches of Nature, and the omnipotence of our Creator and <lb/>Governour, do require.</s></p><p type="main"><s>SAGR. </s><s>I ever accounted extraordinary madne&longs;&longs;e that of tho&longs;e, <lb/>who would make humane comprehen&longs;ion the mea&longs;ure of what na­ <lb/>ture hath a power or knowledge to effect; whereas on the con­ <lb/><arrow.to.target n="marg218"></arrow.to.target> <lb/>trary there is not any the lea&longs;t effect in Nature, which can be fully <lb/>under&longs;tood by the mo&longs;t &longs;peculative wits in the world. </s><s>This their <lb/>&longs;o vain pre&longs;umption of knowing all, can take beginning from no­ <pb xlink:href="040/01/101.jpg" pagenum="85"/>thing, unle&longs;&longs;e from their never having known any thing; for if <lb/>one hath but once onely experienced the perfect knowledg of one <lb/>onely thing, and but truly ta&longs;ted what it is to know, he &longs;hall per­ <lb/>ceive that of infinite other conclu&longs;ions, he under&longs;tands not &longs;o much <lb/>as one.</s></p><p type="margin"><s><margin.target id="marg218"></margin.target><emph type="italics"/>The having a <lb/>perfect knowledg <lb/>of nothing, maketh <lb/>&longs;ome believe they <lb/>under&longs;tand all <lb/>things.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Your di&longs;cour&longs;e is very concluding; in confirmation of <lb/>which we have the example of tho&longs;e who under&longs;tand, or have <lb/>known &longs;ome thing, which the more knowing they are, the more <lb/>they know, and freely confe&longs;&longs;e that they know little; nay, the <lb/>wi&longs;e&longs;t man in all <emph type="italics"/>Greece,<emph.end type="italics"/> and for &longs;uch pronounced by the Oracle, <lb/>openly profe&longs;&longs;ed to know that he knew nothing.</s></p><p type="main"><s>SIMPL. </s><s>It mu&longs;t be granted therefore, either that <emph type="italics"/>Socrates<emph.end type="italics"/> or <lb/>that the <emph type="italics"/>Oracle<emph.end type="italics"/> it &longs;elf was a lyar, <emph type="italics"/>that declaring him to be mo&longs;t <lb/>wi&longs;e, and he confe&longs;&longs;ing that he knew him&longs;elf to be mo&longs;t ig­ <lb/>norant.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Neither one nor the other doth follow, for that both <lb/><arrow.to.target n="marg219"></arrow.to.target> <lb/>the a&longs;&longs;ertions may be true. </s><s>The <emph type="italics"/>Oracle<emph.end type="italics"/> adjudged <emph type="italics"/>Socrates<emph.end type="italics"/> the wi­ <lb/>&longs;e&longs;t of all men, who&longs;e knowledg is limited; <emph type="italics"/>Socrates<emph.end type="italics"/> acknow­ <lb/>ledgeth that he knew nothing in relation to ab&longs;olute wi&longs;dome, <lb/>which is infinite; and becau&longs;e of infinite, much is the &longs;ame part, <lb/>as is little, and as is nothing (for to arrive <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> to the infinite <lb/>number, it is all one to accumulate thou&longs;ands, tens, or ciphers,) <lb/>therefore <emph type="italics"/>Socrates<emph.end type="italics"/> well perceived his wi&longs;dom to be nothing, in <lb/>compari&longs;on of the infinite knowledg which he wanted. </s><s>But yet, <lb/>becau&longs;e there is &longs;ome knowledg found among&longs;t men, and this <lb/>not equally &longs;hared to all, <emph type="italics"/>Socrates<emph.end type="italics"/> might have a greater &longs;hare <lb/>thereof than others, and therefore verified the an&longs;wer of the <lb/><emph type="italics"/>Oracle.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg219"></margin.target><emph type="italics"/>The an&longs;wer of <lb/>the Oracle true in <lb/>judging<emph.end type="italics"/> Socrates <lb/><emph type="italics"/>the wi&longs;eft of his <lb/>time.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I think I very well under&longs;tand this particular among&longs;t <lb/>men, <emph type="italics"/>Simplicius<emph.end type="italics"/> there is a power of operating, but not equally <lb/>di&longs;pen&longs;ed to all; and it is without que&longs;tion, that the power of an <lb/>Emperor is far greater than that of a private per&longs;on; but, both <lb/>this and that are nothing in compari&longs;on of the Divine Omnipo­ <lb/>tence. </s><s>Among&longs;t men, there are &longs;ome that better under&longs;tand <lb/>Agriculture than many others; but the knowledg of planting a <lb/>Vine in a trench, what hath it to do with the knowledg of ma­ <lb/>king it to &longs;prout forth, to attract nouri&longs;hment, to &longs;elect this good <lb/>part from that other, for to make thereof leaves, another to make <lb/>&longs;prouts, another to make grapes, another to make rai&longs;ins, ano­ <lb/>ther to make the huskes of them, which are the works of mo&longs;t <lb/>wi&longs;e Nature? </s><s>This is one only particular act of the innumerable, <lb/>which Nature doth, and in it alone is di&longs;covered an infinite wi&longs;­ <lb/><arrow.to.target n="marg220"></arrow.to.target> <lb/>dom, &longs;o that Divine Wi&longs;dom may be concluded to be infinitely <lb/>infinite.</s></p><p type="margin"><s><margin.target id="marg220"></margin.target><emph type="italics"/>Divine Wi&longs;dom <lb/>infinitely infinise.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Take hereof another example. </s><s>Do we not &longs;ay that the <pb xlink:href="040/01/102.jpg" pagenum="86"/>judicious di&longs;covering of a mo&longs;t lovely <emph type="italics"/>Statua<emph.end type="italics"/> in a piece of Marble, <lb/><arrow.to.target n="marg221"></arrow.to.target> <lb/>hath &longs;ublimated the wit of <emph type="italics"/>Buonarruotti<emph.end type="italics"/> far above the vulgar wits <lb/>of other men? </s><s>And yet this work is onely the imitation of a <lb/>meer aptitude and di&longs;po&longs;ition of exteriour and &longs;uperficial mem­ <lb/>bers of an immoveable man; but what is it in compari&longs;on of a <lb/>man made by nature, compo&longs;ed of as many exteriour and inte­ <lb/>riour members, of &longs;o many mu&longs;cles, tendons, nerves, bones, <lb/>which &longs;erve to &longs;o many and &longs;undry motions? </s><s>but what &longs;hall we <lb/>&longs;ay of the &longs;en&longs;es, and of the powers of the &longs;oul, and la&longs;tly, of <lb/>the under&longs;tanding? </s><s>May we not &longs;ay, and that with rea&longs;on, that <lb/>the &longs;tructure of a Statue fals far &longs;hort of the formation of a living <lb/>man, yea more of a contemptible worm?</s></p><p type="margin"><s><margin.target id="marg221"></margin.target>Buonarruotti, <emph type="italics"/>a <lb/>&longs;tatuary of admi­ <lb/>rable ingenuity.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>And what difference think you, was there betwixt the <lb/>Dove of <emph type="italics"/>Architas,<emph.end type="italics"/> and one made by Nature?</s></p><p type="main"><s>SIMPL. </s><s>Either I am none of the&longs;e knowing men, or el&longs;e <lb/>there is a manife&longs;t contradiction in this your di&longs;cour&longs;e. </s><s>You ac­ <lb/>count under&longs;tanding among&longs;t the greate&longs;t (if you make it not the <lb/>chief of the) <emph type="italics"/>Encomiums<emph.end type="italics"/> a&longs;cribed to man made by Nature, and <lb/>a little before you &longs;aid with <emph type="italics"/>Socrates,<emph.end type="italics"/> that he had no knowledg at <lb/>all; therefore you mu&longs;t &longs;ay, that neither did Nature under&longs;tand <lb/>how to make an under&longs;tanding that under&longs;tandeth.</s></p><p type="main"><s>SALV. </s><s>You argue very cunningly, but to reply to your obje­ <lb/>ction I mu&longs;t have recour&longs;e to a Philo&longs;ophical di&longs;tinction, and &longs;ay <lb/>that the under&longs;tanding is to be taken too ways, that is <emph type="italics"/>inten&longs;ivè,<emph.end type="italics"/> or <lb/><arrow.to.target n="marg222"></arrow.to.target> <lb/><emph type="italics"/>exten&longs;ivè<emph.end type="italics"/>; and that <emph type="italics"/>exten&longs;ive,<emph.end type="italics"/> that is, as to the multitude of intel­ <lb/>ligibles, which are infinite, the under&longs;tanding of man is as no­ <lb/>thing, though he &longs;hould under&longs;tand a thou&longs;and propo&longs;itions; for <lb/>that a thou&longs;and, in re&longs;pect of infinity is but as a cypher: but taking <lb/>the under&longs;tanding <emph type="italics"/>inten&longs;ive,<emph.end type="italics"/> (in as much as that term imports) in­ <lb/>ten&longs;ively, that is, perfectly &longs;ome propo&longs;itions, I &longs;ay, that humane wi&longs;­ <lb/>dom under&longs;tandeth &longs;ome propo&longs;itions &longs;o perfectly, and is as ab&longs;o­ <lb/>lutely certain thereof, as Nature her &longs;elf; and &longs;uch are the pure <lb/>Mathematical &longs;ciences, to wit, Geometry and Arithmetick: in which <lb/>Divine Wi&longs;dom knows infinite more propo&longs;itions, becau&longs;e it knows <lb/>them all; but I believe that the knowledge of tho&longs;e few compre­ <lb/>hended by humane under&longs;tanding, equalleth the divine, as to the <lb/>certainty <emph type="italics"/>objectivè,<emph.end type="italics"/> for that it arriveth to comprehend the nece&longs;­ <lb/>&longs;ity thereof, than which there can be no greater certainty.</s></p><p type="margin"><s><margin.target id="marg222"></margin.target><emph type="italics"/>Man under&longs;tand­ <lb/>eth very well<emph.end type="italics"/> in­ <lb/>ten&longs;ivè, <emph type="italics"/>but little<emph.end type="italics"/> <lb/>exten&longs;ivè.</s></p><p type="main"><s>SIMPL. </s><s>This &longs;eemeth to me a very bold and ra&longs;h expre&longs;&longs;ion.</s></p><p type="main"><s>SALV. </s><s>The&longs;e are common notions, and far from all umbrage <lb/>of temerity, or boldne&longs;s, and detract not in the lea&longs;t from the Ma­ <lb/>je&longs;ty of divine wi&longs;dom; as it nothing dimini&longs;heth the omnipotence <lb/>thereof to &longs;ay, that God cannot make what is once done, to be un­ <lb/>done: but I doubt, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that your &longs;cruple ari&longs;eth from an o­ <lb/>pinion you have, that my words are &longs;omewhat equivocal; there­ <pb xlink:href="040/01/103.jpg" pagenum="87"/>fore the better to expre&longs;s my &longs;elf I &longs;ay, that as to the truth, of <lb/>which Mathematical demon&longs;trations give us the knowledge, it is <lb/>the &longs;ame, which the divine wi&longs;dom knoweth; but this I mu&longs;t grant <lb/>you, that the manner whereby God knoweth the infinite propo­ <lb/><arrow.to.target n="marg223"></arrow.to.target> <lb/>&longs;itions, of which we under&longs;tand &longs;ome few, is highly more excellent <lb/>than ours, which proceedeth by ratiocination, and pa&longs;&longs;eth from con­ <lb/><arrow.to.target n="marg224"></arrow.to.target> <lb/>clu&longs;ion to conclu&longs;ion, whereas his is done at one &longs;ingle thought or <lb/>intuition; and whereas we, for example, to attain the knowledg <lb/>of &longs;ome pa&longs;&longs;ion of the Circle, which hath infinite, beginning <lb/>from one of the mo&longs;t &longs;imple, and taking that for its definition, <lb/>do proceed with argumentation to another, and from that to a <lb/>third, and then to a fourth, <emph type="italics"/>&c.<emph.end type="italics"/> the Divine Wi&longs;dom, by the <lb/>apprehen&longs;ion of its e&longs;&longs;ence comprehends, without temporary raci­ <lb/>ocination, all the&longs;e infinite pa&longs;&longs;ions; which notwith&longs;tanding, are <lb/>in effect virtually compri&longs;ed in the definitions of all things; and, to <lb/><arrow.to.target n="marg225"></arrow.to.target> <lb/>conclude, as being infinite, perhaps are but one alone in their nature, <lb/>and in the Divine Mind; the which neither is wholly unknown to <lb/>humane under&longs;tanding, but onely be-clouded with thick and <lb/><arrow.to.target n="marg226"></arrow.to.target> <lb/>gro&longs;&longs;e mi&longs;ts; which come in part to be di&longs;&longs;ipated and clarified, <lb/>when we are made Ma&longs;ters of any conclu&longs;ions, firmly demon­ <lb/>&longs;trated, and &longs;o perfectly made ours, as that we can &longs;peedily run <lb/>through them; for in &longs;um, what other, is that propo&longs;ition, that <lb/>the &longs;quare of the &longs;ide &longs;ubtending the right angle in any triangle, <lb/>is equal to the &longs;quares of the other two, which include it, but <lb/>onely the Paralellograms being upon common ba&longs;es, and between <lb/>parallels equal among&longs;t them&longs;elves? </s><s>and this, la&longs;tly, is it not the <lb/>&longs;ame, as to &longs;ay that tho&longs;e two &longs;uperficies are equal, of which <lb/>equal parts applyed to equal parts, po&longs;&longs;e&longs;&longs;e equal place? </s><s>Now <lb/><arrow.to.target n="marg227"></arrow.to.target> <lb/>the&longs;e inferences, which our intellect apprehendeth with time and a <lb/>gradual motion, the Divine Wi&longs;dom, like light, penetrateth in <lb/>an in&longs;tant, which is the &longs;ame as to &longs;ay, hath them alwayes pre­ <lb/>&longs;ent: I conclude therefore, that our under&longs;tanding, both as to <lb/>the manner and the multitude of the things comprehended by us, <lb/>is infinitely &longs;urpa&longs;t by the Divine Wi&longs;dom; but yet I do not &longs;o <lb/>vilifie it, as to repute it ab&longs;olutely nothing; yea rather, when I <lb/>con&longs;ider how many and how great mi&longs;teries men have under&longs;tood, <lb/>di&longs;covered, and contrived, I very plainly know and under&longs;tand <lb/>the mind of man to be one of the works, yea one of the mo&longs;t ex­ <lb/>cellent works of God.</s></p><p type="margin"><s><margin.target id="marg223"></margin.target><emph type="italics"/>Gods manner of <lb/>knowing different <lb/>from that of men.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg224"></margin.target><emph type="italics"/>Humane under­ <lb/>&longs;tanding done by <lb/>raciocination.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg225"></margin.target><emph type="italics"/>Definitions con­ <lb/>tein virtually all <lb/>the pa&longs;&longs;ions of the <lb/>things defined.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg226"></margin.target><emph type="italics"/>Infinite Pa&longs;&longs;ions <lb/>are perhaps but <lb/>one onely.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg227"></margin.target><emph type="italics"/>The di&longs;cour&longs;es <lb/>which humane <lb/>rea&longs;on makes in a <lb/>certain time, the <lb/>Divine Wi&longs;dom re­ <lb/>&longs;olveth in a mo­ <lb/>ment; that is, hath <lb/>them alwayes pre­ <lb/>&longs;ent.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I have oft times con&longs;idered with my &longs;elf, in pur&longs;uance <lb/><arrow.to.target n="marg228"></arrow.to.target> <lb/>of that which you &longs;peak of, how great the wit of man is; and <lb/>whil'&longs;t I run thorow &longs;uch and &longs;o many admirable inventions found <lb/>out by him, as well in the Arts, as Sciences; and again reflecting <lb/>upon my own wit, &longs;o far from promi&longs;ing me the di&longs;covery of any <lb/>thing new, that I de&longs;pair of comprehending what is already di&longs;­ <pb xlink:href="040/01/104.jpg" pagenum="88"/>covered, confounded with wonder, and &longs;urpri&longs;ed with de&longs;pera­ <lb/>tion, I account my &longs;elf little le&longs;&longs;e than mi&longs;erable. </s><s>If I behold a <lb/>Statue of &longs;ome excellent Ma&longs;ter, I &longs;ay with my &longs;elf; When wilt <lb/>thou know how to chizzle away the refu&longs;e of a piece of Marble, <lb/>and di&longs;cover &longs;o lovely a figure, as lyeth hid therein? </s><s>When wilt <lb/>thou mix and &longs;pread &longs;o many different colours upon a Cloth, or <lb/>Wall, and repre&longs;ent therewith all vi&longs;ible objects, like a <emph type="italics"/>Michael <lb/>Angelo,<emph.end type="italics"/> a <emph type="italics"/>Raphaello,<emph.end type="italics"/> or a <emph type="italics"/>Tizvano<emph.end type="italics"/>? </s><s>If I behold what inventions <lb/>men have in comparting Mu&longs;ical intervals, in e&longs;tabli&longs;hing Pre­ <lb/>cepts and Rules for the management thereof with admirable de­ <lb/>light to the ear: When &longs;hall I cea&longs;e my a&longs;toni&longs;hment? </s><s>What <lb/>&longs;hall I &longs;ay of &longs;uch and &longs;o various In&longs;truments of that Art? </s><s>The <lb/>reading of excellent Poets, with what admiration doth it &longs;well <lb/>any one that attentively con&longs;idereth the invention of conceits, <lb/>and their explanation? </s><s>What &longs;hall we &longs;ay of Architecture? <lb/><arrow.to.target n="marg229"></arrow.to.target> <lb/>What of Navigation? </s><s>But, above all other &longs;tupendious inventi­ <lb/>ons, what &longs;ublimity of mind was that in him, that imagined to <lb/>him&longs;elf to find out a way to communicate his mo&longs;t &longs;ecret thoughts <lb/>to any other per&longs;on, though very far di&longs;tant from him either in <lb/>time, or place, &longs;peaking with tho&longs;e that are in the <emph type="italics"/>India's<emph.end type="italics"/>; &longs;peak­ <lb/>ing to tho&longs;e that are not yet born, nor &longs;hall be this thou&longs;and, or <lb/>ten thou&longs;and years? </s><s>and with how much facility? </s><s>but by the va­ <lb/><arrow.to.target n="marg230"></arrow.to.target> <lb/>rious collocation of ^{*} twenty little letters upon a paper? </s><s>Let this <lb/>be the Seal of all the admirable inventions of man, and the clo&longs;e <lb/>of our Di&longs;cour&longs;e for this day: For the warmer hours being pa&longs;t, <lb/>I &longs;uppo&longs;e that <emph type="italics"/>Salviatus<emph.end type="italics"/> hath a de&longs;ire to go and take the air in his <lb/>Gondelo; but too morrow we will both wait upon you, to con­ <lb/>tinue the Di&longs;cour&longs;es we have begun, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg228"></margin.target><emph type="italics"/>The wit of man <lb/>admirably acute.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg229"></margin.target><emph type="italics"/>The invention of <lb/>writing &longs;tupendious <lb/>above all others.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg230"></margin.target>* For of &longs;o many <lb/>only the Italian <lb/>Alphabet con&longs;i&longs;ts.</s></p><pb xlink:href="040/01/105.jpg"/><figure id="id.040.01.105.1.jpg" xlink:href="040/01/105/1.jpg"/><figure id="id.040.01.105.2.jpg" xlink:href="040/01/105/2.jpg"/><figure id="id.040.01.105.3.jpg" xlink:href="040/01/105/3.jpg"/><figure id="id.040.01.105.4.jpg" xlink:href="040/01/105/4.jpg"/><figure id="id.040.01.105.5.jpg" xlink:href="040/01/105/5.jpg"/><figure id="id.040.01.105.6.jpg" xlink:href="040/01/105/6.jpg"/><figure id="id.040.01.105.7.jpg" xlink:href="040/01/105/7.jpg"/><p type="caption"><s><emph type="italics"/>Place this Plate <lb/>at the end of <lb/>the first<emph.end type="italics"/><lb/>Dialogue</s></p><pb xlink:href="040/01/106.jpg"/></chap><chap> <pb xlink:href="040/01/107.jpg" pagenum="89"/><p type="head"><s>GALILÆUS <lb/>Galilæus Lyncæus, <lb/>HIS <lb/>SYSTEME <lb/>OF THE <lb/>WORLD.</s></p><p type="head"><s>The Second Dialogue.</s></p><p type="head"><s><emph type="italics"/>INTERLOCVTORS.<emph.end type="italics"/></s></p><p type="head"><s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"><s>SALV. </s><s>The ye&longs;ter-dayes diver&longs;ions which led us <lb/>out of the path of our principal di&longs;cour&longs;e, <lb/>were &longs;uch and &longs;o many, that I know not <lb/>how I can without your a&longs;&longs;i&longs;tance reco­ <lb/>ver the track in which I am to proceed.</s></p><p type="main"><s>SAGR. </s><s>I wonder not, that you, who <lb/>have your fancy charged and laden with <lb/>both what hath been, and is to be &longs;po­ <lb/>ken, do find your &longs;elf in &longs;ome confu&longs;i­ <lb/>on; but I, who as being onely an Auditor, have nothing to bur­ <lb/>then my memory withal, but &longs;uch things as I have heard, may <lb/>happily by a &longs;uccinct rehear&longs;al of them, recover the fir&longs;t thred <lb/>of our Di&longs;cour&longs;e. </s><s>As far therefore as my memory &longs;erves me, the <lb/>&longs;um of ye&longs;terdayes conferences were an examination of the Prin­ <pb xlink:href="040/01/108.jpg" pagenum="90"/>ciples of <emph type="italics"/>Ptolomy<emph.end type="italics"/> and <emph type="italics"/>Copernicus,<emph.end type="italics"/> and which of their opinions is <lb/>the more probable and rational; that, which affirmeth the &longs;ub­ <lb/>&longs;tance of the Cœle&longs;tial bodies to be ingenerable, incorruptible, un­ <lb/>alterable, impa&longs;&longs;ible, and in a word, exempt from all kind of change, <lb/>&longs;ave that of local, and therefore to be a <emph type="italics"/>fifth e&longs;&longs;ence,<emph.end type="italics"/> quite different <lb/>from this of our Elementary bodies, which are generable, corrup­ <lb/>tible, alterable, <emph type="italics"/>&c.<emph.end type="italics"/> or el&longs;e the other, which taking away &longs;uch <lb/>deformity from the parts of the World, holdeth the Earth to en­ <lb/>joy the &longs;ame perfections as the other integral bodies of the uni­ <lb/>ver&longs;e; and e&longs;teemeth it a moveable and erratick Globe, no le&longs;&longs;e <lb/>than the Moon, <emph type="italics"/>Jupiter, Venus,<emph.end type="italics"/> or any other Planet: And la&longs;tly, <lb/>maketh many particular parallels betwixt the Earth and Moon; <lb/>and more with the Moon, than with any other Planet; hap­ <lb/>ly by rea&longs;on we have greater and more certain notice of it, as <lb/>being le&longs;&longs;e di&longs;tant from us. </s><s>And having, la&longs;tly, concluded this <lb/>&longs;econd opinion to have more of probability with it than the fir&longs;t, <lb/>I &longs;hould think it be&longs;t in the &longs;ub&longs;equent di&longs;cour&longs;es to begin to exa­ <lb/>mine whether the Earth be e&longs;teemed immoveable, as it hath <lb/>been till now believed by mo&longs;t men, or el&longs;e moveable, as &longs;ome <lb/>ancient <emph type="italics"/>Philo&longs;ophers<emph.end type="italics"/> held, and others of not very rece&longs;&longs;e times, <lb/>were of opinion; and if it be moveable, to enquire of what <lb/>kind its motion may be?</s></p><p type="main"><s>SALV. </s><s>I &longs;ee already what way I am to take; but before we <lb/>offer to proceed any farther, I am to &longs;ay &longs;omething to you touch­ <lb/>ing tho&longs;e la&longs;t words which you &longs;pake, how that the opinion which <lb/>holds the Earth to be endued with the &longs;ame conditions that the <lb/>Cœle&longs;tial bodies enjoy, &longs;eems to be more true than the contra­ <lb/>ry; for that I affirmed no &longs;uch thing, nor would I have any of the <lb/>Propo&longs;itions in controver&longs;ie, be made to &longs;peak to any definitive <lb/>&longs;en&longs;e: but I onely intended to produce on either part, tho&longs;e rea­ <lb/>&longs;ons and an&longs;wers, arguments and &longs;olutions, which have been hi­ <lb/>therto thought upon by others, together with certain others, <lb/>which I have &longs;tumbled upon in my long &longs;earching thereinto, al­ <lb/>wayes remitting the deci&longs;ion thereof to the judgment of others.</s></p><p type="main"><s>SAGR. </s><s>I was unawares tran&longs;ported by my own &longs;en&longs;e of the <lb/>thing; and believing that others ought to judg as I did, I made <lb/>that conclu&longs;ion univer&longs;al, which &longs;hould have been particular; and <lb/>therefore confe&longs;&longs;e I have erred, and the rather, in that I know <lb/>not what <emph type="italics"/>Simplicius<emph.end type="italics"/> his judgment is in this particular.</s></p><p type="main"><s>SIMPL. </s><s>I mu&longs;t confe&longs;&longs;e, that I have been ruminating all this <lb/>night of what pa&longs;t ye&longs;terday, and to &longs;ay the truth, I meet there­ <lb/>in with many acute, new, aud plau&longs;ible notions; yet neverthele&longs;s, <lb/>I find my &longs;elf over-per&longs;waded by the authority of &longs;o many great <lb/><emph type="italics"/>Writers,<emph.end type="italics"/> and in particular -------<emph type="italics"/>&c.<emph.end type="italics"/> I &longs;ee you &longs;hake your <lb/>head <emph type="italics"/>Sagredus,<emph.end type="italics"/> and &longs;mile to your &longs;elf, as if I had uttered &longs;ome <lb/>great ab&longs;urdity.</s></p> <pb xlink:href="040/01/109.jpg" pagenum="91"/><p type="main"><s>SAGR. </s><s>I not onely &longs;mile, but to tell you true, am ready to <lb/>bur&longs;t with holding in my &longs;elf from laughing outright, for you <lb/>have put me in mind of a very pretty pa&longs;&longs;age, that I was a wit­ <lb/>ne&longs;&longs;e of, not many years &longs;ince, together with &longs;ome others of <lb/>my worthy friends, which I could yet name unto you.</s></p><p type="main"><s>SALV. </s><s>It would be well that you told us what it was, that &longs;o <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> may not &longs;till think that he gave you the occa&longs;ion of <lb/>laughter.</s></p><p type="main"><s>SAGR. </s><s>I am content. </s><s>I found one day, at home in his hou&longs;e, at <lb/><emph type="italics"/>Venice,<emph.end type="italics"/> a famous Phi&longs;ician, to whom &longs;ome flockt for their &longs;tudies, <lb/>and others out of curio&longs;ity, &longs;ometimes came thither to &longs;ee certain A­ <lb/>natomies di&longs;&longs;ected by the hand of a no le&longs;&longs;e learned, than careful <lb/>and experienced Anatomi&longs;t. </s><s>It chanced upon that day, when I was <lb/><arrow.to.target n="marg231"></arrow.to.target> <lb/>there, that he was in &longs;earch of the original and ri&longs;e of the Nerves, <lb/>about which there is a famous controver&longs;ie between the <emph type="italics"/>Galeni&longs;ts<emph.end type="italics"/> <lb/>and <emph type="italics"/>Peripateticks<emph.end type="italics"/>; and the Anatomi&longs;t &longs;hewing, how that the great <lb/>number of Nerves departing from the Brain, as their root, and <lb/>pa&longs;&longs;ing by the nape of the Neck, di&longs;tend them&longs;elves afterwards <lb/>along by the Back-bone, and branch them&longs;elves thorow all the <lb/>Body; and that a very &longs;mall filament, as fine as a thred went to <lb/>the Heart; he turned to a Gentleman whom he knew to be a <emph type="italics"/>Pe­ <lb/>ripatetick<emph.end type="italics"/> Philo&longs;opher, and for who&longs;e &longs;ake he had with extraor­ <lb/>dinary exactne&longs;&longs;e, di&longs;covered and proved every thing, and demand­ <lb/>ed of him, if he was at length &longs;atisfied and per&longs;waded that the origi­ <lb/>nal of the Nerves proceeded from the Brain, and not from the <lb/>Heart? </s><s>To which the Philo&longs;opher, after he had &longs;tood mu&longs;ing a <lb/><arrow.to.target n="marg232"></arrow.to.target> <lb/>while, an&longs;wered; you have made me to &longs;ee this bu&longs;ine&longs;&longs;e &longs;o <lb/>plainly and &longs;en&longs;ibly, that did not the <emph type="italics"/>Text<emph.end type="italics"/> of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> a&longs;&longs;ert the <lb/>contrary, which po&longs;itively affirmeth the Nerves to proceed from <lb/>the Heart, I &longs;hould be con&longs;trained to confe&longs;&longs;e your opinion to be <lb/>true.</s></p><p type="margin"><s><margin.target id="marg231"></margin.target><emph type="italics"/>The original of <lb/>the Nerv s. </s><s>ac­ <lb/>cording to<emph.end type="italics"/> Ari&longs;to­ <lb/>tle, <emph type="italics"/>and according <lb/>to Phi&longs;icians.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg232"></margin.target><emph type="italics"/>The ridiculus <lb/>an&longs;wer of a Philo­ <lb/>&longs;opher, determi­ <lb/>ning the original of <lb/>the Nerves.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I would have you know my Ma&longs;ters, that this contro­ <lb/>ver&longs;ie about the original of the Nerves is not yet &longs;o proved and <lb/>decided, as &longs;ome may perhaps per&longs;wade them&longs;elves.</s></p><p type="main"><s>SAGR. </s><s>Nor que&longs;tionle&longs;&longs;e ever &longs;hall it be, if it find &longs;uch like <lb/>contradictors; but that which you &longs;ay, doth not at all le&longs;&longs;en the <lb/>extravagance of the an&longs;wer of that <emph type="italics"/>Peripatetick,<emph.end type="italics"/> who again&longs;t <lb/>&longs;uch &longs;en&longs;ible experience produced not other experiments, or rea­ <lb/>&longs;ons of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> but his bare authority and pure <emph type="italics"/>ip&longs;e dixit.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had not gained &longs;o great authority, but for <lb/>the force of his Demon&longs;trations, and the profoundne&longs;&longs;e of his <lb/>arguments; but it is requi&longs;ite that we under&longs;tand him, and not <lb/>onely under&longs;tand him, but have &longs;o great familiarity with his <lb/>Books, that we form a perfect <emph type="italics"/>Idea<emph.end type="italics"/> thereof in our minds, &longs;o as <lb/>that every &longs;aying of his may be alwayes as it were, pre&longs;ent in our <pb xlink:href="040/01/110.jpg" pagenum="92"/>memory for he did not write to the vulgar, nor is he obliged to <lb/>&longs;pin out his Sillogi&longs;mes with the trivial method of di&longs;putes; nay <lb/>rather, u&longs;ing a freedome, he hath &longs;ometimes placed the proof <lb/>of one Propo&longs;ition among&longs;t Texts, which &longs;eem to treat of quite <lb/><arrow.to.target n="marg233"></arrow.to.target> <lb/>another point; and therefore it is requi&longs;ite to be ma&longs;ter of all <lb/>that va&longs;t <emph type="italics"/>Idea,<emph.end type="italics"/> and to learn how to connect this pa&longs;&longs;age with that, <lb/>and to combine this Text with another far remote from it; for it <lb/>is not to be que&longs;tioned but that he who hath thus &longs;tudied him, <lb/>knows how to gather from his Books the demon&longs;trations of every <lb/>knowable deduction, for that they contein all things.</s></p><p type="margin"><s><margin.target id="marg233"></margin.target><emph type="italics"/>Requi&longs;ites to fit <lb/>a man to philo&longs;o­ <lb/>phate well after <lb/>the manner of<emph.end type="italics"/> A­ <lb/>ri&longs;totle.</s></p><p type="main"><s>SAGR. </s><s>But good <emph type="italics"/>Simplicius,<emph.end type="italics"/> like as the things &longs;cattered here <lb/>and there in <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> give you no trouble in collecting them, <lb/>but that you per&longs;wade your &longs;elf to be able by comparing and <lb/><arrow.to.target n="marg234"></arrow.to.target> <lb/>connecting &longs;everal &longs;mall &longs;entences to extract thence the juice of <lb/>&longs;ome de&longs;ired conclu&longs;ion, &longs;o this, which you and other egregi­ <lb/>ous Philo&longs;ophers do with the Text of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> I could do by the <lb/><arrow.to.target n="marg235"></arrow.to.target> <lb/>ver&longs;es of <emph type="italics"/>Virgil,<emph.end type="italics"/> or of <emph type="italics"/>Ovid,<emph.end type="italics"/> compo&longs;ing thereof ^{*} <emph type="italics"/>Centones,<emph.end type="italics"/> and <lb/>therewith explaining all the affairs of men, and &longs;ecrets of Na­ <lb/>ture. </s><s>But what talk I of <emph type="italics"/>Virgil,<emph.end type="italics"/> or any other Poet? </s><s>I have a lit­ <lb/>tle Book much &longs;horter than <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ovid,<emph.end type="italics"/> in which are con­ <lb/>teined all the Sciences, and with very little &longs;tudy, one may gather <lb/>out of it a mo&longs;t perfect <emph type="italics"/>Idea,<emph.end type="italics"/> and this is the <emph type="italics"/>Alphabet<emph.end type="italics"/>; and there <lb/>is no doubt but that he who knows how to couple and di&longs;po&longs;e <lb/>aright this and that vowel, with tho&longs;e, or tho&longs;e other con&longs;onants, <lb/>may gather thence the infallible an&longs;wers to all doubts, and de­ <lb/>duce from them the principles of all Sciences and Arts, ju&longs;t in the <lb/>&longs;ame manner as the Painter from divers &longs;imple colours, laid &longs;eve­ <lb/>rally upon his <emph type="italics"/>Pallate,<emph.end type="italics"/> proceedeth by mixing a little of this and <lb/>a little of that, with a little of a third, to repre&longs;ent to the life <lb/>men, plants, buildings, birds, fi&longs;hes, and in a word, counterfeit­ <lb/>ing what ever object is vi&longs;ible, though there be not on the <emph type="italics"/>Pallate<emph.end type="italics"/> <lb/>all the while, either eyes, or feathers, or fins, or leaves, or &longs;tones. <lb/></s><s>Nay, farther, it is nece&longs;&longs;ary, that none of the things to be imita­ <lb/>ted, or any part of them, be actually among colours, if you <lb/>would be able therewith to repre&longs;ent all things; for &longs;hould there <lb/>be among&longs;t them <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> feathers, the&longs;e would &longs;erve to repre&longs;ent <lb/>nothing &longs;ave birds, and plumed creatures.</s></p><p type="margin"><s><margin.target id="marg234"></margin.target><emph type="italics"/>A cunning way <lb/>to gather Philo&longs;o­ <lb/>phy out of any book <lb/>what&longs;oever.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg235"></margin.target>* A word &longs;ignify­ <lb/>ing works compo­ <lb/>&longs;ed of many frag­ <lb/>ments of ver&longs;es <lb/>collected out of the <lb/>Poets.</s></p><p type="main"><s>SALV. </s><s>And there are certain Gentlemen yet living, and in health, <lb/>who were pre&longs;ent, when a Doctor, that was Profe&longs;&longs;or in a fa­ <lb/><arrow.to.target n="marg236"></arrow.to.target> <lb/>mous Academy, hearing the de&longs;cription of the <emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/> by him <lb/>not &longs;een as then, &longs;aid, that the invention was taken from <emph type="italics"/>Ari­ <lb/>&longs;totle,<emph.end type="italics"/> and cau&longs;ing his works to be fetch't, he turned to a place <lb/>where the Philo&longs;opher gives the rea&longs;on, whence it commeth, that <lb/>from the bottom of a very deep Well, one may &longs;ee the &longs;tars in <lb/>Heaven, at noon day; and, addre&longs;&longs;ing him&longs;elf to the company, <pb xlink:href="040/01/111.jpg" pagenum="93"/>&longs;ee here, &longs;aith he, the Well, which repre&longs;enteth the Tube, &longs;ee <lb/>here the gro&longs;s vapours, from whence is taken the invention of <lb/>the Cry&longs;tals, and &longs;ee here la&longs;tly the &longs;ight fortified by the pa&longs;&longs;age <lb/>of the rays through a diaphanous, but more den&longs;e and ob&longs;cure <lb/><emph type="italics"/>medium.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg236"></margin.target><emph type="italics"/>Invention of the<emph.end type="italics"/> <lb/>Tele&longs;cope <emph type="italics"/>taken <lb/>from<emph.end type="italics"/> Ari&longs;totle.</s></p><p type="main"><s>SAGR. </s><s>This is a way to comprehend all things knowable, much <lb/>like to that wherewith a piece of marble conteineth in it one, yea, <lb/>a thou&longs;and very beautiful Statua's, but the difficulty lieth in be­ <lb/>ing able to di&longs;cover them; or we may &longs;ay, that it is like to the <lb/>prophe&longs;ies of Abbot <emph type="italics"/>Joachim,<emph.end type="italics"/> or the an&longs;wers of the Heathen <lb/><emph type="italics"/>Oracles,<emph.end type="italics"/> which are not to be under&longs;tood, till after the things <lb/>fore-told are come to pa&longs;&longs;e.</s></p><p type="main"><s>SALV. </s><s>And why do you not adde the predictions of the <emph type="italics"/>Ge­ <lb/>nethliacks,<emph.end type="italics"/> which are with like cleerne&longs;&longs;e &longs;een after the event, in <lb/>their Horo&longs;copes, or, if you will, Configurations of the Heavens.</s></p><p type="main"><s>SAGR. </s><s>In this manner the Chymi&longs;ts find, being led by their <lb/><arrow.to.target n="marg237"></arrow.to.target> <lb/>melancholly humour, that all the &longs;ublime&longs;t wits of the World <lb/>have writ of nothing el&longs;e in reality, than of the way to make <lb/>Gold; but, that they might tran&longs;mit the &longs;ecret to po&longs;terity with­ <lb/>out di&longs;covering it to the vulgar, they contrived &longs;ome one way, and <lb/>&longs;ome another how to conceal the &longs;ame under &longs;everal maskes; and <lb/>it would make one merry to hear their comments upon the ancient <lb/><emph type="italics"/>Poets,<emph.end type="italics"/> finding out the important mi&longs;teries, which lie hid under <lb/>their Fables; and the &longs;ignification of the Loves of the <emph type="italics"/>Moon,<emph.end type="italics"/> <lb/>and her de&longs;cending to the Earth for <emph type="italics"/>Endimion<emph.end type="italics"/>; her di&longs;plea&longs;ure <lb/>again&longs;t <emph type="italics"/>Acteon,<emph.end type="italics"/> and what was meant by <emph type="italics"/>Jupiters<emph.end type="italics"/> turning him&longs;elf <lb/>into a &longs;howre of <emph type="italics"/>Gold<emph.end type="italics"/>; and into flames of fire; and what great <lb/>&longs;ecrets of Art are conteined in that <emph type="italics"/>Mercury<emph.end type="italics"/> the <emph type="italics"/>Interpreter<emph.end type="italics"/>; in <lb/>tho&longs;e thefts of <emph type="italics"/>Pluto<emph.end type="italics"/>; and in tho&longs;e <emph type="italics"/>Branches<emph.end type="italics"/> of <emph type="italics"/>Gold.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg237"></margin.target><emph type="italics"/>Chymi&longs;ts inter­ <lb/>pret the Eables of <lb/>the Poets to be &longs;e­ <lb/>crets for making of <lb/>Gold.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I believe, and in part know, that there want not in the <lb/>World very extravagant heads, the vanities of whom ought not to <lb/>redound to the prejudice of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> of whom my thinks you <lb/>&longs;peak &longs;ometimes with too little re&longs;pect, and the onely antiquity <lb/>and bare name that he hath acquired in the opinions of &longs;o many <lb/>famous men, &longs;hould &longs;uffice to render him honourable with all <lb/>that profe&longs;&longs;e them&longs;elves learned.</s></p><p type="main"><s>SALV. </s><s>You &longs;tate not the matter rightly, <emph type="italics"/>Simplicius<emph.end type="italics"/>; There <lb/>are &longs;ome of his followers that fear before they are in danger, <lb/>who give us occa&longs;ion, or, to &longs;ay better, would give us cau&longs;e to <lb/>e&longs;teem him le&longs;&longs;e, &longs;hould we con&longs;ent to applaud their <emph type="italics"/>Capricio's.<emph.end type="italics"/> <lb/><arrow.to.target n="marg238"></arrow.to.target> <lb/>And you, pray you tell me, are you for your part &longs;o &longs;imple, as <lb/>not to know that had <emph type="italics"/>Arictotle<emph.end type="italics"/> been pre&longs;ent, to have heard the <lb/>Doctor that would have made him Author of the <emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/> he <lb/>would have been much more di&longs;plea&longs;ed with him, than with tho&longs;e, <lb/>who laught at the Doctor and his Comments? </s><s>Do you que&longs;tion <pb xlink:href="040/01/112.jpg" pagenum="94"/>whether <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> had he but &longs;een the novelties di&longs;covered in Hea­ <lb/>ven, would not have changed his opinion, amended his Books, <lb/>and embraced the more &longs;en&longs;ible Doctrine; rejecting tho&longs;e &longs;illy <lb/>Gulls, which too &longs;crupulou&longs;ly, go about to defend what ever he <lb/>hath &longs;aid; not con&longs;idering, that if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> were &longs;uch a one as <lb/>they fancy him to them&longs;elves, he would be a man of an untracta­ <lb/>ble wit, an ob&longs;tinate mind, a barbarous &longs;oul, a &longs;tubborn will, <lb/>that accounting all men el&longs;e but as &longs;illy &longs;heep, would have his <lb/>Oracles preferred before the Sen&longs;es, Experience, and Nature her <lb/>&longs;elf? </s><s>They are the Sectators of <emph type="italics"/>Aristotle<emph.end type="italics"/> that have given him this <lb/>Authority, and not he that hath u&longs;urped or taken it upon him; <lb/>and becau&longs;e it is more ea&longs;ie for a man to &longs;culk under anothers <lb/>&longs;hield than to &longs;hew him&longs;elf openly, they tremble, and are affraid <lb/>to &longs;tir one &longs;tep from him; and rather than they will admit &longs;ome <lb/>alterations in the Heaven of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> they will impertinently de­ <lb/>ny tho&longs;e they behold in the Heaven of <emph type="italics"/>Nature.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg238"></margin.target><emph type="italics"/>Some of<emph.end type="italics"/> Ari&longs;to­ <lb/>tles <emph type="italics"/>Sectators im­ <lb/>pare the reputation <lb/>of their Ma&longs;ter, in <lb/>going about to en­ <lb/>han&longs;e it.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The&longs;e kind of Drolleries put me in mind of that Statu­ <lb/><arrow.to.target n="marg239"></arrow.to.target> <lb/>ary which having reduced a great piece of Marble to the Image of <lb/>an <emph type="italics"/>Hercules,<emph.end type="italics"/> or a thundring <emph type="italics"/>Jupiter,<emph.end type="italics"/> I know not whether, and <lb/>given it with admirable Art &longs;uch a vivacity and threatning fury, <lb/>that it moved terror in as many as beheld it; he him&longs;elf began <lb/>al&longs;o to be affraid thereof, though all its &longs;prightfulne&longs;&longs;e, and life <lb/>was his own workman&longs;hip; and his affrightment was &longs;uch, that <lb/>he had no longer the courage to affront it with his Chizzels and <lb/>Mallet.</s></p><p type="margin"><s><margin.target id="marg239"></margin.target><emph type="italics"/>A ridiculous <lb/>pa&longs;&longs;age of a certain <lb/>Statuary.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I have many times wondered how the&longs;e nice maintain­ <lb/>ers of what ever fell from <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> are not aware how great a pre­ <lb/>judice they are to his reputation and credit; and how that the <lb/>more they go about to encrea&longs;e his Authority, the more they <lb/>dimini&longs;h it; for while&longs;t I &longs;ee them ob&longs;tinate in their attempts <lb/>to maintain tho&longs;e Propo&longs;itions which I palpably di&longs;cover to <lb/>be manife&longs;tly fal&longs;e; and in their de&longs;ires to per&longs;wade me that <lb/>&longs;o to do, is the part of a Philo&longs;opher; and that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf <lb/>would do the &longs;ame, it much abates in me of the opinion that he <lb/>hath rightly philo&longs;ophated about other conclu&longs;ions, to me more <lb/>ab&longs;tru&longs;e: for if I could &longs;ee them concede and change opinion in <lb/>a manife&longs;t truth, I would believe, that in tho&longs;e in which they <lb/>&longs;hould per&longs;i&longs;t, they may have &longs;ome &longs;olid demon&longs;trations to me un­ <lb/>known, and unheard of.</s></p><p type="main"><s>SAGR. </s><s>Or when they &longs;hould be made to &longs;ee that they have ha­ <lb/>zarded too much of their own and <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>'s repuatation in con­ <lb/>fe&longs;&longs;ing, that they had not under&longs;tood this or that conclu&longs;ion found <lb/>out by &longs;ome other man; would it not be a le&longs;s evil for them to <lb/>&longs;eek for it among&longs;t his Texts, by laying many of them together, <lb/>according to the art intimated to us by <emph type="italics"/>Simplicius<emph.end type="italics"/>? </s><s>for if his <pb xlink:href="040/01/113.jpg" pagenum="95"/>works contain all things knowable, it mu&longs;t follow al&longs;o that they <lb/>may be therein di&longs;covered.</s></p><p type="main"><s>SALV. </s><s>Good <emph type="italics"/>Sagredus,<emph.end type="italics"/> make no je&longs;t of this advice, which me <lb/>thinks you rehear&longs;e in too Ironical a way; for it is not long &longs;ince <lb/>that a very eminent Philo&longs;opher having compo&longs;ed a Book <emph type="italics"/>de animà,<emph.end type="italics"/> <lb/>wherein, citing the opinion of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> about its being or not be­ <lb/>ing immortal, he alledged many Texts, (not any of tho&longs;e hereto­ <lb/>fore quoted by <emph type="italics"/>Alexander ab Alexandro<emph.end type="italics"/>: for in tho&longs;e he &longs;aid, that <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had not &longs;o much as treated of that matter, much le&longs;s de­ <lb/>termined any thing pertaining to the &longs;ame, but others) by him&longs;elf <lb/>found out in other more ab&longs;tru&longs;e places, which tended to an er­ <lb/>roneous &longs;en&longs;e: and being advi&longs;ed, that he would find it an hard <lb/>matter to get a Licence from the Inqui&longs;itors, he writ back unto <lb/><arrow.to.target n="marg240"></arrow.to.target> <lb/>his friend, that he would notwith&longs;tanding, with all expedition <lb/>procure the &longs;ame, for that if no other ob&longs;tacle &longs;hould interpo&longs;e, <lb/>he would not much &longs;cruple to change the Doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>and with other expo&longs;itions, and other Texts to maintain the con­ <lb/>trary opinion, which yet &longs;hould be al&longs;o agreeable to the &longs;en&longs;e of <lb/><emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg240"></margin.target><emph type="italics"/>A brave re&longs;olu­ <lb/>tion of a certain<emph.end type="italics"/> <lb/>Peripatetick <emph type="italics"/>Phi­ <lb/>lo&longs;opher.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Oh mo&longs;t profound Doctor, this! that can command <lb/>me that I &longs;tir not a &longs;tep from <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> but will him&longs;elf lead <lb/>him by the no&longs;e, and make him &longs;peak as he plea&longs;eth. </s><s>See how <lb/>much it importeth to learn to take <emph type="italics"/>Time<emph.end type="italics"/> by the <emph type="italics"/>Fore-top.<emph.end type="italics"/> Nor <lb/>is it &longs;ea&longs;onable to have to do with <emph type="italics"/>Hercules,<emph.end type="italics"/> whil'&longs;t he is en­ <lb/>raged, and among&longs;t the Furies, but when he is telling merry tales <lb/>among&longs;t the <emph type="italics"/>Meonion Damo&longs;els.<emph.end type="italics"/> Ah, unheard of &longs;ordidne&longs;&longs;e of <lb/><arrow.to.target n="marg241"></arrow.to.target> <lb/>&longs;ervile &longs;ouls! to make them&longs;elves willing &longs;laves to other mens opi­ <lb/>nions; to receive them for inviolable Decrees, to engage them­ <lb/>&longs;elves to &longs;eem &longs;atisfied and convinced by arguments, of &longs;uch effi­ <lb/>cacy, and &longs;o manife&longs;tly concludent, that they them&longs;elves can­ <lb/>not certainly re&longs;olve whether they were really writ to that pur­ <lb/>po&longs;e, or &longs;erve to prove that a&longs;&longs;umption in hand, or the contrary. <lb/></s><s>But, which is a greater madne&longs;&longs;e, they are at variance among&longs;t <lb/>them&longs;elves, whether the Author him&longs;elf hath held the affirmative <lb/>part, or the negative. </s><s>What is this, but to make an Oracle of a <lb/>Log, and to run to that for an&longs;wers, to fear that, to reverence <lb/>and adore that?</s></p><p type="margin"><s><margin.target id="marg241"></margin.target><emph type="italics"/>The &longs;ervile &longs;pi­ <lb/>rit of &longs;ome of<emph.end type="italics"/> Ari­ <lb/>&longs;totles <emph type="italics"/>followers.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>But in ca&longs;e we &longs;hould recede from <emph type="italics"/>Aristotle,<emph.end type="italics"/> who have <lb/>we to be our Guid in Philo&longs;ophy? </s><s>Name you &longs;ome Author.</s></p><p type="main"><s>SALV. </s><s>We need a Guid in unknown and uncouth wayes, but <lb/>in champion places, and open plains, the blind only &longs;tand in need <lb/>of a Leader; and for &longs;uch, it is better that they &longs;tay at home. <lb/></s><s>But he that hath eyes in his head, and in his mind, him &longs;hould <lb/>a man choo&longs;e for his Guid. </s><s>Yet mi&longs;take me not, thinking that I <lb/><arrow.to.target n="marg242"></arrow.to.target> <lb/>&longs;peak this, for that I am again&longs;t hearing of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; for on the <pb xlink:href="040/01/114.jpg" pagenum="96"/>contrary, I commend the reading, and diligently &longs;tudying of him; <lb/>and onely blame the &longs;ervile giving ones &longs;elf up a &longs;lave unto him, <lb/>&longs;o, as blindly to &longs;ub&longs;cribe to what ever he delivers, and without <lb/>&longs;earch of any farther rea&longs;on thereof, to receive the &longs;ame for an in­ <lb/>violable decree. </s><s>Which is an abu&longs;e, that carrieth with it ano­ <lb/>ther great inconvenience, to wit, that others will no longer take <lb/>pains to under&longs;tand the validity of his Demon&longs;trations. </s><s>And <lb/>what is more &longs;hameful, than in the midde&longs;t of publique di&longs;putes, <lb/>while&longs;t one per&longs;on is treating of demon&longs;trable conclu&longs;ions, to <lb/>hear aother interpo&longs;e with a pa&longs;&longs;age of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and not &longs;el­ <lb/>dome writ to quite another purpo&longs;e, and with that to &longs;top the <lb/>mouth of his opponent? </s><s>But if you will continue to &longs;tudy in this <lb/>manner, I would have you lay a&longs;ide the name of Philo&longs;ophers; <lb/><arrow.to.target n="marg243"></arrow.to.target> <lb/>and call your &longs;elves either Hi&longs;torians or Doctors of Memory, for <lb/>it is not &longs;it, that tho&longs;e who never philo&longs;ophate, &longs;hould u&longs;urp <lb/>the honourable title of Philo&longs;ophers. </s><s>But it is be&longs;t for us to re­ <lb/>turn to &longs;hore, and not lanch farther into a boundle&longs;&longs;e Gulph, out <lb/>of which we &longs;hall not be able to get before night. </s><s>Therefore <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> come either with arguments and demon&longs;trations of <lb/>your own, or of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and bring us no more Texts and na­ <lb/><arrow.to.target n="marg244"></arrow.to.target> <lb/>ked authorities, for our di&longs;putes are about the Sen&longs;ible World, <lb/>and not one of Paper. </s><s>And fora&longs;much as in our di&longs;cour&longs;es ye&longs;ter­ <lb/>day, we retrein'd the Earth from darkne&longs;&longs;e, and expo&longs;ed it to the <lb/>open skie, &longs;hewing, that the attempt to enumerate it among&longs;t <lb/>tho&longs;e which we call Cœle&longs;tial bodies, was not a po&longs;ition &longs;o foil'd, <lb/>and vanqui&longs;h't, as that it had no life left in it; it followeth next, <lb/>that we proceed to examine what probability there is for holding <lb/>of it fixt, and wholly immoveable, <emph type="italics"/>&longs;cilicet<emph.end type="italics"/> as to its entire Globe, <lb/>what likelyhood there is for making it moveable with &longs;ome motion, <lb/>and of what kind that may be. </s><s>And fora&longs;much as in this &longs;ame <lb/>que&longs;tion I am ambiguous, and <emph type="italics"/>Simplicius<emph.end type="italics"/> is re&longs;olute, as likewi&longs;e <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> for the opinion of its immobility, he &longs;hall one by one <lb/>produce the arguments in favour of their opinion, and I will al­ <lb/>ledge the an&longs;wers and rea&longs;ons on the contrary part; and next <emph type="italics"/>Sa­ <lb/>gredus<emph.end type="italics"/> &longs;hall tell us his thoughts, and to which &longs;ide he finds him­ <lb/>&longs;elf inclined.</s></p><p type="margin"><s><margin.target id="marg242"></margin.target><emph type="italics"/>Too clo&longs;e adhe­ <lb/>ring to<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>is <lb/>blameable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg243"></margin.target><emph type="italics"/>It is not ju&longs;t, that <lb/>tho&longs;e who never <lb/>philo&longs;ophate, &longs;hould <lb/>u&longs;urp the title of <lb/>Philo&longs;ophers.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg244"></margin.target><emph type="italics"/>The Sen&longs;ible <lb/>World.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. Content; provided alwayes that I may re&longs;erve the li­ <lb/>berty to my &longs;elf of alledging what pure natural rea&longs;on &longs;hall &longs;ome­ <lb/>times dictate to me.</s></p><p type="main"><s>SALV. </s><s>Nay more, it is that which I particularly beg of you; <lb/>for, among&longs;t the more ea&longs;ie, and, to &longs;o &longs;peak, material con&longs;idera­ <lb/>tions, I believe there are but few of them that have been omit­ <lb/>ted by Writers, &longs;o that onely &longs;ome of the more &longs;ubtle, and re­ <lb/>mote can be de&longs;ired, or wanting; and to inve&longs;tigate the&longs;e, what <lb/>other ingenuity can be more &longs;it than that of the mo&longs;t acute and <lb/>piercing wit of <emph type="italics"/>Sagredus<emph.end type="italics"/>?</s></p> <pb xlink:href="040/01/115.jpg" pagenum="97"/><p type="main"><s>SAGR. </s><s>I am what ever plea&longs;eth <emph type="italics"/>Salviatus,<emph.end type="italics"/> but I pray you, <lb/>let us not &longs;ally out into another kind of digre&longs;&longs;ion complemental; <lb/>for at this time I am a Philo&longs;opher, and in the Schools, not in the <lb/>Court.</s></p><p type="main"><s>SALV. </s><s>Let our contemplation begin therefore with this con&longs;i­ <lb/>deration, that what&longs;oever motion may be a&longs;cribed to the Earth, <lb/>it is nece&longs;&longs;ary that it be to us, (as inhabitants upon it, and con&longs;e­ <lb/>quently partakers of the &longs;ame) altogether imperceptible, and as if <lb/>it were not at all, &longs;o long as we have regard onely to terre&longs;trial <lb/>things; but yet it is on the contrary, as nece&longs;&longs;ary that the &longs;ame <lb/><arrow.to.target n="marg245"></arrow.to.target> <lb/>motion do &longs;eem common to all other bodies, and vi&longs;ible ob­ <lb/>jects, that being &longs;eparated from the Earth, participate not of the <lb/>&longs;ame. </s><s>So that the true method to find whether any kind of motion <lb/>may be a&longs;cribed to the Earth, and that found, to know what it <lb/>is, is to con&longs;ider and ob&longs;erve if in bodies &longs;eparated from the <lb/>Earth, one may di&longs;cover any appearance of motion, which e­ <lb/><arrow.to.target n="marg246"></arrow.to.target> <lb/>qually &longs;uiteth to all the re&longs;t; for a motion that is onely &longs;een, <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> <lb/>in the <emph type="italics"/>Moon,<emph.end type="italics"/> and that hath nothing to do with <emph type="italics"/>Venus<emph.end type="italics"/> or <emph type="italics"/>Jupiter,<emph.end type="italics"/> <lb/>or any other Stars, cannot any way belong to the Earth, or to <lb/>any other &longs;ave the Moon alone. </s><s>Now there is a mo&longs;t general and <lb/>grand motion above all others, and it is that by which the Sun, <lb/><arrow.to.target n="marg247"></arrow.to.target> <lb/>the Moon, the other Planets, and the Fixed Stars, and in a word, <lb/>the whole Univer&longs;e, the Earth onely excepted, appeareth in our <lb/>thinking to move from the Ea&longs;t towards the We&longs;t, in the &longs;pace of <lb/>twenty four hours; and this, as to this fir&longs;t appearance, hath no <lb/>ob&longs;tacle to hinder it, that it may not belong to the Earth alone, <lb/>as well as to all the World be&longs;ides, the Earth excepted; for the <lb/>&longs;ame a&longs;pects will appear in the one po&longs;ition, as in the other. <lb/></s><s>Hence it is that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy,<emph.end type="italics"/> as having hit upon this con­ <lb/><arrow.to.target n="marg248"></arrow.to.target> <lb/>&longs;ideration, in going about to prove the Earth to be immoveable, <lb/>argue not again&longs;t any other than this <emph type="italics"/>Diurnal<emph.end type="italics"/> Motion; &longs;ave onely <lb/>that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hinteth &longs;omething in ob&longs;cure terms again&longs;t another <lb/>Motion a&longs;cribed to it by an <emph type="italics"/>Ancient,<emph.end type="italics"/> of which we &longs;hall &longs;peak in <lb/>its place.</s></p><p type="margin"><s><margin.target id="marg245"></margin.target><emph type="italics"/>The motions of <lb/>the Earth are im­ <lb/>perceptible to its <lb/>inhabitants.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg246"></margin.target><emph type="italics"/>The Earth can <lb/>have no other mo­ <lb/>tions, than tho&longs;e <lb/>which to us appear <lb/>commune to all the <lb/>rest of the Vni­ <lb/>ver&longs;e, the Earth <lb/>excepted.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg247"></margin.target><emph type="italics"/>The Diurnal Mo­ <lb/>tion, &longs;eemeth com­ <lb/>mune to all the V­ <lb/>niver&longs;e, &longs;ave onely <lb/>the Earth excepted.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg248"></margin.target>Ari&longs;totle <emph type="italics"/>and<emph.end type="italics"/> <lb/>Ptolomy <emph type="italics"/>argue a­ <lb/>gain&longs;t the Diur­ <lb/>nal Motion attri­ <lb/>buted to the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I very well perceive the nece&longs;&longs;ity of your illation: but <lb/>I meet with a doubt which I know not how to free my &longs;elf from, <lb/>and this it is, That <emph type="italics"/>Copernicus<emph.end type="italics"/> a&longs;&longs;igning to the Earth another mo­ <lb/>tion be&longs;ide the Diurnal, which, according to the rule even now laid <lb/>down, ought to be to us, as to appearance, imperceptible in the <lb/>Earth, but vi&longs;ible in all the re&longs;t of the World; me thinks I may <lb/>nece&longs;&longs;arily infer, either that he hath manife&longs;tly erred in a&longs;&longs;igning <lb/>the Earth a motion, to which there appears not a general corre­ <lb/>&longs;pondence in Heaven; or el&longs;e that if there be &longs;uch a congruity <lb/>therein, <emph type="italics"/>Ptolomy<emph.end type="italics"/> on the other hand hath been deficient in not con­ <lb/>futing this, as he hath done the other.</s></p> <pb xlink:href="040/01/116.jpg" pagenum="98"/><p type="main"><s>SALV. </s><s>You have good cau&longs;e for your doubt: and when we <lb/>come to treat of the other Motion, you &longs;hall &longs;ee how far <emph type="italics"/>Coper­ <lb/>nicus<emph.end type="italics"/> excelled <emph type="italics"/>Ptolomey<emph.end type="italics"/> in clearne&longs;s and &longs;ublimity of wit, in that <lb/>he &longs;aw what the other did not, I mean the admirable harmony <lb/>wherein that Motion agreed with all the other Cœle&longs;tial Bodies. <lb/></s><s>But for the pre&longs;ent we will &longs;u&longs;pend this particular, and return to <lb/>our fir&longs;t con&longs;ideration; touching which I will proceed to propo&longs;e <lb/>(begining with things more general) tho&longs;e rea&longs;ons which &longs;eem to <lb/>favour the mobility of the Earth, and then wait the an&longs;wers which <lb/><arrow.to.target n="marg249"></arrow.to.target> <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;hall make thereto. </s><s>And fir&longs;t, if we con&longs;ider onely <lb/>the immen&longs;e magnitude of the Starry Sphere, compared to the <lb/>&longs;malne&longs;s of the Terre&longs;trial Globe, contained therein &longs;o many mil­ <lb/>lions of times; and moreover weigh the velocity of the motion <lb/>which mu&longs;t in a day and night make an entire revolution thereof, <lb/>I cannot per&longs;wade my &longs;elf, that there is any man who believes it <lb/>more rea&longs;onable and credible, that the Cœle&longs;tial Sphere turneth <lb/>round, and the Terre&longs;trial Globe &longs;tands &longs;till.</s></p><p type="margin"><s><margin.target id="marg249"></margin.target><emph type="italics"/>Why the diurnal <lb/>motion more pro­ <lb/>bably &longs;hould belong <lb/>to the Earth, than <lb/>to the re&longs;t of the <lb/>Vniver&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>If from the univer&longs;ality of effects, which may in nature <lb/>have dependence upon &longs;uch like motions, there &longs;hould indifferent­ <lb/>ly follow all the &longs;ame con&longs;equences to an hair, a&longs;well in one <emph type="italics"/>Hypo­ <lb/>the&longs;is<emph.end type="italics"/> as in the other; yet I for my part, as to my fir&longs;t and general <lb/>apprehen&longs;ion, would e&longs;teem, that he which &longs;hould hold it more ra­ <lb/>tional to make the whole Univer&longs;e move, and thereby to &longs;alve the <lb/>Earths mobility, is more unrea&longs;onable than he that being got to <lb/>the top of your Turret, &longs;hould de&longs;ire, to the end onely that he <lb/>might behold the City, and the Fields about it, that the whole <lb/>Country might turn round, that &longs;o he might not be put to the <lb/>trouble to &longs;tir his head. </s><s>And yet doubtle&longs;s the advantages would <lb/>be many and great which the <emph type="italics"/>Copernican Hypothe&longs;is<emph.end type="italics"/> is attended <lb/>with, above tho&longs;e of the <emph type="italics"/>Ptolomaique,<emph.end type="italics"/> which in my opinion re­ <lb/>&longs;embleth, nay &longs;urpa&longs;&longs;eth that other folly; &longs;o that all this makes <lb/>me think that far more probable than this. </s><s>But haply <emph type="italics"/>Ari&longs;totle, <lb/>Ptolomey,<emph.end type="italics"/> and <emph type="italics"/>Simplicius<emph.end type="italics"/> may find the advantages of their Sy­ <lb/>&longs;teme, which they would do well to communicate to us al&longs;o, if <lb/>any &longs;uch there be; or el&longs;e declare to me, that there neither are or <lb/>can be any &longs;uch things.</s></p><p type="main"><s>SALV. </s><s>For my part, as I have not been able, as much as I have <lb/>thought upon it, to find any diver&longs;ity therein; &longs;o I think I have <lb/>found, that no &longs;uch diver&longs;ity can be in them: in &longs;o much that I <lb/><arrow.to.target n="marg250"></arrow.to.target> <lb/>e&longs;teem it to no purpo&longs;e to &longs;eek farther after it. </s><s>Therefore ob­ <lb/>&longs;erve: Motion is &longs;o far Motion, and as Motion operateth, by how <lb/>far it hath relation to things which want Motion: but in tho&longs;e <lb/>things which all equally partake thereof it hath nothing to do, and <lb/>is as if it never were. </s><s>And thus the Merchandi&longs;es with which a <lb/>&longs;hip is laden, &longs;o far move, by how far leaving <emph type="italics"/>London,<emph.end type="italics"/> they pa&longs;s <pb xlink:href="040/01/117.jpg" pagenum="99"/>by <emph type="italics"/>France, Spain, Italy,<emph.end type="italics"/> and &longs;ail to <emph type="italics"/>Aleppo,<emph.end type="italics"/> which <emph type="italics"/>London, France, <lb/>Spain &c.<emph.end type="italics"/> &longs;tand &longs;till, not moving with the &longs;hip: but as to the <lb/>Che&longs;ts, Bales and other Parcels, wherewith the &longs;hip is &longs;tow'd and <lb/>and laden, and in re&longs;pect of the &longs;hip it &longs;elf, the Motion from <emph type="italics"/>Lon­ <lb/>don<emph.end type="italics"/> to <emph type="italics"/>Syria<emph.end type="italics"/> is as much as nothing; and nothing-altereth the re­ <lb/>lation which is between them: and this, becau&longs;e it is common to <lb/>all, and is participated by all alike: and of the Cargo which is in <lb/>the &longs;hip, if a Bale were romag'd from a Che&longs;t but one inch onely, <lb/>this alone would be in that Cargo, a greater Motion in re&longs;pect of <lb/>the Che&longs;t, than the whole Voyage of above three thou&longs;and miles, <lb/>made by them as they were &longs;tived together.</s></p><p type="margin"><s><margin.target id="marg250"></margin.target><emph type="italics"/>Motion, as to the <lb/>things that equally <lb/>move thereby, is as <lb/>of it never were, & <lb/>&longs;o far operates as it <lb/>hath relation to <lb/>things deprived of <lb/>motion.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>This Doctrine is good, &longs;ound, and altogether <emph type="italics"/>Peri­ <lb/>patetick.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I hold it to be much more antient: and &longs;u&longs;pect that <emph type="italics"/>A-<emph.end type="italics"/> <lb/><arrow.to.target n="marg251"></arrow.to.target> <lb/><emph type="italics"/>ri&longs;totle<emph.end type="italics"/> in receiving it from &longs;ome good School, did not fully under­ <lb/>&longs;tand it, and that therefore, having delivered it with &longs;ome altera­ <lb/>tion, it hath been an occa&longs;ion of confu&longs;ion among&longs;t tho&longs;e, who <lb/>would defend whatever he &longs;aith. </s><s>And when he writ, that what­ <lb/>&longs;oever moveth, doth move upon &longs;omething immoveable, I &longs;uppo&longs;e <lb/>that he equivocated, and meant, that whatever moveth, moveth <lb/>in re&longs;pect to &longs;omething immoveable; which propo&longs;ition admitteth <lb/>no doubt, and the other many.</s></p><p type="margin"><s><margin.target id="marg251"></margin.target><emph type="italics"/>A propo&longs;ition ta­ <lb/>ken by<emph.end type="italics"/> Ari&longs;totle <lb/><emph type="italics"/>from the Antients, <lb/>but &longs;omewhat al­ <lb/>tered by him.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Pray you make no digre&longs;&longs;ion, but proceed in the di&longs;­ <lb/>&longs;ertation you began.</s></p><p type="main"><s>SALV. </s><s>It being therefore manife&longs;t, that the motion which is <lb/><arrow.to.target n="marg252"></arrow.to.target> <lb/>common to many moveables, is idle, and as it were, null as to the <lb/>relation of tho&longs;e moveables between them&longs;elves, becau&longs;e that a­ <lb/>mong them&longs;elves they have made no change: and that it is ope­ <lb/>rative onely in the relation that tho&longs;e moveables have to other <lb/>things, which want that motion, among which the habitude is <lb/>changed: and we having divided the Univer&longs;e into two parts, one <lb/>of which is nece&longs;&longs;arily moveable, and the other immoveable; for <lb/>the obtaining of what&longs;oever may depend upon, or be required <lb/>from &longs;uch a motion, it may as well be done by making the Earth <lb/>alone, as by making all the re&longs;t of the World to move: for that <lb/>the operation of &longs;uch a motion con&longs;i&longs;ts in nothing el&longs;e, &longs;ave in <lb/>the relation or habitude which is between the Cœle&longs;tial Bodies, <lb/>and the Earth, the which relation is all that is changed. </s><s>Now if <lb/>for the obtaining of the &longs;ame effect <emph type="italics"/>ad unguem,<emph.end type="italics"/> it be all one whe­ <lb/>ther the Earth alone moveth, the re&longs;t of the Univer&longs;e &longs;tanding <lb/>&longs;till; or that, the Earth onely &longs;tanding &longs;till, the whole Univer&longs;e <lb/><arrow.to.target n="marg253"></arrow.to.target> <lb/>moveth with one and the &longs;ame motion; who would believe, that <lb/>Nature (which by common con&longs;ent, doth not that by many things, <lb/>which may be done by few) hath cho&longs;en to make an innumerable <lb/>number of mo&longs;t va&longs;t bodies move, and that with an unconceivable <pb xlink:href="040/01/118.jpg" pagenum="100"/>velocity, to perform that, which might be done by the moderate <lb/>motion of one alone about its own Centre?</s></p><p type="margin"><s><margin.target id="marg252"></margin.target><emph type="italics"/>The fir&longs;t di&longs;cour&longs;e <lb/>to prove that the <lb/>diurnal motion be­ <lb/>longs to the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg253"></margin.target><emph type="italics"/>Nature never <lb/>doth that by many <lb/>things, which may <lb/>be done by a few.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I do not well under&longs;tand, how this grand motion &longs;ig­ <lb/>ni&longs;ieth nothing as to the Sun, as to the Moon, as to the other Pla­ <lb/>nets, and as to the innumerable multitude of fixed &longs;tars: or why <lb/>you &longs;hould &longs;ay that it is to no purpo&longs;e for the Sun to pa&longs;s from one <lb/>Meridian to another; to ri&longs;e above this Horizon, to &longs;et beneath <lb/>that other; to make it one while day, another while night: the <lb/>like variations are made by the Moon, the other Planets, and the <lb/>fixed &longs;tars them&longs;elves.</s></p><p type="main"><s>SALV. </s><s>All the&longs;e alterations in&longs;tanced by you, are nothing, &longs;ave <lb/>onely in relation to the Earth: and that this is true, do but i­ <lb/><arrow.to.target n="marg254"></arrow.to.target> <lb/>magine the Earth to move, and there will be no &longs;uch thing in the <lb/>World as the ri&longs;ing or &longs;etting of the Sun or Moon, nor Horizons, <lb/>nor Meridians, nor days, nor nights; nor, in a word, will &longs;uch a <lb/>motion cau&longs;e any mutation between the Moon and Sun, or any <lb/>other &longs;tar what&longs;oever, whether fixed or erratick; but all the&longs;e <lb/>changes have relation to the Earth: which all do yet in &longs;um <lb/>import no other than as if the Sun &longs;hould &longs;hew it &longs;elf now to <lb/><emph type="italics"/>China,<emph.end type="italics"/> anon to <emph type="italics"/>Per&longs;ia,<emph.end type="italics"/> then to <emph type="italics"/>Egypt, Greece, France, Spain, A­ <lb/>merica, &c.<emph.end type="italics"/> and the like holdeth in the Moon, and the re&longs;t of the <lb/>Cœle&longs;tial Bodies: which &longs;elf &longs;ame effect falls out exactly in the <lb/>&longs;ame manner, if, without troubling &longs;o great a part of the Univer&longs;e, <lb/><arrow.to.target n="marg255"></arrow.to.target> <lb/>the Terre&longs;trial Globe be made to revolve in it &longs;elf. </s><s>But we will <lb/>augment the difficulty by the addition of this other, which is a <lb/>very great one, namely, that if you will a&longs;cribe this <emph type="italics"/>Great<emph.end type="italics"/> Motion to <lb/>Heaven, you mu&longs;t of nece&longs;&longs;ity make it contrary to the particular <lb/>motion of all the Orbs of the Planets, each of which without <lb/>controver&longs;ie hath its peculiar motion from the We&longs;t towards the <lb/>Ea&longs;t, and this but very ea&longs;ie and moderate: and then you make <lb/>them to be hurried to the contrary part, <emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> from Ea&longs;t to We&longs;t, <lb/>by this mo&longs;t furious diurnal motion: whereas, on the contrary, <lb/>making the Earth to move in it &longs;elf, the contrariety of motions is <lb/>taken away, and the onely motion from We&longs;t to Ea&longs;t is accom­ <lb/>modated to all appearances, and exactly &longs;atisfieth every <emph type="italics"/>Phœno­ <lb/>menon.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg254"></margin.target><emph type="italics"/>The diurnal mo­ <lb/>tion cau&longs;eth no <lb/>mutation among&longs;t <lb/>the Cœle&longs;tial Bo­ <lb/>dies, but all chan­ <lb/>ges have relation <lb/>to the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg255"></margin.target><emph type="italics"/>A &longs;ccond con­ <lb/>firmation that the <lb/>diurnal motion be­ <lb/>longs to the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>As to the contrariety of Motions it would import lit­ <lb/><arrow.to.target n="marg256"></arrow.to.target> <lb/>tle, for <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> demon&longs;trateth, that circular motions, are not con­ <lb/>trary to one another; and that theirs cannot be truly called con­ <lb/>trariety.</s></p><p type="margin"><s><margin.target id="marg256"></margin.target><emph type="italics"/>Circular moti­ <lb/>ons are not contra­ <lb/>ry, according to<emph.end type="italics"/> <lb/>Ari&longs;totle.</s></p><p type="main"><s>SALV. </s><s>Doth <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> demon&longs;trate this, or doth he not rather <lb/>barely affirm it, as &longs;erving to &longs;ome certain de&longs;ign of his? </s><s>If con­ <lb/>traries be tho&longs;e things, that de&longs;troy one another, as he him&longs;elf <lb/>affirmeth, I do not &longs;ee how two moveables that encounter each <lb/>other in a circular line, &longs;hould le&longs;&longs;e prejudice one another, than if <lb/>they interfered in a right line.</s></p> <pb xlink:href="040/01/119.jpg" pagenum="101"/><p type="main"><s>SAGR. </s><s>Hold a little, I pray you. </s><s>Tell me <emph type="italics"/>Simplicius,<emph.end type="italics"/> when <lb/>two Knights encounter each other, tilting in open field, or when <lb/>two whole Squadrons, or two Fleets at Sea, make up to grapple, <lb/>and are broken and &longs;unk, do you call the&longs;e encounters contrary to <lb/>one another?</s></p><p type="main"><s>SIMPL. Yes, we &longs;ay they are contrary.</s></p><p type="main"><s>SAGR. </s><s>How then, is there no contrariety in circular motions. <lb/></s><s>The&longs;e motions, being made upon the &longs;uper&longs;icies of the Earth or <lb/>Water, which are, as you know, &longs;pherical, come to be circular. <lb/></s><s>Can you tell, <emph type="italics"/>Simplicius,<emph.end type="italics"/> which tho&longs;e circular motions be, that <lb/>are not contrary to each other? </s><s>They are (if I mi&longs;take not) tho&longs;e <lb/>of two circles, which touching one another without, one thereof <lb/>being turn'd round, naturally maketh the other move the contra­ <lb/>ry ^{*} way; but if one of them &longs;hall be within the other, it is im­ <lb/><arrow.to.target n="marg257"></arrow.to.target> <lb/>po&longs;&longs;ible that their motion being made towards different points, <lb/>they &longs;hould not ju&longs;tle one another.</s></p><p type="margin"><s><margin.target id="marg257"></margin.target>As you &longs;ee in a <lb/>Mill, wherein the <lb/>implicated cogs &longs;et <lb/>the wheels on mo­ <lb/>ving.</s></p><p type="main"><s>SALV. </s><s>But be they contrary, or not contrary, the&longs;e are but <lb/>alterations of words; and I know, that upon the matter, it would <lb/>be far more proper and agreeable with Nature, if we could &longs;alve <lb/>all with one motion onely, than to introduce two that are (if you <lb/>will not call them contrary) oppo&longs;ite; yet do I not cen&longs;ure this <lb/>introduction (of contrary motions) as impo&longs;&longs;ible; nor pretend I <lb/>from the denial thereof, to inferre a nece&longs;&longs;ary Demon&longs;tration, <lb/>but onely a greater probability, of the other. </s><s>A third rea&longs;on <lb/><arrow.to.target n="marg258"></arrow.to.target> <lb/>which maketh the <emph type="italics"/>Ptolomaique Hypothe&longs;is<emph.end type="italics"/> le&longs;&longs;e probable is, that it <lb/>mo&longs;t unrea&longs;onably confoundeth the order, which we a&longs;&longs;uredly <lb/>&longs;ee to be among&longs;t tho&longs;e Cœle&longs;tial Bodies, the circumgyration of <lb/>which is not que&longs;tionable, but mo&longs;t certain. </s><s>And that Order is, <lb/><arrow.to.target n="marg259"></arrow.to.target> <lb/>that according as an Orb is greater, it fini&longs;heth its revolution in a <lb/>longer time, and the le&longs;&longs;er, in &longs;horter. </s><s>And thus <emph type="italics"/>Saturn<emph.end type="italics"/> de&longs;cri­ <lb/>bing a greater Circle than all the other Planets, compleateth the <lb/>&longs;ame in thirty yeares: <emph type="italics"/>Jupiter<emph.end type="italics"/> fini&longs;heth his; that is le&longs;&longs;e, in <lb/>twelve years: <emph type="italics"/>Mars<emph.end type="italics"/> in two: The Moon runneth thorow hers, &longs;o <lb/>much le&longs;&longs;e than the re&longs;t, in a Moneth onely. </s><s>Nor do we le&longs;&longs;e <lb/>&longs;en&longs;ibly &longs;ee that of the <emph type="italics"/>Medicean Stars,<emph.end type="italics"/> which is neare&longs;t to <emph type="italics"/>Ju-<emph.end type="italics"/> <lb/><arrow.to.target n="marg260"></arrow.to.target> <lb/><emph type="italics"/>piter,<emph.end type="italics"/> to make its revolution in a very &longs;hort time, that is, in four <lb/>and forty hours, or thereabouts, the next to that in three dayes and <lb/>an half, the third in &longs;even dayes, and the mo&longs;t remote in &longs;ixteen. <lb/></s><s>And this rate holdeth well enough, nor will it at all alter, while&longs;t <lb/>we a&longs;&longs;ign the motion of 24 hours to the Terre&longs;trial Globe, for it <lb/>to move round its own center in that time; but if you would have <lb/>the Earth immoveable, it is nece&longs;&longs;ary, that when you have pa&longs;t <lb/>from the &longs;hort period of the Moon, to the others &longs;ucce&longs;&longs;ively <lb/>bigger, until you come to that of <emph type="italics"/>Mars<emph.end type="italics"/> in two years, and from <lb/>thence to that of the bigger Sphere of <emph type="italics"/>Jupiter<emph.end type="italics"/> in twelve years, and <pb xlink:href="040/01/120.jpg" pagenum="102"/>from this to the other yet bigger of <emph type="italics"/>Saturn,<emph.end type="italics"/> who&longs;e period is of <lb/>thirty years, it is nece&longs;&longs;ary, I &longs;ay, that you pa&longs;&longs;e to another <lb/>Sphere incomparably greater &longs;till than that, and make this to ac­ <lb/><arrow.to.target n="marg261"></arrow.to.target> <lb/>compli&longs;h an entire revolution in twenty four hours. </s><s>And this yet is <lb/>the lea&longs;t di&longs;order that can follow. </s><s>For if any one &longs;hould pa&longs;&longs;e <lb/>from the Sphere of <emph type="italics"/>Saturn<emph.end type="italics"/> to the Starry Orb, and make it &longs;o <lb/>much bigger than that of <emph type="italics"/>Saturn,<emph.end type="italics"/> as proportion would require, in <lb/>re&longs;pect of its very &longs;low motion, of many thou&longs;ands of years, then <lb/>it mu&longs;t needs be a <emph type="italics"/>Salt<emph.end type="italics"/> much more ab&longs;urd, to skip from this to <lb/>another bigger, and to make it convertible in twenty four hours. <lb/></s><s>But the motion of the Earth being granted, the order of the pe­ <lb/>riods will be exactly ob&longs;erved, and from the very &longs;low Sphere of <lb/><emph type="italics"/>Saturn,<emph.end type="italics"/> we come to the fixed Stars, which are wholly immovea­ <lb/><arrow.to.target n="marg262"></arrow.to.target> <lb/>ble, and &longs;o avoid a fourth difficulty, which we mu&longs;t of nece&longs;&longs;ity ad­ <lb/>mit, if the Starry Sphere be &longs;uppo&longs;ed moveable, and that is the <lb/><arrow.to.target n="marg263"></arrow.to.target> <lb/>immen&longs;e di&longs;parity between the motions of tho&longs;e &longs;tars them&longs;elves; <lb/>of which &longs;ome would come to move mo&longs;t &longs;wiftly in mo&longs;t va&longs;t cir­ <lb/>cles, others mo&longs;t &longs;lowly in circles very &longs;mall, according as tho&longs;e <lb/>or the&longs;e &longs;hould be found nearer, or more remote from the Poles; <lb/>which &longs;till is accompanied with an inconvenience, as well becau&longs;e <lb/>we &longs;ee tho&longs;e, of who&longs;e motion there is no que&longs;tion to be made, <lb/>to move all in very immen&longs;e circles; as al&longs;o, becau&longs;e it &longs;eems to <lb/>be an act done with no good con&longs;ideration, to con&longs;titute bodies, <lb/>that are de&longs;igned to move circularly, at immen&longs;e di&longs;tances from <lb/>the centre, and afterwards to make them move in very &longs;mall cir­ <lb/>cles. </s><s>And not onely the magnitudes of the circles, and con&longs;e­ <lb/>quently the velocity of the motions of the&longs;e Stars, &longs;hall be mo&longs;t <lb/><arrow.to.target n="marg264"></arrow.to.target> <lb/>different from the circles and motions of tho&longs;e others, but <lb/>(which &longs;hall be the fifth inconvenience) the &longs;elf-&longs;ame Stars <lb/>&longs;hall &longs;ucce&longs;&longs;ively vary its circles and velocities: For that <lb/><arrow.to.target n="marg265"></arrow.to.target> <lb/>tho&longs;e, which two thou&longs;and years &longs;ince were in the Equinoctial, <lb/>and con&longs;equently did with their motion de&longs;cribe very va&longs;t cir­ <lb/>cles, being in our dayes many degrees di&longs;tant from thence, mu&longs;t <lb/>of nece&longs;&longs;ity become more &longs;low of motion, and be reduced to <lb/>move in le&longs;&longs;er circles, and it is not altogether impo&longs;&longs;ible but that <lb/>a time may come, in which &longs;ome of them which in aforetime had <lb/>continually moved, &longs;hall be reduced by uniting with the Pole, to <lb/>a &longs;tate of re&longs;t, and then after &longs;ome time of ce&longs;&longs;ation, &longs;hall return <lb/>to their motion again; whereas the other Stars, touching who&longs;e <lb/>motion none &longs;tand in doubt, do all de&longs;cribe, as hath been &longs;aid, <lb/>the great circle of their Orb, and in that maintain them&longs;elves <lb/>without any variation. </s><s>The ab&longs;urdity is farther enlarged (which <lb/><arrow.to.target n="marg266"></arrow.to.target> <lb/>let be the &longs;ixth inconvenience) to him that more &longs;eriou&longs;ly exami­ <lb/>neth the thing, in that no thought can comprehend what ought to <lb/>be the &longs;olidity of that immen&longs;e Sphere, who&longs;e depth &longs;o &longs;tedfa&longs;tly <pb xlink:href="040/01/121.jpg" pagenum="103"/>holdeth fa&longs;t &longs;uch a multitude of Stars, which without ever chang­ <lb/>ing fite among them&longs;elves, are with &longs;o much concord carried a­ <lb/>bout, with &longs;o great di&longs;parity of motions. </s><s>Or el&longs;e, &longs;uppo&longs;ing the <lb/>Heavens to be fluid, as we are with more rea&longs;on to believe, &longs;o <lb/>as that every Star wandereth to and fro in it, by wayes of its <lb/>own, what rules &longs;hall regulate their motions, and to what pur­ <lb/>po&longs;e, &longs;o, as that being beheld from the Earth, they appear as if <lb/>they were made by one onely Sphere? </s><s>It is my opinion, that they <lb/>might &longs;o much more ea&longs;ily do that, and in a more commodious <lb/>manner, by being con&longs;tituted immoveable, than by being made <lb/>errant, by how much more facile it is to number the quarries in the <lb/>Pavement of a <emph type="italics"/>Piazza,<emph.end type="italics"/> than the rout of boyes which run up and <lb/>down upon them. </s><s>And la&longs;tly, which is the &longs;eventh in&longs;tance, if <lb/><arrow.to.target n="marg267"></arrow.to.target> <lb/>we atribute the Diurnal Motion to the highe&longs;t Heaven, it mu&longs;t be <lb/>con&longs;tituted of &longs;uch a force and efficacy, as to carry along with <lb/>it the innumerable multitude of fixed Stars, Bodies all of va&longs;t <lb/>magnitude, and far bigger than the Earth; and moreover all the <lb/>Spheres of the Planets; notwith&longs;tanding that both the&longs;e and tho&longs;e <lb/>of their own nature move the contrary way. </s><s>And be&longs;ides all this, <lb/>it mu&longs;t be granted, that al&longs;o the Element of Fire, and the great­ <lb/>er part of the Air, are likewi&longs;e forcibly hurried along with the <lb/>re&longs;t, and that the &longs;ole little Globe of the Earth pertinaciou&longs;ly <lb/>&longs;tands &longs;till, and unmoved again&longs;t &longs;uch an impul&longs;e; a thing, which <lb/>in my thinking, is very difficult; nor can I &longs;ee how the Earth, a <lb/>pendent body, and equilibrated upon its centre, expo&longs;ed indif­ <lb/><arrow.to.target n="marg268"></arrow.to.target> <lb/>ferently to either motion or re&longs;t, and environed with a liquid <emph type="italics"/>am­ <lb/>bient,<emph.end type="italics"/> &longs;hould not yield al&longs;o as the re&longs;t, and be carried about. <lb/></s><s>But we find none of the&longs;e ob&longs;tacles in making the Earth to move; <lb/>a &longs;mall body, and in&longs;en&longs;ible, compared to the Univer&longs;e, and <lb/>therefore unable to offer it any violence.</s></p><p type="margin"><s><margin.target id="marg258"></margin.target><emph type="italics"/>A third confir­ <lb/>mation of the &longs;ame <lb/>Doctrine.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg259"></margin.target><emph type="italics"/>The greater Orbs <lb/>make their conver­ <lb/>&longs;ions in greater <lb/>times.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg260"></margin.target><emph type="italics"/>The times of the<emph.end type="italics"/> <lb/>Medicean <emph type="italics"/>Planets <lb/>conver&longs;ions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg261"></margin.target><emph type="italics"/>The motion of<emph.end type="italics"/> <lb/>24 <emph type="italics"/>hours a&longs;cribed <lb/>to the highe&longs;t <lb/>Sphere di&longs;orders <lb/>the period of the <lb/>inferiour.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg262"></margin.target><emph type="italics"/>The fourth Con­ <lb/>firmation.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg263"></margin.target><emph type="italics"/>Great di&longs;parity <lb/>among&longs;t the moti­ <lb/>ons of the particu­ <lb/>lar fixed &longs;tars, if <lb/>their Sphere be <lb/>moveable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg264"></margin.target><emph type="italics"/>The fifth Con­ <lb/>firmation.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg265"></margin.target><emph type="italics"/>The motions of <lb/>the fixed &longs;tars <lb/>would accelerate <lb/>and grow &longs;low in <lb/>divers times, if the <lb/>&longs;tarry Sphere were <lb/>moueable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg266"></margin.target><emph type="italics"/>The &longs;ixth Con­ <lb/>firmatiox.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg267"></margin.target><emph type="italics"/>The Seventh Con­ <lb/>firmation.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg268"></margin.target><emph type="italics"/>The Earth a <lb/>pendent Body, and <lb/>equilibrated in a <lb/>fluid<emph.end type="italics"/> Medium <lb/><emph type="italics"/>&longs;eems unable to <lb/>re&longs;i&longs;t the rapture <lb/>of the Diurnal <lb/>Motion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I find my fancy di&longs;turbed with certain conjectures &longs;o con­ <lb/>fu&longs;edly &longs;prung from your later di&longs;cour&longs;es; that, if I would be ena­ <lb/>bled to apply my &longs;elf with atention to what followeth, I mu&longs;t of ne­ <lb/>ce&longs;&longs;ity attempt whether I can better methodize them, and gather <lb/>thence their true con&longs;truction, if haply any can be made of them; <lb/>and peradventure, the proceeding by interrogations may help me <lb/>the more ea&longs;ily to expre&longs;&longs;e my &longs;elf. </s><s>Therefore I demand fir&longs;t of <emph type="italics"/>Sim­ <lb/>plicius,<emph.end type="italics"/> whether he believeth, that divers motions may natural­ <lb/>ly agree to one and the &longs;ame moveable body, or el&longs;e that it be <lb/>requi&longs;ite its natural and proper motion be onely one.</s></p><p type="main"><s>SIMPL. </s><s>To one &longs;ingle moveable, there can naturally agree <lb/><arrow.to.target n="marg269"></arrow.to.target> <lb/>but one &longs;ole motion, and no more; the re&longs;t all happen acciden­ <lb/>tally and by participation; like as to him that walketh upon the <lb/>Deck of a Ship, his proper motion is that of his walk, his motion <lb/>by participation that which carrieth him to his Port, whither he <pb xlink:href="040/01/122.jpg" pagenum="104"/>would never with his walking have arrived, if the Ship with its <lb/>motion had not wafted him thither.</s></p><p type="margin"><s><margin.target id="marg269"></margin.target><emph type="italics"/>A &longs;ingle move­ <lb/>able hath but onely <lb/>one natural moti­ <lb/>on, and all the <lb/>re&longs;t are by partici­ <lb/>pation.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Tell me &longs;econdly. </s><s>That motion, which is communi­ <lb/>cated to any moveable by participation, while&longs;t it moveth by it <lb/>&longs;elf, with another motion different from the participated, is it <lb/>nece&longs;&longs;ary, that it do re&longs;ide in &longs;ome certain &longs;ubject by it &longs;elf, or <lb/>el&longs;e can it &longs;ub&longs;i&longs;t in nature alone, without other &longs;upport.</s></p><p type="main"><s>SIMPL. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> giveth you an an&longs;wer to all the&longs;e que&longs;tions, <lb/><arrow.to.target n="marg270"></arrow.to.target> <lb/>and tels you, that as of one &longs;ole moveable the motion is but one; <lb/>&longs;o of one &longs;ole motion the moveable is but one; and con&longs;equent­ <lb/>ly, that without the inherence in its &longs;ubject, no motion can ei­ <lb/>ther &longs;ub&longs;i&longs;t, or be imagined.</s></p><p type="margin"><s><margin.target id="marg270"></margin.target><emph type="italics"/>Motion cannot <lb/>be made without <lb/>its moveable &longs;ub­ <lb/>ject.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I would have you tell me in the third place, whether <lb/>you beblieve that the Moon and the other Planets and Cœle&longs;tial <lb/>bodies, have their proper motions, and what they are.</s></p><p type="main"><s>SIMPL. </s><s>They have &longs;o, and they be tho&longs;e according to which <lb/>they run through the Zodiack, the Moon in a Moneth, the Sun <lb/>in a Year, <emph type="italics"/>Mars<emph.end type="italics"/> in two, the Starry Sphere in tho&longs;e &longs;o many thou­ <lb/>&longs;and. </s><s>And the&longs;e are their proper, or natural motions.</s></p><p type="main"><s>SAGR. </s><s>But that motion wherewith I &longs;ee the fixed Stars, and <lb/>with them all the Planets go unitedly from Ea&longs;t to We&longs;t, and re­ <lb/>turn round to the Ea&longs;t again in twenty four hours, how doth it <lb/>agree with them?</s></p><p type="main"><s>SIMPL. </s><s>It &longs;uiteth with them by participation.</s></p><p type="main"><s>SAGR. </s><s>This then re&longs;ides not in them, and not re&longs;iding in <lb/>them, nor being able to &longs;ub&longs;i&longs;t without &longs;ome &longs;ubject in which it <lb/>is re&longs;ident, it mu&longs;t of force be the proper and natural motion of <lb/>&longs;ome other Sphere.</s></p><p type="main"><s>SIMPL. </s><s>For this purpo&longs;e A&longs;tronomers, and Philo&longs;ophers have <lb/>found another high Sphere, above all the re&longs;t, without Stars, to <lb/>which Natural agreeth the Diurnal Motion; and this they call <lb/>the <emph type="italics"/>Primum mobile<emph.end type="italics"/>; the which carrieth along with it all the in­ <lb/>feriour Spheres, contributing and imparting its motion to <lb/>them.</s></p><p type="main"><s>SAGR. </s><s>But when, without introducing other Spheres unknown <lb/>and hugely va&longs;t, without other motions or communicated raptures, <lb/>with leaving to each Sphere its &longs;ole and &longs;imple motion, without <lb/>intermixing contrary motions, but making all turn one way, as <lb/>it is nece&longs;&longs;ary that they do, depending all upon one &longs;ole principle, <lb/>all things proceed orderly, and corre&longs;pond with mo&longs;t perfect har­ <lb/>mony, why do we reject this <emph type="italics"/>Phœnomenon,<emph.end type="italics"/> and give our a&longs;&longs;ent to <lb/>tho&longs;e prodigious and laborious conditions?</s></p><p type="main"><s>SIMPL. </s><s>The difficulty lyeth in finding out this &longs;o natural and <lb/>expeditious way.</s></p> <pb xlink:href="040/01/123.jpg" pagenum="105"/><p type="main"><s>SAGR. </s><s>In my judgment this is found. </s><s>Make the Earth the <lb/><emph type="italics"/>Primum mobile,<emph.end type="italics"/> that is, make it turn round its own <emph type="italics"/>axis<emph.end type="italics"/> in twenty <lb/>four hours, and towards the &longs;ame point with all the other Spheres; <lb/>and without participating this &longs;ame motion to any other Planet or <lb/>Star, all &longs;hall have their ri&longs;ings, &longs;ettings, and in a word, all their <lb/>other appearances.</s></p><p type="main"><s>SIMPL. </s><s>The bu&longs;ine&longs;s is, to be able to make the Earth move <lb/>without athou&longs;and inconveniences.</s></p><p type="main"><s>SALV. </s><s>All the inconveniences &longs;hall be removed as fa&longs;t as you <lb/>propound them: and the things &longs;poken hitherto are onely the <lb/>primary and more general inducements which give us to believe <lb/>that the diurnal conver&longs;ion may not altogether without probabi­ <lb/>lity be applyed to the Earth, rather than to all the re&longs;t of the U­ <lb/>niver&longs;e: the which inducements I impo&longs;e not upon you as invio­ <lb/>lable Axioms, but as hints, which carry with them &longs;omewhat of <lb/>likelihood. </s><s>And in regard I know very well, that one &longs;ole ex­ <lb/><arrow.to.target n="marg271"></arrow.to.target> <lb/>periment, or concludent demon&longs;tration, produced on the contrary <lb/>part, &longs;ufficeth to batter to the ground the&longs;e and a thou&longs;and other <lb/>probable Arguments; therefore it is not fit to &longs;tay here, but proceed <lb/>forwards and hear what <emph type="italics"/>Simplicius<emph.end type="italics"/> an&longs;wereth, and what greater <lb/>probabilities, or &longs;tronger arguments he alledgeth on the contrary.</s></p><p type="margin"><s><margin.target id="marg271"></margin.target><emph type="italics"/>One &longs;ingle ex­ <lb/>periment, or &longs;ound <lb/>demon&longs;tration bat­ <lb/>tereth down all ar­ <lb/>guments meerly <lb/>probable.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I will fir&longs;t &longs;ay &longs;omething in general upon all the&longs;e con­ <lb/>&longs;iderations together, and then I will de&longs;cend to &longs;ome particulars. <lb/></s><s>It &longs;eems that you univer&longs;ally bottom all you &longs;ay upon the greater <lb/>&longs;implicity and facility of producing the &longs;ame effects, whil&longs;t you <lb/>hold, that as to the cau&longs;ing of them, the motion of the Earth a­ <lb/>lone, &longs;erveth <emph type="italics"/>as well<emph.end type="italics"/> as that of all the re&longs;t of the World, the Earth <lb/>deducted: but as to the operations, you e&longs;teem that much ea&longs;ier <lb/>than this. </s><s>To which I reply, that I am al&longs;o of the &longs;ame opinion, <lb/>&longs;o long as I regard my own not onely finite, but feeble power; <lb/>but having a re&longs;pect to the &longs;trength of the <emph type="italics"/>Mover,<emph.end type="italics"/> which is in­ <lb/>finite, its no le&longs;&longs;e ea&longs;ie to move the Univer&longs;e, than the Earth, <lb/>yea than a &longs;traw. </s><s>And if his power be infinite, why &longs;hould he not <lb/><arrow.to.target n="marg272"></arrow.to.target> <lb/>rather exerci&longs;e a greater part thereof than a le&longs;&longs;e? </s><s>Therefore, <lb/>I hold that your di&longs;cour&longs;e in general is not convincing.</s></p><p type="margin"><s><margin.target id="marg272"></margin.target><emph type="italics"/>Of an infinite <lb/>power one would <lb/>think a greater <lb/>part &longs;hould rather <lb/>be imploy'd than a <lb/>le&longs;&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>If I had at any time &longs;aid, that the Univer&longs;e moved not <lb/>for want of power in the <emph type="italics"/>Mover,<emph.end type="italics"/> I &longs;hould have erred, and your <lb/>reproof would have been &longs;ea&longs;onable; and I grant you, that to <lb/>an infinite power, it is as ea&longs;ie to move an hundred thou&longs;and, as <lb/>one. </s><s>But that which I did &longs;ay, concerns not the Mover, but one­ <lb/>ly hath re&longs;pect to the Moveables; and in them, not onely to <lb/>their re&longs;i&longs;tance, which doubtle&longs;&longs;e is le&longs;&longs;er in the Earth, than in <lb/>the Univer&longs;e; but to the many other particulars, but even now <lb/>con&longs;idered. </s><s>As to what you &longs;ay in the next place, that of an in­ <lb/>finite power it is better to exerci&longs;e a great part than a &longs;mall: I an­ <pb xlink:href="040/01/124.jpg" pagenum="106"/>&longs;wer, that of infinite one part is not greater than another, &longs;ince <lb/><arrow.to.target n="marg273"></arrow.to.target> <lb/>both are infinite; nor can it be &longs;aid, that of the infinite number, <lb/>an hundred thou&longs;and is a greater part than two, though that be <lb/>fifty thou&longs;and times greater than this; and if to the moving of <lb/>the Univer&longs;e there be required a finite power, though very great <lb/>in compari&longs;on of that which &longs;ufficeth to move the Earth onely; <lb/>yet is there not implied therein a greater part of the infinite power, <lb/>nor is that part le&longs;&longs;e infinite which remaineth unimploy'd. </s><s>So that <lb/>to apply unto a particular effect, a little more, or a little le&longs;&longs;e <lb/>power, importeth nothing; be&longs;ides that the operation of &longs;uch <lb/>vertue, hath not for its bound or end the Diurnal Motion onely; <lb/>but there are &longs;everal other motions in the World, which we <lb/>know of, and many others there may be, that are to us unknown. <lb/></s><s>Therefore if we re&longs;pect the Moveables, and granting it as out of <lb/>que&longs;tion, that it is a &longs;horter and ea&longs;ier way to move the Earth, <lb/>than the Univer&longs;e; and moreover, having an eye to the &longs;o many <lb/>other abreviations, and facilities that onely this way are to be ob­ <lb/>tained, an infallible Maxime of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> which he teacheth us, <lb/>that, <emph type="italics"/>fru&longs;tra fit per plura, quod pote&longs;t fieri per pauciora,<emph.end type="italics"/> ren­ <lb/>dereth it more probable that the Diurnal Motion belongs to the <lb/>Earth alone, than to the Univer&longs;e, the Earth &longs;ubducted.</s></p><p type="margin"><s><margin.target id="marg273"></margin.target><emph type="italics"/>Of infinity one <lb/>part is no bigger <lb/>than auother, al­ <lb/>though they are <lb/>comparatively un­ <lb/>equal.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>In reciting that Axiom, you have omitted a &longs;mall <lb/>clau&longs;e, which importeth as much as all the re&longs;t, e&longs;pecially in our <lb/>ca&longs;e, that is to &longs;ay, the words <emph type="italics"/>æquè bene.<emph.end type="italics"/> It is requi&longs;ite therefore <lb/>to examine whether this <emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> doth <emph type="italics"/>equally well<emph.end type="italics"/> &longs;atisfie in all <lb/>particulars, as the other.</s></p><p type="main"><s>SALV. </s><s>The knowledg whether both the&longs;e po&longs;itions do <emph type="italics"/>æquè <lb/>bene,<emph.end type="italics"/> &longs;atisfie, may be comprehended from the particular exami­ <lb/>nation of the appearances which they are to &longs;atisfie; for hitherto <lb/>we have di&longs;cour&longs;ed, and will continue to argue <emph type="italics"/>ex hypothe&longs;i,<emph.end type="italics"/> <lb/>namely, &longs;uppo&longs;ing, that as to the &longs;atisfaction of the appearances, <lb/><arrow.to.target n="marg274"></arrow.to.target> <lb/>both the a&longs;&longs;umptions are equally accomodated. </s><s>As to the clau&longs;e <lb/>which you &longs;ay was omitted by me, I have more rea&longs;on to &longs;u&longs;pect <lb/>that it was &longs;uperfluou&longs;ly in&longs;erted by you. </s><s>For the expre&longs;&longs;ion <emph type="italics"/>æquè <lb/>bene,<emph.end type="italics"/> is a relative that nece&longs;&longs;arily requireth two terms at lea&longs;t, <lb/>for a thing cannot have relation to its &longs;elf, nor do we &longs;ay, <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> <lb/>re&longs;t to be <emph type="italics"/>equally good,<emph.end type="italics"/> as re&longs;t. </s><s>And becau&longs;e, when we &longs;ay, <emph type="italics"/>that <lb/>is done in vain by many means, which may be done with fewer,<emph.end type="italics"/> <lb/>we mean, that that which is to be done, ought to be the &longs;ame <lb/>thing, not two different ones; and becau&longs;e the &longs;ame thing can­ <lb/>not be &longs;aid to be done as well as its &longs;elf; therefore, the addition <lb/>of the Phra&longs;e <emph type="italics"/>æquè bene<emph.end type="italics"/> is &longs;uperfluous, and a relation, that hath <lb/>but one term onely.</s></p><p type="margin"><s><margin.target id="marg274"></margin.target><emph type="italics"/>In the Axiome<emph.end type="italics"/> <lb/>Fru&longs;tra fit per plu­ <lb/>ra, &c. <emph type="italics"/>the addi­ <lb/>tion of<emph.end type="italics"/> æque benè, <lb/><emph type="italics"/>is &longs;uperfluous.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Unle&longs;&longs;e you will have the &longs;ame befal us, as did ye&longs;ter­ <lb/>day, let us return to our matter in hand; and let <emph type="italics"/>Simplicius<emph.end type="italics"/> be­ <pb xlink:href="040/01/125.jpg" pagenum="107"/>gin to produce tho&longs;e difficulties that &longs;eem in his opinion, to thwart <lb/>this new di&longs;po&longs;ition of the World.</s></p><p type="main"><s>SIMPL. </s><s>That di&longs;po&longs;ition is not new, but very old, and that <lb/>you may &longs;ee it is &longs;o, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> confuteth it; and his confutations <lb/>are the&longs;e: “Fir&longs;t if the Earth moveth either in it felf about its <lb/><arrow.to.target n="marg275"></arrow.to.target> <lb/>own Centre, or in an Excentrick Circle, it is nece&longs;&longs;ary that that <lb/>&longs;ame motion be violent; for it is not its natural motion, for <lb/>if it were, each of its parts would partake thereof; but each <lb/>of them moveth in a right line towards its Centre. </s><s>It being <lb/>therefore violent and pteternatural, it could never be perpetu­ <lb/>al: But the order of the World is perpetual. </s><s>Therefore, <emph type="italics"/>&c.<emph.end type="italics"/> <lb/>Secondly, all the other moveables that move circularly, &longs;eem <lb/>to ^{*} &longs;tay behind, and to move with more than one motion, the <lb/><arrow.to.target n="marg276"></arrow.to.target> <lb/><emph type="italics"/>Primum Mobile<emph.end type="italics"/> excepted: Whence it would be nece&longs;&longs;ary that <lb/>the Earth al&longs;o do move with two motions; and if that &longs;hould <lb/>be &longs;o, it would inevitably follow, that mutations &longs;hould be <lb/>made in the Fixed Stars, the which none do perceive; nay <lb/>without any variation, the &longs;ame Stars alwayes ri&longs;e from towards <lb/>the &longs;ame places, and in the &longs;ame places do &longs;et. </s><s>Thirdly, the mo­ <lb/>tion of the parts is the &longs;ame with that of the whole, and natural­ <lb/>ly tendeth towards the Centre of the Univer&longs;e; and for the &longs;ame <lb/>cau&longs;e re&longs;t, being arrived thither. </s><s>He thereupon moves the que­ <lb/>&longs;tion whether the motion of the parts hath a tendency to the <lb/>centre of the Univer&longs;e, or to the centre of the Earth; and conclu­ <lb/>deth that it goeth by proper in&longs;tinct to the centre of the Univer&longs;e, <lb/>and <emph type="italics"/>per accidence<emph.end type="italics"/> to that of the Earth; of which point we largely <lb/>di&longs;cour&longs;ed ye&longs;terday. </s><s>He la&longs;tly confirmeth the &longs;ame with a fourth <lb/>argument taken from the experiment of grave bodies, which fal­ <lb/>ing from on high, de&longs;cend perpendicularly unto the Earths&longs;urface; <lb/>and in the &longs;ame manner <emph type="italics"/>Projections<emph.end type="italics"/> &longs;hot perpendicularly upwards, <lb/>do by the &longs;ame lines return perpendicularly down again, though <lb/>they were &longs;hot to a very great height. </s><s>All which arguments nece&longs;­ <lb/>&longs;arily prove their motion to be towards the Centre of the Earth, <lb/>which without moving at all waits for, and receiveth them. </s><s>He <lb/>intimateth in the la&longs;t place that the A&longs;tronomers alledg other <lb/>rea&longs;ons in confirmation of the &longs;ame conclu&longs;ions, I mean of the <lb/>Earths being in the Centre of the Univer&longs;e, and immoveable; <lb/>and in&longs;tanceth onely in one of them, to wit, that all the <emph type="italics"/>Phæ­ <lb/>nomena<emph.end type="italics"/> or appearances that are &longs;een in the motions of the Stars, <lb/>perfectly agree with the po&longs;ition of the Earth in the Centre; <lb/>which would not be &longs;o, were the Earth &longs;eated otherwi&longs;e. <lb/></s><s>The re&longs;t produced by <emph type="italics"/>Ptolomy<emph.end type="italics"/> and the other A&longs;tronomers, I can <lb/>give you now if you plea&longs;e, or after you have &longs;poken what you <lb/>have to &longs;ay in an&longs;wer to the&longs;e of <emph type="italics"/>Ari&longs;totle.”<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg275"></margin.target>Ari&longs;totles <emph type="italics"/>Ar­ <lb/>guments for the <lb/>Earths quie&longs;&longs;ence.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg276"></margin.target>* <emph type="italics"/>Re&longs;tino indietzo,<emph.end type="italics"/> <lb/>which is meant <lb/>here of that moti­ <lb/>on which a bowl <lb/>makes when its <lb/>born by its by as to <lb/>one &longs;ide or other, <lb/>and &longs;o hindered in <lb/>its direct motion.</s></p><p type="main"><s>SALV. </s><s>The arguments which are brought upon this occa&longs;ion <pb xlink:href="040/01/126.jpg" pagenum="108"/>are of two kinds: &longs;ome have re&longs;pect to the accidents Terre&longs;trial, <lb/><arrow.to.target n="marg277"></arrow.to.target> <lb/>without any relation to the Stars, and others are taken from the <lb/><emph type="italics"/>Phænomena<emph.end type="italics"/> and ob&longs;ervations of things Cœle&longs;tial. </s><s>The arguments <lb/>of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> are for the mo&longs;t part taken from things neer at hand, <lb/>and he leaveth the others to <emph type="italics"/>A&longs;tronomers<emph.end type="italics"/>; and therefore it is the <lb/>be&longs;t way, if you like of it, to examine the&longs;e taken from experi­ <lb/>ments touching the Earth, and then proceed to tho&longs;e of the other <lb/>kind. </s><s>And becau&longs;e <emph type="italics"/>Ptolomy, Tycho,<emph.end type="italics"/> and the other <emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> <lb/><arrow.to.target n="marg278"></arrow.to.target> <lb/>and <emph type="italics"/>Philo&longs;ophers,<emph.end type="italics"/> be&longs;ides the arguments of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> by them a&longs;&longs;u­ <lb/>med, confirmed, and made good, do produce certain others; we <lb/>will put them all together, that &longs;o we may not an&longs;wer twice to <lb/>the &longs;ame, or the like objections. </s><s>Therefore <emph type="italics"/>Simplicius,<emph.end type="italics"/> choo&longs;e <lb/>whether you will recite them your &longs;elf, or cau&longs;e me to ea&longs;e you of <lb/>this task, for I am ready to &longs;erve you.</s></p><p type="margin"><s><margin.target id="marg277"></margin.target><emph type="italics"/>Two kindes of <lb/>Arguments tou­ <lb/>ching the Earths <lb/>motion or rest.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg278"></margin.target><emph type="italics"/>Arguments of<emph.end type="italics"/> <lb/>Ptolomy <emph type="italics"/>and<emph.end type="italics"/> Ty­ <lb/>cho, <emph type="italics"/>and other per­ <lb/>&longs;ons, over and a­ <lb/>bove tho&longs;e of<emph.end type="italics"/> Ari­ <lb/>&longs;totle.</s></p><p type="main"><s>SIMPL. </s><s>It is better that you quote them, becau&longs;e, as having <lb/>taken more pains in the &longs;tudy of them, you can produce them with <lb/>more readine&longs;&longs;e, and in greater number. <lb/><arrow.to.target n="marg279"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg279"></margin.target><emph type="italics"/>The fir&longs;t argu­ <lb/>ment taken from <lb/>grave bodies fal­ <lb/>ling from on high <lb/>to the ground.<emph.end type="italics"/></s></p><p type="main"><s>SALV. All, for the &longs;tronge&longs;t rea&longs;on, alledge that of grave bo­ <lb/>dies, which falling downwards from on high, move by a right line, <lb/>that is perpendicular to the &longs;urface of the Earth, an argument <lb/>which is held undeniably to prove that the Earth is immoveable: <lb/>for in ca&longs;e it &longs;hould have the diurnal motion, a Tower, from the <lb/>top of which a &longs;tone is let fall, being carried along by the conver­ <lb/>&longs;ion of the Earth, in the time that the &longs;tone &longs;pends in falling, would <lb/>be tran&longs;ported many hundred yards Ea&longs;tward, and &longs;o far di&longs;tant <lb/>from the Towers foot would the &longs;tone come to ground. </s><s>The <lb/>which effect they back with another experiment; to wit, by let­</s></p><p type="main"><s><arrow.to.target n="marg280"></arrow.to.target> <lb/>ting a bullet of lead fall from the round top of a Ship, that lieth at <lb/>anchor, and ob&longs;erving the mark it makes where it lights, which they <lb/>find to be neer the ^{*} partners of the Ma&longs;t; but if the &longs;ame bullet <lb/><arrow.to.target n="marg281"></arrow.to.target> <lb/>be let fall from the &longs;ame place when the &longs;hip is under &longs;ail, it &longs;hall <lb/>light as far from the former place, as the &longs;hip hath run in the time <lb/>of the leads de&longs;cent; and this for no other rea&longs;on, than becau&longs;e <lb/>the natural motion of the ball being at liberty is by a right line to­ <lb/><arrow.to.target n="marg282"></arrow.to.target> <lb/>wards the centre of the Earth. </s><s>They forti&longs;ie this argument with <lb/>the experiment of a projection &longs;hot on high at a very great di­ <lb/>&longs;tance; as for example, a ball &longs;ent out of a Cannon, erected per­ <lb/>pendicular to the horizon, the which &longs;pendeth &longs;o much time in a&longs;­ <lb/>cending and falling, that in our parallel the Cannon and we both <lb/>&longs;hould be carried by the Earth many miles towards the Ea&longs;t, &longs;o <lb/>that the ball in its return could never come neer the Peece, but <lb/><arrow.to.target n="marg283"></arrow.to.target> <lb/>would fall as far We&longs;t, as the Earth had run Ea&longs;t. </s><s>They againe <lb/>adde a third, and very evident experiment, <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> that &longs;hooting a <lb/>bullet point blank (or as Gunners &longs;ay, neither above nor under me­ <lb/>tal) out of a Culverin towards the Ea&longs;t, and afterwards another, <pb xlink:href="040/01/127.jpg" pagenum="109"/>with the &longs;ame charge, and at the &longs;ame elevation or di&longs;port towards <lb/>the We&longs;t, the range towards the We&longs;t &longs;hould be very much grea­ <lb/>ter then the other towards the Ea&longs;t: for that whil'&longs;t the ball goeth <lb/>We&longs;tward, and the Peece is carried along by the Earth Ea&longs;tward, <lb/>the ball will fall from the Peece as far di&longs;tant as is the aggregate of <lb/>the two motions, one made by it &longs;elf towards the We&longs;t, and the <lb/>other by the Peece carried about by the Earth towards the Ea&longs;t; <lb/>and on the contrary, from the range of the ball &longs;hot Ea&longs;tward you <lb/>are to &longs;ub&longs;tract the &longs;pace the Peece moved, being carried after it. <lb/></s><s>Now &longs;uppo&longs;e, for example, that the range of the ball &longs;hot We&longs;t <lb/>were five miles, and that the Earth in the &longs;ame parallel and in the <lb/>time of the Bals ranging &longs;hould remove three miles, the Ball in this <lb/>ca&longs;e would fall eight miles di&longs;tant from the Culverin, namely, its <lb/>own five We&longs;tward, and the Culverins three miles Ea&longs;tward: but <lb/>the range of the &longs;hot towards the Ea&longs;t would be but two miles <lb/>long, for &longs;o much is the remainder, after you have &longs;ub&longs;tracted <lb/>from the five miles of the range, the three miles which the Peece <lb/>had moved towards the &longs;ame part. </s><s>But experience &longs;heweth the <lb/>Ranges to be equal, therefore the Culverin, and con&longs;equently the <lb/>Earth are immoveable. </s><s>And the &longs;tability of the Earth is no le&longs;fe <lb/><arrow.to.target n="marg284"></arrow.to.target> <lb/>confirmed by two other &longs;hots made North and South; for they <lb/>would never hit the mark, but the Ranges would be alwayes wide, <lb/>or towards the We&longs;t, by meanes of the remove the mark would <lb/>make, being carried along with the Earth towards the Ea&longs;t, whil'&longs;t <lb/>the ball is flying. </s><s>And not onely &longs;hots made by the Meridians, <lb/><arrow.to.target n="marg285"></arrow.to.target> <lb/>but al&longs;o tho&longs;e aimed Ea&longs;t or We&longs;t would prove uncertain; for <lb/>tho&longs;e aim'd Ea&longs;t would be too high, and tho&longs;e directed We&longs;t too <lb/>low, although they were &longs;hot point blank, as I &longs;aid. </s><s>For the <lb/>Range of the Ball in both the &longs;hots being made by the Tangent, <lb/>that is, by a line parallel to the Horizon, and being that in the di­ <lb/>urnal motion, if it be of the Earth, the Horizon goeth continually <lb/>de&longs;cending towards the Ea&longs;t, and ri&longs;ing from the We&longs;t (therefore <lb/>the Oriental Stars &longs;eem to ri&longs;e, and the Occidental to decline) &longs;o <lb/>that the Oriental mark would de&longs;cend below the aime, and there­ <lb/>upon the &longs;hot would fly too high, and the a&longs;cending of the We&longs;t­ <lb/>ern mark would make the &longs;hot aimed that way range too low; &longs;o <lb/>that the Peece would never carry true towards any point; and for <lb/>that experience telleth us the contrary, it is requi&longs;ite to &longs;ay, that <lb/>the Earth is immoveable.</s></p><p type="margin"><s><margin.target id="marg280"></margin.target><emph type="italics"/>Which is confir­ <lb/>med by the experi­ <lb/>ment of a body let <lb/>fall from the round <lb/>top of a Ship.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg281"></margin.target>* That is, at the <lb/>foot of the Ma&longs;t, <lb/>upon the upper <lb/>deck.</s></p><p type="margin"><s><margin.target id="marg282"></margin.target><emph type="italics"/>The &longs;econd ar­ <lb/>gument taken from <lb/>a Projection &longs;hot <lb/>very high.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg283"></margin.target><emph type="italics"/>The third argu­ <lb/>ment taken from <lb/>the &longs;hots of a Can­ <lb/>non, towards the <lb/>Ea&longs;t, and towards <lb/>the West.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg284"></margin.target><emph type="italics"/>This argument <lb/>is confirmed by two <lb/>&longs;hots towards the <lb/>South and towards <lb/>the North.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg285"></margin.target><emph type="italics"/>And it is like­ <lb/>wi&longs;e confirmed by <lb/>two &longs;hots towards <lb/>the Ea&longs;t, and to­ <lb/>wards the We&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>The&longs;e are &longs;olid rea&longs;ons, and &longs;uch as I believe no man <lb/>can an&longs;wer.</s></p><p type="main"><s>SALV. </s><s>Perhaps they are new to you?</s></p><p type="main"><s>SIMPL. </s><s>Really they are; and now I &longs;ee with how many ad­ <lb/>mirable experiments Nature is plea&longs;ed to favour us, wherewith to <lb/>a&longs;&longs;i&longs;t us in the knowledge of the Truth. </s><s>Oh! how exactly one <pb xlink:href="040/01/128.jpg" pagenum="110"/>truth agreeth with another, and all con&longs;pire to render each other <lb/>inexpugnable!</s></p><p type="main"><s>SAGR. </s><s>What pity it is that Guns were not u&longs;ed in <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> <lb/>age, he would with help of them have ea&longs;ily battered down ig­ <lb/>norance, and &longs;poke without hæ&longs;itation of the&longs;e mundane points.</s></p><p type="main"><s>SALV. </s><s>I am very glad that the&longs;e rea&longs;ons are new unto you, that <lb/>&longs;o you may not re&longs;t in the opinion of the <emph type="italics"/>major<emph.end type="italics"/> part of <emph type="italics"/>Peripate­ <lb/>ticks,<emph.end type="italics"/> who believe, that if any one for&longs;akes the Doctrine of <emph type="italics"/>Ari­ <lb/>&longs;totle,<emph.end type="italics"/> it is becau&longs;e they did not under&longs;tand or rightly apprehend <lb/>his demon&longs;trations. </s><s>But you may expect to hear of other Novel­ <lb/><arrow.to.target n="marg286"></arrow.to.target> <lb/>ties, and you &longs;hall &longs;ee the followers of this new Sy&longs;teme produce a­ <lb/>gain&longs;t them&longs;elves ob&longs;ervations, experiences, and rea&longs;ons of farre <lb/>greater force than tho&longs;e alledged by <emph type="italics"/>Aristotle, Ptolomy,<emph.end type="italics"/> and other <lb/>oppo&longs;ers of the &longs;ame conclu&longs;ions, and by this means you &longs;hall come <lb/>to a&longs;certain your &longs;elf that they were not induced through want of <lb/>knowledge or experience to follow that opinion.</s></p><p type="margin"><s><margin.target id="marg286"></margin.target>Copernicus <emph type="italics"/>his <lb/>followers are not <lb/>moved through ig­ <lb/>nor ance of the ar­ <lb/>guments on the o­ <lb/>ther part.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>It is requi&longs;ite that upon this occa&longs;ion I relate unto you <lb/>&longs;ome accidents that befell me, &longs;o &longs;oon as I fir&longs;t began to hear &longs;peak <lb/>of this new doctrine. </s><s>Being very young, and having &longs;carcely fi­ <lb/>ni&longs;hed my cour&longs;e of Philo&longs;ophy, which I left off, as being &longs;et upon <lb/>other employments, there chanced to come into the&longs;e parts a cer­ <lb/>tain Foreigner of <emph type="italics"/>Ro&longs;tock,<emph.end type="italics"/> who&longs;e name, as I remember, was <emph type="italics"/>Chri-<emph.end type="italics"/> <lb/><arrow.to.target n="marg287"></arrow.to.target> <lb/><emph type="italics"/>&longs;tianus Vur&longs;titius,<emph.end type="italics"/> a follower of <emph type="italics"/>Copernicus,<emph.end type="italics"/> who in an <emph type="italics"/>Academy<emph.end type="italics"/> <lb/>made two or three Lectures upon this point, to whom many flock't <lb/>as Auditors; but I thinking they went more for the novelty of the <lb/>&longs;ubject than otherwi&longs;e, did not go to hear him: for I had conclu­ <lb/>ded with my &longs;elf that that opinion could be no other than a &longs;olemn <lb/>madne&longs;&longs;e. </s><s>And que&longs;tioning &longs;ome of tho&longs;e who had been there, I <lb/>perceived they all made a je&longs;t thereof, execpt one, who told me <lb/>that the bu&longs;ine&longs;&longs;e was not altogether to be laugh't at, and becau&longs;e <lb/>this man was reputed by me to be very intelligent and wary, I re­ <lb/>pented that I was not there, and began from that time forward as <lb/>oft as I met with any one of the <emph type="italics"/>Copernican<emph.end type="italics"/> per&longs;wa&longs;ion, to demand <lb/>of them, if they had been alwayes of the &longs;ame judgment; and of as <lb/>many as I examined, I found not &longs;o much as one, who told me not <lb/>that he had been a long time of the contrary opinion, but to have <lb/>changed it for this, as convinced by the &longs;trength of the rea&longs;ons pro­ <lb/>ving the &longs;ame: and afterwards que&longs;tioning them, one by one; to <lb/>&longs;ee whether they were well po&longs;&longs;e&longs;t of the rea&longs;ons of the other &longs;ide; <lb/><arrow.to.target n="marg288"></arrow.to.target> <lb/>I found them all to be very ready and perfect in them; &longs;o that I <lb/>could not truly &longs;ay, that they had took up this opinion out of ig­ <lb/>norance, vanity, or to &longs;hew the acutene&longs;&longs;e of their wits. </s><s>On the <lb/>contrary, of as many of the <emph type="italics"/>Peripateticks<emph.end type="italics"/> and <emph type="italics"/>Ptolomeans<emph.end type="italics"/> as I <lb/>have asked (and out of curio&longs;ity I have talked with many) what <lb/>pains they had taken in the Book of <emph type="italics"/>Copernicus,<emph.end type="italics"/> I found very <pb xlink:href="040/01/129.jpg" pagenum="111"/>few that had &longs;o much as &longs;uperficially peru&longs;ed it; but of tho&longs;e <lb/>whom, I thought, had under&longs;tood the &longs;ame, not one; and more­ <lb/>over, I have enquired among&longs;t the followers of the <emph type="italics"/>Peripatetick<emph.end type="italics"/> <lb/>Doctrine, if ever any of them had held the contrary opinion, and <lb/>likewi&longs;e found none that had. </s><s>Whereupon con&longs;idering that there <lb/>was no man who followed the opinion of <emph type="italics"/>Copernicus,<emph.end type="italics"/> that had <lb/>not been fir&longs;t on the contrary &longs;ide, and that was not very well ac­ <lb/>quainted with the rea&longs;ons of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy<emph.end type="italics"/>; and, on the <lb/>contrary, that there is not one of the followers of <emph type="italics"/>Ptolomy<emph.end type="italics"/> that <lb/>had ever been of the judgment of <emph type="italics"/>Copernicus,<emph.end type="italics"/> and had left that, <lb/>to imbrace this of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> con&longs;idering, I &longs;ay, the&longs;e things, I <lb/>began to think, that one, who leaveth an opinion imbued with <lb/>his milk, and followed by very many, to take up another owned <lb/>by very few, and denied by all the Schools, and that really <lb/>&longs;eems a very great Paradox, mu&longs;t needs have been moved, not <lb/>to &longs;ay forced, by more powerful rea&longs;ons. </s><s>For this cau&longs;e, I am <lb/>become very curious to dive, as they &longs;ay, into the bottom of this <lb/>bu&longs;ine&longs;&longs;e, and account it my great good fortune that I have met <lb/>you two, from whom I may without any trouble, hear all that <lb/>hath been, and, haply, can be &longs;aid on this argument, a&longs;&longs;uring <lb/>my &longs;elf that the &longs;trength of your rea&longs;ons will re&longs;olve all &longs;cruples, <lb/>and bring me to a certainty in this &longs;ubject.</s></p><p type="margin"><s><margin.target id="marg287"></margin.target>Chri&longs;tianus Vur­ <lb/>&longs;titius <emph type="italics"/>read certain <lb/>Lectures touching <lb/>the opinion of<emph.end type="italics"/> Co­ <lb/>pernicus, <emph type="italics"/>& what <lb/>en&longs;ued thereupon.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg288"></margin.target><emph type="italics"/>The followers of<emph.end type="italics"/> <lb/>Copernicus <emph type="italics"/>were <lb/>all fir&longs;t again&longs;t <lb/>that opinion, but <lb/>the Sectators of<emph.end type="italics"/> <lb/>Ari&longs;totle <emph type="italics"/>&<emph.end type="italics"/> Pto­ <lb/>lomy, <emph type="italics"/>were never <lb/>of the other &longs;ide.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>But its po&longs;&longs;ible your opinion and hopes may be di&longs;ap­ <lb/>pointed, and that you may find your &longs;elves more at a lo&longs;&longs;e in the <lb/>end than you was at fir&longs;t.</s></p><p type="main"><s>SAGR. </s><s>I am very confident that this can in no wi&longs;e befal <lb/>me.</s></p><p type="main"><s>SIMPL. </s><s>And why not? </s><s>I have a manife&longs;t example in my &longs;elf, <lb/>that the farther I go, the more I am confounded.</s></p><p type="main"><s>SAGR. </s><s>This is a &longs;ign that tho&longs;e rea&longs;ons that hitherto &longs;eemed <lb/>concluding unto you, and a&longs;&longs;ured you in the truth of your opi­ <lb/>nion, begin to change countenance in your mind, and to let you <lb/>by degrees, if not imbrace, at lea&longs;t look towards the contrary te­ <lb/>nent; but I, that have been hitherto indifferent, do greatly hope <lb/>to acquire re&longs;t and &longs;atisfaction by our future di&longs;cour&longs;es, and you <lb/>will not deny but I may, if you plea&longs;e but to hear what per&longs;wa­ <lb/>deth me to this expectation.</s></p><p type="main"><s>SIMPL. </s><s>I will gladly hearken to the &longs;ame, and &longs;hould be no <lb/>le&longs;&longs;e glad that the like effect might be wrought in me.</s></p><p type="main"><s>SAGR. </s><s>Favour me therefore with an&longs;wering to what I &longs;hall ask <lb/>you. </s><s>And fir&longs;t, tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> is not the conclu&longs;ion, which <lb/>we &longs;eek the truth of, Whether we ought to hold with <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>and <emph type="italics"/>Ptolomy,<emph.end type="italics"/> that the Earth onely abiding without motion in the <lb/>Centre of the Univer&longs;e, the Cœle&longs;tial bodies all move, or el&longs;e, <lb/>Whether the Starry Sphere and the Sun &longs;tanding &longs;till in the Centre, <pb xlink:href="040/01/130.jpg" pagenum="112"/>the Earth is without the &longs;ame, and owner of all tho&longs;e motions that <lb/>in our &longs;eeming belong to the Sun and fixed Stars?</s></p><p type="main"><s>SIMPL. </s><s>The&longs;e are the conclu&longs;ions which are in di&longs;pute.</s></p><p type="main"><s>SAGR. </s><s>And the&longs;e two conclu&longs;ions, are they not of &longs;uch a na­ <lb/>ture, that one of them mu&longs;t nece&longs;&longs;arily be true, and the other <lb/>fal&longs;e?</s></p><p type="main"><s>SIMPL. </s><s>They are &longs;o. </s><s>We are in a <emph type="italics"/>Dilemma,<emph.end type="italics"/> one part of which <lb/>mu&longs;t of nece&longs;&longs;ity be true, and the other untrue; for between Mo­ <lb/>tion and Re&longs;t, which are contradictories, there cannot be in&longs;tanced <lb/>a third, &longs;o as that one cannot &longs;ay the Earth moves not, nor &longs;tands <lb/>&longs;till; the Sun and Stars do not move, and yet &longs;tand not &longs;till.</s></p><p type="main"><s>SAGR. </s><s>The Earth, the Sun, and Stars, what things are they in <lb/>nature? </s><s>are they petite things not worth our notice, or grand and <lb/>worthy of con&longs;ideration?</s></p><p type="main"><s>SIMPL They are principal, noble, integral bodies of the Uni­ <lb/>ver&longs;e, mo&longs;t va&longs;t and con&longs;iderable.</s></p><p type="main"><s>SAGR. </s><s>And Motion, and Re&longs;t, what accidents are they in <lb/>Nature? <lb/><arrow.to.target n="marg289"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg289"></margin.target><emph type="italics"/>Motion and re&longs;t <lb/>principal accidents <lb/>in nature.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>So great and principal, that Nature her &longs;elf is defined <lb/>by them.</s></p><p type="main"><s>SAGR. </s><s>So that moving eternally, and the being wholly immo­ <lb/>veable are two conditions very con&longs;iderable in Nature, and indi­ <lb/>cate very great diver&longs;ity; and e&longs;pecially when a&longs;cribed to the <lb/>principal bodies of the Univer&longs;e, from which can en&longs;ue none but <lb/>very different events.</s></p><p type="main"><s>SIMPL. </s><s>Yea doubtle&longs;&longs;e.</s></p><p type="main"><s>SAGR. </s><s>Now an&longs;wer me to another point. </s><s>Do you believe that <lb/>in <emph type="italics"/>Logick, Rhethorick,<emph.end type="italics"/> the <emph type="italics"/>Phy&longs;icks, Metaphy&longs;icks, Mathematicks,<emph.end type="italics"/> <lb/>and finally, in the univer&longs;ality of Di&longs;putations there are arguments <lb/>&longs;ufficient to per&longs;wade and demon&longs;trate to a per&longs;on the fallacious, <lb/>no le&longs;&longs;e then the true conclu&longs;ions?</s></p><p type="main"><s><arrow.to.target n="marg290"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg290"></margin.target><emph type="italics"/>Vntruths cannot <lb/>be demonstrated, <lb/>as Truths are.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>No Sir; rather I am very confident and certain, that <lb/>for the proving of a true and nece&longs;&longs;ary conclu&longs;ion, there are in </s></p><p type="main"><s><arrow.to.target n="marg291"></arrow.to.target> <lb/>nature not onely one, but many very powerfull demon&longs;trations: <lb/>and that one may di&longs;cu&longs;&longs;e and handle the &longs;ame divers and &longs;undry <lb/>wayes, without ever falling into any ab&longs;urdity; and that the more <lb/>any Sophi&longs;t would di&longs;turb and muddy it, the more clear would its <lb/>certainty appear: And that on the contrary to make a fal&longs;e po&longs;i­ <lb/>tion pa&longs;&longs;e for true, and to per&longs;wade the belief thereof, there can­ <lb/>not be any thing produced but fallacies, Sophi&longs;ms, Paralogi&longs;mes, <lb/>Equivocations, and Di&longs;cour&longs;es vain, incon&longs;i&longs;tant, and full of re­ <lb/>pugnances and contradictions.</s></p><p type="margin"><s><margin.target id="marg291"></margin.target><emph type="italics"/>For proof of true <lb/>conclu&longs;ions, many <lb/>&longs;olid arguments <lb/>may be produced, <lb/>but to prove a fal­ <lb/>&longs;ity, none.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Now if eternal motion, and eternal re&longs;t be &longs;o princi­ <lb/>pal accidents of Nature, and &longs;o different, that there can depend <lb/>on them only mo&longs;t different con&longs;equences, and e&longs;pecially when <pb xlink:href="040/01/131.jpg" pagenum="113"/>applyed to the Sun, and to the Earth, &longs;o va&longs;t and famous bodies <lb/>of the Univer&longs;e; and it being, moreover, impo&longs;&longs;ible, that one of <lb/>two contradictory Propo&longs;itions, &longs;hould not be true, and the other <lb/>fal&longs;e; and that for proof of the fal&longs;e one, any thing can be pro­ <lb/>duced but fallacies; but the true one being per&longs;wadeable by all <lb/>kind of concluding and demon&longs;trative arguments, why &longs;hould <lb/>you think that he, of you two, who &longs;hall be &longs;o fortunate as to <lb/>maintain the true Propo&longs;ition ought not to per&longs;wade me? </s><s>You <lb/>mu&longs;t &longs;uppo&longs;e me to be of a &longs;tupid wit, perver&longs;e judgment, dull <lb/>mind and intellect, and of a blind rea&longs;on, that I &longs;hould not be <lb/>able to di&longs;tingui&longs;h light from darkne&longs;&longs;e, jewels from coals, or <lb/>truth from fal&longs;hood.</s></p><p type="main"><s>SIMPL. </s><s>I tell you now, and have told you upon other <lb/>occa&longs;ions, that the be&longs;t Ma&longs;ter to teach us how to di&longs;cern So­ <lb/>phi&longs;mes, Paralogi&longs;mes, and other fallacies, was <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who <lb/>in this particular can never be deceived.</s></p><p type="main"><s>SAGR. </s><s>You in&longs;i&longs;t upon <emph type="italics"/>Aristotle,<emph.end type="italics"/> who cannot &longs;peak. </s><s>Yet I <lb/>tell you, that if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> were here, he would either yield him­ <lb/><arrow.to.target n="marg292"></arrow.to.target> <lb/>&longs;elf to be per&longs;waded by us, or refuting our arguments, convince <lb/>us by better of his own. </s><s>And you your &longs;elf, when you heard the <lb/>experiments of the Suns related, did you not acknowledg and <lb/>admire them, and confe&longs;&longs;e them more concludent than tho&longs;e of <lb/><emph type="italics"/>Ari&longs;totle?<emph.end type="italics"/> Yet neverthele&longs;&longs;e I cannot perceive that <emph type="italics"/>Salviatus,<emph.end type="italics"/> <lb/>who hath produced them, examined them, and with exqui&longs;ite <lb/>care &longs;can'd them, doth confe&longs;&longs;e him&longs;elf per&longs;waded by them; no <lb/>nor by others of greater force, which he intimated that he was <lb/>about to give us an account of. </s><s>And I know not on what grounds <lb/>you &longs;hould cen&longs;ure Nature, as one that for many Ages hath <lb/>been lazie, and forgetful to produce &longs;peculative <emph type="italics"/>wits<emph.end type="italics"/>; and <lb/>that knoweth not how to make more &longs;uch, unle&longs;&longs;e they be &longs;uch <lb/>kind of men as &longs;lavi&longs;hly giving up their judgments to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> do <lb/>under&longs;tand with his brain, and re&longs;ent with his &longs;en&longs;es. </s><s>But let us <lb/>hear the re&longs;idue of tho&longs;e rea&longs;ons which favour his opinion, that <lb/>we may thereupon proceed to &longs;peak to them; comparing and <lb/>weighing them in the ballance of impartiality.</s></p><p type="margin"><s><margin.target id="marg292"></margin.target>Ari&longs;totle <emph type="italics"/>would <lb/>either refute his <lb/>adver&longs;aries argu­ <lb/>ments, or would <lb/>alter his opinion.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Before I proceed any farther, I mu&longs;t tell <emph type="italics"/>Sagredus,<emph.end type="italics"/> that <lb/>in the&longs;e our Di&longs;putations, I per&longs;onate the <emph type="italics"/>Copernican,<emph.end type="italics"/>, and imi­ <lb/>tate him, as if I were his <emph type="italics"/>Zany<emph.end type="italics"/>; but what hath been effected in <lb/>my private thoughts by the&longs;e arguments which I &longs;eem to alledg in <lb/>his favour, I would not have you to judg by what I &longs;ay, whil'&longs;t <lb/>I am in the heat of acting my part in the Fable; but after I have <lb/>laid by my di&longs;gui&longs;e, for you may chance to find me different <lb/>from what you &longs;ee me upon the Stage. </s><s>Now let us go on.</s></p><p type="main"><s><emph type="italics"/>Ptolomy<emph.end type="italics"/> and his followers produce another experiment like to <lb/><arrow.to.target n="marg293"></arrow.to.target> <lb/>that of the Projections, and it is of things that being &longs;eparated <pb xlink:href="040/01/132.jpg" pagenum="114"/>from the Earth, continue a good &longs;pace of time in the Air, &longs;uch <lb/>as are the Clouds, Birds of flight; and as of them it cannot be <lb/>&longs;aid that they are rapt or tran&longs;parted by the Earth, having no ad­ <lb/>he&longs;ion thereto, it &longs;eems not po&longs;&longs;ible, that they &longs;hould be able to <lb/>keep pace with the velocity thereof; nay it &longs;hould rather &longs;eem <lb/>to us, that they all &longs;wiftly move towards the We&longs;t: And if <lb/>being carried about by the Earth, pa&longs;&longs;e our parallel in twenty <lb/>four hours, which yet is at lea&longs;t &longs;ixteen thou&longs;and miles, how can <lb/>Birds follow &longs;uch a cour&longs;e or revolution? </s><s>Whereas on the con­ <lb/>trary, we &longs;ee them fly as well towards the Ea&longs;t, as towards the <lb/>We&longs;t, or any other part, without any &longs;en&longs;ible difference. </s><s>More­ <lb/><arrow.to.target n="marg294"></arrow.to.target> <lb/>over, if when we run a Hor&longs;e at his &longs;peed, we feel the air beat <lb/>vehemently again&longs;t our face, what an impetuous bla&longs;t ought we <lb/>perpetually to feel from the Ea&longs;t, being carried with &longs;o rapid a <lb/>cour&longs;e again&longs;t the wind? </s><s>and yet no &longs;uch effect is perceived. </s><s>Take <lb/>another very ingenious argument inferred from the following ex­ <lb/><arrow.to.target n="marg295"></arrow.to.target> <lb/>periment. </s><s>The circular motion hath a faculty to extrude and di&longs;­ <lb/>&longs;ipate from its Centre the parts of the moving body, when&longs;oever <lb/>either the motion is not very &longs;low, or tho&longs;e parts are not very <lb/>well fa&longs;tened together; and therefore, if <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> we &longs;hould turn <lb/>one of tho&longs;e great wheels very fa&longs;t about, wherein one or more <lb/>men walking, crane up very great weights, as the huge ma&longs;&longs;ie <lb/>&longs;tone, u&longs;ed by the Callander for pre&longs;&longs;ing of Cloaths; or the <lb/>fraighted Barks which being haled on &longs;hore, are hoi&longs;ted out of <lb/>one river into another; in ca&longs;e the parts of that &longs;ame Wheel &longs;o <lb/>&longs;wiftly turn'd round, be not very well joyn'd and pin'd together, <lb/>they would all be &longs;hattered to pieces; and though many &longs;tones or <lb/>other ponderous &longs;ub&longs;tances, &longs;hould be very fa&longs;t bound to its outward <lb/>Rimme, yet could they not re&longs;i&longs;t the impetuo&longs;ity, which with <lb/>great violence would hurl them every way far from the Wheel, <lb/>and con&longs;equently from its Centre. </s><s>So that if the Earth did move <lb/>with &longs;uch and &longs;o much greater velocity, what gravity, what tena­ <lb/>city of lime or plai&longs;ter would keep together Stones, Buildings, and <lb/>whole Cities, that they &longs;hould not be to&longs;t into the Air by &longs;o pre­ <lb/>cipitous a motion? </s><s>And both men and bea&longs;ts, which are not fa­ <lb/>&longs;tened to the Earth, how could they re&longs;i&longs;t &longs;o great an <emph type="italics"/>impetus<emph.end type="italics"/>? <lb/></s><s>Whereas, on the other &longs;ide, we &longs;ee both the&longs;e, and far le&longs;&longs;e re­ <lb/>&longs;i&longs;tances of pebles, &longs;ands, leaves re&longs;t quietly on the Earth, and <lb/>to return to it in falling, though with a very &longs;low motion. </s><s>See <lb/>here, <emph type="italics"/>Simplicius,<emph.end type="italics"/> the mo&longs;t potent arguments, taken, to &longs;o &longs;peak, <lb/>from things Terre&longs;trial; there remain tho&longs;e of the other kind, <lb/>namely, &longs;uch as have relation to the appearances of Heaven, <lb/>which rea&longs;ons, to confe&longs;&longs;e the truth, tend more to prove the <lb/>Earth to be in the centre of the Univer&longs;e, and con&longs;equently, to <lb/>deprive it of the annual motion about the &longs;ame, a&longs;cribed unto it <pb xlink:href="040/01/133.jpg" pagenum="115"/>by <emph type="italics"/>Copernicus.<emph.end type="italics"/> Which arguments, as being of &longs;omewhat a di&longs;te­ <lb/>rent nature, may be produced, after we have examined the <lb/>&longs;trength of the&longs;e already propounded.</s></p><p type="margin"><s><margin.target id="marg293"></margin.target><emph type="italics"/>An argument <lb/>taken from the <lb/>Clouds, and from <lb/>Birds.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg294"></margin.target><emph type="italics"/>An argument <lb/>taken from the air <lb/>which we feel to <lb/>beat upon us when <lb/>we run a Hor&longs;e at <lb/>full &longs;peed.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg295"></margin.target><emph type="italics"/>An argument <lb/>taken from the <lb/>whirling of circu­ <lb/>lar motion, which <lb/>hath a faculty to <lb/>extrude and di&longs;&longs;i­ <lb/>pate.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>What &longs;ay you <emph type="italics"/>Simplicius<emph.end type="italics"/>? </s><s>do you think that <emph type="italics"/>Salviatus<emph.end type="italics"/> <lb/>is Ma&longs;ter of, and knoweth how to unfold the <emph type="italics"/>Ptolomean<emph.end type="italics"/> and <emph type="italics"/>Ari­ <lb/>&longs;totelian<emph.end type="italics"/> arguments? </s><s>Or do you think that any <emph type="italics"/>Peripatetick<emph.end type="italics"/> is e­ <lb/>qually ver&longs;t in the <emph type="italics"/>Copernican<emph.end type="italics"/> demon&longs;trations?</s></p><p type="main"><s>SIMPL. </s><s>Were it not for the high e&longs;teem, that the pa&longs;t di&longs;cour­ <lb/>&longs;es have begot in me of the learning of <emph type="italics"/>Salviatus,<emph.end type="italics"/> and of the a­ <lb/>cutene&longs;&longs;e of <emph type="italics"/>Sagredus,<emph.end type="italics"/> I would by their good leave have gone my <lb/>way without &longs;taying for their an&longs;wers; it &longs;eeming to me a thing <lb/>impo&longs;&longs;ible, that &longs;o palpable experiments &longs;hould be contradicted; <lb/>and would, without hearing them farther, con&longs;irm my &longs;elf in my <lb/>old per&longs;wa&longs;ion; for though I &longs;hould be made to &longs;ee that it was er­ <lb/>roneous, its being upheld by &longs;o many probable rea&longs;ons, would ren­ <lb/>der it excu&longs;eable. </s><s>And if the&longs;e are fallacies, what true demon&longs;tra­ <lb/>tions were ever &longs;o fair?</s></p><p type="main"><s>SAGR. </s><s>Yet its good that we hear the re&longs;pon&longs;ions of <emph type="italics"/>Salviatus<emph.end type="italics"/>; <lb/>which if they be true, mu&longs;t of nece&longs;&longs;ity be more fair, and that by <lb/>in&longs;inite degrees; and tho&longs;e mu&longs;t be deformed, yea mo&longs;t deformed, <lb/>if the Metaphy &longs;ical Axiome hold, That true and fair are one and <lb/><arrow.to.target n="marg296"></arrow.to.target> <lb/>the &longs;ame thing; as al&longs;o fal&longs;e and deformed. </s><s>Therefore <emph type="italics"/>Salviatus<emph.end type="italics"/> <lb/>let's no longer lo&longs;e time.</s></p><p type="margin"><s><margin.target id="marg296"></margin.target><emph type="italics"/>True and fair <lb/>are one and the <lb/>&longs;ame, as al&longs;o fal&longs;e <lb/>and deformed.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The fir&longs;t Argument alledged by <emph type="italics"/>Simplicius,<emph.end type="italics"/> if I well re­ <lb/>member it, was this. </s><s>The Earth cannot move circularly, becau&longs;e <lb/>&longs;uch motion would be violent to the &longs;ame, and therefore not per­ <lb/>petual: that it is violent, the rea&longs;on was: Becau&longs;e, that had it been <lb/>natural, its parts would likewi&longs;e naturally move round, which is <lb/>impo&longs;&longs;ible, for that it is natural for the parts thereof to move with a <lb/>right motion downwards. </s><s>To this my reply is, that I could glad­ <lb/>ly wi&longs;h, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had more cleerly expre&longs;t him&longs;elf, where he <lb/><arrow.to.target n="marg297"></arrow.to.target> <lb/>&longs;aid; That its parts would likewi&longs;e move circularly; for this mo­ <lb/>ving circularly is to be under&longs;tood two wayes, one is, that every <lb/>particle or atome &longs;eparated from its <emph type="italics"/>Whole<emph.end type="italics"/> would move circularly <lb/>about its particular centre, de&longs;cribing its &longs;mall Circulets; the other <lb/>is, that the whole Globe moving about its centre in twenty four <lb/>hours, the parts al&longs;o would turn about the &longs;ame centre in four and <lb/>twenty hours. </s><s>The fir&longs;t would be no le&longs;&longs;e an impertinency, than <lb/>if one &longs;hould &longs;ay, that every part of the circumference of a Circle <lb/>ought to be a Circle; or becau&longs;e that the Earth is Spherical, that <lb/>therefore every part thereof be a Globe, for &longs;o doth the <emph type="italics"/>Axiome<emph.end type="italics"/> <lb/>require: <emph type="italics"/>Eadem e&longs;t ratio totius, & partium.<emph.end type="italics"/> But if he took it in <lb/>the other &longs;en&longs;e, to wit, that the parts in imitation of the <emph type="italics"/>Whole<emph.end type="italics"/> <lb/>&longs;hould move naturally round the Centre of the whole Globe in <lb/>twenty four hours, I &longs;ay, that they do &longs;o; and it concerns you, <pb xlink:href="040/01/134.jpg" pagenum="116"/>in&longs;tead of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> to prove that they do not.</s></p><p type="margin"><s><margin.target id="marg297"></margin.target><emph type="italics"/>The an&longs;wer to<emph.end type="italics"/> <lb/>Ari&longs;totles <emph type="italics"/>fir&longs;t ar­ <lb/>gument.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>This is proved by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in the &longs;ame place, when he <lb/>&longs;aith, that the natural motion of the parts is the right motion <lb/>downwards to the centre of the Univer&longs;e; &longs;o that the circular <lb/>motion cannot naturally agree therewith.</s></p><p type="main"><s>SALV. </s><s>But do not you &longs;ee, that tho&longs;e very words carry in them <lb/>a confutation of this &longs;olution?</s></p><p type="main"><s>SIMPL. How? </s><s>and where?</s></p><p type="main"><s>SALV. </s><s>Doth not he &longs;ay that the circular motion of the Earth <lb/>would be violent? </s><s>and therefore not eternal? </s><s>and that this is ab­ <lb/>&longs;urd, for that the order of the World is eternal?</s></p><p type="main"><s>SIMPL. </s><s>He &longs;aith &longs;o.</s></p><p type="main"><s>SALV. </s><s>But if that which is violent cannot be eternal, then by <lb/><arrow.to.target n="marg298"></arrow.to.target> <lb/>conver&longs;ion, that which cannot be eternal, cannot be natural: but <lb/>the motion of the Earth downwards cannot be otherwi&longs;e eternal; <lb/>therefore much le&longs;&longs;e can it be natural: nor can any other motion <lb/>be natural to it, &longs;ave onely that which is eternal. </s><s>But if we make <lb/>the Earth move with a circular motion, this may be eternal to it, <lb/>and to its parts, and therefore natural.</s></p><p type="margin"><s><margin.target id="marg298"></margin.target><emph type="italics"/>That which is <lb/>violent, cannot be <lb/>eternal, and that <lb/>which cannot be e­ <lb/>ternal, cannot be <lb/>natural.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>The right motion is mo&longs;t natural to the parts of the <lb/>Earth, and is to them eternal; nor &longs;hall it ever happen that they <lb/>move not with a right motion; alwayes provided that the impe­ <lb/>diments be removed.</s></p><p type="main"><s>SALV. </s><s>You equivocate <emph type="italics"/>Simplicius<emph.end type="italics"/>; and I will try to free you <lb/>from the equivoke. </s><s>Tell me, therefore, do you think that a <lb/>Ship which &longs;hould &longs;ail from the Strait of <emph type="italics"/>Gibralter<emph.end type="italics"/> towards <emph type="italics"/>Pale­ <lb/>&longs;tina<emph.end type="italics"/> can eternally move towards that Coa&longs;t? </s><s>keeping alwayes an <lb/>equal cour&longs;e?</s></p><p type="main"><s>SIMPL. </s><s>No doubtle&longs;&longs;e.</s></p><p type="main"><s>SALV. </s><s>And why not?</s></p><p type="main"><s>SIMPL. </s><s>Becau&longs;e that Voyage is bounded and terminated be­ <lb/>tween the <emph type="italics"/>Herculean<emph.end type="italics"/> Pillars, and the &longs;hore of the <emph type="italics"/>Holy-land<emph.end type="italics"/>; and <lb/>the di&longs;tance being limited, it is pa&longs;t in a finite time, unle&longs;&longs;e one by <lb/>returning back &longs;hould with a contrary motion begin the &longs;ame Voy­ <lb/>age anew; but this would be an interrupted and no continued <lb/>motion.</s></p><p type="main"><s>SALV. </s><s>Very true. </s><s>But the Navigation from the Strait of <emph type="italics"/>Ma­ <lb/>galanes<emph.end type="italics"/> by the <emph type="italics"/>Pacifick<emph.end type="italics"/> Ocean, the <emph type="italics"/>Moluccha's,<emph.end type="italics"/> the Cape <emph type="italics"/>di buona <lb/>Speranza,<emph.end type="italics"/> and from thence by the &longs;ame Strait, and then again by <lb/>the <emph type="italics"/>Pacifick<emph.end type="italics"/> Ocean, &c. </s><s>do you believe that it may be perpe­ <lb/>tuated?</s></p><p type="main"><s>SIMPL. </s><s>It may; for this being a circumgyration, which re­ <lb/>turneth about its &longs;elf, with infinite replications, it may be perpetu­ <lb/>ated without any interruption.</s></p><p type="main"><s>SALV. </s><s>A Ship then may in this Voyage continue &longs;ailing eter­ <lb/>nally.</s></p> <pb xlink:href="040/01/135.jpg" pagenum="117"/><p type="main"><s>SIMPL. </s><s>It may, in ca&longs;e the Ship were incorruptible, but the <lb/>Ship decaying, the Navigation mu&longs;t of nece&longs;&longs;ity come to an end.</s></p><p type="main"><s>SALV. </s><s>But in the Mediterrane, though the Ve&longs;&longs;el were incor­ <lb/>ruptible, yet could &longs;he not &longs;ail perpetually towards <emph type="italics"/>Pale&longs;tina,<emph.end type="italics"/> that <lb/><arrow.to.target n="marg299"></arrow.to.target> <lb/>Voyage being determined. </s><s>Two things then are required, to the <lb/>end a moveable may without intermi&longs;&longs;ion move perpetually; the <lb/>one is, that the motion may of its own nature be indeterminate and <lb/>infinite; the other, that the moveable be likewi&longs;e incorruptible <lb/>and eternal.</s></p><p type="margin"><s><margin.target id="marg299"></margin.target><emph type="italics"/>Two things re­ <lb/>qui&longs;ite to the end a <lb/>motion may per­ <lb/>petuate it &longs;elf; an <lb/>unlimited &longs;pace, <lb/>and an incorrupti­ <lb/>ble moveable.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>All this is nece&longs;&longs;ary.</s></p><p type="main"><s>SALV. </s><s>Therefore you may &longs;ee how of your own accord you <lb/>have confe&longs;&longs;ed it impo&longs;&longs;ible that any moveable &longs;hould move eter­ <lb/>nally in a right line, in regard that right motion, whether it be up­ <lb/><arrow.to.target n="marg300"></arrow.to.target> <lb/>wards, or downwards, is by you your &longs;elf bounded by the circum­ <lb/>ference and centre; &longs;o that if a Moveable, as &longs;uppo&longs;e the Earth <lb/>be eternal, yet fora&longs;much as the right motion is not of its own na­ <lb/>ture eternall, but mo&longs;t ^{*}terminate, it cannot naturally &longs;uit with <lb/><arrow.to.target n="marg301"></arrow.to.target> <lb/>the Earth. </s><s>Nay, as was &longs;aid ^{*} ye&longs;terday, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf is <lb/><arrow.to.target n="marg302"></arrow.to.target> <lb/>con&longs;trained to make the Terre&longs;trial Globe eternally immoveable. <lb/></s><s>When again you &longs;ay, that the parts of the Earth evermore move <lb/>downwards, all impediments being removed, you egregiou&longs;ly equi­ <lb/>vocate; for then, on the other &longs;ide they mu&longs;t be impeded, contra­ <lb/>ried, and forced, if you would have them move; for, when they <lb/>are once fallen to the ground, they mu&longs;t be violently thrown up­ <lb/>wards, that they may a &longs;econd time fall; and as to the impedi­ <lb/>ments, the&longs;e only hinder its arrival at the centre; but if there were <lb/>a <emph type="italics"/>Well,<emph.end type="italics"/> that did pa&longs;&longs;e thorow and beyond the centre, yet would not <lb/>a clod of Earth pa&longs;&longs;e beyond it, unle&longs;&longs;e ina&longs;much as being tran&longs;­ <lb/>ported by its <emph type="italics"/>impetus,<emph.end type="italics"/> it &longs;hould pa&longs;&longs;e the &longs;ame to return thither a­ <lb/>gain, and in the end there to re&longs;t. </s><s>As therefore to the defending, <lb/>that the motion by a right line doth or can agree naturally neither <lb/>to the Earth, nor to any other moveable, whil'&longs;t the Univer&longs;e re­ <lb/>taineth its perfect order, I would have you take no further paines a­ <lb/>bout it, but (unle&longs;&longs;e you will grant them the circular motion) <lb/>your be&longs;t way will be to defend and maintain their immobility.</s></p><p type="margin"><s><margin.target id="marg300"></margin.target><emph type="italics"/>Right motion <lb/>cannot be eternal, <lb/>and con&longs;equently <lb/>cannot be natural <lb/>to the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg301"></margin.target>* Terminati&longs;&longs;imo.</s></p><p type="margin"><s><margin.target id="marg302"></margin.target>* By this expre&longs;&longs;i­ <lb/>on he every where <lb/>means the prece­ <lb/>ding Dialogue, or <lb/><emph type="italics"/>Giornata.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>As to their immoveablene&longs;&longs;e, the arguments of <emph type="italics"/>Ari­ <lb/>&longs;totle,<emph.end type="italics"/> and moreover tho&longs;e alledged by your &longs;elf &longs;eem in my opini­ <lb/>on nece&longs;&longs;arily to conclude the &longs;ame, as yet; and I conceive it will <lb/>be a hard matter to refute them.</s></p><p type="main"><s>SALV. </s><s>Come we therefore to the &longs;econd Argument, which was, <lb/>That tho&longs;e bodies, which we are a&longs;&longs;ured do move circularly, have <lb/><arrow.to.target n="marg303"></arrow.to.target> <lb/>more than one motion, unle&longs;&longs;e it be the <emph type="italics"/>Primum Mobile<emph.end type="italics"/>; and <lb/>therefore, if the Earth did move circularly, it ought to have two <lb/>motions; from which alterations would follow in the ri&longs;ing and <lb/>&longs;etting of the Fixed Stars: Which effect is not perceived to en&longs;ue. <pb xlink:href="040/01/136.jpg" pagenum="118"/>Therefore, &c. </s><s>The mo&longs;t proper and genuine an&longs;wer to this Alle­ <lb/>gation is contained in the Argument it &longs;elf; and even <emph type="italics"/>Aristotle<emph.end type="italics"/> <lb/>puts it in our mouths, which it is impo&longs;&longs;ible, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that you <lb/>&longs;hould not have &longs;een.</s></p><p type="margin"><s><margin.target id="marg303"></margin.target><emph type="italics"/>The an&longs;wer to <lb/>the &longs;econd argu­ <lb/>ment.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I neither have &longs;een it, nor do I yet apprehend it.</s></p><p type="main"><s>SALV. </s><s>This cannot be, &longs;ure, the thing is &longs;o very plain.</s></p><p type="main"><s>SIMPL. </s><s>I will with your leave, ca&longs;t an eye upon the <emph type="italics"/>Text.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>We will command the <emph type="italics"/>Text<emph.end type="italics"/> to be brought forthwith.</s></p><p type="main"><s>SIMPL. </s><s>I alwayes carry it about with me: See here it is, and <lb/>I know the place perfectly well, which is in <emph type="italics"/>lib. 2. De Cælo, cap.<emph.end type="italics"/> <lb/>16. Here it is, <emph type="italics"/>Text<emph.end type="italics"/> 97. <emph type="italics"/>Preterea omnia, quæ feruntur latione <lb/>circulari &longs;ubdeficere videntur, ac moveri pluribus una latione, <lb/>præter primam Sphæram; quare & Terram nece&longs;&longs;ariam e&longs;t, &longs;ive <lb/>circa medium, &longs;ive in medio po&longs;ita feratur, duabus moveri <lb/>lationibus. </s><s>Si autem hoc acciderit, nece&longs;&longs;ariam e&longs;t fieri muta­ <lb/>tiones, ac conver&longs;iones fixorum a&longs;trorum. </s><s>Hoc autem non vide­ <lb/>tur ficri, &longs;ed &longs;emper eadem, apud eadem loca ip&longs;ius, & oriun­ <lb/>tur, & occidunt.<emph.end type="italics"/> [In Engli&longs;h thus:] Furthermore all that are <lb/><arrow.to.target n="marg304"></arrow.to.target> <lb/>carried with circular motion, &longs;eem to ^{*} fore&longs;low, and to move <lb/>with more than one motion, except the fir&longs;t Sphere; wherefore <lb/>it is nece&longs;&longs;ary that the Earth move with two motions, whether <lb/><arrow.to.target n="marg305"></arrow.to.target> <lb/>it be carried about the ^{*} middle, or placed in the middle. </s><s>But <lb/>if it be &longs;o, there would of nece&longs;&longs;ity be alterations and conver&longs;i­ <lb/>ons made among&longs;t the fixed Stars. </s><s>But no &longs;uch thing is &longs;een to <lb/>be done, but the &longs;ame Star doth alwayes ri&longs;e and &longs;et in the &longs;ame <lb/>place. </s><s>In all this I find not any falacy, and my thinks the argu­ <lb/>ment is very forcible.</s></p><p type="margin"><s><margin.target id="marg304"></margin.target>* Subde&longs;icere.</s></p><p type="margin"><s><margin.target id="marg305"></margin.target>* Or Centre.</s></p><p type="main"><s>SALV. </s><s>And this new reading of the place hath confirmed me <lb/>in the fallacy of the Sillogi&longs;me, and moreover, di&longs;covered ano­ <lb/>ther fal&longs;ity. </s><s>Therefore ob&longs;erve. </s><s>The Po&longs;itions, or if you will, <lb/>Conclu&longs;ions, which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> endeavours to oppo&longs;e, are two; one <lb/>is that of tho&longs;e, who placing the Earth in the mid&longs;t of the World, <lb/>do make it move in it &longs;elf about its own centre. </s><s>The other is of <lb/>tho&longs;e, who con&longs;tituting it far from the middle, do make it re­ <lb/>volve with a circular motion about the middle of the Univer&longs;e. <lb/></s><s>And both the&longs;e Po&longs;itions he conjointly impugneth with one and <lb/>the &longs;ame argument. </s><s>Now I affirm that he is out in both the one <lb/>and the other impugnation; and that his error again&longs;t the fir&longs;t <lb/>Po&longs;ition is an Equivoke or Paralogi&longs;me; and his mi&longs;take touch­ <lb/><arrow.to.target n="marg306"></arrow.to.target> <lb/>ing the &longs;econd is a fal&longs;e con&longs;equence. </s><s>Let us begin with the fir&longs;t <lb/>A&longs;&longs;ertion, which con&longs;tituteth the Earth in the mid&longs;t of the <lb/>World, and maketh it move in it &longs;elf about its own centre; and <lb/><arrow.to.target n="marg307"></arrow.to.target> <lb/>let us confront it with the objection of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; &longs;aying, All <lb/>moveables, that move circularly, &longs;eem to ^{*} fore&longs;low, and move <lb/>with more than one Byas, except the fir&longs;t Sphere (that is <emph type="italics"/>the pri-<emph.end type="italics"/> <pb xlink:href="040/01/137.jpg" pagenum="119"/><emph type="italics"/>mum mobile<emph.end type="italics"/>) therefore the Earth moving about its own centre, <lb/>being placed in the middle, mu&longs;t of nece&longs;&longs;ity have two bya&longs;&longs;es, <lb/>and fore&longs;low. </s><s>But if this were &longs;o, it would follow, that there <lb/>&longs;hould be a variation in the ri&longs;ing and &longs;etting of the fixed Stars, <lb/>which we do not perceive to be done: Therefore the Earth doth <lb/>not move, <emph type="italics"/>&c.<emph.end type="italics"/> Here is the Paralogi&longs;me, and to di&longs;cover it, I will <lb/>argue with <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in this manner. </s><s>Thou &longs;ai&longs;t, oh <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>that the Earth placed in the middle of the World, cannot move <lb/>in it &longs;elf (<emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> upon its own <emph type="italics"/>axis<emph.end type="italics"/>) for then it would be requi&longs;ite <lb/>to allow it two bya&longs;&longs;es; &longs;o that, if it &longs;hould not be nece&longs;&longs;ary to <lb/>allow it more than one Byas onely, thou woulde&longs;t not then hold <lb/>it impo&longs;&longs;ible for it to move onely with that one; for thou would'&longs;t <lb/>unnece&longs;&longs;arily have con&longs;ined the impo&longs;&longs;ibility to the plurality of <lb/>bya&longs;&longs;es, if in ca&longs;e it had no more but one, yet it could not move <lb/>with that. </s><s>And becau&longs;e that of all the moveables in the World, <lb/>thou make&longs;t but one alone to move with one &longs;ole byas; and all <lb/>the re&longs;t with more than one; and this &longs;ame moveable thou af­ <lb/>firme&longs;t to be the fir&longs;t Sphere, namely, that by which all the fix­ <lb/>ed and erratick Stars &longs;eem harmoniou&longs;ly to move from Ea&longs;t to <lb/>We&longs;t, if in ca&longs;e the Earth may be that fir&longs;t Sphere, that by mo­ <lb/>ving with one by as onely, may make the Stars appear to move <lb/>from Ea&longs;t to We&longs;t, thou wilt not deny them it: But he that af­ <lb/>firmeth, that the Earth being placed in the mid&longs;t of the World, <lb/>moveth about its own Axis, a&longs;cribes unto it no other motion, <lb/>&longs;ave that by which all the Stars appear to move from Ea&longs;t to We&longs;t; <lb/>and &longs;o it cometh to be that fir&longs;t Sphere, which thou thy &longs;elf ac­ <lb/>knowledge&longs;t to move with but one by as onely. </s><s>It is therefore ne­ <lb/>ce&longs;&longs;ary, oh <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> if thou wilt conclude any thing, that thou <lb/>demon&longs;trate, that the Earth being placed in the mid&longs;t of the <lb/>World, cannot move with &longs;o much as one by as onely; or el&longs;e, <lb/>that much le&longs;&longs;e can the fir&longs;t Sphere have one &longs;ole motion; for o­ <lb/>therwi&longs;e thou doe&longs;t in thy very Sillogi&longs;me both commit the falacy, <lb/>and detect it, denying, and at that very time proving the &longs;ame <lb/>thing. </s><s>I come now to the &longs;econd Po&longs;ition, namely, of tho&longs;e <lb/>who placing the Earth far from the mid&longs;t of the Univer&longs;e, make <lb/>it moveable about the &longs;ame; that is, make it a Planet and erra­ <lb/>tick Star; again&longs;t which the argument is directed, and as to <lb/>form is concludent, but faileth in matter. </s><s>For it being granted, <lb/>that the Earth doth in that manner move, and that with two by­ <lb/>a&longs;&longs;es, yet doth it not nece&longs;&longs;arily follow that though it were &longs;o, <lb/>it &longs;hould make alterations in the ri&longs;ings and &longs;ettings of the fixed <lb/>Stars, as I &longs;hall in its proper place declare. </s><s>And here I could <lb/>gladly excu&longs;e <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; rather I could highly applaud him for ha­ <lb/>ving light upon the mo&longs;t &longs;ubtil argument that could be produced <lb/>again&longs;t the <emph type="italics"/>Copernican Hypothe&longs;is<emph.end type="italics"/>; and if the objection be inge­ <pb xlink:href="040/01/138.jpg" pagenum="120"/>nious, and to outward appearance mo&longs;t powerful, you may &longs;ee <lb/>how much more acute and ingenious the &longs;olution mu&longs;t be, and <lb/>not to be found by a wit le&longs;&longs;e piercing than that of <emph type="italics"/>Copernicus<emph.end type="italics"/>; <lb/>and again from the difficulty in under&longs;tanding it, you may argue <lb/>the &longs;o much greater difficulty in finding it. </s><s>But let us for the pre­ <lb/>&longs;ent &longs;u&longs;pend our an&longs;wer, which you &longs;hall under&longs;tand in due time <lb/>and place, after we have repeated the objection of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and <lb/>that in his favour, much &longs;trengthened. </s><s>Now pa&longs;&longs;e we to <emph type="italics"/>Ari-<emph.end type="italics"/> <lb/><arrow.to.target n="marg308"></arrow.to.target> <lb/><emph type="italics"/>&longs;totles<emph.end type="italics"/> third Argument, touching which we need give no farther <lb/>reply, it having been &longs;ufficiently an&longs;wered betwixt the di&longs;cour&longs;es <lb/>of ye&longs;terday and to day: In as much as he urgeth, that the mo­ <lb/>tion of grave bodies is naturally by a right line to the centre; and <lb/>then enquireth, whether to the centre of the Earth, or to that <lb/>of the Univer&longs;e, and concludeth that they tend naturally to the <lb/>centre of the Univer&longs;e, but accidentally to that of the Earth. <lb/><arrow.to.target n="marg309"></arrow.to.target> <lb/>Therefore we may proceed to the fourth, upon which its requi&longs;ite <lb/>that we &longs;tay &longs;ome time, by rea&longs;on it is founded upon that expe­ <lb/>riment, from whence the greater part of the remaining argu­ <lb/>ments derive all their &longs;trength. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aith therefore, that it is <lb/>a mo&longs;t convincing argument of the Earths immobility, to &longs;ee <lb/>that projections thrown or &longs;hot upright, return perpendicularly <lb/>by the &longs;ame line unto the &longs;ame place from whence they were &longs;hot <lb/>or thrown. </s><s>And this holdeth true, although the motion be of a <lb/>very great height; which could never come to pa&longs;&longs;e, did the <lb/>Earth move: for in the time that the projected body is moving <lb/>upwards and downwards in a &longs;tate of &longs;eparation from the Earth, <lb/>the place from whence the motion of the projection began, would <lb/>be pa&longs;t, by means of the Earths revolution, a great way to­ <lb/>wards the Ea&longs;t, and look how great that &longs;pace was, &longs;o far from <lb/>that place would the projected body in its de&longs;cent come to the <lb/>ground. </s><s>So that hither may be referred the argument taken from <lb/>a bullet &longs;hot from a Canon directly upwards; as al&longs;o that other <lb/>u&longs;ed by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy,<emph.end type="italics"/> of the grave bodies that falling <lb/>from on high, are ob&longs;erved to de&longs;cend by a direct and perpendicu­ <lb/>lar line to the &longs;urface of the Earth. </s><s>Now that I may begin to untie <lb/>the&longs;e knots, I demand of <emph type="italics"/>Simplicius<emph.end type="italics"/> that in ca&longs;e one &longs;hould deny <lb/>to <emph type="italics"/>Ptolomy<emph.end type="italics"/> and <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> that weights in falling freely from on <lb/>high, de&longs;cend by a right and perpendicular line, that is, directly <lb/>to the centre, what means he would u&longs;e to prove it?</s></p><p type="margin"><s><margin.target id="marg306"></margin.target>Ari&longs;totles <emph type="italics"/>argu­ <lb/>ment again&longs;t the <lb/>Earths motion, is <lb/>defective in two <lb/>things<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg307"></margin.target>* The &longs;ame word <lb/>which a little above <lb/>I tendred &longs;tay be­ <lb/>hind, as a bowle <lb/>when it meets with <lb/>ruls.</s></p><p type="margin"><s><margin.target id="marg308"></margin.target><emph type="italics"/>The an&longs;wer to <lb/>the third argu­ <lb/>ment.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg309"></margin.target><emph type="italics"/>The an&longs;wer to <lb/>the fourth argu­ <lb/>ment.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>The means of the &longs;en&longs;es; the which a&longs;&longs;ureth us, that <lb/>that Tower or other altitude, is upright and perpendicular, and <lb/>&longs;heweth us that that &longs;tone, or other grave body, doth &longs;lide along <lb/>the Wall, without inclining a hairs breadth to one &longs;ide or ano­ <lb/>ther, and light at the foot thereof ju&longs;t under the place from whence <lb/>it was let fall.</s></p> <pb xlink:href="040/01/139.jpg" pagenum="121"/><p type="main"><s>SALV. </s><s>But if it &longs;hould happen that the Terre&longs;trial Globe did <lb/>move round, and con&longs;equently carry the Tower al&longs;o along with <lb/>it, and that the &longs;tone did then al&longs;o grate and &longs;lide along the &longs;ide of <lb/>the Tower, what mu&longs;t its motion be then?</s></p><p type="main"><s>SIMPL. </s><s>In this ca&longs;e we may rather &longs;ay its motions: for it <lb/>would have one wherewith to de&longs;cend from the top of the Tower <lb/>to the bottom, and &longs;hould nece&longs;&longs;arily have another to follow the <lb/>cour&longs;e of the &longs;aid Tower.</s></p><p type="main"><s>SALV. </s><s>So that its motion &longs;hould be compounded of two, to <lb/>wit, of that wherewith it mea&longs;ureth the Tower, and of that o­ <lb/>ther wherewith it followeth the &longs;ame: From which compo&longs;ition <lb/>would follow, that the &longs;tone would no longer de&longs;cribe that &longs;imple <lb/>right and perpendicular line, but one tran&longs;ver&longs;e, and perhaps not <lb/>&longs;treight.</s></p><p type="main"><s>SIMPL. </s><s>I can &longs;ay nothing of its non-rectitude, but this I know <lb/>very well, that it would of nece&longs;&longs;ity be tran&longs;ver&longs;e, and different <lb/>from the other directly perpendicular, which it doth de&longs;cribe, the <lb/>Earth &longs;tanding &longs;till.</s></p><p type="main"><s>SALV. </s><s>You &longs;ee then, that upon the meer ob&longs;erving the falling <lb/>&longs;tone to glide along the Tower, you cannot certainly affirm that <lb/>it de&longs;cribeth a line which is &longs;treight and perpendicular, unle&longs;s you <lb/>fir&longs;t &longs;uppo&longs;e that the Earth &longs;tandeth &longs;till.</s></p><p type="main"><s>SIMPL. True; for if the Earth &longs;hould move, the &longs;tones mo­ <lb/>tion would be tran&longs;ver&longs;e, and not perpendicular.</s></p><p type="main"><s>SALV. </s><s>Behold then the Paralogi&longs;m of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomey<emph.end type="italics"/> <lb/><arrow.to.target n="marg310"></arrow.to.target> <lb/>to be evident and manife&longs;t, and di&longs;covered by you your &longs;elf, <lb/>wherein that is &longs;uppo&longs;ed for known, which is intended to be de­ <lb/>mon&longs;trated.</s></p><p type="margin"><s><margin.target id="marg310"></margin.target><emph type="italics"/>The Paralogi&longs;m <lb/>of<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>and<emph.end type="italics"/> <lb/>Ptolomey <emph type="italics"/>in &longs;up­ <lb/>po&longs;ing that for <lb/>known, which is in <lb/>que&longs;tion.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>How can that be? </s><s>To me it appeareth that the <lb/>Syllogi&longs;m is rightly demon&longs;trated without <emph type="italics"/>petitionem principii.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You &longs;hall &longs;ee how it is; an&longs;wer me a little. </s><s>Doth he <lb/>not lay down the conclu&longs;ion as unknown?</s></p><p type="main"><s>SIMPL. Unknown; why otherwi&longs;e the demon&longs;trating it would <lb/>be &longs;uperfluous.</s></p><p type="main"><s>SALV. </s><s>But the middle term, ought not that to be known?</s></p><p type="main"><s>SIMPL. </s><s>Its nece&longs;&longs;ary that it &longs;hould; for otherwi&longs;e it would be <lb/>a proving <emph type="italics"/>ignotum per æquè ignotum.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Our conclu&longs;ion which is to be proved, and which is un­ <lb/>known, is it not the &longs;tability of the Earth?</s></p><p type="main"><s>SIMPL. </s><s>It is the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>The middle term, which ought to be known, is it not the <lb/>&longs;treight and perpendicular de&longs;cent of the &longs;tone?</s></p><p type="main"><s>SIMPL. </s><s>It is &longs;o.</s></p><p type="main"><s>SALV. </s><s>But was it not ju&longs;t now concluded, that we can have <lb/>no certain knowledg whether that &longs;ame &longs;hall be direct and perpen­ <pb xlink:href="040/01/140.jpg" pagenum="122"/>dicular, unle&longs;s we fir&longs;t know that the Earth &longs;tands &longs;till? </s><s>Therefore <lb/>in your Syllogi&longs;m the certainty of the middle term is a&longs;&longs;umed <lb/>from the uncertainty of the conclu&longs;ion. </s><s>You may &longs;ee then, what <lb/>and how great the Paralogi&longs;m is.</s></p><p type="main"><s>SAGR. </s><s>I would, in favour of <emph type="italics"/>Simplicius,<emph.end type="italics"/> defend <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> if it <lb/>were po&longs;&longs;ible, or at lea&longs;t better &longs;atisfie my &longs;elf concerning the <lb/>&longs;trength of your illation. </s><s>You &longs;ay, that the &longs;eeing the &longs;tone rake <lb/>along the Tower, is not &longs;ufficient to a&longs;&longs;ure us, that its motion is <lb/>perpendicular (which is the middle term of the Syllogi&longs;m) unle&longs;s <lb/>it be pre&longs;uppo&longs;ed, that the Earth &longs;tandeth &longs;till, which is the con­ <lb/>clu&longs;ion to be proved: For that if the Tower did move together <lb/>with the Earth, and the &longs;tone did &longs;lide along the &longs;ame, the motion <lb/>of the &longs;tone would be tran&longs;ver&longs;e, and not perpendicular. </s><s>But I <lb/>&longs;hall an&longs;wer, that &longs;hould the Tower move, it would be impo&longs;&longs;ible <lb/>that the &longs;tone &longs;hould fall gliding along the &longs;ide of it; and there­ <lb/>fore from its falling in that manner the &longs;tability of the Earth is in­ <lb/>ferred.</s></p><p type="main"><s>SIMPL. </s><s>It is &longs;o; for if you would have the &longs;tone in de&longs;cend­ <lb/>ing to grate upon the Tower, though it were carried round by <lb/>the Earth, you mu&longs;t allow the &longs;tone two natural motions, to wit, <lb/>the &longs;traight motion towards the Centre, and the circular about <lb/>the Centre, the which is impo&longs;&longs;ible.</s></p><p type="main"><s>SALV. <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> defen&longs;e then con&longs;i&longs;teth in the impo&longs;&longs;ibilitie, <lb/>or at lea&longs;t in his e&longs;teeming it an impo&longs;&longs;ibility, that the &longs;tone &longs;hould <lb/>move with a motion mixt of right and circular: for if he did <lb/>not hold it impo&longs;&longs;ible that the &longs;tone could move to the Centre, <lb/>and about the Centre at once, he mu&longs;t have under&longs;tood, that it <lb/>might come to pa&longs;s that the cadent &longs;tone might in its de&longs;cent, race <lb/>the Tower as well when it moved as when it &longs;tood &longs;till; and con­ <lb/>&longs;equently he mu&longs;t have perceived, that from this grating nothing <lb/>could be inferred touching the mobility or immobility of the <lb/>Earth. </s><s>But this doth not any way excu&longs;e <emph type="italics"/>Aristotle<emph.end type="italics"/>; a&longs;well be­ <lb/>cau&longs;e he ought to have expre&longs;t it, if he had had &longs;uch a conceit, it <lb/>being &longs;o material a part of his Argument; as al&longs;o becau&longs;e it can <lb/>neither be &longs;aid that &longs;uch an effect is impo&longs;&longs;ible, nor that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>did e&longs;teem it &longs;o. </s><s>The fir&longs;t cannot be affirmed, for that by and <lb/>by I &longs;hall &longs;hew that it is not onely po&longs;&longs;ible, but nece&longs;&longs;ary: nor <lb/><arrow.to.target n="marg311"></arrow.to.target> <lb/>much le&longs;s can the &longs;econd be averred, for that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf <lb/>granteth fire to move naturally upwards in a right line, and to <lb/>move about with the diurnal motion, imparted by Heaven to the <lb/>whole Element of Fire, and the greater part of the Air: If there­ <lb/>fore he held it not impo&longs;&longs;ible to mix the right motion upwards, <lb/>with the circular communicated to the Fire and Air from the con­ <lb/>cave of the Moon, much le&longs;s ought he to account impo&longs;&longs;ible the <lb/>mixture of the right motion downwards of the &longs;tone, with the <pb xlink:href="040/01/141.jpg" pagenum="123"/>circular which we pre&longs;uppo&longs;e natural to the whole Terre&longs;trial <lb/>Globe, of which the &longs;tone is a part.</s></p><p type="margin"><s><margin.target id="marg311"></margin.target>Ari&longs;totle <emph type="italics"/>admit­ <lb/>teth that the Fire <lb/>moveth directly <lb/>upwards by na­ <lb/>ture, and round a­ <lb/>bout by participa­ <lb/>tion.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I &longs;ee no &longs;uch thing: for if the element of Fire re­ <lb/>volve round together with the Air, it is a very ea&longs;ie, yea a nece&longs;&longs;ary <lb/>thing, that a &longs;park of fire which from the Earth mounts upwards, <lb/>in pa&longs;&longs;ing thorow the moving air, &longs;hould receive the &longs;ame motion, <lb/>being a body &longs;o thin, light, and ea&longs;ie to be moved: but that a <lb/>very heavy &longs;tone, or a Canon bullet, that de&longs;cendeth from on <lb/>high, and that is at liberty to move whither it will, &longs;hould &longs;uffer <lb/>it &longs;elf to be tran&longs;ported either by the air or any other thing, is <lb/>altogether incredible. </s><s>Be&longs;ides that, we have the Experiment, <lb/>which is &longs;o proper to our purpo&longs;e, of the &longs;tone let fall from the <lb/>round top of the Ma&longs;t of a &longs;hip, which when the &longs;hip lyeth &longs;till, <lb/>falleth at the Partners of the Ma&longs;t; but when the &longs;hip &longs;aileth, falls <lb/>&longs;o far di&longs;tant from that place, by how far the &longs;hip in the time of <lb/>the &longs;tones falling had run forward; which will not be a few fa­ <lb/>thoms, when the &longs;hips cour&longs;e is &longs;wift.</s></p><p type="main"><s>SALV. </s><s>There is a great di&longs;parity between the ca&longs;e of the Ship <lb/><arrow.to.target n="marg312"></arrow.to.target> <lb/>and that of the Earth, if the Terre&longs;trial Globe be &longs;uppo&longs;ed to have <lb/>a diurnal motion. </s><s>For it is a thing very manife&longs;t, that the mo­ <lb/>tion of the Ship, as it is not natural to it, &longs;o the motion of all tho&longs;e <lb/>things that are in it is accidental, whence it is no wonder that the <lb/>&longs;tone which was retained in the round top, being left at liberty, <lb/>de&longs;cendeth downwards without any obligation to follow the mo­ <lb/>tion of the Ship. </s><s>But the diurnal conver&longs;ion is a&longs;cribed to the <lb/>Terre&longs;trial Globe for its proper and natural motion, and con&longs;e­ <lb/>quently, it is &longs;o to all the parts of the &longs;aid Globe; and, as being <lb/>impre&longs;s'd by nature, is indelible in them; and therefore that &longs;tone <lb/>that is on the top of the Tower hath an intrin&longs;ick inclination of <lb/>revolving about the Centre of its <emph type="italics"/>Whole<emph.end type="italics"/> in twenty four hours, and <lb/>this &longs;ame natural in&longs;tinct it exerci&longs;eth eternally, be it placed in any <lb/>&longs;tate what&longs;oever. </s><s>And to be a&longs;&longs;ured of the truth of this, you <lb/>have no more to do but to alter an antiquated impre&longs;&longs;ion made <lb/>in your mind; and to &longs;ay, Like as in that I hitherto holding it to <lb/>be the property of the Terre&longs;trial Globe to re&longs;t immoveable about <lb/>its Centre, did never doubt or que&longs;tion but that all what&longs;oever <lb/>particles thereof do al&longs;o naturally remain in the &longs;ame &longs;tate of re&longs;t: <lb/>So it is rea&longs;on, in ca&longs;e the Terre&longs;trial Globe did move round by <lb/>natural in&longs;tinct in twenty four hours, that the intrin&longs;ick and natu­ <lb/>ral inclination of all its parts &longs;hould al&longs;o be, not to &longs;tand &longs;till, but <lb/><arrow.to.target n="marg313"></arrow.to.target> <lb/>to follow the &longs;ame revolution. </s><s>And thus without running into <lb/>any inconvenience, one may conclude, that in regard the motion <lb/>conferred by the force of ^{*}Oars on the Ship, and by it on all the <lb/>things that are contained within her, is not natural but forreign, it <lb/>is very rea&longs;onable that that &longs;tone, it being &longs;eparated from the &longs;hip, <pb xlink:href="040/01/142.jpg" pagenum="124"/>do reduce its &longs;elf to its natural di&longs;po&longs;ure, and return to exerci&longs;e <lb/><arrow.to.target n="marg314"></arrow.to.target> <lb/>its pure &longs;imple in&longs;tinct given it by nature. </s><s>To this I add, that <lb/>it's nece&longs;&longs;ary, that at lea&longs;t that part of the Air which is beneath the <lb/>greater heights of mountains, &longs;hould be tran&longs;ported and carried <lb/>round by the roughne&longs;s of the Earths &longs;urface; or that, as being <lb/>mixt with many Vapours, and terrene Exhalations, it do na­ <lb/>turally follow the diurnal motion, which occurreth not in the <lb/>Air about the &longs;hip rowed by Oars: So that your arguing <lb/>from the &longs;hip to the Tower hath not the force of an illation; <lb/>becau&longs;e that &longs;tone which falls from the round top of the Ma&longs;t, <lb/>entereth into a <emph type="italics"/>medium,<emph.end type="italics"/> which is unconcern'd in the motion <lb/>of the &longs;hip: but that which departeth from the top of the Tower, <lb/>finds a <emph type="italics"/>medium<emph.end type="italics"/> that hath a motion in common with the whole Ter­ <lb/>re&longs;trial Globe; &longs;o that without being hindred, rather being a&longs;&longs;i&longs;ted <lb/>by the motion of the air, it may follow the univer&longs;al cour&longs;e of the <lb/>Earth.</s></p><p type="margin"><s><margin.target id="marg312"></margin.target><emph type="italics"/>The di&longs;parity be­ <lb/>tween the fall of a <lb/>&longs;tone from the <lb/>round top of a &longs;hip, <lb/>and from the top <lb/>of a tower.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg313"></margin.target>*That you may not <lb/>&longs;u&longs;pect my tran&longs;la­ <lb/>tion, or wonder <lb/>what Oars have to <lb/>do with a &longs;hip, you <lb/>are to know that <lb/>the Author intends <lb/>the Gallies u&longs;ed in <lb/>the Mediterrane.</s></p><p type="margin"><s><margin.target id="marg314"></margin.target><emph type="italics"/>The part of the <lb/>Air inferiour to <lb/>the higher moun­ <lb/>tains doth follow <lb/>the motion of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>I cannot conceive that the air can imprint in a very <lb/><arrow.to.target n="marg315"></arrow.to.target> <lb/>great &longs;tone, or in a gro&longs;s Globe of Wood or Ball of Lead, as <lb/>&longs;uppo&longs;e of two hundred weight, the motion wherewith its &longs;elf is <lb/>moved, and which it doth perhaps communicate to feathers, &longs;now, <lb/>and other very light things: nay, I &longs;ee that a weight of that na­ <lb/>ture, being expo&longs;ed to any the mo&longs;t impetuous wind, is not there­ <lb/>by removed an inch from its place; now con&longs;ider with your &longs;elf <lb/>whether the air will carry it along therewith.</s></p><p type="margin"><s><margin.target id="marg315"></margin.target><emph type="italics"/>The motion of the <lb/>Air apt to carry <lb/>with it light things <lb/>but not heavy.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>There is great difference between your experiment and <lb/>our ca&longs;e. </s><s>You introduce the wind blowing again&longs;t that &longs;tone, <lb/>&longs;uppo&longs;ed in a &longs;tate of re&longs;t, and we expo&longs;e to the air, which already <lb/>moveth, the &longs;tone which doth al&longs;o move with the &longs;ame velocity; <lb/>&longs;o that the air is not to conferr a new motion upon it, but onely <lb/>to maintain, or to &longs;peak better, not to hinder the motion already <lb/>acquired: you would drive the &longs;tone with a &longs;trange and preter­ <lb/>natural motion, and we de&longs;ire to con&longs;erve it in its natural. </s><s>If <lb/>you would produce a more pertinent experiment, you &longs;hould &longs;ay, <lb/>that it is ob&longs;erved, if not with the eye of the forehead, yet with <lb/>that of the mind, what would evene, if an eagle that is carried by <lb/>the cour&longs;e of the wind, &longs;hould let a &longs;tone fall from its talons; <lb/>which, in regard that at its being let go, it went along with the <lb/>wind, and after it was let fall it entered into a <emph type="italics"/>medium<emph.end type="italics"/> that mo­ <lb/>ved with equal velocity, I am very confident that it would not be <lb/>&longs;een to de&longs;cend in its fall perpendicularly, but that following the <lb/>cour&longs;e of the wind, and adding thereto that of its particular gra­ <lb/>vity, it would move with a tran&longs;ver&longs;e motion.</s></p><p type="main"><s>SIMPI. </s><s>But it would fir&longs;t be known how &longs;uch an experiment <lb/>may be made; and then one might judg according to the event. <lb/></s><s>In the mean time the effect of the &longs;hip doth hitherto incline to fa­ <lb/>vour our opinion.</s></p> <pb xlink:href="040/01/143.jpg" pagenum="125"/><p type="main"><s>SALV. </s><s>Well &longs;aid you <emph type="italics"/>hitherto,<emph.end type="italics"/> for perhaps it may anon change <lb/>countenance. </s><s>And that I may no longer hold you in &longs;u&longs;pen&longs;e, <lb/>tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> do you really believe, that the Experiment of <lb/>the &longs;hip &longs;quares &longs;o very well with our purpo&longs;e, as that it ought to <lb/>be believed, that that which we &longs;ee happen in it, ought al&longs;o to <lb/>evene in the Terre&longs;trial Globe?</s></p><p type="main"><s>SIMPL. </s><s>As yet I am of that opinion; and though you have <lb/>alledged &longs;ome &longs;mall di&longs;parities, I do not think them of &longs;o great <lb/>moment, as that they &longs;hould make me change my judgment.</s></p><p type="main"><s>SALV. </s><s>I rather de&longs;ire that you would continue therein, and <lb/>hold for certain, that the effect of the Earth would exactly an&longs;wer <lb/>that of the &longs;hip: provided, that when it &longs;hall appear prejudicial to <lb/>your cau&longs;e, you would not be humorous and alter your thoughts. <lb/></s><s>You may haply &longs;ay, Fora&longs;much as when the &longs;hip &longs;tands &longs;till, the <lb/>&longs;tone falls at the foot of the Ma&longs;t, and when &longs;he is under &longs;ail, it <lb/>lights far from thence, that therefore by conver&longs;ion, from the &longs;tones <lb/>falling at the foot is argued the &longs;hips &longs;tanding &longs;till, and from its <lb/>falling far from thence is argued her moving; and becau&longs;e that <lb/>which occurreth to the &longs;hip, ought likewi&longs;e to befall the Earth: <lb/>that therefore from the falling of the &longs;tone at the foot of the Tow­ <lb/>er is nece&longs;&longs;arily inferred the immobility of the Terre&longs;trial Globe. <lb/></s><s>Is not this your argumentation?</s></p><p type="main"><s>SIMPL. </s><s>It is; and reduced into that conci&longs;ene&longs;s, as that it is <lb/>become mo&longs;t ea&longs;ie to be apprehended.</s></p><p type="main"><s>SALV. </s><s>Now tell me; if the &longs;tone let fall from the Round­ <lb/>top, when the &longs;hip is in a &longs;wift cour&longs;e, &longs;hould fall exactly in <lb/>the &longs;ame place of the &longs;hip, in which it falleth when the &longs;hip is at <lb/>anchor, what &longs;ervice would the&longs;e experiments do you, in order to <lb/>the a&longs;certaining whether the ve&longs;&longs;el doth &longs;tand &longs;till or move?</s></p><p type="main"><s>SIMPL. </s><s>Ju&longs;t none: Like as, for exemple, from the beating of <lb/>the pul&longs;e one cannot know whether a per&longs;on be a&longs;leep or awake, <lb/>&longs;eeing that the pul&longs;e beateth after the &longs;ame manner in &longs;leeping as <lb/>in waking.</s></p><p type="main"><s>SALV. </s><s>Very well. </s><s>Have you ever tryed the experiment of the <lb/>Ship?</s></p><p type="main"><s>SIMPL. </s><s>I have not; but yet I believe that tho&longs;e Authors <lb/>which alledg the &longs;ame, have accurately ob&longs;erved it; be&longs;ides that <lb/>the cau&longs;e of the di&longs;parity is &longs;o manife&longs;tly known, that it admits <lb/>of no que&longs;tion.</s></p><p type="main"><s>SALV. </s><s>That it is po&longs;&longs;ible that tho&longs;e Authors in&longs;tance in it, <lb/>without having made tryal of it, you your &longs;elf are a good te&longs;ti­ <lb/>mony, that without having examined it, alledg it as certain, and in <lb/>a credulous way remit it to their authority; as it is now not onely <lb/>po&longs;&longs;ible, but very probable that they likewi&longs;e did; I mean, did <lb/>remit the &longs;ame to their Predece&longs;&longs;ors, without ever arriving at one <pb xlink:href="040/01/144.jpg" pagenum="126"/>that had made the experiment: for whoever &longs;hall examine the <lb/>&longs;ame, &longs;hall find the event &longs;ucceed quite contrary to what hath <lb/>been written of it: that is, he &longs;hall &longs;ee the &longs;tone fall at all times <lb/>in the &longs;ame place of the Ship, whether it &longs;tand &longs;till, or move with <lb/>any what&longs;oever velocity. </s><s>So that the &longs;ame holding true in the <lb/><arrow.to.target n="marg316"></arrow.to.target> <lb/>Earth, as in the Ship, one cannot from the &longs;tones falling perpen­ <lb/>dicularly at the foot of the Tower, conclude any thing touching <lb/>the motion or re&longs;t of the Earth.</s></p><p type="margin"><s><margin.target id="marg316"></margin.target><emph type="italics"/>The stone falling <lb/>from the Mast of <lb/>a &longs;hip lights in the <lb/>&longs;ame place, whe­ <lb/>ther the &longs;hip doth <lb/>move or ly still.<emph.end type="italics"/></s></p><p type="main"><s>SIMPL. </s><s>If you &longs;hould refer me to any other means than to <lb/>experience, I verily believe our Di&longs;putations would not come to <lb/>an end in ha&longs;te; for this &longs;eemeth to me a thing &longs;o remote from all <lb/>humane rea&longs;on, as that it leaveth not the lea&longs;t place for credulity <lb/>or probability.</s></p><p type="main"><s>SALV. </s><s>And yet it hath left place in me for both.</s></p><p type="main"><s>SIMPL. </s><s>How is this? </s><s>You have not made an hundred, no nor <lb/>one proof thereof, and do you &longs;o confidently affirm it for true? <lb/></s><s>I for my part will return to my incredulity, and to the confidence <lb/>I had that the Experiment hath been tried by the principal Au­ <lb/>thors who made u&longs;e thereof, and that the event &longs;ucceeded as they <lb/>affirm.</s></p><p type="main"><s>SALV. </s><s>I am a&longs;&longs;ured that the effect will en&longs;ue as I tell you; for &longs;o <lb/>it is nece&longs;&longs;ary that it &longs;hould: and I farther add, that you know your <lb/>&longs;elf that it cannot fall out otherwi&longs;e, however you feign or &longs;eem to <lb/>feign that you know it not. </s><s>Yet I am &longs;o good at taming of wits, <lb/>that I will make you confe&longs;s the &longs;ame whether you will or no. </s><s>But <lb/><emph type="italics"/>Sagredus<emph.end type="italics"/> &longs;tands very mute, and yet, if I mi&longs;take not, I &longs;aw him <lb/>make an offer to &longs;peak &longs;omewhat.</s></p><p type="main"><s>SAGR. </s><s>I had an intent to &longs;ay &longs;omething, but to tell you true, I <lb/>know not what it was; for the curio&longs;ity that you have moved in me, <lb/>by promi&longs;ing that you would force <emph type="italics"/>Simplicius<emph.end type="italics"/> to di&longs;cover the <lb/>knowledg which he would conceal from us, hath made me to de­ <lb/>po&longs;e all other thoughts: therefore I pray you to make good your <lb/>vaunt.</s></p><p type="main"><s>SALV. </s><s>Provided that <emph type="italics"/>Simplicius<emph.end type="italics"/> do con&longs;ent to reply to what I <lb/>&longs;hall ask him, I will not fail to do it.</s></p><p type="main"><s>SIMPL. </s><s>I will an&longs;wer what I know, a&longs;&longs;ured that I &longs;hall not be <lb/>much put to it, for that of tho&longs;e things which I hold to be fal&longs;e, <lb/>I think nothing can be known, in regard that Science re&longs;pecteth <lb/>truths and not fal&longs;hoods.</s></p><p type="main"><s>SALV. </s><s>I de&longs;ire not that you &longs;hould &longs;ay or reply, that you know <lb/>any thing, &longs;ave that which you mo&longs;t a&longs;&longs;uredly know. </s><s>Therefore <lb/>tell me; If you had here a flat &longs;uperficies as polite as a Looking­ <lb/>gla&longs;s, and of a &longs;ub&longs;tance as hard as &longs;teel, and that it were not pa­ <lb/>ralel to the Horizon, but &longs;omewhat inclining, and that upon it <lb/>you did put a Ball perfectly &longs;pherical, and of a &longs;ub&longs;tance grave and <pb xlink:href="040/01/145.jpg" pagenum="127"/>hard, as &longs;uppo&longs;e of bra&longs;s; what think you it would do being let <lb/>go? </s><s>do not you believe (as for my part I do) that it would lie <lb/>&longs;till?</s></p><p type="main"><s>SIMPL. </s><s>If that &longs;uperficies were inclining?</s></p><p type="main"><s>SALV. Yes; for &longs;o I have already &longs;uppo&longs;ed.</s></p><p type="main"><s>SIMPL. </s><s>I cannot conceive how it &longs;hould lie &longs;till: nay, I am <lb/>confident that it would move towards the declivity with much pro­ <lb/>pen&longs;ne&longs;s.</s></p><p type="main"><s>SALV. </s><s>Take good heed what you &longs;ay, <emph type="italics"/>Simplicius,<emph.end type="italics"/> for I am <lb/>confident that it would lie &longs;till in what ever place you &longs;hould lay <lb/>it.</s></p><p type="main"><s>SIMPL. </s><s>So long as you make u&longs;e of &longs;uch &longs;uppo&longs;itions, <emph type="italics"/>Sal­ <lb/>viatus,<emph.end type="italics"/> I &longs;hall cea&longs;e to wonder if you inferr mo&longs;t ab&longs;urd con­ <lb/>clu&longs;ions.</s></p><p type="main"><s>SALV. </s><s>Are you a&longs;&longs;ured, then, that it would freely move to­ <lb/>wards the declivity?</s></p><p type="main"><s>SIMPL. </s><s>Who doubts it?</s></p><p type="main"><s>SALV. </s><s>And this you verily believe, not becau&longs;e I told you &longs;o, <lb/>(for I endeavoured to per&longs;wade you to think the contrary) but of <lb/>your &longs;elf, and upon your natural judgment.</s></p><p type="main"><s>SIMPL. </s><s>Now I &longs;ee what you would be at; you &longs;poke not this <lb/>as really believing the &longs;ame; but to try me, and to wre&longs;t matter <lb/>out of my own mouth wherewith to condemn me.</s></p><p type="main"><s>SALV. </s><s>You are in the right. </s><s>And how long would that Ball <lb/>move, and with what velocity? </s><s>But take notice that I in&longs;tanced <lb/>in a Ball exactly round, and a plain exqui&longs;itely poli&longs;hed, that all <lb/>external and accidental impediments might be taken away. </s><s>And <lb/>&longs;o would I have you remove all ob&longs;tructions cau&longs;ed by the Airs re­ <lb/>&longs;i&longs;tance to divi&longs;ion, and all other ca&longs;ual ob&longs;tacles, if any other <lb/>there can be.</s></p><p type="main"><s>SIMPL. </s><s>I very well under&longs;tand your meaning, and as to your <lb/>demand, I an&longs;wer, that the Ball would continue to move <emph type="italics"/>in in­ <lb/>finitum,<emph.end type="italics"/> if the inclination of the plain &longs;hould &longs;o long la&longs;t, and con­ <lb/>tinually with an accelerating motion; for &longs;uch is the nature of <lb/>ponderous moveables, that <emph type="italics"/>vires acquirant eundo<emph.end type="italics"/>: and the great­ <lb/>er the declivity was, the greater the velocity would be.</s></p><p type="main"><s>SALV. </s><s>But if one &longs;hould require that that Ball &longs;hould move <lb/>upwards on that &longs;ame &longs;uperficies, do you believe that it would <lb/>&longs;o do?</s></p><p type="main"><s>SIMPL. </s><s>Not &longs;pontaneou&longs;ly; but being drawn, or violently <lb/>thrown, it may.</s></p><p type="main"><s>SALV. </s><s>And in ca&longs;e it were thru&longs;t forward by the impre&longs;&longs;ion of <lb/>&longs;ome violent <emph type="italics"/>impetus<emph.end type="italics"/> from without, what and how great would <lb/>its motion be?</s></p><p type="main"><s>SIMPL. </s><s>The motion would go continually decrea&longs;ing and re­ <pb xlink:href="040/01/146.jpg" pagenum="128"/>tarding, as being contrary to nature; and would be longer or <lb/>&longs;horter, according to the greater or le&longs;s impul&longs;e, and according to <lb/>the greater or le&longs;s acclivity.</s></p><p type="main"><s>SALV. </s><s>It &longs;eems, then, that hitherto you have explained to me <lb/>the accidents of a moveable upon two different Planes; and that <lb/>in the inclining plane, the grave moveable doth &longs;pontaneou&longs;ly de­ <lb/>&longs;cend, and goeth continually accelerating, and that to retain it in <lb/>re&longs;t, force mu&longs;t be u&longs;ed therein: but that on the a&longs;cending plane, <lb/>there is required a force to thru&longs;t it forward, and al&longs;o to &longs;tay it in <lb/>re&longs;t, and that the motion impre&longs;&longs;ed goeth continually dimini&longs;hing, <lb/>till that in the end it cometh to nothing. </s><s>You &longs;ay yet farther, <lb/>that in both the one and the other ca&longs;e, there do ari&longs;e differences <lb/>from the planes having a greater or le&longs;s declivity or acclivity; &longs;o <lb/>that the greater inclination is attended with the greater velocity; <lb/>and contrariwi&longs;e, upon the a&longs;cending plane, the &longs;ame moveable <lb/>thrown with the &longs;ame force, moveth a greater di&longs;tance, by how <lb/>much the elevation is le&longs;s. </s><s>Now tell me, what would befall the <lb/>&longs;ame moveable upon a &longs;uperficies that had neither acclivity nor <lb/>declivity?</s></p><p type="main"><s>SIMPL. </s><s>Here you mu&longs;t give me a little time to con&longs;ider of an <lb/>an&longs;wer. </s><s>There being no declivity, there can be no natural incli­ <lb/>nation to motion: and there being no acclivity, there can be no <lb/>re&longs;i&longs;tance to being moved; &longs;o that there would ari&longs;e an indiffe­ <lb/>rence between propen&longs;ion and re&longs;i&longs;tance of motion; therefore, <lb/>methinks it ought naturally to &longs;tand &longs;till. </s><s>But I had forgot my <lb/>&longs;elf: it was but even now that <emph type="italics"/>Sagredus<emph.end type="italics"/> gave me to under&longs;tand <lb/>that it would &longs;o do.</s></p><p type="main"><s>SALV. </s><s>So I think, provided one did lay it down gently: but <lb/>if it had an <emph type="italics"/>impetus<emph.end type="italics"/> given it towards any part, what would fol­ <lb/>low?</s></p><p type="main"><s>SIMP. </s><s>There would follow, that it &longs;hould move towards that <lb/>part.</s></p><p type="main"><s>SALV. </s><s>But with what kind of motion? </s><s>with the continually <lb/>accelerated, as in declining planes; or with the &longs;ucce&longs;&longs;ively re­ <lb/>tarded, as in tho&longs;e a&longs;cending.</s></p><p type="main"><s>SIMP. </s><s>I cannot tell how to di&longs;cover any cau&longs;e of acceleration, <lb/>or retardation, there being no declivity or acclivity.</s></p><p type="main"><s>SALV. Well: but if there be no cau&longs;e of retardation, much <lb/>le&longs;s ought there to be any cau&longs;e of re&longs;t. </s><s>How long therefore <lb/>would you have the moveable to move?</s></p><p type="main"><s>SIMP. </s><s>As long as that &longs;uperficies, neither inclined nor decli­ <lb/>ned &longs;hall la&longs;t.</s></p><p type="main"><s>SALV. </s><s>Therefore if &longs;uch a &longs;pace were interminate, the motion <lb/>upon the &longs;ame would likewi&longs;e have no termination, that is, would <lb/>be perpetual.</s></p> <pb xlink:href="040/01/147.jpg" pagenum="129"/><p type="main"><s>SIMP. </s><s>I think &longs;o, if &longs;o be the moveable be of a matter <lb/>durable.</s></p><p type="main"><s>SALV. </s><s>That hath been already &longs;uppo&longs;ed, when it was &longs;aid, <lb/>that all external and accidental impediments were removed, and <lb/>the brittlene&longs;&longs;e of the moveable in this our ca&longs;e, is one of tho&longs;e <lb/>impediments accidental. </s><s>Tell me now, what do you think is the <lb/>cau&longs;e that that &longs;ame Ball moveth &longs;pontaneou&longs;ly upon the inclining <lb/>plane, and not without violence upon the erected?</s></p><p type="main"><s>SIMP. </s><s>Becau&longs;e the inclination of grave bodies is to move to­ <lb/>wards the centre of the Earth, and onely by violence upwards to­ <lb/>wards the circumference; and the inclining &longs;uperficies is that <lb/>which acquireth vicinity to the centre, and the a&longs;cending one, <lb/>remotene&longs;&longs;e.</s></p><p type="main"><s>SALV. </s><s>Therefore a &longs;uperficies, which &longs;hould be neither de­ <lb/>clining nor a&longs;cending, ought in all its parts to be equally di­ <lb/>&longs;tant from the centre. </s><s>But is there any &longs;uch &longs;uperficies in the <lb/>World?</s></p><p type="main"><s>SIMP. </s><s>There is no want thereof: Such is our Terre&longs;trial <lb/>Globe, if it were more even, and not as it is rough and montai­ <lb/>nous; but you have that of the Water, at &longs;uch time as it is calm <lb/>and &longs;till.</s></p><p type="main"><s>SALV. </s><s>Then a &longs;hip which moveth in a calm at Sea, is one of <lb/>tho&longs;e moveables, which run along one of tho&longs;e &longs;uperficies that <lb/>are neither declining nor a&longs;cending, and therefore di&longs;po&longs;ed, in <lb/>ca&longs;e all ob&longs;tacles external and accidental were removed, to move <lb/>with the impul&longs;e once imparted ince&longs;&longs;antly and uniformly.</s></p><p type="main"><s>SIMPL. </s><s>It &longs;hould &longs;eem to be &longs;o.</s></p><p type="main"><s>SALV. </s><s>And that &longs;tone which is on the round top, doth not it <lb/>move, as being together with the &longs;hip carried about by the cir­ <lb/>cumference of a Circle about the Centre; and therefore con&longs;e­ <lb/>quently by a motion in it indelible, if all extern ob&longs;tacles be <lb/>removed? </s><s>And is not this motion as &longs;wift as that of the &longs;hip.</s></p><p type="main"><s>SIMPL. </s><s>Hitherto all is well. </s><s>But what followeth?</s></p><p type="main"><s>SALV. </s><s>Then in good time recant, I pray you, that your la&longs;t <lb/>conclu&longs;ion, if you are &longs;atisfied with the truth of all the pre­ <lb/>mi&longs;es.</s></p><p type="main"><s>SIMPL. </s><s>By my la&longs;t conclu&longs;ion, you mean, That that &longs;ame <lb/>&longs;tone moving with a motion indelibly impre&longs;&longs;ed upon it, is not to <lb/>leave, nay rather is to follow the &longs;hip, and in the end to light in <lb/>the &longs;elf &longs;ame place, where it falleth when the &longs;hip lyeth &longs;till; and <lb/>&longs;o I al&longs;o grant it would do, in ca&longs;e there were no outward impe­ <lb/>diments that might di&longs;turb the &longs;tones motion, after its being let <lb/>go, the which impediments are two, the one is the moveables <lb/>inability to break through the air with its meer <emph type="italics"/>impetus<emph.end type="italics"/> onely, it <lb/>being deprived of that of the &longs;trength of Oars, of which it had <pb xlink:href="040/01/148.jpg" pagenum="130"/>been partaker, as part of the &longs;hip, at the time that it was upon <lb/>the Ma&longs;t; the other is the new motion of de&longs;cent, which al&longs;o <lb/>mu&longs;t needs be an hinderance of that other progre&longs;&longs;ive motion.</s></p><p type="main"><s>SALV. </s><s>As to the impediment of the Air, I do not deny it <lb/>you; and if the thing falling were a light matter, as a feather, <lb/>or a lock of wool, the retardation would be very great, but in <lb/>an heavy &longs;tone is very exceeding &longs;mall. </s><s>And you your &longs;elf but <lb/>even now did &longs;ay, that the force of the mo&longs;t impetuous wind <lb/>&longs;ufficeth not to &longs;tir a great &longs;tone from its place; now do but con­ <lb/>&longs;ider what the calmer air is able to do, being encountred by a <lb/>&longs;tone no more &longs;wift than the whole &longs;hip. </s><s>Neverthele&longs;&longs;e, as I &longs;aid <lb/>before, I do allow you this &longs;mall effect, that may depend upon <lb/>&longs;uch an impediment; like as I know, that you will grant to me, <lb/>that if the air &longs;hould move with the &longs;ame velocity that the &longs;hip <lb/>and &longs;tone hath, then the impediment would be nothing at all. <lb/></s><s>As to the other of the additional motion downwards; in the fir&longs;t <lb/>place it is manife&longs;t, that the&longs;e two, I mean the circular, about <lb/>the centre, and the &longs;treight, towards the centre, are not contra­ <lb/>ries, or de&longs;tructive to one another, or incompatible. </s><s>Becau&longs;e that <lb/>as to the moveable, it hath no repugnance at all to &longs;uch motions, <lb/>for you your &longs;elf have already confe&longs;t the repugnance to be a­ <lb/>gain&longs;t the motion which removeth from the centre, and the incli­ <lb/>nation to be towards the motion which approacheth to the centre. <lb/></s><s>Whence it doth of nece&longs;&longs;ity follow, that the moveable hath nei­ <lb/>ther repugnance, nor propen&longs;ion to the motion which neither ap­ <lb/>proacheth, nor goeth from the centre, nor con&longs;equently is there <lb/>any cau&longs;e for the dimini&longs;hing in it the faculty impre&longs;&longs;ed. </s><s>And for­ <lb/>a&longs;much as the moving cau&longs;e is not one alone, which it hath at­ <lb/>tained by the new operation of retardation; but that they are <lb/>two, di&longs;tinct from each other, of which, the gravity attends on­ <lb/>ly to the drawing of the moveable towards the centre, and the <lb/>vertue impre&longs;s't to the conducting it about the centre, there re­ <lb/>maineth no occa&longs;ion of impediment.</s></p><p type="main"><s>SIMPL. </s><s>Your argumentation, to give you your due, is very <lb/>probable; but in reality it is invelloped with certain intricacies, <lb/>that are not ea&longs;ie to be extricated. </s><s>You have all along built upon <lb/><arrow.to.target n="marg317"></arrow.to.target> <lb/>a &longs;uppo&longs;ition, which the <emph type="italics"/>Peripatetick<emph.end type="italics"/> Schools will not ea&longs;ily grant <lb/>you, as being directly contrary to <emph type="italics"/>Aristotle,<emph.end type="italics"/> and it is to take for <lb/>known and manife&longs;t, That the project &longs;eparated from the proji­ <lb/>cient, continueth the motion by <emph type="italics"/>vertue impre&longs;&longs;ed<emph.end type="italics"/> on it by the <lb/>&longs;aid projicient, which <emph type="italics"/>vertue impre&longs;&longs;ed<emph.end type="italics"/> is a thing as much dete­ <lb/>&longs;ted in <emph type="italics"/>Peripatetick<emph.end type="italics"/> Philo&longs;ophy, as the pa&longs;&longs;age of any accident <lb/>from one &longs;ubject into another. </s><s>Which doctrine doth hold, as I <lb/>believe it is well known unto you, that the project is carried by <lb/>the <emph type="italics"/>medium,<emph.end type="italics"/> which in our ca&longs;e happeneth to be the Air. </s><s>And <pb xlink:href="040/01/149.jpg" pagenum="131"/>therefore if that &longs;tone let fall from the round top, ought to fol­ <lb/>low the motion of the &longs;hip, that effect &longs;hould be a&longs;cribed to the <lb/>Air, and not to the vertue impre&longs;&longs;ed. </s><s>But you pre&longs;uppo&longs;e that <lb/>the Air doth not follow the motion of the &longs;hip, but is tranquil. <lb/></s><s>Moreover, he that letteth it fall, is not to throw it, or to give <lb/>it <emph type="italics"/>impetus<emph.end type="italics"/> with his arm, but ought barely to open his hand and let <lb/>it go; and by this means, the &longs;tone, neither through the vertue <lb/>impre&longs;&longs;ed by the projicient, nor through the help of the Air, <lb/>&longs;hall be able to follow the &longs;hips motion, and therefore &longs;hall be <lb/>left behind.</s></p><p type="margin"><s><margin.target id="marg317"></margin.target><emph type="italics"/>The project ac­ <lb/>cording to<emph.end type="italics"/> Ari&longs;to­ <lb/>tle, <emph type="italics"/>is not moved by <lb/>vertue impre&longs;&longs;ed, <lb/>but by the<emph.end type="italics"/> medium.</s></p><p type="main"><s>SALV. </s><s>I think then that you would &longs;ay, that if the &longs;tone be <lb/>not thrown by the arm of that per&longs;on, it is no longer a pro­ <lb/>jection.</s></p><p type="main"><s>SIMPL. </s><s>It cannot be properly called a motion of projection.</s></p><p type="main"><s>SALV. </s><s>So then that which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;peaks of the motion, the <lb/>moveable, and the mover of the projects, hath nothing to do <lb/>with the bu&longs;ine&longs;&longs;e in hand; and if it concern not our purpo&longs;e, <lb/>why do you alledg the &longs;ame?</s></p><p type="main"><s>SIMP. </s><s>I produce it on the ocea&longs;ion of that impre&longs;&longs;ed vertue, <lb/>named and introduced by you, which having no being in the <lb/>World, can be of no force; for <emph type="italics"/>non-entium nullæ &longs;unt operatio­ <lb/>nes<emph.end type="italics"/>; and therefore not onely of projected, but of all other pre­ <lb/>ternatural motions, the moving cau&longs;e ought to be a&longs;cribed to the <lb/><emph type="italics"/>medium,<emph.end type="italics"/> of which there hath been no due con&longs;ideration had; <lb/>and therefore all that hath been &longs;aid hitherto is to no purpo&longs;e.</s></p><p type="main"><s>SALV. </s><s>Go to now, in good time. </s><s>But tell me, &longs;eeing that <lb/>your in&longs;tance is wholly grounded upon the nullity of the vertue <lb/>impre&longs;&longs;ed, if I &longs;hall demon&longs;trate to you, that the <emph type="italics"/>medium<emph.end type="italics"/> hath <lb/>nothing to do in the continuation of projects, after they are &longs;e­ <lb/>patated from the projicient, will you admit of the impre&longs;&longs;ed ver­ <lb/>tue, or will you make another attempt to overthrow it?</s></p><p type="main"><s>SIMP. </s><s>The operation of the <emph type="italics"/>medium<emph.end type="italics"/> being removed, I &longs;ee not <lb/>how one can have recour&longs;e to any thing el&longs;e &longs;ave the faculty im­ <lb/>pre&longs;&longs;ed by the mover.</s></p><p type="main"><s>SALV. </s><s>It would be well, for the removing, as much as is <lb/>po&longs;&longs;ible, the occa&longs;ions of multiplying contentions, that you <lb/>would explain with as much di&longs;tinctne&longs;&longs;e as may be, what is that <lb/>operation of the <emph type="italics"/>medium<emph.end type="italics"/> in continuing the motion of the project. <lb/><arrow.to.target n="marg318"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg318"></margin.target><emph type="italics"/>Operation of the<emph.end type="italics"/> <lb/>medium <emph type="italics"/>in continu­ <lb/>ing the motion of <lb/>the project.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The projicient hath the &longs;tone in his hand, and with <lb/>force and violence throws his arm, with which jactation the <lb/>&longs;tone doth not move &longs;o much as the circumambient Air; &longs;o that <lb/>when the &longs;tone at its being for&longs;aken by the hand, findeth it &longs;elf <lb/>in the Air, which at the &longs;ame time moveth with impetou&longs;ity, it <lb/>is thereby born away; for, if the air did not operate, the &longs;tone <lb/>would fall at the foot of the projicient or thrower.</s></p> <pb xlink:href="040/01/150.jpg" pagenum="132"/><p type="main"><s><arrow.to.target n="marg319"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg319"></margin.target><emph type="italics"/>Many experi­ <lb/>ments, and rea­ <lb/>&longs;ons again&longs;t the <lb/>cau&longs;e of the moti­ <lb/>on of projects, a&longs;­ <lb/>&longs;igned by<emph.end type="italics"/> Ari&longs;totle.</s></p><p type="main"><s>SALV. </s><s>And was you &longs;o credulous, as to &longs;uffer your &longs;elf to be <lb/>per&longs;waded to believe the&longs;e fopperies, &longs;o long as you had your <lb/>&longs;en&longs;es about you to confute them, and to under&longs;tand the <lb/>truth thereof? </s><s>Therefore tell me, that great &longs;tone, and that <lb/>Canon bullet, which but onely laid upon a table, did continue <lb/>immoveable again&longs;t the mo&longs;t impetuous winds, according as you a <lb/>little before did affirm, if it had been a ball of cork or other light <lb/>&longs;tuffe, think you that the wind would have removed it from its <lb/>place?</s></p><p type="main"><s>SIMP. Yes, and I am a&longs;&longs;ured that it would have blown it <lb/>quite away, and with &longs;o much more velocity, by how much the <lb/>matter was lighter, for upon this rea&longs;on we &longs;ee the clouds to be <lb/>tran&longs;ported with a velocity equal to that of the wind that drives <lb/>them.</s></p><p type="main"><s>SALV. </s><s>And what is the Wind?</s></p><p type="main"><s>SIMP. </s><s>The Wind is defined to be nothing el&longs;e but air moved.</s></p><p type="main"><s>SALV. </s><s>Then the moved air doth carry light things more <lb/>&longs;wiftly, and to a greater di&longs;tance, then it doth heavy.</s></p><p type="main"><s>SIMP. </s><s>Yes certainly.</s></p><p type="main"><s>SALV. </s><s>But if you were to throw with your arm a &longs;tone, and a <lb/>lock of cotton wool, which would move &longs;wi&longs;te&longs;t and farthe&longs;t?</s></p><p type="main"><s>SIMP. </s><s>The &longs;tone by much; nay the wool would fall at my <lb/>feet.</s></p><p type="main"><s>SALV. But, if that which moveth the projected &longs;ub&longs;tance, af­ <lb/>ter it is delivered from the hand, be no other than the air moved <lb/>by the arm, and the moved air do more ea&longs;ily bear away light <lb/>than grave matters, how cometh it that the project of wool flieth <lb/>not farther, and &longs;wifter than that of &longs;tone? </s><s>Certainly it argu­ <lb/>eth that the &longs;tone hath &longs;ome other impul&longs;e be&longs;ides the motion of <lb/>the air. </s><s>Furthermore, if two &longs;trings of equal length did hang <lb/>at yonder beam, and at the end of one there was fa&longs;tened a bul­ <lb/>let of lead, and a ball of cotton wool at the other, and both <lb/>were carried to an equal di&longs;tance from the perpendicular, and <lb/>then let go; it is not to be doubted, but that both the one and <lb/>the other would move towards the perpendicular, and that being <lb/>carried by their own <emph type="italics"/>impetus,<emph.end type="italics"/> they would go a certain &longs;pace be­ <lb/>yond it, and afterwards return thither again. </s><s>But which of the&longs;e <lb/>two pendent Globes do you think, would continue longe&longs;t in mo­ <lb/>tion, before that it would come to re&longs;t in its perpendicularity?</s></p><p type="main"><s>SIMP. </s><s>The ball of lead would &longs;wing to and again many times, <lb/>and that of wool but two or three at the mo&longs;t.</s></p><p type="main"><s>SALV. </s><s>So that that <emph type="italics"/>impetus<emph.end type="italics"/> and that <emph type="italics"/>mobility<emph.end type="italics"/> what&longs;oever is <lb/>the cau&longs;e thereof, would con&longs;erve its &longs;elf longer in grave &longs;ub­ <lb/>&longs;tances, than light; I proceed now to another particular, and de­ <lb/>mand of you, why the air doth not carry away that Lemon <lb/>which is upon that &longs;ame Table?</s></p> <pb xlink:href="040/01/151.jpg" pagenum="133"/><p type="main"><s>SIMP. </s><s>Becau&longs;e that the air it &longs;elf is not moved</s></p><p type="main"><s>SALV. </s><s>It is requi&longs;ite then, that the projicient do confer mo­ <lb/>tion on the Air, with which it afterward moveth the project. </s><s>But <lb/>if &longs;uch a motion cannot be impre&longs;&longs;ed [<emph type="italics"/>i. </s><s>e. </s><s>imparted<emph.end type="italics"/>] it being im­ <lb/>po&longs;&longs;ible to make an accident pa&longs;&longs;e out of one &longs;ubject into another, <lb/>how can it pa&longs;&longs;e from the arm into the Air? </s><s>Will you &longs;ay that the <lb/>Air is not a &longs;ubject different from the arm?</s></p><p type="main"><s>SIMP. </s><s>To this it is an&longs;wered that the Air, in regard it is nei­ <lb/>ther heavy nor light in its own Region, is di&longs;po&longs;ed with facility to <lb/>receive every impul&longs;e, and al&longs;o to retain the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>But if tho&longs;e <emph type="italics"/>penduli<emph.end type="italics"/> even now named, did prove <lb/>unto us, that the moveable, the le&longs;&longs;e it had of gravity, the le&longs;&longs;e <lb/>apt it was to con&longs;erve its motion, how can it be that the Air <lb/>which in the Air hath no gravity at all, doth of it &longs;elf alone re­ <lb/>tain the motion acquired? </s><s>I believe, and know that you by this <lb/>time are of the &longs;ame opinion, that the arm doth not &longs;ooner re­ <lb/>turn to re&longs;t, than doth the circumambient Air. </s><s>Let's go into the <lb/>Chamber, and with a towel let us agitate the Air as much as we <lb/>can, and then holding the cloth &longs;till, let a little candle be <lb/>brought, that was lighted in the next room, or in the &longs;ame place <lb/>let a leaf of beaten Gold be left at liberty to flie any wav, and you <lb/>&longs;hall by the calm vagation of them be a&longs;&longs;ured that the Air is imme­ <lb/>diately reduced to tranquilty. </s><s>I could alledg many other experi­ <lb/>ments to the &longs;ame purpo&longs;e, but if one of the&longs;e &longs;hould not &longs;uf­ <lb/>fice, I &longs;hould think your folly altogether incurable.</s></p><p type="main"><s>SAGR. </s><s>When an arrow is &longs;hot again&longs;t the Wind, how incredi­ <lb/>ble a thing is it, that that &longs;ame &longs;mall filament of air, impelled by <lb/>the bow-&longs;tring, &longs;hould in de&longs;pite of fate go along with the arrow? <lb/></s><s>But I would willingly know another particular of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> to <lb/>which I intreat <emph type="italics"/>Simplicius<emph.end type="italics"/> would vouch&longs;afe me an an&longs;wer. </s><s>Sup­ <lb/>po&longs;ing that with the &longs;ame Bow there were &longs;hot two arrows, one <lb/>ju&longs;t after the u&longs;ual manner, and the other &longs;ide-wayes, placing it <lb/>long-wayes upon the Bow-&longs;tring, and then letting it flie, I would <lb/>know which of them would go farthe&longs;t. </s><s>Favour me, I pray you <lb/>with an an&longs;wer, though the que&longs;tion may &longs;eem to you rather <lb/>ridiculous than otherwi&longs;e; and excu&longs;e me, for that I, who am, as <lb/>you &longs;ee, rather blocki&longs;h, than not, can reach no higher with my <lb/>&longs;peculative faculty.</s></p><p type="main"><s>SIMPL. </s><s>I have never &longs;een an arrow &longs;hot in that manner, yet <lb/>neverthele&longs;&longs;e I believe, that it would not flie &longs;ide-long, the <lb/>twentieth part of the &longs;pace that it goeth end-wayes.</s></p><p type="main"><s>SAGR. </s><s>And for that I am of the &longs;ame opinion, hence it is, that <lb/>I have a doubt ri&longs;en in me, whether <emph type="italics"/>Aristotle<emph.end type="italics"/> doth not contradict <lb/>experience. </s><s>For as to experience, if I lay two arrows upon this <lb/>Table, in a time when a &longs;trong Wind bloweth, one towards <pb xlink:href="040/01/152.jpg" pagenum="134"/>the cour&longs;e of the wind, and the other &longs;idelong, the wind will <lb/>quickly carry away this later, and leave the other where it was; <lb/>and the &longs;ame to my &longs;eeming, ought to happen, if the Doctrine of <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> were true, of tho&longs;e two &longs;hot out of a Bow: fora&longs;much <lb/>as the arrow &longs;hot &longs;ideways is driven by a great quantity of Air, <lb/>moved by the bow&longs;tring, to wit by as much as the &longs;aid &longs;tring is <lb/>long, whereas the other arrow receiveth no greater a quantity of <lb/>air, than the &longs;mall circle of the &longs;trings thickne&longs;s. </s><s>And I cannot <lb/>imagine what may be the rea&longs;on of &longs;uch a difference, but would <lb/>fain know the &longs;ame.</s></p><p type="main"><s>SIMP. </s><s>The cau&longs;e &longs;eemeth to me &longs;ufficiently manife&longs;t; and it <lb/>is, becau&longs;e the arrow &longs;hot endways, hath but a little quantity of <lb/>air to penetrate, and the other is to make its way through a quan­ <lb/>tity as great as its whole length.</s></p><p type="main"><s>SALV. </s><s>Then it &longs;eems the arrows &longs;hot, are to penetrate the air? <lb/></s><s>but if the air goeth along with them, yea, is that which carrieth <lb/>them, what penetration can they make therein? </s><s>Do you not &longs;ee <lb/>that, in this ca&longs;e, the arrow would of nece&longs;&longs;ity move with greater <lb/>velocity than the air? </s><s>and this greater velocity, what doth confer <lb/>it on the arrow? </s><s>Will you &longs;ay the air giveth them a velocity <lb/>greater than its own? </s><s>Know then, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that the bu&longs;ine&longs;s <lb/>proceeds quite contrary to that which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aith, and that the </s></p><p type="main"><s><arrow.to.target n="marg320"></arrow.to.target> <lb/><emph type="italics"/>medium<emph.end type="italics"/> conferreth the motion on the project, is as fal&longs;e, as it is <lb/>true, that it is the onely thing which procureth its ob&longs;truction; and <lb/>having known this, you &longs;hall under&longs;tand without finding any thing <lb/>whereof to make que&longs;tion, that if the air be really moved, it doth <lb/>much better carry the dart along with it longways, than endways, <lb/>for that the air which impelleth it in that po&longs;ture, is much, and in <lb/>this very little. </s><s>But &longs;hooting with the Bow, fora&longs;much as the air <lb/>&longs;tands &longs;till, the tran&longs;ver&longs;e arrow, being to force its pa&longs;&longs;age through <lb/>much air, comes to be much impeded, and the other that was nock't <lb/>ea&longs;ily overcometh the ob&longs;truction of the &longs;mall quantity of air, <lb/>which oppo&longs;eth it &longs;elf thereto.</s></p><p type="margin"><s><margin.target id="marg320"></margin.target><emph type="italics"/>The<emph.end type="italics"/> medium <emph type="italics"/>doth <lb/>impede and not cor­ <lb/>fer the motion of <lb/>projects.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>How many Propo&longs;itions have I ob&longs;erved in <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>(meaning &longs;till in Natural Philo&longs;ophy) that are not onely fal&longs;e, <lb/>but fal&longs;e in &longs;uch &longs;ort, that its diametrical contrary is true, as it <lb/>happens in this ca&longs;e. </s><s>But pur&longs;uing the point in hand, I think that <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> is per&longs;waded, that, from &longs;eeing the &longs;tone always to fall <lb/>in the &longs;ame place, he cannot conjecture either the motion or &longs;ta­ <lb/>bility of the Ship: and if what hath been hitherto &longs;poken, <lb/>&longs;hould not &longs;uffice, there is the Experiment of the <emph type="italics"/>medium<emph.end type="italics"/> which <lb/>may thorowly a&longs;&longs;ure us thereof; in which experiment, the mo&longs;t <lb/>that could be &longs;een would be, that the cadent moveable might be <lb/>left behind, if it were light, and that the air did not follow the <lb/>motion of the &longs;hip: but in ca&longs;e the air &longs;hould move with equal <pb xlink:href="040/01/153.jpg" pagenum="135"/>velocity, no imaginable diver&longs;ity could be found either in this, <lb/>or any other experiment what&longs;oever, as I am anon to tell you. <lb/></s><s>Now if in this ca&longs;e there appeareth no difference at all, what can <lb/>be pretended to be &longs;een in the &longs;tone falling from the top of the <lb/>Tower, where the motion in gyration is not adventitious, and ac­ <lb/>cidental, but natural and eternal; and where the air exactly fol­ <lb/>loweth the motion of the Tower, and the Tower that of the Ter­ <lb/>re&longs;trial Globe? </s><s>have you any thing el&longs;e to &longs;ay, <emph type="italics"/>Simplicius,<emph.end type="italics"/> upon <lb/>this particular?</s></p><p type="main"><s>SIMP. </s><s>No more but this, that I &longs;ee not the mobility of the <lb/>Earth as yet proved.</s></p><p type="main"><s>SALV. </s><s>Nor have I any intention at this time, but onely to <lb/>&longs;hew, that nothing can be concluded from the experiments alledg­ <lb/>ed by our adver&longs;aries for convincing Arguments: as I think I <lb/>&longs;hall prove the others to be.</s></p><p type="main"><s>SAGR. </s><s>I be&longs;eech you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> before you proceed any far­ <lb/>ther, to permit me to &longs;tart certain que&longs;tions, which have been <lb/>rouling in my fancy all the while that you with &longs;o much patience <lb/>and equanimity, was minutely explaining to <emph type="italics"/>Simplicius<emph.end type="italics"/> the expe­ <lb/>riment of the Ship.</s></p><p type="main"><s>SALV. </s><s>We are here met with a purpo&longs;e to di&longs;pute, and it's fit <lb/>that every one &longs;hould move the difficulties that he meets withall, <lb/>for this is the way to come to the knowledg of the truth. <lb/></s><s>Therefore &longs;peak freely.</s></p><p type="main"><s>SAGR. </s><s>If it be true, that the <emph type="italics"/>impetus<emph.end type="italics"/> wherewith the &longs;hip moves, <lb/>doth remain indelibly impre&longs;&longs;'d in the &longs;tone, after it is let fall from <lb/>the Ma&longs;t; and if it be farther true, that this motion brings no im­ <lb/>pediment or retardment to the motion directly downwards, na­ <lb/>tural to the &longs;tone: it's nece&longs;&longs;ary, that there do an effect en&longs;ue of <lb/><arrow.to.target n="marg321"></arrow.to.target> <lb/>a very wonderful nature. </s><s>Let a Ship be &longs;uppo&longs;ed to &longs;tand &longs;till, <lb/>and let the time of the falling of a &longs;tone from the Ma&longs;ts Round-top <lb/>to the ground, be two beats of the pul&longs;e; let the Ship afterwards <lb/>be under &longs;ail, and let the &longs;ame &longs;tone depart from the &longs;ame place, <lb/>and it, according to what hath been premi&longs;ed, &longs;hall &longs;till take up <lb/>the time of two pul&longs;es in its fall, in which time the &longs;hip will have <lb/>run, &longs;uppo&longs;e, twenty yards; To that the true motion of the &longs;tone <lb/>will be a tran&longs;ver&longs;e line, con&longs;iderably longer than the fir&longs;t &longs;traight <lb/>and perpendicular line, which is the length of the ^{*} Ma&longs;t, and yet <lb/><arrow.to.target n="marg322"></arrow.to.target> <lb/>neverthele&longs;s the ^{*} &longs;tone will have pa&longs;t it in the &longs;ame time. </s><s>Let <lb/>it be farther &longs;uppo&longs;ed, that the Ships motion is much more accele­ <lb/>rated, &longs;o that the &longs;tone in falling &longs;hall be to pa&longs;s a tran&longs;ver&longs;e line <lb/>much longer than the other; and in &longs;um, increa&longs;ing the Ships ve­ <lb/><arrow.to.target n="marg323"></arrow.to.target> <lb/>locity as much as you will, the falling &longs;tone &longs;hall de&longs;cribe its tran&longs;­ <lb/>ver&longs;e lines &longs;till longer and longer, and yet &longs;hall pa&longs;s them all in <lb/>tho&longs;e &longs;elf &longs;ame two pul&longs;es. </s><s>And in this fa&longs;hion, if a Canon were <pb xlink:href="040/01/154.jpg" pagenum="136"/>level'd on the top of a Tower, and &longs;hots were made therewith <lb/>point blank, that is, paralel to the Horizon, let the Piece have a <lb/>greater or le&longs;s charge, &longs;o as that the ball may fall &longs;ometimes a <lb/>thou&longs;and yards di&longs;tant, &longs;ometimes four thou&longs;and, &longs;ometimes &longs;ix, <lb/>&longs;ometimes ten, <emph type="italics"/>&c.<emph.end type="italics"/> and all the&longs;e &longs;hots &longs;hall curry or fini&longs;h their <lb/>ranges in times equal to each other, and every one equal to the <lb/>time which the ball would take to pa&longs;s from the mouth of the <lb/>Piece to the ground, being left, without other impul&longs;e, to fall <lb/>&longs;imply downwards in a perpendicular line. </s><s>Now it &longs;eems a very <lb/>admirable thing, that in the &longs;ame &longs;hort time of its falling perpen­ <lb/>dicularly down to the ground, from the height of, &longs;uppo&longs;e, an <lb/>hundred yards, the &longs;ame ball, being thru&longs;t violently out of the <lb/>Piece by the Fire, &longs;hould be able to pa&longs;s one while four hundred, <lb/>another while a thou&longs;and, another while four, another while ten <lb/>thou&longs;and yards, &longs;o as that the &longs;aid ball in all &longs;hots made point <lb/>blank, always continueth an equal time in the air.</s></p><p type="margin"><s><margin.target id="marg321"></margin.target><emph type="italics"/>An admirable <lb/>accident in the mo­ <lb/>tion of projects.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg322"></margin.target>*By the length of <lb/>the ma&longs;t he means <lb/>the di&longs;tance be­ <lb/>tween the upper­ <lb/>deck and Round­ <lb/>top.</s></p><p type="margin"><s><margin.target id="marg323"></margin.target>* La palla.</s></p><p type="main"><s>SALV. </s><s>The con&longs;ideration for its novelty is very pretty, and if <lb/>the effect be true, very admirable: and of the truth thereof, I <lb/>make no que&longs;tion: and were it not for the accidental impediment <lb/>of the air, I verily believe, that, if at the time of the balls going <lb/>out of the Piece, another were let fall from the &longs;ame height di­ <lb/>rectly downwards, they would both come to the ground at the <lb/>&longs;ame in&longs;tant, though that &longs;hould have curried ten thou&longs;and <lb/>miles in its range, and this but an hundred onely: pre&longs;uppo&longs;ing <lb/>the &longs;urface of the Earth to be equal, which to be a&longs;&longs;ured of, the <lb/>experiment may be made upon &longs;ome lake. </s><s>As for the impediment <lb/>which might come from the air, it would con&longs;i&longs;t in retarding the <lb/>extreme &longs;wift motion of the &longs;hot. </s><s>Now, if you think fit, we will <lb/>proceed to the &longs;olution of the other Objections, &longs;eeing that <emph type="italics"/>Sim­ <lb/>plicius<emph.end type="italics"/> (as far as I can &longs;ee) is convinc'd of the nullity of this fir&longs;t, <lb/>taken from things falling from on high downwards.</s></p><p type="main"><s>SIMP. </s><s>I find not all my &longs;cruples removed, but it may be the <lb/>fault is my own, as not being of &longs;o ea&longs;ie and quick an apprehen&longs;ion <lb/>as <emph type="italics"/>Sagredus.<emph.end type="italics"/> And it &longs;eems to me, that if this motion, of which <lb/>the &longs;tone did partake whil&longs;t it was on the Round-top of the Ships <lb/>Ma&longs;t, be, as you &longs;ay, to con&longs;erve it &longs;elf indelibly in the &longs;aid &longs;tone, <lb/>even after it is &longs;eparated from the Ship, it would follow, that like­ <lb/>wi&longs;e in ca&longs;e any one, riding a hor&longs;e that was upon his &longs;peed, &longs;hould <lb/>let a bowl drop out of his hand, that bowl being fallen to the <lb/>ground would continue its motion and follow the hor&longs;es &longs;teps, <lb/>without tarrying behind him: the which effect, I believe, is not <lb/>to be &longs;een, unle&longs;s when he that is upon the hor&longs;e &longs;hould throw it <lb/>with violence that way towards which he runneth; but otherwi&longs;e, <lb/>I believe it will &longs;tay on the ground in the &longs;ame place where it <lb/>fell.</s></p> <pb xlink:href="040/01/155.jpg" pagenum="137"/><p type="main"><s>SALV. </s><s>I believe that you very much deceive your &longs;elf, and am <lb/>certain, that experience will &longs;hew you the contrary, and that the ball <lb/>being once arrived at the ground, will run together with the hor&longs;e, <lb/>not &longs;taying behind him, unle&longs;s &longs;o far as the a&longs;perity and uneven­ <lb/>ne&longs;s of the Earth &longs;hall hinder it. </s><s>And the rea&longs;on &longs;eems to me <lb/>very manife&longs;t: for if you, &longs;tanding &longs;till, throw the &longs;aid ball a­ <lb/>long the ground, do you think it would not continue its motion <lb/>even after you had delivered it out of your hand? </s><s>and that for &longs;o <lb/>much a greater &longs;pace, by how much the &longs;uperficies were more <lb/>&longs;mooth, &longs;o that <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> upon ice it would run a great way?</s></p><p type="main"><s>SIMP. </s><s>There is no doubt of it, if I give it <emph type="italics"/>impetus<emph.end type="italics"/> with my <lb/>arm; but in the other ca&longs;e it is &longs;uppo&longs;ed, that he who is upon the <lb/>hor&longs;e, onely drops it out of his hand:</s></p><p type="main"><s>SALV. </s><s>So I de&longs;ire that it &longs;hould be: but when you throw it <lb/>with your arm, what other remaineth to the ball being once gone <lb/>out of your hand, than the motion received from your arm, which <lb/>motion being con&longs;erved in the boul, it doth continue to carry it <lb/>forward? </s><s>Now, what doth it import, that that <emph type="italics"/>impetus<emph.end type="italics"/> be con­ <lb/>ferred on the ball rather from the arm than from the hor&longs;e? </s><s>Whil&longs;t <lb/>you were on hor&longs;eback, did not your hand, and con&longs;equently the <lb/>ball run as fa&longs;t as the hor&longs;e it &longs;elf? </s><s>Doubtle&longs;s it did: therefore <lb/>in onely opening of the hand, the ball departs with the motion al­ <lb/>ready conceived, not from your arm, by your particular motion, <lb/>but from the motion dependant on the &longs;aid hor&longs;e, which cometh to <lb/>be communicated to you, to your arm, to your hand, and la&longs;tly to <lb/>the ball. </s><s>Nay, I will tell you farther, that if the rider upon his <lb/>&longs;peed fling the ball with his arm to the part contrary to the cour&longs;e, <lb/>it &longs;hall, after it is fallen to the ground, &longs;ometimes (albeit thrown to <lb/>the contrary part) follow the cour&longs;e of the hor&longs;e, and &longs;ometimes lie <lb/>&longs;till on the ground; and &longs;hall onely move contrary to the &longs;aid <lb/>cour&longs;e, when the motion received from the arm, &longs;hall exceed that <lb/>of the carrier in velocity. </s><s>And it is a vanity, that of &longs;ome, who <lb/>&longs;ay that a hor&longs;eman is able to ca&longs;t a javelin thorow the air, that <lb/>way which the hor&longs;e runs, and with the hor&longs;e to follow and over­ <lb/>take the &longs;ame; and la&longs;tly, to catch it again. </s><s>It is, I &longs;ay, a vanity, <lb/>for that to make the project return into the hand, it is requi&longs;ite to <lb/>ca&longs;t it upwards, in the &longs;ame manner as if you &longs;tood &longs;till. </s><s>For, let <lb/>the carrier be never &longs;o &longs;wift, provided it be uniform, and the pro­ <lb/>ject not over-light, it &longs;hall always fall back again into the hand of <lb/>the projicient, though never &longs;o high thrown.</s></p><p type="main"><s>SAGR. </s><s>By this Doctrine I come to know &longs;ome Problems very <lb/><arrow.to.target n="marg324"></arrow.to.target> <lb/>curious upon this &longs;ubject of projections; the fir&longs;t of which mu&longs;t <lb/>&longs;eem very &longs;trange to <emph type="italics"/>Simplicius.<emph.end type="italics"/> And the Problem is this; I af­ <lb/>firm it to be po&longs;&longs;ible, that the ball being barely dropt or let fall, <lb/>by one that any way runneth very &longs;wiftly, being arrived at the <pb xlink:href="040/01/156.jpg" pagenum="138"/>Earth, doth not onely follow the cour&longs;e of that per&longs;on, but doth <lb/>much out go him. </s><s>Which Problem is connexed with this, that <lb/>the moveable being thrown by the projicient above the plane of <lb/>the Horizon, may acquire new velocity, greater by far than that <lb/>confer'd upon it by the projicient. </s><s>The which effect I have with <lb/>admiration ob&longs;erved, in looking upon tho&longs;e who u&longs;e the &longs;port of <lb/>tops, which, &longs;o &longs;oon as they are &longs;et out of the hand, are &longs;een to <lb/>move in the air with a certain velocity, the which they afterwards <lb/>much encrea&longs;e at their coming to the ground; and if whipping <lb/>them, they rub at any uneven place that makes them skip on high, <lb/>they are &longs;een to move very &longs;lowly through the air, and falling a­ <lb/>gain to the Earth, they &longs;till come to move with a greater velocity: <lb/>But that which is yet more &longs;trange, I have farther ob&longs;erved, that <lb/>they not onely turn always more &longs;wiftly on the ground, than in <lb/>the air, but of two &longs;paces both upon the Earth, &longs;ometimes a mo­ <lb/>tion in the &longs;econd &longs;pace is more &longs;wift than in the fir&longs;t. </s><s>Now what <lb/>would <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;ay to this?</s></p><p type="margin"><s><margin.target id="marg324"></margin.target><emph type="italics"/>Sundry curious <lb/>Problems, touch­ <lb/>ing the motions of <lb/>projects.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>He would &longs;ay in the fir&longs;t place, that he had never made <lb/>&longs;uch an ob&longs;ervation. </s><s>Secondly, he would &longs;ay, that he did not be­ <lb/>lieve the &longs;ame. </s><s>He would &longs;ay again, in the third place, that if <lb/>you could a&longs;&longs;ure him thereof, and demon&longs;tratively convince him of <lb/>the &longs;ame, he would account you a great Dæmon.</s></p><p type="main"><s>SAGR. </s><s>I hope then that it is one of the Socratick, not infernal <lb/>ones. </s><s>But that I may make you under&longs;tand this particular, you <lb/>mu&longs;t know, that if a per&longs;on apprehend not a truth of him&longs;elf, it <lb/>is impo&longs;&longs;ible that others &longs;hould make him under&longs;tand it: I may in­ <lb/>deed in&longs;truct you in tho&longs;e things which are neither true nor fal&longs;e; <lb/>but the true, that is, the nece&longs;&longs;ary, namely, &longs;uch as it is impo&longs;&longs;ible <lb/>&longs;hould be otherwi&longs;e, every common capacity either comprehendeth <lb/>them of him&longs;elf, or el&longs;e it is impo&longs;&longs;ible he &longs;hould ever know them. <lb/></s><s>And of this opinion I am confident is <emph type="italics"/>Salviatus<emph.end type="italics"/> al&longs;o: and there­ <lb/>fore I tell you, that the rea&longs;ons of the pre&longs;ent Problems are known <lb/>by you, but it may be, not apprehended.</s></p><p type="main"><s>SIMP. </s><s>Let us, for the pre&longs;ent, pa&longs;s by that controver&longs;ie, and <lb/>permit me to plead ignorance of the&longs;e things you &longs;peak of, and try <lb/>whether you can make me capable of under&longs;tanding the&longs;e Pro­ <lb/>blems.</s></p><p type="main"><s>SAGR. </s><s>This fir&longs;t dependeth upon another, which is, Whence <lb/>cometh it, that &longs;etting a top with the la&longs;h, it runneth farther, and <lb/>con&longs;equently with greater force, than when its &longs;et with the fin­ <lb/>gers?</s></p><p type="main"><s>SIMP. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> al&longs;o makes certain Problems about the&longs;e kinds <lb/>of projects.</s></p><p type="main"><s>SALV. </s><s>He doth &longs;o; and very ingenious they are: particular­ <lb/>ly, That, Whence it cometh to pa&longs;s that round tops run better than <lb/>the &longs;quare?</s></p> <pb xlink:href="040/01/157.jpg" pagenum="139"/><p type="main"><s>SAGR. </s><s>And cannot you, <emph type="italics"/>Simplicius,<emph.end type="italics"/> give a rea&longs;on for this, <lb/>without others prompting you?</s></p><p type="main"><s>SIMP. </s><s>Very good, I can &longs;o; but leave your jeering.</s></p><p type="main"><s>SAGR. </s><s>In like manner you do know the rea&longs;on of this other <lb/>al&longs;o. </s><s>Tell me therefore; know you that a thing which moveth, <lb/>being impeded &longs;tands &longs;till?</s></p><p type="main"><s>SIMP. </s><s>I know it doth, if the impediment be &longs;o great as to <lb/>&longs;uffice.</s></p><p type="main"><s>SAGR. </s><s>Do you know, that moving upon the Earth is a greater <lb/>impediment to the moveable, than moving in the air, the Earth be­ <lb/>ing rough and hard, and the air &longs;oft and yielding?</s></p><p type="main"><s>SIMP. </s><s>And knowing this, I know that the top will turn fa&longs;ter <lb/>in the air, than on the ground, &longs;o that my knowledg is quite con­ <lb/>trary to what you think it.</s></p><p type="main"><s>SAGR. </s><s>Fair and &longs;oftly, <emph type="italics"/>Simplicius.<emph.end type="italics"/> You know that in the <lb/>parts of a moveable, that turneth about its centre, there are found <lb/>motions towards all &longs;ides; &longs;o that &longs;ome a&longs;cend, others de&longs;cend; <lb/>&longs;ome go forwards, others backwards?</s></p><p type="main"><s>SIMP. </s><s>I know it, and <emph type="italics"/>Aristotle<emph.end type="italics"/> taught me the &longs;ame.</s></p><p type="main"><s>SAGR. </s><s>And with what demon&longs;tration, I pray you?</s></p><p type="main"><s>SIMP. </s><s>With that of &longs;en&longs;e.</s></p><p type="main"><s>SAGR. <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> then, hath made you &longs;ee that which without <lb/>him you would not have &longs;een? </s><s>Did he ever lend you his eyes? <lb/></s><s>You would &longs;ay, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath told, adverti&longs;ed, remembered <lb/>you of the &longs;ame; and not taught you it. </s><s>When then a top, with­ <lb/>out changing place, turns round, (or in the childrens phra&longs;e, &longs;leep­ <lb/>eth) not paralel, but erect to the Horizon, &longs;ome of its parts a&longs;cend, <lb/>and the oppo&longs;ite de&longs;cend; the &longs;uperiour go one way, the infe­ <lb/>riour another. </s><s>Fancie now to your &longs;elf, a top, that without chan­ <lb/>ging place, &longs;wiftly turns round in that manner, and &longs;tands &longs;u&longs;pen­ <lb/>ded in the air, and that in that manner turning, it be let fall to the <lb/>Earth perpendicularly, do you believe, that when it is arrived at <lb/>the ground, it will continue to turn round in the &longs;ame manner, <lb/>without changing place, as before?</s></p><p type="main"><s>SIMP. No, Sir.</s></p><p type="main"><s>SAGR. </s><s>What will it do then?</s></p><p type="main"><s>SIMP. </s><s>It will run along the ground very fa&longs;t.</s></p><p type="main"><s>SAGR. </s><s>And towards what part?</s></p><p type="main"><s>SIMP. </s><s>Towards that, whither its ^{*}reeling carrieth it. <lb/><arrow.to.target n="marg325"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg325"></margin.target>* Vertigine.</s></p><p type="main"><s>SAGR. </s><s>In its reeling there are parts, that is the uppermo&longs;t, which <lb/>do move contrary to the inferiour; therefore you mu&longs;t in&longs;tance <lb/>which it &longs;hall obey: for as to the parts a&longs;cending and de&longs;cending, <lb/>the one kind will not yield to the other; nor will they all go <lb/>downwards, being hindered by the Earth, nor upwards as being <lb/>heavy.</s></p> <pb xlink:href="040/01/158.jpg" pagenum="140"/><p type="main"><s>SIMP. </s><s>The top will run reeling along the floor towards that <lb/>part whither its upper parts encline it.</s></p><p type="main"><s>SAGR. </s><s>And why not whither the contrary parts tend, namely, <lb/>tho&longs;e which touch the ground?</s></p><p type="main"><s>SIMP. </s><s>Becau&longs;e tho&longs;e upon the ground happen to be impeded <lb/>by the roughne&longs;s of the touch, that is, by the floors unevenne&longs;s; <lb/>but the &longs;uperiour, which are in the tenuous and flexible air, are <lb/>hindred very little, if at all; and therefore the top will obey their <lb/>inclination.</s></p><p type="main"><s>SAGR. </s><s>So that that taction, if I may &longs;o &longs;ay, of the neither <lb/>parts on the floor, is the cau&longs;e that they &longs;tay, and onely the upper <lb/>parts &longs;pring the top forward.</s></p><p type="main"><s>SALV. </s><s>And therefore, if the top &longs;hould fall upon the ice, or <lb/>other very &longs;mooth &longs;uperficies, it would not &longs;o well run forward, but <lb/>might peradventure continue to revolve in it &longs;elf, (or &longs;leep) with­ <lb/>out acquiring any progre&longs;&longs;ive motion.</s></p><p type="main"><s>SAGR. </s><s>It is an ea&longs;ie thing for it &longs;o to do; but yet neverthe­ <lb/>le&longs;s, it would not &longs;o &longs;peedily come to &longs;leep, as when it falleth on <lb/>a &longs;uperficies &longs;omewhat rugged. </s><s>But tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> when <lb/>the top turning round about it &longs;elf, in that manner, is let fall, why <lb/>doth it not move forwards in the air, as it doth afterwards when it <lb/>is upon the ground?</s></p><p type="main"><s>SIMP. </s><s>Becau&longs;e having air above it, and beneath, neither tho&longs;e <lb/>parts, nor the&longs;e have any where to touch, and not having more oc­ <lb/>ca&longs;ion to go forward than backward, it falls perpendicularly.</s></p><p type="main"><s>SAGR. </s><s>So then the onely reeling about its &longs;elf, without other <lb/><emph type="italics"/>impetus,<emph.end type="italics"/> can drive the top forward, being arrived at the ground, <lb/>very nimbly. </s><s>Now proceed we to what remains. </s><s>That la&longs;h, <lb/>which the driver tyeth to his Top-&longs;tick, and with which, winding <lb/>it about the top, he &longs;ets it (<emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> makes it go) what effect hath it on <lb/>the &longs;aid top?</s></p><p type="main"><s>SIMP. </s><s>It con&longs;trains it to turn round upon its toe, that &longs;o it may <lb/>free it &longs;elf from the Top-la&longs;h.</s></p><p type="main"><s>SAGR. </s><s>So then, when the top arriveth at the ground, it cometh <lb/>all the way turning about its &longs;elf, by means of the la&longs;h. </s><s>Hath it <lb/>not rea&longs;on then to move in it &longs;elf more &longs;wiftly upon the ground, <lb/>than it did whil&longs;t it was in the air?</s></p><p type="main"><s>SIMP. </s><s>Yes doubtle&longs;s; for in the air it had no other impul&longs;e <lb/>than that of the arm of the projicient; and if it had al&longs;o the reel­ <lb/>ing, this (as hath been &longs;aid) in the air drives it not forward at all: <lb/>but arriving at the floor, to the motion of the arm is added the <lb/>progre&longs;&longs;ion of the reeling, whereby the velocity is redoubled. </s><s>And <lb/>I know already very well, that the top skipping from the ground, <lb/>its velocity will demini&longs;h, becau&longs;e the help of its circulation is <lb/>wanting; and returning to the Earth will get it again, and by that <pb xlink:href="040/01/159.jpg" pagenum="141"/>means move again fa&longs;ter, than in the air. </s><s>It onely re&longs;ts for me to <lb/>under&longs;tand, whether in this &longs;econd motion on the Earth it move <lb/>more &longs;wiftly, than in the fir&longs;t; for then it would move <emph type="italics"/>in infini­ <lb/>tum,<emph.end type="italics"/> alwayes accelerating.</s></p><p type="main"><s>SAGR. </s><s>I did not ab&longs;olutely affirm, that this &longs;econd motion is <lb/>more &longs;wift than the fir&longs;t; but that it may happen &longs;o to be &longs;ome­ <lb/>times.</s></p><p type="main"><s>SIMP. </s><s>This is that, which I apprehend not, and which I <lb/>de&longs;ire to know.</s></p><p type="main"><s>SAGR. </s><s>And this al&longs;o you know of your &longs;elf. </s><s>Therefore tell <lb/>me: When you let the top fall out of your hand, without ma­ <lb/>king it turn round (<emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> &longs;etting it) what will it do at its coming to <lb/>the ground?</s></p><p type="main"><s>SIMP. Nothing, but there lie &longs;till.</s></p><p type="main"><s>SAGR. </s><s>May it not chance, that in its fall to the ground it may <lb/>acquire a motion? </s><s>Think better on it.</s></p><p type="main"><s>SIMP. </s><s>Unle&longs;&longs;e we let it fall upon &longs;ome inclining &longs;tone, as <lb/>children do playing at ^{*} <emph type="italics"/>Chio&longs;a,<emph.end type="italics"/> and that falling &longs;ide-wayes upon </s></p><p type="main"><s><arrow.to.target n="marg326"></arrow.to.target> <lb/>the &longs;ame, it do acquire the motion of turning round upon its toe, <lb/>wherewith it afterwards continueth to move progre&longs;&longs;ively on the <lb/>floor, I know not in what other manner it can do any thing but <lb/>lie &longs;till where it falleth.</s></p><p type="margin"><s><margin.target id="marg326"></margin.target>* A Game in <emph type="italics"/>Italy,<emph.end type="italics"/> <lb/>which is, to glide <lb/>bullets down an <lb/>inclining &longs;tone, <lb/><emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>You &longs;ee then that in &longs;ome ca&longs;e it may acquire a new <lb/>revolution. </s><s>When then the top jerked up from the ground, falleth <lb/>down again, why may it not ca&longs;ually hit upon the declivity of <lb/>&longs;ome &longs;tone fixed in the floor, and that hath an inclination that <lb/>way towards which it moveth, and acquiring by that &longs;lip a new <lb/>whirle over and above that conferred by the la&longs;h, why may it <lb/>not redouble its motion, and make it &longs;wifter than it was at its <lb/>fir&longs;t lighting upon the ground?</s></p><p type="main"><s>SIMP. </s><s>Now I &longs;ee that the &longs;ame may ea&longs;ily happen. </s><s>And I <lb/>am thinking that if the top &longs;hould turn the contrary way, in ar­ <lb/>riving at the ground, it would work a contrary effect, that is, <lb/>the motion of the accidental whirl would retard that of the pro­ <lb/>jicient.</s></p><p type="main"><s>SAGR. </s><s>And it would &longs;ometimes wholly retard and &longs;top it, in <lb/>ca&longs;e the revolution of the top were very &longs;wift. </s><s>And from hence a­ <lb/>ri&longs;eth the re&longs;olution of that &longs;light, which the more skilful Tennis <lb/>Players u&longs;e to their advantage; that is, to gull their adver&longs;ary by <lb/>cutting (for &longs;o is their Phra&longs;e) the Ball; which is, to return it <lb/>with a &longs;ide Rachet, in &longs;uch a manner, that it doth thereby ac­ <lb/>quire a motion by it &longs;elf contrary to the projected motion, and &longs;o <lb/>by that means, at its coming to the ground, the rebound, which <lb/>if the ball did not turn in that manner, would be towards the <lb/>adver&longs;ary, giving him the u&longs;ual time to to&longs;&longs;e it back again, doth <pb xlink:href="040/01/160.jpg" pagenum="142"/>fail, and the ball runs tripping along the ground, or rebounds le&longs;&longs;e <lb/>than u&longs;ual, and breaketh the time of the return. </s><s>Hence it is <lb/><arrow.to.target n="marg327"></arrow.to.target> <lb/>that you &longs;ee, tho&longs;e who play at ^{*} Stool-ball, when they play in <lb/>a &longs;tony way, or a place full of. </s><s>holes and rubs that make the ball <lb/>trip an hundred &longs;everal wayes, never &longs;uffering it to come neer the <lb/>mark, to avoid them all, they do not trundle the ball upon the <lb/>ground, but throw it, as if they were to pitch a quait. </s><s>But be­ <lb/>cau&longs;e in throwing the ball, it i&longs;&longs;ueth out of the hand with &longs;ome <lb/>roling conferred by the fingers, when ever the hand is under the <lb/>ball, as it is mo&longs;t commonly held; whereupon the ball in its lighting <lb/>on the ground neer to the mark, between the motion of the pro­ <lb/>jicient and that of the roling, would run a great way from the <lb/>&longs;ame: To make the ball &longs;tay, they hold it artificially, with their <lb/>hand uppermo&longs;t, and it undermo&longs;t, which in its delivery hath <lb/>a contrary twirl or roling conferred upon it by the fingers, by <lb/>means whereof in its coming to the ground neer the mark it &longs;tays <lb/>there, or runs very very little forwards. </s><s>But to return to our <lb/>principal problem which gave occa&longs;ion for &longs;tarting the&longs;e others; I <lb/>&longs;ay it is po&longs;&longs;ible that a per&longs;on carried very &longs;wiftly, may let a ball <lb/>drop out of his hand, that being come to the Earth, &longs;hall not <lb/>onely follow his motion, but al&longs;o out-go it, moving with a great­ <lb/>er velocity. </s><s>And to &longs;ee &longs;uch an effect, I de&longs;ire that the cour&longs;e <lb/>may be that of a Chariot, to which on the out-&longs;ide let a decli­ <lb/>ning board be fa&longs;tened; &longs;o as that the neither part may be towards <lb/>the hor&longs;es, and the upper towards the hind Wheel. </s><s>Now, if in <lb/>the Chariots full career, a man within it, let a ball fall gliding a­ <lb/>long the declivity of that board, it &longs;hall in roling downward ac­ <lb/>quire a particular <emph type="italics"/>vertigo<emph.end type="italics"/> or turning, the which added to the <lb/>motion impre&longs;&longs;ed by the Chariot, will carrie the ball along the <lb/>ground much fa&longs;ter than the Chariot. </s><s>And if one accommodate <lb/>another declining board over again&longs;t it, the motion of the Cha­ <lb/>riot may be qualified &longs;o, that the ball, gliding downwards along <lb/>the board, in its coming to the ground &longs;hall re&longs;t immoveable, <lb/>and al&longs;o &longs;hall &longs;ometimes run the contrary way to the Chariot. </s><s>But <lb/>we are &longs;trayed too far from the purpo&longs;e, therefore if <emph type="italics"/>Simplicius<emph.end type="italics"/> <lb/>be &longs;atisfied with the re&longs;olution of the fir&longs;t argnment again&longs;t the <lb/>Earths mobility, taken from things falling perpendicularly, we <lb/>may pa&longs;&longs;e to the re&longs;t</s></p><p type="margin"><s><margin.target id="marg327"></margin.target>*A Game in <emph type="italics"/>Italy,<emph.end type="italics"/> <lb/>wherein they &longs;trive <lb/>who &longs;hall trundle <lb/>or throw a wooden <lb/>bowle neere&longs;t to an <lb/>a&longs;&longs;igned mark.</s></p><p type="main"><s>SALV. </s><s>The digre&longs;&longs;ions made hitherto, are not &longs;o alienated <lb/>from the matter in hand, as that one can &longs;ay they are wholly <lb/>&longs;trangers to it. </s><s>Be&longs;ides the&longs;e argumentations depend on tho&longs;e <lb/>things that &longs;tart up in the fancy not of one per&longs;on, but of three, <lb/>that we are: And moreover we di&longs;cour&longs;e for our plea&longs;ure, nor <lb/>are we obliged to that &longs;trictne&longs;&longs;e of one who <emph type="italics"/>ex profe&longs;&longs;o<emph.end type="italics"/> treateth <lb/>methodically of an argument, with an intent to publi&longs;h the &longs;ame. <pb xlink:href="040/01/161.jpg" pagenum="143"/>I will not con&longs;ent that our Poem &longs;hould be &longs;o confined to that <lb/>unity, as not to leave us fields open for Ep&longs;ody's, which every <lb/>&longs;mall connection &longs;hould &longs;uffice to introduce; but with almo&longs;t as <lb/>much liberry as if we were met to tell &longs;tories, it &longs;hall be lawful <lb/>for me to &longs;peak, what ever your di&longs;cour&longs;e brings into my mind.</s></p><p type="main"><s>SAGR. </s><s>I like this motion very well; and &longs;ince we are at this <lb/>liberty, let me take leave, before we pa&longs;&longs;e any farther to ask of <lb/>you <emph type="italics"/>Salviatus,<emph.end type="italics"/> whether you did ever con&longs;ider what that line may <lb/>be that is de&longs;cribed by the grave moveable naturally falling down <lb/>from the top of a Tower; and if you have reflected on it, be <lb/>plea&longs;ed to tell me what you think thereof.</s></p><p type="main"><s>SALV. </s><s>I have &longs;ometimes con&longs;idered of it, and make no que­ <lb/>&longs;tion, that if one could be certain of the nature of that motion <lb/>wherewith the grave body de&longs;cendeth to approach the centre of <lb/>the Terre&longs;trial Globe, mixing it &longs;elf afterwards with the common <lb/>circular motion of the diurnal conver&longs;ion; it might be exactly <lb/>found what kind of line that is, that the centre of gravity of the <lb/>moveable de&longs;cribeth in tho&longs;e two motions.</s></p><p type="main"><s>SAGR. </s><s>Touching the &longs;imple motion towards the centre de­ <lb/>pendent on the gravity, I think that one may confidently, with­ <lb/>out error, believe that it is by a right line, as it would be, were <lb/>the Earth immoveable.</s></p><p type="main"><s>SALV. </s><s>As to this particular, we may not onely believe it, but <lb/>experience rendereth us certain of the &longs;ame.</s></p><p type="main"><s>SAGR. </s><s>But how doth experience a&longs;&longs;ure us thereof, if we ne­ <lb/>ver &longs;ee any motions but &longs;uch as are compo&longs;ed of the two, circular <lb/>and de&longs;cending.</s></p><p type="main"><s>SALV. </s><s>Nay rather <emph type="italics"/>Sagredus<emph.end type="italics"/> we onely &longs;ee the &longs;imple motion of <lb/>de&longs;cent; &longs;ince that other circular one common to the Earth, the <lb/>Tower and our &longs;elves remains imperceptible, and as if it never <lb/>were, and there remaineth perceptible to us that of the &longs;tone, one­ <lb/>ly not participated by us, and for this, &longs;en&longs;e demon&longs;trateth that <lb/>it is by a right line, ever parallel to the &longs;aid Tower, which is <lb/>built upright and perpendicular upon the Terre&longs;trial &longs;urface.</s></p><p type="main"><s>SAGR. </s><s>You are in the right; and this was but too plainly de­ <lb/>mon&longs;trated to me even now, &longs;eeing that I could not remember &longs;o <lb/>ea&longs;ie a thing; but this being &longs;o manife&longs;t, what more is it that you <lb/>&longs;ay you de&longs;ire, for under&longs;tanding the nature of this motion <lb/>downwards?</s></p><p type="main"><s>SALV. </s><s>It &longs;ufficeth not to know that it is &longs;treight, but its requi­ <lb/>&longs;ite to know whether it be uniform, or irregular; that is, whe­ <lb/>ther it maintain alwayes one and the &longs;ame velocity, or el&longs;e goeth <lb/>retarding or accelerating.</s></p><p type="main"><s>SAGR. </s><s>It is already clear, that it goeth continually accelle­ <lb/>rating.</s></p> <pb xlink:href="040/01/162.jpg" pagenum="144"/><p type="main"><s>SALV. </s><s>Neither doth this &longs;uffice, but its requi&longs;ite to know ac­ <lb/>cording to what proportion &longs;uch accelleration is made; a Pro­ <lb/>blem, that I believe was never hitherto under&longs;tood by any Phi­ <lb/>lo&longs;opher or Mathematician; although Philo&longs;ophers, and particu­ <lb/>larly the <emph type="italics"/>Peripateticks,<emph.end type="italics"/> have writ great and entire Volumes, <lb/>touching motion.</s></p><p type="main"><s>SIMP. </s><s>Philo&longs;ophers principally bu&longs;ie them&longs;elves about univer­ <lb/>&longs;als; they find the definitions and more common &longs;ymptomes, o­ <lb/>mitting certain &longs;ubtilties and niceties, which are rather curio­ <lb/>&longs;ities to the Mathematicians. </s><s>And <emph type="italics"/>Aristotle<emph.end type="italics"/> did content him&longs;elf <lb/>to de&longs;ine excellently what motion was in general; and of the lo­ <lb/>cal, to &longs;hew the principal qualities, to wit, that one is natural, <lb/>another violent; one is &longs;imple, another compound; one is <lb/>equal, another accellerate; and concerning the accelerate, con­ <lb/>tents him&longs;elf to give the rea&longs;on of acceleration, remitting the <lb/>finding out of the proportion of &longs;uch acceleration, and other <lb/>particular accidents to the Mechanitian, or other inferiour <lb/>Arti&longs;t.</s></p><p type="main"><s>SAGR. </s><s>Very well <emph type="italics"/>Simplicius.<emph.end type="italics"/> But you <emph type="italics"/>Salviatus,<emph.end type="italics"/> when you <lb/>de&longs;cend &longs;ometimes from the Throne of <emph type="italics"/>Peripatetick<emph.end type="italics"/> Maje&longs;ty, <lb/>have you ever thrown away any of your hours in &longs;tudying to find <lb/>this proportion of the acceleration of the motion of de&longs;cending <lb/>grave bodies?</s></p><p type="main"><s>SALV. </s><s>There was no need that I &longs;hould &longs;tudy for it, in regard <lb/>that the Academick our common friend, heretofore &longs;hewed me a <lb/>Treati&longs;e of his ^{*} <emph type="italics"/>De Motu,<emph.end type="italics"/> where this, and many other acci­ <lb/><arrow.to.target n="marg328"></arrow.to.target> <lb/>dents were demon&longs;trated. </s><s>But it would be too great a digre&longs;&longs;ion, <lb/>if for this particular, we &longs;hould interrupt our pre&longs;ent di&longs;cour&longs;e, <lb/>(which yet it &longs;elf is al&longs;o no better than a digre&longs;&longs;ion) and make as <lb/>the Saying is, a Comedy within a Comedy.</s></p><p type="margin"><s><margin.target id="marg328"></margin.target>This is that ex­ <lb/>cellent tract which <lb/>we give the fir&longs;t <lb/>place in our &longs;econd <lb/>Volume.</s></p><p type="main"><s>SAGR. </s><s>I am content to excu&longs;e you from this narration for the <lb/>pre&longs;ent, provided that this may be one of the Propo&longs;itions re&longs;er­ <lb/>ved to be examined among&longs;t the re&longs;t in another particular meeting, <lb/>for that the knowledg thereof is by me very much de&longs;ired; and <lb/>in the mean time let us return to the line de&longs;cribed by the grave <lb/>body in its fall from the top of the Tower to its ba&longs;e.</s></p><p type="main"><s>SALV. </s><s>If the right motion towards the centre of the Earth was <lb/>uniforme, the circular towards the Ea&longs;t being al&longs;o uniforme, you <lb/>would &longs;ee compo&longs;ed of them both a motion by a &longs;piral line, of <lb/>that kind with tho&longs;e defined by <emph type="italics"/>Archimedes<emph.end type="italics"/> in his Book <emph type="italics"/>Dc Spira­ <lb/>libus<emph.end type="italics"/>; which are, when a point moveth uniformly upon a right <lb/>line, while&longs;t that line in the mean time turneth uniformly about <lb/>one of its extreme points fixed, as the centre of his gyration. <lb/></s><s>But becau&longs;e the right motion of grave bodies falling, is continu­ <lb/>ally accelerated, it is nece&longs;&longs;ary, that the line re&longs;ulting of the <pb xlink:href="040/01/163.jpg" pagenum="145"/>compo&longs;ition of the two motions do go alwayes receding with <lb/>greater and greater proportion from the circumference of that cir­ <lb/>cle, which the centre of the &longs;tones gravity would have de&longs;igned, <lb/>if it had alwayes &longs;taid upon the Tower; it followeth of nece&longs;&longs;ity <lb/>that this rece&longs;&longs;ion at the fir&longs;t be but little, yea very &longs;inall, yea, <lb/>more, as &longs;mall as can be imagined, &longs;eeing that the de&longs;cending <lb/>grave body departing from re&longs;t, that is, from the privation of <lb/>motion, towards the bottom and entring into the right motion <lb/>downwards, it mu&longs;t needs pa&longs;&longs;e through all the degrees of tardi­ <lb/>ty, that are betwixt re&longs;t, and any a&longs;&longs;igned velocity; the which <lb/>degrees are infinite; as already hath been at large di&longs;cour&longs;ed and <lb/>proved.</s></p><p type="main"><s>It being &longs;uppo&longs;ed therefore, that the progre&longs;&longs;e of the accele­ <lb/>ration being after this manner, and it being moreover true, that <lb/>the de&longs;cending grave body goeth to terminate in the centre of the <lb/>Earth, it is nece&longs;&longs;ary that the line of its mixt motion be &longs;uch, that <lb/><arrow.to.target n="marg329"></arrow.to.target> <lb/>it go continually receding with greater and greater proportion <lb/>from the top of the Tower, or to &longs;peak more properly, from <lb/>the circumference of the circle de&longs;cribed by the top of the Tower, <lb/>by means of the Earths conver&longs;ion; but that &longs;uch rece&longs;&longs;ions be <lb/>le&longs;&longs;er and le&longs;&longs;er <emph type="italics"/>in infinitum<emph.end type="italics"/>; by how much the moveable finds it <lb/>&longs;elf to be le&longs;&longs;e and le&longs;&longs;e removed from the fir&longs;t term where it <lb/>re&longs;ted. </s><s>Moreover it is nece&longs;&longs;ary, that this line of the compound­ <lb/>ed motion do go to terminate in the centre of the Earth. </s><s>Now <lb/>having pre&longs;uppo&longs;ed the&longs;e two things, I come to de&longs;cribe about <lb/>the centre A [<emph type="italics"/>in Fig. </s><s>1. of this &longs;econd Dialogue<emph.end type="italics"/>;] with the &longs;emi­ <lb/>diameter A B, the circle B I, repre&longs;enting to me the Terre&longs;trial <lb/>Globe, and prolonging the &longs;emidiameter A B to C, I have de­ <lb/>&longs;cribed the height of the Tower B C; the which being carried <lb/>about by the Earth along the circumference B I, de&longs;cribeth with <lb/>its top the arch C D: Dividing, in the next place, the line C A <lb/>in the middle at E; upon the centre E, at the di&longs;tance E C, I de­ <lb/>&longs;cribe the &longs;emicircle C I A: In which, I now affirm, that it is very <lb/>probable that a &longs;tone falling from the top of the Tower C, doth <lb/>move, with a motion mixt of the circular, which is in common, <lb/>and of its peculiar right motion. </s><s>If therefore in the circumference <lb/>C D, certain equal parts C F, F G, G H, H L, be marked, and <lb/>from the points F, G, H, L, right lines be drawn towards the <lb/>centre A, the parts of them intercepted between the two cir­ <lb/>cumferences C D and B I, &longs;hall repre&longs;ent unto us the &longs;ame <lb/>Tower C B, tran&longs;ported by the Terre&longs;trial Globe towards D I; <lb/>in which lines the points where they come to be inter&longs;ected by the <lb/>arch of the &longs;emicircle C I, are the places by whichfrom time to <lb/>time the falling &longs;tone doth pa&longs;&longs;e; which points go continually <lb/>with greater and greater proportion receding from the top of the <pb xlink:href="040/01/164.jpg" pagenum="146"/>Tower. </s><s>And this is the cau&longs;e why the right motion made along <lb/>the &longs;ide of the Tower appeareth to us more and more accelerate. <lb/></s><s>It appeareth al&longs;o, how by rea&longs;on of the infinite acutene&longs;&longs;e of <lb/>the contact of tho&longs;e two circles D C, C I, the rece&longs;&longs;ion of the <lb/>cadent moveable from the circumference C F D; namely, from <lb/>the top of the Tower, is towards the beginning extream &longs;mall, <lb/>which is as much as if one &longs;aid its motion downwards is very &longs;low, <lb/>and more and more &longs;low <emph type="italics"/>in infinitum,<emph.end type="italics"/> according to its vicinity to <lb/>the term C, that is to the &longs;tate of re&longs;t. </s><s>And la&longs;tly it is &longs;een how <lb/>in the end this &longs;ame motion goeth to terminate in the centre of the <lb/>Earth A.</s></p><p type="margin"><s><margin.target id="marg329"></margin.target><emph type="italics"/>The line de&longs;cri­ <lb/>bed by a moveable <lb/>in its natural de­ <lb/>&longs;cent, the motion <lb/>of the Earth a­ <lb/>bout its own centre <lb/>being pre&longs;uppo&longs;ed, <lb/>would probably be <lb/>the circumference <lb/>of a circle.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I under&longs;tand all this very well, nor can I per&longs;wade my <lb/>&longs;elf that the falling moveable doth de&longs;cribe with the centre of its <lb/>gravity any other line, but &longs;uch an one as this.</s></p><p type="main"><s>SALV. </s><s>But &longs;tay a little <emph type="italics"/>Sagredus,<emph.end type="italics"/> for I am to acquaint you <lb/>al&longs;o with three Ob&longs;ervations of mine, that its po&longs;&longs;ible will not di&longs;­ <lb/><arrow.to.target n="marg330"></arrow.to.target> <lb/>plea&longs;e you. </s><s>The fir&longs;t of which is, that if we do well con&longs;ider, the <lb/>moveable moveth not really with any more than onely one motion <lb/>&longs;imply circular, as when being placed upon the Tower, it moved <lb/>with one &longs;ingle and circular motion. </s><s>The &longs;econd is yet more plea­ <lb/><arrow.to.target n="marg331"></arrow.to.target> <lb/>&longs;ant; for, it moveth neither more nor le&longs;&longs;e then if it had &longs;taid con­ <lb/>tinually upon the Tower, being that to the arches C F, F G, G H, <lb/>&c. </s><s>that it would have pa&longs;&longs;ed continuing alwayes upon the Tower, <lb/>the arches of the circumference C I are exactly equal, an&longs;wering <lb/>under the &longs;ame C F, F G, G H, &c. </s><s>Whence followeth the third <lb/><arrow.to.target n="marg332"></arrow.to.target> <lb/>wonder, That the true and real motion of the &longs;tone is never acce­ <lb/>lerated, but alwayes even and uniforme, &longs;ince that all the equal ar­ <lb/>ches noted in the circumference C D, and their re&longs;pondent ones <lb/>marked in the circumference C I, are pa&longs;t in equal times; &longs;o that <lb/>we are left at liberty to &longs;eek new cau&longs;es of acceleration, or of o­ <lb/>ther motions, &longs;eeing that the moveable, as well &longs;tanding upon the <lb/>Tower, as de&longs;cending thence, alwayes moveth in the &longs;ame fa&longs;hion, <lb/>that is, circularly, with the &longs;ame velocity, and with the &longs;ame uni­ <lb/>formity. </s><s>Now tell me what you think of this my fanta&longs;tical con­ <lb/>jecture.</s></p><p type="margin"><s><margin.target id="marg330"></margin.target><emph type="italics"/>A moveable fal­ <lb/>ting from the top of <lb/>the Tower, moveth <lb/>in the circumfe­ <lb/>rence of a circle.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg331"></margin.target><emph type="italics"/>It moveth neither <lb/>more nor le&longs;&longs;e, than <lb/>if it had &longs;taid al­ <lb/>wayes there.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg332"></margin.target><emph type="italics"/>It moveth with <lb/>an uniform, not <lb/>an accelerate mo­ <lb/>tion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I mu&longs;t tell you, that I cannot with words &longs;ufficiently <lb/>expre&longs;&longs;e how admirable it &longs;eemeth to me; and for what at pre­ <lb/>&longs;ent offereth it &longs;elf to my under&longs;tanding, I cannot think that the <lb/>bu&longs;ine&longs;s happeneth otherwi&longs;e; and would to God that all the <lb/>demon&longs;trations of Philo&longs;ophers were but half &longs;o probable as this. <lb/></s><s>However for my perfect &longs;atisfaction I would gladly hear how you <lb/>prove tho&longs;e arches to be equal.</s></p><p type="main"><s>SALV. </s><s>The demon&longs;tration is mo&longs;t ea&longs;ie. </s><s>Suppo&longs;e to your &longs;elf <lb/>a line drawn from I to E. </s><s>And the Semidiameter of the circle CD, <lb/>that is, the line C A, being double the Semidiameter C E of the <pb xlink:href="040/01/165.jpg" pagenum="147"/>circle C I, the circumference &longs;hall be double to the circumference, <lb/>and every arch of the greater circle double to every like arch of <lb/>the le&longs;&longs;er; and con&longs;equently, the half of the arch of the greater <lb/>circle, equal to the whole arch of the le&longs;&longs;e. </s><s>And becau&longs;e the an­ <lb/>gle C E I made in the centre E of the le&longs;&longs;er circle, and which in&longs;i­ <lb/>&longs;teth upon the arch C I, is double the angle C A D, made in the <lb/>centre A of the greater circle, to which the arch C D &longs;ubtendeth; <lb/>therefore the arch C D is half of the arch of the greater circle like <lb/>to the arch C I, and therefore the two arches C D and C I are e­ <lb/>qual; and in the &longs;ame manner we may demon&longs;trate of all their <lb/>parts. </s><s>But that the bu&longs;ine&longs;s, as to the motion of de&longs;cending grave <lb/>bodies, proceedeth exactly thus, I will not at this time affirm; but <lb/>this I will &longs;ay, that if the line de&longs;cribed by the cadent moveable <lb/>be not exactly the &longs;ame with this, it doth extream neerly re&longs;emble <lb/>the &longs;ame.</s></p><p type="main"><s>SAGR. </s><s>But I, <emph type="italics"/>Salviatus,<emph.end type="italics"/> am ju&longs;t now con&longs;idering another par­ <lb/><arrow.to.target n="marg333"></arrow.to.target> <lb/>ticular very admirable; and this it is; That admitting the&longs;e con­ <lb/>&longs;iderations, the right motion doth go wholly ^{*} mounting, and that <lb/><arrow.to.target n="marg334"></arrow.to.target> <lb/>Nature never makes u&longs;e thereof, &longs;ince that, even that that u&longs;e, <lb/>which was from the beginning granted to it, which was of redu­ <lb/>cing the parts of integral bodies to their place, when they were <lb/>&longs;eparated from their whole, and therefore con&longs;tituted in a depra­ <lb/>ved di&longs;po&longs;ition, is taken from it, and a&longs;&longs;igned to the circular <lb/>motion.</s></p><p type="margin"><s><margin.target id="marg333"></margin.target><emph type="italics"/>Right motion <lb/>&longs;eemeth wholly ex­ <lb/>cluded in nature.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg334"></margin.target>* Vadia del tutto a <lb/>monte, <emph type="italics"/>rendered in <lb/>the Latixe<emph.end type="italics"/> omni­ <lb/>no pe&longs;&longs;um eat.</s></p><p type="main"><s>SALV. </s><s>This would nece&longs;&longs;arily follow, if it were concluded <lb/>that the Terre&longs;trial Globe moveth circularly; a thing, which I <lb/>pretend not to be done, but have onely hitherto attempted, as I <lb/>&longs;hall &longs;till, to examine the &longs;trength of tho&longs;e rea&longs;ons, which have <lb/>been alledged by Philo&longs;ophers to prove the immobility of the <lb/>Earth, of which this fir&longs;t taken from things falling perpendicu­ <lb/>larly, hath begat the doubts, that have been mentioned; which <lb/>I know not of what force they may have &longs;eemed to <emph type="italics"/>Simplicius<emph.end type="italics"/>; <lb/>and therefore before I pa&longs;&longs;e to the examination of the remaining <lb/>arguments, it would be convenient that he produce what he hath <lb/>to reply to the contrary.</s></p><p type="main"><s>SIMP. </s><s>As to this fir&longs;t, I confe&longs;&longs;e indeed that I have heard <lb/>&longs;undry pretty notions, which I never thought upon before, and <lb/>in regard they are new unto me, I cannot have an&longs;wers &longs;o ready <lb/>for them, but this argument taken from things falling perpendi­ <lb/>cularly, I e&longs;teem it not one of the &longs;tronge&longs;t proofs of the mobi­ <lb/>lity of the Earth; and I know not what may happen touching the <lb/>&longs;hots of great Guns, e&longs;pecially tho&longs;e aimed contrary to the diur­ <lb/>nal motion.</s></p><p type="main"><s>SAGR. </s><s>The flying of the birds as much puzzleth me as the <lb/>objection of the Gun-&longs;hot, and all the other experiments above <pb xlink:href="040/01/166.jpg" pagenum="148"/>alledged. </s><s>For the&longs;e birds which at their plea&longs;ure flie for­ <lb/>wards and backwards, and wind to and again in a thou&longs;and <lb/>fa&longs;hions, and, which more importeth, lie whole hours upon the <lb/>wing, the&longs;e I &longs;ay do not a little po&longs;e me, nor do I &longs;ee, how a­ <lb/>mong&longs;t &longs;o many circumgyrations, they &longs;hould not lo&longs;e the motion <lb/>of the Earth, and how they &longs;hould be able to keep pace with <lb/>&longs;o great a velocity as that which they &longs;o far exceed with their flight.</s></p><p type="main"><s>SALV. </s><s>To &longs;peak the truth, your &longs;cruple is not without rea&longs;on, <lb/>and its po&longs;&longs;ible <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf could not find an an&longs;wer for it, <lb/>that was to him&longs;elf entirely &longs;atisfactory; and therefore haply pa&longs;t <lb/>it over in &longs;ilence albeit he was, indeed, very brief in examining <lb/>the other allegations of his adver&longs;aries, I believe through his <lb/>height of wit, placed on greater aud &longs;ublimer contemplations, <lb/>like as Lions are not much moved at the barking of little Dogs. <lb/></s><s>We will therefore re&longs;erve the in&longs;tance of birds to the la&longs;t place, <lb/>and for the pre&longs;ent, &longs;ee if we can give <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;atisfaction in <lb/>the others, by &longs;hewing him in our wonted manner, that he him­ <lb/>&longs;elf hath their an&longs;wers at hand, though upon fir&longs;t thoughts he doth <lb/>not di&longs;cover them. </s><s>And to begin with the &longs;hots made at randome, <lb/>with the &longs;elf &longs;ame piece, powder, and ball, the one towards the Ea&longs;t, <lb/>the other towards the We&longs;t, let him tell me what it is that per&longs;wades <lb/>him to think that the Range towards the We&longs;t (if the diurnal con­ <lb/>ver&longs;ion belonged to the Earth) ought to be much longer than that <lb/>towards the Ea&longs;t. <lb/><arrow.to.target n="marg335"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg335"></margin.target><emph type="italics"/>The rea&longs;on why <lb/>a Gun &longs;hould &longs;iem <lb/>to carry farther to­ <lb/>wards the We&longs;t <lb/>than towards the <lb/>Ea&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I am moved &longs;o to think; becau&longs;e in the &longs;hot made to­ <lb/>wards the Ea&longs;t, the ball whil'&longs;t it is out of the piece, is follow­ <lb/>ed by the &longs;aid piece, the which being carried round by the Earth, <lb/>runneth al&longs;o with much velocity towards the &longs;ame part, where­ <lb/>upon the fall of the ball to the ground, cometh to be but little <lb/>di&longs;tant from the piece. </s><s>On the contrary in the &longs;hot towards the <lb/>We&longs;t, before that the ball falleth to the ground, the piece is re­ <lb/>tired very far towards the Ea&longs;t, by which means the &longs;pace be­ <lb/>tween the ball and the piece, that is Range, will appear longer <lb/>than the other, by how much the piece, that is the Earth, had <lb/>run in the time that both the bals were in the air.</s></p><p type="main"><s>SALV. </s><s>I could wi&longs;h, that we did know &longs;ome way to make an <lb/>experiment corre&longs;ponding to the motion of the&longs;e projects, as that <lb/>of the &longs;hip doth to the motion of things perpendicularly falling <lb/>from on high; and I am thinking how it may be done.</s></p><p type="main"><s><arrow.to.target n="marg336"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg336"></margin.target><emph type="italics"/>The experiment <lb/>of a running cha­ <lb/>riot to find out the <lb/>difference of Ran­ <lb/>ges.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I believe, that it would be a very oppo&longs;ite proof, to <lb/>take an open Chariot, and to accomodate therein a ^{*}Stock-bow <lb/>at half elevation, to the end the flight may prove the greate&longs;t </s></p><p type="main"><s><arrow.to.target n="marg337"></arrow.to.target> <lb/>that my be, and whil'&longs;t the hor&longs;es &longs;hall run, to &longs;hoot fir&longs;t towards <lb/>the part whither you drive, and then another backwards towards <lb/>the contrary part, cau&longs;ing &longs;ome one to mark diligently where <lb/>the Chariot was in that moment f time when the &longs;haft came to <pb xlink:href="040/01/167.jpg" pagenum="149"/>the ground, as well in the one &longs;hot as in the other: for thus you <lb/>may &longs;ee exactly how much one &longs;haft flew farther than the other.</s></p><p type="margin"><s><margin.target id="marg337"></margin.target>* Bale&longs;trone da bol­ <lb/>zoni.</s></p><p type="main"><s>SIMP. </s><s>In my thoughts this experiment is very proper: and I <lb/>do not doubt but that the flight, that is, the &longs;pace between the <lb/>&longs;haft and the place where the chariot was at the &longs;hafts fall, will be <lb/>le&longs;s by much when one &longs;hooteth towards the chariots cour&longs;e, than <lb/>when one &longs;hooteth the contrary way. </s><s>For an example, let the <lb/>flight of it &longs;elf be three hundred yards, and the cour&longs;e of the cha­ <lb/>riot in the time whil&longs;t the &longs;haft &longs;tayeth in the air, an hundred <lb/>yards, therefore &longs;hooting towards the cour&longs;e, of the three hundred <lb/>yards of the flight, the chariot will have gone one hundred; &longs;o <lb/>then at the &longs;hafts coming to the ground, the &longs;pace between it and <lb/>the chariot, &longs;hall be but two hundred yards onely; but on the <lb/>contrary, in the other &longs;hoot, the chariot running contrary to the <lb/>&longs;haft, when the &longs;haft &longs;hall have pa&longs;&longs;ed its three hundred yards, and <lb/>the chariot its other hundred the contrary way, the di&longs;tance inter­ <lb/>po&longs;ing &longs;hall be found to be four hundred yards.</s></p><p type="main"><s>SALV. </s><s>Is there any way to &longs;hoot &longs;o that the&longs;e flights may be <lb/>equal?</s></p><p type="main"><s>SIMP. </s><s>I know no other way, unle&longs;s by making the chariot to <lb/>&longs;tand &longs;till.</s></p><p type="main"><s>SALV. </s><s>This we know; but I mean when the chariot runneth <lb/>in full carreer.</s></p><p type="main"><s>SIMP. </s><s>In that ca&longs;e you are to draw the Bow higher in &longs;hoot­ <lb/>ing forwards, and to &longs;lack it in &longs;hooting the contrary way.</s></p><p type="main"><s>SALV. </s><s>Then you &longs;ee that there is one way more. </s><s>But how <lb/>much is the bow to be drawn, and how much &longs;lackened?</s></p><p type="main"><s>SIMP. </s><s>In our ca&longs;e, where we have &longs;uppo&longs;ed that the bow car­ <lb/>ried three hundred yards, it would be requi&longs;ite to draw it &longs;o, as <lb/>that it might carry four hundred, and in the other to &longs;lacken it &longs;o, <lb/>as that it might carry no more than two hundred. </s><s>For &longs;o each <lb/>of the flights would be but three hundred in relation to the chariot, <lb/>the which, with its cour&longs;e of an hundred yards which it &longs;ub&longs;tracts <lb/>from the &longs;hoot of four hundred, and addeth to that of two hun­ <lb/>dred, would reduce them both to three hundred.</s></p><p type="main"><s>SALV. </s><s>But what effect hath the greater or le&longs;s inten&longs;ne&longs;s of the <lb/>bow upon the &longs;haft?</s></p><p type="main"><s>SIMP. </s><s>The &longs;tiffer bow carrieth it with greater velocity, and the <lb/>weaker with le&longs;s; and the &longs;ame &longs;haft flieth &longs;o much farther at one <lb/>time than another, with how much greater velocity it goeth out of <lb/>the tiller at one time, than another.</s></p><p type="main"><s>SALV. </s><s>So that to make the &longs;haft &longs;hot either way, to flie at e­ <lb/>qual di&longs;tance from the running chariot, it is requi&longs;ite, that if in the <lb/>fir&longs;t &longs;hoot of the precedent example, it goeth out of the tiller with <lb/><emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> four degrees of velocity, that then in the other &longs;hoot it de­ <pb xlink:href="040/01/168.jpg" pagenum="150"/>part but with two onely: but if the &longs;ame bow be u&longs;ed, it always <lb/>receiveth thence three degrees.</s></p><p type="main"><s>SIMP. </s><s>It doth &longs;o; and for this rea&longs;on, &longs;hooting with the <lb/>&longs;ame bow in the chariots cour&longs;e, the &longs;hoots cannot be equal.</s></p><p type="main"><s>SALV. </s><s>I had forgot to ask, with what velocity it is &longs;uppo&longs;ed in <lb/>this particular experiment, that the chariot runneth.</s></p><p type="main"><s>SIMP. </s><s>The velocity of the chariot mu&longs;t be &longs;uppo&longs;ed to be one <lb/>degree in compari&longs;on to that of the bow, which is three,</s></p><p type="main"><s>SALV. </s><s>Very right, for &longs;o computation gives it. </s><s>But tell me, <lb/>when the chariot moveth, doth not all things in the &longs;ame move <lb/>with the &longs;ame velocity?</s></p><p type="main"><s>SIMP. </s><s>Yes doubtle&longs;s.</s></p><p type="main"><s>SALV. </s><s>Then &longs;o doth the &longs;haft al&longs;o, and the bow, and the &longs;tring, <lb/>upon which the &longs;haft is nock't.</s></p><p type="main"><s>SIMP. </s><s>They do &longs;o.</s></p><p type="main"><s>SALV. </s><s>Why then, in di&longs;charging the &longs;haft towards the cour&longs;e <lb/>of the chariot, the bow impre&longs;&longs;eth its three degrees of velocity on <lb/>a &longs;haft that had one degree of velocity before, by means of the <lb/>chariot which tran&longs;ported it &longs;o fa&longs;t towards that part; &longs;o that in <lb/>its going off it hath four degrees of velocity. </s><s>On the contrary, <lb/>in the other &longs;hoot, the &longs;ame bow conferreth its &longs;ame three degrees <lb/>of velocity on a &longs;haft that moveth the contrary way, with one de­ <lb/>gree; &longs;o that in its departing from the bow-&longs;tring, it hath no more <lb/>left but onely two degrees of velocity. </s><s>But you your &longs;elf have <lb/>already &longs;aid, that the way to make the &longs;hoots equal, is to cau&longs;e <lb/>that the &longs;haft be let flie the fir&longs;t time with four degrees of velocity, <lb/>and the &longs;econd time with two. </s><s>Therefore without changing the <lb/>bow, the very cour&longs;e of the chariot is that which adju&longs;teth the <lb/><arrow.to.target n="marg338"></arrow.to.target> <lb/>flights, and the experiment doth &longs;o repre&longs;ent them to any one who <lb/>is not either wilfully or naturally incapable of rea&longs;on. </s><s>Now <lb/>apply this di&longs;cour&longs;e to Gunnery, and you &longs;hall find, that whether the <lb/>Earth move or &longs;tand &longs;till, the &longs;hots made with the &longs;ame force, will <lb/>always curry equal ranges, to what part &longs;oever aimed. </s><s>The error <lb/>of <emph type="italics"/>Ari&longs;totle, Ptolomey, Iycho,<emph.end type="italics"/> your &longs;elf, and all the re&longs;t, is ground­ <lb/>ed upon that fixed and &longs;trong per&longs;ua&longs;ion, that the Earth &longs;tandeth <lb/>&longs;till, which you have not judgment nor power to depo&longs;e, no not <lb/>when you have a de&longs;ire to argue of that which would en&longs;ue, pre­ <lb/>&longs;uppo&longs;ing the Earth to move. </s><s>And thus, in the other argument, <lb/>not con&longs;idering that whil'&longs;t the &longs;tone is upon the Tower, it doth, <lb/>as to moving or not moving, the &longs;ame that the Terre&longs;trial Globe <lb/>doth, becau&longs;e you have concluded with your &longs;elf, that the Earth <lb/>&longs;tands &longs;till, you always di&longs;cour&longs;e touching the fall of the &longs;tone, as <lb/>if it were to depart from re&longs;t: whereas it behooveth to &longs;ay, that <lb/>if the Earth &longs;tandeth &longs;till, the &longs;tone departeth from re&longs;t, and de­ <lb/>&longs;cendeth perpendicularly; but if the Earth do move, the &longs;tone <pb xlink:href="040/01/169.jpg" pagenum="151"/>likewi&longs;e moveth with like velocity, nor doth it depart from re&longs;t, <lb/>but from a motion equal to that of the Earth, wherewith it inter­ <lb/>mixeth the &longs;upervenient motion of de&longs;cent, and of tho&longs;e two com­ <lb/>po&longs;eth a third which is tran&longs;ver&longs;al or &longs;ide-ways.</s></p><p type="margin"><s><margin.target id="marg338"></margin.target><emph type="italics"/>The &longs;olution of <lb/>the argument ta­ <lb/>ken from great­ <lb/>Guns &longs;hot towards <lb/>the East & We&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>But for Gods &longs;ake, if it move tran&longs;ver&longs;ly, how is it that <lb/>I behold it to move directly and perpendicularly? </s><s>This is no bet­ <lb/>ter than the denial of manife&longs;t &longs;en&longs;e; and if we may not believe <lb/>&longs;en&longs;e, at what other door &longs;hall we enter into di&longs;qui&longs;itions of Philo­ <lb/>&longs;ophy?</s></p><p type="main"><s>SALV. </s><s>In re&longs;pect to the Earth, to the Tower, and to our &longs;elves, <lb/>which all as one piece move with the diurnal motion together with <lb/>the &longs;tone, the diurnal motion is as if it never had been, and becom­ <lb/>eth in&longs;en&longs;ible, imperceptible, and without any action at all; and <lb/>the onely motion which we can perceive, is that of which we par­ <lb/>take not, that is the de&longs;cent gliding along the &longs;ide of the Tower: <lb/>You are not the fir&longs;t that hath felt great repugnance in apprehen­ <lb/>ding this non-operating of motion upon things to which it is com­ <lb/>mon.</s></p><p type="main"><s>SAGR. </s><s>Now I do remember a certain conceipt, that came one <lb/><arrow.to.target n="marg339"></arrow.to.target> <lb/>day into my fancy, whil&longs;t I &longs;ailed in my voyage to <emph type="italics"/>Aleppo,<emph.end type="italics"/> whither <lb/>I went Con&longs;ul for our Countrey, and po&longs;&longs;ibly it may be of &longs;ome <lb/>u&longs;e, for explaining this nullity of operation of common motion, <lb/>and being as if it never were to all the partakers thereof. </s><s>And if <lb/>it &longs;tand with the good liking of <emph type="italics"/>Simplicius,<emph.end type="italics"/> I will rea&longs;on with <lb/>him upon that which then I thought of by my &longs;elf alone.</s></p><p type="margin"><s><margin.target id="marg339"></margin.target><emph type="italics"/>A notable ca&longs;e <lb/>of<emph.end type="italics"/> Sagredus, <emph type="italics"/>to &longs;hew <lb/>the non-operating <lb/>of common motion.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The novelty of the things which I hear, makes me not <lb/>&longs;o much a patient, as a greedy and curious auditor: therefore go <lb/>on.</s></p><p type="main"><s>SAGR. </s><s>If the neb of a writing pen, that I carried along with <lb/>me in the &longs;hip, through all my navigation from <emph type="italics"/>Venice<emph.end type="italics"/> to ^{*} <emph type="italics"/>Scan-<emph.end type="italics"/> <lb/><arrow.to.target n="marg340"></arrow.to.target> <lb/><emph type="italics"/>deron,<emph.end type="italics"/> had had a facultie of leaving vi&longs;ible marks of its whole voy­ <lb/>age, what &longs;igns, what marks, what lines would it have left?</s></p><p type="margin"><s><margin.target id="marg340"></margin.target>* Ale&longs;&longs;andretta.</s></p><p type="main"><s>SIMP. </s><s>It would have left a line di&longs;tended from <emph type="italics"/>Venice<emph.end type="italics"/> thither, <lb/>not perfectly &longs;treight, or to &longs;ay better, di&longs;tended in a perfect arch <lb/>of a circle, but in &longs;ome places more, in &longs;ome le&longs;s curved, according <lb/>as the ve&longs;&longs;el had gone more or le&longs;s fluctuating; but this its infle­ <lb/>cting in &longs;ome places a fathom or two to the right hand or to the <lb/>left, upwards or downwards, in a length of many hundred miles, <lb/>would have brought but little alteration to the intire tract of the <lb/>line, &longs;o that it would have been hardly &longs;en&longs;ible; and without any <lb/>con&longs;iderable error, might have been called the part of a perfect <lb/>arch.</s></p><p type="main"><s>SAGR. </s><s>So that the true and mo&longs;t exact motion of the neb of <lb/>my pen would have al&longs;o been an arch of a perfect circle, if the <lb/>ve&longs;&longs;els motion, the fluctuation of the billows cea&longs;ing, had been <pb xlink:href="040/01/170.jpg" pagenum="152"/>calm and tranquill. </s><s>And if I had continually held that pen in <lb/>my hand, and had onely moved it &longs;ometimes an inch or two this <lb/>way or that way, what alteration &longs;hould I have made in that its <lb/>principal, and very long tract or &longs;troke?</s></p><p type="main"><s>SIMP. </s><s>Le&longs;s than that which the declining in &longs;everal places from <lb/>ab&longs;olute rectitude, but the quantity of a flea's eye makes in a right <lb/>line of a thou&longs;and yards long.</s></p><p type="main"><s>SAGR. </s><s>If a Painter, then, at our launching from the Port, had <lb/>began to de&longs;ign upon a paper with that pen, and continued his <lb/>work till he came to <emph type="italics"/>Scanderon,<emph.end type="italics"/> he would have been able to have <lb/>taken by its motion a perfect draught of all tho&longs;e figures perfectly <lb/>interwoven and &longs;hadowed on &longs;everal &longs;ides with countreys, build­ <lb/>ings, living creatures, and other things; albeit all the true, real, <lb/>and e&longs;&longs;ential motion traced out by the neb of that pen, would <lb/>have been no other than a very long, but &longs;imple line: and as to <lb/>the proper operation of the Painter, he would have delineated the <lb/>&longs;ame to an hair, if the &longs;hip had &longs;tood &longs;till. </s><s>That therefore of the <lb/>huge long motion of the pen there doth remain no other marks, <lb/>than tho&longs;e tracks drawn upon the paper, the rea&longs;on thereof is be­ <lb/>cau&longs;e the grand motion from <emph type="italics"/>Venice<emph.end type="italics"/> to <emph type="italics"/>Scanderon,<emph.end type="italics"/> was common to <lb/>the paper, the pen, and all that which was in the &longs;hip: but the petty <lb/>motions forwards and backwards, to the right, to the left, com­ <lb/>municated by the fingers of the Painter unto the pen, and not to <lb/>the paper, as being peculiar thereunto, might leave marks of it &longs;elf <lb/>upon the paper, which did not move with that motion. </s><s>Thus it <lb/>is likewi&longs;e true, that the Earth moving, the motion of the &longs;tone in <lb/>de&longs;cending downwards, was really a long tract of many hundreds <lb/>and thou&longs;ands of yards, and if it could have been able to have de­ <lb/>lineated in a calm air, or other &longs;uperficies, the track of its cour&longs;e, <lb/>it would have left behind an huge long tran&longs;ver&longs;e line. </s><s>But that <lb/>part of all this motion which is common to the &longs;tone, the Tower, <lb/>and our &longs;elves, is imperceptible to us, and as if it had never been, <lb/>and that part onely remaineth ob&longs;ervable, of which neither the <lb/>Tower nor we are partakers, which is in fine, that wherewith the <lb/>&longs;tone falling mea&longs;ureth the Tower.</s></p><p type="main"><s>SALV. </s><s>A mo&longs;t witty conceipt to clear up this point, which was <lb/>not a little difficult to many capacities. </s><s>Now if <emph type="italics"/>Simplicius<emph.end type="italics"/> will <lb/>make no farther reply, we may pa&longs;s to the other experiments, the <lb/>unfolding of which will receive no &longs;mall facility from the things <lb/>already declared.</s></p><p type="main"><s>SIMP. </s><s>I have nothing more to &longs;ay: and I was well-nigh tran&longs;­ <lb/>ported with that delineation, and with thinking how tho&longs;e &longs;trokes <lb/>drawn &longs;o many ways, hither, thither, upwards, downwards, for­ <lb/>wards, backwards, and interwoven with thou&longs;ands of turnings, are <lb/>not e&longs;&longs;entially or really other, than &longs;mall pieces of one &longs;ole line <pb xlink:href="040/01/171.jpg" pagenum="153"/>drawn all one way, and the &longs;ame without any other alteration &longs;ave <lb/>the declining the direct rectitude, &longs;ometimes a very in&longs;en&longs;ible mat­ <lb/>ter towards one &longs;ide or another, and the pens moving its neb one <lb/>while &longs;ofter, another while &longs;lower, but with very &longs;mall inequality. <lb/></s><s>And I think that it would in the &longs;ame manner write a letter, and <lb/>that tho&longs;e frollike penmen, who to &longs;hew their command of hand, <lb/>without taking their pen from the paper in one &longs;ole &longs;troke, with <lb/>infinite turnings draw a plea&longs;ant knot, if they were in a boat that <lb/>did tide it along &longs;wiftly they would convert the whole motion <lb/>of the pen, which in reality is but one &longs;ole line, drawn all towards <lb/>one and the &longs;ame part, and very little curved, or declining from <lb/>perfect rectitude, into a knot or flouri&longs;h. </s><s>And I am much plea&longs;ed <lb/>that <emph type="italics"/>S agredus<emph.end type="italics"/> hath helped me to this conceit: therefore let us go <lb/>on, for the hope of meeting with more of them, will make me the <lb/>&longs;tricter in my attention.</s></p><p type="main"><s>SAGR. </s><s>If you have a curio&longs;ity to hear &longs;uch like &longs;ubtilties, which <lb/><arrow.to.target n="marg341"></arrow.to.target> <lb/>occurr not thus to every one, you will find no want of them, e&longs;pe­ <lb/>cially in this particular of Navigation; and do you not think that a <lb/>witty conceit which I met with likewi&longs;e in the &longs;ame voyage, when I <lb/>ob&longs;erved that the ma&longs;t of the &longs;hip, without either breaking or bend­ <lb/>ing, had made a greater voyage with its round-top, that is with its <lb/>top-gallant, than with its foot; for the round top being more di&longs;tant <lb/>from the centre of the Earth than the foot is, it had de&longs;cribed the <lb/>arch of a circle bigger than the circle by which the foot had pa&longs;&longs;ed.</s></p><p type="margin"><s><margin.target id="marg341"></margin.target><emph type="italics"/>Subtilties &longs;uffici­ <lb/>ently in&longs;ipid, ironi­ <lb/>cally, &longs;poken and <lb/>taken from a cer­ <lb/>tain<emph.end type="italics"/> Encyclopædia.</s></p><p type="main"><s>SIMP. </s><s>And thus when a man walketh he goeth farther with <lb/>his head than with his feet.</s></p><p type="main"><s>SAGR. </s><s>You have found out the matter your &longs;elf by help of <lb/>your own mother-wit: But let us not interrupt <emph type="italics"/>Salviatus.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>It plea&longs;eth me to &longs;ee <emph type="italics"/>Simplicius<emph.end type="italics"/> how he &longs;ootheth up <lb/>him&longs;elf in this conceit, if happly it be his own, and that he hath not <lb/>borrowed it from a certain little pamphlet of conclu&longs;ions, where <lb/>there are a great many more &longs;uch fancies no le&longs;s plea&longs;ant & witty. <lb/></s><s>It followeth that we &longs;peak of the peice of Ordinance mounted per­ <lb/><arrow.to.target n="marg342"></arrow.to.target> <lb/>pendicular to the Horizon, that is, of a &longs;hot towards our vertical <lb/>point, and to conclude, of the return of the ball by the &longs;ame line <lb/>unto the &longs;ame peice, though that in the long time which it is &longs;e­ <lb/>parated from the peice, the earth hath tran&longs;ported it many miles <lb/>towards the Ea&longs;t; now it &longs;eemeth, that the ball ought to fall a like <lb/>di&longs;tance from the peice towards the We&longs;t; the which doth not <lb/>happen: therefore the peice without having been moved did &longs;tay <lb/>expecting the &longs;ame. </s><s>The an&longs;wer is the &longs;ame with that of the <lb/><arrow.to.target n="marg343"></arrow.to.target> <lb/>&longs;tone falling from the Tower; and all the fallacy, and equivocati­ <lb/>on con&longs;i&longs;teth in &longs;uppo&longs;ing &longs;till for true, that which is in que&longs;tion; <lb/>for the Opponent hath it &longs;till fixed in his conceit that the <lb/>ball departs from its re&longs;t, being di&longs;charged by the fire <pb xlink:href="040/01/172.jpg" pagenum="154"/>from the piece; and the departing from the &longs;tate of re&longs;t, cannot <lb/>be, unle&longs;&longs;e the immobility of the Terre&longs;trial Globe be pre&longs;uppo­ <lb/>&longs;ed, which is the conclu&longs;ion of that was in di&longs;pute; Therefore, <lb/>I reply, that tho&longs;e who make the Earth moveable, an&longs;wer, that <lb/>the piece, and the ball that is in it, partake of the &longs;ame motion <lb/>with the Earth; nay that they have this together with her from <lb/>nature; and that therefore the ball departs in no other manner <lb/>from its quie&longs;cence, but conjoyned with its motion about the cen­ <lb/>tre, the which by its projection upwards, is neither taken away, <lb/>nor hindered; and in this manner following, the univer&longs;al motion <lb/>of the Earth towards the Ea&longs;t, it alwayes keepeth perpendicular <lb/>over the &longs;aid piece, as well in its ri&longs;e as in its return. </s><s>And the <lb/>&longs;ame you &longs;ee to en&longs;ue, in making the experiment in a &longs;hip with <lb/>a bullet &longs;hot upwards perpendicularly with a Cro&longs;&longs;e-bow, which <lb/>returneth to the &longs;ame place whether the &longs;hip doth move, or &longs;tand <lb/>&longs;till. <lb/><arrow.to.target n="marg344"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg342"></margin.target><emph type="italics"/>An in&longs;tance a­ <lb/>gainst the diurnal <lb/>motion of the earth, <lb/>taken from the &longs;hot <lb/>of a Peece of Ordi­ <lb/>nance perpendicu­ <lb/>larly.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg343"></margin.target><emph type="italics"/>The an&longs;wer to the <lb/>objection, &longs;hewing <lb/>the equivoke.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg344"></margin.target><emph type="italics"/>Another an&longs;wer <lb/>to the &longs;ame objecti­ <lb/>on.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This &longs;atisfieth very well to all; but becau&longs;e that I have <lb/>&longs;een that <emph type="italics"/>Simplicius<emph.end type="italics"/> taketh plea&longs;ure with certain &longs;ubtilties to <lb/>puzzle his companions, I will demand of him whether, &longs;uppo­ <lb/>&longs;ing for this time that the Earth &longs;tandeth &longs;till, and the piece ere­ <lb/>cted upon it perpendicularly, directed to our Zenith, he do at all <lb/>que&longs;tion that to be the true perpendicular &longs;hot, and that the ball <lb/>in departing, and in its return is to go by the &longs;ame right line, <lb/>&longs;till &longs;uppo&longs;ing all external and accidental impediments to be re­ <lb/>moved?</s></p><p type="main"><s>SIMP. </s><s>I under&longs;tand that the matter ought to &longs;ucceed exactly <lb/>in that manner.</s></p><p type="main"><s>SAGR. </s><s>But if the piece were placed, not perpendicularly, but <lb/>inclining towards &longs;ome place, what would the motion of the ball <lb/>be? </s><s>Would it go haply, as in the other &longs;hot, by the perpendi­ <lb/>cular line, and return again by the &longs;ame?</s></p><p type="main"><s>SIMP. </s><s>It would not &longs;o do; but i&longs;&longs;uing out of the piece, it <lb/>would pur&longs;ue its motion by a right line which prolongeth the e­ <lb/>rect perpendicularity of the concave cylinder of the piece, unle&longs;&longs;e <lb/>&longs;o far as its own weight would make it decline from that erection <lb/>towards the Earth.</s></p><p type="main"><s>SAGR. </s><s>So that the mounture of the cylinder is the regulator of <lb/>the motion of the ball, nor doth it, or would it move out of that <lb/>line, if its own gravity did not make it decline downwards. </s><s>And </s></p><p type="main"><s><arrow.to.target n="marg345"></arrow.to.target> <lb/>therefore placing the cylinder perpendicularly, and &longs;hooting the <lb/>ball upwards, it returneth by the &longs;ame right line downwards; be­ <lb/>cau&longs;e the motion of the ball dependent on its gravity is down­ <lb/>ward, by the &longs;ame perpendicular. </s><s>The journey therefore of the <lb/>ball out of the piece, continueth or prolongeth the rectitude or <lb/>perpendicularity of that &longs;mall part of the &longs;aid journey, which it <lb/>made within the &longs;aid piece; is it not &longs;o?</s></p> <pb xlink:href="040/01/173.jpg" pagenum="155"/><p type="margin"><s><margin.target id="marg345"></margin.target><emph type="italics"/>Projects conti­ <lb/>nue their motion <lb/>by the right line <lb/>that followeth the <lb/>direction of the <lb/>motion, made to­ <lb/>gether with the <lb/>projicient, whil'&longs;t <lb/>they were conjoin'd <lb/>therewith.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>So it is, in my opinion.</s></p><p type="main"><s>SAGR. </s><s>Now imagine the cylinder to be erected, and that the <lb/>Earth doth revolve about with a diurnal motion, carrying the <lb/>piece along with it, tell me what &longs;hall be the motion of the ball <lb/>within the cylinder, having given fire?</s></p><p type="main"><s>SIMP. </s><s>It &longs;hall be a &longs;treight and perpendicular motion, the cylin­ <lb/>der being erected perpendicularly.</s></p><p type="main"><s>SAGR. </s><s>Con&longs;ider well what you &longs;ay: for I believe that it will <lb/>not be perpendicular. </s><s>It would indeed be perpendicular, if the <lb/>Earth &longs;tood &longs;till, for &longs;o the ball would have no other motion but <lb/>that proceeding from the fire. </s><s>But in ca&longs;e the Earth turns round, <lb/><arrow.to.target n="marg346"></arrow.to.target> <lb/>the ball that is in the piece, hath likewi&longs;e a diurnal motion, &longs;o <lb/>that there being added to the &longs;ame the impul&longs;e of the fire, it mo­ <lb/>veth from the breech of the piece to the muzzle with two motions, <lb/>from the compo&longs;ition whereof it cometh to pa&longs;&longs;e that the motion <lb/>made by the centre of the balls gravity is an inclining line. </s><s>And <lb/>for your clearer under&longs;tanding the &longs;ame, let the piece A C [<emph type="italics"/>in <lb/>Fig.<emph.end type="italics"/> 2.] be erected, and in it the ball B; it is manife&longs;t, that the <lb/>piece &longs;tanding immoveable, and fire being given to it, the ball <lb/>will make its way out by the mouth A, and with its centre, pa&longs;­ <lb/>&longs;ing thorow the the piece, &longs;hall have de&longs;cribed the perpendicular <lb/>line B A, and it &longs;hall pur&longs;ue that rectitude when it is out of the <lb/>piece, moving toward the Zenith. </s><s>But in ca&longs;e the Earth &longs;hould <lb/>move round, and con&longs;equently carry the piece along with it, in <lb/>the time that the ball driven out of the piece &longs;hall move along <lb/>the cylinder, the piece being carried by the Earth, &longs;hall pa&longs;&longs;e in­ <lb/>to the &longs;ituation D E, and the ball B, in going off, would be at <lb/>the corni&longs;h D, and the motion of the bals centre, would have <lb/>been according to the line B D, no longer perpendicular, but in­ <lb/>clining towards the Ea&longs;t; and the ball (as hath been concluded) <lb/>being to continue its motion through the air, according to the <lb/>direction of the motion made in the piece, the &longs;aid motion &longs;hall <lb/>continue on according to the inclination of the line B D, and &longs;o <lb/>&longs;hall no longer be perpendicular, but inclined towards the Ea&longs;t, <lb/>to which part the piece doth al&longs;o move; whereupon the ball may <lb/>follow the motion of the Eerth, and of the piece. </s><s>Now <emph type="italics"/>Simplicius,<emph.end type="italics"/> <lb/>you &longs;ee it demon&longs;trated, that the Range which you took to be <lb/>perpendicular, is not &longs;o.</s></p><p type="margin"><s><margin.target id="marg346"></margin.target><emph type="italics"/>The revolution <lb/>of the Earth &longs;up­ <lb/>po&longs;ed, the ball in <lb/>the piece erected <lb/>perpendicularly, <lb/>doth not move by a <lb/>perpendicular, but <lb/>an inclined line.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I do not very well under&longs;tand this bu&longs;ine&longs;s; do you, <lb/><emph type="italics"/>Salviatus<emph.end type="italics"/>?</s></p><p type="main"><s>SALV. </s><s>I apprehend it in part; but I have a certain kind of <lb/>&longs;cruple, which I wi&longs;h I knew how to expre&longs;s. </s><s>It &longs;eems to me, that <lb/>according to what hath been &longs;aid, if the Piece be erected perpen­ <lb/>dicular, and the Earth do move, the ball would not be to fall, as <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Tycho<emph.end type="italics"/> will have it, far from the Piece towards the <pb xlink:href="040/01/174.jpg" pagenum="156"/>We&longs;t, nor as you would have it, upon the Piece, but rather far <lb/>di&longs;tant towards the Ea&longs;t. </s><s>For according to your explanation, it <lb/>would have two motions, the which would with one con&longs;ent carry <lb/>it thitherward, to wit, the common motion of the Earth, which <lb/>carrieth the Piece and the ball from C A towards E D; and the <lb/>fire which carrieth it by the inclined line B D, both motions to­ <lb/>wards the Ea&longs;t, and therefore they are &longs;uperiour to the motion of <lb/>the Earth.</s></p><p type="main"><s>SAGR. </s><s>Not &longs;o, Sir. </s><s>The motion which carrieth the ball to­ <lb/>wards the Ea&longs;t, cometh all from the Earth, and the fire hath no <lb/>part at all therein: the motion which mounteth the ball upwards, <lb/>is wholly of fire, wherewith the Earth hath nothing to do. </s><s>And <lb/>that it is &longs;o, if you give not fire, the ball will never go out of the <lb/>Piece, nor yet ri&longs;e upwards a hairs breadth; as al&longs;o if you make <lb/>the Earth immoveable, and give fire, the ball without any incli­ <lb/>nation &longs;hall go perpendicularly upwards. </s><s>The ball therefore ha­ <lb/>ving two motions, one upwards, and the other in gyration, of both <lb/>which the tran&longs;ver&longs;e line B D is compounded, the impul&longs;e upward <lb/>is wholly of fire, the circular cometh wholly from the Earth, and <lb/>is equal to the Earths motion: and being equal to it, the ball <lb/>maintaineth it &longs;elf all the way directly over the mouth of the <lb/>Piece, and at la&longs;t falleth back into the &longs;ame: and becau&longs;e it al­ <lb/>ways ob&longs;erveth the erection of the Piece, it appeareth al&longs;o conti­ <lb/>nually over the head of him that is near the Piece, and therefore <lb/>it appeareth to mount exactly perpendicular towards our Zenith, <lb/>or vertical point.</s></p><p type="main"><s>SIMP. </s><s>I have yet one doubt more remaining, and it is, that in <lb/>regard the motion of the ball is very &longs;wift in the Piece, it &longs;eems <lb/>not po&longs;&longs;ible, that in that moment of time the tran&longs;po&longs;ition of the <lb/>Piece from C A to A D &longs;hould confer &longs;uch an inclination upon <lb/>the tran&longs;ver&longs;e line C D, that by means thereof, the ball when it <lb/>cometh afterwards into the air &longs;hould be able to follow the cour&longs;e <lb/>of the Earth.</s></p><p type="main"><s>SAGR. </s><s>You err upon many accounts; and fir&longs;t, the inclination <lb/>of the tran&longs;ver&longs;e line C D, I believe it is much greater than you <lb/>take it to be, for I verily think that the velocity of the Earths mo­ <lb/>tion, not onely under the Equinoctial, but in our paralel al&longs;o, is <lb/>greater than that of the ball whil&longs;t it moveth in the Piece; &longs;o that <lb/>the interval C E would be ab&longs;olutely much bigger than the whole <lb/>length of the Piece, and the inclination of the tran&longs;ver&longs;e line con­ <lb/>&longs;equently bigger than half a right angle: but be the velocity of <lb/>the Earth more, or be it le&longs;s, in compari&longs;on of the velocity of the <lb/>fire, this imports nothing; for if the velocity of the Earth be &longs;mall, <lb/>and con&longs;equently the inclination of the tran&longs;ver&longs;e line be little <lb/>al&longs;o; there is then al&longs;o need but of little inclination to make the <pb xlink:href="040/01/175.jpg" pagenum="157"/>ball &longs;u&longs;pend it &longs;elf in its range directly over the Piece. </s><s>And in a <lb/>word, if you do but attentively con&longs;ider, you will comprehend, <lb/>that the motion of the Earth in transferring the Piece along with <lb/>it from C A to E D, conferreth upon the tran&longs;ver&longs;e line C D, &longs;o <lb/>much of little or great inclination, as is required to adju&longs;t the <lb/>range to its perpendicularity. </s><s>But you err, &longs;econdly, in that you <lb/>referr the faculty of carrying the ball along with the Earth to the <lb/>impul&longs;e of the fire, and you run into the &longs;ame error, into which <lb/><emph type="italics"/>Salviatus,<emph.end type="italics"/> but even now &longs;eemed to have fallen; for the faculty <lb/>of following the motion of the Earth, is the primary and perpetual <lb/>motion, indelibly and in&longs;eparably imparted to the &longs;aid ball, as to a <lb/>thing terre&longs;trial, and that of its own nature doth and ever &longs;hall <lb/>po&longs;&longs;e&longs;s the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>Let us yield, <emph type="italics"/>Simplicius,<emph.end type="italics"/> for the bu&longs;ine&longs;s is ju&longs;t as he <lb/><arrow.to.target n="marg347"></arrow.to.target> <lb/>&longs;aith. </s><s>And now from this di&longs;cour&longs;e let us come to under&longs;tand the <lb/>rea&longs;on of a Venatorian Problem, of tho&longs;e Fowlers who with their <lb/>guns &longs;hoot a bird flying; and becau&longs;e I did imagine, that in regard <lb/>the bird flieth a great pace, therefore they &longs;hould aim their &longs;hot far <lb/>from the bird, anticipating its flight for a certain &longs;pace, and more <lb/>or le&longs;s according to its velocity and the di&longs;tance of the bird, that <lb/>&longs;o the bullet ha&longs;ting directly to the mark aimed at, it might come <lb/>to arrive at the &longs;elf &longs;ame time in the &longs;ame point with its motion, <lb/>and the bird with its flight, and by that means one to encounter <lb/>the other: and asking one of them, if their practi&longs;e was not &longs;o <lb/>to do; He told me, no; but that the &longs;light was very ea&longs;ie and <lb/>certain, and that they took aim ju&longs;t in the &longs;ame manner as if they <lb/>had &longs;hot at a bird that did &longs;it &longs;till; that is, they made the flying <lb/>bird their mark, and by moving their fowling-piece they followed <lb/>her, keeping their aim &longs;till full upon her, till &longs;uch time as they let <lb/>fly, and in this manner &longs;hot her as they did others &longs;itting &longs;till. </s><s>It is <lb/>nece&longs;&longs;ary therefore that that motion, though &longs;low, which the fowl­ <lb/>ing-piece maketh in turning and following after the flight of the <lb/>bird do communicate it &longs;elf to the bullet al&longs;o, and that it be joyned <lb/>with that of the fire; &longs;o that the ball hath from the fire the mo­ <lb/>tion directly upwards, and from the concave Cylinder of the barrel <lb/>the declination according to the flight of the Bird, ju&longs;t as was &longs;aid <lb/>before of the &longs;hot of a Canon; where the ball receiveth from the <lb/>fire a virtue of mounting upwards towards the Zenith, and from <lb/>the motion of the Earth its winding towards the Ea&longs;t, and of both <lb/>maketh a compound motion that followeth the cour&longs;e of the <lb/>Earth, and that to the beholder &longs;eemeth onely to go directly up­ <lb/>wards, and return again downwards by the &longs;ame line. </s><s>The hold­ <lb/>ing therefore of the gun continually directed towards the mark, <lb/>maketh the &longs;hoot hit right, and that you may keep your gun di­ <lb/>rected to the mark, in ca&longs;e the mark &longs;tands &longs;till, you mu&longs;t al&longs;o hold <pb xlink:href="040/01/176.jpg" pagenum="158"/>your gun &longs;till; and if the mark &longs;hall move, the gun mu&longs;t be kept upon <lb/>the mark by moving. </s><s>And upon this dependeth the proper an&longs;wer <lb/><arrow.to.target n="marg348"></arrow.to.target> <lb/>to the other argument taken from the &longs;hot of a Canon, at the <lb/>mark placed towards the South or North: wherein is alledged, <lb/>that if the Earth &longs;hould move, the &longs;hots would all range We&longs;t­ <lb/>ward of the mark, becau&longs;e that in the time whil&longs;t the ball, being <lb/>forc'd out of the Piece, goeth through the air to the mark, the &longs;aid <lb/>mark being carried toward the Ea&longs;t, would leave the ball to the <lb/>We&longs;tward. </s><s>I an&longs;wer therefore, demanding whether if the Ca­ <lb/>non be aimed true at the mark, and permitted &longs;o to continue, it <lb/>will con&longs;tantly hit the &longs;aid mark, whether the Earth move or &longs;tand <lb/>&longs;till? </s><s>It mu&longs;t be replied, that the aim altereth not at all, for if <lb/>the mark doth &longs;tand &longs;till, the Piece al&longs;o doth &longs;tand &longs;till, and if it, <lb/>being tran&longs;ported by the Earths motion, doth move, the Piece doth <lb/>al&longs;o move at the &longs;ame rate, and, the aim maintained, the &longs;hot <lb/>proveth always true, as by what hath been &longs;aid above, is mani­ <lb/>fe&longs;t.</s></p><p type="margin"><s><margin.target id="marg347"></margin.target><emph type="italics"/>The manner how <lb/>Fowlers &longs;hoot birds <lb/>flying.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg348"></margin.target><emph type="italics"/>The an&longs;wer to <lb/>the objection tak n <lb/>from the &longs;hots of <lb/>great Guns made <lb/>towards the North <lb/>and South.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Stay a little, I entreat you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> till I have pro­ <lb/>pounded a certain conceit touching the&longs;e &longs;hooters of birds flying, <lb/>who&longs;e proceeding I believe to be the &longs;ame which you relate, and <lb/>believe the effect of hitting the bird doth likewi&longs;e follow: but yet <lb/>I cannot think that act altogether conformable to this of &longs;hooting <lb/>in great Guns, which ought to hit as well when the piece and mark <lb/>moveth, as when they both &longs;tand &longs;till; and the&longs;e, in my opinion, <lb/>are the particulars in which they di&longs;agree. </s><s>In &longs;hooting with a <lb/>great Gun both it and the mark move with equal velocity, being <lb/>both tran&longs;ported by the motion of the Terre&longs;trial Globe: and al­ <lb/>beit &longs;ometimes the piece being planted more towards the Pole, <lb/>than the mark, and con&longs;equently its motion being &longs;omewhat flow­ <lb/>er than the motion of the mark, as being made in a le&longs;&longs;er circle, <lb/>&longs;uch a difference is in&longs;en&longs;ible, at that little di&longs;tance of the piece <lb/>from the mark: but in the &longs;hot of the Fowler the motion of the <lb/>Fowling-piece wherewith it goeth following the bird, is very &longs;low <lb/>in compari&longs;on of the flight of the &longs;aid bird; whence me thinks it <lb/>&longs;hould follow, that that &longs;mall motion which the turning of the <lb/>Birding-piece conferreth on the bullet that is within it, cannot, <lb/>when it is once gone forth of it, multiply it &longs;elf in the air, untill it <lb/>come to equal the velocity of the birds flight, &longs;o as that the &longs;aid bullet <lb/>&longs;hould always keep direct upon it: nay, me thinketh the bird <lb/>would anticipate it and leave it behind. </s><s>Let me add, that in this <lb/>act, the air through which the bullet is to pa&longs;s, partaketh not of the <lb/>motion of the bird: whereas in the ca&longs;e of the Canon, both it, <lb/>the mark, and the intermediate air, do equally partake of the com­ <lb/>mon diurnal motion. </s><s>So that the true cau&longs;e of the Marks-man <lb/>his hitting the mark, as it &longs;hould &longs;eem, moreover and be&longs;ides the <pb xlink:href="040/01/177.jpg" pagenum="159"/>following the birds flight with the piece, is his &longs;omewhat anticipa­ <lb/>ting it, taking his aim before it; as al&longs;o his &longs;hooting (as I believe) <lb/>not with one bullet, but with many &longs;mall balls (called &longs;hot) the <lb/>which &longs;cattering in the air po&longs;&longs;e&longs;s a great &longs;pace; and al&longs;o the ex­ <lb/>treme velocity wherewith the&longs;e &longs;hot, being di&longs;charged from the <lb/>Gun, go towards the bird.</s></p><p type="main"><s>SALV. </s><s>See how far the winged wit of <emph type="italics"/>Sagredus<emph.end type="italics"/> anticipateth, <lb/>and out-goeth the dulne&longs;s of mine; which perhaps would have <lb/><arrow.to.target n="marg349"></arrow.to.target> <lb/>light upon the&longs;e di&longs;parities, but not without long &longs;tudie. </s><s>Now <lb/>turning to the matter in hand, there do remain to be con&longs;idered <lb/>by us the &longs;hots at point blank, towards the Ea&longs;t and towards the <lb/>We&longs;t; the fir&longs;t of which, if the Earth did move, would always <lb/>happen to be too high above the mark, and the &longs;econd too low; <lb/>fora&longs;much as the parts of the Earth Ea&longs;tward, by rea&longs;on of the di­ <lb/>urnal motion, do continually de&longs;cend beneath the tangent paralel <lb/>to the Horizon, whereupon the Ea&longs;tern &longs;tars to us appear to a&longs;cend; <lb/>and on the contrary, the parts We&longs;tward do more and more a&longs;­ <lb/>cend, whereupon the We&longs;tern &longs;tars do in our &longs;eeming de&longs;cend: <lb/>and therefore the ranges which are leveled according to the &longs;aid <lb/>tangent at the Oriental mark, (which whil&longs;t the ball pa&longs;&longs;eth <lb/>along by the tangent de&longs;cendeth) &longs;hould prove too high, and the <lb/>Occidental too low by means of the elevation of the mark, whil&longs;t <lb/>the ball pa&longs;&longs;eth along the tangent. </s><s>The an&longs;wer is like to the re&longs;t: <lb/>for as the Ea&longs;tern mark goeth continually de&longs;cending, by rea&longs;on <lb/>of the Earths motion, under a tangent that continueth immove­ <lb/>able; &longs;o likewi&longs;e the piece for the &longs;ame rea&longs;on goeth continually <lb/>inclining, and with its mounture pur&longs;uing the &longs;aid mark: by <lb/>which means the &longs;hot proveth true.</s></p><p type="margin"><s><margin.target id="marg349"></margin.target><emph type="italics"/>The an&longs;wer to the <lb/>Argument taken <lb/>from the &longs;hots at <lb/>point blanck to­ <lb/>wards the Ea&longs;t & <lb/>We&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>But here I think it a convenient opportunity to give notice of <lb/><arrow.to.target n="marg350"></arrow.to.target> <lb/>certain conce&longs;&longs;ions, which are granted perhaps over liberally by <lb/>the followers of <emph type="italics"/>Copernicus<emph.end type="italics"/> unto their Adver&longs;aries: I mean of <lb/>yielding to them certain experiments for &longs;ure and certain, which <lb/>yet the Adver&longs;aries them&longs;elves had never made tryal of: as for <lb/>example, that of things falling from the round-top of a &longs;hip whil&longs;t <lb/>it is in motion, and many others; among&longs;t which I verily believe, <lb/>that this of experimenting whether the &longs;hot made by a Canon to­ <lb/>wards the Ea&longs;t proveth too high, and the We&longs;tern &longs;hot too low, <lb/>is one: and becau&longs;e I believe that they have never made tryal <lb/>thereof, I de&longs;ire that they would tell me what difference they <lb/>think ought to happen between the &longs;aid &longs;hots, &longs;uppo&longs;ing the Earth <lb/>moveable, or &longs;uppo&longs;ing it moveable; and let <emph type="italics"/>Simplieius<emph.end type="italics"/> for this <lb/>time an&longs;wer for them.</s></p><p type="margin"><s><margin.target id="marg350"></margin.target><emph type="italics"/>The followers of <lb/>Copernicus too <lb/>freely admit cer­ <lb/>tain propo&longs;itions for <lb/>true, which are <lb/>very doubtfull.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I will not undertake to an&longs;wer &longs;o confidently as another <lb/>more intelligent perhaps might do; but &longs;hall &longs;peak what thus upon <lb/>the &longs;udden I think they would reply; which is in effect the &longs;ame <pb xlink:href="040/01/178.jpg" pagenum="160"/>with that which hath been &longs;aid already, namely, that in ca&longs;e the <lb/>Earth &longs;hould move, the &longs;hots made Ea&longs;tward would prove too <lb/>high, &c. </s><s>the ball, as it is probable, being to move along the tan­ <lb/>gent.</s></p><p type="main"><s>SALV. </s><s>But if I &longs;hould &longs;ay, that &longs;o it falleth out upon triall, <lb/>how would you cen&longs;ure me?</s></p><p type="main"><s>SIMP. </s><s>It is nece&longs;&longs;ary to proceed to experiments for the pro­ <lb/>ving of it.</s></p><p type="main"><s>SALV. </s><s>But do you think, that there is to be found a Gunner &longs;o <lb/>skilful, as to hit the mark at every &longs;hoot, in a di&longs;tance of <emph type="italics"/>v.g.<emph.end type="italics"/> five <lb/>hundred paces?</s></p><p type="main"><s>SIMP. </s><s>No Sir; nay I believe that there is no one, how good a <lb/>marks-man &longs;oever that would promi&longs;e to come within a pace of <lb/>the mark,</s></p><p type="main"><s>SALV. </s><s>How can we then, with &longs;hots &longs;o uncertain, a&longs;&longs;ure our <lb/>&longs;elves of that which is in di&longs;pute?</s></p><p type="main"><s>SIMP. </s><s>We may be a&longs;&longs;ured thereof two wayes; one, by ma­ <lb/>king many &longs;hots; the other, becau&longs;e in re&longs;pect of the great velo­ <lb/>city of the Earths motion, the deviation from the mark would in <lb/>my opinion be very great.</s></p><p type="main"><s>SALV. </s><s>Very great, that is more than one pace; in regard that <lb/>the varying &longs;o much, yea and more, is granted to happen ordinarily <lb/>even in the Earths mobility.</s></p><p type="main"><s>SIMP. </s><s>I verily believe the variation from the mark would be <lb/>more than &longs;o. <lb/><arrow.to.target n="marg351"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg351"></margin.target><emph type="italics"/>A Computation <lb/>how much the ran­ <lb/>ges of great &longs;hot <lb/>ought to vary from <lb/>the marke, the <lb/>Earths motion be­ <lb/>ing granted.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Now I de&longs;ire that for our &longs;atisfaction we do make thus <lb/>in gro&longs;&longs;e a &longs;light calculation, if you con&longs;ent thereto, which will <lb/>&longs;tand us in &longs;tead likewi&longs;e (if the computation &longs;ucceed as I expect) <lb/>for a warning how we do in other occurrences &longs;uffer our &longs;elves, as <lb/>the &longs;aying is, to be taken with the enemies &longs;houts, and &longs;urrender <lb/>up our belief to what ever fir&longs;t pre&longs;ents it &longs;elf to our fancy. </s><s>And <lb/>now to give all advantages to the <emph type="italics"/>Peripateticks<emph.end type="italics"/> and <emph type="italics"/>Tychonicks,<emph.end type="italics"/> <lb/>let us &longs;uppo&longs;e our &longs;elves to be under the Equinoctial, there to &longs;hoot <lb/>a piece of Ordinance point blank Ea&longs;twards at a mark five hun­ <lb/>dred paces off. </s><s>Fir&longs;t, let us &longs;ee thus (as I &longs;aid) in a level, what <lb/>time the &longs;hot after it is gone out of the Piece taketh to arrive at <lb/>the mark; which we know to be very little, and is certainly no <lb/>more than that wherein a travailer walketh two &longs;teps, which al&longs;o <lb/>is le&longs;s than the &longs;econd of a minute of an hour; for &longs;uppo&longs;ing <lb/>that the travailer walketh three miles in an hour, which are nine <lb/>thou&longs;and paces, being that an hour containes three thou&longs;and, &longs;ix <lb/>hundred &longs;econd minutes, the travailer walketh two &longs;teps and an <lb/>half in a &longs;econd, a &longs;econd therefore is more than the time of the <lb/>balls motion. </s><s>And for that the diurnal revolution is twenty four <lb/>hours, the We&longs;tern horizon ri&longs;eth fifteen degrees in an hour, that <pb xlink:href="040/01/179.jpg" pagenum="161"/>is, fifteen fir&longs;t minutes of a degree, in one fir&longs;t minute of an hour; <lb/>that is, fifteen &longs;econds of a degree, in one &longs;econd of an hour; and <lb/>becau&longs;e one &longs;econd is the time of the &longs;hot, therefore in this time <lb/>the We&longs;tern horizon ri&longs;eth fifteen &longs;econds of a degree, and &longs;o <lb/>much likewi&longs;e the mark; and therefore fifteen &longs;econds of that cir­ <lb/>cle, who&longs;e &longs;emidiameter is five hundred paces (for &longs;o much the di­ <lb/>&longs;tance of the mark from the Piece was &longs;uppo&longs;ed.) Now let us <lb/>look in the table of Arches and Chords (&longs;ee here is <emph type="italics"/>Copernicus<emph.end type="italics"/> his <lb/>book) what part is the chord of fifteen &longs;econds of the &longs;emidiame­ <lb/>ter, that is, five hundred paces. </s><s>Here you &longs;ee the chord (or &longs;ub­ <lb/>ten&longs;e) of a fir&longs;t minute to be le&longs;s than thirty of tho&longs;e parts, of <lb/>which the &longs;emidiameter is an hundred thou&longs;and. </s><s>Therefore the <lb/>chord of a &longs;econd minute &longs;hall be le&longs;s then half of one of tho&longs;e <lb/>parts, that is le&longs;s than one of tho&longs;e parts, of whichthe &longs;emidiame­ <lb/>ter is two hundred thou&longs;and; and therefore the chord of fifteen <lb/>conds &longs;hall be le&longs;s than fifteen of tho&longs;e &longs;ame two hundred thou&longs;and <lb/>parts; but that which is le&longs;s than <emph type="italics"/>(a)<emph.end type="italics"/> fifteen parts of two hun­</s></p><p type="main"><s><arrow.to.target n="marg352"></arrow.to.target> <lb/>dred thou&longs;and, is al&longs;o more than that which is four cente&longs;mes of <lb/>five hundred; therefore the a&longs;cent of the mark in the time of the <lb/>balls motion is le&longs;&longs;e than four cente&longs;mes, that is, than one twenty <lb/>fifth part of a pace; it &longs;hall be therefore <emph type="italics"/>(b)<emph.end type="italics"/> about two inches: <lb/>And &longs;o much con&longs;equently &longs;hall be the variation of each We&longs;tern <lb/>&longs;hot, the Earth being &longs;uppo&longs;ed to have a diurnal motion. </s><s>Now if I <lb/>&longs;hall tell you, that this variation (I mean of falling two inches &longs;hort <lb/>of what they would do in ca&longs;e the Earth did not move) upon tri­ <lb/><arrow.to.target n="marg353"></arrow.to.target> <lb/>all doth happen in all &longs;hots, how will you convince me <emph type="italics"/>Simplicius,<emph.end type="italics"/> <lb/>&longs;hewing me by an experiment that it is not &longs;o? </s><s>Do you not &longs;ee <lb/>that it is impo&longs;&longs;ible to confute me, unle&longs;s you fir&longs;t find out a way <lb/>to &longs;hoot at a mark with &longs;o much exactne&longs;&longs;e, as never to mi&longs;&longs;e an <lb/>hairs bredth? </s><s>For whil&longs;t the ranges of great &longs;hot con&longs;i&longs;t of diffe­ <lb/>rent numbers of paces, as <emph type="italics"/>de facto<emph.end type="italics"/> they do, I will affirm that in <lb/>each of tho&longs;e variations there is contained that of two inches cau­ <lb/>&longs;ed by the motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg352"></margin.target><emph type="italics"/>(a)<emph.end type="italics"/> That is, in <lb/>plainer termes the <lb/>fraction 15/200000, is <lb/>more than the fra­ <lb/>ction 4/50000, for di­ <lb/>viding the denomi­ <lb/>nators by their no­ <lb/>minators, and the <lb/>fir&longs;t produceth <lb/>13333 1/3 the other <lb/>but 12500.</s></p><p type="margin"><s><margin.target id="marg353"></margin.target><emph type="italics"/>(b)<emph.end type="italics"/> It &longs;hall be <lb/>neer 2 2/5 inches, ac­ <lb/>counting the pace <lb/>to be Geometrical, <lb/>containing 5 foot.</s></p><p type="main"><s>SAGR. </s><s>Pardon me, <emph type="italics"/>Salviatus,<emph.end type="italics"/> you are too liberal. </s><s>For I would <lb/><arrow.to.target n="marg354"></arrow.to.target> <lb/>tell the <emph type="italics"/>Peripateticks,<emph.end type="italics"/> that though every &longs;hot &longs;hould hit the very <lb/>centre of the mark, that &longs;hould not in the lea&longs;t di&longs;prove the motion <lb/>of the Earth. </s><s>For the Gunners are &longs;o con&longs;tantly imployed in le­ <lb/>velling the &longs;ight and gun to the mark, as that they can hit the &longs;ame, <lb/>notwith&longs;tanding the motion of the Earth. </s><s>And I &longs;ay, that if the <lb/>Earth &longs;hould &longs;tand &longs;till, the &longs;hots would not prove true; but the <lb/>Occidental would be too low, and the Oriental too high: now let <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> di&longs;prove me if he can.</s></p><p type="margin"><s><margin.target id="marg354"></margin.target><emph type="italics"/>It is demon&longs;tra­ <lb/>ted with great &longs;ub­ <lb/>tilty, that the <lb/>Earths motion &longs;up­ <lb/>po&longs;ed, Canon &longs;hot <lb/>ought not to vary <lb/>more than in re&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>This is a &longs;ubtilty worthy of <emph type="italics"/>Sagredus:<emph.end type="italics"/> But whether <lb/>this variation be to be ob&longs;erved in the motion, or in the re&longs;t of the <lb/>Earth, it mu&longs;t needs be very &longs;mall, it mu&longs;t needs be &longs;wallowed up <pb xlink:href="040/01/180.jpg" pagenum="162"/>in tho&longs;e very great ones which &longs;undry accidents continually pro­ <lb/><arrow.to.target n="marg355"></arrow.to.target> <lb/>duce. </s><s>And all this hath been &longs;poken and granted on good grounds <lb/>to <emph type="italics"/>Simplicius,<emph.end type="italics"/> and only with an intent to adverti&longs;e him how much <lb/>it importeth to be cautious in granting many experiments for true <lb/>to tho&longs;e who never had tried them, but only eagerly alledged them <lb/>ju&longs;t as they ought to be for the &longs;erving their purpo&longs;e: This is &longs;po­ <lb/>ken, I &longs;ay, by way of &longs;urplu&longs;&longs;age and Corollary to <emph type="italics"/>Simplicius,<emph.end type="italics"/> for <lb/><arrow.to.target n="marg356"></arrow.to.target> <lb/>the real truth is, that as concerning the&longs;e &longs;hots, the &longs;ame ought ex­ <lb/>actly to befall a&longs;well in the motion as in the re&longs;t of the Terre&longs;trial <lb/>Globe; as likewi&longs;e it will happen in all the other experiments <lb/>that either have been or can be produced, which have at fir&longs;t blu&longs;h <lb/>&longs;o mnch &longs;emblance of truth, as the antiquated opinion of the <lb/>Earths motion hath of equivocation.</s></p><p type="margin"><s><margin.target id="marg355"></margin.target><emph type="italics"/>It is requi&longs;ite to <lb/>be very cautious in <lb/>admitting experi­ <lb/>ments for true, to <lb/>tho&longs;e who never <lb/>tried them.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg356"></margin.target><emph type="italics"/>Experiments and <lb/>arguments again&longs;t <lb/>the Earths motion <lb/>&longs;eem &longs;o far con­ <lb/>cluding, as they lie <lb/>hid under equi­ <lb/>vokes.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>As for my part I am fully &longs;atisfied, and very well un­ <lb/>der&longs;tand that who &longs;o &longs;hall imprint in his fancy this general com­ <lb/>munity of the diurnal conver&longs;ion among&longs;t all things Terre&longs;trial, <lb/>to all which it naturally agreeth, a&longs;well as in the old conceit of its <lb/>re&longs;t about the centre, &longs;hall doubtle&longs;&longs;e di&longs;cern the fallacy and equi­ <lb/>voke which made the arguments produced &longs;eem eoncluding. <lb/></s><s>There yet remains in me &longs;ome hæ&longs;itancy (as I have hinted be­ <lb/>fore) touching the flight of birds; the which having as it were an <lb/>animate faculty of moving at their plea&longs;ure with a thou&longs;and mo­ <lb/>tions, and to &longs;tay long in the Air &longs;eparated from the Earth, and <lb/>therein with mo&longs;t irregular windings to go fluttering to and again, <lb/>I cannot conceive how among&longs;t &longs;o great a confu&longs;ion of motions, <lb/>they &longs;hould be able to retain the fir&longs;t commune motion; and in <lb/>what manner, having once made any &longs;tay behind, they can get <lb/>it up again, and overtake the &longs;ame with flying, and kcep pace <lb/>with the Towers and trees which hurry with &longs;o precipitant a cour&longs;e <lb/>towards the Ea&longs;t; I &longs;ay &longs;o precipitant, for in the great circle of <lb/>the Globe it is little le&longs;&longs;e than a thou&longs;and miles an hour, whereof <lb/>the flight of the &longs;wallow I believe makes not fifty.</s></p><p type="main"><s>SALV. </s><s>If the birds were to keep pace with the cour&longs;e of the <lb/>trees by help of their wings, they would o&longs; nece&longs;&longs;ity flie very fa&longs;t; <lb/>and if they were deprived of the univer&longs;al conver&longs;ion, they would <lb/>lag as far behind; and their flight would &longs;eem as furious towards <lb/>the We&longs;t, and to him that could di&longs;cern the &longs;ame, it would <lb/>much exceed the flight of an arrow; but I think we could not be <lb/>able to perceive it, no more than we &longs;ee a Canon bullet, whil'&longs;t <lb/>driven by the fury of the fire, it flieth through the Air: But the <lb/>truth is that the proper motion of birds, I mean of their flight, <lb/>hath nothing to do with the univer&longs;al motion, to which it is nei­ <lb/>ther an help, nor an hinderance; and that which maintaineth <lb/>the &longs;aid motion unaltered in the birds, is the Air it &longs;elf, thorough <lb/>which they flie, which naturally following the <emph type="italics"/>Vertigo<emph.end type="italics"/> of the <pb xlink:href="040/01/181.jpg" pagenum="163"/>Earth, like as it carrieth the clouds along with it, &longs;o it tran&longs;porteth <lb/>birds and every thing el&longs;e which is pendent in the &longs;ame; in &longs;o much <lb/>that as to the bu&longs;ine&longs;&longs;e of keeping pace with the Earth, the birds <lb/>need take no care thereof, but for that work might &longs;leep perpe­ <lb/>tually.</s></p><p type="main"><s>SAGR. </s><s>That the Air can carry the clouds along with it, as <lb/>being matters ea&longs;ie for their lightne&longs;&longs;e to be moved and deprived <lb/>of all other contrary inclination, yea more, as being matters that <lb/>partake al&longs;o of the conditions and properties of the Earth; I com­ <lb/>prehend without any difficulty; but that birds, which as having <lb/>life, may move with a motion quite contrary to the diurnal, once <lb/>having &longs;urcea&longs;ed the &longs;aid motion, the Air &longs;hould re&longs;tore them to <lb/>it, &longs;eems to me a little &longs;trange, and the rather for that they are &longs;olid <lb/>and weighty bodies; and withal, we &longs;ee; as hath been &longs;aid, &longs;tones <lb/>and other grave bodies to lie unmoved again&longs;t the <emph type="italics"/>impetus<emph.end type="italics"/> of the <lb/>air; and when they &longs;uffer them&longs;elves to be overcome thereby, <lb/>they never acquire &longs;o much velocity as the wind which carrieth <lb/>them.</s></p><p type="main"><s>SALV. </s><s>We a&longs;cribe not &longs;o little force, <emph type="italics"/>Sagredus,<emph.end type="italics"/> to the moved <lb/>Air, which is able to move and bear before it &longs;hips full fraught, <lb/>to tear up trees by the roots, and overthrow Towers when it <lb/>moveth &longs;wiftly; and yet we cannot &longs;ay that the motion of the <lb/>Air in the&longs;e violent operations is neer &longs;o violent, as that of the <lb/>diurnal revolution.</s></p><p type="main"><s>SIMP. </s><s>You &longs;ee then that the moved Air may al&longs;o cotinue the <lb/>motion of projects, according to the Doctrine of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; and <lb/>it &longs;eemed to me very &longs;trange that he &longs;hould have erred in this <lb/>particular.</s></p><p type="main"><s>SALV. </s><s>It may without doubt, in ca&longs;e it could continue it &longs;elf, <lb/>but lik as when the wind cea&longs;ing neither &longs;hips go on, nor trees are <lb/>blown down, &longs;o the motion in the Air not continuing after the <lb/>&longs;tone is gone out of the hand, and the Air cea&longs;ing to move, it <lb/>followeth that it mu&longs;t be &longs;omething el&longs;e be&longs;ides the Air that ma­ <lb/>keth the projects to move.</s></p><p type="main"><s>SIMP. </s><s>But how upon the winds being laid, doth the &longs;hip cea&longs;e <lb/>to move? </s><s>Nay you may &longs;ee that when the wind is down, and <lb/>the &longs;ails furl'd, the ve&longs;&longs;el continueth to run whole miles.</s></p><p type="main"><s>SALV. </s><s>But this maketh again&longs;t your &longs;elf <emph type="italics"/>Simplicius,<emph.end type="italics"/> for that <lb/>the wind being laid that filling the &longs;ails drove on the &longs;hip, yet ne­ <lb/>verthele&longs;&longs;e doth it without help of the <emph type="italics"/>medium<emph.end type="italics"/> continue its <lb/>cour&longs;e.</s></p><p type="main"><s>SIMP. </s><s>It might be &longs;aid that the water was the <emph type="italics"/>medium<emph.end type="italics"/> which <lb/>carried forward the &longs;hip, and maintain'd it in motion.</s></p><p type="main"><s>SALV. </s><s>It might indeed be &longs;o affirmed, if you would &longs;peak <lb/>quite contrary to truth; for the truth is, that the water, by rea­ <pb xlink:href="040/01/182.jpg" pagenum="164"/>&longs;on of its great re&longs;i&longs;tance to the divi&longs;ion made by the hull of the <lb/>&longs;hip, doth with great noi&longs;e re&longs;i&longs;t the &longs;ame; nor doth it permit it <lb/>of a great while to acquire that velocity which the wind would <lb/>confer upon it, were the ob&longs;tacle of the water removed. </s><s>Per­ <lb/>haps <emph type="italics"/>Simplicius<emph.end type="italics"/> you have never con&longs;idered with what fury the <lb/>water be&longs;ets a bark, whil'&longs;t it forceth its way through a &longs;tanding <lb/>water by help of Oars or Sails: for if you had ever minded that <lb/>effect, you would not now have produced &longs;uch an ab&longs;urdity. <lb/></s><s>And I am thinking that you have hitherto been one of tho&longs;e who <lb/>to find out how &longs;uch things &longs;ucceed, and to come to the know­ <lb/>ledg of natural effects, do not betake them&longs;elves to a Ship, a <lb/>Cro&longs;&longs;e-bow, or a piece of Ordinance, but retire into their &longs;tu­ <lb/>dies, and turn over Indexes and Tables to &longs;ee whether <emph type="italics"/>Aristotle<emph.end type="italics"/> <lb/>hath &longs;poken any thing thereof, and being a&longs;&longs;ured of the true <lb/>&longs;en&longs;e of the Text, neither de&longs;ire nor care for knowing any <lb/>more. <lb/><arrow.to.target n="marg357"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg357"></margin.target><emph type="italics"/>The great feli­ <lb/>city for which they <lb/>are much to be en­ <lb/>vied who per&longs;wade <lb/>them&longs;elves that <lb/>they know every <lb/>thing.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This is a great felicity, and they are to be much en­ <lb/>vied for it. </s><s>For if knowledg be de&longs;ired by all, and if to be wi&longs;e, <lb/>be to think ones &longs;elf &longs;o, they enjoy a very great happine&longs;&longs;e, for <lb/>that they may per&longs;wade them&longs;elves that they know and under&longs;tand <lb/>all things, in &longs;corn of tho&longs;e who knowing, that they under&longs;tand <lb/>not what the&longs;e think they under&longs;tand, and con&longs;equently &longs;eeking <lb/>that they know not the very lea&longs;t particle of what is knowable, <lb/>kill them&longs;elves with waking and &longs;tudying, and con&longs;ume their days <lb/>in experiments and ob&longs;ervations. </s><s>But pray you let us return to <lb/>our birds; touching which you have &longs;aid, that the Air being mo­ <lb/>ved with great velocity, might re&longs;tore unto them that part of the <lb/>diurnal motion which among&longs;t the windings of their flight they <lb/>might have lo&longs;t; to which I reply, that the agitated Air &longs;eemeth <lb/>unable to confer on a &longs;olid and grave body, &longs;o great a velocity as <lb/>its own: And becau&longs;e that of the Air is as great as that of the <lb/>Earth, I cannot think that the Air is able to make good the lo&longs;&longs;e <lb/>of the birds retardation in flight.</s></p><p type="main"><s>SALV. </s><s>Your di&longs;cour&longs;e hath in it much of probability, and to <lb/>&longs;tick at trivial doubts is not for an acute wit; yet neverthele&longs;&longs;e the <lb/>probability being removed, I believed that it hath not a jot more <lb/>force than the others already con&longs;idered and re&longs;olved.</s></p><p type="main"><s>SAGR. </s><s>It is mo&longs;t certain that if it be not nece&longs;&longs;atily conclu­ <lb/>dent, its efficacy mu&longs;t needs be ju&longs;t nothing at all, for it is <lb/>onely when the conclu&longs;ion is nece&longs;&longs;ary that the opponent hath no­ <lb/>thing to alledg on the contrary.</s></p><p type="main"><s>SALV. </s><s>Your making a greater &longs;cruple of this than of the other <lb/>in&longs;tances dependeth, if I mi&longs;take not, upon the birds being ani­ <lb/>mated, and thereby enabled to u&longs;e their &longs;trength at plea&longs;ure a­ <lb/>gain&longs;t the primary motion in-bred in terrene bodies: like as for <pb xlink:href="040/01/183.jpg" pagenum="165"/>example, we &longs;ee them whil'&longs;t they are alive to fly upwards, a thing <lb/>altogether impo&longs;&longs;ible for them to do as they are grave bodies; <lb/>whereas being dead they can onely fall downwards; and there­ <lb/>fore you hold that the rea&longs;ons that are of force in all the kinds of <lb/>projects above named, cannot take place in birds: Now this is <lb/>very true; and becau&longs;e it is &longs;o, <emph type="italics"/>Sagredus,<emph.end type="italics"/> that doth not appear <lb/>to be done in tho&longs;e projects, which we &longs;ee the birds to do. </s><s>For if </s></p><p type="main"><s><arrow.to.target n="marg358"></arrow.to.target> <lb/>from the top of a Tower you let fall a dead bird and a live one, <lb/>the dead bird &longs;hall do the &longs;ame that a &longs;tone doth, that is, it &longs;hall <lb/>fir&longs;t follow the general motion diurnal, and then the motion of <lb/>de&longs;cent, as grave; but if the bird let fall, be a live, what &longs;hall <lb/>hinder it, (there ever remaining in it the diurnal motion) from <lb/>&longs;oaring by help of its wings to what place of the Horizon it &longs;hall <lb/>plea&longs;e? </s><s>and this new motion, as being peculiar to the bird, and <lb/>not participated by us, mu&longs;t of nece&longs;&longs;ity be vi&longs;ible to us; and if <lb/>it be moved by help of its wings towards the We&longs;t, what &longs;hall <lb/>hinder it from returning with a like help of its wings unto the <lb/>Tower. </s><s>And, becau&longs;e, in the la&longs;t place, the birds wending its <lb/>flight towards the We&longs;t was no other than a withdrawing from <lb/>the diurnal motion, (which hath, &longs;upppo&longs;e ten degrees of velocity) <lb/>one degree onely, there did thereupon remain to the bird whil'&longs;t <lb/>it was in its flight nine degrees of velocity, and &longs;o &longs;oon as it did <lb/>alight upon the the Earth, the ten common degrees returned to it, <lb/>to which, by flying towards the Ea&longs;t it might adde one, and with <lb/>tho&longs;e eleven overtake the Tower. </s><s>And in &longs;hort, if we well con­ <lb/>&longs;ider, and more narrowly examine the effects of the flight of <lb/>birds, they differ from the projects &longs;hot or thrown to any part of <lb/>the World in nothing, &longs;ave onely that the projects are moved by an <lb/>external projicient, and the birds by an internal principle. </s><s>And <lb/><arrow.to.target n="marg359"></arrow.to.target> <lb/>here for a final proof of the nullity of all the experiments before <lb/>alledged, I conceive it now a time and place convenient to <lb/>demon&longs;trate a way how to make an exact trial of them all. <lb/></s><s>Shut your &longs;elf up with &longs;ome friend in the grand Cabbin between <lb/>the decks of &longs;ome large Ship, and there procure gnats, flies, and <lb/>&longs;uch other &longs;mall winged creatures: get al&longs;o a great tub (or <lb/>other ve&longs;&longs;el) full of water, and within it put certain fi&longs;hes; let <lb/>al&longs;o a certain bottle be hung up, which drop by drop letteth forth <lb/>its water into another bottle placed underneath, having a narrow <lb/>neck: and, the Ship lying &longs;till, ob&longs;erve diligently how tho&longs;e &longs;mall <lb/>winged animals fly with like velocity towards all parts of the Ca­ <lb/>bin; how the fi&longs;hes &longs;wim indifferently towards all &longs;ides; and how <lb/>the di&longs;tilling drops all fall into the bottle placed underneath. </s><s>And <lb/>ca&longs;ting any thing towards your friend, you need not throw it with <lb/>more force one way then another, provided the di&longs;tances be equal: <lb/>and leaping, as the &longs;aying is, with your feet clo&longs;ed, you will reach <pb xlink:href="040/01/184.jpg" pagenum="166"/>as far one way as another. </s><s>Having ob&longs;erved all the&longs;e particulars, <lb/>though no man doubteth that &longs;o long as the ve&longs;&longs;el &longs;tands &longs;till, they <lb/>ought to &longs;ucceed in this manner; make the Ship to move with <lb/>what velocity you plea&longs;e; for (&longs;o long as the motion is uniforme, <lb/>and not fluctuating this way and that way) you &longs;hall not di&longs;cern <lb/>any the lea&longs;t alteration in all the forenamed effects; nor can you <lb/>gather by any of them whether the Ship doth move or &longs;tand &longs;till. <lb/></s><s>In leaping you &longs;hall reach as far upon the floor, as before; nor for <lb/>that the Ship moveth &longs;hall you make a greater leap towards the <lb/>poop than towards the prow; howbeit in the time that you &longs;taid <lb/>in the Air, the floor under your feet &longs;hall have run the contrary way <lb/>to that of your jump; and throwing any thing to your companion <lb/>you &longs;hall not need to ca&longs;t it with more &longs;trength that it may reach <lb/>him, if he &longs;hall be towards the prow, and you towards the poop, <lb/>then if you &longs;tood in a contrary &longs;ituation; the drops &longs;hall all di&longs;till <lb/>as before into the inferiour bottle and not &longs;o much as one &longs;hall <lb/>fall towards the poop, albeit whil'&longs;t the drop is in the Air, the Ship <lb/>&longs;hall have run many feet; the Fi&longs;hes in their water &longs;hall not &longs;wim <lb/>with more trouble towards the fore-part, than towards the hinder <lb/>part of the tub; but &longs;hall with equal velocity make to the bait <lb/>placed on any &longs;ide of the tub; and la&longs;tly, the flies and gnats <lb/>&longs;hall continue their flight indifferently towards all parts; nor <lb/>&longs;hall they ever happen to be driven together towards the &longs;ide of <lb/>the Cabbin next the prow, as if they were wearied with fol­ <lb/>lowing the &longs;wift cour&longs;e of the Ship, from which through their <lb/>&longs;u&longs;pen&longs;ion in the Air, they had been long &longs;eparated; and if <lb/>burning a few graines of incen&longs;e you make a little &longs;moke, <lb/>you &longs;hall &longs;ee it a&longs;cend on high, and there in manner of a cloud <lb/>&longs;u&longs;pend it &longs;elf, and move indifferently, not inclining more to one <lb/>&longs;ide than another: and of this corre&longs;pondence of effects the cau&longs;e <lb/>is for that the Ships motion is common to all the things contained <lb/>in it, and to the Air al&longs;o; I mean if tho&longs;e things be &longs;hut up in the <lb/>Cabbin: but in ca&longs;e tho&longs;e things were above deck in the open Air, <lb/>and not obliged to follow the cour&longs;e of the Ship, differences more <lb/>or le&longs;&longs;e notable would be ob&longs;erved in &longs;ome of the fore-named ef­ <lb/>fects, and there is no doubt but that the &longs;moke would &longs;tay behind <lb/>as much as the Air it &longs;elf; the flies al&longs;o, and the gnats being hin­ <lb/>dered by the Air would not be able to follow the motion of the <lb/>Ship, if they were &longs;eparated at any di&longs;tance from it. </s><s>But keeping <lb/>neer thereto, becau&longs;e the Ship it &longs;elf as being an unfractuous Fa­ <lb/>brick, carrieth along with it part of its neere&longs;t Air, they would <lb/>follow the &longs;aid Ship without any pains or difficulty. </s><s>And for the <lb/>like rea&longs;on we &longs;ee &longs;ometimes in riding po&longs;t, that the trouble&longs;ome <lb/>flies and ^{*} hornets do follow the hor&longs;es flying &longs;ometimes to one, <lb/><arrow.to.target n="marg360"></arrow.to.target> <lb/>&longs;ometimes to another part of the body, but in the falling drops <pb xlink:href="040/01/185.jpg" pagenum="167"/>the difference would be very &longs;mall; and in the &longs;alts, and projecti­ <lb/>ons of grave bodies altogether imperceptible.</s></p><p type="margin"><s><margin.target id="marg358"></margin.target><emph type="italics"/>The an&longs;wer to <lb/>the argument ta­ <lb/>ken from the flight <lb/>of birds contrary <lb/>to the motion of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg359"></margin.target><emph type="italics"/>An experiment <lb/>with which alone <lb/>is &longs;hewn the nullity <lb/>of all the objecti­ <lb/>ons produced a­ <lb/>gainst the motion <lb/>of the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg360"></margin.target>* Tafaris, <emph type="italics"/>bor&longs;e­ <lb/>flyes.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Though it came not into my thoughts to make triall of <lb/>the&longs;e ob&longs;ervations, when I was at Sea, yet am I confident that they <lb/>will &longs;ucceed in the &longs;ame manner, as you have related; in confirma­ <lb/>tion of which I remember that being in my Cabbin I have asked <lb/>an hundred times whether the Ship moved or &longs;tood &longs;till; and <lb/>&longs;ometimes I have imagined that it moved one way, when it &longs;teered <lb/>quite another way. </s><s>I am therefore as hitherto &longs;atisfied and con­ <lb/>vinced of the nullity of all tho&longs;e experiments that have been pro­ <lb/>duced in proof of the negative part. </s><s>There now remains the ob­ <lb/>jection founded upon that which experience &longs;hews us, namely, that <lb/>a &longs;wift <emph type="italics"/>Vertigo<emph.end type="italics"/> or whirling about hath a faculty to extrude and <lb/>di&longs;per&longs;e the matters adherent to the machine that turns round; <lb/>whereupon many were of opinion, and <emph type="italics"/>Ptolomy<emph.end type="italics"/> among&longs;t the re&longs;t, <lb/>that if the Earth &longs;hould turn round with &longs;o great velocity, the <lb/>&longs;tones and creatures upon it &longs;hould be to&longs;t into the Skie, and <lb/>that there could not be a morter &longs;trong enough to fa&longs;ten buildings <lb/>&longs;o to their foundations, but that they would likewi&longs;e &longs;uffer a like <lb/>extru&longs;ion.</s></p><p type="main"><s>SALV. </s><s>Before I come to an&longs;wer this objection, I cannot but <lb/>take notice of that which I have an hundred times ob&longs;erved, and <lb/>not without laughter, to come into the minds of mo&longs;t men &longs;o &longs;oon <lb/>as ever they hear mention made of this motion of the Earth, which <lb/>is believed by them &longs;o fixt and immoveable, that they not only ne­ <lb/>ver doubted of that re&longs;t, but have ever &longs;trongly believed that all <lb/>other men a&longs;well as they, have held it to be created immoveable, <lb/>and &longs;o to have continued through all &longs;ucceeding ages: and being <lb/><arrow.to.target n="marg361"></arrow.to.target> <lb/>&longs;etled in this per&longs;wa&longs;ion, they &longs;tand amazed to hear that any one <lb/>&longs;hould grant it motion, as if, after that he had held it to be immo­ <lb/>veable, he had fondly thought it to commence its motion then <lb/>(and not till then) when <emph type="italics"/>Pythagoras<emph.end type="italics"/> (or whoever el&longs;e was the fir&longs;t <lb/>hinter of its mobility) &longs;aid that it did move. </s><s>Now that &longs;uch a foo­ <lb/>li&longs;h conceit (I mean of thinking that tho&longs;e who admit the motion <lb/>of the Earth, have fir&longs;t thought it to &longs;tand &longs;till from its creation, <lb/>untill the time of <emph type="italics"/>Pythagoras,<emph.end type="italics"/> and have onely made it moveable <lb/>after that <emph type="italics"/>Pythagor as<emph.end type="italics"/> e&longs;teemed it &longs;o) findeth a place in the mindes <lb/>of the vulgar, and men of &longs;hallow capacities, I do not much won­ <lb/>der; but that &longs;uch per&longs;ons as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy<emph.end type="italics"/> &longs;hould al&longs;o <lb/>run into this childi&longs;h mi&longs;take, is to my thinking a more admirable <lb/>and unpardonable folly.</s></p><p type="margin"><s><margin.target id="marg361"></margin.target><emph type="italics"/>The &longs;tupidity of <lb/>&longs;ome that think the <lb/>Earth to have be­ <lb/>gun to move, when<emph.end type="italics"/> <lb/>Pythagoras <emph type="italics"/>began <lb/>to affirme that it <lb/>did &longs;o.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>You believe then, <emph type="italics"/>Salviatus,<emph.end type="italics"/> that <emph type="italics"/>Ptolomy<emph.end type="italics"/> thought, that <lb/>in his Di&longs;putation he was to maintain the &longs;tability of the Earth <lb/>again&longs;t &longs;uch per&longs;ons, as granting it to have been immoveable, un­ <lb/>till the time of <emph type="italics"/>Pythagoras,<emph.end type="italics"/> did affirm it to have been but then <pb xlink:href="040/01/186.jpg" pagenum="168"/>made moveable, when the &longs;aid <emph type="italics"/>Pythagoras<emph.end type="italics"/> a&longs;cribed unto it mo­ <lb/>tion.</s></p><p type="main"><s>SALV. </s><s>We can think no other, if we do but con&longs;ider the way <lb/><arrow.to.target n="marg362"></arrow.to.target> <lb/>he taketh to confute their a&longs;&longs;ertion; the confutation of which <lb/>con&longs;i&longs;ts in the demolition of buildings, and the to&longs;&longs;ing of &longs;tones, <lb/>living creatures and men them&longs;elves up into the Air. </s><s>And be­ <lb/>cau&longs;e &longs;uch overthrows and extru&longs;ions cannot be made upon buil­ <lb/>dings and men, which were not before on the Earth, nor can men <lb/>be placed, nor buildings erected upon the Earth, unle&longs;&longs;e when it <lb/>&longs;tandeth &longs;till; hence therefore it is cleer, that <emph type="italics"/>Ptolomy<emph.end type="italics"/> argueth a­ <lb/>gain&longs;t tho&longs;e, who having granted the &longs;tability of the Earth for <lb/>&longs;ome time, that is, &longs;o long as living creatures, &longs;tones, and Ma&longs;ons <lb/>were able to abide there, and to build Palaces and Cities, make it <lb/>afterwards precipitately moveable to the overthrow and de&longs;tructi­ <lb/>of Edifices, and living creatures, &c. </s><s>For if he had undertook to <lb/>di&longs;pute again&longs;t &longs;uch as had a&longs;cribed that revolution to the Earth <lb/>from its fir&longs;t creation, he would have confuted them by &longs;aying, <lb/>that if the Earth had alwayes moved, there could never have been <lb/>placed upon it either men or &longs;tones; much le&longs;s could buildings <lb/>have been erected, or Cities founded, &c.</s></p><p type="margin"><s><margin.target id="marg362"></margin.target>Ari&longs;totle <emph type="italics"/>and<emph.end type="italics"/> <lb/>Ptolomy <emph type="italics"/>&longs;eem to <lb/>confute the mobili­ <lb/>ty of the Earth a­ <lb/>gain&longs;t tho&longs;e who <lb/>thought that it ha­ <lb/>ving a long time <lb/>&longs;tood still, did be­ <lb/>gin to move in the <lb/>time of<emph.end type="italics"/> Pythagoras</s></p><p type="main"><s>SIMP. </s><s>I do not well conceive the&longs;e <emph type="italics"/>Ari&longs;totelick<emph.end type="italics"/> and <emph type="italics"/>Ptolo­ <lb/>maick<emph.end type="italics"/> inconveniences.</s></p><p type="main"><s>SALV. <emph type="italics"/>Ptolomey<emph.end type="italics"/> either argueth again&longs;t tho&longs;e who have e&longs;teem­ <lb/>ed the Earth always moveable; or again&longs;t &longs;uch as have held that <lb/>it &longs;tood for &longs;ome time &longs;till, and hath &longs;ince been &longs;et on moving. <lb/></s><s>If again&longs;t the fir&longs;t, he ought to &longs;ay, that the Earth did not always <lb/>move, for that then there would never have been men, animals, or <lb/>edifices on the Earth, its <emph type="italics"/>vertigo<emph.end type="italics"/> not permitting them to &longs;tay <lb/>thereon. </s><s>But in that he arguing, &longs;aith that the Earth doth not <lb/>move, becau&longs;e that bea&longs;ts, men, and hou&longs;es before plac'd on the <lb/>Earth would precipitate, he &longs;uppo&longs;eth the Earth to have been once <lb/>in &longs;uch a &longs;tate, as that it did admit men and bea&longs;ts to &longs;tay, and <lb/>build thereon; the which draweth on the con&longs;equence, that it <lb/>did for &longs;ome time &longs;tand &longs;till, to wit, was apt for the abode of a­ <lb/>nimals and erection of buildings. </s><s>Do you now conceive what I <lb/>would &longs;ay?</s></p><p type="main"><s>SIMP. </s><s>I do, and I do not: but this little importeth to the <lb/>merit of the cau&longs;e; nor can a &longs;mall mi&longs;take of <emph type="italics"/>Ptolomey,<emph.end type="italics"/> com­ <lb/>mitted through inadvertencie be &longs;ufficient to move the Earth, <lb/>when it is immoveable. </s><s>But omitting cavils, let us come to the <lb/>&longs;ub&longs;tance of the argument, which to me &longs;eems unan&longs;werable.</s></p><p type="main"><s>SALV. </s><s>And I, <emph type="italics"/>Simplicius,<emph.end type="italics"/> will drive it home, and re-inforce it, <lb/>by &longs;hewing yet more &longs;en&longs;ibly, that it is true that grave bodies <lb/>turn'd with velocity about a &longs;ettled centre, do acquire an <emph type="italics"/>impetus<emph.end type="italics"/> <lb/>of moving, and receding to a di&longs;tance from that centre, even <pb xlink:href="040/01/187.jpg" pagenum="169"/>then when they are in a &longs;tate of having a propen&longs;ion of moving <lb/>naturally to the &longs;ame. </s><s>Tie a bottle that hath water in it, to <lb/>the end of a cord, and holding the other end fa&longs;t in your hand, <lb/>and making the cord and your arm the &longs;emi-diameter, and the <lb/>knitting of the &longs;houlder the centre, &longs;wing the bottle very fa&longs;t a­ <lb/>bout, &longs;o as that it may de&longs;cribe the circumference of a circle, <lb/>which, whether it be parallel to the Horizon, or perpendicular to <lb/>it, or any way inclined, it &longs;hall in all ca&longs;es follow, that the wa­ <lb/>ter will not fall out of the bottle: nay, he that &longs;hall &longs;wing it, <lb/>&longs;hall find the cord always draw, and &longs;trive to go farther from the <lb/>&longs;houlder. </s><s>And if you bore a hole in the bottom of the bottle, <lb/>you &longs;hall &longs;ee the water &longs;pout forth no le&longs;s upwards into the skie, <lb/>than laterally, and downwards to the Earth; and if in&longs;tead of wa­ <lb/>ter, you &longs;hall put little pebble &longs;tones into the bottle, and &longs;wing it <lb/>in the &longs;ame manner, you &longs;hall find that they will &longs;trive in the like <lb/>manner again&longs;t the cord. </s><s>And la&longs;tly, we &longs;ee boys throw &longs;tones <lb/>a great way, by &longs;winging round a piece of a &longs;tick, at the end of <lb/>which the &longs;tone is let into a &longs;lit <emph type="italics"/>(which &longs;tick is called by them a <lb/>&longs;ling;)<emph.end type="italics"/> all which are arguments of the truth of the conclu&longs;ion, <lb/>to wit, that the <emph type="italics"/>vertigo<emph.end type="italics"/> or &longs;wing conferreth upon the moveable, <lb/>a motion towards the circumference, in ca&longs;e the motion be &longs;wift: <lb/>and therefore if the Earth revolve about its own centre, the mo­ <lb/>tion of the &longs;uperficies, and e&longs;pecially towards the great circle, <lb/>as being incomparably more &longs;wift than tho&longs;e before named, ought <lb/>to extrude all things up into the air.</s></p><p type="main"><s>SIMP. </s><s>The Argument &longs;eemeth to me very well proved and <lb/>inforced; and I believe it would be an hard matter to an&longs;wer and <lb/>overthrow it.</s></p><p type="main"><s>SALV. </s><s>Its &longs;olution dependeth upon certain notions no le&longs;s <lb/>known and believed by you, than by my &longs;elf: but becau&longs;e they <lb/>come not into your mind, therefore it is that you perceive not the <lb/>an&longs;wer; wherefore, without telling you it (for that you know the <lb/>&longs;ame already) I &longs;hall with onely a&longs;&longs;i&longs;ting your memory, make you <lb/>to refute this argument.</s></p><p type="main"><s>SIMP. </s><s>I have often thought of your way of arguing, which <lb/>hath made me almo&longs;t think that you lean to that opinion of <emph type="italics"/>Pla-<emph.end type="italics"/> <lb/><arrow.to.target n="marg363"></arrow.to.target> <lb/><emph type="italics"/>to, Quòd no&longs;trum &longs;cire &longs;it quoddam remini&longs;ci<emph.end type="italics"/>; therefore I intreat <lb/>you to free me from this doubt, by letting me know your judg­ <lb/>ment.</s></p><p type="margin"><s><margin.target id="marg363"></margin.target><emph type="italics"/>Our krowledg is <lb/>a kind of remini&longs;­ <lb/>cence according to<emph.end type="italics"/> <lb/>Plato.</s></p><p type="main"><s>SALV. </s><s>What I think of the opinion of <emph type="italics"/>Plato,<emph.end type="italics"/> you may gather <lb/>from my words and actions. </s><s>I have already in the precedent con­ <lb/>ferences expre&longs;ly declared my &longs;elf more than once; I will pur&longs;ue <lb/>the &longs;ame &longs;tyle in the pre&longs;ent ca&longs;e, which may hereafter &longs;erve you <lb/>for an example, thereby the more ea&longs;ily to gather what my opi­ <lb/>nion is touching the attainment of knowledg, when a time &longs;hall <pb xlink:href="040/01/188.jpg" pagenum="170"/>offer upon &longs;ome other day: but I would not have <emph type="italics"/>Sagredus<emph.end type="italics"/> of­ <lb/>fended at this digre&longs;&longs;ion.</s></p><p type="main"><s>SAGR. </s><s>I am rather very much plea&longs;ed with it, for that I re­ <lb/>member that when I &longs;tudied Logick, I could never comprehend that <lb/>&longs;o much cry'd up and mo&longs;t potent demon&longs;tration of <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Let us go on therefore; and let <emph type="italics"/>Simplicius,<emph.end type="italics"/> tell me <lb/>what that motion is which the &longs;tone maketh that is held fa&longs;t in the <lb/>&longs;lit of the &longs;ling, when the boy &longs;wings it about to throw it a great <lb/>way?</s></p><p type="main"><s>SIMP. </s><s>The motion of the &longs;tone, &longs;o long as it is in the &longs;lit, is <lb/>circular, that is, moveth by the arch of a circle, who&longs;e &longs;tedfa&longs;t <lb/>centre is the knitting of the &longs;houlder, and its &longs;emi-diameter the arm <lb/>and &longs;tick.</s></p><p type="main"><s>SALV. </s><s>And when the &longs;tone leaveth the &longs;ling, what is its mo­ <lb/>tion? </s><s>Doth it continue to follow its former circle, or doth it go <lb/>by another line?</s></p><p type="main"><s>SIMP. </s><s>It will continue no longer to &longs;wing round, for then it <lb/>would not go farther from the arm of the projicient, whereas <lb/>we &longs;ee it go a great way off.</s></p><p type="main"><s>SALV. </s><s>With what motion doth it move then?</s></p><p type="main"><s>SIMP. </s><s>Give me a little time to think thereof; For I have ne­ <lb/>ver con&longs;idered it before.</s></p><p type="main"><s>SALV. </s><s>Hark hither, <emph type="italics"/>Sagredus<emph.end type="italics"/>; this is the <emph type="italics"/>Quoddam remini&longs;ci<emph.end type="italics"/> <lb/>in a &longs;ubject well under&longs;tood. </s><s>You have pau&longs;ed a great while, <lb/><emph type="italics"/>Simplicius.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>As far as I can &longs;ee, the motion received in going out of <lb/>the &longs;ling, can be no other than by a right line; nay, it mu&longs;t ne­ <lb/>ce&longs;&longs;arily be &longs;o, if we &longs;peak of the pure adventitious <emph type="italics"/>impetus.<emph.end type="italics"/> I <lb/>was a little puzled to &longs;ee it make an arch, but becau&longs;e that arch <lb/>bended all the way upwards, and no other way, I conceive that <lb/><arrow.to.target n="marg364"></arrow.to.target> <lb/>that incurvation cometh from the gravity of the &longs;tone, which na­ <lb/>turally draweth it downwards. </s><s>The impre&longs;&longs;ed <emph type="italics"/>impetus,<emph.end type="italics"/> I &longs;ay, <lb/>without re&longs;pecting the natural, is by a right line.</s></p><p type="margin"><s><margin.target id="marg364"></margin.target><emph type="italics"/>The motion im­ <lb/>pre&longs;&longs;ed by the pro­ <lb/>jicient is onely by a <lb/>right line.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>But by what right line? </s><s>Becau&longs;e infinite, and towards <lb/>every &longs;ide may be produced from the &longs;lit of the &longs;ling, and from the <lb/>point of the &longs;tones &longs;eparation from the &longs;ling.</s></p><p type="main"><s>SIMP. </s><s>It moveth by that line which goeth directly from the <lb/>motion which the &longs;tone made in the &longs;ling.</s></p><p type="main"><s>SALV. </s><s>The motion of the &longs;tone whil&longs;t it was in the &longs;lit, you <lb/>have affirmed already to be circular; now circularity oppo&longs;eth <lb/>directne&longs;s, there not being in the circular line any part that is di­ <lb/>rect or &longs;treight.</s></p><p type="main"><s>SIMP I mean not that the projected motion is direct in re­ <lb/>&longs;pect of the whole circle, but in reference to that ultimate point, <lb/>where the circular motion determineth. </s><s>I know what I would <pb xlink:href="040/01/189.jpg" pagenum="171"/>&longs;ay, but do not well know how to expre&longs;s my &longs;elf.</s></p><p type="main"><s>SALV. </s><s>And I al&longs;o perceive that you under&longs;tand the bu&longs;ine&longs;s, <lb/>but that you have not the proper terms, wherewith to expre&longs;s the <lb/>&longs;ame. </s><s>Now the&longs;e I can ea&longs;ily teach you; teach you, that is, as <lb/>to the words, but not as to the truths, which are things. </s><s>And that <lb/>you may plainly &longs;ee that you know the thing I ask you, and onely <lb/>want language to expre&longs;s it, tell me, when you &longs;hoot a bullet out <lb/>of a gun, towards what part is it, that its acquired <emph type="italics"/>impetus<emph.end type="italics"/> carri­ <lb/>eth it?</s></p><p type="main"><s>SIMP. </s><s>Its acquired <emph type="italics"/>impetus<emph.end type="italics"/> carrieth it in a right line, which <lb/>continueth the rectitude of the barrel, that is, which inclineth nei­ <lb/>ther to the right hand nor to the left, nor upwards not down­ <lb/>wards.</s></p><p type="main"><s>SALV. </s><s>Which in &longs;hort is a&longs;much as to &longs;ay, it maketh no angle <lb/>with the line of &longs;treight motion made by the &longs;ling.</s></p><p type="main"><s>SIMP. </s><s>So I would have &longs;aid.</s></p><p type="main"><s>SALV. </s><s>If then the line of the projects motion be to continue <lb/>without making an angle upon the circular line de&longs;cribed by it, <lb/>whil&longs;t it was with the projicient; and if from this circular motion it <lb/>ought to pa&longs;s to the right motion, what ought this right line to be?</s></p><p type="main"><s>SIMP. </s><s>It mu&longs;t needs be that which toucheth the circle in the <lb/>point of &longs;eparation, for that all others, in my opinion, being pro­ <lb/>longed would inter&longs;ect the circumference, and by that means make <lb/>&longs;ome angle therewith.</s></p><p type="main"><s>SALV. </s><s>You have argued very well, and &longs;hewn your &longs;elf half a <lb/>Geometrician. </s><s>Keep in mind therefore, that your true opinion <lb/>is expre&longs;t in the&longs;e words, namely, That the project acquireth an <lb/><emph type="italics"/>impetus<emph.end type="italics"/> of moving by the Tangent, the arch de&longs;cribed by the <lb/>motion of the projicient, in the point of the &longs;aid projects &longs;epara­ <lb/>tion from the projicient.</s></p><p type="main"><s>SIMP. </s><s>I under&longs;tand you very well, and this is that which I <lb/>would &longs;ay.</s></p><p type="main"><s>SALV. </s><s>Of a right line which toucheth a circle, which of its <lb/>points is the neare&longs;t to the centre of that circle?</s></p><p type="main"><s>SIMP. </s><s>That of the contact without doubt: for that is in the <lb/>circumference of a circle, and the re&longs;t without: and the points of <lb/>the circumference are all equidi&longs;tant from the centre.</s></p><p type="main"><s>SALV. </s><s>Therefore a moveable departing from the contact, and <lb/>moving by the &longs;treight Tangent, goeth continually farther and <lb/>farther from the contact, and al&longs;o from the centre of the circle.</s></p><p type="main"><s>SIMP. </s><s>It doth &longs;o doubtle&longs;s.</s></p><p type="main"><s>SALV. </s><s>Now if you have kept in mind the propo&longs;itions, which <lb/>you have told me, lay them together, and tell me what you gather <lb/>from them.</s></p><p type="main"><s>SIMP. </s><s>I think I am not &longs;o forgetful, but that I do remember <pb xlink:href="040/01/190.jpg" pagenum="172"/><arrow.to.target n="marg365"></arrow.to.target> <lb/>them. </s><s>From the things premi&longs;ed I gather that the project &longs;wiftly <lb/>&longs;winged round by the projicient, in its &longs;eparating from it, doth re­ <lb/>tain an <emph type="italics"/>impetus<emph.end type="italics"/> of continuing its motion by the right line, which <lb/>toucheth the circle de&longs;cribed by the motion of the projicient in <lb/>the point of &longs;eparation, by which motion the project goeth con­ <lb/>tinually receding from the centre of the circle de&longs;cribed by the <lb/>motion of the projicient.</s></p><p type="margin"><s><margin.target id="marg365"></margin.target><emph type="italics"/>The project mo­ <lb/>veth by the Tan­ <lb/>gent of the circle of <lb/>the motion prece­ <lb/>dent in the point of <lb/>&longs;eparation.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You know then by this time the rea&longs;on why grave bo­ <lb/>dies &longs;ticking to the rim of a wheele, &longs;wiftly moved, are extruded <lb/>and thrown beyond the circumference to yet a farther di&longs;tance <lb/>from the centre.</s></p><p type="main"><s>SIMP. </s><s>I think I under&longs;tand this very well; but this new know­ <lb/>ledg rather increa&longs;eth than le&longs;&longs;eneth my incredulity that the Earth <lb/>can turn round with &longs;o great velocity, without extruding up into <lb/>the sky, &longs;tones, animals, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>In the &longs;ame manner that you have under&longs;tood all this, <lb/>you &longs;hall, nay you do under&longs;tand the re&longs;t: and with recollecting <lb/>your &longs;elf, you may remember the &longs;ame without the help of o­ <lb/>thers: but that we may lo&longs;e no time, I will help your memory <lb/>therein. </s><s>You do already know of your &longs;elf, that the circular mo­ <lb/>tion of the projicient impre&longs;&longs;eth on the project an <emph type="italics"/>impetus<emph.end type="italics"/> of mo­ <lb/>ving (when they come to &longs;eparate) by the right Tangent, the <lb/>circle of the motion in the point of &longs;eparation, and continuing a­ <lb/>long by the &longs;ame the motion ever goeth receding farther and far­ <lb/>ther from the projicient: and you have &longs;aid, that the project <lb/>would continue to move along by that right line, if there were not <lb/>by its proper weight an inclination of de&longs;cent added unto it; from <lb/>which the incurvation of the line of motion is derived. </s><s>It &longs;eems <lb/>moreover that you knew of your &longs;elf, that this incurvation al­ <lb/>ways bended towards the centre of the Earth, for thither do all <lb/>grave bodies tend. </s><s>Now I proceed a little farther, and ask you, whe­ <lb/>ther the moveable after its &longs;eparation, in continuing the right mo­ <lb/>tion goeth always equally receding from the centre, or if you will, <lb/>from the circumference of that circle, of which the precedent mo­ <lb/>tion was a part; which is as much as to &longs;ay, Whether a moveable, <lb/>that for&longs;aking the point of a Tangent, and moving along by the <lb/>&longs;aid Tangent, doth equally recede from the point of contact, and <lb/>from the circumference of the circle?</s></p><p type="main"><s>SIMP. No, Sir: for the Tangent near to the point of contact, <lb/>recedeth very little from the circumference, wherewith it keepeth <lb/>a very narrow angle, but in its going farther and farther <lb/>off, the di&longs;tance always encrea&longs;eth with a greater proportion; &longs;o <lb/>that in a circle that &longs;hould have <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> ten yards of diameter, a point <lb/>of the Tangent that was di&longs;tant from the contact but two palms, <lb/>would be three or four times as far di&longs;tant from the circumference <pb xlink:href="040/01/191.jpg" pagenum="173"/>of the circle, as a point that was di&longs;tant from the contaction one <lb/>palm, and the point that was di&longs;tant half a palm, I likewi&longs;e believe <lb/>would &longs;car&longs;e recede the fourth part of the di&longs;tance of the &longs;econd: <lb/>fo that within an inch or two of the contact, the &longs;eparation of the <lb/>Tangent from the circumference is &longs;car&longs;e di&longs;cernable.</s></p><p type="main"><s>SALV. </s><s>So that the rece&longs;&longs;ion of the project from the circumfe­ <lb/>rence of the precedent circular motion is very &longs;mall in the begin­ <lb/>ing?</s></p><p type="main"><s>SIMP. </s><s>Almo&longs;t in&longs;en&longs;ible.</s></p><p type="main"><s>SALV. </s><s>Now tell me a little; the project, which from the mo­ <lb/>tion of the projicient receiveth an <emph type="italics"/>impetus<emph.end type="italics"/> of moving along the <lb/>Tangent in a right line, and that would keep unto the &longs;ame, did <lb/>not its own weight depre&longs;s it downwards, how long is it after the <lb/>&longs;eparation, ere it begin to decline downwards.</s></p><p type="main"><s>SIMP. </s><s>I believe that it beginneth pre&longs;ently; for it not ha­ <lb/>ving any thing to uphold it, its proper gravity cannot but ope­ <lb/>rate. <lb/><arrow.to.target n="marg366"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg366"></margin.target><emph type="italics"/>A grave project, <lb/>as &longs;oon as it is &longs;e­ <lb/>parated from the <lb/>projicient begineth <lb/>to decline.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>So that, if that &longs;ame &longs;tone, which being extruded from <lb/>that wheel turn'd about very fa&longs;t, had as great a natural propen­ <lb/>&longs;ion of moving towards the centre of the &longs;aid wheel, as it hath to <lb/>move towards the centre of the Earth, it would be an ea&longs;ie mat­ <lb/>ter for it to return unto the wheel, or rather not to depart from it; <lb/>in regard that upon the begining of the &longs;eparation, the rece&longs;&longs;ion be­ <lb/>ing &longs;o &longs;inall, by rea&longs;on of the infinite acutene&longs;s of the angle of <lb/>contact, every very little of inclination that draweth it back to­ <lb/>wards the centie of the wheel, would be &longs;ufficient to retain it up­ <lb/>on the rim or circumference.</s></p><p type="main"><s>SIMP. </s><s>I que&longs;tion not, but that if one &longs;uppo&longs;e that which nei­ <lb/>ther is, nor can be, to wit, that the inclination of tho&longs;e grave bo­ <lb/>dies was to go towards the centre of the wheel, they would never <lb/>come to be extruded or &longs;haken off.</s></p><p type="main"><s>SALV. </s><s>But I neither do, nor need to &longs;uppo&longs;e that which is not; <lb/>for I will not deny but that the &longs;tones are extruded. </s><s>Yet I &longs;peak <lb/>this by way of &longs;uppo&longs;ition, to the end that you might grant me <lb/>the re&longs;t. </s><s>Now fancy to your &longs;elf, that the Earth is that great <lb/>wheel, which moved with &longs;o great velocity is to extrude the &longs;tones. <lb/></s><s>You could tell me very well even now, that the motion of proje­ <lb/>ction ought to be by that right line which toucheth the Earth in <lb/>the point of &longs;eparation: and this Tangent, how doth it notably <lb/>recede from the &longs;uperficies of the Terre&longs;trial Globe?</s></p><p type="main"><s>SIMP. </s><s>I believe, that in a thou&longs;and yards, it will not recede <lb/>from the Earth an inch.</s></p><p type="main"><s>SALV. </s><s>And did you not &longs;ay, that the project being drawn by <lb/>its own weight, declineth from the Tangent towards the centre of <lb/>the Earth?</s></p> <pb xlink:href="040/01/192.jpg" pagenum="174"/><p type="main"><s>SIMP. </s><s>I &longs;aid &longs;o, and al&longs;o confe&longs;&longs;e the re&longs;t: and do now plainly <lb/>under&longs;tand that the &longs;tone will not &longs;eparate from the Earth, for <lb/>that its rece&longs;&longs;ion in the beginning would be &longs;uch, and &longs;o &longs;mall, <lb/>that it is a thou&longs;and times exceeded by the inclination which the <lb/>&longs;tone hath to move towards the centre of the Earth, which cen­ <lb/>tre in this ca&longs;e is al&longs;o the centre of the wheel. </s><s>And indeed it mu&longs;t <lb/>be confe&longs;&longs;ed that the &longs;tones, the living creatures, and the other <lb/>grave bodies cannot be extruded; but here again the lighter things <lb/>beget in me a new doubt, they having but a very weak propen&longs;ion <lb/>of de&longs;cent towards the centre; &longs;o that there being wanting in <lb/>them that faculty of withdrawing from the &longs;uperficies, I &longs;ee not, <lb/>but that they may be extruded; and you know the rule, that <emph type="italics"/>ad <lb/>de&longs;truendum &longs;ufficit unum.<emph.end type="italics"/></s></p><p type="main"><s>SAVL. </s><s>We will al&longs;o give you &longs;atisfaction in this. </s><s>Tell me <lb/>therefore in the fir&longs;t place, what you under&longs;tand by light matters, <lb/>that is, whether you thereby mean things really &longs;o light, as that <lb/>they go upwards, or el&longs;e not ab&longs;olutely light, but of &longs;o &longs;mall gra­ <lb/>vity, that though they de&longs;cend downwards, it is but very &longs;lowly; <lb/>for if you mean the ab&longs;olutely light, I will be readier than your <lb/>&longs;elf to admit their extru&longs;ion.</s></p><p type="main"><s>SIMP. </s><s>I &longs;peak of the other &longs;ort, &longs;uch as are feathers, wool, cot­ <lb/>ton, and the like; to lift up which every &longs;mall force &longs;ufficeth: <lb/>yet neverthele&longs;&longs;e we &longs;ee they re&longs;t on the Earth very quietly.</s></p><p type="main"><s>SALV. </s><s>This pen, as it hath a natural propen&longs;ion to de&longs;cend to­ <lb/>wards the &longs;uperficies of the Earth, though it be very &longs;mall, yet I <lb/>mu&longs;t tell you that it &longs;ufficeth to keep it from mounting upwards: <lb/>and this again is not unknown to you your &longs;elf; therefore tell me <lb/>if the pen were extruded by the <emph type="italics"/>Vertigo<emph.end type="italics"/> of the Earth, by what <lb/>line would it move?</s></p><p type="main"><s>SIMP. </s><s>By the tangent in the point of &longs;eparation.</s></p><p type="main"><s>SALV. </s><s>And when it &longs;hould be to return, and re-unite it &longs;elf to <lb/>the Earth, by what line would it then move?</s></p><p type="main"><s>SIMP. </s><s>By that which goeth from it to the centre of the <lb/>Earth.</s></p><p type="main"><s>SALV. </s><s>So then here falls under our con&longs;ideration two moti­ <lb/>ons; one the motion of projection, which beginneth from the <lb/>point of contact, and proceedeth along the tangent; and the o­ <lb/>ther the motion of inclination downwards, which beginneth from <lb/>the project it &longs;elf, and goeth by the &longs;ecant towards the centre; and <lb/>if you de&longs;ire that the projection follow, it is nece&longs;&longs;ary that the <emph type="italics"/>im­ <lb/>petus<emph.end type="italics"/> by the tangent overcome the inclination by the &longs;ecant: is it <lb/>not &longs;o?</s></p><p type="main"><s>SIMP. </s><s>So it &longs;eemeth to me.</s></p><p type="main"><s>SALV. </s><s>But what is it that you think nece&longs;&longs;ary in the motion <lb/>of the projicient, to make that it may prevail over that inclina­ <pb xlink:href="040/01/193.jpg" pagenum="175"/>tion, from which en&longs;ueth the &longs;eparation and elongation of the <lb/>pen from the Earth?</s></p><p type="main"><s>SIMP. </s><s>I cannot tell.</s></p><p type="main"><s>SALV. How, do you not know that? </s><s>The moveable is here <lb/>the &longs;ame, that is, the &longs;ame pen; now how can the &longs;ame moveable <lb/>&longs;uperate and exceed it &longs;elf in motion?</s></p><p type="main"><s>SIMP. </s><s>I do not &longs;ee how it can overcome or yield to it &longs;elf in <lb/>motion, unle&longs;&longs;e by moving one while fa&longs;ter, and another while <lb/>&longs;lower.</s></p><p type="main"><s>SALV. </s><s>You &longs;ee then, that you do know it. </s><s>If therefore the <lb/>projection of the pen ought to follow, and its motion by the tan­ <lb/>gent be to overcome its motion by the &longs;ecant, what is it requi&longs;ite <lb/>that their velocities &longs;hould be?</s></p><p type="main"><s>SIMP. </s><s>It is requi&longs;ite that the motion by the tangent be greater <lb/>than that other by the &longs;ecant. </s><s>But wretch that I am! Is it not <lb/>only many thou&longs;and times greater than the de&longs;cending motion of <lb/>the pen, but than that of the &longs;tone? </s><s>And yet like a &longs;imple fellow <lb/>I had &longs;uffered my &longs;elf to be per&longs;waded, that &longs;tones could not be <lb/>extruded by the revolution of the Earth. </s><s>I do therefore revoke <lb/>my former &longs;entence, and &longs;ay, that if the Earth &longs;hould move, <lb/>&longs;tones, Elephants, Towers, and whole Cities would of nece&longs;&longs;ity be <lb/>to&longs;t up into the Air; and becau&longs;e that that doth not evene, I con­ <lb/>clude that the Earth doth not move.</s></p><p type="main"><s>SALV. </s><s>Softly <emph type="italics"/>Simplicius,<emph.end type="italics"/> you go on &longs;o fa&longs;t, that I begin to be <lb/>more afraid for you, than for the pen. </s><s>Re&longs;t a little, and ob&longs;erve what <lb/>I am going to &longs;peap. </s><s>If for the reteining of the &longs;tone or pen an­ <lb/>nexed to the Earths &longs;urface it were nece&longs;&longs;ary that its motion of <lb/>de&longs;cent were greater, or as much as the motion made by the tan­ <lb/>gent; you would have had rea&longs;on to &longs;ay, that it ought of nece&longs;&longs;ity <lb/>to move as fa&longs;t, or fa&longs;ter by the &longs;ecant downwards, than by the <lb/>tangent Ea&longs;twards: But did not you tell me even now, that a <lb/>thou&longs;and yards of di&longs;tance by the tangent from the contact, do <lb/>remove hardly an inch from the circumference? </s><s>It is not &longs;uffici­ <lb/>ent therefore that the motion by the tangent, which is the &longs;ame <lb/>with that of the diurnall <emph type="italics"/>Vertigo,<emph.end type="italics"/> (or ha&longs;ty revolution) be fimply <lb/>more &longs;wift than the motion by the &longs;ecant, which is the &longs;ame with <lb/>that of the pen in de&longs;cending; but it is requi&longs;ite that the &longs;ame be <lb/>&longs;o much more &longs;wift as that the time which &longs;ufficeth for the pen <lb/>to move <emph type="italics"/>v.g.<emph.end type="italics"/> a thou&longs;and yards by the tangent, be in&longs;ufficient for <lb/>it to move one &longs;ole inch by the &longs;ecant. </s><s>The which I tell you &longs;hall <lb/>never be, though you &longs;hould make that motion never &longs;o &longs;wift, <lb/>and this never &longs;o &longs;low.</s></p><p type="main"><s>SIMP. </s><s>And why might not that by the tangent be &longs;o &longs;wift, as <lb/>not to give the pen time to return to the &longs;urface of the Earth?</s></p><p type="main"><s>SALV. </s><s>Try whether you can &longs;tate the ca&longs;e in proper termes, <pb xlink:href="040/01/194.jpg" pagenum="176"/>and I will give you an an&longs;wer. </s><s>Tell me therefore, how much do <lb/>you think &longs;ufficeth to make that motion &longs;wifter than this?</s></p><p type="main"><s>SIMP. </s><s>I will &longs;ay for example, that if that motion by the tan­ <lb/>gent were a million of times &longs;wifter than this by the &longs;ecant, the <lb/>pen, yea, and the &longs;tone al&longs;o would come to be extruded.</s></p><p type="main"><s>SALV. </s><s>You &longs;ay &longs;o, and &longs;ay that which is fal&longs;e, onely for <lb/>want, not of Logick, Phy&longs;icks, or Metaphy&longs;icks, but of Geome­ <lb/>try; for if you did but under&longs;tand its fir&longs;t elements, you would <lb/>know, that from the centre of a circle a right line may be drawn <lb/>to meet the tangent, which inter&longs;ecteth it in &longs;uch a manner, that <lb/>the part of the tangent between the contact and the &longs;ecant, may <lb/>be one, two, or three millions of times greater than that part of <lb/>the &longs;ecant which lieth between the tangent and the circumference, <lb/>and that the neerer and neerer the &longs;ecant &longs;hall be to the contact, <lb/>this proportion &longs;hall grow greater and greater <emph type="italics"/>in infinitum<emph.end type="italics"/>; &longs;o <lb/>that it need not be feared, though the <emph type="italics"/>vertigo<emph.end type="italics"/> be &longs;wift, and the <lb/>motion downwards &longs;low, that the pen or other lighter matter can <lb/>begin to ri&longs;e upwards, for that the inclination downwards always <lb/>exceedeth the velocity of the projection.</s></p><p type="main"><s>SAGR. </s><s>I do not perfectly apprehend this bu&longs;ine&longs;&longs;e.</s></p><p type="main"><s>SALV. </s><s>I will give you a mo&longs;t univer&longs;al yet very ea&longs;ie demon­</s></p><p type="main"><s><arrow.to.target n="marg367"></arrow.to.target> <lb/>&longs;tration thereof. </s><s>Let a proportion be given between B A [<emph type="italics"/>in Fig.<emph.end type="italics"/> <lb/>3.] and C: And let B A be greater than C at plea&longs;ure. </s><s>And let <lb/>there be de&longs;cribed a circle, who&longs;e centre is D. </s><s>From which it is <lb/>required to draw a &longs;ecant, in &longs;uch manner, that the tangent may <lb/>be in proportion to the &longs;aid &longs;ecant, as B A to C. </s><s>Let A I be <lb/>&longs;uppo&longs;ed a third proportional to B A and C. </s><s>And as B I is to <lb/>I A, &longs;o let the diameter F E be to E G; and from the point G, <lb/>let there be drawn the tangent G H. </s><s>I &longs;ay that all this is done as <lb/>was required; and as B A is to C, &longs;o is H G to G E. </s><s>And in re­ <lb/>gard that as B I is to I A, &longs;o is F E to E G; therefore by compo­ <lb/>&longs;ition, as B A is to A I; &longs;o &longs;hall F G be to G E. </s><s>And becau&longs;e C <lb/>is the middle proportion between <emph type="italics"/>B<emph.end type="italics"/> A and A I; and G H is a <lb/>middle term between F G and G E; therefore, as B A is to C, <lb/>&longs;o &longs;hall F G be to G H; that is H G to G E, which was to be <lb/>demon&longs;trated.</s></p><p type="margin"><s><margin.target id="marg367"></margin.target><emph type="italics"/>A geometrical <lb/>demon&longs;tration to <lb/>prove the impo&longs;&longs;i­ <lb/>bility of extru&longs;ion <lb/>by means of the <lb/>terre&longs;trial<emph.end type="italics"/> vertigo.</s></p><p type="main"><s>SAGR. </s><s>I apprehend this demon&longs;tration; yet neverthele&longs;&longs;e, I <lb/>am not left wholly without hæ&longs;itation; for I find certain confu­ <lb/>&longs;ed &longs;cruples role to and again in my mind, which like thick and <lb/>dark clouds, permit me not to di&longs;cern the cleerne&longs;&longs;e and nece&longs;&longs;ity <lb/>of the conclu&longs;ion with that per&longs;picuity, which is u&longs;ual in Mathe­ <lb/>matical Demon&longs;trations. </s><s>And that which I &longs;tick at is this. </s><s>It is <lb/>true that the &longs;paces between the tangent and the circumference do <lb/>gradually dimini&longs;h <emph type="italics"/>in infinitum<emph.end type="italics"/> towards the contact; but it is al&longs;o <lb/>true on the contrary, that the propen&longs;ion of the moveable to <pb xlink:href="040/01/195.jpg" pagenum="177"/>de&longs;cending groweth le&longs;s & le&longs;s in it, the nearer it is to the fir&longs;t term <lb/>of its de&longs;cent; that is, to the &longs;tate of re&longs;t; as is manife&longs;t from that <lb/>which you declare unto us, demon&longs;trating that the de&longs;cending grave <lb/>body departing from re&longs;t, ought to pa&longs;&longs;e thorow all the degrees of <lb/>tardity comprehended between the &longs;aid re&longs;t, & any a&longs;&longs;igned degree <lb/>of velocity, the which grow le&longs;s and le&longs;s <emph type="italics"/>in infinitum.<emph.end type="italics"/> To which may <lb/>be added, that the &longs;aid velocity and propen&longs;ion to motion, doth for <lb/>another rea&longs;on dimini&longs;h to infinity; and it is becau&longs;e the gravity of <lb/>the &longs;aid moveable may infinitely dimini&longs;h. </s><s>So that the cau&longs;es which <lb/>dimini&longs;h the propen&longs;ion of a&longs;cending, and con&longs;equently favour <lb/>the projection, are two; that is, the levity of the moveable, and its <lb/>vicinity to the &longs;tate of re&longs;t; both which are augmentable <emph type="italics"/>in infinit.<emph.end type="italics"/> <lb/>and the&longs;e two on the contrary being to contract but with one &longs;ole <lb/>cau&longs;e of making the projection, I cannot conceive how it alone, al­ <lb/>though it al&longs;o do admit of infinite augmentation, &longs;hould be able to <lb/>remain invincible again&longs;t the union & confederacy of the others, w^{ch} <lb/>are two, and are in like manner capable of infinite augmentation.</s></p><p type="main"><s>SALV. </s><s>This is a doubt worthy of <emph type="italics"/>Sagredus<emph.end type="italics"/>; and to explain it &longs;o as <lb/>that we may more cleerly apprehend it, for that you &longs;ay that you <lb/>your &longs;elf have but a confu&longs;ed <emph type="italics"/>Idea<emph.end type="italics"/> of it, we will di&longs;tingui&longs;h of the <lb/>&longs;ame by reducing it into figure; which may al&longs;o perhaps afford us <lb/>&longs;ome ca&longs;e in re&longs;olving the &longs;ame. </s><s>Let us therefore [<emph type="italics"/>in Fig.<emph.end type="italics"/> 4.] draw <lb/>a perpendicular line towards the centre, and let it be AC, and to it <lb/>at right angles let there be drawn the Horizontal line A <emph type="italics"/>B,<emph.end type="italics"/> upon <lb/>which the motion of the projection ought to be made; now the pro­ <lb/>ject would continue to move along the &longs;ame with an even motion, if <lb/>&longs;o be its gravity did not incline it downwards. </s><s>Let us &longs;uppo&longs;e from <lb/>the point A a right line to be drawn, that may make any angle at <lb/>plea&longs;ure with the line A B; which let be A E, and upon A<emph type="italics"/>B<emph.end type="italics"/> let us <lb/>mark &longs;ome equal &longs;paces AF, FH, HK, and from them let us let fall <lb/>the perpendiculars FG, HI, K L, as far as AE. </s><s>And becau&longs;e, as al <lb/>ready hath been &longs;aid, the de&longs;cending grave body departing from re&longs;t, <lb/>goeth from time to time acquiring a greater degree of velocity, <lb/>according as the &longs;aid time doth &longs;ucce&longs;&longs;ively encrea&longs;e; we may con­ <lb/>ceive the &longs;paces AF, FH, HK, to repre&longs;ent unto us equal times; and <lb/>the perpendiculars FG, HI, KL, degrees of velocity acquired in the <lb/>&longs;aid times; &longs;o that the degree of velocity acquired in the whole time <lb/>A K, is as the line K L, in re&longs;pect to the degree H I, acquired in the <lb/>time AH, and the degree FG in the time AF; the which degrees KL, <lb/>HI, FG, are (as is manife&longs;t) the &longs;ame in proportion, as the times K A, <lb/>HA, F A, and if other perpendiculars were drawn from the points <lb/>marked at plea&longs;ure in the line F A, one might &longs;ucce&longs;&longs;ively find de­ <lb/>grees le&longs;&longs;e and le&longs;&longs;e <emph type="italics"/>in infinitum,<emph.end type="italics"/> proceeding towards the point A, <lb/>repre&longs;enting the fir&longs;t in&longs;tant of time, and the fir&longs;t &longs;tate of re&longs;t. </s><s>And <lb/>this retreat towards A, repre&longs;enteth the fir&longs;t propen&longs;ion to the <pb xlink:href="040/01/196.jpg" pagenum="178"/>motion of de&longs;cent, dimini&longs;hed <emph type="italics"/>in infinitum<emph.end type="italics"/> by the approach of <lb/>the moveable to the fir&longs;t &longs;tate of re&longs;t, which approximation is <lb/>augmentable <emph type="italics"/>in infinitum.<emph.end type="italics"/> Now let us find the other diminution <lb/>of velocity, which likewi&longs;e may proceed to infinity, by the di­ <lb/>minution of the gravity of the moveable, and this &longs;hall be repre­ <lb/>&longs;ented by drawing other lines from the point A, which contein <lb/>angles le&longs;&longs;e than the angle B A E, which would be this line A D, <lb/>the which inter&longs;ecting the parallels K L, H I, F G, in the points <lb/>M, N, and O, repre&longs;ent unto us the degrees F O, H N, K M, <lb/>acquired in the times A F, A H, A K, le&longs;&longs;e than the other de­ <lb/>grees F G, H I, K L, acquired in the &longs;ame times; but the&longs;e <lb/>latter by a moveable more ponderous, and tho&longs;e other by a <lb/>moveable more <emph type="italics"/>light.<emph.end type="italics"/> And it is manife&longs;t, that by the retreat of <lb/>the line E A towards A B, contracting the angle E A B (the <lb/>which may be done <emph type="italics"/>in infinitum,<emph.end type="italics"/> like as the gravity may <emph type="italics"/>in infi­ <lb/>nitum<emph.end type="italics"/> be dimini&longs;hed) the velocity of the cadent moveable may <lb/>in like manner be dimini&longs;hed <emph type="italics"/>in infinitum,<emph.end type="italics"/> and &longs;o con&longs;equently <lb/>the cau&longs;e that impeded the projection; and therefore my thinks <lb/>that the union of the&longs;e two rea&longs;ons again&longs;t the projection, dimi­ <lb/>ni&longs;hed to infinity, cannot be any impediment to the &longs;aid proje­ <lb/>ction. </s><s>And couching the whole argument in its &longs;horte&longs;t terms, we <lb/>will &longs;ay, that by contracting the angle E A B, the degrees of ve­ <lb/>locity L K, I H, G F, are dimini&longs;hed; and moreover by the re­ <lb/>treat of the parallels K L, H I, F G, towards the angle A, the <lb/>fame degrees are again dimini&longs;hed; and both the&longs;e diminutions <lb/>extend to infinity: Therefore the velocity of the motion of de­ <lb/>&longs;cent may very well dimini&longs;h &longs;o much, (it admitting of a two&longs;old <lb/>diminution <emph type="italics"/>in infinitum<emph.end type="italics"/>) as that it may not &longs;uffice to re&longs;tore the <lb/>moveable to the circumference of the wheel, and thereupon may <lb/>occa&longs;ion the projection to be hindered and wholly obviated.</s></p><p type="main"><s>Again on the contrary, to impede the projection, it is nece&longs;­ <lb/>&longs;ary that the &longs;paces by which the project is to de&longs;cend for the <lb/>reuniting it &longs;elf to the Wheel, be made &longs;o &longs;hort and clo&longs;e toge­ <lb/>ther, that though the de&longs;cent of the moveable be retarded, yea <lb/>more, dimini&longs;hed <emph type="italics"/>in infinitum,<emph.end type="italics"/> yet it &longs;ufficeth to reconduct it thither: <lb/>and therefore it would be requi&longs;ite, that you find out a diminuti­ <lb/>on of the &longs;aid &longs;paces, not only produced to infinity, but to &longs;uch an <lb/>infinity, as that it may &longs;uperate the double infinity that is made in <lb/>the diminution of the velocity of the de&longs;cending moveable. </s><s>But <lb/>how can a magnitude be dimini&longs;hed more than another, which <lb/>hath a twofold diminution <emph type="italics"/>in infinitum<emph.end type="italics"/>? </s><s>Now let <emph type="italics"/>Simplicius<emph.end type="italics"/> ob­ <lb/>&longs;erve how hard it is to philo&longs;ophate well in nature, without <emph type="italics"/>Geo­ <lb/>metry.<emph.end type="italics"/> The degrees of velocity dimini&longs;hed <emph type="italics"/>in infinitum,<emph.end type="italics"/> as well <lb/>by the diminution of the gravity of the moveable, as by the ap­ <lb/>proxination to the fir&longs;t term of the motion, that is, to the &longs;tate <pb xlink:href="040/01/197.jpg" pagenum="179"/>of re&longs;t, are alwayes determinate, and an&longs;wer in proportion to the <lb/>parallels comprehended between two right lines that concur in <lb/>an angle, like to the angle B A E, or B A D, or any other <lb/>infinitely more acute, alwayes provided it be rectilineall­ <lb/>But the diminution of the &longs;paces thorow which the moveable is <lb/>to be conducted along the circumference of the wheel, is propor­ <lb/>tionate to another kind of diminution, comprehended between <lb/>lines that contain an angle infinitely more narrow and acute, than <lb/>any rectilineal angle, how acute &longs;oever, which is that in our pre­ <lb/>&longs;ent ca&longs;e. </s><s>Let any point be taken in the perpendicular A C, and <lb/>making it the centre, de&longs;cribe at the di&longs;tance C A, an arch A M P, <lb/>the which &longs;hall inter&longs;ect the parallels that determine the degrees of <lb/>velocity, though they be very minute, and comprehended within <lb/>a mo&longs;t acute rectilineal angle; of which parallels the parts that <lb/>lie between the arch and the tangent A B, are the quantities of <lb/>the &longs;paces, and of the returns upon the wheel, alwayes le&longs;&longs;er (and <lb/>with greater proportion le&longs;&longs;er, by how much neerer they approach <lb/>to the contact) than the &longs;aid parallels of which they are parts. <lb/></s><s>The parallels comprehended between the right lines in retiring to­ <lb/>wards the angle dimini&longs;h alwayes at the &longs;ame rate, as <emph type="italics"/>v.g.<emph.end type="italics"/> A H be­ <lb/>ing divided in two equal parts in F, the parallel H I &longs;hall be dou­ <lb/>ble to F G, and &longs;ub-dividing F A, in two equal parts, the paral­ <lb/>lel produced from the point of the divi&longs;ion &longs;hall be the half of <lb/>F G; and continuing the &longs;ub-divi&longs;ion <emph type="italics"/>in infinitum,<emph.end type="italics"/> the &longs;ub&longs;equent <lb/>parallels &longs;hall be alwayes half of the next preceding; but it doth <lb/>not &longs;o fall out in the lines intercepted between the tangent and <lb/>the circumference of the circle: For if the &longs;ame &longs;ub-divi&longs;ion be <lb/>made in F A; and &longs;uppo&longs;ing for example, that the parallel which <lb/>cometh from the point H, were double unto that which commeth <lb/>from F, this &longs;hall be more then double to the next following, and <lb/>continually the neerer we come towards the contact A, we &longs;hall <lb/>find the precedent lines contein the next following three, four, <lb/>ten, an hundred, a thou&longs;and, an hundred thou&longs;and, an hundred <lb/>millions of times, and more <emph type="italics"/>in infinitum.<emph.end type="italics"/> The brevity therefore of <lb/>&longs;uch lines is &longs;o reduced, that it far exceeds what is requi&longs;ite to make <lb/>the project, though never &longs;o light, return, nay more, continue <lb/>unremoveable upon the circumference.</s></p><p type="main"><s>SAGR. </s><s>I very well comprehend the whole di&longs;cour&longs;e, and upon <lb/>what it layeth all its &longs;tre&longs;&longs;e, yet neverthele&longs;&longs;e methinks that he <lb/>that would take pains to pur&longs;ue it, might yet &longs;tart &longs;ome further <lb/>que&longs;tions, by &longs;aying, that of tho&longs;e two cau&longs;es which render the <lb/>de&longs;cent of the moveable &longs;lower and &longs;lower <emph type="italics"/>in infinitum,<emph.end type="italics"/> it is mani­ <lb/>fe&longs;t, that that which dependeth on the vicinity to the fir&longs;t term of <lb/>the de&longs;cent, increa&longs;eth alwayes in the &longs;ame proportion, like as the <lb/>parallels alwayes retain the &longs;ame proportion to each other, &c. <pb xlink:href="040/01/198.jpg" pagenum="180"/>but that the diminution of the &longs;ame velocity, dependent on the <lb/>diminution of the gravity of the moveable (which vvas the &longs;econd <lb/>cau&longs;e) doth al&longs;o ob&longs;erve the &longs;ame proportion, doth not &longs;o plainly <lb/>appear, And vvho &longs;hall a&longs;&longs;ure us that it doth not proceed accor­ <lb/>ding to the proportion of the lines intercepted between the &longs;ecant, <lb/>and the circumference; or vvhether vvith a greater proportion?</s></p><p type="main"><s>SALV. </s><s>I have a&longs;&longs;umed for a truth, that the velocities of movea­ <lb/>bles de&longs;cending naturally, vvill follovv the proportion of their gra­ <lb/>vities, with the favour of <emph type="italics"/>Simplicius,<emph.end type="italics"/> and of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who doth <lb/>in many places affirm the &longs;ame, as a propo&longs;ition manife&longs;t: You, <lb/>in favour of my adver&longs;ary, bring the &longs;ame into que&longs;tion, and &longs;ay <lb/>that its po&longs;&longs;ible that the velocity increa&longs;eth with greater propor­ <lb/>tion, yea and greater <emph type="italics"/>in infinitum<emph.end type="italics"/> than that of the gravity; &longs;o that <lb/>all that hath been &longs;aid falleth to the ground: For maintaining <lb/>whereof, I &longs;ay, that the proportion of the velocities is much le&longs;&longs;e <lb/>than that of the gravities; and thereby I do not onely &longs;upport <lb/>but confirme the premi&longs;es. </s><s>And for proof of this I appeal unto <lb/>experience, which will &longs;hew us, that a grave body, howbeit thirty <lb/>or fourty times bigger then another; as for example, a ball of <lb/>lead, and another of &longs;ugar, will not move much more than twice <lb/>as fa&longs;t. </s><s>Now if the projection would not be made, albeit the ve­ <lb/>locity of the cadent body &longs;hould dimini&longs;h according to the pro­ <lb/>portion of the gravity, much le&longs;&longs;e would it be made &longs;o long as the <lb/>velocity is but little dimini&longs;hed, by abating much from the gravi­ <lb/>ty. </s><s>But yet &longs;uppo&longs;ing that the velocity dimini&longs;heth with a propor­ <lb/>tion much greater than that wherewith the gravity decrea&longs;eth, nay <lb/>though it were the &longs;elf-&longs;ame wherewith tho&longs;e parallels conteined <lb/>between the tangent and circumference do decrea&longs;e, yet cannot I <lb/>&longs;ee any nece&longs;&longs;ity why I &longs;hould grant the projection of matters of <lb/>never &longs;o great levity; yea I farther averre, that there could no &longs;uch <lb/>projection follow, meaning alwayes of matters not properly and <lb/>ab&longs;olutely light, that is, void of all gravity, and that of their own <lb/>natures move upwards, but that de&longs;cend very &longs;lowly, and <lb/>have very &longs;mall gravity. </s><s>And that which moveth me &longs;o to think <lb/>is, that the diminution of gravity, made according to the propor­ <lb/>tion of the parallels between the tangent and the circumference, <lb/>hath for its ultimate and highe&longs;t term the nullity of weight, as tho&longs;e <lb/>parallels have for their la&longs;t term of their diminution the contact it <lb/>&longs;elf, which is an indivi&longs;ible point: Now gravity never dimini&longs;heth <lb/>&longs;o far as to its la&longs;t term, for then the moveable would cea&longs;e to be <lb/>grave; but yet the &longs;pace of the rever&longs;ion of the project to the <lb/>circumference is reduced to the ultimate minuity, which is when <lb/>the moveable re&longs;teth upon the circumference in the very point of <lb/>contact; &longs;o as that to return thither it hath no need of &longs;pace: <lb/>and therefore let the propen&longs;ion to the motion of de&longs;cent be ne­ <pb xlink:href="040/01/199.jpg" pagenum="181"/>ver &longs;o &longs;mall, yet is it alwayes more than &longs;ufficient to reconduct the <lb/>moveable to the circumference, from which it is di&longs;tant but its lea&longs;t <lb/>&longs;pace, that is, nothing at all.</s></p><p type="main"><s>SAGR. </s><s>Your di&longs;cour&longs;e, I mu&longs;t confe&longs;s, is very accurate; and <lb/>yet no le&longs;s concluding than it is ingenuous; and it mu&longs;t be gran­ <lb/>ted that to go about to handle natural que&longs;tions, without <emph type="italics"/>Geome­ <lb/>try,<emph.end type="italics"/> is to attempt an impo&longs;&longs;ibility.</s></p><p type="main"><s>SALV. </s><s>But <emph type="italics"/>Simplicius<emph.end type="italics"/> will not &longs;ay &longs;o; and yet I do not think <lb/>that he is one of tho&longs;e <emph type="italics"/>Peripateticks<emph.end type="italics"/> that di&longs;&longs;wade their Di&longs;ciples <lb/>from &longs;tudying the <emph type="italics"/>Mathematicks,<emph.end type="italics"/> as Sciences that vitiate the rea­ <lb/>&longs;on, and render it le&longs;&longs;e apt for contemplation.</s></p><p type="main"><s>SIMP. </s><s>I would not do &longs;o much wrong to <emph type="italics"/>Plato,<emph.end type="italics"/> but yet I may <lb/>truly &longs;ay with <emph type="italics"/>Aristotle,<emph.end type="italics"/> that he too much lo&longs;t him&longs;elf in, and too <lb/>much doted upon that his <emph type="italics"/>Geometry<emph.end type="italics"/>: for that in conclu&longs;ion the&longs;e <lb/>Mathematical &longs;ubtilties <emph type="italics"/>Salviatus<emph.end type="italics"/> are true in ab&longs;tract, but applied <lb/>to &longs;en&longs;ible and Phy&longs;ical matter, they hold not good. </s><s>For the <lb/>Mathematicians will very well demon&longs;trate for example, that <lb/><emph type="italics"/>Sphæratangit planum in puncto<emph.end type="italics"/>; a po&longs;ition like to that in di&longs;pute, <lb/>but when one cometh to the matter, things &longs;ucceed quite another <lb/>way. </s><s>And &longs;o I may &longs;ay of the&longs;e angles of contact, and the&longs;e <lb/>proportions; which all evaporate into Air, when they are applied <lb/>to things material and &longs;en&longs;ible.</s></p><p type="main"><s>SALV. </s><s>You do not think then, that the tangent toucheth the <lb/>&longs;uperficies of the terre&longs;trial Globe in one point only?</s></p><p type="main"><s>SIMP. No, not in one &longs;ole point; but I believe that a right <lb/>line goeth many tens and hundreds of yards touching the &longs;urface <lb/>not onely of the Earth, but of the water, before it &longs;eparate from <lb/>the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>But if I grant you this, do not you perceive that it ma­ <lb/>keth &longs;o much the more again&longs;t your cau&longs;e? </s><s>For if it be &longs;uppo&longs;ed <lb/>that the tangent was &longs;eparated from the terre&longs;trial &longs;uperficies, yet <lb/>it hath been however demon&longs;trated that by rea&longs;on of the great a­ <lb/>cuity of the angle of contingence (if happily it may be call'd an <lb/>angle) the project would not &longs;eparate from the &longs;ame; how much <lb/>le&longs;&longs;e cau&longs;e of &longs;eparation would it have, if that angle &longs;hould be <lb/>wholly clo&longs;ed, and the &longs;uperficies and the tangent become all one? <lb/><arrow.to.target n="marg368"></arrow.to.target> <lb/>Perceive you not that the Projection would do the &longs;ame thing up­ <lb/>on the &longs;urface of the Earth, which is a&longs;much as to &longs;ay, it would <lb/>do ju&longs;t nothing at all? </s><s>You &longs;ee then the power of truth, which <lb/>while you &longs;trive to oppo&longs;e it, your own a&longs;&longs;aults them&longs;elves uphold <lb/>and defend it. </s><s>But in regard that you have retracted this errour, <lb/>I would be loth to leave you in that other which you hold, namely, <lb/>that a material Sphere doth not touch a plain in one &longs;ole point: <lb/>and I could wi&longs;h &longs;ome few hours conver&longs;ation with &longs;ome per&longs;ons <lb/>conver&longs;ant in <emph type="italics"/>Geometry,<emph.end type="italics"/> might make you a little more intelligent <pb xlink:href="040/01/200.jpg" pagenum="182"/>among&longs;t tho&longs;e who know nothing thereof. </s><s>Now to &longs;hew you how <lb/>great their errour is who &longs;ay, that a Sphere <emph type="italics"/>v.g.<emph.end type="italics"/> of bra&longs;&longs;e, doth not <lb/>touch a plain <emph type="italics"/>v.g.<emph.end type="italics"/> of &longs;teel in one &longs;ole point, Tell me what con­ <lb/>ceipt you would entertain of one that &longs;hould con&longs;tantly aver, that <lb/>the Sphere is not truly a Sphere.</s></p><p type="margin"><s><margin.target id="marg368"></margin.target><emph type="italics"/>The truth <lb/>&longs;ometimes gaines <lb/>&longs;trength by con­ <lb/>tradiction.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I would e&longs;teem him wholly devoid of rea&longs;on.</s></p><p type="main"><s>SALV. </s><s>He is in the &longs;ame ca&longs;e who &longs;aith that the material Sphere <lb/><arrow.to.target n="marg369"></arrow.to.target> <lb/>doth not touch a plain, al&longs;o material, in one onely point; for to <lb/>&longs;ay this is the &longs;ame, as to affirm that the Sphere is not a Sphere. <lb/></s><s>And that this is true, tell me in what it is that you con&longs;titute the <lb/>Sphere to con&longs;i&longs;t, that is, what it is that maketh the Sphere differ <lb/>from all other &longs;olid bodies.</s></p><p type="margin"><s><margin.target id="marg369"></margin.target><emph type="italics"/>The sphere al­ <lb/>though material, <lb/>toucheth the mate­ <lb/>rial plane but in <lb/>one point onely.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I believe that the e&longs;&longs;ence of a Sphere con&longs;i&longs;teth in ha­ <lb/><arrow.to.target n="marg370"></arrow.to.target> <lb/>ving all the right lines produced from its centre to the circumfe­ <lb/>rence, equal.</s></p><p type="margin"><s><margin.target id="marg370"></margin.target><emph type="italics"/>The definition of <lb/>the &longs;phere.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>So that, if tho&longs;e lines &longs;hould not be equal, there &longs;ame <lb/>&longs;olidity would be no longer a &longs;phere?</s></p><p type="main"><s>SIMP. True.</s></p><p type="main"><s>SALV. </s><s>Go to; tell me whether you believe that among&longs;t the <lb/>many lines that may be drawn between two points, that may be <lb/>more than one right line onely.</s></p><p type="main"><s>SIMP. </s><s>There can be but one.</s></p><p type="main"><s>SALV. </s><s>But yet you under&longs;tand that this onely right line &longs;hall <lb/>again of nece&longs;&longs;ity be the &longs;horte&longs;t of them all?</s></p><p type="main"><s>SIMP. </s><s>I know it, and al&longs;o have a demon&longs;tration thereof, pro­ <lb/>duced by a great <emph type="italics"/>Peripatetick<emph.end type="italics"/> Philo&longs;opher, and as I take it, if my <lb/>memory do not deceive me, he alledgeth it by way of reprehending <lb/><emph type="italics"/>Archimedes,<emph.end type="italics"/> that &longs;uppo&longs;eth it as known, when it may be demon­ <lb/>&longs;trated.</s></p><p type="main"><s>SALV. </s><s>This mu&longs;t needs be a great Mathematician, that knew <lb/>how to demon&longs;trate that which <emph type="italics"/>Archimedes<emph.end type="italics"/> neither did, nor could <lb/>demon&longs;trate. </s><s>And if you remember his demon&longs;tration, I would <lb/>gladly hear it: for I remember very well, that <emph type="italics"/>Archimedes<emph.end type="italics"/> in his <lb/>Books, <emph type="italics"/>de Sphærà & Cylindro,<emph.end type="italics"/> placeth this Propo&longs;ition among&longs;t the <lb/><emph type="italics"/>Po&longs;tulata<emph.end type="italics"/>; and I verily believe that he thought it demon&longs;trated.</s></p><p type="main"><s>SIMP. </s><s>I think I &longs;hall remember it, for it is very ea&longs;ie and <lb/>&longs;hort.</s></p><p type="main"><s>SALV. </s><s>The di&longs;grace of <emph type="italics"/>Archimedes,<emph.end type="italics"/> and the honour of this Phi­ <lb/>lo&longs;opher &longs;hall be &longs;o much the greater.</s></p><p type="main"><s>SIMP. </s><s>I will de&longs;cribe the Figure of it. </s><s>Between the points <lb/><arrow.to.target n="marg371"></arrow.to.target> <lb/>A and B, [<emph type="italics"/>in Fig.<emph.end type="italics"/> 5.] draw the right line A B, and the curve line <lb/>A C B, of which we will prove the right to be the &longs;horter: and <lb/>the proof is this; take a point in the curve-line, which let be C, <lb/>and draw two other lines, A C and C B, which two lines together; <lb/>are longer than the &longs;ole line A B, for &longs;o demon&longs;trateth <emph type="italics"/>Euelid.<emph.end type="italics"/> <pb xlink:href="040/01/201.jpg" pagenum="183"/>But the curve-line A C B, is greater than the two right-lines A C, <lb/>and C B; therefore, <emph type="italics"/>à fortiori,<emph.end type="italics"/> the curve-line A C B, is much <lb/>greater than the right line A B, which was to be demon&longs;trated. <lb/><arrow.to.target n="marg372"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg371"></margin.target><emph type="italics"/>The demon&longs;tra­ <lb/>tion of a Peripate­ <lb/>tick, to prove the <lb/>right line to be the <lb/>&longs;horte&longs;t of all lines.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg372"></margin.target><emph type="italics"/>The Paralogi&longs;m <lb/>of the &longs;ame Peripa­ <lb/>tetick, which pro­ <lb/>veth<emph.end type="italics"/> ignotum per <lb/>ignotius.</s></p><p type="main"><s>SALV. </s><s>I do not think that if one &longs;hould ran&longs;ack all the Para­ <lb/>logi&longs;ms of the world, there could be found one more commodious <lb/>than this, to give an example of the mo&longs;t &longs;olemn fallacy of all <lb/>fallacies, namely, than that which proveth <emph type="italics"/>ignotum per ignotius.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>How &longs;o?</s></p><p type="main"><s>SALV. </s><s>Do you ask me how &longs;o? </s><s>The unknown conclu&longs;ion <lb/>which you de&longs;ire to prove, is it not, that the curved line A C B, is <lb/>longer than the right line A B; the middle term which is taken <lb/>for known, is that the curve-line A C B, is greater than the two <lb/>lines A C and C B, the which are known to be greater than A B; <lb/>And if it be unknown whether the curve-line be greater than the <lb/>&longs;ingle right-line A B, &longs;hall it not be much more unknown whether <lb/>it be greater than the two right lines A C & C B, which are known <lb/>to be greater than the &longs;ole line A B, & yet you a&longs;&longs;ume it as known?</s></p><p type="main"><s>SIMP. </s><s>I do not yet very well perceive wherein lyeth the fal­ <lb/>lacy.</s></p><p type="main"><s>SALV. </s><s>As the two right lines are greater than A B, (as may be <lb/>known by <emph type="italics"/>Euclid<emph.end type="italics"/>) and in as much as the curve line is longer than <lb/>the two right lines A C and B C, &longs;hall it not not be much greater <lb/>than the &longs;ole right line A B?</s></p><p type="main"><s>SIMP. </s><s>It &longs;hall &longs;o.</s></p><p type="main"><s>SALV. </s><s>That the curve-line A C B, is greater than the right <lb/>line A B, is the conclu&longs;ion more known than the middle term, <lb/>which is, that the &longs;ame curve-line is greater than the two right­ <lb/>lines A C and C B. </s><s>Now when the middle term is le&longs;s known <lb/>than the conclu&longs;ion, it is called a proving <emph type="italics"/>ignotum per ignotius.<emph.end type="italics"/> <lb/>But to return to our purpo&longs;e, it is &longs;ufficient that you know the <lb/>right line to be the &longs;horte&longs;t of all the lines that can be drawn be­ <lb/>tween two points. </s><s>And as to the principal conclu&longs;ion, you &longs;ay, <lb/>that the material &longs;phere doth not touch the &longs;phere in one &longs;ole <lb/>point. </s><s>What then is its contact?</s></p><p type="main"><s>SIMP. </s><s>It &longs;hall be a part of its &longs;uperficies.</s></p><p type="main"><s>SALV. </s><s>And the contact likewi&longs;e of another &longs;phere equal to the <lb/>fir&longs;t, &longs;hall be al&longs;o a like particle of its &longs;uperficies?</s></p><p type="main"><s>SIMP. </s><s>There is no rea&longs;on vvhy it &longs;hould be othervvi&longs;e.</s></p><p type="main"><s>SALV. </s><s>Then the tvvo &longs;pheres vvhich touch each other, &longs;hall <lb/>touch vvith the tvvo &longs;ame particles of a &longs;uperficies, for each of them <lb/>agreeing to one and the &longs;ame plane, they mu&longs;t of nece&longs;&longs;ity agree <lb/>in like manner to each other. </s><s>Imagine now that the two &longs;pheres </s></p><p type="main"><s><arrow.to.target n="marg373"></arrow.to.target> <lb/>[<emph type="italics"/>in Fig.<emph.end type="italics"/> 6.] who&longs;e centres are A and B, do touch one another: <lb/>and let their centres be conjoyned by the right line A B, which <lb/>pa&longs;&longs;eth through the contact. </s><s>It pa&longs;&longs;eth thorow the point C, and <pb xlink:href="040/01/202.jpg" pagenum="184"/>another point in the contact being taken as D, conjoyn the two <lb/>right lines A D and B D, &longs;o as that they make the triangle A D B; <lb/>of which the two &longs;ides A D and D B &longs;hall be equal to the other one <lb/>A C B, both tho&longs;e and this containing two &longs;emidiameters, which <lb/>by the definition of the &longs;phere are all equal: and thus the right <lb/>line A B, drawn between the two centres A and B, &longs;hall not be the <lb/>&longs;horte&longs;t of all, the two lines A D and D B being equal to it: which <lb/>by your own conce&longs;&longs;ion is ab&longs;urd.</s></p><p type="margin"><s><margin.target id="marg373"></margin.target><emph type="italics"/>A demon &longs;tration <lb/>that the &longs;phere tou­ <lb/>cheth the plane but <lb/>in one point.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>This demon&longs;tration holdeth in the ab&longs;tracted, but not in <lb/>the material &longs;pheres.</s></p><p type="main"><s>SALV. </s><s>In&longs;tance then wherein the fallacy of my argument con­ <lb/>&longs;i&longs;teth, if as you &longs;ay it is not concluding in the material &longs;pheres, but <lb/>holdeth good in the immaterial and ab&longs;tracted. <lb/><arrow.to.target n="marg374"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg374"></margin.target><emph type="italics"/>Why the &longs;phere in <lb/>ab&longs;tract, toucheth <lb/>the plane onely in <lb/>one point, and not <lb/>the material in <lb/>conerete.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The material &longs;pheres are &longs;ubject to many accidents, <lb/>which the immaterial are free from. </s><s>And becau&longs;e it cannot be, <lb/>that a &longs;phere of metal pa&longs;&longs;ing along a plane, its own weight &longs;hould <lb/>not &longs;o depre&longs;s it, as that the plain &longs;hould yield &longs;omewhat, or that <lb/>the &longs;phere it &longs;elf &longs;hould not in the contact admit of &longs;ome impre&longs;&longs;i­ <lb/>on. </s><s>Moreover, it is very hard for that plane to be perfect, if for <lb/>nothing el&longs;e, yet at lea&longs;t for that its matter is porous: and per­ <lb/>haps it will be no le&longs;s difficult to find a &longs;phere &longs;o perfect, as that <lb/>it hath all the lines from the centre to the &longs;uperficies, exactly <lb/>equal.</s></p><p type="main"><s>SALV. </s><s>I very readily grant you all this that you have &longs;aid; but <lb/>it is very much be&longs;ide our purpo&longs;e: for whil&longs;t you go about to <lb/>&longs;hew me that a material &longs;phere toucheth not a material plane in <lb/>one point alone, you make u&longs;e of a &longs;phere that is not a &longs;phere, and <lb/>of a plane that is not a plane; for that, according to what you <lb/>&longs;ay, either the&longs;e things cannot be found in the world, or if they <lb/>may be found, they are &longs;poiled in applying them to work the effect. <lb/></s><s>It had been therefore a le&longs;s evil, for you to have granted the con­ <lb/>clu&longs;ion, but conditionally, to wit, that if there could be made of <lb/>matter a &longs;phere and a plane that were and could continue perfect, <lb/>they would touch in one &longs;ole point, and then to have denied that <lb/>any &longs;uch could be made.</s></p><p type="main"><s>SIMP. </s><s>I believe that the propo&longs;ition of Philo&longs;ophers is to be <lb/>under&longs;tood in this &longs;en&longs;e; for it is not to be doubted, but that the <lb/>imperfection of the matter, maketh the matters taken in con­ <lb/>crete, to di&longs;agree with tho&longs;e taken in ab&longs;tract.</s></p><p type="main"><s>SALV. What, do they not agree? </s><s>Why, that which you your <lb/>&longs;elf &longs;ay at this in&longs;tant, proveth that they punctually agree.</s></p><p type="main"><s>SIMP. </s><s>How can that be?</s></p><p type="main"><s>SALV. </s><s>Do you not &longs;ay, that through the imperfection of the <lb/>matter, that body which ought to be perfectly &longs;pherical, and that <lb/>plane which ought to be perfectly level, do not prove to be the <pb xlink:href="040/01/203.jpg" pagenum="185"/>&longs;ame in concrete, as they are imagined to be in ab&longs;tract?</s></p><p type="main"><s>SIMP. </s><s>This I do affirm.</s></p><p type="main"><s>SALV. </s><s>Then when ever in concrete you do apply a material Sphere </s></p><p type="main"><s><arrow.to.target n="marg375"></arrow.to.target> <lb/>to a material plane, youapply an imperfect Sphere to an imperfect <lb/>plane, & the&longs;e you &longs;ay do not touch only in one point. </s><s>But I mu&longs;t <lb/>tell you, that even in ab&longs;tract an immaterial Sphere, that is, not a <lb/>perfect Sphere, may touch an immaterial plane, that is, not a per­ <lb/>fect plane, not in one point, but with part of its &longs;uperficies, &longs;o that <lb/>hitherto that which falleth out in concrete, doth in like manner <lb/>hold true in ab&longs;tract. </s><s>And it would be a new thing that the com­ <lb/>putations and rates made in ab&longs;tract numbers, &longs;hould not after­ <lb/>wards an&longs;wer to the Coines of Gold and Silver, and to the mer­ <lb/>chandizes in concrete. </s><s>But do you know <emph type="italics"/>Simplicius,<emph.end type="italics"/> how this <lb/>commeth to pa&longs;&longs;e? </s><s>Like as to make that the computations agree <lb/>with the Sugars, the Silks, the Wools, it is nece&longs;&longs;ary that the <lb/>accomptant reckon his tares of che&longs;ts, bags, and &longs;uch other things: <lb/>So when the <emph type="italics"/>Geometricall Philo&longs;opher<emph.end type="italics"/> would ob&longs;erve in concrete <lb/>the effects demon&longs;trated in ab&longs;tract, he mu&longs;t defalke the impedi­ <lb/>ments of the matter, and if he know how to do that, I do a&longs;&longs;ure <lb/>you, the things &longs;hall jump no le&longs;&longs;e exactly, than <emph type="italics"/>Arithmstical<emph.end type="italics"/> <lb/>computations. </s><s>The errours therefore lyeth neither in ab&longs;tract, nor <lb/>in concrete, nor in <emph type="italics"/>Geometry,<emph.end type="italics"/> nor in <emph type="italics"/>Phy&longs;icks,<emph.end type="italics"/> but in the Calcula­ <lb/>tor, that knoweth not how to adju&longs;t his accompts. </s><s>Therefore if <lb/>you had a perfect Sphere and plane, though they were material, <lb/>you need not doubt but that they would touch onely in one point. <lb/></s><s>And if &longs;uch a Sphere was and is impo&longs;&longs;ible to be procured, it was <lb/>much be&longs;ides the purpo&longs;e to &longs;ay, <emph type="italics"/>Quod Sphæra ænea non tangit in <lb/>puncto.<emph.end type="italics"/> Furthermore, if I grant you <emph type="italics"/>Simplicius,<emph.end type="italics"/> that in matter a <lb/>figure cannot be procured that is perfectly &longs;pherical, or perfectly <lb/>level: Do you think there may be had two materiall bodies, <lb/>who&longs;e &longs;uperficies in &longs;ome part, and in &longs;ome &longs;ort are incurvated as <lb/>irregularly as can be de&longs;ired?</s></p><p type="margin"><s><margin.target id="marg375"></margin.target><emph type="italics"/>Things are ex­ <lb/>actly the &longs;ame in <lb/>ab&longs;tract as in con­ <lb/>crete.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Of the&longs;e I believe that there is no want.</s></p><p type="main"><s>SALV. </s><s>If &longs;uch there be, then they al&longs;o will touch in one &longs;ole <lb/><arrow.to.target n="marg376"></arrow.to.target> <lb/>point; for this contact in but one point alone is not the &longs;ole and <lb/>peculiar priviledge of the perfect Sphere and perfect plane. </s><s>Nay, he <lb/>that &longs;hould pro&longs;ecute this point with more &longs;ubtil contemplations <lb/>would finde that it is much harder to procure two bodies that <lb/><arrow.to.target n="marg377"></arrow.to.target> <lb/>touch with part of their &longs;nper&longs;icies, than with one point onely. <lb/></s><s>For if two &longs;uperficies be required to combine well together, it is <lb/>nece&longs;&longs;ary either, that they be both exactly plane, or that if one be <lb/>convex, the other be concave; but in &longs;uch a manner concave, <lb/>that the concavity do exactly an&longs;wer to the convexity of the other: <lb/>the which conditions are much harder to be found, in regard of <lb/>their too narrow determination, than tho&longs;e others, which in their <lb/>ca&longs;uall latitude are infinite.</s></p> <pb xlink:href="040/01/204.jpg" pagenum="186"/><p type="margin"><s><margin.target id="marg376"></margin.target><emph type="italics"/>Contact in a &longs;in­ <lb/>gle point is not pe­ <lb/>culiar to the per­ <lb/>fect Spheres onely? <lb/></s><s>but belongeth to all <lb/>curved figures.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg377"></margin.target><emph type="italics"/>It is more diffi­ <lb/>cult to find Figures <lb/>that touch with a <lb/>part of their &longs;ur­ <lb/>face, than in one <lb/>&longs;ole point.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>You believe then, that two &longs;tones, or two pieces of I­ <lb/>ron taken at chance, and put together, do for the mo&longs;t part touch <lb/>in one &longs;ole point?</s></p><p type="main"><s>SALV. </s><s>In ca&longs;ual encounters, I do not think they do; as well <lb/>becau&longs;e for the mo&longs;t part there will be &longs;ome &longs;mall yielding filth <lb/>upon them, as becau&longs;e that no diligence is u&longs;ed in applying them <lb/>without &longs;triking one another; and every &longs;mall matter &longs;ufficeth to <lb/>make the one &longs;uperficies yield &longs;omewhat to the other; &longs;o that <lb/>they interchangeably, at lea&longs;t in &longs;ome &longs;mall particle, receive &longs;igure <lb/>from the impre&longs;&longs;ion of each other. </s><s>But in ca&longs;e their &longs;uperficies <lb/>were very ter&longs;e and polite, and that they were both laid upon a <lb/>table, that &longs;o one might not pre&longs;&longs;e upon the other, and gently put <lb/>towards one another, I que&longs;tion not, but that they might be <lb/>brought to the &longs;imple contact in one onely point.</s></p><p type="main"><s>SAGR. </s><s>It is requi&longs;ite, with your permi&longs;&longs;ion, that I propound a <lb/>certain &longs;cruple of mine, which came into my minde, whil'&longs;t I heard <lb/>propo&longs;ed by <emph type="italics"/>Simplicius,<emph.end type="italics"/> the impo&longs;&longs;ibility of finding a materiall <lb/>and &longs;olid body, that is, perfectly of a Spherical figure, and whil'&longs;t <lb/>J law <emph type="italics"/>Salviatus<emph.end type="italics"/> in a certain manner, not gain&longs;aying, to give his <lb/>con&longs;ent thereto; therefore I would know, whether there would <lb/>be the &longs;ame difficulty in forming a &longs;olid of &longs;ome other figure, that <lb/>is, to expre&longs;&longs;e my &longs;elf better, whether there is more difficulty in <lb/>reducing a piece of Marble into the figure of a perfect Sphere, than <lb/>into a perfect Pyramid, or into a perfect Hor&longs;e, or into a perfect <lb/>Gra&longs;&longs;e-hopper?</s></p><p type="main"><s>SALV. </s><s>To this I will make you the fir&longs;t an&longs;wer: and in the <lb/>fir&longs;t place, I will acquit my &longs;elf of the a&longs;&longs;ent which you think I <lb/>gave to <emph type="italics"/>Simplicius,<emph.end type="italics"/> which was only for a time; for I had it al&longs;o in <lb/>my thoughts, betore I intended to enter upon any other matter, to <lb/>&longs;peak that, which, it may be, is the &longs;ame, or very like to that which <lb/>you are about to &longs;ay, And an&longs;wering to your fir&longs;t que&longs;tion, I &longs;ay, <lb/><arrow.to.target n="marg378"></arrow.to.target> <lb/>that if any figure can be given to a Solid, the Spherical is the ea&longs;i­ <lb/>e&longs;t of all others, as it is likewi&longs;e the mo&longs;t &longs;imple, and holdeth the <lb/>&longs;ame place among&longs;t &longs;olid figures, as the Circle holdeth among&longs;t <lb/><arrow.to.target n="marg379"></arrow.to.target> <lb/>the &longs;uperficial. </s><s>The de&longs;cription of which Circle, as being more ea­ <lb/>&longs;ie than all the re&longs;t, hath alone been judged by <emph type="italics"/>Mathematicians<emph.end type="italics"/> <lb/>worthy to be put among&longs;t the ^{*} <emph type="italics"/>po&longs;tulata<emph.end type="italics"/> belonging to the de&longs;cri­ <lb/><arrow.to.target n="marg380"></arrow.to.target> <lb/>ption of all other figures. </s><s>And the formation of the Sphere is <lb/>&longs;o very ea&longs;ie, that if in a plain plate of hard metal you take an <lb/>empty or hollow circle, within which any Solid goeth ca&longs;ually re­ <lb/>volving that was before but gro&longs;ly rounded, it &longs;hall, without any <lb/>other artifice be reduced to a Spherical figure, as perfect as is po&longs;­ <lb/>&longs;ible for it to be; provided, that that &longs;ame Solid be not le&longs;&longs;e than <lb/>the Sphere that would pa&longs;&longs;e thorow that Circle. </s><s>And that which is <lb/>yet more worthy of our con&longs;ideration is, that within the &longs;elf-&longs;ame <pb xlink:href="040/01/205.jpg" pagenum="187"/>incavity one may form Spheres of &longs;everal magnitudes. </s><s>But what <lb/><arrow.to.target n="marg381"></arrow.to.target> <lb/>is required to the making of an Hor&longs;e, or (as you &longs;ay) of a Gra&longs;s­ <lb/>hopper, I leave to you to judge, who know that there are but few <lb/>&longs;tatuaries in the world able to undertake &longs;uch a piece of work. <lb/></s><s>And I think that herein <emph type="italics"/>Simplicius<emph.end type="italics"/> will not di&longs;&longs;ent from me.</s></p><p type="margin"><s><margin.target id="marg378"></margin.target><emph type="italics"/>The Sphericall <lb/>Figure is ea&longs;ier to <lb/>be made than any <lb/>other.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg379"></margin.target><emph type="italics"/>The circular Fi­ <lb/>gure only is placed <lb/>amongst the<emph.end type="italics"/> po&longs;tu­ <lb/>lata <emph type="italics"/>of Mathema­ <lb/>ticians.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg380"></margin.target>* Demands or <lb/>Petitions.</s></p><p type="margin"><s><margin.target id="marg381"></margin.target><emph type="italics"/>Sphericall Fi­ <lb/>gures of &longs;undry <lb/>magnitudes may <lb/>be made with one <lb/>onely in&longs;trument.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I know not whether I do at all diffent from you; my <lb/>opinion is this, that none of the afore-named figures can be per­ <lb/>fectly obteined; but for the approaching as neer as is po&longs;&longs;ible to <lb/>the mo&longs;t perfect degree, I believe that it is incomparably more ea­ <lb/>&longs;ie to reduce the Solid into a Spherical figure, than into the &longs;hape <lb/>of an Hor&longs;e, or Gra&longs;&longs;e-hopper?</s></p><p type="main"><s>SAGR. </s><s>And this greater difficulty, wherein think you doth it <lb/>depend?</s></p><p type="main"><s>SIMP. </s><s>Like as the great facility in forming the Sphere ari&longs;eth <lb/><arrow.to.target n="marg382"></arrow.to.target> <lb/>from its ab&longs;olute &longs;implicity and uniformity &longs;o the great irregu­ <lb/>larity rendereth the con&longs;truction of all other figures difficult.</s></p><p type="margin"><s><margin.target id="marg382"></margin.target><emph type="italics"/>Irregular forms <lb/>difficult to be in­ <lb/>troduced.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Therefore the irregularity being the cau&longs;e of the diffi­ <lb/>culty, than the figure of a &longs;tone broken with an hammer by <lb/>chance, &longs;hall be one of the figures that are difficult to be introdu­ <lb/>ced, it being perhaps more irregular than that of the hor&longs;e?</s></p><p type="main"><s>SIMP. </s><s>So it &longs;hould be.</s></p><p type="main"><s>SAGR. </s><s>But tell me; that figure what ever it is which the &longs;tone <lb/>hath, hath it the &longs;ame in perfection, or no?</s></p><p type="main"><s>SIMP. </s><s>What it hath, it hath &longs;o perfectly, that nothing can be <lb/>more exact.</s></p><p type="main"><s>SAGR. Then, if of figures that are irregular, and con&longs;equent­ <lb/>ly hard to be procured, there are yet infinite which are mo&longs;t per­ <lb/>fectly obteined, with what rea&longs;on can it be &longs;aid, that the mo&longs;t <lb/>&longs;imple, and con&longs;equently the mo&longs;t ea&longs;ie of all, is impo&longs;&longs;ible to be <lb/>procured?</s></p><p type="main"><s>SALV. Gentlemen, with your favour, I may &longs;ay that we have <lb/>&longs;allied out into a di&longs;pute not much more worth than the wool of a <lb/>goat; and whereas our argumentations &longs;hould continually be con­ <lb/>ver&longs;ant about &longs;erious and weighty points, we con&longs;ume our time in <lb/><arrow.to.target n="marg383"></arrow.to.target> <lb/>frivolous and impertinent wranglings. </s><s>Let us call to minde, I pray <lb/>you, that the &longs;earch of the worlds con&longs;titution, is one of the grea­ <lb/>te&longs;t and noble&longs;t Problems that are in nature; and &longs;o much the <lb/>greater, ina&longs;much as it is directed to the re&longs;olving of that other; <lb/>to wit, of the cau&longs;e of the Seas ebbing and flowing, enquired in­ <lb/>to by all the famous men, that have hitherto been in the world, <lb/>and po&longs;&longs;ibly found out by none of them. </s><s>Therefore if we have <lb/>nothing more remaining for the full confutation of the argument <lb/>taken from the Earths <emph type="italics"/>vertigo,<emph.end type="italics"/> which was the la&longs;t, alledged to <lb/>prove its immobility upon its own centre, let us pa&longs;&longs;e to the ex­ <lb/>amination of tho&longs;e things that are alledged for, and again&longs;t the <lb/><emph type="italics"/>Annual Motion.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/206.jpg" pagenum="188"/><p type="margin"><s><margin.target id="marg383"></margin.target><emph type="italics"/>The con&longs;titution <lb/>of the Univer&longs;e is <lb/>one of the mo&longs;t no­ <lb/>ble Problems.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I would not have you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> mea&longs;ure our wits by <lb/>the &longs;cale of yours: you, who u&longs;e to be continually bu&longs;ied about <lb/>the &longs;ublime&longs;t contemplations, e&longs;teem tho&longs;e notions frivolous and <lb/>below you, which we think matters worthy of our profounde&longs;t <lb/>thoughts: yet &longs;ometimes for our &longs;atisfaction do not di&longs;dain to <lb/>&longs;toop &longs;o low as to give way a little to our curio&longs;ity. </s><s>As to the <lb/>refutation of the la&longs;t argument, taken from the extru&longs;ions of the <lb/>diurnal <emph type="italics"/>vertigo,<emph.end type="italics"/> far le&longs;s than what hath been &longs;aid, would have <lb/>given me &longs;atisfaction: and yet the things &longs;uperfluou&longs;ly &longs;poken, <lb/>&longs;eemed to me &longs;o ingenious, that they have been &longs;o far from wea­ <lb/>rying my fancy, as that they have, by rea&longs;on of their novelty, en­ <lb/>tertained me all along with &longs;o great delight, that I know not how <lb/>to de&longs;ire greater: Therefore, if you have any other &longs;peculation <lb/>to add, produce it, for I, as to my own particular, &longs;hall gladly <lb/>hearken to it.</s></p><p type="main"><s>SALV. </s><s>I have always taken great delight in tho&longs;e things which <lb/>I have had the fortune to di&longs;cover, and next to that, which is my <lb/>chief content, I find great plea&longs;ure in imparting them to &longs;ome <lb/>friends, that apprehendeth and &longs;eemeth to like them: Now, in re­ <lb/>gard you are one of the&longs;e, &longs;lacking a little the reins of my ambi­ <lb/>tion, which is much plea&longs;ed when I &longs;hew my &longs;elf more per&longs;pi­ <lb/>cacious, than &longs;ome other that hath the reputation of a &longs;harp <lb/>&longs;ight, I will for a full and true mea&longs;ure of the pa&longs;t di&longs;pute, pro­ <lb/>duce another fallacy of the Sectators of <emph type="italics"/>Ptolomey<emph.end type="italics"/> and <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>which I take from the argument alledged.</s></p><p type="main"><s>SAGR. </s><s>See how greedily I wait to hear it.</s></p><p type="main"><s>SALV. </s><s>We have hitherto over-pa&longs;&longs;ed, and granted to <emph type="italics"/>Ptolomey,<emph.end type="italics"/> <lb/>as an effect indubitable, that the extru&longs;ion of the &longs;tone proceed­ <lb/>ing from the velocity of the wheel turn'd round upon its centre, <lb/>the cau&longs;e of the &longs;aid extru&longs;ion encrea&longs;eth in proportion, as the ve­ <lb/>locity of the <emph type="italics"/>vertigo<emph.end type="italics"/> (or whirling) is augmented: from whence <lb/>it was inferred, that the velocity of the Earth's <emph type="italics"/>vertigo<emph.end type="italics"/> being <lb/>very much greater than that of any machin what&longs;oever, that we <lb/>can make to turn round artificially; the extru&longs;ion of &longs;tones, of <lb/>animals, &c. </s><s>would con&longs;equently be far more violent. </s><s>Now, I <lb/>ob&longs;erve that there is a great fallacy in this di&longs;cour&longs;e, in that we do <lb/>compare the&longs;e velocities indifferently and ab&longs;olutely to one ano­ <lb/>ther. </s><s>It's true, that if I compare the velocities of the &longs;ame wheel, <lb/>or of two wheels equal to each other, that which &longs;hall be more <lb/>&longs;wiftly turn'd round, &longs;hall extrude the &longs;tone with greater vio­ <lb/>lence; and the velocity encrea&longs;ing, the cau&longs;e of the projection <lb/>&longs;hall likewi&longs;e encrea&longs;e: but when the velocity is augmented, not <lb/>by encrea&longs;ing the velocity in the &longs;ame wheel, which would be by <lb/>cau&longs;ing it to make a greater number of revolutions in equal times; <lb/>but by encrea&longs;ing the diameter, and making the wheel greater, &longs;o <lb/>as that the conver&longs;ion taking up the &longs;ame time in the le&longs;&longs;er wheel, <pb xlink:href="040/01/207.jpg" pagenum="189"/>as in the greater, the velocity is greater onely in the bigger wheel, <lb/><arrow.to.target n="marg384"></arrow.to.target> <lb/>for that its circumference is bigger; there is no man that thinketh <lb/>that the cau&longs;e of the extru&longs;ion in the great wheel will encrea&longs;e ac­ <lb/>cording to the proportion of the velocity of its circumference, to <lb/>the velocity of the circumference of the other le&longs;&longs;er wheel; for that <lb/>this is mo&longs;t fal&longs;e, as by a mo&longs;t expeditious experiment I &longs;hall thus <lb/>gro&longs;ly declare: We may &longs;ling a &longs;tone with a &longs;tick of a yard long, <lb/>farther than we can do with a &longs;tick &longs;ix yards long, though <lb/>the motion of the end of the long &longs;tick, that is of the &longs;tone placed <lb/>in the &longs;lit thereof, were more than double as &longs;wift as the mo­ <lb/>tion of the end of the other &longs;horter &longs;tick, as it would be if <lb/>the velocities were &longs;uch that the le&longs;&longs;er &longs;tick &longs;hould turn thrice <lb/>round in the time whil&longs;t the greater is making one onely con­ <lb/>ver&longs;ion.</s></p><p type="margin"><s><margin.target id="marg384"></margin.target><emph type="italics"/>The cau&longs;e of the <lb/>projection increa&longs;­ <lb/>eth not according <lb/>to the proportion of <lb/>the velocity, in­ <lb/>crea&longs;ed by making <lb/>the wheel bigger.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This which you tell me, <emph type="italics"/>Salviatus,<emph.end type="italics"/> mu&longs;t, I &longs;ee, needs <lb/>&longs;ucceed in this very manner; but I do not &longs;o readily apprehend <lb/>the cau&longs;e why equal velocities &longs;hould not operate equally in <lb/>extruding projects, but that of the le&longs;&longs;er wheel much more than <lb/>the other of the greater wheel; therefore I intreat you to tell me <lb/>how this cometh to pa&longs;s.</s></p><p type="main"><s>SIMP. Herein, <emph type="italics"/>Sagredus,<emph.end type="italics"/> you &longs;eem to differ much from your <lb/>&longs;elf, for that you were wont to penetrate all things in an in&longs;tant, <lb/>and now you have overlook'd a fallacy couched in the experiment <lb/>of the &longs;tick, which I my &longs;elf have been able to di&longs;cover: and this <lb/>is the different manner of operating, in making the projection one <lb/>while with the &longs;hort &longs;ling and another while with the long one, <lb/>for if you will have the &longs;tone fly out of the &longs;lit, you need not con­ <lb/>tinue its motion uniformly, but at &longs;uch time as it is at the &longs;wifte&longs;t, <lb/>you are to &longs;tay your arm, and &longs;top the velocity of the &longs;tick; where­ <lb/>upon the &longs;tone which was in its &longs;wifte&longs;t motion, flyeth out, and <lb/>moveth with impetuo&longs;ity: but now that &longs;top cannot be made in <lb/>the great &longs;tick, which by rea&longs;on of its length and flexibility, doth <lb/>not entirely obey the check of the arm, but continueth to accom­ <lb/>pany the &longs;tone for &longs;ome &longs;pace, and holdeth it in with &longs;o much le&longs;s <lb/>force, and not as if you had with a &longs;tiff &longs;ling &longs;ent it going with a <lb/>jerk: for if both the &longs;ticks or &longs;lings &longs;hould be check'd by one and <lb/>the &longs;ame ob&longs;tacle, I do believe they would fly a&longs;well out of the <lb/>one, as out of the other, howbeit their motions were equally <lb/>&longs;wift.</s></p><p type="main"><s>SAGR. </s><s>With the permi&longs;&longs;ion of <emph type="italics"/>Salviatus,<emph.end type="italics"/> I will an&longs;wer &longs;ome­ <lb/>thing to <emph type="italics"/>Simplicius,<emph.end type="italics"/> in regard he hath addre&longs;&longs;ed him&longs;elf to me; <lb/>and I &longs;ay, that in his di&longs;cour&longs;e there is &longs;omewhat good <lb/>and &longs;omewhat bad: good, becau&longs;e it is almo&longs;t all true; <lb/>bad, becau&longs;e it doth not agree with our ca&longs;e: Truth is, that when <lb/>that which carrieth the &longs;tones with velocity, &longs;hall meet with a <pb xlink:href="040/01/208.jpg" pagenum="190"/>check that is immoveable, they &longs;hall fly out with great impetuo­ <lb/>&longs;ity: the &longs;ame effect following in that ca&longs;e, which we &longs;ee dayly <lb/>to fall out in a boat that running a &longs;wift cour&longs;e, runs a-ground, or <lb/>meets with &longs;ome &longs;udden &longs;top, for all tho&longs;e in the boat, being &longs;ur­ <lb/><arrow.to.target n="marg385"></arrow.to.target> <lb/>prized, &longs;tumble forwards, and fall towards the part whither the <lb/>boat &longs;teered. </s><s>And in ca&longs;e the Earth &longs;hould meet with &longs;uch a <lb/>check, as &longs;hould be able to re&longs;i&longs;t and arre&longs;t its <emph type="italics"/>vertigo,<emph.end type="italics"/> then indeed <lb/>I do believe that not onely bea&longs;ts, buildings and cities, but moun­ <lb/>tains, lakes and &longs;eas would overturn, and the globe it &longs;elf would <lb/>go near to &longs;hake in pieces; but nothing of all this concerns our <lb/>pre&longs;ent purpo&longs;e, for we &longs;peak of what may follow to the motion <lb/>of the Earth, it being turn'd round uniformly, and quietly about <lb/>its own centre, howbeit with a great velocity. </s><s>That likewi&longs;e <lb/>which you &longs;ay of the &longs;lings, is true in part; but was not alledged <lb/>by <emph type="italics"/>Salviatus,<emph.end type="italics"/> as a thing that punctually agreed with the matter <lb/>whereof we treat, but onely, as an example, for &longs;o in gro&longs;s it may <lb/>prompt us in the more accurate con&longs;ideration of that point, whe­ <lb/>ther, the velocity increa&longs;ing at any rate, the cau&longs;e of the proje­ <lb/>ction doth increa&longs;e at the &longs;ame rate: &longs;o that <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> if a wheel of <lb/>ten yards diameter, moving in &longs;uch a manner that a point of its <lb/>circumference will pa&longs;s an hundred yards in a minute of an hour, <lb/>and &longs;o hath an <emph type="italics"/>impetus<emph.end type="italics"/> able to extrude a &longs;tone, that &longs;ame <emph type="italics"/>impetus<emph.end type="italics"/> <lb/>&longs;hall be increa&longs;ed an hundred thou&longs;and times in a wheel of a million <lb/>of yards diameter; the which <emph type="italics"/>Salviatus<emph.end type="italics"/> denieth, and I incline to his <lb/>opinion; but not knowing the rea&longs;on thereof, I have reque&longs;ted it <lb/>of him, and &longs;tand impatiently expecting it.</s></p><p type="margin"><s><margin.target id="marg385"></margin.target><emph type="italics"/>Graming the di­ <lb/>urnal<emph.end type="italics"/> vertigo <emph type="italics"/>of <lb/>the Earth, & that <lb/>by &longs;ome &longs;udden &longs;top <lb/>or ob&longs;tacle it were <lb/>arre&longs;ted, hou&longs;es, <lb/>mountains them­ <lb/>&longs;elves, and perhaps <lb/>the whole Globe <lb/>would be &longs;haken n <lb/>pieces.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I am ready to give you the be&longs;t &longs;atisfaction, that my <lb/>abilities will give leave: And though in my fir&longs;t di&longs;cour&longs;e you <lb/>thought that I had enquired into things e&longs;tranged from our pur­ <lb/>po&longs;e, yet neverthele&longs;&longs;e I believe that in the &longs;equel of the di&longs;pute, <lb/>you will find that they do not prove &longs;o. </s><s>Therefore let <emph type="italics"/>Sagredus<emph.end type="italics"/> <lb/>tell me wherein he hath ob&longs;erved that the re&longs;i&longs;tance of any move­ <lb/>able to motion doth con&longs;i&longs;t.</s></p><p type="main"><s>SAGR. </s><s>I &longs;ee not for the pre&longs;ent that the moveable hath any <lb/>internal re&longs;i&longs;tance to motion, unle&longs;&longs;e it be its natural inclination <lb/>and propen&longs;ion to the contrary motion, as in grave bodies, that <lb/>have a propen&longs;ion to the motion downwards, the re&longs;i&longs;tance is to <lb/>the motion upwards; and I &longs;aid an internal re&longs;i&longs;tance, becau&longs;e <lb/>of this, I think, it is you intend to &longs;peak, and not of the external <lb/>re&longs;i&longs;tances, which are many and accidental.</s></p><p type="main"><s>SALV. </s><s>It is that indeed I mean, and your nimblene&longs;&longs;e of wit <lb/>hath been too hard for my craftine&longs;&longs;e, but if I have been too <lb/>&longs;hort in asking the que&longs;tion, I doubt whether <emph type="italics"/>Sagredus<emph.end type="italics"/> hath been <lb/>full enough in his an&longs;wer to &longs;atis&longs;ie the demand; and whether <lb/>there be not in the moveable, be&longs;ides the natural inclination to the <pb xlink:href="040/01/209.jpg" pagenum="191"/>contrary term, another intrin&longs;ick and natural quality, which ma­ <lb/><arrow.to.target n="marg386"></arrow.to.target> <lb/>keth it aver&longs;e to motion. </s><s>Therefore tell me again; do you not <lb/>think that the inclination <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> of grave bodies to move down­ <lb/>wards, is equal to the re&longs;i&longs;tance of the &longs;ame to the motion of pro­ <lb/>jection upwards?</s></p><p type="margin"><s><margin.target id="marg386"></margin.target><emph type="italics"/>The inclination of <lb/>grave bodies to the <lb/>motion downwards, <lb/>is equal to their <lb/>re&longs;i&longs;tance to the <lb/>motion upwards.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I believe that it is exactly the &longs;ame. </s><s>And for this rea&longs;on <lb/>I &longs;ee that two equal weights being put into a ballance, they do <lb/>&longs;tand &longs;till in <emph type="italics"/>equilibrium,<emph.end type="italics"/> the gravity of the one re&longs;i&longs;ting its be­ <lb/>ing rai&longs;ed by the gravity wherewith the other pre&longs;&longs;ing down­ <lb/>wards would rai&longs;e it.</s></p><p type="main"><s>SALV. </s><s>Very well; &longs;o that if you would have one rai&longs;e up the <lb/>other, you mu&longs;t encrea&longs;e the weight of that which depre&longs;&longs;eth, <lb/>or le&longs;&longs;en the weight of the other. </s><s>But if the re&longs;i&longs;tance to a&longs;cend­ <lb/>ing motion cun&longs;i&longs;t onely in gravity, how cometh it to pa&longs;&longs;e, that <lb/><arrow.to.target n="marg387"></arrow.to.target> <lb/>in ballances of unequal arms, to wit in the ^{*} <emph type="italics"/>Stiliard,<emph.end type="italics"/> a weight <lb/>&longs;ometimes of an hundred pounds, with its pre&longs;&longs;ion downwards, <lb/>doth not &longs;uffice to rai&longs;e up on of four pounds; that &longs;hall counter­ <lb/>poi&longs;e with it, nay this of four, de&longs;cending &longs;hall rai&longs;e up that <lb/>of an hundred; for &longs;uch is the effect of the pendant weight upon <lb/>the weight which we would weigh? </s><s>If the re&longs;i&longs;tance to motion <lb/>re&longs;ideth onely in the gravity, how can the arm with its weight of <lb/>four pounds onely, re&longs;i&longs;t the weight of a &longs;ack of wool, or bale of <lb/>&longs;ilk, which &longs;hall be eight hundred, or a thou&longs;and weight; yea <lb/>more, how can it overcome the &longs;ack with its moment, and rai&longs;e <lb/>it up? </s><s>It mu&longs;t therefore be confe&longs;t <emph type="italics"/>Sagredus,<emph.end type="italics"/> that here it maketh <lb/>u&longs;e of &longs;ome other re&longs;i&longs;tance, and other force, be&longs;ides that of <lb/>&longs;imple gravity.</s></p><p type="margin"><s><margin.target id="marg387"></margin.target>* A portable bal­ <lb/>lance wherewith <lb/>market-people <lb/>weigh their com­ <lb/>modities, giving it <lb/>gravity by remo­ <lb/>ving the weight <lb/>farther from the <lb/>cock: call'd by the <lb/>Latines, <emph type="italics"/>Campana <lb/>trutina.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>It mu&longs;t needs be &longs;o; therefore tell me what this &longs;e­ <lb/>cond virtue &longs;hould be.</s></p><p type="main"><s>SALV. </s><s>It is that which was not in the ballance of equal <lb/>arms; you &longs;ee then what variety there is in the Stiliard; and up­ <lb/>on this doubtle&longs;&longs;e dependeth the cau&longs;e of the new effect.</s></p><p type="main"><s>SAGR. </s><s>I think that your putting me to it a &longs;econd time, hath <lb/>made me remember &longs;omething that may be to the purpo&longs;e. </s><s>In <lb/>both the&longs;e beams the bu&longs;ine&longs;s is done by the weight, and by the <lb/>motion; in the ballance, the motions are equal, and therefore the <lb/>one weight mu&longs;t exceed it in gravity before it can move it; in the <lb/>&longs;tiliard, the le&longs;&longs;er weight will not move the greater, unle&longs;s when <lb/>this latter moveth little, as being &longs;lung at a le&longs;&longs;er di&longs;tance, and the <lb/>other much, as hanging at a greater di&longs;tance from the lacquet or <lb/>cock. </s><s>It is nece&longs;&longs;ary therefore to conclude, that the le&longs;&longs;er weight <lb/>overcometh the re&longs;i&longs;tance of the greater, by moving much, whil&longs;t <lb/>the other is moved but little.</s></p><p type="main"><s>SALV. </s><s>Which is as much as to &longs;ay, that the velocity of the <lb/>moveable le&longs;s grave, compen&longs;ateth the gravity of the moveable <lb/>more grave and le&longs;s &longs;wift. <pb xlink:href="040/01/210.jpg" pagenum="192"/><arrow.to.target n="marg388"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg388"></margin.target><emph type="italics"/>The greater velo­ <lb/>city exactly com­ <lb/>pen&longs;ates thegreater <lb/>gravity.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>But do you think that the velocity doth fully make <lb/>good the gravity? </s><s>that is, that the moment and force of a move­ <lb/>able of <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> four pounds weight, is as great as that of one of an <lb/>hundred weight, when&longs;oever that the fir&longs;t hath an hundred degrees <lb/>of velocity, and the later but four onely?</s></p><p type="main"><s>SALV. </s><s>Yes doubtle&longs;s, as I am able by many experiments to <lb/>demon&longs;trate: but for the pre&longs;ent, let this onely of the &longs;tiliard <lb/>&longs;uffice: in which you &longs;ee that the light end of the beam is then <lb/>able to &longs;u&longs;tain and equilibrate the great Wool &longs;ack, when its di­ <lb/>&longs;tance from the centre, upon which the &longs;tiliard re&longs;teth and turn­ <lb/>eth, &longs;hall &longs;o much exceed the le&longs;&longs;er di&longs;tance, by how much the ab­ <lb/>&longs;olute gravity of the Wool-&longs;ack exceedeth that of the pendent <lb/>weight. </s><s>And we &longs;ee nothing that can cau&longs;e this in&longs;ufficiencie in <lb/>the great &longs;ack of Wool, to rai&longs;e with its weight the pendent <lb/>weight &longs;o much le&longs;s grave, &longs;ave the di&longs;parity of the motions which <lb/>the one and the other &longs;hould make, whil&longs;t that the Wool &longs;ack by <lb/>de&longs;cending but one inch onely, will rai&longs;e the pendent weight an <lb/>hundred inclies: (&longs;uppo&longs;ing that the &longs;ack did weigh an hundred <lb/>times as much, and that the di&longs;tance of the &longs;mall weight from the <lb/>centre of the beam were an hundred times greater, than the di­ <lb/>&longs;tance between the &longs;aid centre and the point of the &longs;acks &longs;u&longs;pen&longs;i­ <lb/>on.) And again, the pendent weight its moving the &longs;pace of an <lb/>hundred inches, in the time that the &longs;ack moveth but one inch <lb/>onely, is the &longs;ame as to &longs;ay, that the velocity of the motion of the <lb/>little pendent weight, is an hundred times greater than the velo­ <lb/>city of the motion of the &longs;ack. </s><s>Now fix it in your belief, as a <lb/>true and manife&longs;t axiom, that the re&longs;i&longs;tance which proceedeth from <lb/>the velocity of motion, compen&longs;ateth that which dependeth on <lb/>the gravity of another moveable: So that con&longs;equently, a move­ <lb/>able of one pound, that moveth with an hundred degrees of ve­ <lb/>locity, doth as much re&longs;i&longs;t all ob&longs;truction, as another moveable <lb/>of an hundred weight, who&longs;e velocity is but one degree onely. <lb/></s><s>And two equal moveables will equally re&longs;i&longs;t their being moved, <lb/>if that they &longs;hall be moved with equal velocity: but if one be <lb/>to be moved more &longs;wiftly than the other, it &longs;hall make greater re­ <lb/>&longs;i&longs;tance, according to the greater velocity that &longs;hall be conferred <lb/>on it. </s><s>The&longs;e things being premi&longs;ed, let us proceed to the expla­ <lb/>nation of our Problem; and for the better under&longs;tanding of <lb/>things, let us make a &longs;hort Scheme thereof. </s><s>Let two unequal <lb/>wheels be de&longs;cribed about this centre A, [<emph type="italics"/>in Fig.<emph.end type="italics"/> 7.] and let the <lb/>circumference of the le&longs;&longs;er be B G, and of the greater C E H, and <lb/>let the &longs;emidiameter A B C, be perpendicular to the Horizon; and <lb/>by the points B and C, let us draw the right lined Tangents B F <lb/>and C D; and in the arches B G and C E, take two equal parts <lb/>B G and C E: and let the two wheels be &longs;uppo&longs;ed to be turn'd <pb xlink:href="040/01/211.jpg" pagenum="193"/>round upon their centres with equal velocities, &longs;o as that two mo­ <lb/>veables, which &longs;uppo&longs;e for example to be two &longs;tones placed in the <lb/>points B and C, come to be carried along the circumferences B G <lb/>and C E, with equal velocities; &longs;o that in the &longs;ame time that the <lb/>&longs;tone B &longs;hall have run the arch B G, the &longs;tone C will have pa&longs;t the <lb/>arch C E. </s><s>I &longs;ay now, that the whirl or <emph type="italics"/>vertigo<emph.end type="italics"/> of the le&longs;&longs;er wheel <lb/>is much more potent to make the projection of the &longs;tone B, than <lb/>the <emph type="italics"/>vertigo<emph.end type="italics"/> of the bigger wheel to make that of the &longs;tone C. <lb/></s><s>Therefore the projection, as we have already declared, being to be <lb/>made along the tangent, when the &longs;tones B and C are to &longs;eparate <lb/>from their wheels, and to begin the motion of projection from the <lb/>points B and C, then &longs;hall they be extruded by the <emph type="italics"/>impetus<emph.end type="italics"/> con­ <lb/>ceived from the <emph type="italics"/>vertigo<emph.end type="italics"/> by (or along) the tangents B F and C D. <lb/></s><s>The two &longs;tones therefore have equal impetuo&longs;ities of running a­ <lb/>long the tangents B F and C D, and would run along the &longs;ame, if <lb/>they were not turn'd a&longs;ide by &longs;ome other force: is it not &longs;o <emph type="italics"/>Sa­ <lb/>gredus<emph.end type="italics"/>?</s></p><p type="main"><s>SAGR. </s><s>In my opinion the bu&longs;ine&longs;&longs;e is as you &longs;ay.</s></p><p type="main"><s>SALV. </s><s>But what force, think you, &longs;hould that be which averts <lb/>the &longs;tones from moving by the tangents, along which they are cer­ <lb/>tainly driven by the <emph type="italics"/>impetus<emph.end type="italics"/> of the <emph type="italics"/>vertigo.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>It is either their own gravity, or el&longs;e &longs;ome glutinous <lb/>matter that holdeth them fa&longs;t and clo&longs;e to the wheels.</s></p><p type="main"><s>SALV. </s><s>But for the diverting of a moveable from the motion <lb/>to which nature inciteth it, is there not required greater or le&longs;&longs;er <lb/>force, according as the deviation is intended to be greater or le&longs;­ <lb/>&longs;er? </s><s>that is, according as the &longs;aid moveable in its deviation hath a <lb/>greater or le&longs;&longs;er &longs;pace to move in the &longs;ame time?</s></p><p type="main"><s>SAGR. </s><s>Yes certainly: for it was concluded even now, that to <lb/>make a moveable to move; the movent vertue mu&longs;t be increa&longs;ed <lb/>in proportion to the velocity wherewith it is to move.</s></p><p type="main"><s>SALV. </s><s>Now con&longs;ider, that for the deviating the &longs;tone upon <lb/>the le&longs;&longs;e wheel from the motion of projection, which it would <lb/>make by the tangent B F, and for the holding of it fa&longs;t to the <lb/>wheel, it is required, that its own gravity draw it back the whole <lb/>length of the &longs;ecant F G, or of the perpendicular rai&longs;ed from the <lb/>point G, to the line B F, whereas in the greater wheel the retracti­ <lb/>on needs to be no more than the &longs;ecant D E, or the perpendicu­ <lb/>lar let fall from the tangent D G to the point E, le&longs;&longs;e by much <lb/>than F G, and alwayes le&longs;&longs;er and le&longs;&longs;er according as the wheel is <lb/>made bigger. </s><s>And fora&longs;much as the&longs;e retractions (as I may call <lb/>them) are required to be made in equal times, that is, whil'&longs;t the <lb/>wheels pa&longs;&longs;e the two equal arches B G and C E, that of the &longs;tone <lb/>B, that is, the retraction F G ought to be more &longs;wift than the o­ <lb/>ther D E; and therefore much greater force will be required for <pb xlink:href="040/01/212.jpg" pagenum="194"/>holding fa&longs;t the &longs;tone B to its little wheel, than for the holding <lb/>the &longs;tone C to its great one, which is as much as to &longs;ay, that &longs;uch <lb/>a &longs;mall thing will impede the extru&longs;ion in the great wheel, as will <lb/>not at all hinder it in the little one. </s><s>It is manife&longs;t therefore that <lb/>the more the wheel augmenteth, the more the cau&longs;e of the pro­ <lb/>jection dimini&longs;heth.</s></p><p type="main"><s>SAGR. </s><s>From this which I now under&longs;tand, by help of your mi­ <lb/>nute di&longs;&longs;ertation, I am induced to think, that I am able to &longs;atisfie <lb/>my judgment in a very few words. </s><s>For equal <emph type="italics"/>impetus<emph.end type="italics"/> being im­ <lb/>pre&longs;&longs;ed on both the &longs;tones that move along the tangents, by the <lb/>equal velocity of the two wheels, we &longs;ee the great circumference, <lb/>by means of its &longs;mall deviation from the tangent, to go &longs;econding, <lb/>as it were, and in a fair way refraining in the &longs;tone the appetite, if <lb/>I may &longs;o &longs;ay, of &longs;eparating from the circumference; &longs;o that any <lb/>&longs;mall retention, either of its own inclination, or of &longs;ome glutina­ <lb/>tion &longs;ufficeth to hold it fa&longs;t to the wheel. </s><s>Which, again, is not a­ <lb/>ble to work the like effect in the little wheel, which but little pro­ <lb/>&longs;ecuting the direction of the tangent, &longs;eeketh with too much ea­ <lb/>gerne&longs;&longs;e to hold fa&longs;t the &longs;tone; and the re&longs;triction and glutination <lb/>not being &longs;tronger than that which holdeth the other &longs;tone fa&longs;t to </s></p><p type="main"><s><arrow.to.target n="marg389"></arrow.to.target> <lb/>the greater wheel, it ^{*} breaks loo&longs;e, and runneth along the tan­ <lb/>gent. </s><s>Therefore I do not only finde that all tho&longs;e have erred, <lb/>who have believed the cau&longs;e of the projection to increa&longs;e accor­ <lb/>ding to the augmentation of the <emph type="italics"/>vertigo's<emph.end type="italics"/> velocity; but I am <lb/>further thinking, that the projection dimini&longs;hing in the inlarging of <lb/>the wheel, &longs;o long as the &longs;ame velocity is reteined in tho&longs;e wheels; <lb/>it may po&longs;&longs;ibly be true, that he that would make the great wheel <lb/>extrude things like the little one, would be forced to increa&longs;e <lb/>them as much in velocity, as they increa&longs;e in diameter, which he <lb/>might do, by making them to fini&longs;h their conver&longs;ions in equal <lb/>times; and thus we may conclude, that the Earths revolution or <lb/><emph type="italics"/>vertigo<emph.end type="italics"/> would be no more able to extrude &longs;tones, than any little <lb/>wheel that goeth &longs;o &longs;lowly, as that it maketh but one turn in twen­ <lb/>ty four hours.</s></p><p type="margin"><s><margin.target id="marg389"></margin.target>* Strappar la ca­ <lb/>vezza, <emph type="italics"/>is to break <lb/>the bridle.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>We will enquire no further into this point for the pre­ <lb/>&longs;ent: let it &longs;uffice that we have abundantly (if I deceive not my <lb/>&longs;elf) demon&longs;trated the invalidity of the argument, which at fir&longs;t <lb/>&longs;ight &longs;eemed very concluding, and was &longs;o held by very famous <lb/>men: and I &longs;hall think my time and words well be&longs;towed, if I <lb/>have but gained &longs;ome belief in the opinion of <emph type="italics"/>Simplicius,<emph.end type="italics"/> I will <lb/>not &longs;ay or the Earths mobility, but only that the opinion of tho&longs;e <lb/>that believe it, is not &longs;o ridiculous and fond, as the rout of vulgar <lb/>Philo&longs;ophers e&longs;teem it.</s></p><p type="main"><s>SIMP. </s><s>The an&longs;wers hitherto produced again&longs;t the arguments <lb/>brought again&longs;t this <emph type="italics"/>Diurnal Revolution<emph.end type="italics"/> of the Earth taken from <pb xlink:href="040/01/213.jpg" pagenum="195"/>grave bodies falling from the top of a Tower, and from proje­ <lb/>ctions made perpendicularly upwards, or according to any inclina­ <lb/>tion &longs;idewayes towards the Ea&longs;t, We&longs;t, North, South, &c. </s><s>have <lb/>&longs;omewhat abated in me the antiquated incredulity I had conceived <lb/>again&longs;t that opinion: but other greater doubts run in my mind <lb/>at this very in&longs;tant, which I know not in the lea&longs;t how to free my <lb/>&longs;elf of, and haply you your &longs;elf will not be able to re&longs;olve them; <lb/>nay, its po&longs;&longs;ible you may not have heard them, for they are very <lb/>modern. </s><s>And the&longs;e are the objections of two Authours, that <emph type="italics"/>ex <lb/>profe&longs;&longs;o<emph.end type="italics"/> write again&longs;t <emph type="italics"/>Copernicus.<emph.end type="italics"/> Some of which are read in a <lb/><arrow.to.target n="marg390"></arrow.to.target> <lb/>little Tract of natural conclu&longs;ions; The re&longs;t are by a great both <lb/>Philo&longs;opher and Mathematician, in&longs;erted in a Treati&longs;e which he <lb/>hath written in favour of <emph type="italics"/>Aristotle,<emph.end type="italics"/> and his opinion touching the <lb/>inalterability of the Heavens, where he proveth, that not onely <lb/>the Comets, but al&longs;o the new &longs;tars, namely, that <emph type="italics"/>anno<emph.end type="italics"/> 1572. in <lb/><emph type="italics"/>Ca&longs;&longs;iopeia,<emph.end type="italics"/> and that <emph type="italics"/>anno<emph.end type="italics"/> 1604. in <emph type="italics"/>Sagittarius<emph.end type="italics"/> were not above the <lb/>Spheres of the Planets, but ab&longs;olutely beneath the concave of <lb/>the Moon in the Elementary Sphere, and this he demon&longs;trateth a­ <lb/>gain&longs;t <emph type="italics"/>Tycho, Kepler,<emph.end type="italics"/> and many other Aftronomical Ob&longs;ervators, <lb/>and beateth them at their own weapon; to wit, the Doctrine of <lb/>Parallaxes. </s><s>If you like thereof, I will give you the rea&longs;ons of <lb/>both the&longs;e Authours, for I have read them more than once, <lb/>with attention; and you may examine their &longs;trength, and give <lb/>your opinion thereon.</s></p><p type="margin"><s><margin.target id="marg390"></margin.target><emph type="italics"/>Other objections <lb/>of two modern Au­ <lb/>thors against<emph.end type="italics"/> Co­ <lb/>pernicus.</s></p><p type="main"><s>SALV. </s><s>In regard that our principal end is to bring upon the <lb/>&longs;tage, and to con&longs;ider what ever hath been &longs;aid for, or again&longs;t the <lb/>two Sy&longs;temes, <emph type="italics"/>Ptolomaick,<emph.end type="italics"/> and <emph type="italics"/>Copernican,<emph.end type="italics"/> it is not good to omit <lb/>any thing that hath been written on this &longs;ubject.</s></p><p type="main"><s>SIMP. </s><s>I will begin therefore with the objections which I finde <lb/>in the Treati&longs;e of Conclu&longs;ions, and afterwards proceed to the <lb/><arrow.to.target n="marg391"></arrow.to.target> <lb/>re&longs;t. </s><s>In the fir&longs;t place then, he be&longs;toweth much paines in calcu­ <lb/>lating exactly how many miles an hour a point of the terre&longs;trial <lb/>Globe &longs;ituate under the Equinoctial, goeth, and how many miles <lb/>are pa&longs;t by other points &longs;ituate in other parallels: and not being <lb/>content with finding out &longs;uch motions in horary times, he findeth <lb/>them al&longs;o in a minute of an hour; and not contenting him&longs;elf <lb/>with a minute, he findes them al&longs;o in a &longs;econd minute; yea more, <lb/>he goeth on to &longs;hew plainly, how many miles a Cannon bullet <lb/>would go in the &longs;ame time, being placed in the concave of the Lu­ <lb/><arrow.to.target n="marg392"></arrow.to.target> <lb/>nar Orb, &longs;uppo&longs;ing it al&longs;o as big as <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf repre&longs;enteth <lb/>it, to take away all &longs;ubterfuges from his adver&longs;ary. </s><s>And having <lb/>made this mo&longs;t ingenious and exqui&longs;ite &longs;upputation, he &longs;heweth, <lb/>that a grave body falling from thence above would con&longs;ume more <lb/>than &longs;ix dayes in attaining to the centre of the Earth, to which all <lb/>grave bodies naturally move. </s><s>Now if by the ab&longs;olute Divine <pb xlink:href="040/01/214.jpg" pagenum="196"/>Power, or by &longs;ome Angel, a very great Cannon bullet were carri­ <lb/>ed up thither, and placed in our Zenith or vertical point, and from <lb/>thence let go at liberty, it is in his, and al&longs;o in my opinion, a mo&longs;t <lb/>incredible thing that it, in de&longs;cending downwards, &longs;hould all the <lb/>way maintain it &longs;elf in our vertical line, continuing to turn round <lb/>with the Earth, about its centre, for &longs;o many dayes, de&longs;cribing <lb/>under the Equinoctial a Spiral line in the plain of the great circle <lb/>it &longs;elf: and under other Parallels, Spiral lines about Cones, and <lb/>under the Poles falling by a &longs;imple right line. </s><s>He, in the next <lb/>place, &longs;tabli&longs;heth and confirmeth this great improbability by pro­ <lb/>ving, in the way of interrogations, many difficulties impo&longs;&longs;ible to <lb/>be removed by the followers of <emph type="italics"/>Copernicus<emph.end type="italics"/>; and they are, if I do <lb/>well remember-----.</s></p><p type="margin"><s><margin.target id="marg391"></margin.target><emph type="italics"/>The fir&longs;t obje­ <lb/>ction of the mo­ <lb/>dern Author of <lb/>the little tract of<emph.end type="italics"/> <lb/>Conclu&longs;ions.</s></p><p type="margin"><s><margin.target id="marg392"></margin.target><emph type="italics"/>A Cannon bul­ <lb/>let would &longs;pend <lb/>more than &longs;ix days <lb/>in falling from the <lb/>Concave of the <lb/>Moon to the cen­ <lb/>tre of the Earth, <lb/>according to the o­ <lb/>pinion of that mo­ <lb/>dern Author of the<emph.end type="italics"/> <lb/>Conclu&longs;ions.</s></p><p type="main"><s>SALV. </s><s>Take up a little, good <emph type="italics"/>Simplicius,<emph.end type="italics"/> and do not load me <lb/>with &longs;o many novelties at once: I have but a bad memory, and <lb/>therefore I mu&longs;t not go too fa&longs;t. </s><s>And in regard it cometh into <lb/>my minde, that I once undertook to calculate how long time &longs;uch a <lb/>grave body falling from the concave of the Moon, would be in <lb/>pa&longs;&longs;ing to the centre of the Earth, and that I think I remember <lb/>that the time would not be &longs;o long; it would be fit that you &longs;hew <lb/>us by what rule this Author made his calculation.</s></p><p type="main"><s>SIMP. </s><s>He hath done it by proving his intent <emph type="italics"/>à fortiori,<emph.end type="italics"/> a &longs;uffi­ <lb/>cient advantage for his adver&longs;aries, &longs;uppo&longs;ing that the velocity of <lb/>the body falling along the vertical line, towards the centre of the <lb/>Earth, were equal to the velocity of its circular motion, which it <lb/>made in the grand circle of the concave of the Lunar Orb. <lb/></s><s>Which by equation would come to pa&longs;&longs;e in an hour, twelve thou­ <lb/>&longs;and &longs;ix hundred German miles, a thing which indeed &longs;avours of <lb/>impo&longs;&longs;ibility: Yet neverthele&longs;&longs;e, to &longs;hew his abundant caution, <lb/>and to give all advantages to his adver&longs;aries, he &longs;uppo&longs;eth it for <lb/>true, and concludeth, that the time o&longs; the fall ought however to <lb/>be more than &longs;ix dayes.</s></p><p type="main"><s>SALV. </s><s>And is this the &longs;um of his method? </s><s>And doth he by <lb/>this demon&longs;tration prove the time of the fall to be above &longs;ix <lb/>dayes?</s></p><p type="main"><s>SAGR. </s><s>Me thinks that he hath behaved him&longs;elf too mode&longs;tly, <lb/>for that having it in the power of his will to give what velocity he <lb/>plea&longs;ed to &longs;uch a de&longs;cending body, and might a&longs;well have made it <lb/>&longs;ix moneths, nay, &longs;ix years in falling to the Earth, he is content <lb/>with &longs;ix dayes. </s><s>But, good <emph type="italics"/>Salviatus,<emph.end type="italics"/> &longs;harpen my appetite a lit­ <lb/>tle, by telling me in what manner you made your computation, in <lb/>regard you &longs;ay, that you have heretofore ca&longs;t it up: for I am con­ <lb/>fident that if the que&longs;tion had not required &longs;ome ingenuity in <lb/>working it, you would never have applied your minde unto <lb/>it.</s></p> <pb xlink:href="040/01/215.jpg" pagenum="197"/><p type="main"><s>SALV. </s><s>It is not enough, <emph type="italics"/>Sagredus,<emph.end type="italics"/> that the &longs;ubjects be noble <lb/>and great, but the bu&longs;ine&longs;&longs;e con&longs;i&longs;ts in handling it nobly. </s><s>And <lb/>who knoweth not, that in the di&longs;&longs;ection of the members of <lb/>a bea&longs;t, there may be di&longs;covered infinite wonders of provident <lb/>and prudent Nature; and yet for one, that the Anatomi&longs;t di&longs;­ <lb/>&longs;ects, the butcher cuts up a thou&longs;and. </s><s>Thus I, who am now <lb/>&longs;eeking how to &longs;atisfie your demand, cannot tell with which of the <lb/>two &longs;hapes I had be&longs;t to appear on the Stage; but yet, taking <lb/>heart from the example of <emph type="italics"/>Simplicius,<emph.end type="italics"/> his Authour, I will, with­ <lb/>out more delays, give you an account (if I have not forgot) how <lb/>I proceeded. </s><s>But before I go any further, I mu&longs;t not omit to tell <lb/>you, that I much fear that <emph type="italics"/>Simplicius<emph.end type="italics"/> hath not faithfully related <lb/>the manner how this his Authour found, that the Cannon bul­ <lb/>let in coming from the concave of the Moon to the centre of the <lb/>Earth, would &longs;pend more than fix dayes: for if he had &longs;uppo­ <lb/>&longs;ed that its velocity in de&longs;cending was equal to that of the <lb/>concave (as <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;aith he doth &longs;uppo&longs;e) he would have <lb/>&longs;hewn him&longs;elf ignorant of the fir&longs;t, and more &longs;imple principles <lb/>of <emph type="italics"/>Geometry<emph.end type="italics"/>; yea, I admire that <emph type="italics"/>Simplicius,<emph.end type="italics"/> in admitting the <lb/>&longs;uppo&longs;ition which he &longs;peaketh of, doth not &longs;ee the mon&longs;trous ab­ <lb/>&longs;urdity that is couched in it.</s></p><p type="main"><s>SIMP. </s><s>Its po&longs;&longs;ible that I may have erred in relating it; but <lb/>that I &longs;ee any fallacy in it, I am &longs;ure is not true.</s></p><p type="main"><s>SALV. </s><s>Perhaps I did not rightly apprehend that which you <lb/>&longs;aid, Do you not &longs;ay, that this Authour maketh the velocity <lb/>of the bullet in de&longs;cending equall to that which it had in tur­ <lb/>ning round, being in the concave of the Moon, and that com­ <lb/>ming down with the &longs;ame velocity, it would reach to the centre <lb/>in &longs;ix dayes?</s></p><p type="main"><s>SIMP. So, as I think, he writeth.</s></p><p type="main"><s>SALV. </s><s>And do not you perceive a &longs;hamefull errour therein? <lb/></s><s>But que&longs;tionle&longs;&longs;e you di&longs;&longs;emble it: For it cannot be, but that <lb/>you &longs;hould know that the &longs;emidiameter of the Circle is le&longs;&longs;e than <lb/><arrow.to.target n="marg393"></arrow.to.target> <lb/>the &longs;ixth part of the circumference; and that con&longs;equently, the <lb/>time in which the moveable &longs;hall pa&longs;&longs;e the &longs;emidiameter, &longs;hall be <lb/>le&longs;&longs;e than the &longs;ixth part of the time; in which, being moved <lb/>with the &longs;ame velocity, it would pa&longs;&longs;e the circumference; and <lb/>that therefore the bullet de&longs;cending with the velocity, where­ <lb/>with it moved in the concave, will arrive in le&longs;&longs;e than four hours <lb/>at the centre, &longs;uppo&longs;ing that in the concave one revolution <lb/>&longs;hould be con&longs;ummate in twenty four hours, as he mu&longs;t of ne­ <lb/>ce&longs;&longs;ity have &longs;uppo&longs;ed it, for to keep it all the way in the &longs;ame <lb/>vertical line.</s></p><p type="margin"><s><margin.target id="marg393"></margin.target><emph type="italics"/>A &longs;hamefull <lb/>errour in the Ar­ <lb/>gument taken from <lb/>the bullets falling <lb/>out of the Moons <lb/>concave.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Now I thorowly perceive the mi&longs;take: but yet I <lb/>would not lay it upon him unde&longs;ervedly, for it's po&longs;&longs;ible that I <pb xlink:href="040/01/216.jpg" pagenum="198"/>may have erred in rehear&longs;ing his Argument, and to avoid running <lb/>into the &longs;ame mi&longs;takes for the future, I could wi&longs;h I had his <lb/>Book; and if you had any body to &longs;end for it, I would take it <lb/>for a great favour.</s></p><p type="main"><s>SAGR. </s><s>You &longs;hall not want a Lacquey that will runne for it <lb/>with all &longs;peed: and he &longs;hall do it pre&longs;ently, without lo&longs;ing any <lb/>time; in the mean time <emph type="italics"/>Salviatus<emph.end type="italics"/> may plea&longs;e to oblige us with his <lb/>computation.</s></p><p type="main"><s>SIMP. </s><s>If he go, he &longs;hall finde it lie open upon my Desk, <lb/>together with that of the other Author, who al&longs;o argueth a­ <lb/>gain&longs;t <emph type="italics"/>Copernicus.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>We will make him bring that al&longs;o for the more cer­ <lb/>tainty: and in the interim <emph type="italics"/>Salviatus<emph.end type="italics"/> &longs;hall make his calculation: I <lb/>have di&longs;patch't away a me&longs;&longs;enger.</s></p><p type="main"><s>SALV. </s><s>Above all things it mu&longs;t be con&longs;idered, that the motion <lb/>of de&longs;cending grave bodies is not uniform, but departing from <lb/><arrow.to.target n="marg394"></arrow.to.target> <lb/>re&longs;t they go continually accelerating: An effect known and ob­ <lb/>&longs;erved by all men, unle&longs;&longs;e it be by the forementioned modern Au­ <lb/>thour, who not &longs;peaking of acceleration, maketh it even and u­ <lb/>niforme. </s><s>But this general notion is of no avail, if it be not known <lb/>according to what proportion this increa&longs;e of velocity is made; a <lb/>conclu&longs;ion that hath been until our times unknown to all <emph type="italics"/>Philo&longs;o­ <lb/>phers<emph.end type="italics"/>; and was fir&longs;t found out & demon&longs;trated by the ^{*} <emph type="italics"/>Academick,<emph.end type="italics"/> <lb/><arrow.to.target n="marg395"></arrow.to.target> <lb/>our common friend, who in &longs;ome of his ^{*} writings not yet publi&longs;h­ <lb/><arrow.to.target n="marg396"></arrow.to.target> <lb/>ed, but in familiarity &longs;hewn to me, and &longs;ome others of his ac­ <lb/>quaintance he proveth, how that the acceleration of the right mo­ <lb/>tion of grave bodies, is made according to the numbers uneven <lb/>beginning <emph type="italics"/>ab unitate,<emph.end type="italics"/> that is, any number of equal times being a&longs;­ <lb/>&longs;igned, if in the fir&longs;t time the moveable departing from re&longs;t &longs;hall <lb/><arrow.to.target n="marg397"></arrow.to.target> <lb/>have pa&longs;&longs;ed &longs;uch a certain &longs;pace, as for example, an ell, in the &longs;e­ <lb/>cond time it &longs;hall have pa&longs;&longs;ed three ells, in the third five, in the <lb/>fourth &longs;even, and &longs;o progre&longs;&longs;ively, according to the following odd <lb/>numbers; which in &longs;hort is the &longs;ame, as if I &longs;hould &longs;ay, that the <lb/>&longs;paces pa&longs;&longs;ed by the moveable departing from its re&longs;t, are unto <lb/><arrow.to.target n="marg398"></arrow.to.target> <lb/>each other in proportion double to the proportion of the times, <lb/>in which tho&longs;e &longs;paces are mea&longs;ured; or we will &longs;ay, that the <lb/>&longs;paces pa&longs;&longs;ed are to each other, as the &longs;quares of their times.</s></p><p type="margin"><s><margin.target id="marg394"></margin.target><emph type="italics"/>An exact com­ <lb/>pute of the time of <lb/>the fall of the Ca­ <lb/>non bullet from the <lb/>Moons concave to <lb/>the Earths centre.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg395"></margin.target>* The Author.</s></p><p type="margin"><s><margin.target id="marg396"></margin.target>* By the&longs;e <emph type="italics"/>Wri­ <lb/>tings,<emph.end type="italics"/> he every <lb/>where meanes his <lb/>Dialogues, <emph type="italics"/>De mo­ <lb/>tu,<emph.end type="italics"/> which I promi&longs;e <lb/>to give you in my <lb/>&longs;econd Volume.</s></p><p type="margin"><s><margin.target id="marg397"></margin.target><emph type="italics"/>Acceleration of <lb/>the natural motion <lb/>of grave bodies is <lb/>made according to <lb/>the odde numbers <lb/>beginning at unity.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg398"></margin.target><emph type="italics"/>The &longs;paces pa&longs;t <lb/>by the falling <lb/>grave body are as <lb/>the &longs;quares of their <lb/>times.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This is truly admirable: and do you &longs;ay that there is <lb/>a Mathematical demon&longs;tration for it?</s></p><p type="main"><s>SALV. Yes, purely Mathematical; and not onely for this, but <lb/>for many other very admirable pa&longs;&longs;ions, pertaining to natural mo­ <lb/>tions, and to projects al&longs;o, all invented, and demon&longs;trated by <emph type="italics"/>Our<emph.end type="italics"/> <lb/><arrow.to.target n="marg399"></arrow.to.target> <lb/><emph type="italics"/>Friend,<emph.end type="italics"/> and I have &longs;een and con&longs;idered them all to my very great <lb/>content and admiration, &longs;eeing a new compleat Doctrine to &longs;pring <lb/>up touching a &longs;ubject, upon which have been written hundreds of <pb xlink:href="040/01/217.jpg" pagenum="199"/>Volumes; and yet not &longs;o much as one of the infinite admirable <lb/>conclu&longs;ions that tho&longs;e his writings contain, hath ever been ob­ <lb/>&longs;erved, or under&longs;tood by any one, before <emph type="italics"/>Our Friend<emph.end type="italics"/> made <lb/>them out.</s></p><p type="margin"><s><margin.target id="marg399"></margin.target><emph type="italics"/>An intire and <lb/>new Science of the<emph.end type="italics"/> <lb/>Academick <emph type="italics"/>concer­ <lb/>ning local motion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>You make me lo&longs;e the de&longs;ire I had to under&longs;tand <lb/>more in our di&longs;putes in hand, onely that I may hear &longs;ome of <lb/>tho&longs;e demon&longs;trations which you &longs;peak of; therefore either give <lb/>them me pre&longs;ently, or at lea&longs;t promi&longs;e me upon your word, to <lb/>appoint a particular conference concerning them, at which <emph type="italics"/>Sim­ <lb/>plicius<emph.end type="italics"/> al&longs;o may be pre&longs;ent, if he &longs;hall have a mind to hear the <lb/>pa&longs;&longs;ions and accidents of the primary effect in Nature.</s></p><p type="main"><s>SIMP. </s><s>I &longs;hall undoubtedly be much plea&longs;ed therewith, though <lb/>indeed, as to what concerneth Natural Philo&longs;ophy, I do not think <lb/>that it is nece&longs;&longs;ary to de&longs;cend unto minute particularities, a gene­ <lb/>ral knowledg of the definition of motion, and of the di&longs;tin­ <lb/>ction of natural and violent, even and accelerate, and the like, <lb/>&longs;ufficing: For if this were not &longs;ufficient, I do not think that <emph type="italics"/>Ari­ <lb/>&longs;totle<emph.end type="italics"/> would have omitted to have taught us what ever more was <lb/>nece&longs;&longs;ary.</s></p><p type="main"><s>SALV. </s><s>It may be &longs;o. </s><s>But let us not lo&longs;e more time about <lb/>this, which I promi&longs;e to &longs;pend half a day apart in, for your &longs;atis­ <lb/>faction; nay, now I remember, I did promi&longs;e you once before to <lb/>&longs;atisfie you herein. </s><s>Returning therefore to our begun calcula­ <lb/>tion of the time, wherein the grave cadent body would pa&longs;s from <lb/>the concave of the Moon to the centre of the Earth, that we may <lb/>not proceed arbitrarily and at randon, but with a Logical method, <lb/>we will fir&longs;t attempt to a&longs;certain our &longs;elves by experiments often <lb/>repeated, in how long time a ball <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> of Iron de&longs;cendeth to the <lb/>Earth from an altitude of an hundred yards.</s></p><p type="main"><s>SAGR. </s><s>Let us therefore take a ball of &longs;uch a determinate <lb/>weight, and let it be the &longs;ame wherewith we intend to make the <lb/>computation of the time of de&longs;cent from the Moon.</s></p><p type="main"><s>SALV. </s><s>This is not material, for that a ball of one, of ten, of an <lb/>hundred, of a thou&longs;and pounds, will all mea&longs;ure the &longs;ame hundred <lb/>yards in the &longs;ame time.</s></p><p type="main"><s>SIMP. </s><s>But this I cannot believe, nor much le&longs;s doth <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>think &longs;o, who writeth, that the velocities of de&longs;cending grave <lb/>bodies, are in the &longs;ame proportion to one another, as their gra­ <lb/>vities.</s></p><p type="main"><s>SALV. </s><s>If you will admit this for true, <emph type="italics"/>Simplicius,<emph.end type="italics"/> you mu&longs;t be­ <lb/><arrow.to.target n="marg400"></arrow.to.target> <lb/>lieve al&longs;o, that two balls of the &longs;ame matter, being let fall in the <lb/>&longs;ame moment, one of an hundred pounds, and another of one, <lb/>from an altitude of an hundred yards, the great one arriveth at the <lb/>ground, before the other is de&longs;cended but one yard onely: Now <lb/>bring your fancy, if you can, to imagine, that you &longs;ee the great <pb xlink:href="040/01/218.jpg" pagenum="200"/>ball got to the ground, when the little one is &longs;till within le&longs;s than <lb/>a yard of the top of the Tower.</s></p><p type="margin"><s><margin.target id="marg400"></margin.target><emph type="italics"/>The error of<emph.end type="italics"/> Ari­ <lb/>&longs;totle <emph type="italics"/>in affirming, <lb/>falling grave bo­ <lb/>dies to move accor­ <lb/>ding to the propor­ <lb/>tion of their gravi­ <lb/>ties.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>That this propo&longs;ition is mo&longs;t fal&longs;e, I make no doubt in <lb/>the world; but yet that yours is ab&longs;olutely true, I cannot well <lb/>a&longs;&longs;ure my &longs;elf: neverthele&longs;s, I believe it, &longs;eeing that you &longs;o re­ <lb/>&longs;olutely affirm it; which I am &longs;ure you would not do, if you had <lb/>not certain experience, or &longs;ome clear demon&longs;tration thereof.</s></p><p type="main"><s>SALV. </s><s>I have both: and when we &longs;hall handle the bu&longs;ine&longs;s <lb/>of motions apart, I will communicate them: in the interim, that <lb/>we may have no more occa&longs;ions of interrupting our di&longs;cour&longs;e, we <lb/>will &longs;uppo&longs;e, that we are to make our computation upon a ball of <lb/><arrow.to.target n="marg401"></arrow.to.target> <lb/>Iron of an hundred <emph type="italics"/>(a)<emph.end type="italics"/> pounds, the which by reiterated experi­ <lb/>ments de&longs;cendeth from the altitude of an hundred <emph type="italics"/>(b)<emph.end type="italics"/> yards, in <lb/>five &longs;econd-minutes of an hour. </s><s>And becau&longs;e, as we have &longs;aid, <lb/>the &longs;paces that are mea&longs;ured by the cadent moveable, increa&longs;e in <lb/>double proportion; that is, according to the &longs;quares of the times, <lb/>being that the time of one fir&longs;t-minute is duodecuple to the time <lb/>of five &longs;econds, if we multiply the hundred yards by the &longs;quare of <lb/>12, that is by 144, we &longs;hall have 14400, which &longs;hall be the num­ <lb/>ber of yards that the &longs;ame moveable &longs;hall pa&longs;s in one fir&longs;t-minute <lb/>of an hour: and following the &longs;ame rule becau&longs;e one hour is 60 <lb/>minutes, multiplying 14400, the number of yards pa&longs;t in one mi­ <lb/>nute, by the &longs;quare of 60, that is, by 3600, there &longs;hall come forth <lb/>51840000, the number of yards to be pa&longs;&longs;ed in an hour, which <lb/>make 17280 miles. </s><s>And de&longs;iring to know the &longs;pace that the &longs;aid <lb/>ball would pa&longs;s in 4 hours, let us multiply 17280 by 16, (which <lb/>is the &longs;quare of 4) and the product will be 276480 miles: which <lb/>number is much greater than the di&longs;tance from the Lunar concave <lb/>to the centre of the Earth, which is but 196000 miles, making the <lb/>di&longs;tance of the concave 56 &longs;emidiameters of the Earth, as that mo­ <lb/>dern Author doth; and the &longs;emidiameter of the Earth 3500 miles, <lb/><arrow.to.target n="marg402"></arrow.to.target> <lb/>of 3000 ^{*}<emph type="italics"/>Braces<emph.end type="italics"/> to a †mile, which are our <emph type="italics"/>Italian<emph.end type="italics"/> miles.</s></p><p type="margin"><s><margin.target id="marg401"></margin.target><emph type="italics"/>(a) (b)<emph.end type="italics"/> Note that <lb/>the&longs;e Calculations <lb/>are made in <emph type="italics"/>Itali­ <lb/>an<emph.end type="italics"/> weights and <lb/>mea&longs;ures. </s><s>And 100 <lb/>pounds <emph type="italics"/>Haverdu­ <lb/>poi&longs;e<emph.end type="italics"/> make 131 <emph type="italics"/>l. <lb/></s><s>Florentine.<emph.end type="italics"/> And <lb/>100 Engli&longs;h yards <lb/>makes 150 2/5 Braces <lb/><emph type="italics"/>Florent.<emph.end type="italics"/> &longs;o that the <lb/>brace or yard of <lb/>our <emph type="italics"/>Author<emph.end type="italics"/> is 3/4 <lb/>of cur yard.</s></p><p type="margin"><s><margin.target id="marg402"></margin.target>* The <emph type="italics"/>Italian<emph.end type="italics"/> mea­ <lb/>&longs;ure which I com­ <lb/>monly tran&longs;l te <lb/>yards.</s></p><p type="main"><s>Therefore, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that &longs;pace from the concave of the Moon <lb/>to the centre of the Earth, which your Accomptant &longs;aid could <lb/><arrow.to.target n="marg403"></arrow.to.target> <lb/>not be pa&longs;&longs;ed under more than &longs;ix days, you &longs;ee that (computing <lb/>by experience, and not upon the fingers ends) that it &longs;hall be pa&longs;­ <lb/>&longs;ed in much le&longs;s than four hours; and making the computation <lb/>exact, it &longs;hall be pa&longs;&longs;ed by the moveable in 3 hours, 22 <emph type="italics"/>min. </s><s>prim.<emph.end type="italics"/> <lb/>and 4 &longs;econds.</s></p><p type="margin"><s><margin.target id="marg403"></margin.target>† The <emph type="italics"/>Italian<emph.end type="italics"/> mile <lb/>is 1000/1056 of our mile.</s></p><p type="main"><s>SAGR. </s><s>I be&longs;eech you, dear Sir, do not defraud me of this ex­ <lb/>act calculation, for it mu&longs;t needs be very excellent.</s></p><p type="main"><s>SALV. </s><s>So indeed it is: therefore having (as I have &longs;aid) by <lb/>diligent tryal ob&longs;erved, that &longs;uch a moveable pa&longs;&longs;eth in its de&longs;cent, <lb/>the height of 100 yards in 5 &longs;econds of an hour, we will &longs;ay, if <lb/>100 yards are pa&longs;&longs;ed in 5 &longs;econds; in how many &longs;econds &longs;hall <pb xlink:href="040/01/219.jpg" pagenum="201"/>588000000 yards (for &longs;o many are in 56 diameters of the Earth) <lb/>be pa&longs;&longs;ed? </s><s>The rule for this work is, that the third number mu&longs;t <lb/>be multiplied by the &longs;quare of the &longs;econd, of which doth come <lb/>14700000000, which ought to be divided by the fir&longs;t, that is, by <lb/>100, and the root &longs;quare of the quotient, that is, 12124 is the <lb/>number &longs;ought, namely 12124 <emph type="italics"/>min. </s><s>&longs;ecun.<emph.end type="italics"/> of an hour, which are <lb/>3 hours, 22 <emph type="italics"/>min. </s><s>prim.<emph.end type="italics"/> and 4 &longs;econds.</s></p><p type="main"><s>SAGR. </s><s>I have &longs;een the working, but I know nothing of the <lb/>rea&longs;on for &longs;o working, nor do I now think it a time to ask it.</s></p><p type="main"><s>SALV. </s><s>Yet I will give it, though you do not ask it, becau&longs;e it <lb/>is very ea&longs;ie. </s><s>Let us mark the&longs;e three numbers with the Letters <lb/>A fir&longs;t, B &longs;econd, C <lb/><figure id="id.040.01.219.1.jpg" xlink:href="040/01/219/1.jpg"/> <lb/>third. </s><s>A and C are the <lb/>numbers of the &longs;paces, <lb/>B is the number of the <lb/>time; the fourth number <lb/>is &longs;ought, of the time <lb/>al&longs;o. </s><s>And becau&longs;e we <lb/>know, that look what <lb/>proportion the &longs;pace A, <lb/>hath to the &longs;puace C, the <lb/>&longs;ame proportion &longs;hall the <lb/>&longs;quare of the time B <lb/>have to the &longs;qare of the <lb/>time, which is &longs;ought. <lb/></s><s>Therefore by the Golden Rule, let the number C be multi­ <lb/>plied by the &longs;quare of the number B, and let the product be di­ <lb/>vided by the number A, and the quotient &longs;hall be the &longs;quare of <lb/>the number &longs;ought, and its &longs;quare root &longs;hall be the number it &longs;elf <lb/>that is &longs;ought. </s><s>Now you &longs;ee how ea&longs;ie it is to be under&longs;tood.</s></p><p type="main"><s>SAGR. </s><s>So are all truths, when once they are found out, but the <lb/>difficulty lyeth in finding them. </s><s>I very well apprehend it, and kindly <lb/>thank you. </s><s>And if there remain any other curio&longs;ity touching this <lb/>point, I pray you let us hear it; for if I may &longs;peak my mind, I <lb/>will with the favour of <emph type="italics"/>Simplicius,<emph.end type="italics"/> that from your di&longs;cour&longs;es I al­ <lb/>wayes learn &longs;ome new motion, but from tho&longs;e of his Philo&longs;o­ <lb/>phers, I do not remember that I have learn't any thing of mo­ <lb/>ment.</s></p><p type="main"><s>SALV. </s><s>There might be much more &longs;aid touching the&longs;e local <lb/>motions; but according to agreement, we will re&longs;erve it to a par­ <lb/>ticular conference, and for the pre&longs;ent I will &longs;peak &longs;omething <lb/>touching the Author named by <emph type="italics"/>Simplicius,<emph.end type="italics"/> who thinketh he hath <lb/>given a great advantage to the adver&longs;e party in granting that, that <lb/>Canon bullet in falling from the concave of the Moon may de­ <lb/>&longs;cend with a velocity equal to the velocity wherewith it would <pb xlink:href="040/01/220.jpg" pagenum="202"/>turn round, &longs;taying there above, and moving along with the di­ <lb/>urnal conver&longs;ion. </s><s>Now I tell him, that that &longs;ame ball falling from <lb/>the concave unto the centre, will acquire a degree of velocity <lb/>much more than double the velocity of the diurnal motion of the <lb/>Lunar concave; and this I will make out by &longs;olid and not imper­ <lb/><arrow.to.target n="marg404"></arrow.to.target> <lb/>tinent &longs;uppo&longs;itions. </s><s>You mu&longs;t know therefore that the grave <lb/>body falling and acquiring all the way new velocity according <lb/>to the proportion already mentioned, hath in any what&longs;oever <lb/>place of the line of its motion &longs;uch a degree of velocity, that if it <lb/>&longs;hould continue to move therewith, uniformly without farther <lb/>encrea&longs;ing it; in another time like to that of its de&longs;cent, it would <lb/>pa&longs;&longs;e a &longs;pace double to that pa&longs;&longs;ed in the line of the precedent <lb/>motion of de&longs;cent. </s><s>And thus for example, if that ball in coming <lb/>from the concave of the Moon to its centre hath &longs;pent three hours, <lb/>22 min. <emph type="italics"/>prim.<emph.end type="italics"/> and 4 &longs;econds, I &longs;ay, that being arrived at the cen­ <lb/>tre, it &longs;hall find it &longs;elf con&longs;tituted in &longs;uch a degree of velocity, that <lb/>if with that, without farther encrea&longs;ing it, it &longs;hould continue to <lb/>move uniformly, it would in other 3 hours, 22 min. <emph type="italics"/>prim.<emph.end type="italics"/> and <lb/>4 &longs;econds, pa&longs;&longs;e double that &longs;pace, namely as much as the whole <lb/>diameter of the Lunar Orb; and becau&longs;e from the Moons con­ <lb/>cave to the centre are 196000 miles, which the ball pa&longs;&longs;eth in 3 <lb/>hours 22 <emph type="italics"/>prim.<emph.end type="italics"/> min. </s><s>and 4 &longs;econds, therefore (according to what <lb/>hath been &longs;aid) the ball continuing to move with the velocity <lb/>which it is found to have in its arrival at the centre, it would <lb/>pa&longs;&longs;e in other 3 hours 22 min. </s><s>prim. </s><s>and 4 &longs;econds, a &longs;pace dou­ <lb/>ble to that, namely 392000 miles; but the &longs;ame continuing in <lb/>the concave of the Moon, which is in circuit 1232000 miles, and <lb/>moving therewith in a diurnal motion, it would make in the &longs;ame <lb/>time, that is in 3 hours 22 min. </s><s>prim. </s><s>and 4 &longs;econds, 172880 <lb/>miles, which are fewer by many than the half of the 392000 <lb/>miles. </s><s>You &longs;ee then that the motion in the concave is not as the <lb/>modern Author &longs;aith, that is, of a velocity impo&longs;&longs;ible for the fall­ <lb/>ing ball to partake of, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg404"></margin.target><emph type="italics"/>The falling move­ <lb/>able if it move with <lb/>a degree of veloci­ <lb/>ty acquired in a <lb/>like time with an <lb/>uniform motion, it <lb/>&longs;hall paß a &longs;pace <lb/>double to that pa&longs;­ <lb/>&longs;ed with the acce­ <lb/>leratedmotion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The di&longs;cour&longs;e would pa&longs;s for current, and would give <lb/>me full &longs;atisfaction, if that particular was but &longs;alved, of the mo­ <lb/>ving of the moveable by a double &longs;pace to that pa&longs;&longs;ed in falling <lb/>in another time equal to that of the de&longs;cent, in ca&longs;e it doth continue <lb/>to move uniformly with the greate&longs;t degree of velocity acquired <lb/>in de&longs;cending. </s><s>A propo&longs;ition which you al&longs;o once before &longs;uppo­ <lb/>&longs;ed as true, but never demon&longs;trated.</s></p><p type="main"><s>SALV. </s><s>This is one of the demon&longs;trations of <emph type="italics"/>Our Friend,<emph.end type="italics"/> and <lb/>you &longs;hall &longs;ee it in due time; but for the pre&longs;ent, I will with &longs;ome <lb/>conjectures (not teach you any thing that is new, but) remember you <lb/>of a certain contrary opinion, and &longs;hew you, that it may haply &longs;o be. <lb/></s><s>A bullet of lead hanging in a long and fine thread fa&longs;tened to the <pb xlink:href="040/01/221.jpg" pagenum="203"/>roof, if we remove it far from perpendicularity, and then let it go, <lb/>have you not ob&longs;erved that, it declining, will pa&longs;s freely, and well <lb/>near as far to the other &longs;ide of the perpendicular?</s></p><p type="main"><s>SAGR. </s><s>I have ob&longs;erved it very well, and find (e&longs;pecially if the <lb/>plummet be of any con&longs;iderable weight) that it ri&longs;eth &longs;o little le&longs;s <lb/>than it de&longs;cended, &longs;o that I have &longs;ometimes thought, that the a­ <lb/>&longs;cending arch is equal to that de&longs;cending, and thereupon made it <lb/>a que&longs;tion whether the vibrations might not perpetuate them&longs;elves; <lb/>and I believe that they might, if that it were po&longs;&longs;ible to remove <lb/><arrow.to.target n="marg405"></arrow.to.target> <lb/>the impediment of the Air, which re&longs;i&longs;ting penetration, doth &longs;ome <lb/>&longs;mall matter retard and impede the motion of the <emph type="italics"/>pendulum,<emph.end type="italics"/> <lb/>though indeed that impediment is but &longs;mall: in favour of which <lb/>opinion the great number of vibrations that are made before the <lb/>moveable wholly cea&longs;eth to move, &longs;eems to plead.</s></p><p type="margin"><s><margin.target id="marg405"></margin.target><emph type="italics"/>The motion of <lb/>grave<emph.end type="italics"/> penduli <lb/><emph type="italics"/>might be perpetua­ <lb/>ted, impediments <lb/>being removed.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The motion would not be perpetual, <emph type="italics"/>Sagredus,<emph.end type="italics"/> al­ <lb/>though the impediment of the Air were totally removed, becau&longs;e <lb/>there is another much more ab&longs;tru&longs;e.</s></p><p type="main"><s>SAGR. </s><s>And what is that? </s><s>as for my part I can think of no <lb/>other?</s></p><p type="main"><s>SALV. </s><s>You will be plea&longs;ed when you hear it, but I &longs;hall not <lb/>tell it you till anon: in the mean time, let us proceed. </s><s>I have <lb/>propo&longs;ed the ob&longs;ervation of this <emph type="italics"/>Pendulum,<emph.end type="italics"/> to the intent, that you <lb/>&longs;hould under&longs;tand, that the <emph type="italics"/>impetus<emph.end type="italics"/> acquired in the de&longs;cending <lb/>arch, where the motion is natural, is of it &longs;elf able to drive the <lb/>&longs;aid ball with a violent motion, as far on the other &longs;ide in the like <lb/>a&longs;cending arch; if &longs;o, I &longs;ay, of it &longs;elf, all external impediments <lb/>being removed: I believe al&longs;o that every one takes it for granted, <lb/>that as in the de&longs;cending arch the velocity all the way increa&longs;eth, <lb/>till it come to the lowe&longs;t point, or its perpendicularity; &longs;o from <lb/>this point, by the other a&longs;cending arch, it all the wav dimini&longs;heth, <lb/>untill it come to its extreme and highe&longs;t point: and dimini&longs;hing <lb/>with the &longs;ame proportions, where with it did before increa&longs;e, &longs;o that <lb/>the dgrees of the velocities in the points equidi&longs;tant from the point <lb/>of perpendicularity, are equal to each other. </s><s>Hence it &longs;eemeth <lb/>to me (arguing with all due mode&longs;ty) that I might ea&longs;ily be induced <lb/>to believe, that if the Terre&longs;trial Globe were bored thorow the <lb/><arrow.to.target n="marg406"></arrow.to.target> <lb/>centre, a Canon bullet de&longs;cending through that Well, would ac­ <lb/>quire by that time it came to the centre, &longs;uch an impul&longs;e of velo­ <lb/>city, that, it having pa&longs;&longs;ed beyond the centre, would &longs;pring it up­ <lb/>wards the other way, as great a &longs;pace, as that was wherewith it had <lb/>de&longs;cended, all the way beyond the centre dimini&longs;hing the velocity <lb/>with decrea&longs;ements like to the increa&longs;ements acquired in the de­ <lb/>&longs;cent: and the time &longs;pent in this &longs;econd motion of a&longs;cent, I be­ <lb/>lieve, would be equal to the time of de&longs;cent. </s><s>Now if the move­ <lb/>able by dimini&longs;hing that its greate&longs;t degree of velocity which it <pb xlink:href="040/01/222.jpg" pagenum="204"/>had in the centre, &longs;ucce&longs;&longs;ively until it come to total extinction, <lb/>do carry the moveable in &longs;uch a time &longs;uch a certain &longs;pace, as it had <lb/>gone in &longs;uch a like quantity of time, by the acqui&longs;t of velocity <lb/>from the total privation of it until it came to that its greate&longs;t degree; <lb/>it &longs;eemeth very rea&longs;onable, that if it &longs;hould move always with the <lb/>&longs;aid greate&longs;t degree of velocity it would pa&longs;s, in &longs;uch another <lb/>quantity of time, both tho&longs;e &longs;paces: For if we do but in our <lb/>mind &longs;ucce&longs;&longs;ively divide tho&longs;e velocities into ri&longs;ing and falling <lb/>degrees, as <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> the&longs;e numbers in the margine; &longs;o that the <lb/>fir&longs;t &longs;ort unto 10 be &longs;uppo&longs;ed the increa&longs;ing velocities, and the <lb/>others unto 1, be the decrea&longs;ing; and let tho&longs;e of the time <lb/>of the de&longs;cent, and the others of the time of the a&longs;cent being <lb/>added all together, make as many, as if one of the two &longs;ums of <lb/>them had been all of the greate&longs;t degrees, and therefore the <lb/>whole &longs;pace pa&longs;&longs;ed by all the degrees of the increa&longs;ing veloci­ <lb/>ties, and decrea&longs;ing, (which put together is the whole diame­ <lb/>ter) ought to be equal to the &longs;pace pa&longs;&longs;ed by the greate&longs;t velo­ <lb/>cities, that are in number half the aggregate of the increa&longs;ing <lb/>and decrea&longs;ing velocities. </s><s>I know that I have but ob&longs;curely <lb/>expre&longs;&longs;ed my &longs;elf, and I wi&longs;h I may be under&longs;tood.</s></p><p type="margin"><s><margin.target id="marg406"></margin.target><emph type="italics"/>If the Terre&longs;trial <lb/>Globe were perfo­ <lb/>rated, a grave bo­ <lb/>dy de&longs;cending by <lb/>that bore, would <lb/>paß and a&longs;cend as <lb/>far beyond the cen­ <lb/>tre, as it did de­ <lb/>&longs;cend.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I think I under&longs;tand you very well; and al&longs;o that I <lb/>can in a few words &longs;hew, that I do under&longs;tand you. </s><s>You had <lb/>a mind to &longs;ay, that the motion begining from re&longs;t, and all the <lb/>way increa&longs;ing the velocity with equal augmentations, &longs;uch as <lb/>are tho&longs;e of continuate numbers begining at 1, rather at 0, <lb/>which repre&longs;enteth the &longs;tate of re&longs;t, di&longs;po&longs;ed as in the margine: <lb/>and continued at plea&longs;ure, &longs;o as that the lea&longs;t degree may be 0, <lb/>and the greate&longs;t <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> 5, all the&longs;e degrees of velocity wherewith <lb/>the moveable is moved, make the &longs;um of 15; but if the <lb/>moveable &longs;hould move with as many degrees in number as <lb/>the&longs;e are, and each of them equal to the bigge&longs;t, which is 5, the <lb/>aggregate of all the&longs;e la&longs;t velocities would be double to the <lb/>others, namely 30. And therefore the moveable moving with <lb/>a like time, but with uniform velocity, which is that of the <lb/>highe&longs;t degree 5, ought to pa&longs;s a &longs;pace double to that which it <lb/>pa&longs;&longs;eth in the accelerate time, which beginneth at the &longs;tate of re&longs;t.</s></p><p type="main"><s>SALV. </s><s>According to your quick and piercing way of appre­ <lb/>hending things, you have explained the whole bu&longs;ine&longs;s with more <lb/>plainne&longs;s than I my &longs;elf; and put me al&longs;o in mind of adding &longs;ome­ <lb/>thing more: for in the accelerate motion, the augmentation be­ <lb/>ing continual, you cannot divide the degrees of velocity, which <lb/>continually increa&longs;e, into any determinate number, becau&longs;e chan­ <lb/>ging every moment, they are evermore infinite. </s><s>Therefore we <lb/>&longs;hall be the better able to exemplifie our intentions by de&longs;cribing <lb/>a Triangle, which let be this A B C, [<emph type="italics"/>in Fig.<emph.end type="italics"/> 8.] taking in the <pb xlink:href="040/01/223.jpg" pagenum="205"/>&longs;ide A C, as many equal parts as we plea&longs;e, A D, D E, E F, F G, <lb/>and drawing by the points D, E, F, G, right lines parallel to the ba&longs;e <lb/>B C. </s><s>Now let us imagine the parts marked in the line A C, to be <lb/>equal times, and let the parallels drawn by the points D, E, F, G, <lb/>repre&longs;ent unto us the degrees of velocity accelerated, and increa&longs;­ <lb/>ing equally in equal times; and let the point A be the &longs;tate of re&longs;t, <lb/>from which the moveable departing, hath <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> in the time A D, <lb/>acquired the degree of velocity D H, in the &longs;econd time we will <lb/>&longs;uppo&longs;e, that it hath increa&longs;ed the velocity from D H, as far as to <lb/>E I, and &longs;o &longs;uppo&longs;ing it to have grown greater in the &longs;ucceeding <lb/>times, according to the increa&longs;e of the lines F K, G L, <emph type="italics"/>&c.<emph.end type="italics"/> but <lb/><arrow.to.target n="marg407"></arrow.to.target> <lb/>becau&longs;e the acceleration is made continually from moment to mo­ <lb/>ment, and not disjunctly from one certain part of time to another; <lb/>the point A being put for the lowe&longs;t moment of velocity, that is, <lb/>for the &longs;tate of re&longs;t, and A D for the fir&longs;t in&longs;tant of time follow­ <lb/>ing; it is manife&longs;t, that before the acqui&longs;t of the degree of velocity <lb/>D H, made in the time A D, the moveable mu&longs;t have pa&longs;t by <lb/>infinite other le&longs;&longs;er and le&longs;&longs;er degrees gained in the infinite in&longs;tants <lb/>that are in the time D A, an&longs;wering the infinite points that are in <lb/>the line D A; therefore to repre&longs;ent unto us the infinite degrees <lb/>of velocity that precede the degree D H, it is nece&longs;&longs;ary to imagine <lb/>infinite lines &longs;ucce&longs;&longs;ively le&longs;&longs;er and le&longs;&longs;er, which are &longs;uppo&longs;ed to <lb/>be drawn by the infinite points of the line D A, and parallels to <lb/>D H, the which infinite lines repre&longs;ent unto us the &longs;uperficies of <lb/>the Triangle A H D, and thus we may imagine any &longs;pace pa&longs;&longs;ed <lb/>by the moveable, with a motion which begining at re&longs;t, goeth uni­ <lb/>formly accelerating, to have &longs;pent and made u&longs;e of infinite degrees <lb/>of velocity, increa&longs;ing according to the infinite lines that begin­ <lb/>ing from the point A, are &longs;uppo&longs;ed to be drawn parallel to the <lb/>line H D, and to the re&longs;t I E, K F, L G, the motion continuing as <lb/>far as one will.</s></p><p type="margin"><s><margin.target id="marg407"></margin.target><emph type="italics"/>The acceleration <lb/>of grave bodies na­ <lb/>turally de&longs;cendent, <lb/>increa&longs;eth from <lb/>moment to moment.<emph.end type="italics"/></s></p><p type="main"><s>Now let us compleat the whole Parallelogram A M B C, and let <lb/>us prolong as far as to the &longs;ide thereof B M, not onely the Parallels <lb/>marked in the Triangle, but tho&longs;e infinite others imagined to be <lb/>drawn from all the points of the &longs;ide A C; and like as B C, was <lb/>the greate&longs;t of tho&longs;e infinite parallels of the Triangle, repre&longs;ent­ <lb/>ing unto us the greate&longs;t degree of velocity acquired by the move­ <lb/>able in the accelerate motion, and the whole &longs;uperficies of the &longs;aid <lb/>Triangle, was the ma&longs;s and &longs;um of the whole velocity, wherewith <lb/>in the time A C it pa&longs;&longs;ed &longs;uch a certain &longs;pace, &longs;o the parallelogram <lb/>is now a ma&longs;s and aggregate of a like number of degrees of ve­ <lb/>locity, but each equal to the greate&longs;t B C, the which ma&longs;s of ve­ <lb/>locities will be double to the ma&longs;s of the increa&longs;ing velocities in <lb/>the Triangle, like as the &longs;aid Parallelogram is double to the Tri­ <lb/>angle: and therefore if the moveable, that falling did make u&longs;e <pb xlink:href="040/01/224.jpg" pagenum="206"/>of the accelerated degrees of velocity, an&longs;wering to the triangle <lb/>A B C, hath pa&longs;&longs;ed in &longs;uch a time &longs;uch a &longs;pace, it is very rea&longs;onable <lb/>and probable, that making u&longs;e of the uniform velocities an&longs;wering <lb/>to the parallelogram, it &longs;hall pa&longs;&longs;e with an even motion in the <lb/>&longs;ame time a &longs;pace double to that pa&longs;&longs;ed by the accelerate mo­ <lb/>tion.</s></p><p type="main"><s>SAGR. </s><s>I am entirely &longs;atisfied. </s><s>And if you call this a probable <lb/>Di&longs;cour&longs;e, what &longs;hall the nece&longs;&longs;ary demon&longs;trations be? </s><s>I wi&longs;h <lb/>that in the whole body of common Philo&longs;ophy, I could find one <lb/>that was but thus concludent. <lb/><arrow.to.target n="marg408"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg408"></margin.target><emph type="italics"/>In natural Sci­ <lb/>ences it is not ne­ <lb/>ce&longs;&longs;ary to &longs;eek Ma­ <lb/>thematicall evi­ <lb/>dence.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>It is not nece&longs;&longs;ary in natural Philo&longs;ophy to &longs;eek exqui­ <lb/>&longs;ite Mathematical evidence.</s></p><p type="main"><s>SAGR. </s><s>But this point of motion, is it not a natural que&longs;tion? <lb/></s><s>and yet I cannot find that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath demon&longs;trated any the <lb/>lea&longs;t accident of it. </s><s>But let us no longer divert our intended <lb/>Theme, nor do you fail, I pray you <emph type="italics"/>Salviatus,<emph.end type="italics"/> to tell me that <lb/>which you hinted to me to be the cau&longs;e of the <emph type="italics"/>Pendulum's<emph.end type="italics"/> qui­ <lb/>e&longs;cence, be&longs;ides the re&longs;i&longs;tance of the <emph type="italics"/>Medium<emph.end type="italics"/> ro penetration.</s></p><p type="main"><s>SALV. </s><s>Tell me; of two <emph type="italics"/>penduli<emph.end type="italics"/> hanging at unequal di&longs;tan­ <lb/>ces, doth not that which is fa&longs;tned to the longer threed make its <lb/>vibrations more &longs;eldome?</s></p><p type="main"><s><arrow.to.target n="marg409"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg409"></margin.target><emph type="italics"/>The<emph.end type="italics"/> pendulum <lb/><emph type="italics"/>hanging at a long­ <lb/>er threed, maketh <lb/>its vibrations more <lb/>&longs;eldome than the<emph.end type="italics"/> <lb/>pendulum <emph type="italics"/>hanging <lb/>at a &longs;horter threed.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. Yes, if they be moved to equall di&longs;tances from their <lb/>perpendicularity.</s></p><p type="main"><s>SALV. </s><s>This greater or le&longs;&longs;e elongation importeth nothing at <lb/>all, for the &longs;ame <emph type="italics"/>pendulum<emph.end type="italics"/> alwayes maketh its reciprocations in e­ <lb/>quall times, be they longer or &longs;horter, that is, though the <emph type="italics"/>pendulum<emph.end type="italics"/></s></p><p type="main"><s><arrow.to.target n="marg410"></arrow.to.target> <lb/>be little or much removed from its perpendicularity, and if they <lb/>are not ab&longs;olutely equal, they are in&longs;en&longs;ibly different, as expe­ <lb/>rience may &longs;hew you: and though they were very unequal, yet <lb/>would they not di&longs;countenance, but favour our cau&longs;e. </s><s>There­ <lb/>fore let us draw the perpendicular A B [<emph type="italics"/>in Fig.<emph.end type="italics"/> 9.] and hang from <lb/>the point A, upon the threed A C, a plummet C, and another up­ <lb/>on the &longs;ame threed al&longs;o, which let be E, and the threed A C, being <lb/>removed from its perpendicularity, and then letting go the plum­ <lb/>mets C and E, they &longs;hall move by the arches C B D, E G F, and <lb/>the plummet E, as hanging at a le&longs;&longs;er di&longs;tance, and withall, as <lb/>(by what you &longs;aid) le&longs;&longs;e removed, will return back again fa&longs;ter, <lb/>and make its vibrations more frequent than the plummet C, and <lb/>therefore &longs;hall hinder the &longs;aid plummet C, from running &longs;o much <lb/>farther towards the term D, as it would do, if it were free: and <lb/>thus the plummet E bringing unto it in every vibration continuall <lb/><arrow.to.target n="marg411"></arrow.to.target> <lb/>impediment, it &longs;hall finally reduce it to quie&longs;cence. </s><s>Now the <lb/>&longs;ame threed, (taking away the middle plummet) is a compo&longs;ition <lb/>of many grave <emph type="italics"/>penduli,<emph.end type="italics"/> that is, each of its parts is &longs;uch a <emph type="italics"/>pendu­ <lb/>lum<emph.end type="italics"/> fa&longs;tned neerer and neerer to the point A, and therefore di&longs;po­ <pb xlink:href="040/01/225.jpg" pagenum="207"/>&longs;ed to make its vibrations &longs;ucce&longs;&longs;ively more and more frequent; <lb/>and con&longs;equently is able to bring a continual impediment to the <lb/>plummet C; and for a proof that this is &longs;o, if we do but ob&longs;erve <lb/>the thread A C, we &longs;hall &longs;ee it di&longs;tended not directly, but in an <lb/>arch; and if in&longs;tead of the thread we take a chain, we &longs;hall di&longs;­ <lb/>cern the effect more per&longs;ectly; and e&longs;pecially removing the gra­ <lb/><arrow.to.target n="marg412"></arrow.to.target> <lb/>vity C, to a con&longs;iderable di&longs;tance from the perpendicular A B, for <lb/>that the chain being compo&longs;ed of many loo&longs;e particles, and each of <lb/>them of &longs;ome weight, the arches A E C, and A F D, will appear <lb/>notably incurvated. </s><s>By rea&longs;on therefore, that the parts of the <lb/>chain, according as they are neerer to the point A, de&longs;ire to make <lb/>their vibrations more frequent, they permit not the lower parts of <lb/>the &longs;aid chain to &longs;wing &longs;o far as naturally they would: and by <lb/>continual detracting from the vibrations of the plummet C, they <lb/>finally make it cea&longs;e to move, although the impediment of the air <lb/>might be removed.</s></p><p type="margin"><s><margin.target id="marg410"></margin.target><emph type="italics"/>The vibrations <lb/>of the &longs;ame<emph.end type="italics"/> pen­ <lb/>dulum <emph type="italics"/>are made <lb/>with the &longs;ame fre­ <lb/>quency, whether <lb/>they be &longs;mall or <lb/>great.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg411"></margin.target><emph type="italics"/>The cau&longs;e which <lb/>impedeth the<emph.end type="italics"/> pen­ <lb/>dulum, <emph type="italics"/>and redu­ <lb/>ceth it to re&longs;t.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg412"></margin.target><emph type="italics"/>The thread or <lb/>chain to which a<emph.end type="italics"/> <lb/>pendulum <emph type="italics"/>is fa&longs;t­ <lb/>ned, maketh an <lb/>arch, and doth not <lb/>&longs;tretch it &longs;elfe <lb/>&longs;treight out in its <lb/>vibrations.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The books are now come; here take them <emph type="italics"/>Simplicius,<emph.end type="italics"/> <lb/>and find the place you are in doubt of.</s></p><p type="main"><s>SIMP. See, here it is where he beginneth to argue again&longs;t the <lb/>diurnal motion of the Earth, he having fir&longs;t confuted the annual. <lb/><emph type="italics"/>Motus terræ annuus a&longs;&longs;errere<emph.end type="italics"/> Copernicanos <emph type="italics"/>cogit conver&longs;ionem e­ <lb/>ju&longs;dem quotidianam; alias idem terræ Hemi&longs;phærium continenter <lb/>ad Solem e&longs;&longs;et conver&longs;um obumbrato &longs;emper aver&longs;o. [In Engli&longs;h <lb/>thus:]<emph.end type="italics"/> The annual motion of the Earth doth compell the <emph type="italics"/>Co­ <lb/>pernicans<emph.end type="italics"/> to a&longs;&longs;ert the daily conver&longs;ion thereof; otherwi&longs;e the <lb/>&longs;ame Hemi&longs;phere of the Earth would be continually turned to­ <lb/>wards the Sun, the &longs;hady &longs;ide being always aver&longs;e. </s><s>And &longs;o one <lb/>half of the Earth would never come to &longs;ee the Sun.</s></p><p type="main"><s>SALV. </s><s>I find at the very &longs;ir&longs;t &longs;ight, that this man hath not rightly <lb/>apprehended the <emph type="italics"/>Copernican Hypothe&longs;is,<emph.end type="italics"/> for if he had but taken <lb/>notice how he alwayes makes the Axis of the terre&longs;trial Globe <lb/>perpetually parallel to it &longs;elf, he would not have &longs;aid, that one <lb/>half of the Earth would never &longs;ee the Sun, but that the year <lb/>would be one entire natural day, that is, that thorow all parts of <lb/>the Earth there would be &longs;ix moneths day, and &longs;ix moneths night, <lb/>as it now befalleth to the inhabitants under the Pole, but let <lb/>this mi&longs;take be forgiven him, and let us come to what remai­ <lb/>neth.</s></p><p type="main"><s>SIMP. </s><s>It followeth, <emph type="italics"/>Hanc autem gyrationem Terræ im­ <lb/>po&longs;&longs;ibilem e&longs;&longs;e &longs;ic demon&longs;tramus.<emph.end type="italics"/> Which &longs;peaks in Engli&longs;h thus: <lb/>That this gyration of the Earth is impo&longs;&longs;ible we thus demon&longs;trate. <lb/></s><s>That which en&longs;ueth is the declaration of the following figure, <lb/>wherein is delineated many de&longs;cending grave bodies, and a&longs;cend­ <lb/>ing light bodies, and birds that fly too and again in the air, &c.</s></p><p type="main"><s>SAGR. </s><s>Let us &longs;ee them, I pray you. </s><s>Oh! what fine figures, <pb xlink:href="040/01/226.jpg" pagenum="208"/>what birds, what balls, and what other pretty things are here?</s></p><p type="main"><s>SIMP. </s><s>The&longs;e are balls which come from the concave of the <lb/>Moon.</s></p><p type="main"><s>SAGR. </s><s>And what is this?</s></p><p type="main"><s>SIMP. </s><s>This is a kind of Shell-fi&longs;h, which here at <emph type="italics"/>Venice<emph.end type="italics"/> they <lb/>call <emph type="italics"/>buovoli<emph.end type="italics"/>; and this al&longs;o came from the Moons concave.</s></p><p type="main"><s>SAGR. Indeed, it &longs;eems then, that the Moon hath a great pow­ <lb/><arrow.to.target n="marg413"></arrow.to.target> <lb/>er over the&longs;e Oy&longs;ter-fi&longs;hes, which we call ^{*} <emph type="italics"/>armed &longs;i&longs;bes.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg413"></margin.target>* Pe&longs;ci armai, <emph type="italics"/>or<emph.end type="italics"/> <lb/>armati.</s></p><p type="main"><s>SIMP. </s><s>And this is that calculation, which I mentioned, of this <lb/>Journey in a natural day, in an hour, in a fir&longs;t minute, and in a <lb/>&longs;econd, which a point of the Earth would make placed under the <lb/>Equinoctial, and al&longs;o in the parallel of 48 <emph type="italics"/>gr.<emph.end type="italics"/> And then followeth <lb/>this, which I doubted I had committed &longs;ome mi&longs;take in reciting, <lb/>therefore let us read it. <emph type="italics"/>His po&longs;itis, nece&longs;&longs;e est, terra circulariter <lb/>mota, omnia ex aëre eidem, &c. </s><s>Quod &longs;i ha&longs;ce pilas æquales po­ <lb/>nemus pondere, magnitudine, gravitate, & in concavo Sphæræ Lu­ <lb/>naris po&longs;itas libero de&longs;cen&longs;ui permittamus, &longs;i motum deor&longs;um æque­ <lb/>mus celeritate motui circum, (quod tamen &longs;ecus e&longs;t, cum pila A, <lb/>&c.) elabentur minimum (ut multum cedamus adver&longs;ariis) dies <lb/>&longs;ex: quo tempore &longs;exies circa terram, &c. [In Engli&longs;b thus.]<emph.end type="italics"/> <lb/>The&longs;e things being &longs;uppo&longs;ed, it is nece&longs;&longs;ary, the Earth being cir­ <lb/>cularly moved, that all things from the air to the &longs;ame, &c. </s><s>So <lb/>that if we &longs;uppo&longs;e the&longs;e balls to be equal in magnitude and gra­ <lb/>vity, and being placed in the concave of the Lunar Sphere, we <lb/>permit them a free de&longs;cent, and if we make the motion down­ <lb/>wards equal in velocity to the motion about, (which neverthele&longs;s <lb/>is otherwi&longs;e, if the ball A, &c.) they &longs;hall be falling at lea&longs;t (that <lb/>we may grant much to our adver&longs;aries) &longs;ix dayes; in which time <lb/>they &longs;hall be turned &longs;ix times about the Earth, &c.</s></p><p type="main"><s>SALV. </s><s>You have but too faithfully cited the argument of this <lb/>per&longs;on. </s><s>From hence you may collect <emph type="italics"/>Simplicius,<emph.end type="italics"/> with what cau­ <lb/>tion they ought to proceed, who would give them&longs;elves up to be­ <lb/>lieve others in tho&longs;e things, which perhaps they do not believe <lb/>them&longs;elves. </s><s>For me thinks it a thing impo&longs;&longs;ible, but that this Au­ <lb/>thor was advi&longs;ed, that he did de&longs;ign to him&longs;elf a circle, who&longs;e dia­ <lb/>meter (which among&longs;t Mathematicians, is le&longs;&longs;e than one third part <lb/>of the circumference) is above 72 times bigger than it &longs;elf: an <lb/>errour that affirmeth that to be con&longs;iderably more than 200, <lb/>which is le&longs;&longs;e than one.</s></p><p type="main"><s>SAGR. </s><s>It may be, that the&longs;e Mathematical proportions, which <lb/>are true in ab&longs;tract, being once applied in concrete to Phy&longs;ical and <lb/>Elementary circles, do not &longs;o exactly agree: And yet, I think, <lb/>that the Cooper, to find the &longs;emidiameter of the bottom, which he <lb/>is to fit to the Cask, doth make u&longs;e of the rule of Mathematicians <lb/>in ab&longs;tract, although &longs;uch bottomes be things meerly material, <pb xlink:href="040/01/227.jpg" pagenum="209"/>and concrete: therefore let <emph type="italics"/>Simplicius<emph.end type="italics"/> plead in excu&longs;e of this <lb/>Author; and whether he chinks that the Phy&longs;icks can differ &longs;o <lb/>very much from the Mathematicks.</s></p><p type="main"><s>SIMP. </s><s>The &longs;ub&longs;tractions are in my opinion in&longs;ufficient to &longs;alve <lb/>this difference, which is &longs;o extreamly too great to be reconciled: <lb/>and in this ca&longs;e I have no more to &longs;ay but that, <emph type="italics"/>Quandoque bonus <lb/>dormitet Homerus.<emph.end type="italics"/> But &longs;uppo&longs;ing the calculation of ^{*} <emph type="italics"/>Salviatus<emph.end type="italics"/> <lb/><arrow.to.target n="marg414"></arrow.to.target> <lb/>to be more exact, and that the time of the de&longs;cent of the ball <lb/>were no more than three hours; yet me thinks, that coming from <lb/>the concave of the Moon, which is &longs;o great a di&longs;tance off, it would <lb/>be an admirable thing, that it &longs;hould have an in&longs;tinct of maintain­ <lb/>ing it &longs;elf all the way over the &longs;elf-&longs;ame point of the Earth, over <lb/>which it did hang in its departure thence and not rather be left a <lb/>very great way behind.</s></p><p type="margin"><s><margin.target id="marg414"></margin.target>* Not <emph type="italics"/>Sagre­ <lb/>dus,<emph.end type="italics"/> as the Latine <lb/>ha hit.</s></p><p type="main"><s>SALV. </s><s>The effect may be admirable, and not admirable, but <lb/>natural and ordinary, according as the things precedent may fall <lb/>out. </s><s>For if the ball (according to the Authors &longs;uppo&longs;itions) <lb/>whil&longs;t it &longs;taid in the concave of the Moon, had the circular motion <lb/>of twenty four hours together with the Earth, and with the re&longs;t of <lb/>the things contained within the &longs;aid Concave; that very vertue <lb/>which made it turn round before its de&longs;cent, will continue it in <lb/>the &longs;ame motion in its de&longs;cending. </s><s>And &longs;o far it is from not keep­ <lb/>ing pace with the motion of the Earth, and from &longs;taying behind, <lb/>that it is more likely to out-go it; being that in its approaches to <lb/>the Earth, the motion of gyration is to be made with circles con­ <lb/>tinually le&longs;&longs;er and le&longs;&longs;er; &longs;o that the ball retaining in it &longs;elf that <lb/>&longs;elf-&longs;ame velocity which it had in the concave, it ought to antici­ <lb/>pate, as I have &longs;aid, the <emph type="italics"/>vertigo<emph.end type="italics"/> or conver&longs;ion of the Earth. </s><s>But <lb/>if the ball in the concave did want that circulation, it is not obli­ <lb/>ged in de&longs;cending to maintain it &longs;elf perpendicularly over that <lb/>point of the Earth, which was ju&longs;t under it when the de&longs;cent be­ <lb/>gan. </s><s>Nor will <emph type="italics"/>Copernicus,<emph.end type="italics"/> or any of his followers affirm the <lb/>&longs;ame.</s></p><p type="main"><s>SIMP. </s><s>But the Author maketh an objection, as you &longs;ee, de­ <lb/>manding on what principle this circular motion of grave and light <lb/>bodies, doth depend: that is, whether upon an internal or an ex­ <lb/>ternal principle.</s></p><p type="main"><s>SALV. </s><s>Keeping to the Probleme of which we &longs;peak, I &longs;ay, <lb/>that that very principle which made the ball turn round, whil'&longs;t it <lb/>was in the Lunar concave, is the &longs;ame that maintaineth al&longs;o the <lb/>circulation in the de&longs;cent: yet I leave the Author at liberty to <lb/>make it internal or external at his plea&longs;ure.</s></p><p type="main"><s>SIMP. </s><s>The Author proveth, that it can neither be inward nor <lb/>outward.</s></p><p type="main"><s>SALV. </s><s>And I will &longs;ay then, that the ball in the concave did <pb xlink:href="040/01/228.jpg" pagenum="210"/>not move, and &longs;o he &longs;hall not be bound to &longs;hew how that in de&longs;­ <lb/>cending it continueth all the way vertically over one point, for <lb/>that it will not do any &longs;uch thing.</s></p><p type="main"><s>SIMP. </s><s>Very well; But if grave bodies, and light can have no <lb/>principle, either internal or external of moving circularly, than <lb/>neither can the terre&longs;trial Globe move with a circular motion: and <lb/>thus you have the intent of the Author.</s></p><p type="main"><s>SALV. </s><s>I did not &longs;ay, that the Earth had no principle, either <lb/>interne, or externe to the motion of gyration, but I &longs;ay, that I do <lb/>not know which of the two it hath; and yet my not knowing it <lb/>hath not a power to deprive it of the &longs;ame; but if this Author <lb/>can tell by what principle other mundane bodies are moved round, <lb/>of who&longs;e motion there is no doubt; I &longs;ay, that that which ma­ <lb/>keth the Earth to move, is a vertue, like to that, by which <emph type="italics"/>Mars<emph.end type="italics"/> <lb/>and <emph type="italics"/>Jupiter<emph.end type="italics"/> are moved, and wherewith he believes that the &longs;tarry <lb/>Sphere it &longs;elf al&longs;o doth move; and if he will but a&longs;&longs;ure me, who is <lb/>the mover of one of the&longs;e moveables, I will undertake to be able <lb/>to tell him who maketh the Earth to move. </s><s>Nay more; I will <lb/>undertake to do the &longs;ame, if he can but tell me, who moveth the <lb/>parts of the Earth downwards.</s></p><p type="main"><s>SIMP. </s><s>The cau&longs;e of this is mo&longs;t manife&longs;t, and every one knows <lb/>that it is gravity.</s></p><p type="main"><s>SALV. </s><s>You are out, <emph type="italics"/>Simplicius,<emph.end type="italics"/> you &longs;hould &longs;ay, that every <lb/>one knowes, that it is called Gravity: but I do not que&longs;tion you <lb/>about the name, but the e&longs;&longs;ence of the thing, of which e&longs;&longs;ence <lb/>you know not a tittle more than you know the e&longs;&longs;ence of the <lb/>mover of the &longs;tars in gyration; unle&longs;&longs;e it be the name that hath <lb/>been put to this, and made familiar, and dome&longs;tical, by the many <lb/><arrow.to.target n="marg415"></arrow.to.target> <lb/>experiences which we &longs;ee thereof every hour in the day,: but not <lb/>as if we really under&longs;tand any more, what principle or vertue that <lb/>is which moveth a &longs;tone downwards, than we know who moveth <lb/>it upwards, when it is &longs;eparated from the projicient, or who mo­ <lb/>veth the Moon round, except (as I have &longs;aid) onely the name, <lb/>which more particularly and properly we have a&longs;&longs;igned to the mo­ <lb/>tion of de&longs;cent, namely, Gravity; whereas for the cau&longs;e of cir­ <lb/>cular motion, in more general termes, we a&longs;&longs;ign the <emph type="italics"/>Vertue impre&longs;­ <lb/>&longs;ed,<emph.end type="italics"/> and call the &longs;ame an <emph type="italics"/>Intelligence,<emph.end type="italics"/> either a&longs;&longs;i&longs;ting, or informing; <lb/>and to infinite other motions we a&longs;cribe Nature for their cau&longs;e.</s></p><p type="margin"><s><margin.target id="marg415"></margin.target><emph type="italics"/>We know no more <lb/>who moveth grave <lb/>bodies downwards; <lb/>than who moveth <lb/>the Stars round, <lb/>nor know we any <lb/>thing of the&longs;e cau­ <lb/>&longs;es, more than the <lb/>names impo&longs;ed on <lb/>them by us.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>It is my opinion, that this Author asketh far le&longs;&longs;e than <lb/>that, to which you deny to make an&longs;wer; for he doth not ask <lb/>what is nominally and particularly the principle that moveth <lb/>grave and light bodies circularly, but what&longs;oever it be, he de&longs;i­ <lb/>reth to know, whether you think it intrin&longs;ecal, or extrin&longs;ecal: <lb/>For howbeit, <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> I do not know, what kind of thing that gravity <lb/>is, by which the Earth de&longs;cendeth; yet I know that it is an intern <pb xlink:href="040/01/229.jpg" pagenum="211"/>principle, &longs;eeing that if it be not hindered, it moveth &longs;pontane­ <lb/>ou&longs;ly: and on the contrary, I know that the principle which mo­ <lb/>veth it upwards, is external, although that I do not know, what <lb/>thing that vertue is, impre&longs;&longs;ed on it by the projicient.</s></p><p type="main"><s>SALV. </s><s>Into how many que&longs;tions mu&longs;t we excurre, if we would <lb/>decide all the difficulties, which &longs;ucce&longs;&longs;ively have dependance one <lb/>upon another! You call that an external (and you al&longs;o call it a <lb/>preternatural and violent) principle, which moveth the grave pro­ <lb/>ject upwards; but its po&longs;&longs;ible that it may be no le&longs;&longs;e interne and <lb/>natural, than that which moveth it downwards; it may peradven­ <lb/><arrow.to.target n="marg416"></arrow.to.target> <lb/>ture be called external and violent, &longs;o long as the moveable is joy­ <lb/>ned to the projicient; but being &longs;eparated, what external thing <lb/>remaineth for a mover of the arrow, or ball? </s><s>In &longs;umme, it mu&longs;t <lb/>nece&longs;&longs;arliy be granted, that that vertue which carrieth &longs;uch a move­ <lb/>able upwards, is no le&longs;&longs;e interne, than that which moveth it down­ <lb/>wards; and I think the motion of grave bodies a&longs;cending by the <lb/><emph type="italics"/>impetus<emph.end type="italics"/> conceived, to be altogether as natural, as the motion of <lb/>de&longs;cent depending on gravity.</s></p><p type="margin"><s><margin.target id="marg416"></margin.target><emph type="italics"/>The vertue which <lb/>carrieth grave pro­ <lb/>jects upwards, is <lb/>no le&longs;&longs;e natural to <lb/>them, than the <lb/>gravity which mo­ <lb/>veth them down­ <lb/>wards.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I will never grant this; for the motion of de&longs;cent hath <lb/>its principle internal, natural, and perpetual, and the motion of <lb/>a&longs;cent hath its principle externe, violent, and finite.</s></p><p type="main"><s>SALV. </s><s>If you refu&longs;e to grant me, that the principles of the <lb/>motions of grave bodies downwards and upwards, are equally in­ <lb/><arrow.to.target n="marg417"></arrow.to.target> <lb/>ternal and natural; what would you do, if I &longs;hould &longs;ay, that they <lb/>may al&longs;o be the &longs;ame in number?</s></p><p type="margin"><s><margin.target id="marg417"></margin.target><emph type="italics"/>Contrary prin­ <lb/>ciples cannot natu­ <lb/>rally re&longs;ide in the <lb/>&longs;ame &longs;ubject.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I leave it to you to judge.</s></p><p type="main"><s>SALV. </s><s>But I de&longs;ire you your &longs;elf to be the Judge: Therefore <lb/>tell me, Do you believe that in the &longs;ame natural body, there may <lb/>re&longs;ide interne principles, that are contrary to one another?</s></p><p type="main"><s>SIMP. </s><s>I do verily believe there cannot.</s></p><p type="main"><s>SALV. </s><s>What do you think to be the natural inclination of <lb/>Earth, of Lead, of Gold, and in &longs;um, of the mo&longs;t ponderous mat­ <lb/>ters; that is, to what motion do you believe that their interne <lb/>principle draweth them?</s></p><p type="main"><s>SIMP. </s><s>To that towards the centre of things grave, that is, to <lb/>the centre of the Univer&longs;e, and of the Earth, whither, if they be <lb/>not hindered, it will carry them.</s></p><p type="main"><s>SALV. </s><s>So that, if the Terre&longs;trial Globe were bored thorow, <lb/>and a Well made that &longs;hould pa&longs;&longs;e through the centre of it, a <lb/>Cannon bullet being let fall into the &longs;ame, as being moved by a <lb/>natural and intrin&longs;ick principle, would pa&longs;&longs;e to the centre; and it <lb/>would make all this motion &longs;pontaneou&longs;ly, and by intrin&longs;ick prin­ <lb/>ciple, is it not &longs;o?</s></p><p type="main"><s>SIMP. </s><s>So I verily believe.</s></p><p type="main"><s>SALV. </s><s>But when it is arrived at the centre, do you think that <pb xlink:href="040/01/230.jpg" pagenum="212"/>it will pa&longs;&longs;e any further, or el&longs;e that there it would immediately <lb/>&longs;tand &longs;till, and move no further?</s></p><p type="main"><s>SIMP. </s><s>I believe that it would continue to move a great way <lb/>further.</s></p><p type="main"><s>SALV. </s><s>But this motion beyond the centre, would it not be up­ <lb/>wards, and according to your a&longs;&longs;ertion preternatural, and violent? <lb/></s><s>And yet on what other principle do you make it to depend, but <lb/>only upon the &longs;elf &longs;ame, which did carry the ball to the centre, <lb/>and which you called intrin&longs;ecal, and natural? </s><s>Finde, if you can, <lb/>another external projicient, that overtaketh it again to drive it <lb/>upwards. </s><s>And this that hath been &longs;aid of the motion thorow <lb/>the centre, is al&longs;o &longs;een by us here above; for the interne <emph type="italics"/>impetus<emph.end type="italics"/> <lb/><arrow.to.target n="marg418"></arrow.to.target> <lb/>of a grave body falling along a declining &longs;uperficies, if the &longs;aid <lb/>&longs;uperficies be reflected the other way, it &longs;hall carry it, without a <lb/>jot interrupting the motion, al&longs;o upwards. </s><s>A ball of lead that <lb/>hangeth by a thread, being removed from its perpendicularity, de­ <lb/>&longs;cendeth &longs;pontaneou&longs;ly, as being drawn by its internal inclination, <lb/>and without any interpo&longs;ure of re&longs;t, pa&longs;&longs;eth beyond the lowe&longs;t <lb/>point of perpendicularity: and without any additional mover, <lb/>moveth upwards. </s><s>I know that you will not deny, but that the <lb/>principle of grave bodies that moveth them downwards, is no le&longs;s <lb/>natural, and intrin&longs;ecal, than that principle of light bodies, which <lb/>moveth them upwards: &longs;o that I propo&longs;e to your con&longs;ideration a <lb/>ball of lead, which de&longs;cending through the Air from a great al­ <lb/>titude, and &longs;o moving by an intern principle, and comming to a <lb/>depth of water, continueth its de&longs;cent, and without any other ex­ <lb/>terne mover, &longs;ubmergeth a great way; and yet the motion of <lb/>de&longs;cent in the water is preternatural unto it; but yet neverthele&longs;s <lb/>dependeth on a principle that is internal, and not external to the <lb/>ball. </s><s>You &longs;ee it demon&longs;trated then, that a moveable may be <lb/>moved by one and the &longs;ame internal principle, with contrary mo­ <lb/>tions.</s></p><p type="margin"><s><margin.target id="marg418"></margin.target><emph type="italics"/>The natural mo­ <lb/>tion changeth it <lb/>&longs;elfe into that <lb/>which is called pre­ <lb/>ternatural and vi­ <lb/>olent.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I believe there are &longs;olutions to all the&longs;e objections, <lb/>though for the pre&longs;ent I do not remember them; but however it <lb/>be, the Author continueth to demand, on what principle this cir­ <lb/>cular motion of grave and light bodies dependeth; that is, whe­ <lb/>ther on a principle internal, or external; and proceeding for­ <lb/>wards, &longs;heweth, that it can be neither on the one, nor on the other, <lb/>&longs;aying; <emph type="italics"/>Si ab externo; Deu&longs;ne illum excitat per continuum mira­ <lb/>culum? </s><s>an verò Angelus, an aër? </s><s>Et hunc quidem multi a&longs;&longs;ig­ <lb/>nant. </s><s>Sed contra----[In Engli&longs;h thus]<emph.end type="italics"/> If from an externe prin­ <lb/>ciple; Whether God doth not excite it by a continued Miracle? <lb/></s><s>or an Angel, or the Air? </s><s>And indeed many do a&longs;&longs;ign this. </s><s>But <lb/>on the contrary-----.</s></p><p type="main"><s>SALV. </s><s>Trouble not your &longs;elf to read his argument; for I am <pb xlink:href="040/01/231.jpg" pagenum="213"/>none of tho&longs;e who a&longs;cribe that principle to the ambient air. </s><s>As <lb/>to the Miracle, or an Angel, I &longs;hould rather incline to this &longs;ide; for <lb/>that which taketh beginning from a Divine Miracle, or from an <lb/>Angelical operation; as for in&longs;tance, the tran&longs;portation of a Can­ <lb/>non ball or bullet into the concave of the Moon, doth in all pro­ <lb/>bability depend on the vertue of the &longs;ame principle for perform­ <lb/>ing the re&longs;t. </s><s>But, as to the Air, it &longs;erveth my turn, that it doth <lb/>not hinder the circular motion of the moveables, which we did <lb/>&longs;uppo&longs;e to move thorow it. </s><s>And to prove that, it &longs;ufficeth (nor is <lb/>more required) that it moveth with the &longs;ame motion, and fini&longs;h­ <lb/>eth its circulations with the &longs;ame velocity, that the Terre&longs;trial <lb/>Globe doth.</s></p><p type="main"><s>SIMP. </s><s>And he likewi&longs;e makes his oppo&longs;ition to this al&longs;o; <lb/>demanding who carrieth the air about, Nature, or Violence? <lb/></s><s>And proveth, that it cannot be Nature, alledging that that is con­ <lb/>trary to truth, experience, and to <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf.</s></p><p type="main"><s>SALV. </s><s>It is not contrary to <emph type="italics"/>Copernicus<emph.end type="italics"/> in the lea&longs;t, who writeth <lb/>no &longs;uch thing; and this Author a&longs;cribes the&longs;e things to him with <lb/>two exce&longs;&longs;ive courte&longs;ie. </s><s>It's true, he &longs;aith, and for my part I <lb/>think he &longs;aith well, that the part of the air neer to the Earth, be­ <lb/>ing rather a terre&longs;trial evaporation, may have the &longs;ame nature, <lb/>and naturally follow its motion; or, as being contiguous to it, <lb/>may follow it in the &longs;ame manner, as the Peripateticks &longs;ay, that <lb/>the &longs;uperiour part of it, and the Element of fire, follow the mo­ <lb/>tion of the Lunar Concave, &longs;o that it lyeth upon them to declare, <lb/>whether that motion be natural, or violent.</s></p><p type="main"><s>SIMP. </s><s>The Author will reply, that if <emph type="italics"/>Copernicus<emph.end type="italics"/> maketh only <lb/>the inferiour part of the Air to move, and &longs;uppo&longs;eth the upper <lb/>part thereof to want the &longs;aid motion, he cannot give a rea&longs;on, how <lb/>that quiet air can be able to carry tho&longs;e grave bodies along with <lb/>it, and make them keep pace with the motion of the Earth.</s></p><p type="main"><s>SALV. <emph type="italics"/>Copernicus<emph.end type="italics"/> will &longs;ay, that this natural propen&longs;ion of the <lb/><arrow.to.target n="marg419"></arrow.to.target> <lb/>elementary bodies to &longs;ollow the motion of the Earth, hath a li­ <lb/>mited Sphere, out of which &longs;uch a natural inclination would cea&longs;e; <lb/>be&longs;ides that, as I have &longs;aid, the Air is not that which carrieth the <lb/>moveables along with it; which being &longs;eparated from the Earth, <lb/>do follow its motion; &longs;o that all the objections come to nothing, <lb/>which this Author produceth to prove, that the Air cannot cau&longs;e <lb/>&longs;uch effects.</s></p><p type="margin"><s><margin.target id="marg419"></margin.target><emph type="italics"/>The propen&longs;ion <lb/>of elementary bo­ <lb/>dies to follow the <lb/>Earth, hath a li­ <lb/>mited Sphere of <lb/>activity.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>To &longs;hew therefore, that that cannot be, it will be nece&longs;­ <lb/>&longs;ary to &longs;ay, that &longs;uch like effects depend on an interne principle, <lb/>again&longs;t which po&longs;ition, <emph type="italics"/>oboriuntur difficillimæ, immò inextricabiles <lb/>quæ&longs;tiones &longs;ecundæ,<emph.end type="italics"/> of which &longs;ort are the&longs;e that follow. <emph type="italics"/>Princi­ <lb/>pium illud internum vel e&longs;t accidens, vel &longs;ub&longs;tantia. </s><s>Si primum; <lb/>quale nam illud? </s><s>nam qualitas locomotiva circum, hactenus nulla<emph.end type="italics"/> <pb xlink:href="040/01/232.jpg" pagenum="214"/><emph type="italics"/>videtur agnita. (In Engli&longs;h thus:)<emph.end type="italics"/> Contrary to which po&longs;ition <lb/>there do ari&longs;e mo&longs;t difficult, yea inextricable &longs;econd que&longs;tions, <lb/>&longs;uch as the&longs;e; That intern principle is either an accident, or a <lb/>&longs;ub&longs;tance. </s><s>If the fir&longs;t; what manner of accident is it? </s><s>For a <lb/>locomotive quality about the centre, &longs;eemeth to be hitherto ac­ <lb/>knowledged by none.</s></p><p type="main"><s>SALV. How, is there no &longs;uch thing acknowledged? </s><s>Is it not <lb/>known to us, that all the&longs;e elementary matters move round, to­ <lb/>gether with the Earth? </s><s>You &longs;ee how this Author &longs;uppo&longs;eth for <lb/>true, that which is in que&longs;tion.</s></p><p type="main"><s>SIMP. </s><s>He &longs;aith, that we do not &longs;ee the &longs;ame; and me thinks, <lb/>he hath therein rea&longs;on on his &longs;ide.</s></p><p type="main"><s>SALV. </s><s>We &longs;ee it not, becau&longs;e we turn round together with <lb/>them.</s></p><p type="main"><s>SIMP. </s><s>Hear his other Argument. <emph type="italics"/>Quæ etiam &longs;i e&longs;&longs;et, quo­ <lb/>modo tamen inveniretur in rebus tam contrariis? </s><s>in igne, ut in a­ <lb/>quâ; in aëre, ut in terra; in viventibus, ut in anima carentibus? <lb/>[in Engli&longs;h thus:]<emph.end type="italics"/> Which although it were, yet how could it be <lb/>found in things &longs;o contrary? </s><s>in the fire, as in the water? </s><s>in the <lb/>air, as in the earth? </s><s>in living creatures, as in things wanting <lb/>life?</s></p><p type="main"><s>SALV. </s><s>Suppo&longs;ing for this time, that water and fire are contra­ <lb/>ries; as al&longs;o the air and earth; (of which yet much may be &longs;aid) <lb/>the mo&longs;t that could follow from thence would be, that tho&longs;e mo­ <lb/>tions cannot be common to them, that are contrary to one ano­ <lb/>ther: &longs;o that <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> the motion upwards, which naturally agreeth <lb/>to fire, cannot agree to water; but that, like as it is by nature con­ <lb/>trary to fire: &longs;o to it that motion &longs;uiteth, which is contrary to the <lb/>motion of fire, which &longs;hall be the motion <emph type="italics"/>deor&longs;ùm<emph.end type="italics"/>; but the cir­ <lb/>cular motion, which is not contrary either to the motion <emph type="italics"/>&longs;ur&longs;ùm,<emph.end type="italics"/> <lb/>or to the motion <emph type="italics"/>deor&longs;ùm,<emph.end type="italics"/> but may mix with both, as <emph type="italics"/>Aristotle<emph.end type="italics"/> <lb/>him&longs;elf affirmeth, why may it not equally &longs;uit with grave bodies <lb/>and with light? </s><s>The motions in the next place, which cannot be <lb/>common to things alive, and dead, are tho&longs;e which depend on the <lb/>&longs;oul: but tho&longs;e which belong to the body, in as much as it is ele­ <lb/>mentary, and con&longs;equently participateth of the qualities of the e­ <lb/>lements, why may not they be common as well to the dead corps, <lb/>as to the living body? </s><s>And therefore, if the circular motion be <lb/>proper to the elements, it ought to be common to the mixt bodies <lb/>al&longs;o.</s></p><p type="main"><s>SAGR. </s><s>It mu&longs;t needs be, that this Author holdeth, that a dead <lb/>cat, falling from a window, it is not po&longs;&longs;ible that a live cat al&longs;o <lb/>could fall; it not being a thing convenient, that a carca&longs;e &longs;hould <lb/>partake of the qualities which &longs;uit with things alive.</s></p><p type="main"><s>SALV. </s><s>Therefore the di&longs;cour&longs;e of this Author concludeth <pb xlink:href="040/01/233.jpg" pagenum="215"/>nothing again&longs;t one that &longs;hould affirm, that the principle of the cir­ <lb/>cular motions of grave and light bodies is an intern accident: I <lb/>know not how he may prove, that it cannot be a &longs;ub&longs;tance.</s></p><p type="main"><s>SIMP. </s><s>He brings many Arguments again&longs;t this. </s><s>The fir&longs;t of <lb/>which is in the&longs;e words: <emph type="italics"/>Si &longs;ecundum (nempè, &longs;i dieas tale princi­ <lb/>pium e&longs;&longs;e &longs;ub&longs;tantiam) illud e&longs;t aut materia, aut forma, aut compo­ <lb/>&longs;itum. </s><s>Sed repugnant iterum tot diver&longs;æ rerum naturæ, quales <lb/>&longs;unt aves, limaces, &longs;axa, &longs;agittæ, nives, fumi, grandines, pi&longs;ces, <lb/>&c. </s><s>quæ tamen omnia &longs;pecie & genere differentia, moverentur à <lb/>naturâ &longs;uâ circulariter, ip&longs;a naturis diver&longs;i&longs;&longs;ima, &c. [In Engli&longs;h <lb/>thus]<emph.end type="italics"/> If the &longs;econd, (that is, if you &longs;hall &longs;ay that this principle is <lb/>a &longs;ub&longs;tance) it is either matter, or form, or a compound of both. <lb/></s><s>But &longs;uch diver&longs;e natures of things are again repugnant, &longs;uch as are <lb/>birds, &longs;nails, &longs;tones, darts, &longs;nows, &longs;moaks, hails, fi&longs;hes, &c. </s><s>all <lb/>which notwith&longs;tanding their differences in &longs;pecies and kind, are <lb/>moved of their own nature circularly, they being of their natures <lb/>mo&longs;t different, &c.</s></p><p type="main"><s>SALV. </s><s>If the&longs;e things before named are of diver&longs;e natures, and <lb/>things of diver&longs;e natures cannot have a motion in common, it mu&longs;t <lb/>follow, if you would give &longs;atisfaction to all, that you are to think <lb/>of, more than two motions onely of upwards and downwards: and <lb/>if there mu&longs;t be one for the arrows, another for the &longs;nails, another <lb/>for the &longs;tones, and another for fi&longs;hes; then are you to bethink your <lb/>&longs;elf of worms, topazes and mu&longs;hrums, which are not le&longs;s different <lb/>in nature from one another, than &longs;now and hail.</s></p><p type="main"><s>SIMP. </s><s>It &longs;eems that you make a je&longs;t of the&longs;e Arguments.</s></p><p type="main"><s>SALV. </s><s>No indeed, <emph type="italics"/>Simplicius,<emph.end type="italics"/> but it hath been already an­ <lb/>&longs;wered above, to wit, that if one motion, whether downwards or <lb/>upwards, can agree with all tho&longs;e things afore named, a circular <lb/>motion may no le&longs;s agree with them: and as you are a <emph type="italics"/>Peripate­ <lb/>tick,<emph.end type="italics"/> do not you put a greater difference between an elementary <lb/>comet and a celeftial &longs;tar, than between a fi&longs;h and a bird? </s><s>and <lb/>yet both tho&longs;e move circularly. </s><s>Now propo&longs;e your &longs;econd Ar­ <lb/>gument.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Si terra &longs;taret per voluntatem Dei, rotaréntne cætera, an <lb/>non? </s><s>&longs;i hoc, fal&longs;um e&longs;t à naturâ gyrare; &longs;i illud, redeunt priores <lb/>quæ&longs;tiones. </s><s>Et &longs;anè mirum e&longs;&longs;et, quòd Gavia pi&longs;ciculo, Alauda <lb/>nidulo &longs;uo, & corvus limaci, petraque, etiam volans, imminere <lb/>non po&longs;&longs;et. [Which I thus render<emph.end type="italics"/>:] If the Earth be &longs;uppo&longs;ed to <lb/>&longs;tand &longs;till by the will of God, &longs;hould the re&longs;t of bodies turn round <lb/>or no? </s><s>If not, then it's fal&longs;e that they are revolved by nature; if <lb/>the other, the former que&longs;tions will return upon us. </s><s>And <lb/>truly it would be &longs;trange that the Sea-pie &longs;hould not be able to <lb/>hover over the &longs;mall fi&longs;h, the Lark over her ne&longs;t, and the Crow o­ <lb/>ver the &longs;nail and rock, though flying.</s></p> <pb xlink:href="040/01/234.jpg" pagenum="216"/><p type="main"><s>SALV. </s><s>I would an&longs;wer for my &longs;elf in general terms, that if <lb/>it were appointed by the will of God, that the Earth &longs;hould cea&longs;e <lb/>from its diurnal revolution, tho&longs;e birds would do what ever &longs;hould <lb/>plea&longs;e the &longs;ame Divine will. </s><s>But if this Author de&longs;ire a more <lb/>particular an&longs;wer, I &longs;hould tell him, that they would do quite con­ <lb/>trary to what they do now, if whil&longs;t they, being &longs;eparated from <lb/>the Earth, do bear them&longs;elves up in the air, the Terre&longs;trial Globe <lb/>by the will of God, &longs;hould all on a &longs;udden be put upon a precipi­ <lb/>tate motion; it concerneth this Author now to a&longs;certain us what <lb/>would in this ca&longs;e &longs;ucceed.</s></p><p type="main"><s>SAGR. </s><s>I pray you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> at my reque&longs;t to grant to this <lb/>Author, that the Earth &longs;tanding &longs;till by the will of God, the other <lb/>things, &longs;eparated from it, would continue to turn round of their <lb/>own natural motion, and let us hear what impo&longs;&longs;ibilities or incon­ <lb/>veniences would follow: for I, as to my own particular, do not <lb/>&longs;ee how there can be greater di&longs;orders, than the&longs;e produced by the <lb/>Author him&longs;elf, that is, that Larks, though they &longs;hould flie, could <lb/>not be able to hover over their ne&longs;ts, nor Crows over &longs;nails, or <lb/>rocks: from whence would follow, that Crows mu&longs;t &longs;uffer for <lb/>want of &longs;nails, and young Larks mu&longs;t die of hunger, and cold, not <lb/>being able to be fed or &longs;heltered by the wings of the old ones. <lb/></s><s>This is all the ruine that I can conceive would follow, &longs;uppo&longs;ing <lb/>the Authors &longs;peech to be true. </s><s>Do you &longs;ee, <emph type="italics"/>Simplicius,<emph.end type="italics"/> if grea­ <lb/>ter inconveniences would happen?</s></p><p type="main"><s>SIMP. </s><s>I know not how to di&longs;cover greater; but it is very cre­ <lb/>dible, that the Author be&longs;ides the&longs;e, di&longs;covered other di&longs;orders in <lb/>Nature, which perhaps in reverend re&longs;pect of her, he was not will­ <lb/>ing to in&longs;tance in. </s><s>Therefore let us proceed to the third Obje­ <lb/>ction. <emph type="italics"/>In&longs;uper quî fit, ut istæ res tam variæ tantùm moveantur <lb/>ab Occa&longs;u in Ortum, parallelæ ad Æquatorem? </s><s>ut &longs;emper movean­ <lb/>tur, nunquam quie&longs;cant? [which &longs;peaks to this &longs;en&longs;e:]<emph.end type="italics"/> Moreover, <lb/>how comes it to pa&longs;s that the&longs;e things, &longs;o diver&longs;e, are onely moved <lb/>from the We&longs;t towards the Ea&longs;t, parallel to the Æquinoctial? <lb/></s><s>that they always move, and never re&longs;t?</s></p><p type="main"><s>SALV. </s><s>They move from We&longs;t to Ea&longs;t parallel to the Æqui­ <lb/>noctial without cea&longs;ing, in the &longs;ame manner as you believe the <lb/>fixed &longs;tars to move from Ea&longs;t to We&longs;t, parallel to the Æquinocti­ <lb/>al, without ever re&longs;ting.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Quarè, quò &longs;unt altiores, celeriùs; quò humiliores, tar­ <lb/>diùs? (i. </s><s>e.)<emph.end type="italics"/> Why are the higher the &longs;wifter, and the lower the <lb/>&longs;lower?</s></p><p type="main"><s>SALV. </s><s>Becau&longs;e that in a Sphere or circle, that turns about up­ <lb/>on its own centre, the remoter parts de&longs;cribe greater circuits, and <lb/>the parts nearer at hand de&longs;cribe le&longs;&longs;er in the &longs;ame time.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Quare, quæ Æquinoctiali propriores, in majori; quæ<emph.end type="italics"/> <pb xlink:href="040/01/235.jpg" pagenum="217"/><emph type="italics"/>remotiores, in minori circulo feruntur? [&longs;cilicet:]<emph.end type="italics"/> Why are <lb/>tho&longs;e near the Æquinoctial carried about in a greater circle, and <lb/>tho&longs;e which are remote in a le&longs;&longs;er?</s></p><p type="main"><s>SALV. </s><s>To imitate the &longs;tarry Sphere, in which tho&longs;e neare&longs;t <lb/>to the Æquinoctial, move in greater circles, than the more re­ <lb/>mote.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Quarè Pila eadem &longs;ub Æquinoctiali tota circa centrum <lb/>terr æ, ambitu maximo, celeritate incredibili; &longs;ub Polo verò circa <lb/>centrum proprium, gyro nullo, tarditate &longs;upremâ volveretur? <lb/>[That is:]<emph.end type="italics"/> Why is the &longs;ame ball under the Æquinoctial wholly <lb/>turned round the centre of the Earth in the greate&longs;t circumfe­ <lb/>rence, with an incredible celerity; but under the Pole about its <lb/>own centre, in no circuite, but with the ultimate degree of tar­ <lb/>dity?</s></p><p type="main"><s>SALV. </s><s>To imitate the &longs;tars of the Firmament, that would do <lb/>the like if they had the diurnal motion.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Quare eadem res, pila v. </s><s>g. </s><s>plumbea, &longs;i &longs;emel terram <lb/>circuivit, de&longs;cripto circulo maximo, eandem ubique non circum­ <lb/>migret &longs;ecundùm circulum maximum, &longs;ed tran&longs;lata extra Æquino­ <lb/>ctialem in circulis minoribus agetur? [Which &longs;peaketh thus:]<emph.end type="italics"/> <lb/>Why doth not the &longs;ame thing, as for example, a ball of lead <lb/>turn round every where according to the &longs;ame great circle, if once <lb/>de&longs;cribing a great circle, it hath incompa&longs;&longs;ed the Earth, but being <lb/>removed from the Æquinoctial, doth move in le&longs;&longs;er circles?</s></p><p type="main"><s>SALV. </s><s>Becau&longs;e &longs;o would, nay, according to the doctrine of <lb/><emph type="italics"/>Ptolomey,<emph.end type="italics"/> &longs;o have &longs;ome fixed &longs;tars done, which once were very <lb/>near the Æquinoctial, and de&longs;cribed very va&longs;t circles, and now that <lb/>they are farther off, de&longs;cribe le&longs;&longs;er.</s></p><p type="main"><s>SAGR. </s><s>If I could now but keep in mind all the&longs;e fine no­ <lb/>tions, I &longs;hould think that I had made a great purcha&longs;e; I mu&longs;t <lb/>needs intreat you, <emph type="italics"/>Simplicius,<emph.end type="italics"/> to lend me this Book, for there can­ <lb/>not chu&longs;e but be a &longs;ea of rare and ingenious matters contained in <lb/>it.</s></p><p type="main"><s>SIMP. </s><s>I will pre&longs;ent you with it.</s></p><p type="main"><s>SAGR. </s><s>Not &longs;o, Sir; I would not deprive you of it: but are <lb/>the Queries yet at an end?</s></p><p type="main"><s>SIMP. </s><s>No Sir; hearken therefore. <emph type="italics"/>Si latio circularis gra­ <lb/>vibus & levibus e&longs;t naturalis, qualis e&longs;t ea quæ fit &longs;ecundùm line­ <lb/>am rectam? </s><s>Nam &longs;i naturalis, quomodo & is motus qui circum est, <lb/>naturalis e&longs;t, cùm &longs;pecie differat à recto? </s><s>Si violentus, quî fit, ut <lb/>mi&longs;&longs;ile ignitum &longs;ur&longs;ùm evolans &longs;cintillo&longs;um caput &longs;ur&longs;ùm à terrâ, <lb/>non autem circum volvatur, &c. [Which take in our idiom:]<emph.end type="italics"/> If <lb/>a circular lation is natural to heavy and light things, what is that <lb/>which is made according to a right line? </s><s>For if it be natural, how <lb/>then is that motion which is about the centre natural, &longs;eeing it <pb xlink:href="040/01/236.jpg" pagenum="218"/>differs in &longs;pecies from a right motion? </s><s>If it be violent, how is it <lb/>that a fiery dart flying upwards, &longs;parkling over our heads at a di­ <lb/>&longs;tance from the Earth, but not turning about, <emph type="italics"/>&c.<emph.end type="italics"/> <lb/><arrow.to.target n="marg420"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg420"></margin.target><emph type="italics"/>Of the mixt mo­ <lb/>tion we &longs;ee not the <lb/>part that is circu­ <lb/>lar, becau&longs;e we <lb/>partake thereof.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>It hath been &longs;aid already very often, that the circular <lb/>motion is natural to the whole, and to its parts, whil&longs;t they are in <lb/>perfect di&longs;po&longs;ure, and the right is to reduce to order the parts <lb/>di&longs;ordered; though indeed it is better to &longs;ay, that neither the <lb/>parts ordered or di&longs;ordered ever move with a right motion, but <lb/>with one mixed, which might as well be averred meerly circular: <lb/>but to us but one part onely of this motion is vi&longs;ible and ob&longs;er­ <lb/>vable, that is, the part of the right, the other part of the circular <lb/>being imperceptible to us, becau&longs;e we partake thereof. </s><s>And this <lb/>an&longs;wers to the rays which move upwards, and round about, but we <lb/>cannot di&longs;tingui&longs;h their circular motion, for that, with that we our <lb/>&longs;elves move al&longs;o. </s><s>But I believe that this Author never thought <lb/>of this mixture; for you may &longs;ee that he re&longs;olutely &longs;aith, that the <lb/>rays go directly upwards, and not at all in gyration.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Quare centrum &longs;phære delap&longs;æ &longs;ub Æquatore &longs;piram de­ <lb/>&longs;cribit in ejus plano: &longs;ub aliis parallelis &longs;piram de&longs;cribit in cono? <lb/></s><s>&longs;ub Polo de&longs;cendit in axe lineam gyralem, decurrens in &longs;uperficie <lb/>cylindricâ con&longs;ignatam<emph.end type="italics"/>? (In Engli&longs;h to this purpo&longs;e:) Why doth <lb/>the centre of a falling Globe under the Æquinoctial de&longs;cribe a <lb/>&longs;piral line in the plane of the Æquator; and in other parallels <lb/>a &longs;piral about a Cone; and under the Pole de&longs;cend in the <lb/>axis de&longs;cribing a gyral line, running in a Cylindrical Super&longs;i­ <lb/>cies?</s></p><p type="main"><s>SALV. </s><s>Becau&longs;e of the lines drawn from the Centre to the cir­ <lb/>cumference of the &longs;phere, which are tho&longs;e by which <emph type="italics"/>graves<emph.end type="italics"/> de­ <lb/>fcend, that which terminates in the Æquinoctial de&longs;igneth a cir­ <lb/>cle, and tho&longs;e that terminate in other parallels de&longs;cribe conical <lb/>&longs;uperficies; now the axis de&longs;cribeth nothing at all, but continueth <lb/>in its own being. </s><s>And if I may give you my judgment freely, I <lb/>will &longs;ay, that I cannot draw from all the&longs;e Queries, any &longs;en&longs;e that <lb/>interfereth with the motion of the Earth; for if I demand of this <lb/>Author, (granting him that the Earth doth not move) what would <lb/>follow in all the&longs;e particulars, &longs;uppo&longs;ing that it do move, as <emph type="italics"/>Co­ <lb/>pernicus<emph.end type="italics"/> will have it; I am very confident, that he would &longs;ay that <lb/>all the&longs;e effects would happen, that he hath objected, as inconve­ <lb/>niences to di&longs;prove its mobility: &longs;o that in this mans opinion ne­ <lb/>ce&longs;&longs;ary con&longs;equences are accounted ab&longs;urdities: but I be&longs;eech <lb/>you, if there be any more, di&longs;patch them, and free us &longs;peedily <lb/>from this weari&longs;om task.</s></p><p type="main"><s>SIMP. </s><s>In this which follows he oppo&longs;es <emph type="italics"/>Copernicus<emph.end type="italics"/> & his Sectators, <lb/>who affirm, that the motion of the parts &longs;eparated from their whole, <lb/>is onely to unite them&longs;elves to their whole; but that the moving <pb xlink:href="040/01/237.jpg" pagenum="219"/>circularly along with the vertigenous diurnal revolution is ab&longs;o­ <lb/>lutely natural: again&longs;t which he objecteth, &longs;aying, that according <lb/>to the&longs;e mens opinion; <emph type="italics"/>Si tota terra, unà cum aquâ in nihilum <lb/>redigeretur, nulla grando aut pluvia è nube decideret, &longs;ed natu­ <lb/>raliter tantùm circumferetur, neque ignis ullus, aut igneum a&longs;cen­ <lb/>deret, cùm illorum non improbabili &longs;ententià ignis nullus &longs;it &longs;uprà.<emph.end type="italics"/> <lb/>[Which I tran&longs;late to this &longs;en&longs;e:] If the whole Earth, together <lb/>with the Water were reduced into nothing, no hail or rain would <lb/>fall from the clouds, but would be onely naturally carried round; <lb/>neither any fire or fiery thing would a&longs;cend, &longs;eeing to the&longs;e that men <lb/>it is no improbable opinion that there is no fire above.</s></p><p type="main"><s>SALV. </s><s>The providence of this Philo&longs;opher is admirable, and <lb/>worthy of great applau&longs;e, for he is not content to provide for <lb/>things that might happen, the cour&longs;e of Nature continuing, but <lb/>will &longs;hew hic care in what may follow from tho&longs;e things that he <lb/>very well knows &longs;hall never come to pa&longs;s. </s><s>I will grant him there­ <lb/>fore, (that I may get &longs;om pretty pa&longs;&longs;ages out of him) that if the <lb/>Earth and Water &longs;hould be reduced to nothing, there would be no <lb/>more hails or rains, nor would igneal matters a&longs;cend any longer <lb/>upwards, but would continually turn round: what will follow? <lb/></s><s>what will the Philo&longs;opher &longs;ay then?</s></p><p type="main"><s>SIMP. </s><s>The objection is in the words which immediately fol­ <lb/>low; here they are: <emph type="italics"/>Quibus tamen experientia & ratio adver­ <lb/>&longs;atur.<emph.end type="italics"/> Which neverthele&longs;s (&longs;aith he) is contrary to experience and <lb/>rea&longs;on.</s></p><p type="main"><s>SALV. </s><s>Now I mu&longs;t yield, &longs;eeing he hath &longs;o great an advan­ <lb/>tage of me as experience, of which I am unprovided. </s><s>For as yet <lb/>I never had the fortune to &longs;ee the Terre&longs;trial Globe and the ele­ <lb/>ment of Water turn'd to nothing, &longs;o as to have been able to ob­ <lb/>&longs;erve what the hail and water did in that little Chaos. </s><s>But he <lb/>perhaps tells us for our in&longs;truction what they did.</s></p><p type="main"><s>SIMP. No, he doth not.</s></p><p type="main"><s>SALV. </s><s>I would give any thing to change a word or two with <lb/>this per&longs;on, to ask him, whether when this Globe vani&longs;hed, it car­ <lb/>ried away with it the common centre of gravity, as I believe it did; <lb/>in which ca&longs;e, I think that the hail and water would remain in&longs;en­ <lb/>&longs;ate and &longs;tupid among&longs;t the clouds, without knowing what to do <lb/>with them&longs;elves. </s><s>It might be al&longs;o, that attracted by that great <lb/>void <emph type="italics"/>Vacuum,<emph.end type="italics"/> left by the Earths ab&longs;enting, all the ambients would <lb/>be rarified, and particularly, the air, which is extreme ea&longs;ily drawn, <lb/>and would run thither with very great ha&longs;te to fill it up. </s><s>And <lb/>perhaps the more &longs;olid and material bodies, as birds, (for there <lb/>would in all probability be many of them &longs;cattered up and down <lb/>in the air) would retire more towards the centre of the great va­ <lb/>cant &longs;phere; (for it &longs;eemeth very rea&longs;onable, that &longs;ub&longs;tances that <pb xlink:href="040/01/238.jpg" pagenum="220"/>under &longs;mall bulk contain much matter, &longs;hould have narrower pla­ <lb/>ces a&longs;&longs;igned them, leaving the more &longs;pacious to the more rarified) <lb/>and there being dead of hunger, and re&longs;olved into Earth, would <lb/>form a new little Globe, with that little water, which at that time <lb/>was among the clouds. </s><s>It might be al&longs;o, that tho&longs;e matters as <lb/>not beholding the light, would not perceive the Earths departure, <lb/>but like blind things, would de&longs;cend according to their u&longs;ual cu&longs;tom <lb/>to the centre, whither they would now go, if that globe did not <lb/>hinder them. </s><s>And la&longs;tly, that I may give this Philo&longs;opher a le&longs;s <lb/>irre&longs;olute an&longs;wer, I do tell him, that I know as much of what <lb/>would follow upon the annihilation of the Terre&longs;trial Globe, as <lb/>he would have done that was to have followed in and about the <lb/>&longs;ame, before it was created. </s><s>And becau&longs;e I am certain he will <lb/>&longs;ay, that he would never have been able to have known any of <lb/>all tho&longs;e things which experience alone hath made him knowing <lb/>in, he ought not to deny me pardon, and to excu&longs;e me if I know <lb/>not that which he knows, touching what would en&longs;ue upon the <lb/>annihilation of the &longs;aid Globe: for that I want that experience <lb/>which he hath. </s><s>Let us hear if he have any thing el&longs;e to &longs;ay.</s></p><p type="main"><s>SIMP. </s><s>There remains this figure, which repre&longs;ents the Terre­ <lb/>&longs;trial Globe with a great cavity about its centre, full of air; and <lb/>to &longs;hew that <emph type="italics"/>Graves<emph.end type="italics"/> move not downwards to unite with the Ter­ <lb/>re&longs;trial Globe, as <emph type="italics"/>Copernicus<emph.end type="italics"/> &longs;aith, he con&longs;tituteth this &longs;tone in <lb/>the centre; and demandeth, it being left at liberty, what it would <lb/>do; and he placeth another in the &longs;pace of this great vacuum, and <lb/>asketh the &longs;ame que&longs;tion. </s><s>Saying, as to the fir&longs;t: <emph type="italics"/>Lapis in centro <lb/>con&longs;titutus, aut a&longs;cendet ad terram in punctum aliquod, aut non. </s><s>Si <lb/>&longs;ecundum; fal&longs;um est, partes ob &longs;olam &longs;ejunctionem à toto, ad il­ <lb/>lud moveri. </s><s>Si primum; omnis ratio & experientia renititur, <lb/>neque gravia in &longs;uœ gravitatis centro conquie&longs;cent. </s><s>Item &longs;i &longs;u­ <lb/>&longs;pen&longs;us lapis, liberatus decidat in centrum, &longs;eparabit &longs;e à toto, con­ <lb/>tra<emph.end type="italics"/> Copernicum<emph type="italics"/>: &longs;i pendeat, refragatur omnis experientia, cùm <lb/>videamus integros fornices corruere.<emph.end type="italics"/> (Wherein he &longs;aith:) The <lb/>&longs;tone placed in the centre, either a&longs;cendeth to the Earth in &longs;ome <lb/>point, or no. </s><s>If the &longs;econd, it is fal&longs;e that the parts &longs;eparated <lb/>from the whole, move unto it. </s><s>If the fir&longs;t; it contradicteth all <lb/>rea&longs;on and experience, nor doth the grave body re&longs;t in the centre <lb/>of its gravity. </s><s>And if the &longs;tone being &longs;u&longs;pended in the air, be let <lb/>go, do de&longs;cend to the centre, it will &longs;eparate from its whole, con­ <lb/>trary to <emph type="italics"/>Copernicus:<emph.end type="italics"/> if it do hang in the air, it contradicteth all <lb/>experience: &longs;ince we &longs;ee whole Vaults to fall down.</s></p><p type="main"><s>SALV. </s><s>I will an&longs;wer, though with great di&longs;advantage to my <lb/>&longs;elf, &longs;eeing I have to do with one who hath &longs;een by experience, <lb/>what the&longs;e &longs;tones do in this great Cave: a thing, which for my <lb/>part I have not &longs;een; and will &longs;ay, that things grave have an exi­ <pb xlink:href="040/01/239.jpg" pagenum="221"/>&longs;tence before the common centre of gravity: &longs;o that it is not one </s></p><p type="main"><s><arrow.to.target n="marg421"></arrow.to.target> <lb/>centre alone, which is no other than indivi&longs;ible point, and therefore <lb/>of no efficacie, that can attract unto it grave matters; but that tho&longs;e <lb/>matters con&longs;piring naturally to unite, form to them&longs;elves a com­ <lb/>mon centre, which is that about which parts of equal moment <lb/>con&longs;i&longs;t: &longs;o that I hold, that if the great aggregate of grave bo­ <lb/><arrow.to.target n="marg422"></arrow.to.target> <lb/>dies were gathered all into any one place, the &longs;mall parts that were <lb/>&longs;eparated from their whole, would follow the &longs;ame, and if they <lb/>were not hindered, would penetrate wherever they &longs;hould find <lb/>parts le&longs;s grave than them&longs;elves: but coming where they &longs;hould <lb/>meet with matters more grave, they would de&longs;cend no farther. <lb/></s><s>And therefore I hold, that in the Cave full of air, the whole Vault <lb/>would pre&longs;s, and violently re&longs;t it &longs;elf onely upon that air, in ca&longs;e <lb/>its hardne&longs;s could not be overcome and broken by its gravity; but <lb/>loo&longs;e &longs;tones, I believe, would de&longs;cend to the centre, and not &longs;wim <lb/>above in the air: nor may it be &longs;aid, that they move not to their <lb/>whole, though they move whither all the parts of the whole <lb/>would transfer them&longs;elves, if all impediments were removed.</s></p><p type="margin"><s><margin.target id="marg421"></margin.target><emph type="italics"/>Things grave are <lb/>before the centre of <lb/>gravity.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg422"></margin.target><emph type="italics"/>The great ma&longs;s <lb/>of grave bodies be­ <lb/>ing transferred out <lb/>of their place, the <lb/>&longs;eparated parts <lb/>would follow that <lb/>maß.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>That which remaineth, is a certain Errour which he ob­ <lb/>&longs;erveth in a Di&longs;ciple of <emph type="italics"/>Copernicus,<emph.end type="italics"/> who making the Earth to <lb/>move with an annual motion, and a diurnal, in the &longs;ame manner <lb/>as the Cart-wheel moveth upon the circle of the Earth, and in it <lb/>&longs;elf, did con&longs;titute the Terre&longs;trial Globe too great, or the great <lb/>Orb too little; for that 365 revolutions of the Æquinoctial, are <lb/>le&longs;s by far than the circumference of the great Orb.</s></p><p type="main"><s>SALV. </s><s>Take notice that you mi&longs;take, and tell us the direct <lb/>contrary to what mu&longs;t needs be written in that Book; for you <lb/>&longs;hould &longs;ay, that that &longs;ame <emph type="italics"/>Copernican<emph.end type="italics"/> Author did con&longs;titute the <lb/>Terre&longs;trial Globe too little, and the great Orb too big; and not <lb/>the Terre&longs;trial Globe too big, and the annual too little.</s></p><p type="main"><s>SIMP. </s><s>The mi&longs;take is not mine; &longs;ee here the words of the <lb/>Book. <emph type="italics"/>Non videt, quòd vel circulum annuum æquo minorem, vel <lb/>orbem terreum ju&longs;to multò fabricet majorem.<emph.end type="italics"/> (In Engli&longs;h thus:) <lb/>He &longs;eeth not, that he either maketh the annual circle equal to the <lb/>le&longs;s, or the Terre&longs;trial Orb much too big.</s></p><p type="main"><s>SALV. </s><s>I cannot tell whether the fir&longs;t Author erred or no, &longs;ince <lb/>the Author of this Tractate doth not name him; but the error of <lb/>this Book is certain and unpardonable, whether that follower of <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> erred or not erred; for that your Author pa&longs;&longs;eth by &longs;o <lb/>material an error, without either detecting or correcting it. </s><s>But <lb/>let him be forgiven this fault, as an error rather of inadvertencie, <lb/>than of any thing el&longs;e: Farthermore, were it not, that I am al­ <lb/>ready wearied and tired with talking and &longs;pending &longs;o mnch time <lb/>with very little profit, in the&longs;e frivolous janglings and alterca­ <lb/>tions, I could &longs;hew, that it is not impo&longs;&longs;ible for a circle, though <pb xlink:href="040/01/240.jpg" pagenum="222"/><arrow.to.target n="marg423"></arrow.to.target> <lb/>no bigger than a Cart-wheel, with making not 365, but le&longs;&longs;e than <lb/>20 revolutions, to de&longs;cribe and mea&longs;ure the circumference, not <lb/>onely of the grand Orb, but of one a thou&longs;and times greater; <lb/>and this I &longs; y to &longs;hew, that there do not want far greater &longs;ubtil­ <lb/>ties, than this wherewith your Author goeth about to detect the <lb/>errour of <emph type="italics"/>Copernicus<emph.end type="italics"/>: but I pray you, let us breath a little, that <lb/>&longs;o we may proceed to the other Philo&longs;opher, that oppo&longs;eth of the <lb/>&longs;ame <emph type="italics"/>Copernicus.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg423"></margin.target><emph type="italics"/>It is not impo&longs;&longs;i­ <lb/>ble with the cir­ <lb/>cumference of a <lb/>&longs;mall circle few <lb/>times revolved to <lb/>mea&longs;ure and de­ <lb/>&longs;cribe a line bigger <lb/>than any great cir­ <lb/>cle what &longs;oever.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>To confe&longs;&longs;e the truth, I &longs;tand as much in need of re­ <lb/>&longs;pite as either of you; though I have onely wearied my eares: <lb/>and were it not that I hope to hear more ingenious things from <lb/>this other Author, I que&longs;tion whether I &longs;hould not go my ways, to <lb/><arrow.to.target n="marg424"></arrow.to.target> <lb/>take the air in my ^{*} Plea&longs;ure-boat.</s></p><p type="margin"><s><margin.target id="marg424"></margin.target>Gondola.</s></p><p type="main"><s>SIMP. </s><s>I believe that you will hear things of greater moment; <lb/>for this is a mo&longs;t accompli&longs;hed Philo&longs;opher, and a great Mathema­ <lb/>tician, and hath confuted <emph type="italics"/>Tycho<emph.end type="italics"/> in the bu&longs;ine&longs;&longs;e of the Comets, <lb/>and new Stars. <lb/><arrow.to.target n="marg425"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg425"></margin.target>* The name of <lb/>the <emph type="italics"/>Author<emph.end type="italics"/> is <emph type="italics"/>Sci­ <lb/>pie Claramontius.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Perhaps he is the &longs;ame with the Author of the Book, <lb/>called <emph type="italics"/>Anti-Tycho<emph.end type="italics"/>?</s></p><p type="main"><s>SIMP. </s><s>He is the very &longs;ame: but the confutation of the new <lb/>Stars is not in his <emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> onely &longs;o far as he proveth, that they <lb/>were not prejudicial to the inalterability and ingenerability of the <lb/>Heavens, as I told you before; but after he had publi&longs;hed his <lb/><emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> having found out, by help of the Parallaxes, a way to <lb/>demon&longs;trate, that they al&longs;o are things elementary, and contained <lb/>within the concave of the Moon, he hath writ this other Book, <lb/><emph type="italics"/>de tribus uovis Stellis, &c.<emph.end type="italics"/> and therein al&longs;o in&longs;erted the Argu­ <lb/>ments again&longs;t <emph type="italics"/>Copernicus<emph.end type="italics"/>: I have already &longs;hewn you what he <lb/>harh written touching the&longs;e new Stars in his <emph type="italics"/>Anti-Tycho,<emph.end type="italics"/> where he <lb/>denied not, but that they were in the Heavens; but he proved, that <lb/>their production altered not the inalterability of the Heavens, and <lb/>that he did, with a Di&longs;cour&longs;e purely philo&longs;ophical, in the &longs;ame man <lb/>ner as you have already heard. </s><s>And I then forgot to tell you, how <lb/>that he afterwards did finde out a way to remove them out of the <lb/>Heavens; for he proceeding in this confutation, by way of com­ <lb/>putations and parallaxes, matters little or nothing at all under­ <lb/>&longs;tood by me, I did not mention them to you, but have bent all my <lb/>&longs;tudies upon the&longs;e arguments again&longs;t the motion of the Earth, <lb/>which are purely natural.</s></p><p type="main"><s>SALV. </s><s>I under&longs;tand you very well: and it will be convenient <lb/>after we have heard what he hath to &longs;ay again&longs;t <emph type="italics"/>Copernicus,<emph.end type="italics"/> that <lb/>we hear, or &longs;ee at lea&longs;t the manner wherewith he, by way of Pa­ <lb/>rallaxes, proveth tho&longs;e new &longs;tars to be elementary, which &longs;o many <lb/>famous A&longs;tronomers con&longs;titute to be all very high, and among&longs;t <lb/>the &longs;tars of the Firmament; and as this Author accompli&longs;heth &longs;uch <pb xlink:href="040/01/241.jpg" pagenum="223"/>an enterprize of pulling the new &longs;tars out of heaven, and placing <lb/>them in the elementary Sphere, he &longs;hall be worthy to be highly <lb/>exalted, and transferred him&longs;elf among&longs;t the &longs;tars, or at lea&longs;t, <lb/>that his name be by fame eternized among&longs;t them. </s><s>Yet before we <lb/>enter upon this, let us hear what he alledgeth again&longs;t the opinion <lb/>of <emph type="italics"/>Copernicus,<emph.end type="italics"/> and do you begin to recite his Arguments.</s></p><p type="main"><s>SIMP. </s><s>It will not be nece&longs;&longs;ary that we read them <emph type="italics"/>ad verbum,<emph.end type="italics"/> <lb/>becau&longs;e they are very prolix; but I, as you may &longs;ee, in reading <lb/>them &longs;everal times attentively, have marked in the margine tho&longs;e <lb/>words, wherein the &longs;trength of his arguments lie, and it will <lb/>&longs;uffice to read them. </s><s>The &longs;ir&longs;t Argument beginneth here. <emph type="italics"/>Et<emph.end type="italics"/></s></p><p type="main"><s><arrow.to.target n="marg426"></arrow.to.target> <lb/><emph type="italics"/>primo, &longs;i opinio Copernici recipiatur, Criterium naturalis Philo­ <lb/>&longs;ophiæ, ni pror&longs;us tollatur, vehementer &longs;altem labefactari <lb/>videtur.<emph.end type="italics"/> [In our Idiom thus] And fir&longs;t, if <emph type="italics"/>Copernicus<emph.end type="italics"/> his opinion <lb/>be imbraced, the <emph type="italics"/>Criterium<emph.end type="italics"/> of natural Philo&longs;ophy will be, if not <lb/>wholly &longs;ubverted, yet at lea&longs;t extreamly &longs;haken.</s></p><p type="margin"><s><margin.target id="marg426"></margin.target><emph type="italics"/>The opinion of<emph.end type="italics"/> <lb/>Copernicus <emph type="italics"/>over­ <lb/>throws the<emph.end type="italics"/> Crite­ <lb/>rium <emph type="italics"/>of Philo&longs;ophy<emph.end type="italics"/></s></p><p type="main"><s>Which, according to the opinion of all the &longs;ects of Philo&longs;ophers <lb/>requireth, that Sen&longs;e and Experience be our guides in philo&longs;opha­ <lb/>ting: But in the <emph type="italics"/>Copernican<emph.end type="italics"/> po&longs;ition the Sen&longs;es are greatly delu­ <lb/>ded, whil'&longs;t that they vi&longs;ibly di&longs;cover neer at hand in a pure <emph type="italics"/>Medi­ <lb/>um,<emph.end type="italics"/> the grave&longs;t bodies to de&longs;cend perpendicularly downwards, ne­ <lb/>ver deviating a &longs;ingle hairs breadth from rectitude; and yet accor­ <lb/>ding to the opinion of <emph type="italics"/>Copernicus,<emph.end type="italics"/> the &longs;ight in &longs;o manife&longs;t a thing <lb/>is deceived, and that motion is not reall &longs;traight, but mixt of <lb/>right and circular.</s></p><p type="main"><s>SALV. </s><s>This is the fir&longs;t argument, that <emph type="italics"/>Ari&longs;totle, Ptolomy,<emph.end type="italics"/> and <lb/>all their followers do produce; to which we have abundant­ <lb/>ly an&longs;wered, and &longs;hewn the Paralogi&longs;me, and with &longs;ufficient <lb/>plainne&longs;&longs;e proved, that the motion in common to us and other mo­ <lb/>veables, is, as if there were no &longs;uch thing; but becau&longs;e true con­ <lb/>clu&longs;ions meet with a thou&longs;and accidents, that confirme them, I <lb/><arrow.to.target n="marg427"></arrow.to.target> <lb/>will, with the favour of this Philo&longs;opher, adde &longs;omething more; <lb/>and you <emph type="italics"/>Simplicius<emph.end type="italics"/> per&longs;onating him, an&longs;wer me to what I &longs;hall <lb/>ask you: And fir&longs;t tell me, what effect hath that &longs;tone upon you, <lb/><arrow.to.target n="marg428"></arrow.to.target> <lb/>which falling from the top of the Tower, is the cau&longs;e that you per­ <lb/>ceive that motion; for if its fall doth operate upon you neither <lb/>more nor le&longs;&longs;e, than its &longs;tanding &longs;till on the Towers top, you <lb/>doubtle&longs;&longs;e could not di&longs;cern its de&longs;cent, or di&longs;tingui&longs;h its moving <lb/>from its lying &longs;till.</s></p><p type="margin"><s><margin.target id="marg427"></margin.target><emph type="italics"/>Common motion <lb/>is, as if it never <lb/>were.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg428"></margin.target><emph type="italics"/>The argument <lb/>taken from things <lb/>falling perpendicu­ <lb/>larly, another way <lb/>confuted.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I comprehend its moving, in relation to the Tower, <lb/>for that I &longs;ee it one while ju&longs;t again&longs;t &longs;uch a mark in the &longs;aid <lb/>Tower, and another while again&longs;t another lower, and &longs;o &longs;ucce&longs;­ <lb/>&longs;ively, till that at la&longs;t I perceive it arrived at the ground.</s></p><p type="main"><s>SALV. </s><s>Then if that &longs;tone were let fall from the tallons of an <lb/>Eagle flying, and &longs;hould de&longs;cend thorow the &longs;imple invi&longs;ible Air, <pb xlink:href="040/01/242.jpg" pagenum="224"/>and you had no other object vi&longs;ible and &longs;table, wherewith to make <lb/>compari&longs;ons to that, you could not perceive its motion?</s></p><p type="main"><s>SIMP. No, nor the &longs;tone it &longs;elf; for if I would &longs;ee it, when <lb/><arrow.to.target n="marg429"></arrow.to.target> <lb/>it is at the highe&longs;t, I mu&longs;t rai&longs;e up my head, and as it de&longs;cendeth <lb/>I mu&longs;t hold it lower and lower, and in a word, mu&longs;t continually <lb/>move either that, or my eyes, following the motion of the &longs;aid <lb/>&longs;tone.</s></p><p type="margin"><s><margin.target id="marg429"></margin.target><emph type="italics"/>Whence the mo­ <lb/>tion of a cadent bo­ <lb/>dy is collected.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You have now rightly an&longs;wered: you know then that <lb/><arrow.to.target n="marg430"></arrow.to.target> <lb/>the &longs;tone lyeth &longs;till, when without moving your eye, you alwayes <lb/>&longs;ee it before you; and you know that it moveth, when for the <lb/>keeping it in &longs;ight, you mu&longs;t move the organ of &longs;ight, the eye. </s><s>So <lb/>then when ever without moving your eye, you continually be­ <lb/>hold an object in the &longs;elf &longs;ame a&longs;pect, you do always judge it <lb/>immoveable.</s></p><p type="margin"><s><margin.target id="marg430"></margin.target><emph type="italics"/>The motion of <lb/>the eye argueth <lb/>the motion of the <lb/>object looked on.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I think it mu&longs;t needs be &longs;o.</s></p><p type="main"><s>SALV. </s><s>Now fancy your &longs;elf to be in a &longs;hip, and to have fixed <lb/>your eye on the point of the Sail-yard: Do you think, that be­ <lb/>cau&longs;e the &longs;hip moveth very fa&longs;t, you mu&longs;t move your eye, to keep <lb/>your &longs;ight alwayes upon the point of the Sail-yard, and to fol­ <lb/>low its motion?</s></p><p type="main"><s>SIMP. </s><s>I am certain, that I &longs;hould need to make no change at <lb/>all; and that not only in the &longs;ight; but if I had aimed a Musket <lb/>at it, I &longs;hould never have need, let the &longs;hip move how it will, <lb/>to &longs;tir it an hairs breadth to keep it full upon the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>And this happens becau&longs;e the motion, which the Ship <lb/>conferreth on the Sail-yard, it conferreth al&longs;o upon you, and upon <lb/>your eye; &longs;o that you need not &longs;tir it a jot to behold the top of <lb/>the Sail-yard: and con&longs;equently, it will &longs;eem to you immovea­ <lb/>able. </s><s>Now this Di&longs;cour&longs;e being applied to the revolution of the <lb/>Earth, and to the &longs;tone placed in the top of the Tower, in which <lb/>you cannot di&longs;cern any motion, becau&longs;e that you have that mo­ <lb/>tion which is nece&longs;&longs;ary for the following of it, in common with it <lb/>from the Earth; &longs;o that you need not move your eye. </s><s>When a­ <lb/>gain there is conferred upon it the motion of de&longs;cent, which is its <lb/>particular motion, and not yours, and that it is intermixed with the <lb/>circular, that part of the circular which is common to the &longs;tone, <lb/>and to the eye, continueth to be imperceptible, and the right one­ <lb/>ly is perceived, for that to the perception of it, you mu&longs;t follow it <lb/>with your eye, looking lower and lower. </s><s>I wi&longs;h for the undecei­ <lb/>ving of this Philo&longs;opher, that I could advi&longs;e him, that &longs;ome time <lb/><arrow.to.target n="marg431"></arrow.to.target> <lb/>or other going by water, he would carry along with him a Ve&longs;&longs;el <lb/>of rea&longs;onable depth full of water, and prepare a ball of wax, or <lb/>other matter that would de&longs;cend very &longs;lowly to the bottome, &longs;o <lb/>that in a minute of an hour, it would &longs;carce &longs;ink a yard; and that <lb/>rowing the boat as fa&longs;t as could be, &longs;o that in a minute of an hour <pb xlink:href="040/01/243.jpg" pagenum="225"/>it &longs;hould run above an hundred yards, he would let the ball &longs;ub­ <lb/>merge into the water, & freely de&longs;cend, & diligently ob&longs;erve its mo­ <lb/>tion. </s><s>If he would but do thus, he &longs;hould &longs;ee, fir&longs;t, that it would go in a <lb/>direct line towards that point of the bottom of the ve&longs;&longs;el, whither it <lb/>would tend, if the boat &longs;hould &longs;tand &longs;till; & to his eye, and in rela­ <lb/>tion to the ve&longs;&longs;el, that motion would appear mo&longs;t &longs;traight and per­ <lb/>pendicular, and yet he could not &longs;ay, but that it would be compo&longs;ed <lb/>of the right motion downwards, and of the circular about the ele­ <lb/>ment of water. </s><s>And if the&longs;e things befall in matters not natural, <lb/>and in things that we may experiment in their &longs;tate of re&longs;t; & then <lb/>again in the contrary &longs;tate of motion, and yet as to appearance no <lb/>diver&longs;ity at all is di&longs;covered, & that they &longs;eem to deceive our &longs;en&longs;e <lb/>what can we di&longs;tingui&longs;h touching the Earth, which hath been per­ <lb/>petually in the &longs;ame con&longs;titution, as to motion and re&longs;t? </s><s>And in <lb/>what time can we experiment whether any difference is di&longs;cernable <lb/>among&longs;t the&longs;e accidents of local motion, in its diver&longs;e &longs;tates of mo­ <lb/>tion and re&longs;t, if it eternally indureth in but one onely of them?</s></p><p type="margin"><s><margin.target id="marg431"></margin.target><emph type="italics"/>An experiment <lb/>that &longs;heweth how <lb/>the common motion <lb/>is imperceptible.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The&longs;e Di&longs;cour&longs;es have &longs;omewhat whetted my &longs;tomack, <lb/>which tho&longs;e fi&longs;hes, and &longs;nails had in part nau&longs;eated; and the former <lb/>made me call to minde the correction of an errour, that hath &longs;o <lb/>much appearance of truth, that I know not whether one of a <lb/>thou&longs;and would refu&longs;e to admit it as unque&longs;tionable. </s><s>And it was <lb/>this, that &longs;ailing into <emph type="italics"/>Syria,<emph.end type="italics"/> and carrying with me a very good <lb/><emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/> that had been be&longs;towed on me by our <emph type="italics"/>Common Friend,<emph.end type="italics"/> <lb/>who not many dayes before had invented, I propo&longs;ed to the Ma­ <lb/>riners, that it would be of great benefit in Navigation to make u&longs;e <lb/>of it upon the round top of a &longs;hip, to di&longs;cover and kenne Ve&longs;&longs;els <lb/>afar off. </s><s>The benefit was approved, but there was objected the <lb/><arrow.to.target n="marg432"></arrow.to.target> <lb/>difficulty of u&longs;ing it, by rea&longs;on of the Ships continual fluctuation; <lb/>and e&longs;pecially on the round top, where the agitation is &longs;o much <lb/>greater, and that it would be better for any one that would make <lb/>u&longs;e thereof to &longs;tand at the Partners upon the upper Deck, where <lb/>the to&longs;&longs;ing is le&longs;&longs;e than in any other place of the Ship. </s><s>I (for I <lb/>will not conceal my errour) concurred in the &longs;ame opinion, and <lb/>for that time &longs;aid no more: nor can I tell you by what hints I was <lb/>moved to return to ruminate with my &longs;elf upon this bu&longs;ine&longs;&longs;e, and <lb/>in the end came to di&longs;cover my &longs;implicity (although excu&longs;able) in <lb/>admitting that for true, which is mo&longs;t fal&longs;e; fal&longs;e I &longs;ay, that the <lb/>great agitation of the basket or round top, in compari&longs;on of the <lb/>&longs;mall one below, at the partners of the Ma&longs;t, &longs;hould render the <lb/>u&longs;e of the <emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> more difficult in finding out the object.</s></p><p type="margin"><s><margin.target id="marg432"></margin.target><emph type="italics"/>An ingenuous <lb/>con&longs;ideration a­ <lb/>bout the po&longs;&longs;ibility <lb/>of u&longs;ing the<emph.end type="italics"/> Tele&longs;­ <lb/>cope <emph type="italics"/>with as much <lb/>facility on the <lb/>round top of the <lb/>Ma&longs;t of a &longs;hip, <lb/>as on the Deck.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I &longs;hould have accompanied the Mariners, and your &longs;elf <lb/>at the beginning.</s></p><p type="main"><s>SIMP. </s><s>And &longs;o &longs;hould I have done, and &longs;till do: nor can I be­ <lb/>lieve, if I &longs;hould think of it an hundred years, that I could under­ <lb/>&longs;tand it otherwi&longs;e.</s></p> <pb xlink:href="040/01/244.jpg" pagenum="226"/><p type="main"><s>SAGR. </s><s>I may then, it &longs;eems, for once prove a Ma&longs;ter to you both. <lb/></s><s>And becau&longs;e the proceeding by interrogatories doth in my opinion <lb/>much dilucidate things, be&longs;ides the plea&longs;ure which it affords of con­ <lb/>founding our companion, forcing from him that which he thought he <lb/>knew not, I will make u&longs;e of that artifice. </s><s>And fir&longs;t, I &longs;uppo&longs;e that the <lb/>Ship, Gally, or other Ve&longs;&longs;el, which we would di&longs;cover, is a great way <lb/>off, that is, four, &longs;ix, ten, or twenty ^{*} miles, for that to kenne tho&longs;e <lb/><arrow.to.target n="marg433"></arrow.to.target> <lb/>neer at hand there is no need of the&longs;e Gla&longs;&longs;es: & con&longs;equently, the <lb/><emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> may at &longs;uch a di&longs;tance of four or &longs;ix miles conveniently <lb/>di&longs;cover the whole Ve&longs;&longs;el, & a muchgreater bulk. </s><s>Now I demand <lb/>what for &longs;pecies, & how many for number are the motions that are <lb/>made upon the round top, depending on the fluctuation of the Ship.</s></p><p type="margin"><s><margin.target id="marg433"></margin.target>* I deviate here <lb/>from the &longs;trict Sea <lb/>Diallect, which <lb/>denominatesall di­ <lb/>&longs;tances by Leagues.</s></p><p type="main"><s>SALV. </s><s>We will &longs;uppo&longs;e that the Ship goeth towards the Ea&longs;t. <lb/></s><s>Fir&longs;t, in a calme Sea, it would have no other motion than <lb/><arrow.to.target n="marg434"></arrow.to.target> <lb/>this of progre&longs;&longs;ion, but adding the undulation of the Waves, <lb/>there &longs;hall re&longs;ult thence one, which alternately hoy&longs;ting and low­ <lb/>ering the poop and prow, maketh the round top, to lean forwards <lb/>and backwards; other waves driving the ve&longs;&longs;el &longs;idewayes, bow the <lb/>Ma&longs;t to the Starboard and Larboard; others, may bring the &longs;hip <lb/>&longs;omewhat abovt, and bear her away by the Mi&longs;ne from Ea&longs;t, one <lb/><arrow.to.target n="marg435"></arrow.to.target> <lb/>while towards the ^{*} Northea&longs;t; another while toward the South­ <lb/>ea&longs;t; others bearing her up by the Carine may make her onely to <lb/>ri&longs;e, and fall; and in &longs;um, the&longs;e motions are for &longs;pecies two, one <lb/>that changeth the direction of the <emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> angularly, the other <lb/>lineally, without changing angle, that is, alwayes keeping the <lb/>tube of the In&longs;trument parallel to its &longs;elf.</s></p><p type="margin"><s><margin.target id="marg434"></margin.target><emph type="italics"/>Different moti­ <lb/>ons depending on <lb/>the fluctuation of <lb/>the Ship.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg435"></margin.target>* <emph type="italics"/>Greco,<emph.end type="italics"/> which <lb/>the Latine Tran­ <lb/>&longs;lator according to <lb/>his u&longs;ual carele&longs;&longs;e­ <lb/>ne&longs;&longs;e (to call it no <lb/>wor&longs;e) tran&longs;lates <lb/><emph type="italics"/>Corum Ventum,<emph.end type="italics"/> <lb/>the Northwe&longs;t <lb/>Wind, for <emph type="italics"/>Ventum <lb/>Libanotum.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Tell me, in the next place, if we, having fir&longs;t directed <lb/><arrow.to.target n="marg436"></arrow.to.target> <lb/>the <emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> yonder away towards the Tower of ^{*} <emph type="italics"/>Burano,<emph.end type="italics"/> &longs;ix <lb/>miles from hence, do turn it angularly to the right hand, or to the <lb/>left, or el&longs;e upwards or downwards, but a ^{*}&longs;traws breadth, what ef­ <lb/><arrow.to.target n="marg437"></arrow.to.target> <lb/>fect &longs;hall it have upon us touching the finding out of the &longs;aid tower?</s></p><p type="margin"><s><margin.target id="marg436"></margin.target><emph type="italics"/>Two mutations <lb/>made in the Tele­ <lb/>&longs;cope, depending on <lb/>the agitation of the <lb/>Ship.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg437"></margin.target>* This is a Ca&longs;tle <lb/>&longs;ix Italian miles <lb/>from <emph type="italics"/>Venice<emph.end type="italics"/> <lb/>Northwards.</s></p><p type="main"><s>SALV. </s><s>It would make us immediately lo&longs;e &longs;ight of it, for &longs;uch <lb/>a declination, though &longs;mall here, may import there hundreds and <lb/><arrow.to.target n="marg438"></arrow.to.target> <lb/>thou&longs;ands of yards.</s></p><p type="margin"><s><margin.target id="marg438"></margin.target>* <emph type="italics"/>Vnnerod' ug­ <lb/>na,<emph.end type="italics"/> the black or <lb/>paring of a nail.</s></p><p type="main"><s>SAGR. </s><s>But if without changing the angle, keeping the tube <lb/>alwayes parallel to it &longs;elf, we &longs;hould transfer it ten or twelve <lb/>yards farther off to the right or left hand, upwards or downwards, <lb/>what alteration would it make as to the Tower?</s></p><p type="main"><s>SALV. </s><s>The change would be ab&longs;olutely undi&longs;cernable; for <lb/>that the &longs;paces here and there being contained between parallel <lb/>rayes, the mutations made here and there, ought to be equal, and <lb/>becau&longs;e the &longs;pace which the In&longs;trument di&longs;covers yonder, is capa­ <lb/>ble of many of tho&longs;e Towers; therefore we &longs;hall not lo&longs;e &longs;ight of it.</s></p><p type="main"><s>SAGR. </s><s>Returning now to the Ship, we may undoubtedly af­ <lb/>firm, that the <emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> moving to the right or left, upwards, or <pb xlink:href="040/01/245.jpg" pagenum="227"/>downwards, and al&longs;o forwards or backwards ten or fifteen fathom, <lb/>keeping it all the while parallel to its &longs;elf, the vi&longs;ive ray cannot <lb/>&longs;tray from the point ob&longs;erved in the object, more than tho&longs;e fif­ <lb/>teen fathom; and becau&longs;e in a di&longs;tance of eight or ten miles, the <lb/>In&longs;trument takes in a much greater &longs;pace than the Gally or other <lb/>Ve&longs;&longs;el kenn'd; therefore that &longs;mall mutation &longs;hall not make me <lb/>lo&longs;e &longs;ight of her. </s><s>The impediment therefore, and the cau&longs;e of <lb/>lo&longs;ing the object cannot befall us, unle&longs;&longs;e upon the mutation made <lb/>angularly; &longs;ince that <emph type="italics"/>Tele&longs;copes<emph.end type="italics"/> tran&longs;portation higher or lower, to <lb/>the right, or to the left, by the agitation of the &longs;hip, cannot import <lb/>any great number of fathomes. </s><s>Now &longs;uppo&longs;e that you had two <lb/><emph type="italics"/>Tele&longs;copes<emph.end type="italics"/> fixed, one at the Partners clo&longs;e by the Deck, and the o­ <lb/>ther at the round top, nay at the main top, or main top-gallant <lb/>top, where you hang forth the <emph type="italics"/>Pennon<emph.end type="italics"/> or &longs;treamer, and that they <lb/>be both directed to the Ve&longs;&longs;el that is ten miles off, tell me, whe­ <lb/>ther you believe that any agitation of the &longs;hip, & inclination of the <lb/>Ma&longs;t, can make greater changes, as to the angle, in the higher tube, <lb/>than in the lower? </s><s>One wave ari&longs;ing, the prow will make the main <lb/>top give back fifteen or twenty fathom more than the foot of the <lb/>Ma&longs;t, and it &longs;hall carry the upper tube along with it &longs;o greata &longs;pace, <lb/>& the lower it may be not a palm; but the angle &longs;hall change in one <lb/>In&longs;trument a&longs;well as in the other; and likewi&longs;e a &longs;ide-billow &longs;hall <lb/>bear the higher tube an hundred times as far to the Larboard or <lb/>Starboard, as it will the other below; but the angles change not at <lb/>all, or el&longs;e alter both alike. </s><s>But the mutation to the right hand or <lb/>left, forwards or backwards, upwards or downwards, bringeth no <lb/>&longs;en&longs;ible impediment in the kenning of objects remote, though the <lb/>alteration of the angle maketh great change therein; Therefore it <lb/>mu&longs;t of nece&longs;&longs;ity be confe&longs;&longs;ed, that the u&longs;e of the <emph type="italics"/>Tele&longs;cope<emph.end type="italics"/> on the <lb/>round top is no more difficult than upon the Deck at the Partners; <lb/>&longs;eeing that the angular mutations are alike in both places.</s></p><p type="main"><s>SALV. </s><s>How much circum&longs;pection is there to be u&longs;ed in affirming <lb/>or denying a propo&longs;ition? </s><s>I &longs;ay again, thar hearing it re&longs;olutely affir­ <lb/>med, that there is a greater motion made on the Ma&longs;ts top, than at <lb/>its partners, every one will per&longs;wade him&longs;elf, that the u&longs;e of the <emph type="italics"/>Te­ <lb/>le&longs;cope<emph.end type="italics"/> is much more difficult above than below. </s><s>And thus al&longs;o I w <lb/>ill excu&longs;e tho&longs;e Philo&longs;ophers, who grow impatient and fly out into <lb/>pa&longs;&longs;ion again&longs;t &longs;uch as will not grant them, that that Cannon bullet <lb/>which they cleerly &longs;ee to fall in a right line perpendicularly, doth <lb/>ab&longs;olutely move in that manner; but will have its motion to be by <lb/>an arch, and al&longs;o very much inclined and tran&longs;ver&longs;al: but let us <lb/>leave them in the&longs;e labyrinths, and let us hear the other objections, <lb/>that our Author in hand brings again&longs;t <emph type="italics"/>Copernicus.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The Author goeth on to demon&longs;trate that in the Do­ <lb/>ctrine of <emph type="italics"/>Copernicus,<emph.end type="italics"/> it is requi&longs;ite to deny the Sen&longs;es, and the <pb xlink:href="040/01/246.jpg" pagenum="228"/>greate&longs;t Sen&longs;ations, as for in&longs;tance it would be, if we that feel the <lb/><arrow.to.target n="marg439"></arrow.to.target> <lb/>re&longs;pirations of a gentle gale, &longs;hould not feel the impul&longs;e of a per­ <lb/>petual winde that beateth upon us with a velocity that runs more <lb/>than 2529 miles an hour, for &longs;o much is the &longs;pace that the centre <lb/>of the Earth in its annual motion pa&longs;&longs;eth in an hour upon the cir­ <lb/>cumference of the grand Orb, as he diligently calculates; and <lb/>becau&longs;e, as he &longs;aith, by the judgment of <emph type="italics"/>Copernicus, Cum terra <lb/>movetur circumpo&longs;itus aër, motus tamen ejus, velocior licet ac ra­ <lb/>pidior celerrimo quocunque vento, à nohis non &longs;entiretur, &longs;ed &longs;um­ <lb/>ma tum tranquilitas reputaretur, ni&longs;i alius motus accederet. </s><s>Quid <lb/>e&longs;t verò decipi &longs;en&longs;um, ni&longs;i hæc e&longs;&longs;et deceptio<emph.end type="italics"/>? [<emph type="italics"/>Which I make to <lb/>&longs;peak to this &longs;en&longs;e.<emph.end type="italics"/>] The circumpo&longs;ed air is moved with the Earth, <lb/>yet its motion, although more &longs;peedy and rapid than the &longs;wifte&longs;t <lb/>wind what&longs;oever, would not be perceived by us, but then would <lb/>be thought a great tranquillity, unle&longs;&longs;e &longs;ome other motion &longs;hould <lb/>happen; what then is the deception of the &longs;en&longs;e, if this be <lb/>not?</s></p><p type="margin"><s><margin.target id="marg439"></margin.target><emph type="italics"/>The annual mo­ <lb/>tion of the Earth <lb/>mu&longs;t cau&longs;e a per­ <lb/>petual and &longs;trong <lb/>winde.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>It mu&longs;t needs be that this Philo&longs;opher thinketh, that <lb/>that Earth which <emph type="italics"/>Copernicus<emph.end type="italics"/> maketh to turn round, together with <lb/>the ambient air along the circumference of the great Orb, is not that <lb/>whereon we inhabit, but &longs;ome other &longs;eparated from this; for that this <lb/>of ours carrieth us al&longs;o along with it with the &longs;ame velocity, as al­ <lb/><arrow.to.target n="marg440"></arrow.to.target> <lb/>&longs;o the circumjacent air: And what beating of the air can we feel, <lb/>when we fly with equal &longs;peed from that which &longs;hould acco&longs;t us? <lb/></s><s>This Gentleman forgot, that we no le&longs;s than the Earth and air are <lb/>carried about, and that con&longs;equently we are always touch'd by <lb/>one and the &longs;ame part of the air, which yet doth not make us feel <lb/>it.</s></p><p type="margin"><s><margin.target id="marg440"></margin.target><emph type="italics"/>The air alwayes <lb/>touching us with <lb/>the &longs;ame part of it <lb/>cannot make us <lb/>feel it.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>But I rather think that he did not &longs;o think; hear the <lb/>words which immediately follow. <emph type="italics"/>Præterea nos quoque rotamur <lb/>ex circumductione terræ &c.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Now I can no longer help nor excu&longs;e him; do you <lb/>plead for him and bring him off, <emph type="italics"/>Simplicius.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I cannot thus upon the &longs;udden think of an excu&longs;e that <lb/>plea&longs;eth me.</s></p><p type="main"><s>SALV. </s><s>Go to; take this whole night to think on it, and de­ <lb/>fend him to morrow; in the mean time let us hear &longs;ome other of <lb/>his objections.</s></p><p type="main"><s>SIMP. </s><s>He pro&longs;ecuteth the &longs;ame Objection, &longs;hewing, that in the <lb/><arrow.to.target n="marg441"></arrow.to.target> <lb/>way of <emph type="italics"/>Copernicus,<emph.end type="italics"/> a man mu&longs;t deny his own &longs;en&longs;es. </s><s>For that <lb/>this principle whereby we turn round with the Earth, either is <lb/>intrin&longs;ick to us, or external; that is, a rapture of that Earth; and <lb/>if it be this &longs;econd, we not feeling any &longs;uch rapture, it mu&longs;t be <lb/>confe&longs;&longs;ed that the &longs;en&longs;e of feeling, doth not feel its own object <lb/>touching it, nor its impre&longs;&longs;ion on the &longs;en&longs;ible part: but if the prin­ <pb xlink:href="040/01/247.jpg" pagenum="229"/>ciple be intrin&longs;ecal, we &longs;hall not perceive a local motion that is de­ <lb/>rived from our &longs;elves, and we &longs;hall never di&longs;cover a propen&longs;ion per­ <lb/>petually annexed to our &longs;elves.</s></p><p type="margin"><s><margin.target id="marg441"></margin.target><emph type="italics"/>He that will fol­ <lb/>low<emph.end type="italics"/> Copernicus, <lb/><emph type="italics"/>must deny his &longs;er­ <lb/>&longs;es.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>So that the in&longs;tance of this Philo&longs;opher lays its &longs;tre&longs;s up­ <lb/>on this, that whether the principle by which we move round with <lb/>the Earth be either extern, or intern, yet however we mu&longs;t per­ <lb/>ceive it, and not perceiving it, it is neither the one nor the other, <lb/>and therefore we move not, nor con&longs;equently the Earth. </s><s>Now I <lb/><arrow.to.target n="marg442"></arrow.to.target> <lb/>&longs;ay, that it may be both ways, and yet we not perceive the &longs;ame. <lb/></s><s>And that it may be external, the experiment of the boat &longs;upera­ <lb/>bundantly &longs;atis&longs;ieth me; I &longs;ay, &longs;uperabundantly, becau&longs;e it being <lb/>in our power at all times to make it move, and al&longs;o to make it <lb/>&longs;tand &longs;till, and with great exactne&longs;s to make ob&longs;ervation, whether <lb/>by &longs;ome diver&longs;ity that may be comprehended by the &longs;en&longs;e of feel­ <lb/>ing, we can come to know whether it moveth or no, &longs;eeing that <lb/>as yet no &longs;uch &longs;cience is obtained: Will it then be any matter of <lb/>wonder, if the &longs;ame accident is unknown to us on the Earth, the <lb/>which may have carried us about perpetually, and we, without our <lb/><arrow.to.target n="marg443"></arrow.to.target> <lb/>being ever able to experiment its re&longs;t? </s><s>You, <emph type="italics"/>Simplicius,<emph.end type="italics"/> as I be­ <lb/>lieve, have gone by boat many times to <emph type="italics"/>Padoua,<emph.end type="italics"/> and if you will <lb/>confe&longs;s the truth, you never felt in your &longs;elf the participation of <lb/>that motion, unle&longs;s when the boat running a-ground, or encoun­ <lb/>tring &longs;ome ob&longs;tacle, did &longs;top, and that you with the other Pa&longs;&longs;en­ <lb/>gers being taken on a &longs;udden, were with danger over-&longs;et. </s><s>It <lb/>would be nece&longs;&longs;ary that the Terre&longs;trial Globe &longs;hould meet with <lb/>&longs;ome rub that might arre&longs;t it, for I a&longs;&longs;ure you, that then you <lb/>would di&longs;cern the impul&longs;e re&longs;iding in you, when it &longs;hould to&longs;s you <lb/>up towards the Stars. </s><s>It's true, that by the other &longs;en&longs;es, but yet <lb/><arrow.to.target n="marg444"></arrow.to.target> <lb/>a&longs;&longs;i&longs;ted by Rea&longs;on, you may perceive the motion of the boat, that <lb/>is, with the &longs;ight, in that you &longs;ee the trees and buildings placed on <lb/>the &longs;hoar, which being &longs;eparated from the boat, &longs;eem to move the <lb/><arrow.to.target n="marg445"></arrow.to.target> <lb/>contrary way. </s><s>But if you would by &longs;uch an experiment receive <lb/>intire &longs;atisfaction in this bu&longs;ine&longs;s of the Terre&longs;trial motion, look <lb/>on the &longs;tars, which upon this rea&longs;on &longs;eem to move the contrary <lb/>way. </s><s>As to the wondering that we &longs;hould not feel &longs;uch a prin­ <lb/>ciple, &longs;uppo&longs;ing it to be internal, is a le&longs;s rea&longs;onable conceit; for <lb/>if we do not feel &longs;uch a one, that cometh to us from without, <lb/>and that frequently goeth away, with what rea&longs;on can we expect <lb/>to feel it, if it immutably and continually re&longs;ides in us? </s><s>Now let <lb/>us &longs;ee what you have farther to allege on this argument.</s></p><p type="margin"><s><margin.target id="marg442"></margin.target><emph type="italics"/>Our motion may <lb/>be either interne or <lb/>externe, and yet <lb/>we never perceive <lb/>or feel it.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg443"></margin.target><emph type="italics"/>The motion of a <lb/>Boat in&longs;en&longs;ible to <lb/>tho&longs;e that are with <lb/>in it, as to the &longs;en&longs;e <lb/>of feeling.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg444"></margin.target><emph type="italics"/>The boats moti­ <lb/>on is perceptible to <lb/>the &longs;ight joyn'd <lb/>with rea&longs;on.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg445"></margin.target><emph type="italics"/>The terre&longs;trial <lb/>motion collected <lb/>from the &longs;tars.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Take this &longs;hort exclamation. <emph type="italics"/>Ex hac itaque opinione <lb/>nece&longs;&longs;e est diffidere no&longs;tris &longs;en&longs;ibus, ut penitùs fall acibus vel &longs;tupidis <lb/>in &longs;en&longs;ilibus, etiam conjuncti&longs;&longs;imis, dijudicandis. </s><s>Quam ergò ve­ <lb/>ritatem &longs;perare po&longs;&longs;umus à facultate adeò fallaci ortum trabentem<emph.end type="italics"/>? <lb/>[Which I render thus:] From this opinion likewi&longs;e, we mu&longs;t of <pb xlink:href="040/01/248.jpg" pagenum="230"/>nece&longs;&longs;ity &longs;u&longs;pect our own &longs;en&longs;es, as wholly fallible, or &longs;tupid in <lb/>judging of &longs;en&longs;ible things even very near at hand. </s><s>What truth <lb/>therefore can we hope for, to be derived from &longs;o deceiveable a fa­ <lb/>culty?</s></p><p type="main"><s>SALV. </s><s>But I de&longs;ire not to deduce precepts more profitable, or <lb/>more certain, learning to be more circum&longs;pect and le&longs;s confident <lb/>about that which at fir&longs;t blu&longs;h is repre&longs;ented to us by the &longs;en&longs;es, <lb/>which may ea&longs;ily deceive us. </s><s>And I would not have this Author <lb/>trouble him&longs;elf in attemptiug to make us comprehend by &longs;en&longs;e, <lb/>that this motion of de&longs;cending Graves is &longs;imply right, and of <lb/>no other kind; nor let him exclaim that a thing &longs;o clear, manife&longs;t, <lb/>and obvious &longs;hould be brought in que&longs;tion; for in &longs;o doing, he <lb/>maketh others believe, that he thinketh tho&longs;e that deny that mo­ <lb/>tion to be ab&longs;olutely &longs;treight, but rather circular, the &longs;tone did <lb/>&longs;en&longs;ibly &longs;ee it to move in an arch, &longs;eeing that he inviteth their &longs;en&longs;es <lb/>more than their Rea&longs;on, to judg of that effect: which is not true, <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> for like as I, that am indifferent in all the&longs;e opini­ <lb/>ons, and onely in the manner of a Comedian, per&longs;onate <emph type="italics"/>Coperni­ <lb/>cus<emph.end type="italics"/> in the&longs;e our repre&longs;entations, have never &longs;een, nor thought <lb/>that I have &longs;een that &longs;tone fall otherwi&longs;e than perpendicularly, <lb/>&longs;o I believe, that to the eyes of all others it &longs;eemed to do the <lb/>&longs;ame. </s><s>Better it is therefore, that depo&longs;ing that appearance in <lb/>which all agree, we make u&longs;e of our Rea&longs;on, either to confirm the <lb/>reality of that, or to di&longs;cover its fallacy.</s></p><p type="main"><s>SAGR. </s><s>If I could any time meet with this Philo&longs;opher, who <lb/>yet me thinks is more &longs;ublime than the re&longs;t of the followers of <lb/>the &longs;ame doctrines, I would in token of my affection put him in <lb/>mind of an accident which he hath doubtle&longs;s very often beheld; <lb/>from which, with great conformity to that which we now di&longs;cour&longs;e <lb/>of, it may be collected how ea&longs;ily one may be deceived by the bare <lb/>appearance, or, if you will, repre&longs;entation of the &longs;en&longs;e. </s><s>And the <lb/>accident is, the Moons &longs;eeming to follow tho&longs;e that walk the &longs;treets <lb/>in the night, with a pace equal to theirs, whil&longs;t they &longs;ee it go gli­ <lb/>ding along the Roofs of hou&longs;es, upon which it &longs;heweth ju&longs;t like a <lb/>cat, that really running along the ridges of hou&longs;es, leaveth them <lb/>behind. </s><s>An appearance that, did not rea&longs;on interpo&longs;e, would but <lb/>too manife&longs;tly delude the &longs;ight.</s></p><p type="main"><s>SIMP. </s><s>Indeed there want not experiments that render us cer­ <lb/><arrow.to.target n="marg446"></arrow.to.target> <lb/>tain of the fallacy of the meer &longs;en&longs;es; therefore &longs;u&longs;pending &longs;uch <lb/>&longs;en&longs;ations for the pre&longs;ent, let us hear the Arguments that follow <lb/>which are taken, as he &longs;aith, <emph type="italics"/>ex rerum naturâ.<emph.end type="italics"/> The fir&longs;t of which <lb/>is, that the Earth cannot of its own nature move with three moti­ <lb/>ons very different; or otherwi&longs;e we mu&longs;t deny many manife&longs;t <lb/><arrow.to.target n="marg447"></arrow.to.target> <lb/>Axioms. </s><s>The fir&longs;t whereof is, that <emph type="italics"/>Omnïs effectus dependeat ab <lb/>aliquâ cau&longs;â; [i. </s><s>e.]<emph.end type="italics"/> that every effect dependeth on &longs;ome cau&longs;e. <pb xlink:href="040/01/249.jpg" pagenum="231"/>The &longs;econd, that <emph type="italics"/>Nulla res &longs;eip&longs;am producat; [i. </s><s>e.]<emph.end type="italics"/> that nothing <lb/>produceth it &longs;elf: from whence it follows, that it is not po&longs;&longs;i­ <lb/>ble that the mover and moved &longs;hould be totally the &longs;ame thing: <lb/>And this is manife&longs;t, not onely in things that are moved by an ex­ <lb/>trin&longs;ick mover; but it is gathered al&longs;o from the principles pro­ <lb/>pounded, that the &longs;ame holdeth true in the natural motion depen­ <lb/>dent on an intrin&longs;ick principle; otherwi&longs;e, being that the mover, <lb/>as a mover, is the cau&longs;e, and the thing moved, as moved, is the <lb/>effect, the &longs;ame thing would totally be both the cau&longs;e and effect. <lb/></s><s>Therefore a body doth not move its whole &longs;elf, that is, &longs;o as <lb/>that all moveth, and all is moved; but its nece&longs;&longs;ary in the thing <lb/>moved to di&longs;tingui&longs;h in &longs;ome manner the efficient principle of the <lb/>motion, and that which with that motion is moved. </s><s>The third <lb/>Axiom is, that <emph type="italics"/>in rebus quæ &longs;en&longs;ui &longs;ubjiciuntur, unum, quatenus <lb/>unum, unam &longs;olam rem producat; i. </s><s>e.<emph.end type="italics"/> That in things &longs;ubject to <lb/>the &longs;en&longs;es, one, as it is one, produceth but onely one thing: That <lb/>is, the &longs;oul in animals produceth its true divers operations, as the <lb/>&longs;ight, the hearing, the &longs;mell, generation, <emph type="italics"/>&c.<emph.end type="italics"/> but all the&longs;e with <lb/>&longs;everal in&longs;truments. </s><s>And in &longs;hort, in things &longs;en&longs;ible, the diver&longs;i­ <lb/>ty of operations, is ob&longs;erved to derive it &longs;elf from the diver&longs;ity <lb/>that is in the cau&longs;e. </s><s>Now if we put all the&longs;e Axioms together, it <lb/><arrow.to.target n="marg448"></arrow.to.target> <lb/>will be a thing very manife&longs;t, that one &longs;imple body, as is the <lb/>Earth, cannot of its own nature move at the &longs;ame time with <lb/>three motions, very divers: For by the foregoing &longs;uppo&longs;itions, <lb/>all moveth not its &longs;elf all; it is nece&longs;fary therefore to di&longs;tingui&longs;h <lb/>in it three principles of its three motions; otherwi&longs;e one and the <lb/>&longs;ame principle would produce many motions; but if it contein in <lb/>it three principles of natural motions, be&longs;ides the part moved, it <lb/>&longs;hall not be a &longs;imple body, but compounded of three principle <lb/>movers, and of the part moved. </s><s>If therefore the Earth be a &longs;im­ <lb/><arrow.to.target n="marg449"></arrow.to.target> <lb/>ple body, it &longs;hall not move with three motions; nay more, it will <lb/>not move with any of tho&longs;e which <emph type="italics"/>Copernicus<emph.end type="italics"/> a&longs;cribeth to it, it <lb/>being to move but with one alone, for that it is manife&longs;t, by the <lb/>rea&longs;ons of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that it moveth to its centre, as its parts do <lb/>&longs;hew, which de&longs;cend at right angles to the Earths Spherical <lb/>Surface.</s></p><p type="margin"><s><margin.target id="marg446"></margin.target><emph type="italics"/>Arguments a­ <lb/>gain&longs;t the Earths <lb/>motion taken,<emph.end type="italics"/> ex <lb/>rerum natura.</s></p><p type="margin"><s><margin.target id="marg447"></margin.target><emph type="italics"/>Three Axioms <lb/>that are &longs;uppo&longs;ed <lb/>manife&longs;t.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg448"></margin.target><emph type="italics"/>A &longs;imple body <lb/>as the Earth, can­ <lb/>not move with <lb/>three &longs;everal moti­ <lb/>ons.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg449"></margin.target><emph type="italics"/>The Earth can­ <lb/>not move with any <lb/>of the motions a&longs;&longs;i­ <lb/>gned it by<emph.end type="italics"/> Coperni­ <lb/>cus.</s></p><p type="main"><s>SALV. </s><s>Many things might be &longs;aid, and con&longs;idered touching <lb/>the connection of this argument; but in regard that we can re­ <lb/><arrow.to.target n="marg450"></arrow.to.target> <lb/>&longs;olve it in few words, I will not at this time without need inlarge <lb/>upon it; and &longs;o much the rather, becau&longs;e the &longs;ame Author hath <lb/>furni&longs;hed me with an an&longs;wer, when he &longs;aith that from one &longs;ole prin­ <lb/>ple in animals, there are produced divers operations; &longs;o that for <lb/>the pre&longs;ent my an&longs;wer &longs;hall be, that in the &longs;ame manner the Earth <lb/>from one onely principle deriveth &longs;everal operations.</s></p><p type="margin"><s><margin.target id="marg450"></margin.target><emph type="italics"/>An&longs;wers to the <lb/>arguments contra­ <lb/>ry to the Earths <lb/>motion, taken<emph.end type="italics"/> ex <lb/>rerum natura.</s></p><p type="main"><s>SIMP. </s><s>But this an&longs;wer will not at all &longs;atisfie the Author who <pb xlink:href="040/01/250.jpg" pagenum="232"/>makes the objection, yea, it is totally overthrown by that which <lb/>immediately after he addeth for a greater confirmation of his argu­ <lb/>ment, as you &longs;hall hear. </s><s>He re-inforceth his argument, I &longs;ay, with <lb/><arrow.to.target n="marg451"></arrow.to.target> <lb/>another Axiome, which is this; That <emph type="italics"/>natura in rebus nece&longs;&longs;ari is <lb/>nec deficiat, nec abundat: i.e.<emph.end type="italics"/> That nature in things nece&longs;&longs;ary is <lb/>neither defective, nor &longs;uperfluous. </s><s>This is obvious to the ob&longs;er­ <lb/><arrow.to.target n="marg452"></arrow.to.target> <lb/>vers of natural things, and chiefly of animals, in which, becau&longs;e <lb/>they are to move with many motions, Nature hath made many <lb/>flexures, and hath thereunto commodiou&longs;ly knitted the parts for <lb/>motion, as to the knees, to the hips, for the inabling of living <lb/>creatures to go, and run at their plea&longs;ure. </s><s>Moreover in man he <lb/>hath framed many flexions, and joynts, in the elbow, and hand, to <lb/>enable them to perform many motions. </s><s>From the&longs;e things the ar­ <lb/><arrow.to.target n="marg453"></arrow.to.target> <lb/>gument is taken again&longs;t the threefold motion of the Earth. [<emph type="italics"/>Ei­ <lb/>ther the Body, that is one, and continuate, without any manner of <lb/>knittings or flexions, can exerci&longs;e divers motions, or cannot: If it <lb/>can without them, then in vain hath nature framed the flexures in <lb/>animals; which is contrary to the Axiome: but if it cannot with­ <lb/>out them, then the Earth, one body, and continuate, and deprived of <lb/>flexures, and joynts, cannot of its own nature move with plurali­ <lb/>ty of motions.<emph.end type="italics"/>] You &longs;ee now how craftily he falls upon your an­ <lb/>&longs;wer, as if he had fore&longs;een it.</s></p><p type="margin"><s><margin.target id="marg451"></margin.target><emph type="italics"/>A fourth Ax­ <lb/>iome again&longs;t the <lb/>motion of the Earth<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg452"></margin.target><emph type="italics"/>Flexures nece&longs;­ <lb/>&longs;ary in animals for <lb/>the diver&longs;ity of <lb/>their motions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg453"></margin.target><emph type="italics"/>Another argu­ <lb/>ment again&longs;t the <lb/>three fold motion of <lb/>the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Are you &longs;erious, or do you je&longs;t?</s></p><p type="main"><s>SIMP. </s><s>I &longs;peak it with the be&longs;t judgment I have.</s></p><p type="main"><s>SALV. </s><s>You mu&longs;t therefore &longs;ee that you have as fortunate an <lb/>hand in defending the reply of this Philo&longs;opher, again&longs;t &longs;ome o­ <lb/>ther rejoynders made to him; therefore an&longs;wer for him, I pray <lb/>you, &longs;eeing we cannot have him here. </s><s>You fir&longs;t admit it for true, <lb/>that Nature hath made the joynts, flexures, and knuckles of li­ <lb/>ving creatures, to the intent that they might move with &longs;nndry <lb/>and divers motions; and I deny this propo&longs;ition; and &longs;ay, that <lb/>the&longs;e flexions are made, that the animal may move one, or more <lb/><arrow.to.target n="marg454"></arrow.to.target> <lb/>of its parts, the re&longs;t remaining immoved: and I &longs;ay, that as to the <lb/>&longs;pecies and differences of motions tho&longs;e are of one kind alone, to <lb/>wit, all circular, and for this cau&longs;e you &longs;ee all the ends of the mo­ <lb/><arrow.to.target n="marg455"></arrow.to.target> <lb/>veable bones to be convex or concave, and of the&longs;e &longs;ome are &longs;phe­ <lb/>rical, as are tho&longs;e that are to move every way, as in the &longs;houlder­ <lb/><arrow.to.target n="marg456"></arrow.to.target> <lb/>joynt, the arme of the En&longs;igne doth, in di&longs;playing the Colours, <lb/>and that of the Falconer in bringing his Hawk to the lure; and <lb/>&longs;uch is the flexure of the elbow, upon which the hand turns round, <lb/>in boring with an augure: others are circular onely one way, and <lb/>as it were cylindrical, which &longs;erve for the members that bend one­ <lb/><arrow.to.target n="marg457"></arrow.to.target> <lb/>ly in one fa&longs;hion, as the joynts of the fingers one above another, <lb/>&c. </s><s>But without more particular inductions, one only general di&longs;­ <lb/>cour&longs;e may make this truth under&longs;tood; and this is, that of a &longs;olid <pb xlink:href="040/01/251.jpg" pagenum="233"/>body that moveth, one of its extreams &longs;tanding &longs;till without chan­ <lb/>ching place, the motion mu&longs;t needs be circular, and no other: and <lb/><arrow.to.target n="marg458"></arrow.to.target> <lb/>becau&longs;e in the living creatures moving, one of its members doth <lb/>not &longs;eparate from the other its conterminal, therefore that motion <lb/>is of nece&longs;&longs;ity circular.</s></p><p type="margin"><s><margin.target id="marg454"></margin.target><emph type="italics"/>The Flexures in <lb/>animals are not <lb/>made for the di­ <lb/>ver&longs;ity of motions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg455"></margin.target><emph type="italics"/>The motions of <lb/>animals are of one <lb/>&longs;ort.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg456"></margin.target><emph type="italics"/>The ends of the <lb/>bones are all ro­ <lb/>tund.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg457"></margin.target><emph type="italics"/>It is demon&longs;tra­ <lb/>ted, that the ends <lb/>of the bones are of <lb/>nece&longs;&longs;ity to be ro­ <lb/>tund.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg458"></margin.target><emph type="italics"/>The motions of <lb/>animals are all <lb/>circular.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>How can this be? </s><s>For I &longs;ee the animal move with an <lb/>hundred motions that are not circular, and very different from one <lb/>another, as to run, to skip, to climbe, to de&longs;cend, to &longs;wim, and <lb/>many others. <lb/><arrow.to.target n="marg459"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg459"></margin.target><emph type="italics"/>Secondary moti­ <lb/>ons of animals de­ <lb/>pendent on the fir&longs;t<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Tis well: but the&longs;e are &longs;econdary motions, depending <lb/>on the preceding motions of the joynts and flexures. </s><s>Upon the <lb/>plying of the legs to the knees, and the thighs to the hips, which <lb/>are circular motions of the parts, is produced, as con&longs;equents, the <lb/>skip, or running, which are motions of the whole body, and the&longs;e <lb/>may po&longs;&longs;ibly not be circular. </s><s>Now becau&longs;e one part of the ter­</s></p><p type="main"><s><arrow.to.target n="marg460"></arrow.to.target> <lb/>re&longs;trial Globe is not required to move upon another part immove­ <lb/>able, but that the motion is to be of the whole body, there is no <lb/>need in it of flexures.</s></p><p type="margin"><s><margin.target id="marg460"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Terre&longs;triall <lb/>Globe <emph type="italics"/>hath noe <lb/>need of flexures.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>This (will the aduer&longs;ary rejoyn) might be, if the moti­ <lb/>on were but one alone, but they being three, and tho&longs;e very dif­ <lb/>ferent from each other, it is not po&longs;&longs;ible that they &longs;hould concur in <lb/><arrow.to.target n="marg461"></arrow.to.target> <lb/>an ^{*} articulate body.</s></p><p type="margin"><s><margin.target id="marg461"></margin.target>* Without joynts</s></p><p type="main"><s>SALV. </s><s>I verily believe that this would be the an&longs;wer of the <lb/>Philo&longs;opher. </s><s>Again&longs;t which I make oppo&longs;ition another way; and <lb/>ask you, whether you think that by way of joynts and flexures one <lb/>may adapt the terre&longs;trial Globe to the participation of three diffe­ <lb/>rent circular motions? </s><s>Do you not an&longs;wer me? </s><s>Seeing you are <lb/>&longs;peechle&longs;&longs;e, I will undertake to an&longs;wer for the Philo&longs;opher, who <lb/>would ab&longs;olutely reply that they might; for that otherwi&longs;e it <lb/>would have been &longs;uperfluous, and be&longs;ides the purpo&longs;e to have pro­ <lb/>po&longs;ed to con&longs;ideration, that nature maketh the flexions, to the <lb/>end, the moveable may move with different motions; and that <lb/>therefore the terre&longs;trial Globe having no flexures, it cannot have <lb/>tho&longs;e three motions which are a&longs;cribed to it. </s><s>For if he had <lb/>thought, that neither by help of flexures, it could be rendered apt <lb/>for &longs;uch motions, he would have freely affirmed, that the Globe <lb/>could not move with three motions. </s><s>Now granting this, I intreat <lb/><arrow.to.target n="marg462"></arrow.to.target> <lb/>you, and by you, if it were po&longs;&longs;ible, that Philo&longs;opher, Au­ <lb/>thor of the Argument, to be &longs;o courteous as to teach me in what <lb/>manner tho&longs;e flexures &longs;hould be accommodated, &longs;o that tho&longs;e <lb/>three motions might commodiou&longs;ly be excerci&longs;ed; and I grant you <lb/>four or &longs;ix moneths time to think of an an&longs;wer. </s><s>As to me, it &longs;eem­ <lb/>eth that one principle onely may cau&longs;e a plurality of motions in <lb/><arrow.to.target n="marg463"></arrow.to.target> <lb/>the Terre&longs;trial Globe, ju&longs;t in the &longs;ame manner that, as I told you <lb/>before, one onely principle with the help of various in&longs;truments <pb xlink:href="040/01/252.jpg" pagenum="234"/>produceth &longs;undry and divers motions in living creatures. </s><s>And as <lb/>to the flexures there is no need of them, the motions being of the <lb/>whole, and not of &longs;ome particular parts; and becau&longs;e they are <lb/>to be circular, the meer &longs;pherical figure is the mo&longs;t perfect articu­ <lb/>lation or flection that can be de&longs;ired.</s></p><p type="margin"><s><margin.target id="marg462"></margin.target><emph type="italics"/>It is de&longs;ired to <lb/>know, by means of <lb/>what flexures and <lb/>joynts the<emph.end type="italics"/> Terre­ <lb/>&longs;trial Globe <emph type="italics"/>might <lb/>move with three <lb/>diver&longs;e motions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg463"></margin.target><emph type="italics"/>One only princi­ <lb/>ple may cau&longs;e a <lb/>plurality of moti­ <lb/>ons in the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The mo&longs;t that ought to be granted upon this, would be, <lb/>that it may hold true in one &longs;ingle motion, but in three different <lb/>motions, in my opinion, and that of the Author, it is impo&longs;&longs;i­ <lb/>ble; as he going on, pro&longs;ecuting the objection, writes in the fol­ <lb/>lowing words. <emph type="italics"/>Let us &longs;uppo&longs;e, with<emph.end type="italics"/> Copernicus, <emph type="italics"/>that the Earth <lb/>moveth of its own faculty, and upon an intrin&longs;ick principle from <lb/>We&longs;t to Ea&longs;t in the plane of the Ecliptick; and again, that it al&longs;o <lb/>by an intrin&longs;ick principle revolveth about its centre, from Ea&longs;t to <lb/>We&longs;t; and for a third motion, that it of its own inclination defle­ <lb/>cteth from North to South, and &longs;o back again.<emph.end type="italics"/> It being a conti­ <lb/>nuate body, and not knit together with joints and flections, our <lb/>fancy and our judgment will never be able to comprehend, that <lb/>one and the &longs;ame natural and indi&longs;tinct principle, that is, that <lb/>one and the &longs;ame propen&longs;ion, &longs;hould actuate it at the &longs;ame in&longs;tant <lb/>with different, and as it were of contrary motions. </s><s>I cannot be­ <lb/>lieve that any one would &longs;ay &longs;uch a thing, unle&longs;&longs;e he had under­ <lb/>took to maintain this po&longs;ition right or wrong.</s></p><p type="main"><s>SALV. </s><s>Stay a little; and find me out this place in the Book. <lb/><emph type="italics"/>Fingamus modo cum Copernico terram aliqua &longs;uâ vi, & ab indito <lb/>principio impelli ab Occa&longs;u ad Ortum in Eclipticæ plano; tum rur­ <lb/>&longs;us revolvi ab indito etiam principio, circa &longs;uimet centrum, ab<emph.end type="italics"/> <lb/><arrow.to.target n="marg464"></arrow.to.target> <lb/><emph type="italics"/>Ortu in Occa&longs;um; tertio de&longs;lecti rur&longs;us &longs;u opte nutu à &longs;eptentrio­ <lb/>ne in Au&longs;trum, & vici&longs;&longs;im.<emph.end type="italics"/> I had thought, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that <lb/>that you might have erred in reciting the words of the Au­ <lb/>thor, but now I &longs;ee that he, and that very gro&longs;&longs;ely, decei­ <lb/>veth him&longs;elf; and to my grief, I find that he hath &longs;et him&longs;elf to <lb/>oppo&longs;e a po&longs;ition, which he hath not well under&longs;tood; for the&longs;e <lb/>are not the motions which <emph type="italics"/>Copernicus<emph.end type="italics"/> a&longs;&longs;ignes to the Earth. <lb/></s><s>Where doth he find that <emph type="italics"/>Copernicus<emph.end type="italics"/> maketh the annual motion <lb/>by the Ecliptick contrary to the motion about its own centre? </s><s>It <lb/>mu&longs;t needs be that he never read his Book, which in an hundred <lb/>places, and in the very fir&longs;t Chapters affirmeth tho&longs;e motions to <lb/>be both towards the &longs;ame parts, that is from We&longs;t to Ea&longs;t. <lb/></s><s>But without others telling him, ought he not of him&longs;elf to com­ <lb/>prehend, that attributing to the Earth the motions that are ta <lb/>ken, one of them from the Sun, and the other from the <emph type="italics"/>pri­ <lb/>mum wobile,<emph.end type="italics"/> they mu&longs;t of nece&longs;&longs;ity both move one and the &longs;ame <lb/>way. <lb/><arrow.to.target n="marg465"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg464"></margin.target><emph type="italics"/>A gro&longs;&longs;e error <lb/>of the oppo&longs;er of<emph.end type="italics"/> <lb/>Copernicus.</s></p><p type="margin"><s><margin.target id="marg465"></margin.target><emph type="italics"/>A &longs;ubtil and <lb/>withal &longs;imple ar­ <lb/>gument again&longs;t<emph.end type="italics"/> <lb/>Copernicus.</s></p><p type="main"><s>SIMP. </s><s>Take heed that you do not erre your &longs;elf, and <emph type="italics"/>Coperni­ <lb/>cus<emph.end type="italics"/> al&longs;o. </s><s>The Diurnal motion of the <emph type="italics"/>primum mobile,<emph.end type="italics"/> is it not from <pb xlink:href="040/01/253.jpg" pagenum="235"/>Ea&longs;t to We&longs;t? </s><s>And the annual motion of the Sun through the <lb/>Ecliptick, is it not on the contrary from We&longs;t to Ea&longs;t? </s><s>How <lb/>then can you make the&longs;e motions being conferred on the Earth, of <lb/>contraries to become con&longs;i&longs;tents?</s></p><p type="main"><s>SAGR. Certainly, <emph type="italics"/>Simplicius<emph.end type="italics"/> hath di&longs;covered to us the original <lb/>cau&longs;e of error of this Philo&longs;opher; and in all probability he <lb/>would have &longs;aid the very &longs;ame.</s></p><p type="main"><s>SALV. </s><s>Now if it be in our power, let us at lea&longs;t recover <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> from this errour, who &longs;eeing the Stars in their ri&longs;ing <lb/>to appear above the Oriental Horizon, will make it no difficult <lb/>thing to under&longs;tand, that in ca&longs;e that motion &longs;hould not belong </s></p><p type="main"><s><arrow.to.target n="marg466"></arrow.to.target> <lb/>to the Stars, it would be nece&longs;&longs;ary to confe&longs;&longs;e, that the Horizon, <lb/>with a contrary motion would go down; and that con&longs;equently <lb/>the Earth would reoolve in it &longs;elf a contrary way to that where­ <lb/>with the Stars &longs;eem to move, that is from We&longs;t to Ea&longs;t, which <lb/>is according to the order of the Signes of the Zodiack. </s><s>As, in the <lb/>next place, to the other motion, the Sun being fixed in the cen­ <lb/>tre of the Zodiack, and the Earth moveable about its circumfe­ <lb/>rence, to make the Sun &longs;eem unto us to move about the &longs;aid Zo­ <lb/>diack, according to the order of the Signes, it is nece&longs;&longs;ary, that <lb/>the E arth move according to the &longs;ame order, to the end that the <lb/>Sun may &longs;eem to us to po&longs;&longs;e&longs;&longs;e alwayes that degree in the Zodiack, <lb/>that is oppo&longs;ite to the degree in which we find the Earth; and thus <lb/>the Earth running, <emph type="italics"/>verbi gratia,<emph.end type="italics"/> through <emph type="italics"/>Aries,<emph.end type="italics"/> the Sun will <lb/>appear to run thorow <emph type="italics"/>Libra<emph.end type="italics"/>; and the Earth pa&longs;&longs;ing thorow the <lb/>&longs;igne <emph type="italics"/>Taurus,<emph.end type="italics"/> the Sun will pa&longs;&longs;e thorow <emph type="italics"/>Scorpio,<emph.end type="italics"/> and &longs;o the <lb/>Earth going thorow <emph type="italics"/>Gemini,<emph.end type="italics"/> the Sun &longs;eemeth to go thorow <emph type="italics"/>Sa­ <lb/>gittarius<emph.end type="italics"/>; but this is moving both the &longs;ame way, that is accord­ <lb/>ing to the order of the &longs;ignes; as al&longs;o was the revolution of the <lb/>Earth about its own centre.</s></p><p type="margin"><s><margin.target id="marg466"></margin.target><emph type="italics"/>The error of the <lb/>Antagoni&longs;t is ma­ <lb/>nife&longs;t, by decla­ <lb/>ring that the an­ <lb/>nual and diurnal <lb/>motions belonging <lb/>to the Earth are <lb/>both one way, and <lb/>not contrary.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I under&longs;tand you very well, and know not what to al­ <lb/>ledge in excu&longs;e of &longs;o gro&longs;&longs;e an error.</s></p><p type="main"><s>SALV. </s><s>And yet, <emph type="italics"/>Simplicius,<emph.end type="italics"/> there is one yet wor&longs;e then this; and <lb/>it is, that he makes the Earth move by the diurnal motion about <lb/>its own centre from Ea&longs;t to We&longs;t; and perceives not that if this <lb/>were &longs;o, the motion of twenty four hours appropriated by him <lb/>to the Univer&longs;e, would, in our &longs;eeming, proceed from We&longs;t to <lb/>Ea&longs;t; the quite contrary to that which we behold.</s></p><p type="main"><s>SIMP. </s><s>Oh &longs;trange! Why I, that have &longs;carce &longs;een the fir&longs;t <lb/>elements of the Sphere, would not, I am confident, have erred <lb/>&longs;o horribly.</s></p><p type="main"><s>SALV. </s><s>Judg now what pains this Antagoni&longs;t may be thought <lb/>to have taken in the Books of <emph type="italics"/>Copernicus,<emph.end type="italics"/> if he ab&longs;olutely invert <lb/><arrow.to.target n="marg467"></arrow.to.target> <lb/>the &longs;en&longs;e of this grand and principal Hypothe&longs;is, upon which is <lb/>founded the whole &longs;umme of tho&longs;e things wherein <emph type="italics"/>Copernicus<emph.end type="italics"/> <pb xlink:href="040/01/254.jpg" pagenum="236"/>di&longs;&longs;enteth from the doctrine of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy.<emph.end type="italics"/> As again, <lb/><arrow.to.target n="marg468"></arrow.to.target> <lb/>to this third motion, which the Author a&longs;&longs;ignes to the Terre&longs;trial <lb/>Globe, as the judgment of <emph type="italics"/>Copernicus,<emph.end type="italics"/> I know not which he would <lb/>mean thereby: it is not that que&longs;tionle&longs;&longs;e, which <emph type="italics"/>Copernicus<emph.end type="italics"/> a&longs;­ <lb/>cribes unto it conjunctly with the other two, annual and diurnal, <lb/>which hath nothing to do with declining towards the South and <lb/>North; but onely &longs;erveth to keep the axis of the diurnal revoluti­ <lb/>on continually parallel to it &longs;elf; &longs;o that it mu&longs;t be confe&longs;t, that <lb/>either the Authour did not under&longs;tand this, or that el&longs;e he di&longs;&longs;em­ <lb/>bled it. </s><s>But although this great mi&longs;take &longs;ufficeth to free us from <lb/>any obligation of a farther enquiry into his objections; yet ne­ <lb/>verthele&longs;&longs;e I &longs;hall have them in e&longs;teem; as indeed they de&longs;erve to <lb/>be valued much before the many others of impertinent Antago­ <lb/>ni&longs;ts. </s><s>Returning therefore to his objection, I &longs;ay, that the two <lb/>motions, annual and diurnal, are not in the lea&longs;t contrary, nay are <lb/>towards the &longs;ame way, and therefore may depend on one and the <lb/>&longs;ame principle. </s><s>The third is of it &longs;elf, and voluntarily &longs;o con&longs;equen­ <lb/>tial to the annual, that we need not trouble our &longs;elves (as I &longs;hall <lb/>&longs;hew in its place) to &longs;tudy for principles either internal or external, <lb/>from which, as from its cau&longs;e, to make it produced.</s></p><p type="margin"><s><margin.target id="marg467"></margin.target><emph type="italics"/>By another gro&longs;s <lb/>error it is &longs;een that <lb/>the Antagoni&longs;t had <lb/>but little &longs;tudied<emph.end type="italics"/> <lb/>Copernicus.</s></p><p type="margin"><s><margin.target id="marg468"></margin.target><emph type="italics"/>It is que&longs;tioned, <lb/>whether the oppo­ <lb/>nent under&longs;tood <lb/>the third motion <lb/>a&longs;&longs;igned to the <lb/>Earth by<emph.end type="italics"/> Coperni­ <lb/>cus.</s></p><p type="main"><s>SAGR. </s><s>I &longs;hall al&longs;o, as being induced thereto by natural rea&longs;on, <lb/>&longs;ay &longs;omething to this Antagoni&longs;t. </s><s>He will condemn <emph type="italics"/>Copernicus,<emph.end type="italics"/> <lb/>unle&longs;&longs;e I be able to an&longs;wer him to all objections, and to &longs;atisfie <lb/>him in all que&longs;tions he &longs;hall ask; as if my ignorance were a nece&longs;­ <lb/>&longs;ary argument of the fal&longs;hood of his Doctrine. </s><s>But if this way of <lb/>condemning Writers be in his judgment legal, he ought not to <lb/>think it unrea&longs;onable, if I &longs;hould not approve of <emph type="italics"/>Arî&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Pto­ <lb/>lomy,<emph.end type="italics"/> when he cannot re&longs;olve, better than my &longs;elf, tho&longs;e doubts <lb/>which I propound to him, touching their Doctrine. </s><s>He asketh me, <lb/>what are the principles by which the Terre&longs;trial Globe is moved <lb/><arrow.to.target n="marg469"></arrow.to.target> <lb/>with the Annual motion through the Zodiack, and with the Diur­ <lb/>nal through the Equinoctial about its own axis. </s><s>I an&longs;wer, that <lb/>they are like to tho&longs;e by which <emph type="italics"/>Saturn<emph.end type="italics"/> is moved about the Zodi­ <lb/>ack in thirty years, and about its own centre in a much &longs;horter <lb/>time along the Equinoctial, as the collateral apparition and oc­ <lb/>cultation of its Globes doth evince. </s><s>They are principles like to <lb/>tho&longs;e, whereby he &longs;crupleth not to grant, that the Sun runneth tho­ <lb/>row the Ecliptick in a year, and revolveth about its own centre <lb/>parallel to the Equinoctial in le&longs;&longs;e than a moneth, as its &longs;pots doth <lb/>&longs;en&longs;ibly demon&longs;trate. </s><s>They are things like to tho&longs;e whereby the <lb/>Medicean Stars run through the Zodiack in twelve years, and <lb/>all the while revolve in &longs;mall circles, and &longs;hort periods of time a­ <lb/>bout <emph type="italics"/>Jupiter.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg469"></margin.target><emph type="italics"/>The &longs;ame argu­ <lb/>ment an&longs;wered by <lb/>examples of the <lb/>like motions in o­ <lb/>ther cœle&longs;tial bo­ <lb/>dies.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>This Author will deny all the&longs;e things, as delu&longs;ions of <lb/>the fight, cau&longs;ed by the cry&longs;tals of the <emph type="italics"/>Tele&longs;cope.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/255.jpg" pagenum="237"/><p type="main"><s>SAGR. </s><s>But this would be to draw a further inconvenience up­ <lb/>on him&longs;elf, in that he holdeth, that the bare eye cannot be decei­ <lb/>ved in judging of the right motion of de&longs;cending graves, and yet <lb/>holds that it is deceived in beholding the&longs;e other motions at &longs;uch <lb/>time as its vi&longs;ive vertue is perfected, and augmented to thirty times <lb/>as much as it was before. </s><s>We tell him therefore, that the Earth in <lb/>like manner partaketh of the plurality of motions: and it is per­ <lb/>haps the &longs;ame, whereby the Load&longs;tone hath its motion down­ <lb/>wards, as grave, and two circular motions, one Horizontal, and the <lb/>other Vertical under the Meridian. </s><s>But what more; tell me, <emph type="italics"/>Sim­ <lb/>plicius,<emph.end type="italics"/> between which do you think this Author would put a <lb/>greater difference, 'twixt right and circular motion, or 'twixt moti­ <lb/>on and re&longs;t?</s></p><p type="main"><s>SIMP. 'Twixt motion and re&longs;t, certainly. </s><s>And this is mani­ <lb/><arrow.to.target n="marg470"></arrow.to.target> <lb/>fe&longs;t, for that circular motion is not contrary to the right, according <lb/>to <emph type="italics"/>Aristotle<emph.end type="italics"/>; nay, he granteth that they may mix with each o­ <lb/>ther; which it is impo&longs;&longs;ible for motion and re&longs;t to do.</s></p><p type="margin"><s><margin.target id="marg470"></margin.target><emph type="italics"/>Motion and re&longs;t <lb/>are more different <lb/>than right motion <lb/>and circular.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Therefore its a propo&longs;ition le&longs;&longs;e improbable to place <lb/>in one natural body two internal principles, one to right motion, <lb/>and the other to circular, than two &longs;uch interne principles one to <lb/>motion, and the other to re&longs;t. </s><s>Now both the&longs;e po&longs;itions agree to <lb/><arrow.to.target n="marg471"></arrow.to.target> <lb/>the natural inclination that re&longs;ideth in the parts of the Earth to re­ <lb/>turn to their whole, when by violence they are divided from it; <lb/>and they onely di&longs;&longs;ent in the operation of the whole: for the lat­ <lb/>ter of them will have it by an interne principle to &longs;tand &longs;till, and <lb/>the former a&longs;cribeth to it the circular motion. </s><s>But by your con­ <lb/>ce&longs;&longs;ion, and the confe&longs;&longs;ion of this Philo&longs;opher, two principles, one <lb/>to motion, and the other to re&longs;t, are incompatible together, like as <lb/>their effects are incompatible: but now this evenes not in the two <lb/>motions, right, and circular, which have no repugnance to each <lb/>other.</s></p><p type="margin"><s><margin.target id="marg471"></margin.target><emph type="italics"/>One may more <lb/>rationally a&longs;cribe <lb/>to the Earth two <lb/>internal principles <lb/>to the right, and <lb/>circular motion, <lb/>than two to motion <lb/>and re&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Adde this more, that in all probability it may be that <lb/><arrow.to.target n="marg472"></arrow.to.target> <lb/>the motion, that the part of the Earth &longs;eparated doth make whil&longs;t <lb/>it returneth towards its whole, is al&longs;o circular, as hath been alrea­ <lb/>dy declared; &longs;o that in all re&longs;pects, as far as concernes the pre&longs;ent <lb/>ca&longs;e, Mobility &longs;eemeth more likely than Re&longs;t. </s><s>Now proceed, <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> to what remains.</s></p><p type="margin"><s><margin.target id="marg472"></margin.target><emph type="italics"/>The motion of <lb/>the parts of the <lb/>Earth returning to <lb/>their whole may be <lb/>circular.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The Authour backs his Argument with producing ano­ <lb/>ther ab&longs;urdity, that is, that the &longs;ame motions agree to Natures ex­ <lb/>treamly different; but experience &longs;heweth, that the operations <lb/><arrow.to.target n="marg473"></arrow.to.target> <lb/>and motions of different natures, are different; and Rea&longs;on con­ <lb/>firmeth the &longs;ame: for otherwi&longs;e we &longs;hould have no way left to <lb/>know and di&longs;tingui&longs;h of natures, if they &longs;hould not have their <lb/>particular motions and operations, that might guide us to the <lb/>knowledge of their &longs;ub&longs;tances.</s></p> <pb xlink:href="040/01/256.jpg" pagenum="238"/><p type="margin"><s><margin.target id="marg473"></margin.target><emph type="italics"/>The diver&longs;ity of <lb/>motions helpeth us <lb/>in knowing the di­ <lb/>ver&longs;ity of natures.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I have twice or thrice ob&longs;erved in the di&longs;cour&longs;es of this <lb/>Authour, that to prove that a thing is &longs;o, or &longs;o, he &longs;till alledgeth, <lb/>that in that manner it is conformable with our under&longs;tanding; or <lb/>that otherwi&longs;e we &longs;hould never be able to conceive of it; or that <lb/>the <emph type="italics"/>Criterium<emph.end type="italics"/> of Philo&longs;ophy would be overthrown. </s><s>As if that na­ <lb/><arrow.to.target n="marg474"></arrow.to.target> <lb/>ture had fir&longs;t made mens brains, and then di&longs;po&longs;ed all things in <lb/>conformity to the capacity of their intellects. </s><s>But I incline rather <lb/>to think that Nature fir&longs;t made the things them&longs;elves, as &longs;he be&longs;t <lb/>liked, and afterwards framed the rea&longs;on of men capable of con­ <lb/>ceiving (though not without great pains) &longs;ome part of her &longs;e­ <lb/>crets.</s></p><p type="margin"><s><margin.target id="marg474"></margin.target><emph type="italics"/>Nature fir&longs;t <lb/>made things as &longs;he <lb/>plea&longs;ed, and after­ <lb/>wards capacitated <lb/>mens under&longs;tand­ <lb/>ings for conceiving <lb/>of them.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I am of the &longs;ame opinion. </s><s>But tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> <lb/>which are the&longs;e different natures, to which, contrary to expe­ <lb/>rience and rea&longs;on, <emph type="italics"/>Copernicus<emph.end type="italics"/> a&longs;&longs;ignes the &longs;ame motions and ope­ <lb/>rations.</s></p><p type="main"><s>SIMP. </s><s>They are the&longs;e. </s><s>The Water, the Air, (which doubt­ <lb/>le&longs;&longs;e are Natures different from the Earth) and all things that <lb/>are in tho&longs;e elements compri&longs;ed, &longs;hall each of them have tho&longs;e <lb/>three motions, which <emph type="italics"/>Copernicus<emph.end type="italics"/> pretends to be in the Terre&longs;triall <lb/>Globe; and my Authour proceedeth to demon&longs;trate Geometri­ <lb/><arrow.to.target n="marg475"></arrow.to.target> <lb/>cally, that, according to the <emph type="italics"/>Copernican<emph.end type="italics"/> Doctrine, a cloud that is <lb/>&longs;u&longs;pended in the Air, and that hangeth a long time over our <lb/>heads without changing place, mu&longs;t of nece&longs;&longs;ity have all tho&longs;e three <lb/>motions that belong to the Terre&longs;trial Globe. </s><s>The demon&longs;tra­ <lb/>tion is this, which you may read your &longs;elf, for I cannot repeat it <lb/>without book.</s></p><p type="margin"><s><margin.target id="marg475"></margin.target>Copernicus <emph type="italics"/>er­ <lb/>roneou&longs;ly a&longs;&longs;igneth <lb/>the &longs;ame operations <lb/>to different natures<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I &longs;hall not &longs;tand reading of it, nay I think it an imper­ <lb/>tinency in him to have in&longs;erted it, for I am certain, that no <lb/><emph type="italics"/>Copernican<emph.end type="italics"/> will deny the &longs;ame. </s><s>Therefore admitting him what he <lb/>would demon&longs;trate, let us &longs;peak to the objection, which in my <lb/>judgment hath no great &longs;trength to conclude any thing contrary <lb/>to the <emph type="italics"/>Copernican Hypothe&longs;is,<emph.end type="italics"/> &longs;eeing that it derogates nothing from <lb/>tho&longs;e motions, and tho&longs;e operations, whereby we come to the <lb/>knowledge of the natures, &c. </s><s>An&longs;wer me, I pray you, <emph type="italics"/>Simplici­ <lb/>us:<emph.end type="italics"/> Tho&longs;e accidents wherein &longs;ome things exactly concur, can <lb/>they &longs;erve to inform us of the different natures of tho&longs;e things? <lb/><arrow.to.target n="marg476"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg476"></margin.target><emph type="italics"/>From commune <lb/>accidents one can­ <lb/>not know different <lb/>natures.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>No Sir: nay rather the contrary, for from the idendity <lb/>of operations and of accidents nothing can be inferred, but an <lb/>idendity of natures.</s></p><p type="main"><s>SALV. </s><s>So that the different natures of the Water, Earth, Air, <lb/>and other things conteined in the&longs;e Elements, is not by you argu­ <lb/>ed from tho&longs;e operations, wherein all the&longs;e Elements and their af­ <lb/>fixes agree, but from other operations; is it &longs;o?</s></p><p type="main"><s>SIMP. </s><s>The very &longs;ame.</s></p><p type="main"><s>SALV. </s><s>So that he who &longs;hould leave in the Elements all tho&longs;e <pb xlink:href="040/01/257.jpg" pagenum="239"/>motions, operations, and other accidents, by which their natures <lb/>are di&longs;tingui&longs;hed, would not deprive us of the power of coming <lb/>to the knowledge of them; although he &longs;hould remove tho&longs;e o­ <lb/>perations, in which they unitedly concur, and which for that rea&longs;on <lb/>are of no u&longs;e for the di&longs;tingui&longs;hing of tho&longs;e natures.</s></p><p type="main"><s>SIMP. </s><s>I think your di&longs;&longs;ertation to be very good.</s></p><p type="main"><s>SALV. </s><s>But that the Earth, Water, Air, are of a nature equally <lb/>con&longs;tituted immoveable about the centre, is it not the opinion of <lb/>your &longs;elf, <emph type="italics"/>Ari&longs;totle, Prolomy,<emph.end type="italics"/> and all their &longs;ectators?</s></p><p type="main"><s>SIMP. </s><s>Its on all hands granted as an undeniable truth.</s></p><p type="main"><s>SALV. </s><s>Then from this common natural condition of quie&longs;­ <lb/>cence about the centre, there is no argument drawn of the different <lb/>natures of the&longs;e Elements, and things elementary, but that <lb/>knowledge mu&longs;t be collected from other qualities not common; <lb/>and therefore who&longs;o &longs;hould deprive the Elements of this common <lb/>re&longs;t only, and &longs;hould leave unto them all their other operations, <lb/>would not in the lea&longs;t block up the way that leadeth to the know­ <lb/>ledge of their e&longs;&longs;ences. </s><s>But <emph type="italics"/>Copernicus<emph.end type="italics"/> depriveth them onely of <lb/>this common re&longs;t, and changeth the &longs;ame into a common motion, <lb/>leaving them gravity, levity, the motions upwards, downwards, </s></p><p type="main"><s><arrow.to.target n="marg477"></arrow.to.target> <lb/>&longs;lower, fa&longs;ter, rarity, den&longs;ity, the qualities of hot, cold, dry, moi&longs;t, <lb/>and in a word, all things be&longs;ides. </s><s>Therefore &longs;uch an ab&longs;urdity, as <lb/>this Authour imagineth to him&longs;elf, is no <emph type="italics"/>Copernican<emph.end type="italics"/> po&longs;ition; nor <lb/>doth the concurrence in an identity of motion import any more or <lb/>le&longs;s, than the concurrence in an identity of re&longs;t about the diver&longs;i­ <lb/>fying, or not diver&longs;ifying of natures. </s><s>Now tell us, if there be any <lb/>argument to the contrary.</s></p><p type="margin"><s><margin.target id="marg477"></margin.target><emph type="italics"/>The concurrence <lb/>of the Elements in <lb/>a common motion <lb/>importeth no more <lb/>or le&longs;&longs;e, than their <lb/>concurrence in a <lb/>common re&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>There followeth a fourth objection, taken from a natu­ <lb/><arrow.to.target n="marg478"></arrow.to.target> <lb/>ral ob&longs;ervation, which is, <emph type="italics"/>That bodies of the &longs;ame kind, have mo­ <lb/>tions that agree in kinde, or el&longs;e they agree in re&longs;t. </s><s>But by the<emph.end type="italics"/> Co­ <lb/>pernican Hypothe&longs;is, <emph type="italics"/>bodies that agree in kinde, and are mo&longs;t &longs;em-<emph.end type="italics"/> <lb/><arrow.to.target n="marg479"></arrow.to.target> <lb/><emph type="italics"/>blable to one another, would be very di&longs;crepant, yea diametrically <lb/>repugnant as to motion; for that Stars &longs;o like to one another, would <lb/>be neverthele&longs;&longs;e &longs;o unlike in motion, as that &longs;ix Planets would perpe­ <lb/>tually turn round; but the Sun and all the fixeed Stars would &longs;tand <lb/>perpetually immoveable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg478"></margin.target><emph type="italics"/>A fourth argu­ <lb/>ment again&longs;t<emph.end type="italics"/> Co­ <lb/>pernicus.</s></p><p type="margin"><s><margin.target id="marg479"></margin.target><emph type="italics"/>Bodies of the <lb/>&longs;ame kinde have <lb/>motions that agree <lb/>in kinde.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The forme of the argument appeareth good; but yet <lb/>I believe that the application or matter is defective: and if the <lb/>Authour will but per&longs;i&longs;t in his a&longs;&longs;umption, the con&longs;equence &longs;hall <lb/>make directly again&longs;t him. </s><s>The Argument runs thus; Among&longs;t <lb/>mundane bodies, &longs;ix there are that do perpetually move, and they <lb/><arrow.to.target n="marg480"></arrow.to.target> <lb/>are the &longs;ix Planets; of the re&longs;t, that is, of the Earth, Sun, and <lb/>fixed Stars, it is di&longs;putable which of them moveth, and which <lb/>&longs;tands &longs;till, it being nece&longs;&longs;ary, that if the Earth &longs;tand &longs;till, the Sun <lb/>and &longs;ixed Stars do move; and it being al&longs;o po&longs;&longs;ible, that the Sun <pb xlink:href="040/01/258.jpg" pagenum="240"/>and fixed Stars may &longs;tand immoveable, in ca&longs;e the Earth &longs;hould <lb/>move: the matter of fact in di&longs;pute is, to which of them we may <lb/>with mo&longs;t convenience a&longs;cribe motion, and to which re&longs;t. </s><s>Natural <lb/>rea&longs;on dictates, that motion ought to be a&longs;&longs;igned to the bodies, <lb/>which in kind and e&longs;&longs;ence mo&longs;t agree with tho&longs;e bodies which do <lb/>undoubtedly move, and re&longs;t to tho&longs;e which mo&longs;t di&longs;&longs;ent from them; <lb/>and in regard that an eternal re&longs;t and perpetual motion are mo&longs;t <lb/>different, it is manife&longs;t, that the nature of the body always move­ <lb/>able ought to be mo&longs;t different from the body alwayes &longs;table. <lb/></s><s>Therefore, in regard that we are dubious of motion and re&longs;t, <lb/>let us enquire, whether by the help of &longs;ome other eminent affecti­ <lb/>on, we may di&longs;cover, which mo&longs;t agreeth with the bodies certain­ <lb/>ly moveable, either the Earth, or the Sun and fixed Stars. </s><s>But &longs;ee <lb/>how Nature, in favour of our nece&longs;&longs;ity and de&longs;ire, pre&longs;ents us <lb/>with two eminent qualities, and no le&longs;s different than motion and <lb/>re&longs;t, and they are light and darkne&longs;s, to wit, the being by nature <lb/>mo&longs;t bright, and the being ob&longs;cure, and wholly deprived of light: <lb/>the bodies therefore adorned with an internal and eternal &longs;plen­ <lb/>dour, are mo&longs;t different in e&longs;&longs;ence from tho&longs;e deprived of light: <lb/>The Earth is deprived of light, the Sun is mo&longs;t &longs;plendid in it &longs;elf, <lb/>and &longs;o are the fixed Stars. </s><s>The &longs;ix Planets do ab&longs;olutely <lb/>want light, as the Earth; therefore their e&longs;&longs;ence agreeth with <lb/>the Earth, and differeth from the Sun and fixed Stars. </s><s>There­ <lb/>fore is the Earth moveable, immoveable the Sunne and Starry <lb/>Sphere.</s></p><p type="margin"><s><margin.target id="marg480"></margin.target><emph type="italics"/>From the Earths <lb/>ob&longs;curity, and the <lb/>&longs;plendour of the <lb/>Sun, and fixed <lb/>Stars, is argued, <lb/>that it is movea­ <lb/>ble, and they im­ <lb/>moveable.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>But the Authour will not grant, that the &longs;ix Planets are <lb/>tenebro&longs;e, and by that negative will he abide. </s><s>Or he will argue <lb/>the great conformity of nature between the &longs;ix Planets, and the <lb/>Sun, and Fixed Stars; and the di&longs;parity between them and the <lb/>Earth from other conditions than from tenebro&longs;ity and light; yea, <lb/>now I remember in the fifth objection, which followeth, he layeth <lb/>down the va&longs;t difference between the Earth and the Cœle&longs;tial <lb/><arrow.to.target n="marg481"></arrow.to.target> <lb/>Bodies, in which he writeth, <emph type="italics"/>That the<emph.end type="italics"/> Copernican Hypothe&longs;is <lb/><emph type="italics"/>would make great confu&longs;ion and perturbation in the Sy&longs;teme of the <lb/>Vniver&longs;e, and amongst its parts:<emph.end type="italics"/> As for in&longs;tance, among&longs;t Cœ­ <lb/><arrow.to.target n="marg482"></arrow.to.target> <lb/>bodies that are immutable and incorruptible, according to <emph type="italics"/>Ari&longs;to­ <lb/>tle, Tycho,<emph.end type="italics"/> and others; among&longs;t bodies, I &longs;ay, of &longs;uch nobility, by <lb/>the confe&longs;&longs;ion of every one, and <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf, who affirmeth <lb/>them to be ordinate, and di&longs;po&longs;ed in a perfect con&longs;titution, and <lb/>removeth from them all incon&longs;tancy of vertue among&longs;t, the&longs;e bo­ <lb/>dies, I &longs;ay once more, &longs;o pure, that is to &longs;ay, among&longs;t <emph type="italics"/>Venus, Mars, <lb/>&c.<emph.end type="italics"/> to place the very &longs;ink of all corruptible matters, to wit, the <lb/>Earth, Water, Air, and all mixt bodies.</s></p><p type="margin"><s><margin.target id="marg481"></margin.target><emph type="italics"/>A fifih argu­ <lb/>ment again&longs;t<emph.end type="italics"/> Co­ <lb/>pernicus.</s></p><p type="margin"><s><margin.target id="marg482"></margin.target><emph type="italics"/>Another diffe­ <lb/>rence between the <lb/>Earth and the Cœ­ <lb/>le&longs;tial bodies, ta­ <lb/>ken from purity & <lb/>impurity.<emph.end type="italics"/></s></p><p type="main"><s>But how much properer a di&longs;tribution, and more with nature, <lb/>yea with God him&longs;elf, the Architect, is it, to &longs;eque&longs;ter the pure <pb xlink:href="040/01/259.jpg" pagenum="241"/>from the impure, the mortal from the immortal, as other Schools <lb/>teach; which tell us that the&longs;e impure and frail matters are con­ <lb/>teined within the angu&longs;t concave of the Lunar Orb, above which <lb/>with uninterrupted Series the things Cele&longs;tial di&longs;tend them&longs;elves.</s></p><p type="main"><s>SALV. It's true that the Copernican Sy&longs;teme introduceth di­ <lb/><arrow.to.target n="marg483"></arrow.to.target> <lb/>&longs;traction in the univer&longs;e of <emph type="italics"/>Aristotle<emph.end type="italics"/>; but we &longs;peak of our own <lb/>Univer&longs;e, that is true and real. </s><s>Again if this Author will infer <lb/>the di&longs;parity of e&longs;&longs;ence between the Earth and Cele&longs;tial bodies <lb/>from the incorruptibility of them, and the corruptibility of it in <lb/>the method of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> from which di&longs;parity he concludeth mo­ <lb/>tion to belong to the Sun and fixed Stars, and the immobility of <lb/>the Earth, he will flatter him&longs;elf with a Paralogi&longs;me, &longs;uppo&longs;ing <lb/><arrow.to.target n="marg484"></arrow.to.target> <lb/>that which is in que&longs;tion; for <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> inferreth the incorruptibi­ <lb/>lity of Cele&longs;tial bodies from motion, which is in di&longs;pute, whe­ <lb/>ther it belongeth to them or to the Earth. </s><s>Of the vanity of the&longs;e <lb/>Rhetorical Illations enough hath been &longs;poken. </s><s>And what can be <lb/><arrow.to.target n="marg485"></arrow.to.target> <lb/>more fond, than to &longs;ay, that the Earth and Elements are bani­ <lb/>&longs;hed and &longs;eque&longs;tred from the Cele&longs;tial Spheres, and confined <lb/>within the Lunar Orb? </s><s>Is, not then the Moons Orb one of the <lb/>Cele&longs;tial Spheres, and according to con&longs;ent compri&longs;ed in the <lb/>middle of all the re&longs;t? </s><s>Its a new way to &longs;eparate the pure from <lb/>the impure, and the &longs;ick from the &longs;ound, to a&longs;&longs;igne the infected <lb/>quarters in the heart of the City: I had thought that the ^{*} Pe&longs;t­ <lb/><arrow.to.target n="marg486"></arrow.to.target> <lb/>hou&longs;e ought to have been removed as far off as was po&longs;&longs;ible. <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> admireth the di&longs;po&longs;ition of the parts of the Univer&longs;e, <lb/>for that God hath con&longs;tituted the grand Lamp, which is to give <lb/>light all over his Temple in the centre of it, and not on one <lb/>&longs;ide. </s><s>And as to the Earths being betwixt <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mars,<emph.end type="italics"/> <lb/>we will but hint the &longs;ame; and do you, in favour of this Author, <lb/>trie to remove it thence. </s><s>But let us not ^{*} mix the&longs;e Rhetorical <lb/><arrow.to.target n="marg487"></arrow.to.target> <lb/>Flowers with &longs;olid Demon&longs;trations, rather let us leave them to <lb/>the Orators, or if you will to the Poets, who know how in their <lb/>drolling way to exalt by their pray&longs;es things mo&longs;t &longs;ordid, yea and <lb/>&longs;ometimes mo&longs;t pernicious. </s><s>And if any thing el&longs;e remain, let us <lb/>di&longs;patch it, as we have done the re&longs;t.</s></p><p type="margin"><s><margin.target id="marg483"></margin.target>Copernicus <emph type="italics"/>in <lb/>troduceth confu&longs;ion <lb/>in the Univer&longs;e of<emph.end type="italics"/> <lb/>Ari&longs;totle.</s></p><p type="margin"><s><margin.target id="marg484"></margin.target><emph type="italics"/>The Paralogi&longs;me <lb/>of the Author of <lb/>Anti-Tycho.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg485"></margin.target><emph type="italics"/>It &longs;eemeth a <lb/>folly to affirm the <lb/>Earth to be with­ <lb/>out the Heavens.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg486"></margin.target>* Lazeretto</s></p><p type="margin"><s><margin.target id="marg487"></margin.target>* <emph type="italics"/>Intrecciare,<emph.end type="italics"/> to <lb/>twine flowers in a <lb/>garland.</s></p><p type="main"><s>SIMP. </s><s>There is the &longs;ixth and la&longs;t argument, wherein he ma­ <lb/><arrow.to.target n="marg488"></arrow.to.target> <lb/>keth it a very improbale thing. [<emph type="italics"/>That a corruptible and di&longs;&longs;ipable <lb/>body &longs;hould move with a perpetual and regular motion; and this <lb/>he confirmeth with the example of living creatures, which moving <lb/>with a motion natural to them, yet grow weary, and have need of <lb/>repo&longs;e to re&longs;tore their &longs;trength.<emph.end type="italics"/>] But what hath this motion to do <lb/>with that of the Earth, that in compari&longs;on to theirs is immen&longs;e? <lb/></s><s>Be&longs;ides, to make it move with three motions that run and draw <lb/>&longs;everal wayes: Who would ever a&longs;&longs;ert &longs;uch Paradoxes, unle&longs;&longs;e <lb/>he had &longs;worn to be their defender? </s><s>Nor doth that avail in this <pb xlink:href="040/01/260.jpg" pagenum="242"/>ca&longs;e, which <emph type="italics"/>Copernicus<emph.end type="italics"/> alledgeth, that by rea&longs;on this motion is <lb/>natural to the Earth and not violent, it worketh contrary effects <lb/>to violent motions; and that tho&longs;e things di&longs;&longs;olve and cannot <lb/>long &longs;ub&longs;i&longs;t, to which impul&longs;e is conferred, but tho&longs;e &longs;o made <lb/>by nature do continue in their perfect di&longs;po&longs;ure; this an&longs;wer &longs;uf­ <lb/>ficeth not, I &longs;ay, for it is overthrown by that of ours. </s><s>For the a­ <lb/>nimal is a natural body, and not made by art, and its motion is <lb/>natural, deriving it &longs;elf from the &longs;oul, that is, from an intrin&longs;ick <lb/>principle; and that motion is violent, who&longs;e beginning is with­ <lb/>out, and on which the thing moved conferreth nothing; how­ <lb/>ever, if the animal continueth its motion any long time, it grows <lb/>weary, and al&longs;o dyeth, if it ob&longs;tinately &longs;trive to per&longs;i&longs;t therein. <lb/></s><s>You &longs;ee then that in nature we meet on all &longs;ides with notions con­ <lb/>trary to the <emph type="italics"/>Copernican Hypothe&longs;is,<emph.end type="italics"/> and none in favour of it. </s><s>And <lb/>for that I have nothing more wherein to take the part of this Op­ <lb/>ponent, hear what he produceth again&longs;t <emph type="italics"/>Keplerus<emph.end type="italics"/> (with whom <lb/>he di&longs;puteth) upon that argument, which the &longs;aid <emph type="italics"/>Kepler<emph.end type="italics"/> bringeth <lb/>again&longs;t tho&longs;e who think it an inconvenient, nay impo&longs;&longs;ible thing, <lb/>to augment the Starry Sphere immen&longs;ely, as the <emph type="italics"/>Copernican<emph.end type="italics"/> Hy­ <lb/>pothe&longs;is requireth. <emph type="italics"/>Kepler<emph.end type="italics"/> therefore in&longs;tanceth, &longs;aying: <emph type="italics"/>Difficili­ <lb/>us ect, accidens præter modulum &longs;ubjecti intendere, quàm &longs;ub-<emph.end type="italics"/> <lb/><arrow.to.target n="marg489"></arrow.to.target> <lb/><emph type="italics"/>jectum &longs;ine accidente augere. </s><s>Copernicus ergo veri&longs;imilius facit, <lb/>qui auget Orbem Stellarum fixarum ab&longs;que motu, quam Ptolomæus, <lb/>qui auget motum fixarum immen&longs;à velocitate.<emph.end type="italics"/> [Which makes this <lb/>Engli&longs;h.] Its harder to &longs;tretch the accident beyond the model of the <lb/>&longs;ubject than to augment the &longs;ubject without the accident. <emph type="italics"/>Coperni-<emph.end type="italics"/> <lb/>hath more probability on his &longs;ide, who encrea&longs;eth the Orb of the <lb/>fixed Stars without motion, than <emph type="italics"/>Ptolomy<emph.end type="italics"/> who augmenteth the <lb/>motion of the fixed Stars to an immen&longs;e degree of velocity. <lb/><arrow.to.target n="marg490"></arrow.to.target> <lb/>Which objection the Author an&longs;wereth, wondering how much <lb/><emph type="italics"/>Kepler<emph.end type="italics"/> deceived him&longs;elf, in &longs;aying, that in the Ptolomaick Hypothe­ <lb/>&longs;is the motion encrea&longs;eth beyond the model of the &longs;ubject, for in <lb/>his judgment it doth not encrea&longs;e, &longs;ave onely in conformity to the <lb/>model, and that according to its encrea&longs;ement, the velocity of <lb/><arrow.to.target n="marg491"></arrow.to.target> <lb/>the motion is augmented. </s><s>Which he proveth by &longs;uppo&longs;ing a ma­ <lb/>chine to be framed, that maketh one revolution in twenty four <lb/>hours, which motion &longs;hall be called mo&longs;t &longs;low; afterwards &longs;up­ <lb/>po&longs;ing its &longs;emidiameter to be prolonged, as far as to the di&longs;tance <lb/>of the Sun, its extreme will equal the velocity of the Sun; and <lb/>it being cantinued out unto the Starry Sphere, it will equal the <lb/>velocity of the fixed Stars, though in the circumferrnce of the <lb/>machine it be very &longs;low. </s><s>Now applying this con&longs;ideration of the <lb/>machine to the Starry Sphere, let us imagine any point in its &longs;e­ <lb/>midiameter, as neer to the centre as is the &longs;emidiameter of the ma­ <lb/>chine; the &longs;ame motion that in the Starry Sphere is exceeding <pb xlink:href="040/01/261.jpg" pagenum="243"/>&longs;wift, &longs;hall in that point be exceeding &longs;low; But the great mag­ <lb/>nitude of the body is that which maketh it of exceeding &longs;low, to <lb/>become exceeding &longs;wift, although it continueth &longs;till the &longs;ame, and <lb/>thus the velocity encrea&longs;eth, not beyond the model of the &longs;ub­ <lb/>ject, but rather according to it, and to its magnitude; very dif­ <lb/>ferently from the imagination of <emph type="italics"/>Kepler.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg488"></margin.target><emph type="italics"/>A &longs;ixth argu­ <lb/>ment again&longs;t<emph.end type="italics"/> Co­ <lb/>pernicus, <emph type="italics"/>taken <lb/>from animals, who <lb/>have need of re&longs;t, <lb/>though their moli­ <lb/>on be natural.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg489"></margin.target><emph type="italics"/>An argument <lb/>from<emph.end type="italics"/> Kepler <emph type="italics"/>in fa­ <lb/>vour of<emph.end type="italics"/> Coperni­ <lb/>cus.</s></p><p type="margin"><s><margin.target id="marg490"></margin.target><emph type="italics"/>The Author of <lb/>the Anti Tycho op­ <lb/>po&longs;eth<emph.end type="italics"/> Kepler.</s></p><p type="margin"><s><margin.target id="marg491"></margin.target><emph type="italics"/>The velocity of <lb/>the circular moti­ <lb/>on increa&longs;eth, ac­ <lb/>cording to the en­ <lb/>crea&longs;e of the dia­ <lb/>meter of the circle.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I do not believe that this Author hath entertained &longs;o <lb/>mean and poor a conceit of <emph type="italics"/>Kepler,<emph.end type="italics"/> as to per&longs;wade him&longs;elf that <lb/>he did not under&longs;tand, that the highe&longs;t term of a line drawn from <lb/>the centre unro the Starry Sphere, moveth more &longs;wiftly than a <lb/>point of the &longs;ame line taken within a yard or two of the centre. </s><s>And <lb/>therefore of nece&longs;&longs;ity he mu&longs;t have conceived and comprehend­ <lb/><arrow.to.target n="marg492"></arrow.to.target> <lb/>ed that the mind and intention of <emph type="italics"/>Kepler<emph.end type="italics"/> was to have &longs;aid, that <lb/>it is le&longs;&longs;e inconvenient to encrea&longs;e an immoveable body to an ex­ <lb/>traordinary magnitude, than to a&longs;cribe an extraordinary velocity <lb/>to a body, though very bigge, having regard to the model, <lb/>that is to the gauge, and to the example of other natural bodies; <lb/>in which we &longs;ee, that the di&longs;tance from the centre encrea&longs;ing, the <lb/>velocity dimini&longs;heth; that is, that the periods of their circulati­ <lb/>ons take up longer times. </s><s>But in re&longs;t which is not capable of aug­ <lb/><arrow.to.target n="marg493"></arrow.to.target> <lb/>mentation or diminution, the grandure or &longs;malne&longs;&longs;e of the body <lb/>maketh no differeuce. </s><s>So that if the an&longs;wer of the Author would <lb/>be directed again&longs;t the argument of <emph type="italics"/>Kepler,<emph.end type="italics"/> it is nece&longs;&longs;ary, that <lb/>that Author doth hold, that to the movent principle its one and the <lb/>&longs;ame to move in the &longs;ame time a body very &longs;mall, or very im­ <lb/>men&longs;e, in regard that the augmentation of velocity in&longs;eparably <lb/>attends the augmentation of the ma&longs;&longs;e. </s><s>But this again is contrary <lb/><arrow.to.target n="marg494"></arrow.to.target> <lb/>to the Architectonical rule of nature, which doth in the le&longs;&longs;er <lb/>Spheres, as we &longs;ee in the Planets, and mo&longs;t &longs;en&longs;ibly in the Medi­ <lb/>cean Stars, ob&longs;erve to make the le&longs;&longs;er Orbs to circulate in &longs;horter <lb/>times: Whence the time of <emph type="italics"/>Saturns<emph.end type="italics"/> revolution is longer than all <lb/>the times of the other le&longs;&longs;er Spheres, it being thirty years; now <lb/>the pa&longs;&longs;ing from this to a Sphere very much bigger, and to make <lb/>it move in 24. hours, may very well be &longs;aid to exceed the rules of <lb/>the model. </s><s>So that if we would but attentively con&longs;ider it, the <lb/>Authors an&longs;wer oppo&longs;eth not the intent and &longs;en&longs;e of the argument, <lb/>but the expre&longs;&longs;ing and manner of delivering of it; where again <lb/>the Author is injurious, and cannot deny but that he artificially <lb/>di&longs;&longs;embled his under&longs;tanding of the words, that he might charge <lb/><emph type="italics"/>Kepler<emph.end type="italics"/> with gro&longs;&longs;e ignorance; but the impo&longs;ture was &longs;o very dull <lb/>and obvions, that he could not with all his craft alter the opini­ <lb/>on which <emph type="italics"/>Kepler<emph.end type="italics"/> hath begot of his Doctrine in the minds of all <lb/>the Learned. </s><s>As in the next place, to the in&longs;tance again&longs;t the <lb/>perpetual motion of the Earth, taken from the impo&longs;&longs;ibility of <lb/>its moving long without wearine&longs;&longs;e, in regard that living crea­ <pb xlink:href="040/01/262.jpg" pagenum="244"/>tures them&longs;elves, which yet move naturally, and from an intern <lb/>principle, do grow weary, and have need of re&longs;t to relax and re­ <lb/>fre&longs;h their members --------</s></p><p type="margin"><s><margin.target id="marg492"></margin.target><emph type="italics"/>An explanation <lb/>of the true &longs;en&longs;e of<emph.end type="italics"/> <lb/>Kepler <emph type="italics"/>and his de­ <lb/>fence.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg493"></margin.target><emph type="italics"/>The greatne&longs;&longs;e <lb/>and &longs;malne&longs;&longs;e of <lb/>the body make a <lb/>difference in moti­ <lb/>on and not in re&longs;t.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg494"></margin.target><emph type="italics"/>The order of na­ <lb/>ture is to make the <lb/>le&longs;&longs;er Orbs to cir­ <lb/>culate in &longs;horter <lb/>times, and the big­ <lb/>ger in longer times.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Methinks I hear <emph type="italics"/>Kepler<emph.end type="italics"/> an&longs;wer him to that, that <lb/>there are &longs;ome kinde of animals which refre&longs;h them&longs;elves after <lb/>wearine&longs;&longs;e, by rowling on the Earth; and that therefore there <lb/><arrow.to.target n="marg495"></arrow.to.target> <lb/>is no need to fear that the Terre&longs;trial Globe &longs;hould tire, nay it <lb/>may be rea&longs;onably affirmed, that it enjoyeth a perpetual & mo&longs;t <lb/>tranquil repo&longs;e, keeping it &longs;elf in an eternal rowling.</s></p><p type="margin"><s><margin.target id="marg495"></margin.target><emph type="italics"/>The feigned an­ <lb/>&longs;wer of<emph.end type="italics"/> Kepler <emph type="italics"/>co­ <lb/>vered with an ar­ <lb/>tificial Irony.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You are too tart and Satyrical, <emph type="italics"/>Sagredus:<emph.end type="italics"/> but let us <lb/>lay a&longs;ide je&longs;ts, whil&longs;t we are treating of &longs;erious things.</s></p><p type="main"><s>SAGR. </s><s>Excu&longs;e me, <emph type="italics"/>Salviatus,<emph.end type="italics"/> this that I &longs;ay is not &longs;o ab&longs;o­ <lb/>lutely be&longs;ides the bu&longs;ine&longs;s, as you perhaps make it; for a motion <lb/>that &longs;erveth in&longs;tead of re&longs;t, and removeth wearine&longs;s from a body <lb/>tired with travail, may much more ea&longs;ily &longs;erve to prevent the co­ <lb/><arrow.to.target n="marg496"></arrow.to.target> <lb/>ming of that wearine&longs;s, like as preventive remedies are more ea&longs;ie <lb/>than curative. </s><s>And I hold for certain, that if the motion of ani­ <lb/>mals &longs;hould proceed in the &longs;ame manner as this that is a&longs;cribed to <lb/>the Earth, they would never grow weary; Seeing that the weari­ <lb/>ne&longs;s of the living creature, deriveth it &longs;elf, in my opinion, from <lb/><arrow.to.target n="marg497"></arrow.to.target> <lb/>the imployment of but one part alone in the moving of its &longs;elf, <lb/>and all the re&longs;t of the body; as <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> in walking, the thighs and <lb/>the legs onely are imployed for carrying them&longs;elves and all the <lb/>re&longs;t: on the contrary, you &longs;ee the motion of the heart to be as it <lb/>were indefatigable, becau&longs;e it moveth it &longs;elf alone. </s><s>Be&longs;ides, I <lb/><arrow.to.target n="marg498"></arrow.to.target> <lb/>know not how true it may be, that the motion of the animal is na­ <lb/>tural, and not rather violent: nay, I believe that one may truly <lb/>&longs;ay, that the &longs;oul naturally moveth the members of an animal with <lb/>a motion preternatural, for if the motion upwards is preternatu­ <lb/>ral to grave bodies, the lifting up of the legs, and the thighs, <lb/>which are grave bodies, in walking, cannot be done without vio­ <lb/>lence, and therefore not without labour to the mover. </s><s>The <lb/>climbing upwards by a ladder carrieth the grave body contrary to <lb/>its natural inclination upwards, from whence followeth wearine&longs;s, <lb/>by rea&longs;on of the bodies natural aver&longs;ne&longs;s to that motion: but in <lb/>moving a moveable with a motion, to which it hath no aver&longs;ion, <lb/><arrow.to.target n="marg499"></arrow.to.target> <lb/>what la&longs;&longs;itude, what diminution of vertue and &longs;trength need we <lb/>fear in the mover? </s><s>and how &longs;hould the forces wa&longs;te, where they <lb/>are not at all imployed?</s></p><p type="margin"><s><margin.target id="marg496"></margin.target><emph type="italics"/>Animals would <lb/>not grow weary of <lb/>their motion, pro­ <lb/>ceeding as that <lb/>which is a&longs;&longs;igned <lb/>to the terre&longs;trial <lb/>Globe.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg497"></margin.target><emph type="italics"/>The cau&longs;e of the <lb/>wearine&longs;&longs;e of ani­ <lb/>mals.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg498"></margin.target><emph type="italics"/>The motion of <lb/>an animal is rather <lb/>to be called violent <lb/>than natural.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg499"></margin.target><emph type="italics"/>The &longs;trength di­ <lb/>mini&longs;heth not, <lb/>where it is not im­ <lb/>ployed.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>They are the contrary motions wherewith the Earth is <lb/>pretended to move, again&longs;t which the Authour produceth his ar­ <lb/>gument.</s></p><p type="main"><s>SAGR. </s><s>It hath been &longs;aid already, that they are no wi&longs;e con­ <lb/>traries, and that herein the Authour is extteamly deceived, &longs;o <lb/>that the whole &longs;trength of the argument recoileth upon the Op­ <pb xlink:href="040/01/263.jpg" pagenum="245"/>ponent him&longs;elf, whil&longs;t he will make the <emph type="italics"/>Fir&longs;t Mover<emph.end type="italics"/> to hurry <lb/><arrow.to.target n="marg500"></arrow.to.target> <lb/>along with it all the inferiour Spheres, contrary to the motion <lb/>which they them&longs;elves at the &longs;ame time exerci&longs;e. </s><s>It belongs there­ <lb/>fore to the <emph type="italics"/>Primum Mobile<emph.end type="italics"/> to grow weary, which be&longs;ides the <lb/>moving of its &longs;elf is made to carry &longs;o many other Spheres, and <lb/>which al&longs;o &longs;trive again&longs;t it with a contrary motion. </s><s>So that <lb/>the ultimate conclu&longs;ion that the Authour inferred, &longs;aying, that <lb/>di&longs;cour&longs;ing of the effects of Nature, a man alwayes meets with <lb/>things that favour the opinion of <emph type="italics"/>Ari&longs;toile<emph.end type="italics"/> and <emph type="italics"/>Ptolomy,<emph.end type="italics"/> and ne­ <lb/>ver any one that doth not interfer with <emph type="italics"/>Copernicus,<emph.end type="italics"/> &longs;tands in need <lb/>of great con&longs;ideration; and it is better to &longs;ay, that one of the&longs;e <lb/>two <emph type="italics"/>Hypothe&longs;es<emph.end type="italics"/> being true, and the other nece&longs;&longs;arily fal&longs;e, it is <lb/>impo&longs;&longs;ible that a man &longs;hould ever be able to finde any argu­ <lb/>ment, experience, or right rea&longs;on, in favour of that which is <lb/><arrow.to.target n="marg501"></arrow.to.target> <lb/>fal&longs;e, like as to the truth none of the&longs;e things can be repugnant. <lb/></s><s>Va&longs;t difference, therefore, mu&longs;t needs be found between the rea­ <lb/>&longs;ons and arguments produced by the one and other party, for and <lb/>again&longs;t the&longs;e two opinions, the force of which I leave you your <lb/>&longs;elf to judge of, <emph type="italics"/>Simplicius.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg500"></margin.target><emph type="italics"/>The argument <lb/>of<emph.end type="italics"/> Claramontius <lb/><emph type="italics"/>recoileth upon him­ <lb/>&longs;elf.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg501"></margin.target><emph type="italics"/>True Propo&longs;iti­ <lb/>ons meet with ma­ <lb/>ny conclu&longs;ive ar­ <lb/>guments, &longs;o do not <lb/>the fal&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>But you, <emph type="italics"/>Sagredus,<emph.end type="italics"/> being tran&longs;ported by the velocity <lb/>of your wit, have taken my words out of my mouth, whil&longs;t I was <lb/>about to &longs;ay &longs;omething, touching this la&longs;t argument of the Author; <lb/>and although you have more then &longs;ufficiently refuted him, yet <lb/>neverthele&longs;&longs;e I will adde &longs;omewhat, which then ran in my minde. <lb/></s><s>He propo&longs;eth it as a thing very unlikely, that a body di&longs;&longs;ipable <lb/>and corruptible, as the Earth, &longs;hould perpetually move with a re­ <lb/>gular motion, c&longs;pecially for that we &longs;ee living creatures in the end <lb/>to grow weary, and to &longs;tand in need of re&longs;t: and the improbability <lb/>is increa&longs;ed, in that the &longs;aid motion is required to be of velocity <lb/>incomparable and immen&longs;e, in re&longs;pect to that of animals. </s><s>Now, I <lb/>cannot &longs;ee why the velocity of the Earth &longs;hould, at pre&longs;ent, trou­ <lb/>ble it; &longs;o long as that of the &longs;tarry Sphere &longs;o very much bigger <lb/>doth not occa&longs;ion in it any di&longs;turbance more con&longs;iderable, than that <lb/>which the velocity of a machine, that in 24 hours maketh but one <lb/>&longs;ole revolution, produceth in the &longs;ame. </s><s>If the being of the velo­ <lb/>city of the Earths conver&longs;ion, according to the model of that ma­ <lb/>chine, inferreth things of no greater moment than that, let the Au­ <lb/>thor cea&longs;e to fear the Earths growing weary; for that not one of <lb/>the mo&longs;t feeble and &longs;low-pac't animals, no not a Chamæleon would <lb/><arrow.to.target n="marg502"></arrow.to.target> <lb/>tire in moving no more than ^{*} four or five yards in 24 hours; but <lb/>if he plea&longs;e to con&longs;ider the velocity to be no longer, in relation to <lb/><arrow.to.target n="marg503"></arrow.to.target> <lb/>the model of the machine, but ab&longs;olutely, and ina&longs;much as the <lb/>moveable in 24 hours is to pa&longs;s a very great &longs;pace, he ought to &longs;hew <lb/>him&longs;elf &longs;o much more re&longs;erved in granting it to the &longs;tarry Sphere, <lb/>which with a velocity incomparably greater than that of the <pb xlink:href="040/01/264.jpg" pagenum="246"/>Earth is to carry along with it a thou&longs;and bodies, each much big­ <lb/>ger than the Terre&longs;trial Globe.</s></p><p type="margin"><s><margin.target id="marg502"></margin.target>* Cinque ò &longs;ei <lb/>braccia Fiorentini.</s></p><p type="margin"><s><margin.target id="marg503"></margin.target><emph type="italics"/>Wearineß more <lb/>to be feared in the <lb/>&longs;tarry Sphere than <lb/>in the terre&longs;triall <lb/>Globe.<emph.end type="italics"/></s></p><p type="main"><s>Here it remains for us to &longs;ee the proofs, whereby the Authour <lb/>concludes the new &longs;tars <emph type="italics"/>Anno<emph.end type="italics"/> 1572. and <emph type="italics"/>Anno<emph.end type="italics"/> 1604. to be &longs;ublu­ <lb/>nary, and not cœle&longs;tial, as the <emph type="italics"/>Astronomers<emph.end type="italics"/> of tho&longs;e times were <lb/>generally per&longs;waded; an enterprize very great certainly; but I <lb/>have con&longs;idered, that it will be better, in regard the Book is new <lb/>and long, by rea&longs;on of its many calculations, that between this e­ <lb/>vening and to morrow morning I make them as plain as I can, and <lb/>&longs;o meeting you again to morrow to continue our wonted confe­ <lb/>rences, give you a brief of what I &longs;hall ob&longs;erve therein; and if we <lb/>have time left, we will &longs;ay &longs;omething of the <emph type="italics"/>Annual motion<emph.end type="italics"/> a&longs;cri­ <lb/>bed to the Earth. </s><s>In the mean time, if either of you, and <emph type="italics"/>Simpli­ <lb/>cius<emph.end type="italics"/> in particular, hath any thing to &longs;ay more, touching what relates <lb/>to the <emph type="italics"/>Diurnal motion,<emph.end type="italics"/> at large examined by me, we have a little <lb/>time &longs;till left to treat thereof.</s></p><p type="main"><s>SIMP. </s><s>I have no more to &longs;ay, unle&longs;&longs;e it be this, that the di&longs;cour­ <lb/>&longs;es that this day have falne under our debate, have appeared to me <lb/>fraught with very acute and ingenious notions, alledged on <emph type="italics"/>Coper­ <lb/>nicus<emph.end type="italics"/> his &longs;ide, in confirmation of the motion of the Earth, but yet <lb/>I find not my &longs;elf per&longs;waded to believe it; for in &longs;hort, the things <lb/>that have been &longs;aid conclude no more but this, that the rea&longs;ons <lb/>for the &longs;tability of the Earth are not nece&longs;&longs;ary; but all the while <lb/>no demon&longs;tration hath been produced on the other &longs;ide, that doth <lb/>nece&longs;&longs;arily convince and prove its mobility.</s></p><p type="main"><s>SALV. </s><s>I never undertook, <emph type="italics"/>Simplicius,<emph.end type="italics"/> to remove you from that <lb/>your opinion; much le&longs;s dare I pre&longs;ume to determine definitively <lb/>in this controver&longs;ie: it onely was, and &longs;till &longs;hall be in the en&longs;uing <lb/>di&longs;putations my intent, to make it appear to you, that tho&longs;e who <lb/>have thought that mo&longs;t &longs;wift motion of 24 hours doth belong to <lb/>the Earth alone, and not to the Univer&longs;e, the Earth onely exclu­ <lb/>ded, were not induced to believe, that &longs;o it might and ought to do <lb/>out of any blind per&longs;wa&longs;ion; but that they did very well &longs;ee, try, <lb/>and examine the rea&longs;ons on the contrary &longs;ide, and al&longs;o not &longs;light­ <lb/>ly an&longs;wer them. </s><s>With the &longs;ame intention, if it &longs;tand with your <lb/>liking, and that of <emph type="italics"/>Sagredus,<emph.end type="italics"/> we may pa&longs;&longs;e to the con&longs;ideration of <lb/>that other motion; fir&longs;t, by <emph type="italics"/>Aristarchus Samius,<emph.end type="italics"/> and afterwards <lb/>by <emph type="italics"/>Nicholaus Copernicus<emph.end type="italics"/> a&longs;cribed to the &longs;aid Terre&longs;trial Globe, <lb/>which is, as, I believe, you have heretofore heard, made under the <lb/>Zodiack within the &longs;pace of a year about the Sun, immoveably <lb/>placed in the centre of the &longs;aid Zodiack.</s></p><p type="main"><s>SIMP. </s><s>The di&longs;qui&longs;ition is &longs;o great, and &longs;o noble, that I &longs;hall <lb/>gladly hearken to the di&longs;cu&longs;&longs;ion thereof, per&longs;wading my &longs;elf that I <lb/>&longs;hall hear what ever can be &longs;aid of that matter. </s><s>And I will after­ <pb xlink:href="040/01/265.jpg" pagenum="247"/>wards by my &longs;elf, according to my u&longs;ual cu&longs;tome, make more de­ <lb/>liberate reflexions upon what hath been, and is to be &longs;poken; and <lb/>if I &longs;hould gain no more but this, it will be no &longs;mall benefit <lb/>that I &longs;hall be able to di&longs;cour&longs;e more Logically.</s></p><p type="main"><s>SAGR. Therefore, that we may no further weary <emph type="italics"/>Salviatus,<emph.end type="italics"/> <lb/>we will put a period to the di&longs;putations of this day, and re­ <lb/>a&longs;&longs;ume our conference to morrow in the u&longs;ual manner, with hope <lb/>to hear very plea&longs;ing novelties.</s></p><p type="main"><s>SIMP. </s><s>I will leave with you the Book <emph type="italics"/>De &longs;tellis novis,<emph.end type="italics"/> and car­ <lb/>ry back this of the Conclu&longs;ions, to &longs;ee what is written therein a­ <lb/>gain&longs;t the Annual motion, which are to be the arguments of our <lb/>di&longs;cour&longs;e to morrow.</s></p><pb xlink:href="040/01/266.jpg"/><pb xlink:href="040/01/267.jpg"/><figure id="id.040.01.267.1.jpg" xlink:href="040/01/267/1.jpg"/><figure id="id.040.01.267.2.jpg" xlink:href="040/01/267/2.jpg"/><figure id="id.040.01.267.3.jpg" xlink:href="040/01/267/3.jpg"/><figure id="id.040.01.267.4.jpg" xlink:href="040/01/267/4.jpg"/><figure id="id.040.01.267.5.jpg" xlink:href="040/01/267/5.jpg"/><figure id="id.040.01.267.6.jpg" xlink:href="040/01/267/6.jpg"/><figure id="id.040.01.267.7.jpg" xlink:href="040/01/267/7.jpg"/><figure id="id.040.01.267.8.jpg" xlink:href="040/01/267/8.jpg"/><figure id="id.040.01.267.9.jpg" xlink:href="040/01/267/9.jpg"/><p type="caption"><s><emph type="italics"/>Place this Plate <lb/>at the end of <lb/>the Second<emph.end type="italics"/><lb/>Dialogue.</s></p> </chap><chap><pb xlink:href="040/01/268.jpg"/> <pb xlink:href="040/01/269.jpg" pagenum="249"/><p type="head"><s>GALILÆUS <lb/>Galilæus Lyncæus, <lb/>HIS <lb/>SYSTEME <lb/>OF THE <lb/>WORLD.</s></p><p type="head"><s>The Third Dialogue.</s></p><p type="head"><s><emph type="italics"/>INTERLOCVTORS.<emph.end type="italics"/></s></p><p type="head"><s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"><s>SAGR. </s><s>The great de&longs;ire wherewith I have expected <lb/>your coming, that I might hear the novel <lb/>conceits touching the annual conver&longs;i­ <lb/>on of this our Globe, hath made me <lb/>think the houres of the la&longs;t night, and <lb/>tho&longs;e of this morning very tedious, al­ <lb/>though I &longs;pent them not idly, but lying <lb/>awake I imployed a good part thereof in <lb/>ruminating upon our ye&longs;terdayes di&longs;cour­ <lb/>&longs;es, weighing the rea&longs;ons alledged by both parties, in favour of <lb/>the two contrary Hypothe&longs;es, that of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy,<emph.end type="italics"/> and <lb/>this of <emph type="italics"/>Ari&longs;tarchus,<emph.end type="italics"/> and <emph type="italics"/>Copernicus.<emph.end type="italics"/> And really methinks, that <lb/>which ever of the&longs;e parties have been deceived, they are worthy of <lb/>excu&longs;e, &longs;o &longs;pecious and valid in appearance are the rea&longs;ons that <lb/>may have per&longs;waded them either way; though neverthele&longs;&longs;e we <pb xlink:href="040/01/270.jpg" pagenum="250"/>do for the mo&longs;t part clo&longs;e with tho&longs;e produced by the grave Au­ <lb/>thours fir&longs;t above mentioned. </s><s>But albeit that the <emph type="italics"/>Peripatetick Hy­ <lb/>pothe&longs;is,<emph.end type="italics"/> by rea&longs;on of its antiquity, hath had many followers and <lb/>fautors, and the other very few; fir&longs;t, for its ob&longs;curity, and next, <lb/>for its novelty, yet methinks I di&longs;cover among&longs;t tho&longs;e many, <lb/>and particularly among&longs;t the modernes &longs;ome, who for the &longs;up­ <lb/>port of the opinion by them e&longs;teemed true, have introduced <lb/>other rea&longs;ons &longs;ufficiently childi&longs;h, I could &longs;ay ridiculous.</s></p><p type="main"><s>SALV. </s><s>I have met with the like, and &longs;o much wor&longs;e than <lb/><arrow.to.target n="marg504"></arrow.to.target> <lb/>yours, that I blu&longs;h to rehear&longs;e them, not &longs;o much to &longs;pare the fame <lb/>of their Authours, the names of whom might be perpetually con­ <lb/>cealed, as becau&longs;e I am a&longs;hamed &longs;o much to &longs;tain the honour of <lb/>mankinde. </s><s>In ob&longs;erving of the&longs;e men, I have found that &longs;ome <lb/>there are who prepo&longs;terou&longs;ly rea&longs;oning, fir&longs;t &longs;tabli&longs;h the conclu­ <lb/>&longs;ion in their fancy, and (either becau&longs;e it is their own, or el&longs;e be­ <lb/>longs to a per&longs;on whom they much confide in) &longs;o firmly imprint <lb/>it in their opinions, that it is altogether impo&longs;&longs;ible ever wholly to <lb/>efface it: and tho&longs;e rea&longs;ons which they them&longs;elves &longs;tumble upon, <lb/>or which they hear others to alledge in confirmation of the con­ <lb/>ceit entertained, though never &longs;o &longs;imple and in&longs;ipid, in&longs;tantly find <lb/>credit and applau&longs;e with them: but on the contrary, tho&longs;e which <lb/>are brought again&longs;t their opinion, though ingenuous and conclu­ <lb/>ding, they receive not only with nau&longs;eating, but with di&longs;dain and <lb/>bitter indignation, yea, you &longs;hall have one of the&longs;e &longs;o inraged, as <lb/>that he will not be backward to try all wayes to &longs;uppre&longs;s and &longs;ilence <lb/>their adver&longs;aries: and of this I my &longs;elf have had &longs;ome experience.</s></p><p type="margin"><s><margin.target id="marg504"></margin.target><emph type="italics"/>Some in arguing <lb/>fir&longs;t fix in their <lb/>minds the conclu­ <lb/>&longs;ion beleeved by <lb/>them, and then a­ <lb/>dapt their rea&longs;ons <lb/>to that.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Indeed the&longs;e men deduce not the conclu&longs;ion from the <lb/>premi&longs;es, nor confirme them with rea&longs;ons, but accomodate, or to <lb/>&longs;ay better, di&longs;commodate and di&longs;tort the premi&longs;es and arguments <lb/>to make them &longs;peak in favour of their pre-a&longs;&longs;umed and pertinaci­ <lb/>ous conclu&longs;ions. </s><s>It is not good therefore to contract familiarity <lb/>with the&longs;e men; and the rather, for that their conver&longs;ation is not <lb/>only unplea&longs;ant, but al&longs;o dangerous. </s><s>Yet let us continue our con­ <lb/>ference with <emph type="italics"/>Simplicius<emph.end type="italics"/> however, whom I have known this long <lb/>while for a man of great ingenuity, and altogether void of malice: <lb/>be&longs;ides he is well ver&longs;t in the Peripatetick Doctrine; &longs;o that I may <lb/>a&longs;&longs;ure my &longs;elf, that what &longs;hall not fall within the reach of his rea­ <lb/>&longs;on for the &longs;upport of the <emph type="italics"/>Ari&longs;totelian<emph.end type="italics"/> Hypothe&longs;is, will not ea&longs;ily <lb/>be found out by others. </s><s>But &longs;ee yonder he comes, quite out of <lb/>winde, who&longs;e company we have &longs;o long de&longs;ired: we were ju&longs;t now <lb/>&longs;peaking again&longs;t the &longs;mall ha&longs;t you made to come to us.</s></p><p type="main"><s>SIMP. </s><s>You mu&longs;t not blame me, but <emph type="italics"/>Neptune,<emph.end type="italics"/> for this my long <lb/>&longs;tay; which in the ebbe of this mornings tide hath in a manner <lb/>drain'd away the waters, for the <emph type="italics"/>Gondola<emph.end type="italics"/> that brought me, being <lb/>entered not far from hence into a certain Channel, wanting depth, <pb xlink:href="040/01/271.jpg" pagenum="251"/>where I was &longs;tranded, and forced to &longs;tay there more than a full <lb/>hour, in expecting the return of the tide: and there waiting in <lb/>this manner, without being able to get out of the boat, which on a <lb/>&longs;udden ran a ground, I ob&longs;erved a certain accident, which to me <lb/><arrow.to.target n="marg505"></arrow.to.target> <lb/>&longs;eemed very &longs;trange; and it was this, that in the waters ebbing <lb/>I &longs;aw it retreat very fa&longs;t by &longs;everal &longs;mall rivolets, the ouze being <lb/>in many places di&longs;covered, and whil&longs;t I &longs;tood looking upon this ef­ <lb/>fect, I &longs;aw this motion in an in&longs;tant to cea&longs;e, and without a mi­ <lb/>nutes interval the &longs;ame water to begin to return back again, and <lb/>the tide from ebbing to become young flood, without &longs;tanding <lb/>&longs;till a moment: an effect that as long as I have dwelt in <emph type="italics"/>Venice,<emph.end type="italics"/> <lb/>I never took notice of before.</s></p><p type="margin"><s><margin.target id="marg505"></margin.target><emph type="italics"/>The motion of <lb/>the water in ebbing <lb/>and flowing not in­ <lb/>terrupted by re&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>It is very much, that you &longs;hould be left thus on ground, <lb/>among&longs;t &longs;mall Channels; in which rivolets, as having very little <lb/>declivity, the ri&longs;ing or falling of the main &longs;ea, the thickne&longs;s onely <lb/>of a paper is &longs;ufficient to make the water to ebbe and flow for good <lb/>long &longs;paces of time: like as in &longs;ome creeks of the Sea, its flowing <lb/>four or &longs;ix ^{*} yards onely, maketh the water to overflow the adja­ <lb/>cent Mar&longs;hes for &longs;ome hundreds and thou&longs;ands of ^{*} acres. <lb/><arrow.to.target n="marg506"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg506"></margin.target>* Pertiche vene­ <lb/>tiani.</s></p><p type="main"><s>SIMP. </s><s>This I know very well, but I &longs;hould have thought, that <lb/>between the ultimate terme of ebbing, and the fir&longs;t beginnng to <lb/>flow, there &longs;hould have interpo&longs;ed &longs;ome con&longs;iderable interval of <lb/>re&longs;t.</s></p><p type="main"><s>SAGR. </s><s>This will appear unto you, if you ca&longs;t your eye upon <lb/>the bank or piles, where the&longs;e mutations are made perpendicular­ <lb/>ly, but not that there is any real time of ce&longs;&longs;ation.</s></p><p type="main"><s>SIMP. </s><s>I did think, that becau&longs;e the&longs;e two motions were con­ <lb/>trary, there ought to be in the mid&longs;t between them &longs;ome kind of <lb/>re&longs;t; conformable to the Doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> which demon&longs;trates. <lb/></s><s>that <emph type="italics"/>in puncto regre&longs;&longs;us mediat quies.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I very well remember this place: but I bear in minde <lb/>al&longs;o, that when I read Philo&longs;ophy, I was not thorowly &longs;atisfied <lb/>with <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> demon&longs;tration; but that I had many experiments <lb/>on the contrary, which I could &longs;till rehear&longs;e unto you, but I am <lb/>unwilling to &longs;ally out into any other digre&longs;&longs;ions, we being met <lb/>here to di&longs;cour&longs;e of the propo&longs;ed mattes, if it be po&longs;&longs;ible, without <lb/>the&longs;e excur&longs;ions wherewith we have interrupted our di&longs;putes in <lb/>tho&longs;e dayes that are pa&longs;t.</s></p><p type="main"><s>SIMP. </s><s>And yet we may with convenience, if not interrupt <lb/>them, at lea&longs;t prolong them very much, for returning ye&longs;ter­ <lb/>day home, I &longs;et my &longs;el&longs; to read the Tractate of Conclu&longs;ions, where <lb/>I find Demon&longs;trations again&longs;t this annual motion a&longs;cribed to the <lb/>Earth, very &longs;olid; and becau&longs;e I would not tru&longs;t my memory with <lb/>the punctual relation of them, I have brought back the Book a­ <lb/>long with me.</s></p> <pb xlink:href="040/01/272.jpg" pagenum="252"/><p type="main"><s>SAGR. </s><s>You have done very well; but if we would re-a&longs;&longs;ume <lb/>our Di&longs;putations according to ye&longs;terdayes appointment, it is re­ <lb/>qui&longs;ite that we fir&longs;t hear what account <emph type="italics"/>Salviatus<emph.end type="italics"/> hath to give us <lb/>of the Book, <emph type="italics"/>De &longs;tellis novis,<emph.end type="italics"/> and then without interruption we <lb/>may proceed to the Annual motion. </s><s>Now what &longs;ay you, <emph type="italics"/>Salvia­ <lb/>tus<emph.end type="italics"/> touching tho&longs;e &longs;tars? </s><s>Are they really pull'd down from Hea­ <lb/>ven to the&longs;e lower regions, by vertue of that Authours calculati­ <lb/>ons, whom <emph type="italics"/>Simplicius<emph.end type="italics"/> mentioneth?</s></p><p type="main"><s>SALV. </s><s>I &longs;et my &longs;elf la&longs;t night to peru&longs;e his proceedings, and I <lb/>have this morning had another view of him, to &longs;ee whether that <lb/>which he &longs;eemed over night to affirm, were really his &longs;en&longs;e, or my <lb/>dreams and phanta&longs;tical nocturnal imaginations; and in the clo&longs;e <lb/>found to my great grief that tho&longs;e things were really written and <lb/>printed, which for the reputation-&longs;ake of this Philo&longs;opher I was <lb/>unwilling to believe. </s><s>It is in my judgment impo&longs;&longs;ible, but that he <lb/>&longs;hould perceive the vanity of his undertaking, a&longs;well becau&longs;e it is <lb/>too apert, as becau&longs;e I remember, that I have heard him mentio­ <lb/>ned with applau&longs;e by the <emph type="italics"/>Academick our Friend<emph.end type="italics"/>: it &longs;eemeth to <lb/>me al&longs;o to be a thing very unlikely, that in complacency to others, <lb/>he &longs;hould be induced to &longs;et &longs;o low a value upon his reputation, as <lb/>to give con&longs;ent to the publication of a work, for which he could <lb/>expect no other than the cen&longs;ure of the Learned.</s></p><p type="main"><s>SAGR. Yea, but you know, that tho&longs;e will be much fewer <lb/>than one for an hundred, compared to tho&longs;e that &longs;hall celebrate <lb/>and extoll him above the greate&longs;t wits that are, or ever have been <lb/>in the world: He is one that hath mentioned the Peripate­ <lb/>tick inalterability of Heaven again&longs;t a troop of <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> and <lb/>that to their greater di&longs;grace hath foiled them at their own wea­ <lb/>pons; and what do you think four or five in a Countrey that di&longs;­ <lb/>cern his triflings, can do again&longs;t the innumerable multitude, that, <lb/>not being able to di&longs;cover or comprehend them, &longs;uffer them&longs;elves <lb/>to be taken with words, and &longs;o much more applaud him, by how <lb/>much the le&longs;&longs;e they under&longs;tand him? </s><s>You may adde al&longs;o, that <lb/>tho&longs;e few who under&longs;tand, &longs;corn to give an an&longs;wer to papers &longs;o <lb/>trivial and unconcludent; and that upon very good rea&longs;ons, be­ <lb/>cau&longs;e to the intelligent there is no need thereof, and to tho&longs;e that <lb/>do not under&longs;tand, it is but labour lo&longs;t.</s></p><p type="main"><s>SALV. </s><s>The mo&longs;t de&longs;erved puni&longs;hment of their demerits would <lb/>certainly be &longs;ilence, if there were not other rea&longs;ons, for which it <lb/>is haply no le&longs;&longs;e than nece&longs;&longs;ary to re&longs;ent their timerity: one of <lb/>which is, that we <emph type="italics"/>Italians<emph.end type="italics"/> thereby incur the cen&longs;ure of Illiterates, <lb/>and attract the laughter of Forreigners; and e&longs;pecially to &longs;uch <lb/>who are &longs;eparated from our Religion; and I could &longs;hew you ma­ <lb/>ny of tho&longs;e of no &longs;mall eminency, who &longs;coff at our <emph type="italics"/>Academick,<emph.end type="italics"/> <lb/>and the many Mathematicians that are in <emph type="italics"/>Italie,<emph.end type="italics"/> for &longs;uffering the <pb xlink:href="040/01/273.jpg" pagenum="253"/>follies of &longs;uch a ^{*} Fabler again&longs;t <emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> to come into the </s></p><p type="main"><s><arrow.to.target n="marg507"></arrow.to.target> <lb/>light, and to be openly maintained without contradiction; but <lb/>this al&longs;o might be di&longs;pen&longs;ed with, in re&longs;pect of the other greater <lb/>occa&longs;ions of laughter, wherewith we may confront them depend­ <lb/>ing on the di&longs;&longs;imulation of the intelligent, touching the follies of <lb/>the&longs;e opponents of the Doctrines that they well enough under­ <lb/>&longs;tand.</s></p><p type="margin"><s><margin.target id="marg507"></margin.target>* Lorenzini.</s></p><p type="main"><s>SAGR. </s><s>I de&longs;ire not a greater proof of tho&longs;e mens petulancy, <lb/>and the infelicity of a <emph type="italics"/>Copernican,<emph.end type="italics"/> &longs;ubject to be oppo&longs;ed by &longs;uch <lb/>as under&longs;tand not &longs;o much as the very fir&longs;t po&longs;itions, upon which <lb/>he undertakes the quarrel.</s></p><p type="main"><s>SALV. </s><s>You will be no le&longs;&longs;e a&longs;toni&longs;hed at their method in con­ <lb/>futing the <emph type="italics"/>Astronomers,<emph.end type="italics"/> who affirm the new Stars to be &longs;uperiour <lb/>to the Orbs of the Planets; and peradventure in the ^{†} Firmament <lb/><arrow.to.target n="marg508"></arrow.to.target> <lb/>it &longs;elf.</s></p><p type="margin"><s><margin.target id="marg508"></margin.target>† He taketh the <lb/>Firmament for the <lb/>Starry Sphere, and <lb/>as we vulgarly re­ <lb/>ceive the word.</s></p><p type="main"><s>SAGR. </s><s>But how could you in &longs;o &longs;hort a time examine all this <lb/>Book, which is &longs;o great a Volume, and mu&longs;t needs contain very <lb/>many demon&longs;trations.?</s></p><p type="main"><s>SALV. </s><s>I have confined my &longs;elf to the&longs;e his fir&longs;t confutations, in <lb/>which with twelve demon&longs;trations founded upon the ob&longs;ervations <lb/>of twelve <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> (who all held, that the Star, <emph type="italics"/>Anno<emph.end type="italics"/> 1572. <lb/>which appeared in <emph type="italics"/>Ca&longs;&longs;iopeia,<emph.end type="italics"/> was in the Firmament) he proveth it <lb/>on the contrary, to be beneath the Moon, conferring, two by two, <lb/>the meridian altitudes, proceeding in the method that you &longs;hall <lb/>under&longs;tand by and by. </s><s>And becau&longs;e, I think, that in the exami­ <lb/>nation of this his fir&longs;t progre&longs;&longs;ion, I have di&longs;covered in this Au­ <lb/>thour a great unlikelihood of his ability to conclude any thing a­ <lb/>gain&longs;t the <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> in favour of the <emph type="italics"/>Peripatetick Philo&longs;ophers,<emph.end type="italics"/> <lb/>and that their opinion is more and more concludently confirmed, <lb/>I could not apply my &longs;elf with the like patience in examining his <lb/>other methods, but have given a very &longs;light glance upon them, <lb/>and am certain, that the defect that is in the&longs;e fir&longs;t impugnations, <lb/>is likewi&longs;e in the re&longs;t. </s><s>And as you &longs;hall &longs;ee, by experience, very <lb/>few words will &longs;uffice to confute this whole Book, though compi­ <lb/>led with &longs;o great a number of laborious calculations, as here you <lb/><arrow.to.target n="marg509"></arrow.to.target> <lb/>&longs;ee. </s><s>Therefore ob&longs;erve my proceedings. </s><s>This Authour under­ <lb/>taketh, as I &longs;ay, to wound his adver&longs;aries with their own weapons, <lb/><emph type="italics"/>i.e.<emph.end type="italics"/> a great number of ob&longs;ervations made by them&longs;elves, to wit, by <lb/>twelve or thirteen Authours in number, and upon part of them he <lb/>makes his &longs;upputations, and concludeth tho&longs;e &longs;tars to have been <lb/>below the Moon. </s><s>Now becau&longs;e the proceeding by interrogato­ <lb/>ries very much plea&longs;eth me, in regard the Authour him&longs;elf is not <lb/>here, let <emph type="italics"/>Simplicius<emph.end type="italics"/> an&longs;wer me to the que&longs;tions that I &longs;hall ask <lb/>him, as he thinks he him&longs;elf would, if he were pre&longs;ent. </s><s>And pre­ <lb/>&longs;uppo&longs;ing that we &longs;peak of the fore&longs;aid Star, of <emph type="italics"/>Anno<emph.end type="italics"/> 1572. ap­ <pb xlink:href="040/01/274.jpg" pagenum="254"/>pearing in <emph type="italics"/>Ca&longs;&longs;iopeia,<emph.end type="italics"/> tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> whether you believe that <lb/>it might be in the &longs;ame time placed in divers places, that is, a­ <lb/>mong&longs;t the Elements, aud al&longs;o among&longs;t the planetary Orbs, and <lb/>al&longs;o above the&longs;e among&longs;t the fixed Stars, and yet again infinitely <lb/>more high.</s></p><p type="margin"><s><margin.target id="marg509"></margin.target><emph type="italics"/>The method ob­ <lb/>&longs;erved by<emph.end type="italics"/> Clar. <emph type="italics"/>in <lb/>confuting the A­ <lb/>&longs;tronomers, and by<emph.end type="italics"/> <lb/>Salviatus <emph type="italics"/>in confu­ <lb/>ting him.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>There is no doubt, but that it ought to be confe&longs;&longs;ed <lb/>that it is but in one only place, and at one &longs;ole and determinate <lb/>di&longs;tance from the Earth.</s></p><p type="main"><s>SALV. </s><s>Therefore if the ob&longs;ervations made by the A&longs;trono­ <lb/>mers were exact, and the calculations made by this Author were <lb/>not erroneous, it were ea&longs;ie from all tho&longs;e and all the&longs;e to re­ <lb/>collect the &longs;ame di&longs;tances alwayes to an hair, is not this true?</s></p><p type="main"><s>SIMP. </s><s>My rea&longs;on hitherto tells me that &longs;o it mu&longs;t needs be; <lb/>nor do I believe that the Author would contradict it</s></p><p type="main"><s>SALV. </s><s>But when of many and many computations that have <lb/>been made, there &longs;hould not be &longs;o much as two onely that prove <lb/>true, what would you think of them?</s></p><p type="main"><s>SIMP. </s><s>I would think that they were all fal&longs;e, either through <lb/>the fault of the computi&longs;t, or through the defect of the ob&longs;er­ <lb/>vators, and at the mo&longs;t that could be &longs;aid, I would &longs;ay, that but <lb/>onely one of them and no more was true; but as yet I know not <lb/>which to choo&longs;e.</s></p><p type="main"><s>SALV. </s><s>Would you then from fal&longs;e fundamentals deduce and <lb/>e&longs;tabli&longs;h a doubtful conclu&longs;ion for ttue? </s><s>Certainly no. </s><s>Now the <lb/>calculations of this Author are &longs;uch, that no one of them agrees <lb/>with another, you may &longs;ee then what credit is to be given to <lb/>them.</s></p><p type="main"><s>SIMP. Indeed, if it be &longs;o, this is a notable failing.</s></p><p type="main"><s>SAGR. </s><s>But by the way I have a mind to help <emph type="italics"/>Simplicius,<emph.end type="italics"/> and <lb/>the Author by telling <emph type="italics"/>Salviatus,<emph.end type="italics"/> that his arguments would hold <lb/>good if the Author had undertook to go about to find out exact­ <lb/>ly the di&longs;tance of the Star from the Earth, which I do not think <lb/>to be his intention; but onely to demon&longs;trate that from tho&longs;e <lb/>ob&longs;ervations he collected that the Star was &longs;ublunary. </s><s>So <lb/>that if from tho&longs;e ob&longs;ervations, and from all the computations <lb/>made thereon, the height of the Star be alwayes collected to be <lb/>le&longs;&longs;e than that of the Moon, it &longs;erves the Authors turn to con­ <lb/>vince all tho&longs;e A&longs;tronomers of mo&longs;t impardonable ignorance, <lb/>that through the defect either of Geometry or Arithmetick, have <lb/>not known how to draw true conclu&longs;ions from their own ob&longs;erva­ <lb/>tions them&longs;elves.</s></p><p type="main"><s>SALV. </s><s>It will be convenient therefore that I turn my &longs;elf to <lb/>you, <emph type="italics"/>Sagredus,<emph.end type="italics"/> who &longs;o cunningly aphold the Doctrine of this <lb/>Author. </s><s>And to &longs;ee whether I can make <emph type="italics"/>Simplicius,<emph.end type="italics"/> though not <lb/>very expert in calcnlations, and demon&longs;trations to apprehend the <pb xlink:href="040/01/275.jpg" pagenum="255"/>inconclu&longs;ivene&longs;&longs;e at lea&longs;t of the demon&longs;trations of this Author, <lb/>fir&longs;t propo&longs;ed to con&longs;ideration, and how both he, and all the <lb/>A&longs;tronomers with whom he contendeth, do agree that the new <lb/>Star had not any motion of its own, and onely went round with <lb/>the diurnal motion of the <emph type="italics"/>primum mobile<emph.end type="italics"/>; but di&longs;&longs;ent about the <lb/>placing of it, the one party putting it in the Cele&longs;tial Region, <lb/>that is above the Moon, and haply above the fixed Stars, and <lb/>the other judging it to be neer to the Earth, that is, under the <lb/>concave of the Lunar Orb. </s><s>And becau&longs;e the &longs;ituation of the new <lb/>&longs;tar, of which we &longs;peak, was towards the North, and at no very <lb/>great di&longs;tance from the Pole, &longs;o that to us <emph type="italics"/>Septentrionals,<emph.end type="italics"/> it did <lb/>never &longs;et, it was an ea&longs;ie matter with A&longs;tronomical in&longs;truments <lb/>to have taken its &longs;everal meridian altitudes, as well its &longs;malle&longs;t <lb/>under the Pole, as its greate&longs;t above the &longs;ame; from the compa­ <lb/>ring of which altitudes, made in &longs;everal places of the Earth, <lb/>&longs;ituate at different di&longs;tances from the North, that is, different <lb/>from one another in relation to polar altitudes, the &longs;tars di&longs;tance <lb/>might be inferred: For if it was in the Firmament among&longs;t the <lb/><arrow.to.target n="marg510"></arrow.to.target> <lb/>other fixed &longs;tars, its meridian altitudes taken in divers elevations <lb/>of the pole, ought nece&longs;&longs;arily to differ from each other with the <lb/>&longs;ame variations that are found among&longs;t tho&longs;e elevations them­ <lb/>&longs;elves; that is, for example, if the elevation of the &longs;tar above <lb/>the horizon was 30 degrees, taken in the place where the polar <lb/>altitude was <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> 45 degrees, the elevation of the &longs;ame &longs;tar <lb/>ought to have been encrea&longs;ed 4 or 5 degrees in tho&longs;e more Nor­ <lb/>thernly places where the pole was higher by the &longs;aid 4 or 5 de­ <lb/>grees. </s><s>But if the &longs;tars di&longs;tance from the Earth was but very little, <lb/>in compari&longs;on of that of the Firmament; its meridian altitudes <lb/>ought approaching to the North to encrea&longs;e con&longs;iderably more <lb/>than the polar altitudes; and by that greater encrea&longs;e, that is, <lb/>by the exce&longs;&longs;e of the encrea&longs;e of the &longs;tars elevation, above the <lb/>encrea&longs;e of the polar elevation (which is called the difference of <lb/>Parallaxes) is readily calculated with a cleer and &longs;ure method, <lb/>the &longs;tars di&longs;tance from the centre of the Earth. </s><s>Now this Author <lb/>taketh the ob&longs;ervations made by thirteen A&longs;tronomers in &longs;undry <lb/>elevations of the pole, and conferring a part of them at his plea­ <lb/>&longs;ure, he computeth by twelve collations the new &longs;tars height to <lb/>have been alwayes beneath the Moon; but this he adventures to <lb/>do in hopes to find &longs;o gro&longs;&longs;e ignorance in all tho&longs;e, into who&longs;e <lb/>hands his book might come, that to &longs;peak the truth, it hath turn'd <lb/>my &longs;tomack; and I wait to &longs;ee how tho&longs;e other A&longs;tronomers, and <lb/>particularly <emph type="italics"/>Kepler,<emph.end type="italics"/> again&longs;t whom this Author principally in­ <lb/>veigheth, can contein them&longs;elves in &longs;ilence, for he doth not u&longs;e <lb/>to hold his tongue on &longs;uch occa&longs;ions; unle&longs;&longs;e he did po&longs;&longs;ibly <lb/>think the enterprize too much below him. </s><s>Now to give you to <pb xlink:href="040/01/276.jpg" pagenum="256"/>under&longs;tand the &longs;ame, I have upon this paper tran&longs;cribed the con­ <lb/>clu&longs;ions that he inferreth from his twelve indagations; the fir&longs;t of <lb/>which is upon the two ob&longs;ervations: <lb/><arrow.to.target n="table1"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg510"></margin.target><emph type="italics"/>The greate&longs;t and <lb/>lea&longs;t elevations of <lb/>the new &longs;tar differ <lb/>not from each o­ <lb/>ther more than the <lb/>polar allitudes, the <lb/>&longs;aid &longs;tar being in <lb/>the Firmnment.<emph.end type="italics"/></s></p><table><table.target id="table1"></table.target><row><cell>Of <emph type="italics"/>Maurolicus<emph.end type="italics"/> and <emph type="italics"/>Hainzelius,<emph.end type="italics"/> from which the Star is collected to have been di&longs;tant from the centre le&longs;&longs;e than 3 &longs;emidiameters of the Earth, the difference of Parallaxes being 4 <emph type="italics"/>gr. 42 m.<emph.end type="italics"/>30 <emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell><cell>3 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>2. And is calculated on the ob&longs;ervations of <emph type="italics"/>Hain-zelius,<emph.end type="italics"/> with Parall. of 8. <emph type="italics"/>m. 30 &longs;ec.<emph.end type="italics"/> and its di-&longs;tance from the centre is computed to be more than</cell><cell>25 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>3. And upon the ob&longs;ervations of <emph type="italics"/>Tycho<emph.end type="italics"/> and <emph type="italics"/>Hain-zelius,<emph.end type="italics"/> with Parall. of 10 <emph type="italics"/>m.<emph.end type="italics"/> and the di&longs;tance of the centre is collected to be little le&longs;&longs;e than</cell><cell>19 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>4. And upon the ob&longs;ervations of <emph type="italics"/>Tycho<emph.end type="italics"/> and the <emph type="italics"/>Landgrave,<emph.end type="italics"/> with Parall. of 14 <emph type="italics"/>m.<emph.end type="italics"/> the di&longs;tance from the centre is made to be about</cell><cell>10 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>5. And upon the ob&longs;ervations of <emph type="italics"/>Hainzelius<emph.end type="italics"/> and <emph type="italics"/>Gemma,<emph.end type="italics"/> with Parall. of 42 <emph type="italics"/>m. 30 &longs;ec.<emph.end type="italics"/> whereby the di&longs;tance is gathered to be about</cell><cell>4 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>6. And upon the ob&longs;ervations of the <emph type="italics"/>Landgrave<emph.end type="italics"/>and <emph type="italics"/>Camerarius,<emph.end type="italics"/> with Parall. of 8 <emph type="italics"/>m.<emph.end type="italics"/> the di-&longs;tance is concluded to be about</cell><cell>4 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>7. And upon the ob&longs;ervations of <emph type="italics"/>Tycho<emph.end type="italics"/> and <emph type="italics"/>Hage-cius,<emph.end type="italics"/> with Parall. of 6 <emph type="italics"/>m.<emph.end type="italics"/> and the di&longs;tance is made</cell><cell>31 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>8. And upon the ob&longs;ervations of <emph type="italics"/>Hagecius<emph.end type="italics"/> and <emph type="italics"/>Vr-&longs;inus<emph.end type="italics"/> with Parall. of 43 <emph type="italics"/>m.<emph.end type="italics"/> and the &longs;tars di&longs;tance from the &longs;uperficies of the Earth is rendred</cell><cell>1/2 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>9. And upon the ob&longs;ervations of <emph type="italics"/>Landgravius<emph.end type="italics"/> and <emph type="italics"/>Bu&longs;chius,<emph.end type="italics"/> with Parall. of 15 <emph type="italics"/>m.<emph.end type="italics"/> and the di-&longs;tance from the &longs;uperficies of the Earth is by &longs;upputation</cell><cell>1/48 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>10. And upon the ob&longs;ervations of <emph type="italics"/>Maurolice<emph.end type="italics"/> and <emph type="italics"/>Munocius,<emph.end type="italics"/> with Parall. of 4 <emph type="italics"/>m. 30 &longs;ec.<emph.end type="italics"/> and the compnted di&longs;tance from the Earths &longs;urface is</cell><cell>1/5 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row><row><cell>11. And upon the ob&longs;ervations of <emph type="italics"/>Munocius<emph.end type="italics"/> and <emph type="italics"/>Gemma,<emph.end type="italics"/> with Parall. of 55 <emph type="italics"/>m.<emph.end type="italics"/> and the di&longs;tance from the centre is rendred</cell><cell>13 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row> <pb xlink:href="040/01/277.jpg" pagenum="257"/><row><cell>12. And upon the ob&longs;ervations of <emph type="italics"/>Muno&longs;ius<emph.end type="italics"/> and <emph type="italics"/>Vr&longs;inus<emph.end type="italics"/> with Parall. of 1 <emph type="italics"/>gr. 36 m.<emph.end type="italics"/> and the di-&longs;tance from the centre cometh forth le&longs;&longs;e than</cell><cell>7 <emph type="italics"/>&longs;emid.<emph.end type="italics"/></cell></row></table><p type="main"><s>The&longs;e are twelve indagations made by the Author at his electi­ <lb/>on, among&longs;t many which, as he &longs;aith, might be made by combi­ <lb/>ning the ob&longs;ervations of the&longs;e thirteen ob&longs;ervators. </s><s>The which <lb/>twelve we may believe to be the mo&longs;t favourable to prove his <lb/>intention.</s></p><p type="main"><s>SAGR. </s><s>I would know whether among&longs;t the &longs;o many other in­ <lb/>dagations pretermitted by the Author, there were not &longs;ome that <lb/>made again&longs;t him, that is, from which calculating one might find <lb/>the new &longs;tar to have been above the Moon, as at the very fir&longs;t <lb/>&longs;ight I think we may rea&longs;onably que&longs;tion; in regard I &longs;ee the&longs;e <lb/>already produced to be &longs;o different from one another, that &longs;ome <lb/>of them give me the di&longs;tance of the &longs;aid &longs;tar from the Earth, 4, 6, <lb/>10, 100, a thou&longs;and, and an hundred thou&longs;and times bigger one <lb/>than another; &longs;o that I may well &longs;u&longs;pect that among&longs;t tho&longs;e that <lb/>he did not calculate, there was &longs;ome one in fauour of the adver&longs;e <lb/>party. </s><s>And I gue&longs;&longs;e this to be the more probable, for that I can­ <lb/>not conceive that tho&longs;e A&longs;tronomers the ob&longs;ervators could want <lb/>the knowledg and practice of the&longs;e computations, which I think <lb/>do not depend upon the ab&longs;truce&longs;t things in the World. </s><s>And in­ <lb/>deed it will &longs;eem to me a thing more than miraculous, if whil&longs;t in <lb/>the&longs;e twelve inve&longs;tigations onely, there are &longs;ome that make the <lb/>&longs;tar to be di&longs;tant from the Earth but a few miles, and others that <lb/>make it to be but a very fmall matter below the Moon, there are <lb/>none to be found that in favour of the contrary part do make it <lb/>&longs;o much as twenty yards above the Lunar Orb. </s><s>And that which <lb/>&longs;hall be yet again more extravagant, that all tho&longs;e A&longs;tronomers <lb/>&longs;hould have been &longs;o blind as not to have di&longs;covered that their &longs;o <lb/>apparent mi&longs;take.</s></p><p type="main"><s>SALV. </s><s>Begin now to prepare your ears to hear with infinite <lb/>admiration to what exce&longs;&longs;es of confidence of ones own authority <lb/>and others folly, the de&longs;ire of contradicting and &longs;hewing ones <lb/>&longs;elf wi&longs;er than others, tran&longs;ports a man. </s><s>Among&longs;t the indaga­ <lb/>tions omitted by the Author, there are &longs;uch to be found as make <lb/>the new &longs;tar not onely above the Moon, but above the fixed <lb/>&longs;tars al&longs;o. </s><s>And the&longs;e are not a few, but the greater part, as you <lb/>&longs;hall &longs;ee in this other paper, where I have &longs;et them down.</s></p><p type="main"><s>SAGR. </s><s>But what &longs;aith the Author to the&longs;e? </s><s>It may be he did <lb/>not think of them?</s></p><p type="main"><s>SALV. </s><s>He hath thought of them but too much: but &longs;aith, that <lb/>the ob&longs;ervations upon which the calculations make the &longs;tar to be <lb/>infinitely remote, are erroneous, and that they cannot be com­ <lb/>bined to one another.</s></p> <pb xlink:href="040/01/278.jpg" pagenum="258"/><p type="main"><s>SIMP. </s><s>But this &longs;eemeth to me a very lame eva&longs;ion; for the ad­ <lb/>ver&longs;e party may with as much rea&longs;on reply, that tho&longs;e are errone­ <lb/>ous wherewith he collecteth the &longs;tar to have been in the Elemen­ <lb/>tary Region.</s></p><p type="main"><s>SALV. </s><s>Oh <emph type="italics"/>Simplicius,<emph.end type="italics"/> if I could but make you comprehend <lb/>the craft, though no great craftine&longs;&longs;e of this Author, I &longs;hould <lb/>make you to wonder, and al&longs;o to be angry to &longs;ee how that he <lb/>palliating his &longs;agacity with the vail of the &longs;implicity of your &longs;elf; <lb/>and the re&longs;t of meer Philo&longs;ophers, would in&longs;inuate him&longs;elf into <lb/>your good opinion, by tickling your cars, and &longs;welling your am­ <lb/>bition, pretending to have convinced and &longs;ilenced the&longs;e petty <lb/>A&longs;tronomers, who went about to a&longs;&longs;ault the impregnable inalte­ <lb/>rability of the <emph type="italics"/>Peripatetick<emph.end type="italics"/> Heaven, and which is more, to have <lb/>foild and conquered them with their own arms. </s><s>I will try with all <lb/>my ability to do the &longs;ame; and in the mean time let <emph type="italics"/>Sagredus<emph.end type="italics"/> <lb/>take it in good part, if <emph type="italics"/>Simplicius<emph.end type="italics"/> and I try his patience, perhaps <lb/>a little too much, whil&longs;t that with a &longs;uperfluous circumlocution <lb/>(&longs;uperfluous I &longs;ay to his mo&longs;t nimble apprehen&longs;ion) I go about to <lb/>make out a thing, which it is not convenient &longs;hould be hid and <lb/>unknown unto him.</s></p><p type="main"><s>SAGR. </s><s>I &longs;hall not onely without wearine&longs;&longs;e, but al&longs;o with <lb/>much delight hearken to your di&longs;cour&longs;es; and &longs;o ought all <emph type="italics"/>Peripa­ <lb/>tetick<emph.end type="italics"/> Philo&longs;ophers, to the end they may know how much they <lb/>are oblieged to this their Protector.</s></p><p type="main"><s>SALV. </s><s>Tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> whether you do well comprehend, <lb/>how, the new &longs;tar being placed in the meridian circle yonder to­ <lb/>wards the North, the &longs;ame to one that from the South &longs;hould <lb/>go towards the North, would &longs;eem to ri&longs;e higher and higher a­ <lb/>bove the Horizon, as much as the Pole, although it &longs;hould have <lb/>been &longs;cituate among&longs;t the fixed &longs;tars; but, that in ca&longs;e it were <lb/>con&longs;iderably lower, that is nearer to the Earth, it would appear <lb/>to a&longs;cend more than the &longs;aid pole, and &longs;till more by how much <lb/>its vicinity was greater?</s></p><p type="main"><s>SIMP. </s><s>I think that I do very well conceive the &longs;ame; in to­ <lb/>ken whereof I will try if I can make a mathematical Scheme of <lb/>it, and in this great circle <emph type="italics"/>[in Fig. </s><s>1. of this Dialogue.]<emph.end type="italics"/> I will <lb/>marke the pole P; and in the&longs;e two lower circles I will note two <lb/>&longs;tars beheld from one place on the Earth, which let be A; and <lb/>let the two &longs;tars be the&longs;e B and C, beheld in the &longs;ame line A B C, <lb/>which line I prolong till it meet with a fixed &longs;tar in D. </s><s>And then <lb/>walking along the Earth, till I come to the term E, the two <lb/>&longs;tars will appear to me &longs;eparated from the fixed &longs;tar D, and ad­ <lb/>vanced neerer to the pole P, and the lower &longs;tar B more, which <lb/>will appear to me in G, and the &longs;tar C le&longs;&longs;e, which will ap <lb/>pear to me in F, but the fixed &longs;tar D will have kept the &longs;ame <lb/>di&longs;tance from the Pole.</s></p> <pb xlink:href="040/01/279.jpg" pagenum="259"/><p type="main"><s>SALV. </s><s>I &longs;ee that you under&longs;tand the bu&longs;ine&longs;&longs;e very well. </s><s>I be­ <lb/>lieve that you do likewi&longs;e comprehend, that, in regard the &longs;tar B <lb/>is lower than C, the angle which is made by the rayes of the <lb/>&longs;ight, which departing from the two places A and E, meet in C, <lb/>to wit, this angle A C E, is more narrow, or if we will &longs;ay more <lb/>acute than the angle con&longs;tituted in B, by the rayes A B and <lb/>E <emph type="italics"/>B.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>This I likewi&longs;e under&longs;tand very well.</s></p><p type="main"><s>SALV. </s><s>And al&longs;o, the Earth beine very little and almo&longs;t in&longs;en­ <lb/>&longs;ible, in re&longs;pect of the Firmament <emph type="italics"/>(or Starry Sphere<emph.end type="italics"/>;) and con­ <lb/>&longs;equently the &longs;pace A E, paced on the Earth, being very &longs;mall in <lb/>compari&longs;on of the immen&longs;e length of the lines E G and E F, pa&longs;­ <lb/>&longs;ing from the Earth unto the Firmament, you thereby collect that <lb/>the &longs;tar C might ri&longs;e and a&longs;cend &longs;o much and &longs;o much above the <lb/>Earth, that the angle therein made by the rayes which depart <lb/>from the &longs;aid &longs;tationary points A and E, might become mo&longs;t a­ <lb/>cute, and as it were ab&longs;olutely null and in&longs;en&longs;ible.</s></p><p type="main"><s>SIMP. </s><s>And this al&longs;o is mo&longs;t manife&longs;t to &longs;en&longs;e.</s></p><p type="main"><s>SALV. </s><s>Now you know <emph type="italics"/>Simplicius<emph.end type="italics"/> that A&longs;tronomers and Ma­ <lb/>thematicians have found infallible rules by way of Geometry and <lb/>Arithmetick, to be able by help of the quantity of the&longs;e angles <lb/><emph type="italics"/>B<emph.end type="italics"/> and C, and of their differences, with the additional knowledg <lb/>of the di&longs;tance of the two places A and E, to find to a foot the <lb/>remotene&longs;&longs;e of &longs;ublime bodies; provided alwayes that the afore­ <lb/>&longs;aid di&longs;tance, and angles be exactly taken.</s></p><p type="main"><s>SIMP. </s><s>So that if the Rules dependent on <emph type="italics"/>Geometry<emph.end type="italics"/> and <emph type="italics"/>A&longs;tro­ <lb/>nomy<emph.end type="italics"/> be true, all the fallacies and errours that might be met with <lb/>in attempting to inve&longs;tigate tho&longs;e altitudes of new Stars or Co­ <lb/>mets, or other things mu&longs;t of nece&longs;&longs;ity depend on the di&longs;tance A E, <lb/>and on the angles B and C, not well mea&longs;ured. </s><s>And thus all tho&longs;e <lb/>differences which are found in the&longs;e twelve workings depend, not <lb/>on the de&longs;ects of the rules of the Calculations, but on the errours <lb/>committed in finding out tho&longs;e angles, and tho&longs;e di&longs;tances, by means <lb/>of the In&longs;trumental Ob&longs;ervations.</s></p><p type="main"><s>SALV. True; and of this there is no doubt to be made. </s><s>Now <lb/>it is nece&longs;&longs;ary that you ob&longs;erve inten&longs;ely, how in removing the Star <lb/>from B to C, whereupon the angle alwayes grows more acute, the <lb/>ray E B G goeth farther and farther off from the ray A B D in <lb/>the part beneath the angle, as you may &longs;ee in the line E C F, <lb/>who&longs;e inferiour part E C is more remote from the part A C, than <lb/>is the part E B, but it can never happen, that by any what&longs;oever <lb/>immen&longs;e rece&longs;&longs;ion, the lines A D and E F &longs;hould totally &longs;ever from <lb/>each other, they being finally to go and conjoyn in the Star: and <lb/>onely this may be &longs;aid, that they would &longs;eparate, and reduce them­ <lb/>&longs;elves to parallels, if &longs;o be the rece&longs;&longs;ion &longs;hould be infinite, which <pb xlink:href="040/01/280.jpg" pagenum="260"/>ca&longs;e is not to be &longs;uppo&longs;ed. </s><s>But becau&longs;e (ob&longs;erve well) the di&longs;tance <lb/>of the Firmament, in relation to the &longs;mallne&longs;&longs;e of the Earth, as <lb/>hath been &longs;aid, is to be accounted, as if it were infinite; therefore <lb/>the angle conteined betwixt the two rayes, that being drawn from <lb/>the points A and E, go to determine in a fixed Star, is e&longs;teemed <lb/>nothing, and tho&longs;e rayes held to be two parallel lines; and there­ <lb/>fore it is concluded, that then only may the New Star be affirmed <lb/>to have been in the Firmament, when from the collating of the <lb/>Ob&longs;ervations made in divers places, the &longs;aid angle is, by calcula­ <lb/>tion, gathered to be in&longs;en&longs;ible, and the lines, as it were, parallels. <lb/></s><s>But if the angle be of a con&longs;iderable quantity, the New Star mu&longs;t <lb/>of nece&longs;&longs;ity be lower than tho&longs;e fixed; and al&longs;o than the Moon, in <lb/>ca&longs;e the angle A B E &longs;hould be greater than that which would be <lb/>made in the Moons centre.</s></p><p type="main"><s>SIMP. </s><s>Then the remotene&longs;&longs;e of the Moon is not &longs;o great, that <lb/>a like angle &longs;hould be ^{*}in&longs;en&longs;ible in her? <lb/><arrow.to.target n="marg511"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg511"></margin.target>* Imperceptible.</s></p><p type="main"><s>SALV. </s><s>No Sir; nay it is &longs;en&longs;ible, not onely in the Moon, but <lb/>in the Sun al&longs;o.</s></p><p type="main"><s>SIMP. </s><s>But if this be &longs;o, it's po&longs;&longs;ible that the &longs;aid angle may <lb/>be ob&longs;erved in the New Star, without nece&longs;&longs;itating it to be inferi­ <lb/>our to the Sun, a&longs;well as to the Moon.</s></p><p type="main"><s>SALV. </s><s>This may very well be, yea, and is in the pre&longs;ent ca&longs;e, <lb/>as you &longs;hall &longs;ee in due place; that is, when I &longs;hall have made plain <lb/>the way, in &longs;uch manner that you al&longs;o, though not very perfect in <lb/><emph type="italics"/>A&longs;tronomical<emph.end type="italics"/> calculations, may clearly &longs;ee, and, as it were, with <lb/>your hands feel how that this Authour had it more in his eye to <lb/>write in complacency of the <emph type="italics"/>Peripateticks,<emph.end type="italics"/> by palliating and di&longs;­ <lb/>&longs;embling &longs;undry things, than to e&longs;tabli&longs;h the truth, by producing <lb/>them with naked &longs;incerity: therefore let us proceed forwards. </s><s>By <lb/>the things hitherto &longs;poken, I &longs;uppo&longs;e that you comprehend very <lb/>well how that the di&longs;tance of the new Star can never be <lb/>made &longs;o immen&longs;e, that the angle &longs;o often named &longs;hall wholly di&longs;­ <lb/>appear, and that the two rayes of the Ob&longs;ervators at the places <lb/>A and E, &longs;hall become altogether parallels: and you may con&longs;e­ <lb/>quently comprehend to the full, that if the calculations &longs;hould <lb/>collect from the ob&longs;ervations, that that angle was totally null, or <lb/>that the lines were truly parallels, we &longs;hould be certain that the <lb/>ob&longs;ervations were at lea&longs;t in &longs;ome &longs;mall particular erroneous: <lb/>But, if the calculations &longs;hould give us the &longs;aid lines to be &longs;epara­ <lb/>ted not only to equidi&longs;tance, that is, &longs;o as to be parallel, but to <lb/>have pa&longs;t beyond that terme, and to be dilated more above than <lb/>below, then mu&longs;t it be re&longs;olutely concluded, that the ob&longs;ervations <lb/>were made with le&longs;&longs;e accuratene&longs;&longs;e, and in a word, to be errone­ <lb/>ous; as leading us to a manife&longs;t impo&longs;&longs;ibility. </s><s>In the next place, <lb/>you mu&longs;t believe me, and &longs;uppo&longs;e it for true, that two right lines <pb xlink:href="040/01/281.jpg" pagenum="261"/>which depart from two points marked upon another right line, are <lb/>then wider above than below, when the angles included between <lb/>them upon that right line are greater than two right angles; and <lb/>if the&longs;e angles &longs;hould be equal to two right angles, the lines would <lb/>be parallels; but if they were le&longs;s than two right angles, the lines <lb/>would be concurrent, and being continued out would undoubted­ <lb/>ly inter&longs;ect the triangle.</s></p><p type="main"><s>SIMP. </s><s>Without taking it upon tru&longs;t from you, I know the <lb/>&longs;ame; and am not &longs;o very naked of <emph type="italics"/>Geometry,<emph.end type="italics"/> as not to know a <lb/>Propo&longs;ition, which I have had occa&longs;ion of reading very often in <lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that is, that the three angles of all triangles are equall to <lb/>two right angles: &longs;o that if I take in my Figure the triangle ABE, <lb/>it being &longs;uppo&longs;ed that the line E A is right; I very well conceive, <lb/>that its three angles A, E, B, are equal to two right angles; and <lb/>that con&longs;equently the two angles E and A are le&longs;&longs;e than two right <lb/>angles, &longs;o much as is the angle B. </s><s>Whereupon widening the lines <lb/>A B and E B (&longs;till keeping them from moving out of the points A <lb/>and E) untill that the angle conteined by them towards the parts <lb/>B, di&longs;appear, the two angles beneath &longs;hall be equal to two right <lb/>angles, and tho&longs;e lines &longs;hall be reduced to parallels: and if one <lb/>&longs;hould proceed to enlarge them yet more, the angles at the points <lb/>E and A would become greater than two right angles.</s></p><p type="main"><s>SALV. </s><s>You are an <emph type="italics"/>Archimedes,<emph.end type="italics"/> and have freed me from the <lb/>expence of more words in declaring to you, that when&longs;oever the <lb/>calculations make the two angles A and E to be greater than two <lb/>right angles, the ob&longs;ervations without more adoe will prove erro­ <lb/>neous. </s><s>This is that which I had a de&longs;ire that you &longs;hould perfect­ <lb/>ly under&longs;tand, and which I doubted that I was not able &longs;o to make <lb/>out, as that a meer <emph type="italics"/>Peripatetick<emph.end type="italics"/> Philo&longs;opher might attain to the <lb/>certain knowledg thereof. </s><s>Now let us go on to what remains. <lb/></s><s>And re-a&longs;&longs;uming that which even now you granted me, namely, <lb/>that the new &longs;tar could not po&longs;&longs;ibly be in many places, but in one <lb/>alone, when ever the &longs;upputations made upon the ob&longs;ervations of <lb/>the&longs;e A&longs;tronomers do not a&longs;&longs;ign it the &longs;ame place, its nece&longs;&longs;ary <lb/>that it be an errour in the ob&longs;ervations, that is, either in taking the <lb/>altitudes of the pole, or in taking the elevations of the &longs;tar, or in <lb/>the one or other working. </s><s>Now for that in the many workings <lb/>made with the combinations two by two, there are very few of <lb/>the ob&longs;ervations that do agree to place the &longs;tar in the &longs;ame &longs;itua­ <lb/>tion; therefore the&longs;e few onely may happily be the non-errone­ <lb/>ous, but the others are all ab&longs;olutely fal&longs;e.</s></p><p type="main"><s>SAGR. </s><s>It will be nece&longs;&longs;ary then to give more credit to the&longs;e <lb/>few alone, than to all the re&longs;t together, and becau&longs;e you &longs;ay, <lb/>that the&longs;e which accord are very few, and I among&longs;t the&longs;e 12, <lb/>do find two that &longs;o accord, which both make the di&longs;tance of the <pb xlink:href="040/01/282.jpg" pagenum="262"/>&longs;tar from the centre of the Earth 4 &longs;emidiameters, which are the&longs;e, <lb/>the fifth and &longs;ixth, therefore it is more probable that the new &longs;tar <lb/>was elementary, than cele&longs;tial.</s></p><p type="main"><s>SALV. </s><s>You mi&longs;take the point; for if you note well it was not <lb/>written, that the di&longs;tance was exactly 4 &longs;emidiameters, but about <lb/>4 &longs;emidiameters; and yet you &longs;hall &longs;ee that tho&longs;e two di&longs;tances <lb/>differed from each other many hundreds of miles. </s><s>Here they are; <lb/>you &longs;ee that this fifth, which is 13389 <emph type="italics"/>Italian<emph.end type="italics"/> miles, exceeds the <lb/>&longs;ixth, which is 13100 miles, by almo&longs;t 300 miles.</s></p><p type="main"><s>SAGR. </s><s>Which then are tho&longs;e few that agree in placing the &longs;tar <lb/>in the &longs;ame &longs;ituation?</s></p><p type="main"><s>SALV. </s><s>They are, to the di&longs;grace of this Author five workings, <lb/>which all place it in the firmament, as you &longs;hall &longs;ee in this note, <lb/>where I have &longs;et down many other combinations. </s><s>But I will grant <lb/>the Author more than peradventure he would demand of me, which <lb/>is in &longs;um, that in each combination of the ob&longs;ervations there is <lb/>&longs;ome error; which I believe to be ab&longs;olutely nece&longs;&longs;ary; for the <lb/>ob&longs;ervations being four in number that &longs;erve for one working, <lb/>that is, two different altitudes of the Pole, and two different eleva­ <lb/>tions of the &longs;tar, made by different ob&longs;ervers, in different pla­ <lb/>ces, with different in&longs;truments, who ever hath any &longs;mall know­</s></p><p type="main"><s><arrow.to.target n="marg512"></arrow.to.target> <lb/>ledg of this art, will &longs;ay, that among&longs;t all the four, it is impo&longs;&longs;ible <lb/>but there will be &longs;ome error; and e&longs;pecially &longs;ince we &longs;ee that in <lb/>taking but one onely altitude of the Pole, with the &longs;ame in&longs;tru­ <lb/>ment, in the &longs;ame place, by the &longs;ame ob&longs;erver, that hath re­ <lb/>peated the ob&longs;ervation a thou&longs;and times, there will &longs;till be a titu­ <lb/>bation of one, or &longs;ometimes of many minutes, as in this &longs;ame <lb/>book you may &longs;ee in &longs;everal places. </s><s>The&longs;e things pre&longs;uppo&longs;ed, <lb/>I ask you <emph type="italics"/>Simplicius<emph.end type="italics"/> whether you believe that this Authour held <lb/>the&longs;e thirteen ob&longs;ervators for wi&longs;e, under&longs;tanding and expert men <lb/>in u&longs;ing tho&longs;e in&longs;truments, or el&longs;e for inexpert, and bunglers?</s></p><p type="margin"><s><margin.target id="marg512"></margin.target><emph type="italics"/>A&longs;tronomical In­ <lb/>struments are very <lb/>&longs;ubject to errour.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>It mu&longs;t needs be that he e&longs;teemed them very acute and <lb/>intelligent; for if he had thought them unskilful in the bu&longs;ine&longs;&longs;e, <lb/>he might have omitted his &longs;ixth book as inconclu&longs;ive, as being <lb/>founded upon &longs;uppo&longs;itions very erroneous; and might take us for <lb/>exce&longs;&longs;ively &longs;imple, if he &longs;hould think he could with their inex­ <lb/>pertne&longs;&longs;e per&longs;wade us to believe a fal&longs;e po&longs;ition of his for truth.</s></p><p type="main"><s>SALV. </s><s>Therefore the&longs;e ob&longs;ervators being &longs;uch, and that yet <lb/>notwith&longs;tanding they did erre, and &longs;o con&longs;equently needed cor­ <lb/>rection, that &longs;o one might from their ob&longs;ervations infer the <lb/>be&longs;t hints that may be; it is convenient that we apply unto them <lb/>the lea&longs;t and neere&longs;t emendations and corrections that may be; <lb/>&longs;o that they do but &longs;uffice to reduce the ob&longs;ervations from impo&longs;­ <lb/>&longs;ibility to po&longs;&longs;ibility; &longs;o as <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> if one may but correct a mani­ <lb/>fe&longs;t errour, and an apparent impo&longs;&longs;ibility of one of their ob&longs;er­ <pb xlink:href="040/01/283.jpg" pagenum="263"/>vations by the addition or &longs;ub&longs;traction of two or three minutes, and <lb/>with that amendment to reduce it to po&longs;&longs;ibility, a man ought <lb/>not to e&longs;&longs;ay to adju&longs;t it by the addition or &longs;ub&longs;traction of fifteen, <lb/>twenty, or fifty.</s></p><p type="main"><s>SIMP. </s><s>I think the Authour would not deny this: for granting <lb/>that they are expert and judicious men, it ought to be thought that <lb/>they did rather erre little than much.</s></p><p type="main"><s>SALV. </s><s>Ob&longs;erve again; The places where the new Star is pla­ <lb/>ced, are &longs;ome of them manife&longs;tly impo&longs;&longs;ible, and others po&longs;&longs;ible. <lb/></s><s>Ab&longs;olutely impo&longs;&longs;ible it is, that it &longs;hould be an infinite &longs;pace &longs;upe­ <lb/>riour to the fixed Stars, for there is no &longs;uch place in the world; <lb/>and if there were, the Star there &longs;cituate would have been imper­ <lb/>ceptible to us: it is al&longs;o impo&longs;&longs;ible that it &longs;hould go creeping along <lb/>the &longs;uperficies of the Earth; and much le&longs;&longs;e that it &longs;hould be <lb/>within the &longs;aid Terre&longs;trial Globe. </s><s>Places po&longs;&longs;ible are the&longs;e that <lb/>be in controver&longs;ie, it not interferring with our under&longs;tanding, that <lb/>a vi&longs;ible object in the likene&longs;&longs;e of a Star might be a&longs;well above the <lb/>Moon, as below it. </s><s>Now whil&longs;t one goeth about to compute by <lb/>the way of Ob&longs;ervations and Calculations made with the utmo&longs;t <lb/>certainty that humane diligence can attain unto what its place was, <lb/>it is found that the greate&longs;t part of tho&longs;e Calculations make it <lb/>more than infinitely &longs;uperiour to the Firmament, others make it <lb/>very neer to the &longs;urface of the Earth, and &longs;ome al&longs;o under the <lb/>&longs;ame; and of the re&longs;t, which place it in &longs;ituations not impo&longs;&longs;ible, <lb/>none of them agree with each other; in&longs;omuch that it mu&longs;t be <lb/>confe&longs;&longs;ed, that all tho&longs;e ob&longs;ervations are nece&longs;&longs;arily fal&longs;e; &longs;o that <lb/>if we would neverthele&longs;s collect &longs;ome fruit from &longs;o many laborious <lb/>calculations, we mu&longs;t have recour&longs;e to the corrections, amending <lb/>all the ob&longs;ervations.</s></p><p type="main"><s>SIMP. </s><s>But the Authour will &longs;ay, that of the ob&longs;ervations that <lb/>a&longs;&longs;ign to the Star impo&longs;&longs;ible places, there ought no account to be <lb/>made, as being extreamly erroneous and fal&longs;e; and tho&longs;e onely <lb/>ought to be accepted, that con&longs;titute it in places not impo&longs;&longs;ible: <lb/>and among&longs;t the&longs;e a man ought to &longs;eek, by help of the mo&longs;t pro­ <lb/>bable, and mo&longs;t numerous concurrences, not if the particular and <lb/>exact &longs;ituation, that is, its true di&longs;tance from the centre of the <lb/>Earth, at lea&longs;t, whether it was among&longs;t the Elements, or el&longs;e a­ <lb/>mong&longs;t the Cœle&longs;tial bodies.</s></p><p type="main"><s>SALV. </s><s>The di&longs;cour&longs;e which you now make, is the &longs;elf &longs;ame <lb/>that the Author made, in favour of his cau&longs;e, but with too unrea­ <lb/>&longs;onable a di&longs;advantage to his adver&longs;aries; and this is that princi­ <lb/>pal point that hath made me exce&longs;&longs;ively to wonder at the too great <lb/>confidence that he expre&longs;&longs;ed to have, no le&longs;s of his own authority, <lb/>than of the blindne&longs;s and inadvertency of the A&longs;tronomers; in <lb/>favour of whom I will &longs;peak, and you &longs;hall an&longs;wer for the Author. <pb xlink:href="040/01/284.jpg" pagenum="264"/>And fir&longs;t, I ask you, whether the A&longs;tronomers, in ob&longs;erving with <lb/>their In&longs;truments, and &longs;eeking <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> how great the elevation of a <lb/>Star is above the Horizon, may deviate from the truth, a&longs;well in <lb/>making it too great, as too little; that is, may erroneou&longs;ly com­ <lb/>pute, that it is &longs;ometime higher than the truth, and &longs;ometimes low­ <lb/>er; or el&longs;e whether the errour mu&longs;t needs be alwayes of one <lb/>kinde, to wit, that erring they alwayes make it too much, and ne­ <lb/>ver too little, or alwayes too little, and never too much?</s></p><p type="main"><s>SIMP. </s><s>I doubt not, but that it is as ea&longs;ie to commit an errour <lb/>the one way, as the other.</s></p><p type="main"><s>SALV. </s><s>I believe the Author would an&longs;wer the &longs;ame. </s><s>Now of <lb/>the&longs;e two kinds of errours, which are contraries, and into which the <lb/>ob&longs;ervators of the new &longs;tar may equally have fallen, applied to <lb/>calculations, one &longs;ort will make the &longs;tar higher, and the other lower <lb/>than really it is. </s><s>And becau&longs;e we have already agreed, that all <lb/>the ob&longs;ervations are fal&longs;e; upon what ground would this Au­ <lb/>thor have us to accept tho&longs;e for mo&longs;t congruous with the truth, <lb/>that &longs;hew the &longs;tar to have been near at hand, than the others that <lb/>&longs;hew it exce&longs;&longs;ively remote?</s></p><p type="main"><s>SIMP. </s><s>By what I have, as yet, collected of the Authors mind, <lb/>I &longs;ee not that he doth refu&longs;e tho&longs;e ob&longs;ervations, and indagations <lb/>that might make the &longs;tar more remote than the Moon, and al&longs;o <lb/>than the Sun, but only tho&longs;e that make it remote (as you your &longs;elf <lb/>have &longs;aid) more than an infinite di&longs;tance; the which di&longs;tance, be­ <lb/>cau&longs;e you al&longs;o do refu&longs;e it as impo&longs;&longs;ible, he al&longs;o pa&longs;&longs;eth over, as <lb/>being convicted of infinite fal&longs;hood; as al&longs;o tho&longs;e ob&longs;ervations <lb/>are of impo&longs;&longs;ibility. </s><s>Methinks, therefore, that if you would con­ <lb/>vince the Author, you ought to produce &longs;upputations, more exact, <lb/>or more in number, or of more diligent ob&longs;ervers, which con&longs;titute <lb/>the &longs;tar in &longs;uch and &longs;uch a di&longs;tance above the Moon, or above the <lb/>Sun, and to be brief, in a place po&longs;&longs;ible for it to be in, like as he <lb/>produceth the&longs;e twelve, which all place the &longs;tar beneath the Moon <lb/>in places that have a being in the world, and where it is po&longs;&longs;ible for <lb/>it to be.</s></p><p type="main"><s>SALV. </s><s>But <emph type="italics"/>Simplicius<emph.end type="italics"/> yours and the Authors Equivocation <lb/>lyeth in this, yours in one re&longs;pect, and the Authors in another; I <lb/>di&longs;cover by your &longs;peech that you have formed a conceit to your <lb/>&longs;elf, that the exorbitancies that are commited in the e&longs;tabli&longs;hing <lb/>the di&longs;tance of the Star do encrea&longs;e &longs;ucce&longs;&longs;ively, according to the <lb/>proportion of the errors that are made by the In&longs;trument, in tak­ <lb/>ing the ob&longs;ervations, and that by conver&longs;ion, from the greatne&longs;s <lb/>of the exorbitancies, may be argued the greatne&longs;&longs;e of the error; <lb/>and that thereforefore hearing it to be infered from &longs;uch an ob&longs;er­ <lb/>vation, that the di&longs;tance of the &longs;tar is infinite, it is nece&longs;&longs;ary, that <lb/>the errour in ob&longs;erving was infinite, and therefore not to be amend­ <pb xlink:href="040/01/285.jpg" pagenum="265"/>ed, and as &longs;uch to be refu&longs;ed; but the bu&longs;ine&longs;&longs;e doth not &longs;ucceed <lb/>in that manner, my <emph type="italics"/>Simplicius,<emph.end type="italics"/> and I excu&longs;e you for not having <lb/>comprehended the matter as it is, in regard of your &longs;mall experi­ <lb/>ence in &longs;uch affairs; but yet cannot I under that cloak palliate the <lb/>error of the Author, who di&longs;&longs;embling the knowledge of this which <lb/>he did per&longs;wade him&longs;elf that we in good earne&longs;t did not under­ <lb/>&longs;tand, hath hoped to make u&longs;e of our ignorance, to gain the bet­ <lb/>ter credit to his Doctrine, among the multitude of illiterate men. <lb/></s><s>Therefore for an adverti&longs;ement to tho&longs;e who are more credulous <lb/>then intelligent, and to recover you from error, know that its po&longs;­ <lb/>&longs;ible (and that for the mo&longs;t part it will come to pa&longs;&longs;e) that an <lb/>ob&longs;ervation, that giveth you the &longs;tar <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> at the di&longs;tance of <emph type="italics"/>Sa­ <lb/>turn,<emph.end type="italics"/> by the adition or &longs;ub&longs;traction of but one &longs;ole minute from <lb/>the elevation taken with the in&longs;trument, &longs;hall make it to become <lb/>infinitely di&longs;tant; and therefore of po&longs;&longs;ible, impo&longs;&longs;ible, and by <lb/>conver&longs;ion, tho&longs;e calculations which being grounded upon tho&longs;e <lb/>ob&longs;ervations, make the &longs;tar infinitely remote, may po&longs;&longs;ibly often­ <lb/>times with the addition or &longs;ubduction of one &longs;ole minute, reduce it <lb/>to a po&longs;&longs;ible &longs;cituation: and this which I &longs;ay of a minute, may al­ <lb/>&longs;o happen in the correction of half a minute, a &longs;ixth part, and le&longs;s. <lb/></s><s>Now fix it well in your mind, that in the highe&longs;t di&longs;tances, that is <lb/><emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> the height of <emph type="italics"/>Saturn,<emph.end type="italics"/> or that of the fixed Stars, very &longs;mall <lb/>errors made by the Ob&longs;ervator, with the in&longs;trument, render the <lb/>&longs;cituation determinate and po&longs;&longs;ible, infinite & impo&longs;&longs;ible. </s><s>This doth <lb/>not &longs;o evene in the &longs;ublunary di&longs;tances, and near the earth, where <lb/>it may happen that the ob&longs;ervation by which the Star is collected to <lb/>be remote <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> 4. Semidiameters terre&longs;trial, may encrea&longs;e or dimi­ <lb/>ni&longs;h, not onely one minute but ten, and an hundred, and many <lb/>more, without being rendred by the calculation either infinitely <lb/>remote, or &longs;o much as &longs;uperior to the Moon. </s><s>You may hence <lb/>comprehend that the greatne&longs;&longs;e of the error (to &longs;o &longs;peak) in&longs;tru­ <lb/>mental, are not to be valued by the event of the calculation, but <lb/>by the quantity it &longs;elf of degrees and minutes numbred upon the <lb/>in&longs;trument, and the&longs;e ob&longs;ervations are to be called more ju&longs;t or <lb/>le&longs;s erroneous, which with the addition or &longs;ub&longs;traction of fewer <lb/>minutes, re&longs;tore the &longs;tar to a po&longs;&longs;ible &longs;ituation; and among&longs;t the <lb/>po&longs;&longs;ible places, the true one may be believed to have been that, a­ <lb/>bout which a greater number of di&longs;tances concurre upon calcula­ <lb/>ting the more exact ob&longs;ervations.</s></p><p type="main"><s>SIMP. </s><s>I do not very well apprehend this which you &longs;ay: nor <lb/>can I of my &longs;elf conceive how it can be, that in greater di&longs;tances, <lb/>greater exorbitancies can ari&longs;e from the errour of one minute only, <lb/>than in the &longs;maller from ten or an hundred; and therefore would <lb/>gladly under&longs;tand the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>You &longs;hall &longs;ee it, if not Theorically, yet at lea&longs;t Practi­ <pb xlink:href="040/01/286.jpg" pagenum="266"/>cally, by this &longs;hort a&longs;&longs;umption, that I have made of all the combi­ <lb/>nations, and of part of the workings pretermitted by the Author, <lb/>which I have calculated upon this &longs;ame paper.</s></p><p type="main"><s>SAGR. </s><s>You mu&longs;t then from ye&longs;terday, till now, which yet is <lb/>not above eighteen hours, have done nothing but compute, with­ <lb/>out taking either food or &longs;leep.</s></p><p type="main"><s>SALV. </s><s>I have refre&longs;hed my &longs;elf both tho&longs;e wayes; but truth is, <lb/>make the&longs;e &longs;upputations with great brevity; and, if I may &longs;peak <lb/>the truth, I have much admired, that this Author goeth &longs;o farre a­ <lb/>bout, and introduceth &longs;o many computations no wi&longs;e nece&longs;sary to <lb/>the que&longs;tion in di&longs;pute. </s><s>And for a full knowledge of this, and al­ <lb/>&longs;o to the end it may &longs;oon be &longs;een, how that from the ob&longs;ervations <lb/>of the A&longs;tronomers, whereof this Author makes u&longs;e, it is more pro­ <lb/>bably gathered, that the new &longs;tar might have been above the <lb/>Moon, and al&longs;o above all the Planets, yea among&longs;t the fixed &longs;tars, <lb/>and yet higher &longs;till than they, I have tran&longs;cribed upon this paper <lb/>all the ob&longs;ervations &longs;et down by the &longs;aid Authour, which were <lb/>made by thirteen A&longs;tronomers, wherein are noted the Polar alti­ <lb/>tude, and the altitudes of the &longs;tar in the meridian, a&longs;well the <lb/>le&longs;&longs;er under the Pole, as the greater and higher, and they are <lb/>the&longs;e. <lb/><arrow.to.target n="table2"></arrow.to.target> <lb/><arrow.to.target n="table3"></arrow.to.target> <pb xlink:href="040/01/287.jpg" pagenum="267"/><arrow.to.target n="table4"></arrow.to.target> <lb/><arrow.to.target n="table5"></arrow.to.target> <lb/><arrow.to.target n="table6"></arrow.to.target> <lb/><arrow.to.target n="table7"></arrow.to.target></s></p> <pb xlink:href="040/01/288.jpg" pagenum="268"/><table><table.target id="table2"></table.target><row><cell></cell><cell><emph type="italics"/>Tycho.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Altitude of the Pole</cell><cell>55</cell><cell>58</cell><cell></cell></row><row><cell>Altitude of the Star</cell><cell>84</cell><cell>00</cell><cell>the greate&longs;t.</cell></row><row><cell></cell><cell>27</cell><cell>57</cell><cell>the lea&longs;t.</cell></row><row><cell>And the&longs;e are, according to the fir&longs;t paper: but accor-ding to the &longs;econd, the greate&longs;t is ------------</cell><cell>27</cell><cell>45</cell><cell></cell></row></table><table><table.target id="table3"></table.target><row><cell></cell><cell><emph type="italics"/>Hainzelius.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell></row><row><cell>Altitude of the Pole</cell><cell>48</cell><cell>22</cell><cell></cell></row><row><cell>Altitude of the Star</cell><cell>76</cell><cell>34</cell><cell></cell></row><row><cell></cell><cell>76</cell><cell>33</cell><cell>45</cell></row><row><cell></cell><cell>76</cell><cell>35</cell><cell></cell></row><row><cell></cell><cell>20</cell><cell>09</cell><cell>40</cell></row><row><cell></cell><cell>20</cell><cell>09</cell><cell>30</cell></row><row><cell></cell><cell>20</cell><cell>09</cell><cell>20</cell></row></table><table><table.target id="table4"></table.target><row><cell><emph type="italics"/>Peucerus<emph.end type="italics"/> and <emph type="italics"/>Sculerus.<emph.end type="italics"/></cell><cell></cell><cell></cell><cell><emph type="italics"/>Landgravius.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of the pole</cell><cell>51</cell><cell>54</cell><cell>Altitude of the pole</cell><cell>51</cell><cell>18</cell></row><row><cell>Altitude of the Star</cell><cell>79</cell><cell>56</cell><cell>Altitude of the Star</cell><cell>79</cell><cell>30</cell></row><row><cell></cell><cell>23</cell><cell>33</cell><cell></cell><cell></cell><cell></cell></row></table><table><table.target id="table5"></table.target><row><cell></cell><cell><emph type="italics"/>Camerarius.<emph.end type="italics"/></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of the pole</cell><cell>52</cell><cell>24</cell></row><row><cell>Altitude of the Star</cell><cell>80</cell><cell>30</cell></row><row><cell></cell><cell>80</cell><cell>27</cell></row><row><cell></cell><cell>80</cell><cell>26</cell></row><row><cell></cell><cell>24</cell><cell>28</cell></row><row><cell></cell><cell>24</cell><cell>20</cell></row><row><cell></cell><cell>24</cell><cell>17</cell></row></table><table><table.target id="table6"></table.target><row><cell><emph type="italics"/>Hagecius<emph.end type="italics"/></cell><cell></cell><cell></cell><cell><emph type="italics"/>Maurolycus.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of the pole</cell><cell>48</cell><cell>22</cell><cell>Altitude of the pole</cell><cell>38</cell><cell>30</cell></row><row><cell>Altitude of the Star</cell><cell>20</cell><cell>15</cell><cell>Altitude of the Star</cell><cell>62</cell><cell>00</cell></row><row><cell><emph type="italics"/>Munocius.<emph.end type="italics"/></cell><cell></cell><cell></cell><cell><emph type="italics"/>Vr&longs;inus.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of the pole</cell><cell>39</cell><cell>30</cell><cell>Altitude of the pole</cell><cell>49</cell><cell>24</cell></row><row><cell>Altitude of the &longs;tar</cell><cell>67</cell><cell>30</cell><cell>Altitude of the &longs;tar</cell><cell>79</cell><cell>00</cell></row><row><cell></cell><cell>11</cell><cell>30</cell><cell></cell><cell>22</cell><cell>00</cell></row><row><cell><emph type="italics"/>Reinholdus.<emph.end type="italics"/></cell><cell></cell><cell></cell><cell><emph type="italics"/>Buchius.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of the pole</cell><cell>51</cell><cell>18</cell><cell>Altitude of the pole</cell><cell>51</cell><cell>10</cell></row><row><cell>Altitude of the &longs;tar</cell><cell>79</cell><cell>30</cell><cell>Altitude of the &longs;tar</cell><cell>79</cell><cell>20</cell></row><row><cell></cell><cell>23</cell><cell>02</cell><cell></cell><cell>22</cell><cell>40</cell></row></table><table><table.target id="table7"></table.target><row><cell><emph type="italics"/>Gemma.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of the pole</cell><cell>50</cell><cell>50</cell></row><row><cell>Altitude of the &longs;tar</cell><cell>79</cell><cell>45</cell></row></table><p type="main"><s>Now to &longs;ee my whole proceeding, we may begin from the&longs;e <lb/>calculations, which are four, omitted by the Author, perhaps be­ <lb/>cau&longs;e they make again&longs;t him, in regard they place the &longs;tar above <lb/>the moon by many &longs;emidiameters of the Earth. </s><s>The fir&longs;t of <lb/>which is this, computed upon the ob&longs;ervations of the Landgrave of <lb/><emph type="italics"/>Ha&longs;&longs;ia,<emph.end type="italics"/> and <emph type="italics"/>Tycho<emph.end type="italics"/>; which are, even by the Authors conce&longs;&longs;ion, <lb/>two of the mo&longs;t exact ob&longs;ervers: and in this fir&longs;t, I will declare <lb/>the order that I hold in the working; which &longs;hall &longs;erve for all the <lb/>re&longs;t, in that they are all made by the &longs;ame rule, not varying in any <lb/>thing, &longs;ave in the quantity of the given &longs;ummes, that is, in the <lb/>number of the degrees of the Poles altitude, and of the new Stars <lb/>elevation above the Horizon, the di&longs;tance of which from the cen­ <lb/>tre of the Earth, in proportion to the &longs;emidiameter of the terre­ <lb/>&longs;trial Globe is &longs;ought, touching which it nothing imports in this <lb/>ca&longs;e, to know how many miles that &longs;emidiameter conteineth; <lb/>whereupon the re&longs;olving that, and the di&longs;tance of places where <lb/>the ob&longs;ervations were made, as this Author doth, is but time and <lb/>labour lo&longs;t; nor do I know why he hath made the &longs;ame, and e&longs;pe­ <lb/>cially why at the la&longs;t he goeth about to reduce the miles found, in­ <lb/>to &longs;emidiameters of the Terre&longs;trial Globe.</s></p><p type="main"><s>SIMP. </s><s>Perhaps he doth this to finde with &longs;uch &longs;mall mea&longs;ures, <lb/>and with their fractions the di&longs;tance of the Star terminated to three <lb/>or four inches; for we that do not under&longs;tand your rules of Arith­ <lb/>metick, are &longs;tupified in hearing your conclu&longs;ions; as for in&longs;tance, <lb/>whil&longs;t we read; Therefore the new Star or Comet was di&longs;tant <lb/>from the Earths centre three hundred &longs;eventy and three thou&longs;and <lb/>eight hundred and &longs;even miles; and moreover, two hundred and <lb/>eleven, four chou&longs;and ninety &longs;evenths 373807 211/4097, and upon the&longs;e <lb/>preci&longs;e punctualities, wherein you take notice of &longs;uch &longs;mall mat­ <lb/>ters, we do conceive it to be impo&longs;&longs;ible, that you, who in our cal­ <lb/>culations keep an account of an inch, can at the clo&longs;e deceive us &longs;o <lb/>much as an hundred miles.</s></p><p type="main"><s>SALV. </s><s>This your rea&longs;on and excu&longs;e would pa&longs;&longs;e for currant, <lb/>if in a di&longs;tance of thou&longs;ands of miles, a yard over or under were <lb/>of any great moment, and if the &longs;uppo&longs;itions that we take for <lb/>true, were &longs;o certain, as that they could a&longs;&longs;ure us of producing an <lb/>indubitable truth in the conclu&longs;ion; but here you &longs;ee in the twelve <lb/>workings of the Author, the di&longs;tances of the Star, which from <lb/>them one may conclude to have been different from each other, <lb/>(and therefore wide of the truth) for many hundreds and thou­ <lb/>&longs;ands of miles: now whil&longs;t that I am more than certain, that that <lb/>which I &longs;eek mu&longs;t needs differ from the truth by hundreds of miles, <lb/>to what purpp&longs;e is it to be &longs;o curious in our calculations, for fear <lb/>of mi&longs;&longs;ing the quantity of an inch? </s><s>But let us proceed, at la&longs;t, <lb/>to the working, which I re&longs;olve in this manner. <emph type="italics"/>Tycho,<emph.end type="italics"/> as may be <pb xlink:href="040/01/289.jpg" pagenum="269"/>&longs;een in that &longs;ame note ob&longs;erved the &longs;tar in the polar altitude of 55 <lb/>degrees and 58 <emph type="italics"/>mi. </s><s>pri.<emph.end type="italics"/> And the polar altitude of the <emph type="italics"/>Landgrave<emph.end type="italics"/> <lb/>was 51 degrees and 18 <emph type="italics"/>mi. </s><s>pri.<emph.end type="italics"/> The altitude of the &longs;tar in the Me­ <lb/>ridian taken by <emph type="italics"/>Tycho<emph.end type="italics"/> was 27 degrees 45 <emph type="italics"/>mi. </s><s>pri.<emph.end type="italics"/> The <emph type="italics"/>Land­ <lb/>grave<emph.end type="italics"/> found its altitude 23 degrees 3 <emph type="italics"/>mi. </s><s>pri.<emph.end type="italics"/> The which altitudes <lb/>are the&longs;e noted here, as you &longs;ee. <lb/><arrow.to.target n="table8"></arrow.to.target></s></p><table><table.target id="table8"></table.target><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Tycho<emph.end type="italics"/> Pole</cell><cell>55</cell><cell>58</cell><cell>* 27</cell><cell>45</cell></row><row><cell><emph type="italics"/>Landgr.<emph.end type="italics"/> Pole</cell><cell>51</cell><cell>18</cell><cell>* 23</cell><cell>3</cell></row></table><p type="main"><s>This done, &longs;ub&longs;tract the le&longs;&longs;e from the greater, and there remains <lb/>the&longs;e differences here underneath. <lb/><arrow.to.target n="table9"></arrow.to.target></s></p><table><table.target id="table9"></table.target><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell></cell><cell>4</cell><cell>40</cell></row><row><cell></cell><cell>4</cell><cell>42</cell></row><row><cell>Parall.</cell><cell></cell><cell>2</cell></row></table><p type="main"><s>Where the difference of the poles altitudes 4 <emph type="italics"/>gr. </s><s>4 mi. </s><s>pr.<emph.end type="italics"/> <lb/>is le&longs;&longs;e than the difference of the altitudes of the Star 4 <emph type="italics"/>gr. </s><s>42 mi. <lb/></s><s>pr.<emph.end type="italics"/> and therefore we have the difference of parallaxes, 0 <emph type="italics"/>gr. </s><s>2 mi. <lb/></s><s>pri.<emph.end type="italics"/> The&longs;e things being found, take the Authours own figure <lb/>[<emph type="italics"/>Fig. </s><s>2.<emph.end type="italics"/>] in which the point B is the &longs;tation of the <emph type="italics"/>Landgrave,<emph.end type="italics"/> <lb/>D the &longs;tation of <emph type="italics"/>Tycho,<emph.end type="italics"/> C the place of the &longs;tar, A the centre <lb/>of the Earth, A B E the vertical line of the <emph type="italics"/>Landgrave,<emph.end type="italics"/> A D F <lb/><arrow.to.target n="table10"></arrow.to.target> <lb/><arrow.to.target n="table11"></arrow.to.target> <lb/><arrow.to.target n="table12"></arrow.to.target> <lb/>of <emph type="italics"/>Tycho,<emph.end type="italics"/> and the angle B C D the difference of Parallaxes. </s><s>And <pb xlink:href="040/01/290.jpg" pagenum="270"/>becau&longs;e the angle B A D, conteined between the vertical lines, is <lb/>equal to the difference of the Polar altitudes, it &longs;hall be 4<emph type="italics"/>gr. </s><s>40m.<emph.end type="italics"/> <lb/>which I note here apart; and I finde the chord of it by the Table <lb/>of Arches and Chords, and &longs;et it down neer unto it, which is 8142 <lb/>parts, of which the &longs;emidiameter A B is 100000. Next, I finde <lb/>the angle B D C with ea&longs;e, for the half of the angle B A D, which <lb/>is 2 <emph type="italics"/>gr. </s><s>20 m.<emph.end type="italics"/> added to a right angle, giveth the angle B D F 92 <emph type="italics"/>gr.<emph.end type="italics"/> <lb/>20 <emph type="italics"/>m.<emph.end type="italics"/> to which adding the angle C D F, which is the di&longs;tance from <lb/>the vertical point of the greate&longs;t altitude of the Star, which here is <lb/>62 <emph type="italics"/>gr. </s><s>15 m.<emph.end type="italics"/> it giveth us the quantity of the angle B D C, <lb/>154 <emph type="italics"/>grad. </s><s>45 min.<emph.end type="italics"/> the which I &longs;et down together with its Sine, <lb/>taken out of the Table, which is 42657, and under this I note <lb/>the angle of the Parallax B C D 0 <emph type="italics"/>gr. </s><s>2 m.<emph.end type="italics"/> with its Sine 58. <lb/>And becau&longs;e in the Triangle B C D, the &longs;ide D B is to the &longs;ide <lb/>B C; as the &longs;ine of the oppo&longs;ite angle B C D, to the &longs;ine of the <lb/>oppo&longs;ite angle B D C: therefore, if the line B D were 58. B C <lb/>would be 42657. And becau&longs;e the Chord D B is 8142. of tho&longs;e <lb/>parts whereof the &longs;emidiameter B A is 100000. and we &longs;eek to <lb/>know how many of tho&longs;e parts is B C; therefore we will &longs;ay, by <lb/>the Golden Rule, if when B D is 58. B G is 42657. in ca&longs;e the <lb/>&longs;aid D B were 8142. how much would B C be? </s><s>I multiply the <lb/>&longs;econd term by the third, and the product is 347313294. which <lb/>ought to be divided by the fir&longs;t, namely, by 58. and the quotient <lb/>&longs;hall be the number of the parts of the line B C, whereof the &longs;e­ <lb/>midiameter A B is 100000. And to know how many &longs;emidiame­ <lb/>ters B A, the &longs;aid line B C doth contein, it will be nece&longs;&longs;ary anew <lb/>to divide the &longs;aid quotient &longs;o found by 100000. and we &longs;hall have <lb/>the number o&longs; &longs;emidiameters conteined in B G. </s><s>Now the num­ <lb/>ber 347313294. divided by 58. giveth 5988160 1/4. as here you <lb/>may &longs;ee. <lb/><arrow.to.target n="table13"></arrow.to.target></s></p><table><table.target id="table10"></table.target><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell>Its chord 8142 of tho&longs;e</cell></row><row><cell>Ang. B A D</cell><cell>4</cell><cell>40</cell><cell>parts, whereof the &longs;emid.</cell></row><row><cell>B D F</cell><cell>92</cell><cell>20</cell><cell>A B is an 100000.</cell></row></table><table><table.target id="table11"></table.target><row><cell>B D C</cell><cell>154</cell><cell>45</cell><cell>Sines</cell><cell>42657</cell></row><row><cell>B C D</cell><cell>0</cell><cell>2</cell><cell></cell><cell>58</cell></row></table><table><table.target id="table12"></table.target><row><cell>58</cell><cell>42657</cell><cell>8142</cell></row><row><cell></cell><cell>8142</cell><cell></cell></row><row><cell></cell><cell>85314</cell><cell></cell></row><row><cell></cell><cell>170628</cell><cell></cell></row><row><cell></cell><cell>42657</cell><cell></cell></row><row><cell></cell><cell>341256</cell><cell></cell></row><row><cell></cell><cell>59</cell><cell></cell></row><row><cell>58</cell><cell>3473</cell><cell>13294</cell></row><row><cell></cell><cell>571</cell><cell></cell></row><row><cell></cell><cell>5</cell><cell></cell></row></table><table><table.target id="table13"></table.target><row><cell></cell><cell>5988160 1/4</cell></row><row><cell>58</cell><cell>347313294</cell></row><row><cell></cell><cell>5717941</cell></row><row><cell></cell><cell>543</cell></row></table><p type="main"><s>And this divided by 100000. the product is 59 88160/100000 <lb/><arrow.to.target n="table14"></arrow.to.target></s></p><table><table.target id="table14"></table.target><row><cell>1 |00000</cell><cell>| 59 |</cell><cell>88160.</cell></row></table><p type="main"><s>But we may much abbreviate the operation, dividing the fir&longs;t <lb/>quotient found, that is, 347313294. by the product of the multi­ <lb/>plication of the two numbers 58. and 100000. that is, <pb xlink:href="040/01/291.jpg" pagenum="271"/><arrow.to.target n="table15"></arrow.to.target></s></p><table><table.target id="table15"></table.target><row><cell></cell><cell>59</cell><cell></cell></row><row><cell>58 00000</cell><cell>3473</cell><cell>13294</cell></row><row><cell></cell><cell>571</cell><cell></cell></row><row><cell></cell><cell>5</cell><cell></cell></row></table><p type="main"><s>And this way al&longs;o there will come forth 59 5113294/5800000</s></p><p type="main"><s>And &longs;o many &longs;emidiameters are contained in the line B C, to <lb/>which one being added for the line A B, we &longs;hall have little le&longs;&longs;e <lb/>than 61. &longs;emidiameters for the two lines A B C; and therefore <lb/>the right di&longs;tance from the centre A, to the Star C, &longs;hall be more <lb/>than 60. &longs;emidiameters, and therefore it is &longs;uperiour to the Moon, <lb/>according to <emph type="italics"/>Ptolomy,<emph.end type="italics"/> more than 27. &longs;emidiameters, and according <lb/>to <emph type="italics"/>Copernicus,<emph.end type="italics"/> more than 8. &longs;uppo&longs;ing that the di&longs;tance of the <lb/>Moon from the centre of the Earth by <emph type="italics"/>Copernicus<emph.end type="italics"/> his account is <lb/>what the Author maketh it, 52 &longs;emidiameters. </s><s>With this &longs;ame <lb/>working, I find by the ob&longs;ervations of <emph type="italics"/>Camerarius,<emph.end type="italics"/> and of <emph type="italics"/>Muno­ <lb/>&longs;ius,<emph.end type="italics"/> that the Star was &longs;ituate in that &longs;ame di&longs;tance, to wit, &longs;ome­ <lb/>what more than 60. &longs;emidiameters. </s><s>The&longs;e are the ob&longs;ervations, <lb/>and the&longs;e following next after them the calculations. <lb/><arrow.to.target n="table16"></arrow.to.target> <lb/><arrow.to.target n="table17"></arrow.to.target></s></p><table><table.target id="table16"></table.target><row><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitude of <emph type="italics"/>Camerar.<emph.end type="italics"/></cell><cell>52</cell><cell>24</cell><cell>Altitude of</cell><cell>24</cell><cell>28</cell></row><row><cell>the Pole <emph type="italics"/>Muno&longs;.<emph.end type="italics"/></cell><cell>39</cell><cell>30</cell><cell>the Star</cell><cell>11</cell><cell>30</cell></row><row><cell>Differences of the</cell><cell>12</cell><cell>54</cell><cell>Differences</cell><cell>12</cell><cell>58</cell></row><row><cell>Polar Altitudes</cell><cell></cell><cell></cell><cell>of the alt. of *</cell><cell>12</cell><cell>54</cell></row><row><cell></cell><cell>Difference of Parallaxes</cell><cell></cell><cell></cell><cell>00</cell><cell>04. ang. BCD.</cell></row></table><table><table.target id="table17"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell>B A D</cell><cell>12</cell><cell>54</cell><cell>and its chord or &longs;ubten&longs;e 22466.</cell><cell></cell></row><row><cell>Angles</cell><cell>B D C</cell><cell>161</cell><cell>59</cell><cell>Sines</cell><cell>30930</cell></row><row><cell></cell><cell>B C D</cell><cell>00</cell><cell>04</cell><cell></cell><cell>116</cell></row></table><p type="main"><s><emph type="italics"/>The Golden Rule.<emph.end type="italics"/> <lb/><arrow.to.target n="table18"></arrow.to.target> <lb/><arrow.to.target n="table19"></arrow.to.target></s></p> <pb xlink:href="040/01/292.jpg" pagenum="272"/><table><table.target id="table18"></table.target><row><cell></cell><cell>22466</cell><cell></cell></row><row><cell>116</cell><cell>30930</cell><cell>22466</cell></row><row><cell></cell><cell>673980</cell><cell></cell></row><row><cell></cell><cell>202194</cell><cell></cell></row><row><cell></cell><cell>67398</cell><cell></cell></row></table><table><table.target id="table19"></table.target><row><cell></cell><cell>59</cell><cell>_______</cell><cell>Di&longs;tance B C 59. and</cell></row><row><cell>116</cell><cell>6948</cell><cell>73380</cell><cell>almo&longs;t 60. &longs;emidiameters.</cell></row><row><cell></cell><cell>1144</cell><cell></cell><cell></cell></row><row><cell></cell><cell>10</cell><cell></cell><cell></cell></row></table><p type="main"><s>The next working is made upon two ob&longs;ervations of <emph type="italics"/>Tycho,<emph.end type="italics"/> and <lb/>of <emph type="italics"/>Muno&longs;ius,<emph.end type="italics"/> from which the Star is calculated to be di&longs;tant from <lb/>the Centre of the Earth 478 Semidiameters and more. <lb/><arrow.to.target n="table20"></arrow.to.target> <lb/><arrow.to.target n="table21"></arrow.to.target> <lb/><arrow.to.target n="table22"></arrow.to.target></s></p><table><table.target id="table20"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitudes</cell><cell><emph type="italics"/>Tycho.<emph.end type="italics"/></cell><cell>55</cell><cell>58</cell><cell>Altitude</cell><cell>84</cell><cell>00</cell></row><row><cell>of the Pole.</cell><cell><emph type="italics"/>Muno&longs;.<emph.end type="italics"/></cell><cell>39</cell><cell>30</cell><cell>of the Star.</cell><cell>67</cell><cell>30</cell></row></table><table><table.target id="table21"></table.target><row><cell>Differences of the</cell><cell>16</cell><cell>28</cell><cell>Differ. of the</cell><cell>16 30</cell></row><row><cell>Polar Altitudes.</cell><cell></cell><cell></cell><cell>Alt. of the *</cell><cell>16 28</cell></row><row><cell></cell><cell>Difference of Parallax.</cell><cell></cell><cell></cell><cell>0 2 and ang. BCD</cell></row></table><table><table.target id="table22"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>B A D.<emph.end type="italics"/></cell><cell>16</cell><cell>28</cell><cell>its chord</cell><cell>28640</cell></row><row><cell>Angles</cell><cell><emph type="italics"/>B D C.<emph.end type="italics"/></cell><cell>104</cell><cell>14</cell><cell>Sines</cell><cell>96930</cell></row><row><cell></cell><cell><emph type="italics"/>B C D.<emph.end type="italics"/></cell><cell>0</cell><cell>2</cell><cell></cell><cell>58</cell></row></table><p type="main"><s><emph type="italics"/>The Golden Rule.<emph.end type="italics"/> <lb/><arrow.to.target n="table23"></arrow.to.target></s></p><table><table.target id="table23"></table.target><row><cell>58</cell><cell>96930</cell><cell>28640</cell></row><row><cell></cell><cell>28640</cell><cell></cell></row><row><cell></cell><cell>3877200</cell><cell></cell></row><row><cell></cell><cell>58158</cell><cell></cell></row><row><cell></cell><cell>77544</cell><cell></cell></row><row><cell></cell><cell>19386</cell><cell></cell></row><row><cell></cell><cell>478</cell><cell></cell></row><row><cell>58</cell><cell>27760</cell><cell>75200</cell></row><row><cell></cell><cell>4506</cell><cell></cell></row><row><cell></cell><cell>53</cell><cell></cell></row></table><p type="main"><s>The&longs;e workings following make the Star remote from the Cen­ <lb/>tre, more than 358 Semidiameters. <lb/><arrow.to.target n="table24"></arrow.to.target> <lb/><arrow.to.target n="table25"></arrow.to.target></s></p> <pb xlink:href="040/01/293.jpg" pagenum="273"/><table><table.target id="table24"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell>Altitudes</cell><cell><emph type="italics"/>Peucerus<emph.end type="italics"/></cell><cell>51</cell><cell>54</cell><cell>Altitude</cell><cell>79</cell><cell>56</cell></row><row><cell>of the Pole.</cell><cell><emph type="italics"/>Muno&longs;ius<emph.end type="italics"/></cell><cell>39</cell><cell>30</cell><cell>of the *</cell><cell>47</cell><cell>30</cell></row><row><cell></cell><cell></cell><cell>12</cell><cell>24</cell><cell></cell><cell>12</cell><cell>26</cell></row><row><cell></cell><cell></cell><cell></cell><cell></cell><cell></cell><cell>12</cell><cell>24</cell></row><row><cell></cell><cell></cell><cell></cell><cell></cell><cell></cell><cell>0</cell><cell>2</cell></row></table><table><table.target id="table25"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"/>B A D.<emph.end type="italics"/></cell><cell>12</cell><cell>24</cell><cell>its chord</cell><cell>21600</cell></row><row><cell>Angles</cell><cell><emph type="italics"/>B D C.<emph.end type="italics"/></cell><cell>106</cell><cell>16</cell><cell>Sines</cell><cell>95996</cell></row><row><cell></cell><cell><emph type="italics"/>B C D.<emph.end type="italics"/></cell><cell>0</cell><cell>2</cell><cell></cell><cell>58</cell></row></table><p type="main"><s>The Golden Rule. <lb/><arrow.to.target n="table26"></arrow.to.target></s></p><table><table.target id="table26"></table.target><row><cell>58</cell><cell>----95996</cell><cell>----21600</cell></row><row><cell></cell><cell>21600</cell><cell></cell></row><row><cell></cell><cell>57597600</cell><cell></cell></row><row><cell></cell><cell>95996</cell><cell></cell></row><row><cell></cell><cell>191992</cell><cell></cell></row><row><cell></cell><cell>357</cell><cell></cell></row><row><cell>58</cell><cell>20735</cell><cell>13600</cell></row><row><cell></cell><cell>3339</cell><cell></cell></row><row><cell></cell><cell>42</cell><cell></cell></row></table><p type="main"><s>From this other working the &longs;tar is found to be di&longs;tant from the <lb/>centre more than 716. &longs;emidiameters. <lb/><arrow.to.target n="table27"></arrow.to.target> <lb/><arrow.to.target n="table28"></arrow.to.target></s></p><table><table.target id="table27"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell></row><row><cell>Altitudes</cell><cell><emph type="italics"/>Landgr.<emph.end type="italics"/></cell><cell>51</cell><cell>18</cell><cell>Altitude</cell><cell>79</cell><cell>30</cell><cell>00</cell></row><row><cell>of the Pole</cell><cell><emph type="italics"/>Hainzel.<emph.end type="italics"/></cell><cell>48</cell><cell>22</cell><cell>of the Star</cell><cell>76</cell><cell>33</cell><cell>45</cell></row><row><cell></cell><cell></cell><cell>2</cell><cell>56</cell><cell></cell><cell>2</cell><cell>56</cell><cell>15</cell></row><row><cell></cell><cell></cell><cell></cell><cell></cell><cell></cell><cell>2</cell><cell>56</cell><cell></cell></row><row><cell></cell><cell></cell><cell></cell><cell></cell><cell></cell><cell>0</cell><cell>00</cell><cell>15</cell></row></table><table><table.target id="table28"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell>B A D</cell><cell>2</cell><cell>56</cell><cell>00</cell><cell>its Chord</cell><cell>5120</cell></row><row><cell>Angles</cell><cell>B D C</cell><cell>101</cell><cell>58</cell><cell>00</cell><cell>Sines</cell><cell>97845</cell></row><row><cell></cell><cell>B C D</cell><cell>0</cell><cell>00</cell><cell>15</cell><cell></cell><cell>7</cell></row></table><p type="main"><s>The Golden Rule. <lb/><arrow.to.target n="table29"></arrow.to.target></s></p><table><table.target id="table29"></table.target><row><cell>7</cell><cell>----97845</cell><cell>----5120</cell></row><row><cell></cell><cell>5120</cell><cell></cell></row><row><cell></cell><cell>1956900</cell><cell></cell></row><row><cell></cell><cell>57845</cell><cell></cell></row><row><cell></cell><cell>489225</cell><cell></cell></row><row><cell></cell><cell>715</cell><cell></cell></row><row><cell>7</cell><cell>5009</cell><cell>66400</cell></row><row><cell></cell><cell>4</cell><cell></cell></row></table><p type="main"><s>The&longs;e as you &longs;ee are five workings which place the &longs;tar very <lb/>much above the Moon. </s><s>And here I de&longs;ire you to con&longs;ider upon <lb/>that particular, which even now I told you, namely, that in great <pb xlink:href="040/01/294.jpg" pagenum="274"/>di&longs;tances, the mutations, or if you plea&longs;e corrections, of a ve­ <lb/>ry few minutes, removeth the &longs;tar a very great way farther off. <lb/></s><s>As for example, in the fir&longs;t of the&longs;e workings, where the calcu­ <lb/>lation made the &longs;tar 60. &longs;emidiameters remote from the centre, <lb/>with the Parallax of 2. minutes; he that would maintain that it <lb/>was in the Firmament, is to correct in the ob&longs;ervations but onely <lb/>two minutes, nay le&longs;&longs;e, for then the Parallax cea&longs;eth, or be­ <lb/>commeth &longs;o &longs;mall, that it removeth the &longs;tar to an immen&longs;e di­ <lb/>&longs;tance, which by all is received to be the Firmament. </s><s>In the &longs;e­ <lb/>cond indagation, or working, the correction of le&longs;&longs;e than 4 <emph type="italics"/>m. <lb/></s><s>prim.<emph.end type="italics"/> doth the &longs;ame. </s><s>In the third, and fourth, like as in the fir&longs;t, <lb/>two minutes onely mount the &longs;tar even above the Firmament. <lb/></s><s>In the la&longs;t preceding, a quarter of a minute, that is 15. &longs;econds, <lb/>gives us the &longs;ame. </s><s>But it doth not &longs;o occur in the &longs;ublunary alti­ <lb/>tudes; for if you fancy to your &longs;elf what di&longs;tance you mo&longs;t <lb/>like, and go about to correct the workings made by the Au­ <lb/>thour, and adju&longs;t them &longs;o as that they all an&longs;wer in the &longs;ame <lb/>determinate di&longs;tance, you will find how much greater correcti­ <lb/>ons they do require.</s></p><p type="main"><s>SAGR. </s><s>It cannot but help us in our fuller under&longs;tanding of <lb/>things, to &longs;ee &longs;ome examples of this which you &longs;peak of.</s></p><p type="main"><s>SALV. </s><s>Do you a&longs;&longs;ign any what&longs;oever determinate &longs;ublunary <lb/>di&longs;tance at plea&longs;ure in which to con&longs;titute the &longs;tar, for with &longs;mall <lb/>ado we may a&longs;&longs;ertain our &longs;elves whether corrections like to the&longs;e, <lb/>which we &longs;ee do &longs;uffice to reduce it among&longs;t the fixed &longs;tars, will <lb/>reduce it to the place by you a&longs;&longs;igned.</s></p><p type="main"><s>SAGR. </s><s>To take a di&longs;tance that may favour the Authour, we <lb/>will &longs;uppo&longs;e it to be that which is the greate&longs;t of all tho&longs;e found <lb/>by him in his 12 workings; for whil&longs;t it is in controver&longs;ie be­ <lb/>tween him and A&longs;tronomers, and that they affirm the &longs;tar to <lb/>have been &longs;uperiour to the Moon, and he that it was inferiour, <lb/>very &longs;mall &longs;pace that he proveth it to have been lower, giveth <lb/>him the victory.</s></p><p type="main"><s>SALV. </s><s>Let us therefore take the &longs;eventh working wrought <lb/>upon the ob&longs;ervations of <emph type="italics"/>Tycho<emph.end type="italics"/> and <emph type="italics"/>Thaddæus Hagecius,<emph.end type="italics"/> by <lb/>which the Authour found the &longs;tar to have been di&longs;tant from the <lb/>centre 32. &longs;emidiameters, which &longs;ituation is mo&longs;t favourable to <lb/>his purpo&longs;e; and to give him all advantages, let us moreover <lb/>place it in the di&longs;tance mo&longs;t disfavouring the <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> which <lb/>is to &longs;ituate it above the Firmament. </s><s>That therefore being &longs;up­ <lb/>po&longs;ed, let us &longs;eek in the next place what corrections it would be ne­ <lb/>ce&longs;&longs;ary to apply to his other 11 workings. </s><s>And let us begin at the <lb/>fir&longs;t calculated upon the ob&longs;ervations of <emph type="italics"/>Hainzelius<emph.end type="italics"/> and <emph type="italics"/>Mauroice<emph.end type="italics"/>; <lb/>in which the Authour findeth the di&longs;tance from the centre about <lb/>3. &longs;emidiameters with the Parallax of 4 <emph type="italics"/>gr. </s><s>42 m. </s><s>30. &longs;ec.<emph.end type="italics"/> Let <pb xlink:href="040/01/295.jpg" pagenum="275"/>us &longs;ee whether by withdrawing it 20. minutes onely, it will ri&longs;e <lb/>to the height of 32. &longs;emidiameters: See the &longs;hort and true opera­ <lb/>tion. </s><s>Multiply the &longs;ine of the angle B D C, by the &longs;ine of the <lb/><arrow.to.target n="table30"></arrow.to.target> <lb/><arrow.to.target n="table31"></arrow.to.target> <lb/><arrow.to.target n="table32"></arrow.to.target> <lb/>chord B D, and divide the product, the five la&longs;t figures being cut <lb/>off by the &longs;ine of the Parallax, and the quotient will be 28. &longs;e­ <lb/>midiameters, and an half, &longs;o that though you make a correction <lb/>of 4 <emph type="italics"/>gr. </s><s>22 min. </s><s>30 &longs;ec.<emph.end type="italics"/> taken from 4 <emph type="italics"/>gr. </s><s>42 min. </s><s>30 &longs;ec.<emph.end type="italics"/> it &longs;hall <lb/>not elevate the &longs;tar to the altitude of 32. &longs;emidiameters, which <lb/>correction for <emph type="italics"/>Simplicius<emph.end type="italics"/> his under&longs;tanding it, is of 262. minutes, <lb/>and an half.</s></p><table><table.target id="table30"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Hainzelius<emph.end type="italics"/></cell><cell>Pole</cell><cell>48</cell><cell>32</cell><cell>----*</cell><cell>76</cell><cell>34</cell><cell>30</cell></row><row><cell><emph type="italics"/>Maurolicus<emph.end type="italics"/></cell><cell>Pole</cell><cell>38</cell><cell>30</cell><cell>----*</cell><cell>62</cell><cell>00</cell><cell>00</cell></row><row><cell></cell><cell></cell><cell>9</cell><cell>52</cell><cell></cell><cell>14</cell><cell>34</cell><cell>30</cell></row><row><cell></cell><cell></cell><cell></cell><cell></cell><cell></cell><cell>9</cell><cell>52</cell><cell>00</cell></row><row><cell></cell><cell></cell><cell></cell><cell></cell><cell>Parallax</cell><cell>4</cell><cell>42</cell><cell>30</cell></row></table><table><table.target id="table31"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell></cell><cell>B A D</cell><cell>9</cell><cell>52</cell><cell>00</cell><cell>Chord</cell><cell>17200</cell></row><row><cell>Angles</cell><cell>B D C</cell><cell>108</cell><cell>21</cell><cell>30</cell><cell>Sine</cell><cell>94910</cell></row><row><cell></cell><cell>B C D</cell><cell>0</cell><cell>20</cell><cell>00</cell><cell>Sine</cell><cell>582</cell></row></table><table><table.target id="table32"></table.target><row><cell></cell><cell>94910</cell><cell></cell></row><row><cell></cell><cell>17200</cell><cell></cell></row><row><cell></cell><cell>18982000</cell><cell></cell></row><row><cell></cell><cell>66437</cell><cell></cell></row><row><cell></cell><cell>9491</cell><cell></cell></row><row><cell></cell><cell>28</cell><cell></cell></row><row><cell>582</cell><cell>16324</cell><cell>52000</cell></row><row><cell></cell><cell>4688</cell><cell></cell></row><row><cell></cell><cell>2</cell><cell></cell></row></table><p type="main"><s>In the &longs;econd operation made upon the ob&longs;ervations of <emph type="italics"/>Hain­ <lb/>zelius,<emph.end type="italics"/> and <emph type="italics"/>Sculerus,<emph.end type="italics"/> with the Parallax of 0 <emph type="italics"/>gr. </s><s>8 min. </s><s>30 &longs;ec.<emph.end type="italics"/> <lb/>the &longs;tar is found in the height of 25. &longs;emidiameters or therea­ <lb/>bouts, as may be &longs;een in the &longs;ub&longs;equent working. <lb/><arrow.to.target n="table33"></arrow.to.target> <pb xlink:href="040/01/296.jpg" pagenum="276"/><arrow.to.target n="table34"></arrow.to.target></s></p><table><table.target id="table33"></table.target><row><cell>B D</cell><cell>Chord</cell><cell>6166</cell></row><row><cell>B D C</cell><cell>Sines</cell><cell>97987</cell></row><row><cell>B C D</cell><cell></cell><cell>247</cell></row></table><table><table.target id="table34"></table.target><row><cell></cell><cell>97987</cell><cell></cell></row><row><cell></cell><cell>6166</cell><cell></cell></row><row><cell></cell><cell>587922</cell><cell></cell></row><row><cell></cell><cell>587922</cell><cell></cell></row><row><cell></cell><cell>97987</cell><cell></cell></row><row><cell></cell><cell>587922</cell><cell></cell></row><row><cell></cell><cell>24</cell><cell></cell></row><row><cell>247</cell><cell>6041</cell><cell>87842</cell></row><row><cell></cell><cell>1103</cell><cell></cell></row><row><cell></cell><cell>11</cell><cell></cell></row></table><p type="main"><s>And bringing back the Parallax 0 <emph type="italics"/>gr. </s><s>8 m. </s><s>30 &longs;ec.<emph.end type="italics"/> to 7 <emph type="italics"/>gr.<emph.end type="italics"/> <lb/>7 <emph type="italics"/>m.<emph.end type="italics"/> who&longs;e &longs;ine is 204, the &longs;tar elevateth to 30 &longs;emidiameters or <lb/>thereabouts; therefore the correction of 0 <emph type="italics"/>gr. </s><s>1 mi. </s><s>30 &longs;ec.<emph.end type="italics"/> doth <lb/>not &longs;uffice. <lb/><arrow.to.target n="table35"></arrow.to.target></s></p><table><table.target id="table35"></table.target><row><cell></cell><cell>20</cell><cell></cell></row><row><cell>204</cell><cell>6041</cell><cell>87342</cell></row><row><cell></cell><cell>1965</cell><cell></cell></row><row><cell></cell><cell>12</cell><cell></cell></row></table><p type="main"><s>Now let us &longs;ee what correction is requi&longs;ite for the third work­ <lb/>ing made upon the ob&longs;ervations of <emph type="italics"/>Hainzelius<emph.end type="italics"/> and <emph type="italics"/>Tycho,<emph.end type="italics"/> which <lb/>rendereth the &longs;tar about 19 &longs;emidiameters high, with the Pa­ <lb/>rallax of 10 <emph type="italics"/>m. </s><s>pri.<emph.end type="italics"/> The u&longs;ual angles and their &longs;ines, and chord <lb/>found by the Authour, are the&longs;e next following; and they re­ <lb/>move the &longs;tar (as al&longs;o in the Authours working) 19 &longs;emidia­ <lb/>meters from the centre of the Earth. </s><s>It is nece&longs;&longs;ary therefore for <lb/>the rai&longs;ing of it, to dimini&longs;h the Parallax according to the Rule <lb/>which he likewi&longs;e ob&longs;erveth in the ninth working. </s><s>Let us there­ <lb/>fore &longs;uppo&longs;e the Parallax to be 6 <emph type="italics"/>m. </s><s>prim.<emph.end type="italics"/> who&longs;e &longs;ine is 175, and <lb/>the divi&longs;ion being made, there is found likewi&longs;e le&longs;&longs;e than 31 <lb/>&longs;emidiameters for the &longs;tars di&longs;tance. </s><s>And therefore the correcti­ <lb/>on of 4 <emph type="italics"/>min. </s><s>prim.<emph.end type="italics"/> is too little to &longs;erve the Authours purpo&longs;e. <lb/><arrow.to.target n="table36"></arrow.to.target> <pb xlink:href="040/01/297.jpg" pagenum="277"/><arrow.to.target n="table37"></arrow.to.target></s></p><table><table.target id="table36"></table.target><row><cell></cell><cell>B A D</cell><cell>7</cell><cell>36</cell><cell>Chord</cell><cell>13254</cell></row><row><cell>Angles</cell><cell>B D C</cell><cell>155</cell><cell>52</cell><cell>Sine</cell><cell>40886</cell></row><row><cell></cell><cell>B C D</cell><cell>0</cell><cell>10</cell><cell>Sine</cell><cell>291</cell></row></table><table><table.target id="table37"></table.target><row><cell></cell><cell>13254</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell>40886</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell>79524</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell>106032</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell>106032</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell>53016</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell>18</cell><cell></cell><cell></cell><cell>30</cell></row><row><cell>291</cell><cell>5419</cell><cell>03044</cell><cell>175</cell><cell>5419</cell></row><row><cell></cell><cell>250</cell><cell></cell><cell></cell><cell>16</cell></row><row><cell></cell><cell>181</cell><cell></cell><cell></cell><cell></cell></row></table><p type="main"><s>Let us come to the fourth working, and the re&longs;t with the &longs;ame <lb/>rule, and with the chords and &longs;ines found out by the Authour <lb/>him&longs;elf; in this the Parallax is 14 <emph type="italics"/>m. </s><s>prim.<emph.end type="italics"/> and the height found <lb/>le&longs;&longs;e than 10 &longs;emidiameters, and dimini&longs;hing the Parallax from <lb/>14 <emph type="italics"/>min.<emph.end type="italics"/> to 4 <emph type="italics"/>min.<emph.end type="italics"/> yet neverthele&longs;&longs;e you &longs;ee that the &longs;tar doth not <lb/>elevate full 31 &longs;emidiameters. </s><s>Therefore 10 <emph type="italics"/>min.<emph.end type="italics"/> in 14 <emph type="italics"/>min.<emph.end type="italics"/> doth <lb/>not &longs;uffice. <lb/><arrow.to.target n="table38"></arrow.to.target> <lb/><arrow.to.target n="table39"></arrow.to.target></s></p><table><table.target id="table38"></table.target><row><cell></cell><cell>B A D</cell><cell>Chord</cell><cell>8142</cell></row><row><cell>Angles</cell><cell>B D C</cell><cell>Sine</cell><cell>43235</cell></row><row><cell></cell><cell>B C D</cell><cell>Sine</cell><cell>407</cell></row></table><table><table.target id="table39"></table.target><row><cell></cell><cell>43235</cell><cell></cell></row><row><cell></cell><cell>8142</cell><cell></cell></row><row><cell></cell><cell>86470</cell><cell></cell></row><row><cell></cell><cell>172940</cell><cell></cell></row><row><cell></cell><cell>43235</cell><cell></cell></row><row><cell></cell><cell>345880</cell><cell></cell></row><row><cell></cell><cell>30</cell><cell></cell></row><row><cell>116</cell><cell>3520</cell><cell>19370</cell></row><row><cell></cell><cell>4</cell><cell></cell></row></table><p type="main"><s>In the fifth operation of the Authour we have the &longs;ines and the <lb/>chord as you &longs;ee, and the Parallax is 0 <emph type="italics"/>gr. </s><s>42 m. </s><s>30 &longs;ec.<emph.end type="italics"/> which <lb/>rendereth the height of the &longs;tar about 4 &longs;emidiameters, and cor­ <lb/>recting the Parallax, with reducing it from 0 <emph type="italics"/>gr. </s><s>42 m. </s><s>30 &longs;ec.<emph.end type="italics"/> <lb/>to 0 <emph type="italics"/>gr. </s><s>5 m.<emph.end type="italics"/> onely, doth not &longs;uffice to rai&longs;e it to &longs;o much as 28 &longs;e­ <lb/>midiameters, the correction therefore of 0 <emph type="italics"/>gr. </s><s>37 m. </s><s>30 &longs;ec.<emph.end type="italics"/> is <lb/>too little. <lb/><arrow.to.target n="table40"></arrow.to.target> <pb xlink:href="040/01/298.jpg" pagenum="278"/><arrow.to.target n="table41"></arrow.to.target></s></p><table><table.target id="table40"></table.target><row><cell></cell><cell>B A D</cell><cell>Chord</cell><cell>4034</cell></row><row><cell>Angles</cell><cell>B D C</cell><cell>Sine</cell><cell>97998</cell></row><row><cell></cell><cell>B C D</cell><cell></cell><cell>1236</cell></row></table><table><table.target id="table41"></table.target><row><cell></cell><cell>97998</cell><cell></cell></row><row><cell></cell><cell>4034</cell><cell></cell></row><row><cell></cell><cell>391992</cell><cell></cell></row><row><cell></cell><cell>293994</cell><cell></cell></row><row><cell></cell><cell>391992</cell><cell></cell></row><row><cell></cell><cell>27</cell><cell></cell></row><row><cell>145</cell><cell>3953</cell><cell>23932</cell></row><row><cell></cell><cell>1058</cell><cell></cell></row><row><cell></cell><cell>3</cell><cell></cell></row></table><p type="main"><s>In the &longs;ixth operation the chord, the &longs;ines and Parallax are as <lb/>followeth, and the &longs;tar is found to be about 4 &longs;emidiameters; let <lb/>us &longs;ee whether it will be reduced, abating the Parallax from 8 <emph type="italics"/>m.<emph.end type="italics"/> <lb/>to 1 <emph type="italics"/>m.<emph.end type="italics"/> onely; Here is the operation, and the &longs;tar rai&longs;ed but to <lb/>27. &longs;emidiameters or thereabout; therefore the correction of 7 <emph type="italics"/>m.<emph.end type="italics"/> <lb/>in 8 <emph type="italics"/>m.<emph.end type="italics"/> doth not &longs;uffice. <lb/><arrow.to.target n="table42"></arrow.to.target> <lb/><arrow.to.target n="table43"></arrow.to.target></s></p><table><table.target id="table42"></table.target><row><cell>B D</cell><cell>Chord</cell><cell>1920</cell></row><row><cell>B D C</cell><cell>Sine</cell><cell>40248</cell></row><row><cell>B C D 8 <emph type="italics"/>gr.<emph.end type="italics"/></cell><cell>Sine</cell><cell>233</cell></row></table><table><table.target id="table43"></table.target><row><cell></cell><cell>40248</cell><cell></cell></row><row><cell></cell><cell>1920</cell><cell></cell></row><row><cell></cell><cell>804960</cell><cell></cell></row><row><cell></cell><cell>362232</cell><cell></cell></row><row><cell></cell><cell>40248</cell><cell></cell></row><row><cell></cell><cell>26</cell><cell></cell></row><row><cell>29</cell><cell>772</cell><cell>76160</cell></row><row><cell></cell><cell>198</cell><cell></cell></row><row><cell></cell><cell>1</cell><cell></cell></row></table><p type="main"><s>In the eighth operation the chord, the &longs;ines, and the Parallax, <lb/>as you &longs;ee, are the&longs;e en&longs;uing, and hence the Authour calculates <lb/>the height of the &longs;tar to be 1. &longs;emidiameter and an half, with the <lb/>Parallax of 43. <emph type="italics"/>min.<emph.end type="italics"/> which reduced to 1 <emph type="italics"/>min.<emph.end type="italics"/> yet notwith&longs;tand­ <lb/>ing giveth the &longs;tar le&longs;&longs;e remote than 24. &longs;emidiameters, the corre­ <lb/>ction therefore of 42. <emph type="italics"/>min.<emph.end type="italics"/> is not enough. <lb/><arrow.to.target n="table44"></arrow.to.target> <pb xlink:href="040/01/299.jpg" pagenum="279"/><arrow.to.target n="table45"></arrow.to.target></s></p><table><table.target id="table44"></table.target><row><cell>B D</cell><cell>Chord</cell><cell>1804</cell></row><row><cell>B D C</cell><cell>Sine</cell><cell>36643</cell></row><row><cell>B C D</cell><cell>Sine</cell><cell>29</cell></row></table><table><table.target id="table45"></table.target><row><cell></cell><cell>36643</cell><cell></cell></row><row><cell></cell><cell>1804</cell><cell></cell></row><row><cell></cell><cell>146572</cell><cell></cell></row><row><cell></cell><cell>293144</cell><cell></cell></row><row><cell></cell><cell>36643</cell><cell></cell></row><row><cell></cell><cell>22</cell><cell></cell></row><row><cell>29</cell><cell>661</cell><cell>03972</cell></row><row><cell></cell><cell>83</cell><cell></cell></row><row><cell></cell><cell>2</cell><cell></cell></row></table><p type="main"><s>Let us now &longs;ee the ninth. </s><s>Here is the chord, the &longs;ines and <lb/>the Parallax which is 15 <emph type="italics"/>m.<emph.end type="italics"/> From whence the Authour calcu­ <lb/>lates the di&longs;tance of the &longs;tar from the &longs;uperficies of the Earth <lb/>to be le&longs;&longs;e than a ^{*} &longs;even and fortieth part of a &longs;emidiameter, <lb/><arrow.to.target n="marg513"></arrow.to.target> <lb/>but this is an errour in the calcultaion, for it cometh forth truly, <lb/>as we &longs;hall &longs;ee here below, more than a &longs;ifth: See here the quo­ <lb/>tienr is 90/436, which is more than one fifth. <lb/><arrow.to.target n="table46"></arrow.to.target> <lb/><arrow.to.target n="table47"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg513"></margin.target>* Here the La­ <lb/>tine ver&longs;ion is erro­ <lb/>neous, making it <lb/>a fortieth part of, <lb/><emph type="italics"/>&c.<emph.end type="italics"/></s></p><table><table.target id="table46"></table.target><row><cell>B D</cell><cell>Chord</cell><cell>232</cell></row><row><cell>B D C</cell><cell>Sine</cell><cell>39046</cell></row><row><cell>B C D</cell><cell>Sine</cell><cell>436</cell></row></table><table><table.target id="table47"></table.target><row><cell></cell><cell>39046</cell><cell></cell></row><row><cell></cell><cell>232</cell><cell></cell></row><row><cell></cell><cell>78092</cell><cell></cell></row><row><cell></cell><cell>117138</cell><cell></cell></row><row><cell></cell><cell>78092</cell><cell></cell></row><row><cell>436</cell><cell>90</cell><cell>58672</cell></row></table><p type="main"><s>That which the Authour pre&longs;ently after &longs;ubjoyns in way of <lb/>amending the ob&longs;ervations, that is, that it &longs;u&longs;&longs;iceth not to re­ <lb/>duce the difference of Parallax, neither to a minute, nor yet <lb/>to the eighth part of a minute is true. </s><s>But I &longs;ay, that neither <lb/>will the tenth part of a minute reduce the height of the &longs;tar to <lb/>32. &longs;emidiameters; for the &longs;ine of the tenth part of a minute, <lb/>that is of &longs;ix &longs;econds, is 3; by which if we according to our Rule <lb/>&longs;hould divide 90. or we may &longs;ay, if we &longs;hould divide 9058672. <lb/>by 300000. the quotient will be 30 58672/100000, that is little more <lb/>than 30. &longs;emidiameters and an half.</s></p><p type="main"><s>The tenth giveth the altitude of the &longs;tar one fifth of a &longs;emi­ <lb/>diameter, with the&longs;e angles, &longs;ines, and Parallax, that is, 4 <emph type="italics"/>gr.<emph.end type="italics"/> <pb xlink:href="040/01/300.jpg" pagenum="280"/>30 <emph type="italics"/>m.<emph.end type="italics"/> which I &longs;ee that being reduced from 4 <emph type="italics"/>gr. </s><s>30 min.<emph.end type="italics"/> to 2 <emph type="italics"/>min.<emph.end type="italics"/> <lb/>yet neverthele&longs;&longs;e it elevates not the &longs;tar to 29. &longs;emidiameters. <lb/><arrow.to.target n="table48"></arrow.to.target> <lb/><arrow.to.target n="table49"></arrow.to.target></s></p><table><table.target id="table48"></table.target><row><cell>B D</cell><cell></cell><cell>Chord</cell><cell>1746</cell></row><row><cell>B D C</cell><cell></cell><cell>Sine</cell><cell>92050</cell></row><row><cell>B C D</cell><cell>4 <emph type="italics"/>gr. 30 m.<emph.end type="italics"/></cell><cell>Sine</cell><cell>7846</cell></row></table><table><table.target id="table49"></table.target><row><cell></cell><cell>92050</cell><cell></cell></row><row><cell></cell><cell>17460</cell><cell></cell></row><row><cell></cell><cell>552300</cell><cell></cell></row><row><cell></cell><cell>36820</cell><cell></cell></row><row><cell></cell><cell>64435</cell><cell></cell></row><row><cell></cell><cell>9205</cell><cell></cell></row><row><cell></cell><cell>27</cell><cell></cell></row><row><cell>58</cell><cell>1607</cell><cell>19300</cell></row><row><cell></cell><cell>441</cell><cell></cell></row><row><cell></cell><cell>4</cell><cell></cell></row></table><p type="main"><s>The eleventh rendereth the &longs;tar to the Authour remote about <lb/>13. &longs;emidiameters, with the Parallax of 55. <emph type="italics"/>min.<emph.end type="italics"/> let us &longs;ee, re­ <lb/>ducing it to 20 <emph type="italics"/>min.<emph.end type="italics"/> whether it will exalt the &longs;tar: See here the <lb/>calculation elevates it to little le&longs;&longs;e than 33. &longs;emidiameters, the <lb/>correction therefore is little le&longs;&longs;e than 35. <emph type="italics"/>min.<emph.end type="italics"/> in 55. <emph type="italics"/>min.<emph.end type="italics"/> <lb/><arrow.to.target n="table50"></arrow.to.target> <lb/><arrow.to.target n="table51"></arrow.to.target></s></p><table><table.target id="table50"></table.target><row><cell>B D</cell><cell></cell><cell>Chord</cell><cell>19748</cell></row><row><cell>B D C</cell><cell></cell><cell>Sine</cell><cell>96166</cell></row><row><cell>B C D</cell><cell>o <emph type="italics"/>gr. 55 m.<emph.end type="italics"/></cell><cell>Sine</cell><cell>1600</cell></row></table><table><table.target id="table51"></table.target><row><cell></cell><cell>96166</cell><cell></cell></row><row><cell></cell><cell>19748</cell><cell></cell></row><row><cell></cell><cell>639328</cell><cell></cell></row><row><cell></cell><cell>384664</cell><cell></cell></row><row><cell></cell><cell>673162</cell><cell></cell></row><row><cell></cell><cell>865494</cell><cell></cell></row><row><cell></cell><cell>96166</cell><cell></cell></row><row><cell></cell><cell>32</cell><cell></cell></row><row><cell>582</cell><cell>18990</cell><cell>56168</cell></row><row><cell></cell><cell>1536</cell><cell></cell></row><row><cell></cell><cell>56</cell><cell></cell></row></table><p type="main"><s>The twelfth with the Parallax of 1. <emph type="italics"/>gr. </s><s>36. min.<emph.end type="italics"/> maketh the <lb/>&longs;tar le&longs;&longs;e high than 6. &longs;emidiameters, reducing the Parallax to <lb/>20 <emph type="italics"/>min.<emph.end type="italics"/> it carrieth the &longs;tar to le&longs;&longs;e than 30. &longs;emidiameters di­ <lb/>&longs;tance, therefore the correction of 1 <emph type="italics"/>gr. </s><s>16. min.<emph.end type="italics"/> &longs;ufficeth not. <pb xlink:href="040/01/301.jpg" pagenum="281"/><arrow.to.target n="table52"></arrow.to.target> <lb/><arrow.to.target n="table53"></arrow.to.target></s></p><table><table.target id="table52"></table.target><row><cell>B D</cell><cell></cell><cell>Chord</cell><cell>17258</cell></row><row><cell>B D C</cell><cell></cell><cell>Sine</cell><cell>96150</cell></row><row><cell>B C D</cell><cell>1 <emph type="italics"/>gr. 36 m.<emph.end type="italics"/></cell><cell>Sine</cell><cell>2792</cell></row></table><table><table.target id="table53"></table.target><row><cell></cell><cell>17258</cell><cell></cell></row><row><cell></cell><cell>96150</cell><cell></cell></row><row><cell></cell><cell>862900</cell><cell></cell></row><row><cell></cell><cell>17258</cell><cell></cell></row><row><cell></cell><cell>103548</cell><cell></cell></row><row><cell></cell><cell>155322</cell><cell></cell></row><row><cell></cell><cell>28</cell><cell></cell></row><row><cell>582</cell><cell>16593</cell><cell>56700</cell></row><row><cell></cell><cell>4957</cell><cell></cell></row><row><cell></cell><cell>29</cell><cell></cell></row></table><p type="head"><s><emph type="italics"/>The&longs;e are the Corrections of the Parallaxes <lb/>of the ten workings of the Author, to <lb/>reduce the Star to the altitude of<emph.end type="italics"/> <lb/>32 <emph type="italics"/>Semidiameters.<emph.end type="italics"/> <lb/><arrow.to.target n="table54"></arrow.to.target> <lb/><arrow.to.target n="table55"></arrow.to.target></s></p><table><table.target id="table54"></table.target><row><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell><emph type="italics"/>&longs;ec.<emph.end type="italics"/></cell></row><row><cell>04</cell><cell>22</cell><cell>30</cell><cell>in</cell><cell>04</cell><cell>42</cell><cell>30</cell></row><row><cell>00</cell><cell>04</cell><cell>00</cell><cell>in</cell><cell>00</cell><cell>10</cell><cell>00</cell></row><row><cell>00</cell><cell>10</cell><cell>00</cell><cell>in</cell><cell>00</cell><cell>14</cell><cell>00</cell></row><row><cell>00</cell><cell>37</cell><cell>00</cell><cell>in</cell><cell>00</cell><cell>42</cell><cell>30</cell></row><row><cell>00</cell><cell>07</cell><cell>00</cell><cell>in</cell><cell>00</cell><cell>18</cell><cell>00</cell></row><row><cell>00</cell><cell>42</cell><cell>00</cell><cell>in</cell><cell>00</cell><cell>43</cell><cell>00</cell></row><row><cell>00</cell><cell>14</cell><cell>50</cell><cell>in</cell><cell>00</cell><cell>15</cell><cell>00</cell></row><row><cell>04</cell><cell>28</cell><cell>00</cell><cell>in</cell><cell>04</cell><cell>30</cell><cell>00</cell></row><row><cell>00</cell><cell>35</cell><cell>00</cell><cell>in</cell><cell>00</cell><cell>55</cell><cell>00</cell></row><row><cell>01</cell><cell>16</cell><cell>00</cell><cell>in</cell><cell>01</cell><cell>36</cell><cell>00</cell></row></table><table><table.target id="table55"></table.target><row><cell>216</cell><cell>296.60</cell></row><row><cell>540</cell><cell>240.9</cell></row><row><cell>765</cell><cell>836.540</cell></row></table><p type="main"><s>From hence we &longs;ee, that to reduce the Star to 32. Semidiame­ <lb/>ters in altitude, it is requi&longs;ite from the &longs;um of the Parallaxes 836. <lb/>to &longs;ubtract 756. and to reduce them to 80. nor yet doth that <lb/>correction &longs;uffice.</s></p> <pb xlink:href="040/01/302.jpg" pagenum="282"/><p type="main"><s>Here we &longs;ee al&longs;o, (as I have noted even now) that &longs;hould the <lb/>Authour con&longs;ent to a&longs;&longs;ign the di&longs;tance of 32. Semidiameters for <lb/>the true height of the Star, the correction of tho&longs;e his 10. workings, <lb/>(I &longs;ay 10. becau&longs;e the &longs;econd being very high, is reduced to the <lb/>height of 32. Semidiameters, with 2. minutes correction) to make <lb/>them all to re&longs;tore the &longs;aid Star to that di&longs;tance, would require &longs;uch <lb/>a reduction of Parallaxes, that among&longs;t the whole number of &longs;ub <lb/>&longs;tractions they &longs;hould make more than 756 <emph type="italics"/>m. </s><s>pr.<emph.end type="italics"/> whereas in the <lb/>5. calculated by me, which do place the Star above the Moon, to <lb/>correct them in &longs;uch &longs;ort, as to con&longs;titute it in the Firmament, <lb/>the correction onely of 10. minutes, and one fourth &longs;ufficeth.</s></p><p type="main"><s>Now adde to the&longs;e, other 5. workings, that place the Star pre­ <lb/>ci&longs;ely in the Firmament, without need of any correction at all, <lb/>and we &longs;hall have ten workings or indagations that agree to place <lb/>it in the Firmament, with the correction onely of 5. of them (as <lb/>hath been &longs;een) but 10. <emph type="italics"/>m.<emph.end type="italics"/> and 15 <emph type="italics"/>&longs;ec.<emph.end type="italics"/> Whereas for the correcti­ <lb/>on of tho&longs;e 10. of the Authour, to reduce them to the altitude of <lb/>32. &longs;emidiameters, there will need the emendations of 756 mi­ <lb/>nutes in 836. that is, there mu&longs;t from the &longs;umme 836 be &longs;ub&longs;tra­ <lb/>cted 756. if you would have the Star elevated to the altitude of <lb/>32. &longs;emidiameters, and yet that correction doth not fully &longs;erve.</s></p><p type="main"><s>The workings that immediately without any correction free the <lb/>Star from Parallaxes, and therefore place it in the Firmament, <lb/>and that al&longs;o in the remote&longs;t parts of it, and in a word, as high <lb/>as the Pole it &longs;elf, are the&longs;e 5. noted here. <lb/><arrow.to.target n="table56"></arrow.to.target></s></p><table><table.target id="table56"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Camerar.<emph.end type="italics"/></cell><cell>Polar altit.</cell><cell>52</cell><cell>24</cell><cell>Altit. of the Star</cell><cell>80</cell><cell>26</cell></row><row><cell><emph type="italics"/>Peucerus<emph.end type="italics"/></cell><cell></cell><cell>51</cell><cell>54</cell><cell></cell><cell>79</cell><cell>56</cell></row><row><cell></cell><cell></cell><cell>0</cell><cell>30</cell><cell></cell><cell>0</cell><cell>30</cell></row><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Landgrav.<emph.end type="italics"/></cell><cell>Polar altit.</cell><cell>51</cell><cell>18</cell><cell>Altit. of the Star</cell><cell>79</cell><cell>30</cell></row><row><cell><emph type="italics"/>Hainzel.<emph.end type="italics"/></cell><cell></cell><cell>48</cell><cell>22</cell><cell></cell><cell>76</cell><cell>34</cell></row><row><cell></cell><cell></cell><cell>2</cell><cell>56</cell><cell></cell><cell>2</cell><cell>56</cell></row><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Tycho<emph.end type="italics"/></cell><cell>Polar altit.</cell><cell>55</cell><cell>58</cell><cell>Altit. of the Star</cell><cell>84</cell><cell>00</cell></row><row><cell><emph type="italics"/>Peucerus<emph.end type="italics"/></cell><cell></cell><cell>51</cell><cell>54</cell><cell></cell><cell>79</cell><cell>56</cell></row><row><cell></cell><cell></cell><cell>4</cell><cell>4</cell><cell></cell><cell>4</cell><cell>4</cell></row> <pb xlink:href="040/01/303.jpg" pagenum="283"/><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Reinhold.<emph.end type="italics"/></cell><cell>Polar altit.</cell><cell>51</cell><cell>18</cell><cell>Altit. of the Star</cell><cell>79</cell><cell>30</cell></row><row><cell><emph type="italics"/>Hainzel.<emph.end type="italics"/></cell><cell></cell><cell>48</cell><cell>22</cell><cell></cell><cell>36</cell><cell>34</cell></row><row><cell></cell><cell></cell><cell>2</cell><cell>56</cell><cell></cell><cell>2</cell><cell>56</cell></row><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Camerar.<emph.end type="italics"/></cell><cell>Polar altit.</cell><cell>52</cell><cell>24</cell><cell>Altit. of the Star</cell><cell>24</cell><cell>17</cell></row><row><cell><emph type="italics"/>Hagecius<emph.end type="italics"/></cell><cell></cell><cell>48</cell><cell>22</cell><cell></cell><cell>20</cell><cell>15</cell></row><row><cell></cell><cell></cell><cell>4</cell><cell>2</cell><cell></cell><cell>4</cell><cell>2</cell></row></table><p type="main"><s>Of the remaining combinations that might be made of the Ob­ <lb/>&longs;ervations of all the&longs;e A&longs;tronomers, tho&longs;e that make the Stars &longs;ub­ <lb/>lime to an infinite di&longs;tance, are many in number, namely, about <lb/>30. more than tho&longs;e who give the Star, by calculation, to be be­ <lb/>low the Moon; and becau&longs;e (as it was agreed npon between us) it <lb/>is to be believed that the Ob&longs;ervators have erred rather little than <lb/>much, it is a manife&longs;t thing that the corrections to be applied to <lb/>the Ob&longs;ervaations, which make the &longs;tar of an infinite altitude, to <lb/>reduce it lower, do &longs;ooner, and with le&longs;&longs;er amendment place it in <lb/>the Firmament, than beneath the Moon; &longs;o that all the&longs;e applaud <lb/>the opinion of tho&longs;e who put it among&longs;t the fixed Stars. </s><s>You may <lb/>adde, that the corrections required for tho&longs;e emendations, are <lb/>much le&longs;&longs;er than tho&longs;e, by which the Star from an unlikely proxi­ <lb/>mity may be removed to the height more favourable for this Au­ <lb/>thour, as by the foregoing examples hath been &longs;een; among&longs;t <lb/>which impo&longs;&longs;ible proximities, there are three that &longs;eem to remove <lb/>the Star from the Earths centre, a le&longs;&longs;e di&longs;tance than one Semidi­ <lb/>ameter, making it, as it were, to turn round under ground, and <lb/>the&longs;e are tho&longs;e combinations, wherein the Polar altitude of one <lb/>of the Ob&longs;ervators being greater than the Polar altitude of the <lb/>other, the elevation of the Star taken by the fir&longs;t, is le&longs;&longs;er than the <lb/>elation of the Star taken by the latter.</s></p><p type="main"><s>The fir&longs;t of the&longs;e is this of the <emph type="italics"/>Landgrave<emph.end type="italics"/> with <emph type="italics"/>Gemma,<emph.end type="italics"/> <lb/>where the Polar altitude of the <emph type="italics"/>Landgrave 51 gr. </s><s>18 min.<emph.end type="italics"/> is <lb/>greater than the Polar altitude of <emph type="italics"/>Gemma,<emph.end type="italics"/> which is 50 <emph type="italics"/>gr. </s><s>50 m.<emph.end type="italics"/> <lb/>But the altitude of the Star of the <emph type="italics"/>Landgrave 79 gr. </s><s>30 min.<emph.end type="italics"/> <lb/>is le&longs;&longs;er than that of the Star, of <emph type="italics"/>Gemma 79 gr. </s><s>45 min.<emph.end type="italics"/> <lb/><arrow.to.target n="table57"></arrow.to.target></s></p> <pb xlink:href="040/01/304.jpg" pagenum="284"/><table><table.target id="table57"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Landgrave<emph.end type="italics"/></cell><cell>Polar altit.</cell><cell>51</cell><cell>18</cell><cell>Altit. of the Star</cell><cell>79</cell><cell>30</cell></row><row><cell><emph type="italics"/>Gemma<emph.end type="italics"/></cell><cell></cell><cell>50</cell><cell>50</cell><cell></cell><cell>79</cell><cell>45</cell></row></table><p type="main"><s>The other two are the&longs;e below. <lb/><arrow.to.target n="table58"></arrow.to.target></s></p><table><table.target id="table58"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell></row><row><cell><emph type="italics"/>Bu&longs;chius.<emph.end type="italics"/></cell><cell>Polar Altitude</cell><cell>51</cell><cell>10</cell><cell>Altit. of the Star</cell><cell>79</cell><cell>20</cell></row><row><cell><emph type="italics"/>Gemma.<emph.end type="italics"/></cell><cell></cell><cell>50</cell><cell>50</cell><cell></cell><cell>79</cell><cell>45</cell></row><row><cell><emph type="italics"/>Reinholdus.<emph.end type="italics"/></cell><cell>Polar Altitude</cell><cell>51</cell><cell>18</cell><cell>Altit. of the Star</cell><cell>79</cell><cell>30</cell></row><row><cell><emph type="italics"/>Gemma.<emph.end type="italics"/></cell><cell></cell><cell>50</cell><cell>50</cell><cell></cell><cell>79</cell><cell>45</cell></row></table><p type="main"><s>From what I have hitherto demon&longs;trated, you may gue&longs;&longs;e how <lb/>much this fir&longs;t way of finding out the di&longs;tance of the Star, and <lb/>proving it &longs;ublunary introduced by the Authour, maketh again&longs;t <lb/>him&longs;elf, and how much more probably and clearly the di&longs;tance <lb/>thereof is collected to have been among&longs;t the more remote fixed <lb/>Stars.</s></p><p type="main"><s>SIMP. </s><s>As to this particular, I think that the inefficacy of the <lb/>Authors demonftrations is very plainly di&longs;covered; But I &longs;ee that all <lb/>this was compri&longs;ed in but a few leaves of his Book, and it may be, <lb/>that &longs;ome other of his Arguments are more conclu&longs;ive then the&longs;e <lb/>fir&longs;t.</s></p><p type="main"><s>SALV. </s><s>Rather they mu&longs;t needs be le&longs;&longs;e valid, if we will take <lb/>tho&longs;e that lead the way for a proof of the re&longs;t: For (as it is clear) <lb/>the uncertainty and inconclu&longs;ivene&longs;&longs;e of tho&longs;e, is manife&longs;tly ob­ <lb/>&longs;erved to derive it &longs;elf from the errours committed in the in&longs;tru­ <lb/>mental ob&longs;ervations, upon which the Polar Altitude, and height <lb/>of the Star was thought to have been ju&longs;tly taken, all in effect <lb/>having ea&longs;ily erred; And yet to find the Altitude of the Pole, A­ <lb/>&longs;tronomers have had Ages of time to apply them&longs;elves to it, at their <lb/>lea&longs;ure: and the Meridian Altitudes of the Star are ea&longs;ier to be <lb/>ob&longs;erved, as being mo&longs;t terminate, and yielding the Ob&longs;ervator <lb/>&longs;ome time to continue the &longs;ame, in regard they change not &longs;en&longs;ibly, <lb/>in a &longs;hort time, as tho&longs;e do that are remote from the Meridian. </s><s>And <lb/>if this be &longs;o, as it is mo&longs;t certain, what credit &longs;hall we give to Calcu­ <lb/>lations founded upon Ob&longs;ervations more numerous, more difficult <lb/>to be wrought, more momentary in variation, and we may add, <lb/>with In&longs;truments more incommodious and erroneous? </s><s>Upon a <lb/>&longs;light peru&longs;al of the en&longs;uing demon&longs;trations, I &longs;ee that the Com­ <lb/>putations are made upon Altitudes of the Star taken in different <lb/>Vertical Circles, which are called by the Arabick name, <emph type="italics"/>Azimuths<emph.end type="italics"/>; in <lb/>which ob&longs;ervations moveable in&longs;truments are made u&longs;e of, not on­ <lb/>ly in the Vertical Circles, but in the Horizon al&longs;o, at the &longs;ame time; <lb/>in&longs;omuch that it is requi&longs;ite in the &longs;ame moment that the altitude <lb/>is taken, to have ob&longs;erved, in the Horizon, the di&longs;tance of the Vir­ <pb xlink:href="040/01/305.jpg" pagenum="285"/>tical point in which the Star is, from the Meridian; Moreover, <lb/>after a con&longs;iderable interval of time, the operation mu&longs;t be re­ <lb/>peated, and exact account kept of the time that pa&longs;&longs;ed, tru&longs;ting <lb/>either to Dials, or to other ob&longs;ervations of the Stars. </s><s>Such an <emph type="italics"/>Olio<emph.end type="italics"/> <lb/>of Ob&longs;ervations doth he &longs;et before you, comparing them with <lb/>&longs;uch another made by another ob&longs;erver in another place with a­ <lb/>nother different in&longs;trument, and at another time; and from this <lb/>the Authour &longs;eeks to collect what would have been, the Elevations <lb/>of the Star, and Horizontal Latitudes happened in the time and <lb/>hour of the other fir&longs;t ob&longs;ervations, and upon &longs;uch a coæquation he <lb/>in the end grounds his account. </s><s>Now I refer it to you, what credit <lb/>is to be given to that which is deduced from &longs;uch like workings. <lb/></s><s>Moreover, I doubt not in the lea&longs;t, but that if any one would tor­ <lb/>ture him&longs;elf with &longs;uch tedious computations, he would find, as in <lb/>tho&longs;e aforegoing, that there were more that would favour the ad­ <lb/>ver&longs;e party, than the Authour: But I think it not worth the while <lb/>to take &longs;o much pains in a thing, which is not, among&longs;t tho&longs;e prima­ <lb/>ry ones, by us under&longs;tood.</s></p><p type="main"><s>SAGR. </s><s>I am of your Opinion in this particular: But this bu&longs;i­ <lb/>ne&longs;&longs;e being environed with &longs;o many intricacies, uncertainties, and <lb/>errours, upon what confidence have &longs;o many A&longs;tronomers po&longs;itive­ <lb/>ly pronounced the new Star to have been &longs;o high?</s></p><p type="main"><s>SALV. </s><s>Upon two &longs;orts of ob&longs;ervations mo&longs;t plain, mo&longs;t ea&longs;ie, <lb/>and mo&longs;t certain; one only of which is more than &longs;ufficient to a&longs;&longs;ure <lb/>us, that it was &longs;cituate in the Firmament, or at lea&longs;t by a great <lb/>di&longs;tance &longs;uperiour to the Moon. </s><s>One of which is taken from the <lb/>equality, or little differing inequality of its di&longs;tances from the <lb/>Pole, a&longs;well whil&longs;t it was in the lowe&longs;t part of the Meridian, as <lb/>when it was in the uppermo&longs;t: The other is its having perpetual­ <lb/>ly kept the &longs;ame di&longs;tances from certain of the fixed Stars, adjacent <lb/>to it, and particularly from the eleventh of <emph type="italics"/>Ca&longs;&longs;iopea,<emph.end type="italics"/> no more <lb/>remote from it than one degree and an half; from which two par­ <lb/>ticulars is undoubtedly inferred, either the ab&longs;olute want of Paral­ <lb/>lax, or &longs;uch a &longs;malne&longs;&longs;e thereof, that it doth a&longs;&longs;ure us with very <lb/>expeditious Calculations of its great di&longs;tance from the Earth.</s></p><p type="main"><s>SAGR. </s><s>But the&longs;e things, were they not known to this Author? <lb/></s><s>and if he &longs;aw them, what doth he &longs;ay unto them?</s></p><p type="main"><s>SALV. </s><s>We are wont to &longs;ay, of one that having no reply that <lb/>is able to cover his fault, produceth frivolous excu&longs;es, <emph type="italics"/>cerca di at­ <lb/>taccar&longs;i alle funi del cielo,<emph.end type="italics"/> [He &longs;trives to take hold of the Cords of <lb/>Heaven;] but this Authour runs, not to the Cords, but to the Spi­ <lb/>ders Web of Heaven; as you &longs;hall plainly &longs;ee in our examination <lb/>of the&longs;e two particulars even now hinted. </s><s>And fir&longs;t, that which <lb/>&longs;heweth us the Polar di&longs;tances of the Ob&longs;ervators one by one, I <lb/>have noted down in the&longs;e brief Calculations; For a full under­ <pb xlink:href="040/01/306.jpg" pagenum="286"/>&longs;tanding of which, I ought fir&longs;t to adverti&longs;e you, that when ever <lb/>the new Star, or other Phænomenon is near to the earth, turning <lb/>with a Diurnal motion about the Pole, it will &longs;eem to be farther <lb/>off from the &longs;aid Pole, whil&longs;t it is in the lower part of the Meridi­ <lb/>an, then whil&longs;t it is above, as in this Figure [<emph type="italics"/>being fig. </s><s>third of <lb/>this Dial.<emph.end type="italics"/>] may be &longs;een. </s><s>In which the point T. denotes the cen­ <lb/>tre of the Earth; O the place of the Ob&longs;ervator; the Arch VPC <lb/>the Firmament; P. the Pole. </s><s>The <emph type="italics"/>Phænomenon,<emph.end type="italics"/> [<emph type="italics"/>or appearance<emph.end type="italics"/>] <lb/>moving along the Circle F S. is &longs;een one while under the Pole by <lb/>the Ray O F C. and another while above, according to the Ray <lb/>O S D. &longs;o that the places &longs;een in the Firmament are D. and C. but <lb/>the true places in re&longs;pect of the Centre T, are B, and A, equidi­ <lb/>&longs;tant from the Pole. </s><s>Where it is manife&longs;t that the apparent place <lb/>of the <emph type="italics"/>Phænomenon<emph.end type="italics"/> S, that is the point D, is nearer to the Pole than <lb/>the other apparent place C, &longs;een along the Line or Ray O F C, <lb/>which is the fir&longs;t thing to be noted. </s><s>In the &longs;econd place you mu&longs;t <lb/>note that the exces of the apparent inferiour di&longs;tance from the Pole, <lb/>over and above the apparent &longs;uperiour di&longs;tance from the &longs;aid Pole, <lb/>is greater than the Inferiour Parallax of the <emph type="italics"/>Phænomenon,<emph.end type="italics"/> that is, I <lb/>&longs;ay, that the exce&longs;&longs;e of the Arch C P, (the apparent inferior di­ <lb/>&longs;tance) over and above the Arch P D, (the apparent &longs;uperior di­ <lb/>&longs;tance) is greater then the Arch C A, (that is the inferiour Para­ <lb/>lax.) Which is ea&longs;ily proved; for the Arch C P. more exceedeth <lb/>P D, then P B; P B, being bigger than P D, but P B. is equal to <lb/>P A, and the exce&longs;&longs;e of C P, above P A, is the arch, C A, there­ <lb/>fore the exce&longs;&longs;e of the arch C P above the arch P D, is great­ <lb/>er than the arch C A, which is the parallax of the Phænomenon <lb/>placed in F, which was to be demon&longs;trated. </s><s>And to give all ad­ <lb/>vantages to the Author, let us &longs;uppo&longs;e that the parallax of the &longs;tar <lb/>in F, is the whole exce&longs;&longs;e of the arch C P (that is of the inferiour <lb/>di&longs;tance from the pole) above the arch P D (the inferiour di­ <lb/>&longs;tance.) I proceed in the next place to examine that which the <lb/>ob&longs;ervations of all A&longs;tronomers cited by the Authour giveth us, <lb/>among&longs;t which, there is not one that maketh not again&longs;t him&longs;elf <lb/>and his purpo&longs;e. </s><s>And let us begin with the&longs;e of <emph type="italics"/>Bu&longs;chius,<emph.end type="italics"/> who <lb/>findeth the &longs;tars di&longs;tance from the pole, when it was &longs;uperiour, to be <lb/>28 <emph type="italics"/>gr. </s><s>10 m.<emph.end type="italics"/> and the inferiour to be 28 <emph type="italics"/>gr. </s><s>30 m.<emph.end type="italics"/> &longs;o that the ex­ <lb/>ce&longs;&longs;e is 0 <emph type="italics"/>gr. </s><s>20 m.<emph.end type="italics"/> which let us take (in favour of the Author) as <lb/>if it all were the parallax of the &longs;tar in F, that is the angle T F O. <lb/></s><s>Then the di&longs;tance from the <emph type="italics"/>Vertex<emph.end type="italics"/> [or Zenith] that is the arch <lb/>C V, is 67 <emph type="italics"/>gr. </s><s>20 m.<emph.end type="italics"/> The&longs;e two things being found, prolong the <lb/>line C O, and from it let fall the perpendicular T I, and let us <lb/>con&longs;ider the triangle T O I, of which the angle I is right angle, <lb/>and the angle I O T known, as being vertical to the angle V O C, <lb/>the di&longs;tance of the &longs;tar from the <emph type="italics"/>Vertex,<emph.end type="italics"/> Moreover in the triangle <pb xlink:href="040/01/307.jpg" pagenum="287"/>T I F, which is al&longs;o rectangular, there is known the angle F, ta­ <lb/>ken by the parallax. </s><s>Then note in &longs;ome place apart the two an­ <lb/>gles I O T and I F T, and of them take the &longs;ines, which are <lb/>here &longs;et down to them, as you &longs;een. </s><s>And becau&longs;e in the triangle <lb/>I O T, the &longs;ine T I is 92276. of tho&longs;e parts, whereof the whole <lb/>&longs;ine TO is 100000; and moreover in the triangle I F T, the &longs;ine T I <lb/>is 582. of tho&longs;e parts, whereof the whole &longs;ine T F is 100000, to <lb/>find how many T F is of tho&longs;e parts, whereof T O is 100000; <lb/>we will &longs;ay by the Rule of three: If T I be 582. T F is an <lb/>100000. but if T I were 92276. how much would T F be. <lb/></s><s>Let us multiply 92276. by 100000. and the product will be <lb/>9227600000. and this mu&longs;t be divided by 582. and the quotient <lb/>will be 15854982. and &longs;o many &longs;hall there be in T F of tho&longs;e <lb/>parts, of which there are in T O an 100000. So that if it were <lb/>required to know how many lines T O, are in T F, we would <lb/>divide 15854982 by 100000. and there will come forth 158. and <lb/>very near an half; and &longs;o many diameters &longs;hall be the di&longs;tance <lb/>of the &longs;tar F, from the centre T, and to abreviate the opera­ <lb/>tion, we &longs;eeing, that the product of the multiplication of 92276. <lb/>by 100000, ought to be divided fir&longs;t by 582, and then the quo­ <lb/>tient of that divi&longs;ion by 100000. we may without multiplying <lb/>92276. by 100000. and with one onely divi&longs;ion of the &longs;ine <lb/>92276. by the &longs;ine 582. &longs;oon obtain the &longs;ame &longs;olution, as may <lb/>be &longs;een there below; where 92276. divided by 582. giveth us the <lb/>&longs;aid 158 1/2, or thereabouts. </s><s>Let us bear in mind therefore, that <lb/>the onely divi&longs;ion of the &longs;ine T I, as the &longs;ine of the angle T O I <lb/>by the &longs;ine T I, as the &longs;ine of the angle I F T, giveth us the di­ <lb/>&longs;tance &longs;ought T F, in &longs;o many diameters T O. <lb/><arrow.to.target n="table59"></arrow.to.target> <lb/><arrow.to.target n="table60"></arrow.to.target> <lb/><arrow.to.target n="table61"></arrow.to.target></s></p> <pb xlink:href="040/01/308.jpg" pagenum="288"/><table><table.target id="table59"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Angles</cell><cell>I O T</cell><cell>67</cell><cell>20</cell><cell>Sines</cell><cell>92276</cell></row><row><cell></cell><cell>I F T</cell><cell>0</cell><cell>20</cell><cell></cell><cell>582</cell></row></table><table><table.target id="table60"></table.target><row><cell>T I</cell><cell>T F</cell><cell>T I</cell><cell>T F</cell></row><row><cell>582</cell><cell>10000</cell><cell>92276</cell><cell>0</cell></row></table><table><table.target id="table61"></table.target><row><cell></cell><cell>15854982</cell><cell></cell></row><row><cell>582</cell><cell>9227600000</cell><cell></cell></row><row><cell></cell><cell>3407002746</cell><cell></cell></row><row><cell></cell><cell>49297867</cell><cell></cell></row><row><cell></cell><cell>325414</cell><cell></cell></row><row><cell>100000</cell><cell>158</cell><cell>54982</cell></row><row><cell></cell><cell>158</cell><cell></cell></row><row><cell>582</cell><cell>92276</cell><cell></cell></row><row><cell></cell><cell>34070</cell><cell></cell></row><row><cell></cell><cell>492</cell><cell></cell></row><row><cell></cell><cell>3</cell><cell></cell></row></table><p type="main"><s>See next that which the ob&longs;ervations of <emph type="italics"/>Peucerus<emph.end type="italics"/> giveth us, in <lb/>which the inferiour di&longs;tance from the Pole is 28 <emph type="italics"/>gr. </s><s>21 m.<emph.end type="italics"/> and the <lb/>&longs;uperiour 28 <emph type="italics"/>gr. </s><s>2 m.<emph.end type="italics"/> the difference 0 <emph type="italics"/>gr. </s><s>19 m.<emph.end type="italics"/> and the di&longs;tance <lb/>from the vertical point 66 <emph type="italics"/>gr. </s><s>27 m.<emph.end type="italics"/> from which particulars is ga­ <lb/>thered the &longs;tars di&longs;tance from the centre almo&longs;t 166 &longs;emedia­ <lb/>meters. <lb/><arrow.to.target n="table62"></arrow.to.target> <lb/><arrow.to.target n="table63"></arrow.to.target></s></p><table><table.target id="table62"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Angles</cell><cell>I A C</cell><cell>66</cell><cell>27</cell><cell>Sines</cell><cell>91672</cell></row><row><cell></cell><cell>I E C</cell><cell>0</cell><cell>19</cell><cell></cell><cell>553</cell></row></table><table><table.target id="table63"></table.target><row><cell></cell><cell>165 427/553</cell></row><row><cell>553</cell><cell>91672</cell></row><row><cell></cell><cell>36397</cell></row><row><cell></cell><cell>312</cell></row><row><cell></cell><cell>4</cell></row></table><p type="main"><s>Here take what <emph type="italics"/>Tycho<emph.end type="italics"/> his ob&longs;ervation holdeth forth to us, in­ <lb/>terpreted with greate&longs;t favour to the adver&longs;ary; to wit, the inferi­ <lb/>our di&longs;tance from the pole is 28 <emph type="italics"/>gr. </s><s>13 m.<emph.end type="italics"/> and the &longs;uperiour 28 <emph type="italics"/>gr. <lb/></s><s>2 m.<emph.end type="italics"/> omitting the difference which is 0 <emph type="italics"/>gr. </s><s>11 m.<emph.end type="italics"/> as if all were one <lb/>Parallax; the di&longs;tance from the vertical point 62 <emph type="italics"/>gr. </s><s>15 m.<emph.end type="italics"/> Behold <lb/>here below the operation, and the di&longs;tance of the &longs;tar from the <lb/>centre found to be 976 9/16 &longs;emidiameters. <lb/><arrow.to.target n="table64"></arrow.to.target> <lb/><arrow.to.target n="table65"></arrow.to.target></s></p><table><table.target id="table64"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Angles</cell><cell>I A C</cell><cell>62</cell><cell>15</cell><cell>Sines</cell><cell>88500</cell></row><row><cell></cell><cell>I E C</cell><cell>0</cell><cell>11</cell><cell></cell><cell>320</cell></row></table><table><table.target id="table65"></table.target><row><cell></cell><cell>276 9/16</cell></row><row><cell>320</cell><cell>88500</cell></row><row><cell></cell><cell>2418</cell></row><row><cell></cell><cell>1</cell></row></table><p type="main"><s>The ob&longs;ervation of <emph type="italics"/>Reinholdus,<emph.end type="italics"/> which is the next en&longs;uing, giv­ <lb/>eth us the di&longs;tance of the Star from the Centre 793. Semidia­ <lb/>meters. <lb/><arrow.to.target n="table66"></arrow.to.target> <lb/><arrow.to.target n="table67"></arrow.to.target></s></p> <pb xlink:href="040/01/309.jpg" pagenum="289"/><table><table.target id="table66"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Angles</cell><cell>I A C</cell><cell>66</cell><cell>58</cell><cell>Sines</cell><cell>92026</cell></row><row><cell></cell><cell>I E C</cell><cell>0</cell><cell>4</cell><cell></cell><cell>116</cell></row></table><table><table.target id="table67"></table.target><row><cell></cell><cell>793 38/116</cell></row><row><cell>116</cell><cell>92026</cell></row><row><cell></cell><cell>10888</cell></row><row><cell></cell><cell>33</cell></row></table><p type="main"><s>From the following ob&longs;ervation of the <emph type="italics"/>Landgrave,<emph.end type="italics"/> the di&longs;tance <lb/>of the Star from the Centre is made to be 1057, Semidiameters. <lb/><arrow.to.target n="table68"></arrow.to.target> <lb/><arrow.to.target n="table69"></arrow.to.target></s></p><table><table.target id="table68"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Angles</cell><cell>I A C</cell><cell>66</cell><cell>57</cell><cell>Sines</cell><cell>92012</cell></row><row><cell></cell><cell>I E C</cell><cell>0</cell><cell>3</cell><cell></cell><cell>87</cell></row></table><table><table.target id="table69"></table.target><row><cell></cell><cell>1057 53/87</cell></row><row><cell>87</cell><cell>92012</cell></row><row><cell></cell><cell>5663</cell></row><row><cell></cell><cell>5</cell></row></table><p type="main"><s>Two of the mo&longs;t favourable ob&longs;ervations for the Authour be­ <lb/>ing taken from <emph type="italics"/>Camerarius,<emph.end type="italics"/> the di&longs;tance of the Star from the Cen­ <lb/>tre is found to be 3143 Semidiameters. <lb/><arrow.to.target n="table70"></arrow.to.target> <lb/><arrow.to.target n="table71"></arrow.to.target></s></p><table><table.target id="table70"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"/>gr.<emph.end type="italics"/></cell><cell><emph type="italics"/>m.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Angles</cell><cell>I A C</cell><cell>65</cell><cell>43</cell><cell>Sines</cell><cell>91152</cell></row><row><cell></cell><cell>I E C</cell><cell>0</cell><cell>1</cell><cell></cell><cell>29</cell></row></table><table><table.target id="table71"></table.target><row><cell></cell><cell>3143</cell></row><row><cell>29</cell><cell>91152</cell></row><row><cell></cell><cell>4295</cell></row></table><p type="main"><s>The Ob&longs;ervation of <emph type="italics"/>Muno&longs;ius<emph.end type="italics"/> giveth no <emph type="italics"/>Parallax,<emph.end type="italics"/> and there­ <lb/>fore rendreth the new Star among&longs;t the highe&longs;t of the fixed. </s><s>That <lb/>of <emph type="italics"/>Hainzelius<emph.end type="italics"/> makes it infinitely remote, but with the correction <lb/>of an half <emph type="italics"/>min. </s><s>prim.<emph.end type="italics"/> placeth it among&longs;t the fixed Stars. </s><s>And the <lb/>&longs;ame is collected from <emph type="italics"/>Vr&longs;inus,<emph.end type="italics"/> with the correction of 12. <emph type="italics"/>min. </s><s>prim.<emph.end type="italics"/> <lb/>The other A&longs;tronomers have not given us the di&longs;tance above and <lb/>below the Pole, &longs;o that nothing can be concluded from them. </s><s>By <lb/>this time you &longs;ee, that all the ob&longs;ervations of all the&longs;e men con&longs;pire <lb/>again&longs;t the Author, in placing the Star in the Heavenly and high­ <lb/>e&longs;t Regions.</s></p><p type="main"><s>SAGR. </s><s>But what defence hath he for him&longs;elf again&longs;t &longs;o manife&longs;t <lb/>contradictions?</s></p><p type="main"><s>SALV. </s><s>He betakes him&longs;elf to one of tho&longs;e weak threads which <lb/>I &longs;peak of; &longs;aying that the <emph type="italics"/>Parallaxes<emph.end type="italics"/> come to be le&longs;&longs;ened by means <lb/>of the refractions, which opperating contrarily &longs;ublimate the <emph type="italics"/>Phæ­ <lb/>nomenon,<emph.end type="italics"/> whereas the <emph type="italics"/>Parallaxes<emph.end type="italics"/> aba&longs;e it. </s><s>Now of what little <lb/>&longs;tead this lamentable refuge is, judge by this, that in ca&longs;e that effectof <lb/>the refractions were of &longs;uch an efficacy, as that which not long time <lb/>&longs;ince &longs;ome A&longs;tronomers have introduced, the mo&longs;t that they could <lb/>work touching the elevating a <emph type="italics"/>Phæuomenon<emph.end type="italics"/> above the Horizon <pb xlink:href="040/01/310.jpg" pagenum="290"/>more than truth, when it is before hand 23. or 24. Degrees high, <lb/>would be the le&longs;&longs;ening its <emph type="italics"/>Parallax<emph.end type="italics"/> about 3. minutes, the which <lb/>abatement is too &longs;mall to pull down the Star below the Moon, and <lb/>in &longs;ome ca&longs;es is le&longs;&longs;e than the advantage given him by us in admit­ <lb/>ting that the exce&longs;&longs;e of the inferiour di&longs;tance from the Pole above <lb/>the Superiour, is all <emph type="italics"/>Parallax,<emph.end type="italics"/> the which advantage is far more clear <lb/>and palpable than the effect of Refracton, of the greatne&longs;&longs;e of <lb/>which I &longs;tand in doubt, and not without rea&longs;on. </s><s>But be&longs;ides, I <lb/>demand of the Author, whether he thinks that tho&longs;e A&longs;tronomers, <lb/>of who&longs;e ob&longs;ervations he maketh u&longs;e, had knowledge of the&longs;e ef­ <lb/>fects of Refractions, and con&longs;idered the &longs;ame, or no; if they did <lb/>know and con&longs;ider them, it is rea&longs;onable to think that the, kept ac­ <lb/>count of them in a&longs;&longs;igning the true Elevation of the Star, making <lb/>in tho&longs;e degrees of Altitude di&longs;covered with the In&longs;truments, &longs;uch <lb/>abatements as were convenient on the account of the alterations <lb/>made by the Refractions; in&longs;omuch that the di&longs;tances by them de­ <lb/>livered, were in the end tho&longs;e corrected and exact, and not the ap­ <lb/>parent and fal&longs;e ones. </s><s>But if he think that tho&longs;e Authors made <lb/>no reflection upon the &longs;aid Refractions, it mu&longs;t be confe&longs;&longs;ed, that <lb/>they had in like manner erred in determining all tho&longs;e things which <lb/>cannot be perfectly adju&longs;ted without allowance for the Refracti­ <lb/>ons; among&longs;t which things one is the preci&longs;e inve&longs;tigation of the <lb/>Polar Altitudes, which are commonly taken from the two Meridi­ <lb/>an Altitudes of &longs;ome of the fixed Stars that are con&longs;tantly vi&longs;ible, <lb/>which Altitudes will come to be altered by Refraction in the &longs;ame <lb/>manner, ju&longs;t as tho&longs;e of the new Star; &longs;o that the Polar Altitude <lb/>that is deduced from them, will prove to be defective, and to par­ <lb/>take of the &longs;elf &longs;ame want which this Author a&longs;&longs;igns to the Alti­ <lb/>tudes a&longs;cribed to the new Star, to wit, both that and the&longs;e will <lb/>be with equal fal&longs;hood placed higher than really they are. </s><s>But any <lb/>&longs;uch errour, as far as concerns our pre&longs;ent bu&longs;ine&longs;&longs;e, doth no pre­ <lb/>judce at all: For we not needing to know any more, but onely <lb/>the difference between the two di&longs;tances of the new Star from the <lb/>Pole at &longs;uch time as it was inferiour and &longs;uperiour, it is evident that <lb/>&longs;uch di&longs;tances would be the &longs;ame, taking the alteration of Refra­ <lb/>ction commonly for the Star and for the Pole, or for them when <lb/>commonly amended. </s><s>The Authors Argument would indeed have <lb/>had &longs;ome &longs;trength, though very &longs;mall, if he had a&longs;&longs;ured us that <lb/>the Altitude of the Pole had been once preci&longs;ely a&longs;&longs;igned, and cor­ <lb/>rected from the errour depending on refraction, from which a­ <lb/>gain the A&longs;tronomers had not kept them&longs;elves in a&longs;&longs;igning the al­ <lb/>titudes of the new Star; but he hath not a&longs;certained us of that, <lb/>nor perhaps could he have done, nor haply, (and this is more pro­ <lb/>bable) was that caution wanting in the Ob&longs;ervators.</s></p><p type="main"><s>SAGR. </s><s>This argument is in my judgment &longs;ufficiently an&longs;wer­ <pb xlink:href="040/01/311.jpg" pagenum="291"/>ed; therefore tell me how he di&longs;-ingageth him&longs;elf in the next place <lb/>from that particular of the Stars having con&longs;tantly kept the &longs;ame <lb/>di&longs;tance from the fixed Stars circumjacent to it.</s></p><p type="main"><s>SALV. </s><s>He betakes him&longs;elf, in like manner, to two threads, yet <lb/>more unable to uphold him than the former: one of which is like­ <lb/>wi&longs;e fa&longs;tened to refraction, but &longs;o much le&longs;s firmly, in that he <lb/>&longs;aith, that refraction operating upon the new Star, and &longs;ublimating <lb/>it higher than its true &longs;ituation, maketh the &longs;eeming di&longs;tances un­ <lb/>tain to be di&longs;tingui&longs;hed from the true, when compared to the cir­ <lb/>cumpo&longs;ed fixed Stars that environ it. </s><s>Nor can I &longs;ufficiently ad­ <lb/>mire how he can di&longs;&longs;emble his knowing how that the &longs;ame refra­ <lb/>ction will work alike upon the new Star, as upon the antient one <lb/>its neighbour, elevating both equally, &longs;o as that &longs;uch a like acci­ <lb/>dent altereth not the &longs;pace betwixt them. </s><s>His other &longs;ubterfuge is <lb/>yet more unhappy, and carryeth with it much of ridiculous, it be­ <lb/>ing founded upon the errour that may ari&longs;e in the in&longs;trumen talo­ <lb/>peration it &longs;elf; whil&longs;t that the Ob&longs;ervator not being able to <lb/>con&longs;titute the centre of the eyes pupil in the centre of the Sex­ <lb/>tant (an In&longs;trument imployed in ob&longs;erving the di&longs;tance between <lb/>two Stars) but holding it elevated above that centre, as much as <lb/>the &longs;aid pupil is di&longs;tant from I know not what bone of the cheek, <lb/>again&longs;t which the end of the In&longs;trument re&longs;teth, there is formed <lb/>in the eye an angle more acute than that which is made by the &longs;ides <lb/>of the In&longs;trument; which angle of rayes differeth al&longs;o from it <lb/>&longs;elf, at &longs;uch time as a man looketh upon Stars, not much elevated <lb/>above the Horizon, and the &longs;ame being afterwards placed at a <lb/>great height; that angle, &longs;aith he, is made different, while the In­ <lb/>&longs;trument goeth a&longs;cending, the head &longs;tanding &longs;till: but if in moun­ <lb/>ting the In&longs;trument, the neck &longs;hould bend backwards, and the <lb/>head go ri&longs;ing, together with the In&longs;trument, the angle would then <lb/>continue the &longs;ame. </s><s>So that the Authours an&longs;wer &longs;uppo&longs;eth that <lb/>the Ob&longs;ervators in u&longs;ing the In&longs;trument have not rai&longs;ed the head, <lb/>as they ought to have done; a thing which hath nothing of likeli­ <lb/>hood in it. </s><s>But granting that &longs;o it had been, I leave you to judge <lb/>what difference can be between two acute angles of two equicru­ <lb/>ral triangles, the &longs;ides of one of which triangles are each four <lb/>[<emph type="italics"/>Italian] Braces<emph.end type="italics"/> [<emph type="italics"/>i.e.<emph.end type="italics"/> about three Engli&longs;h yards] and tho&longs;e of the <lb/>other, four braces within the quantity of the diameter of a Pea; <lb/>for the differences cannot be ab&longs;olutely greater between the length <lb/>of the two vi&longs;ive rayes, whil&longs;t the line is drawn perpendicularly <lb/>from the centre of the pupil, upon the plain of the Rule of the <lb/>Sextant (which line is no bigger than the breath of the thumb) <lb/>and the length of the &longs;ame rayes, whil&longs;t elevating the Sextant, <lb/>without rai&longs;ing the head together with it, that &longs;ame line no longer <lb/>falleth perpendicularly upon the &longs;aid plane, but inclineth, making <pb xlink:href="040/01/312.jpg" pagenum="292"/>the angle towards the circumference &longs;omething acute. </s><s>But wholly <lb/>to free this Authour from the&longs;e unhappy lies, let him know, (in re­ <lb/>gard it appears that he is not very skilful in the u&longs;e of A&longs;tronomi­ <lb/>call In&longs;truments) that in the &longs;ides of the Sextant or Quadrant <lb/><arrow.to.target n="marg514"></arrow.to.target> <lb/>there are placed two ^{*} Sights, one in the centre, and the other at <lb/>the other at the oppo&longs;ite end, which are rai&longs;ed an inch or more a­ <lb/>bove the plane of the Rule; and through the tops of tho&longs;e &longs;ights <lb/>the ray of the eye is made to pa&longs;&longs;e, which eye likewi&longs;e is held an <lb/>hands breadth or two, or it may be more, from the In&longs;trument; &longs;o <lb/>that neither the pupil, nor any bone of the cheek, nor of the whole <lb/>body toucheth or &longs;tayeth it &longs;elf upon the In&longs;trument, nor much <lb/>le&longs;&longs;e is the In&longs;trument upheld or mounted in the armes, e&longs;pecially <lb/>if it be one of tho&longs;e great ones, as is u&longs;ual, which weighing tens, <lb/>hundreds, and al&longs;o thou&longs;ands of pounds, are placed upon very <lb/>&longs;trong feet or frames: &longs;o that the whole objection vani&longs;heth. <lb/></s><s>The&longs;e are the &longs;ubterfuges of this Authour, which, though they were <lb/>all of &longs;teel, would not &longs;ecure him the hundredth part of a minute; <lb/>and with the&longs;e he conceits to make us believe, that he hath com­ <lb/>pen&longs;ated that difference, which importeth more than an hundred <lb/>minutes; I mean, that of the not ob&longs;erving a notable difference <lb/>in the di&longs;tances between one of the fixed &longs;tars, and the new &longs;tar in <lb/>in any of their circulations; which, had it been neer to the Moon, <lb/>it ought to have been very con&longs;picuous to the meer &longs;ight, without <lb/>any In&longs;trument, e&longs;pecially comparing it with the eleventh of <emph type="italics"/>Ca&longs;­ <lb/>&longs;iopeia,<emph.end type="italics"/> its neighbour, within 1 <emph type="italics"/>gr. </s><s>30 m.<emph.end type="italics"/> which ought to have va­ <lb/>ried from it more than two diameters of the moon, as the more <lb/>intelligent A&longs;tronomers of t' o&longs;e times do well note.</s></p><p type="margin"><s><margin.target id="marg514"></margin.target>* Traguardi.</s></p><p type="main"><s>SAGR. </s><s>Methinks I &longs;ee that unfortunate Husbandman, who af­ <lb/>ter all his expected crops, have been beaten down and de&longs;troyed by <lb/>a &longs;torm, goeth up and down with a langui&longs;hing and down-ca&longs;t <lb/>look, gleaning up every &longs;mall ear that would not &longs;uffice to keep a <lb/>chicken alive one &longs;ole day.</s></p><p type="main"><s>SALV. Truly, this Authour came out too &longs;lenderly provided <lb/>with armes again&longs;t the a&longs;&longs;ailants of the Heavens inalterability, and <lb/>with too brittle a chain attempted to pull down the new &longs;tar of <lb/><emph type="italics"/>Ca&longs;&longs;iopeia<emph.end type="italics"/> from the highe&longs;t Regions, to the&longs;e &longs;o low and elementa­ <lb/>ry. </s><s>And for that I think that we have &longs;ufficiently demon&longs;trated <lb/>the va&longs;t difference that is between the arguments of tho&longs;e A&longs;tro­ <lb/>nomers, and of this their Antagoni&longs;t, it will be convenient that we <lb/>leave this particular, and return to our principal matter; in which <lb/>there pre&longs;ents it &longs;elf to our con&longs;ideration the annual motion com­ <lb/>monly a&longs;cribed to the Sun, but by <emph type="italics"/>Aristarchus Samius<emph.end type="italics"/> fir&longs;t of all, <lb/>and after by <emph type="italics"/>Copernicus<emph.end type="italics"/> taken from the Sun, and transferred upon <lb/>the Earth; again&longs;t which Hypothe&longs;is, methinks I &longs;ee <emph type="italics"/>Simplicius<emph.end type="italics"/> to <lb/>come &longs;trongly provided, and particularly with the &longs;word and <pb xlink:href="040/01/313.jpg" pagenum="293"/>buckler of the little Treati&longs;e of <emph type="italics"/>Conclu&longs;ions,<emph.end type="italics"/> or Di&longs;qui&longs;itions Ma­ <lb/>thematical, the oppugnations of which it would be good to be­ <lb/>gin to produce.</s></p><p type="main"><s>SIMP. </s><s>I will, if you &longs;o plea&longs;e, re&longs;erve them to the la&longs;t, as tho&longs;e <lb/>that are of late&longs;t invention.</s></p><p type="main"><s>SALV. </s><s>It will therefore be nece&longs;&longs;ary, that in conformity to the <lb/>method hitherto ob&longs;erved, you do orderly, one by one, propound <lb/>the arguments, on the contrary, a&longs;well of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> as of the o­ <lb/>ther ancients, which &longs;hall be my task al&longs;o, that &longs;o nothing may e­ <lb/>&longs;cape our &longs;trict con&longs;ideration and examination; and likewi&longs;e <emph type="italics"/>Sa­ <lb/>gredus,<emph.end type="italics"/> with the vivacity of his wit, &longs;hall interpo&longs;e his thoughts, as <lb/>he &longs;hall finde him&longs;elf inclined.</s></p><p type="main"><s>SAGR. </s><s>I will do it with my wonted freedome; and your com­ <lb/>mands &longs;hall oblige you to excu&longs;e me in &longs;o doing.</s></p><p type="main"><s>SALV. </s><s>The favour will challenge thanks, and not an excu&longs;e. <lb/></s><s>But now let <emph type="italics"/>Simplicius<emph.end type="italics"/> begin to propo&longs;e tho&longs;e doubts which di&longs;­ <lb/>&longs;wade him from believing that the Earth, in like manner, as the <lb/>other pianets, may move round about a fixed centre.</s></p><p type="main"><s>SIMP. </s><s>The fir&longs;t and greate&longs;t difficulty is the repugnance and <lb/>incompatibility that is between being in the centre, and being far <lb/>from it; for if the Terre&longs;trial Globe were to move in a year by <lb/>the circumference of a circle, that is, under the Zodiack, it is im­ <lb/>po&longs;&longs;ible that it &longs;hould, at the &longs;ame time, be in the centre of the Zo­ <lb/>diack; but that the Earth is in the &longs;aid centre <emph type="italics"/>Aristotle, Ptolomy,<emph.end type="italics"/> <lb/>and others have many wayes proved.</s></p><p type="main"><s>SALV. </s><s>You very well argue, aud there is no que&longs;tion but that <lb/>one that would make the Earth to move in the circumference of a <lb/>circle, mu&longs;t fir&longs;t of nece&longs;&longs;ity prove, that it is not in the centre of <lb/>that &longs;ame circle; it now followeth, that we enquire, whether the <lb/>Earth be, or be not in that centre, about which, I &longs;ay, that it tur­ <lb/>neth, and you &longs;ay that it is fixed; and before we &longs;peak of this, it <lb/>is likewi&longs;e nece&longs;&longs;ary that we declare our &longs;elves, whether you and I <lb/>have both the &longs;ame conceit of this centre, or no. </s><s>Therefore tell <lb/>me, what and where is this your intended centre?</s></p><p type="main"><s>SIMP. </s><s>When I &longs;peak of the centre, I mean that of the Uni­ <lb/>ver&longs;e, that of the World, that of the Starry Sphere.</s></p><p type="main"><s>SALV. </s><s>Although I might very rationally put it in di&longs;pute, whe­ <lb/>ther there be any &longs;uch centre in nature, or no; being that neither <lb/><arrow.to.target n="marg515"></arrow.to.target> <lb/>you nor any one el&longs;e hath ever proved, whether the World be fi­ <lb/>nite and figurate, or el&longs;e infinite and interminate; yet neverthele&longs;s <lb/>granting you, for the pre&longs;ent, that it is finite, and of a terminate <lb/>Spherical Figure, and that thereupon it hath its centre; it will be <lb/>requi&longs;ite to &longs;ee how credible it is that the Earth, and not rather <lb/>&longs;ome other body, doth po&longs;&longs;e&longs;&longs;e the &longs;aid centre.</s></p><p type="margin"><s><margin.target id="marg515"></margin.target><emph type="italics"/>It hath not been <lb/>hitherto proved by <lb/>any, whether the <lb/>World be finite or <lb/>infinite.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>That the world is finite, terminato, and &longs;pherical, <emph type="italics"/>Ari-<emph.end type="italics"/> <pb xlink:href="040/01/314.jpg" pagenum="294"/><emph type="italics"/>&longs;totle<emph.end type="italics"/> proveth with an hundred demon&longs;trations. <lb/><arrow.to.target n="marg516"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg516"></margin.target><emph type="italics"/>The Demon&longs;tra­ <lb/>tions of<emph.end type="italics"/> Ari&longs;totle <lb/><emph type="italics"/>to Prove that the <lb/>Vniver&longs;e is finite, <lb/>are all nullified by <lb/>denying it to be <lb/>moveable.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>All which in the end are reduced to one alone, and that <lb/>one to none at all; for if I deny his a&longs;&longs;umption, to wit, that the <lb/>Univer&longs;e is moveable, all his demon&longs;trations come to nothing, for <lb/>he onely proveth the Univer&longs;e to be finite and terminate, for that <lb/>it is moveable. </s><s>But that we may not multiply di&longs;putes, let it be <lb/>granted for once, that the World is finite, &longs;pherical, and hath <lb/>its centre. </s><s>And &longs;eeing that that centre and figure is argued from <lb/>its mobility, it will, without doubt, be very rea&longs;onable, if from the <lb/>circular motions of mundane bodies we proceed to the particular <lb/>inve&longs;tigation of that centres proper place: Nay <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf </s></p><p type="main"><s><arrow.to.target n="marg517"></arrow.to.target> <lb/>hath argued and determined in the &longs;ame manner, making that <lb/>&longs;ame to be the centre of the Univer&longs;e about which all the Cœle­ <lb/>le&longs;tial Spheres revolve, and in which he beleived the Terre&longs;trial <lb/>Globe to have been placed. </s><s>Now tell me <emph type="italics"/>Simplicius,<emph.end type="italics"/> if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/><arrow.to.target n="marg518"></arrow.to.target> <lb/>&longs;hould be con&longs;trained by evident experience to alter in part this <lb/>his di&longs;po&longs;ure and order of the Univer&longs;e, and confe&longs;&longs;e him&longs;elf to <lb/>have been deceived in one of the&longs;e two propo&longs;itions, namely, ei­ <lb/>ther in placing the Earth in the centre, or in &longs;aying, that the <lb/>Cœle&longs;tial Spheres do move about that centre, which of the two <lb/>confe&longs;&longs;ions think you would he choo&longs;e?</s></p><p type="margin"><s><margin.target id="marg517"></margin.target><emph type="italics"/>Ari&longs;totle makes <lb/>that point to be the <lb/>centre of the Uni­ <lb/>ver&longs;e about which <lb/>all the Cele&longs;tial <lb/>Spheres do revolve.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg518"></margin.target><emph type="italics"/>A que&longs;tion is <lb/>put, in ca&longs;e that <lb/>if<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>were <lb/>forced to receive <lb/>one of two propo&longs;i­ <lb/>tions that make a­ <lb/>gain&longs;t his doctrine, <lb/>which he would <lb/>admit.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I believe, that if it &longs;hould &longs;o fall out, the <emph type="italics"/>Peripate­ <lb/>ticks.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I do not ask the <emph type="italics"/>Peripateticks,<emph.end type="italics"/> I demand of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <lb/>for as to tho&longs;e, I know very well what they would reply; they, as <lb/>ob&longs;ervant and humble va&longs;&longs;als of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> would deny all the ex­ <lb/>periments and all the ob&longs;ervations in the World, nay, would al&longs;o <lb/>refu&longs;e to &longs;ee them, that they might not be forced to acknowledg <lb/>them, and would &longs;ay that the World &longs;tands as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> writeth, <lb/>and not as nature will have it, for depriving them of the &longs;hield <lb/>of his Authority, with what do you think they would appear in the <lb/>field? </s><s>Tell me therefore what you are per&longs;waded <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him­ <lb/>&longs;elf would do in the ca&longs;e.</s></p><p type="main"><s>SIMP. </s><s>To tell you the truth, I know not how to re&longs;olve <lb/>which of the two inconveniences is to be e&longs;teemed the le&longs;&longs;er.</s></p><p type="main"><s>SALV. </s><s>Apply not I pray you this term of inconvenience to a <lb/>thing which po&longs;&longs;ibly may of nece&longs;&longs;ity be &longs;o. </s><s>It was an inconveni­ <lb/>ence to place the Earth in the centre of the Cœle&longs;tial revolutions; <lb/>but &longs;eeing you know not to which part he would incline, I e­ <lb/>&longs;teeming him to be a man of great judgment, let us examine <lb/>which of the two choices is the more rational, and that we will <lb/>hold that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> would have received. </s><s>Rea&longs;&longs;uming therefore our <lb/>di&longs;cour&longs;e from the beginning, we &longs;uppo&longs;e with the good liking of <lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that the World (of the magnitude of which we have <lb/>no &longs;en&longs;ible notice beyond the fixed &longs;tars) as being of a &longs;pherical <pb xlink:href="040/01/315.jpg" pagenum="295"/>figure; and moveth circularly, hath nece&longs;&longs;arily, and in re&longs;pect of <lb/>its figure a centre; and we being moreover certain, that within <lb/>the &longs;tarry Sphere there are many Orbs, the one within another, <lb/>with their &longs;tars, which likewi&longs;e do move circulary, it is in di&longs;pute <lb/>whether it is mo&longs;t rea&longs;onable to believe and to &longs;ay that the&longs;e con­ <lb/>teined Orbs do move round the &longs;aid centre of the World, or el&longs;e <lb/>about &longs;ome other centre far remote from that? </s><s>Tell me now <emph type="italics"/>Sim­ <lb/>plicius<emph.end type="italics"/> what you think concerning this particular.</s></p><p type="main"><s>SIMP. </s><s>If we could &longs;tay upon this onely &longs;uppo&longs;ition, and that <lb/><arrow.to.target n="marg519"></arrow.to.target> <lb/>we were &longs;ure that we might encounter nothing el&longs;e that might di­ <lb/>&longs;turb us, I would &longs;ay that it were much more rea&longs;onable to af­ <lb/>firm that the Orb containing, and the parts contained, do all <lb/>move about one common centre, than about divers.</s></p><p type="margin"><s><margin.target id="marg519"></margin.target><emph type="italics"/>Its more ratio­ <lb/>nal that the Orb <lb/>conteining, and the <lb/>parts conteined, do <lb/>move all about one <lb/>centre, than uoon <lb/>divers.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Now if it were true that the centre of the World is the <lb/><arrow.to.target n="marg520"></arrow.to.target> <lb/>&longs;ame about which the Orbs of mundane bodies, that is to &longs;ay, of <lb/>the Planets, move, it is mo&longs;t certain that it is not the Earth, but <lb/>the Sun rather that is fixed in the centre of the World. </s><s>So that as <lb/>to this fir&longs;t &longs;imple and general apprehen&longs;ion, the middle place <lb/>belongeth to the Sun, and the Earth is as far remote from the <lb/>centre, as it is from that &longs;ame Sun.</s></p><p type="margin"><s><margin.target id="marg520"></margin.target><emph type="italics"/>If the centre of <lb/>the World be the <lb/>&longs;ame with that a­ <lb/>bout which the via­ <lb/>nees move the Sun <lb/>and not the Earth <lb/>is placed in it.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>But from whence do you argue that not the Earth, but <lb/>the Sun is in the centre of the Planetary revolutions?</s></p><p type="main"><s>SALV. </s><s>I infer the &longs;ame from mo&longs;t evident, and therefore ne­ <lb/>ce&longs;&longs;arily concludent ob&longs;ervations, of which the mo&longs;t palpable to <lb/><arrow.to.target n="marg521"></arrow.to.target> <lb/>exclude the Earth from the &longs;aid centre, and to place the Sun <lb/>therein, are, the &longs;eeing all the Planets one while neerer and ano­ <lb/>ther while farther off from the Earth with &longs;o great differences, that <lb/>for example, <emph type="italics"/>Venus<emph.end type="italics"/> when it is at the farthe&longs;t, is &longs;ix times more <lb/>remote from us, than when it is neere&longs;t, and <emph type="italics"/>Mars<emph.end type="italics"/> ri&longs;eth almo&longs;t <lb/>eight times as high at one time as at another. </s><s>See therefore whe­ <lb/>ther <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> was not &longs;omewhat mi&longs;taken in thinking that it was <lb/>at all times couidi&longs;tant from us.</s></p><p type="margin"><s><margin.target id="marg521"></margin.target><emph type="italics"/>Ob&longs;ervations from <lb/>whence it is col­ <lb/>lected that the Sun <lb/>and not the Earth <lb/>is in the centre of <lb/>the Cele&longs;tial revo­ <lb/>lutions.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>What in the next place are the tokens that their moti­ <lb/>ons are about the Sun?</s></p><p type="main"><s>SALV. </s><s>It is argued in the three &longs;uperiour planets <emph type="italics"/>Mars, Jupi­ <lb/>ter,<emph.end type="italics"/> and <emph type="italics"/>Saturn,<emph.end type="italics"/> in that we find them alwayes neere&longs;t to the <lb/>Earth when they are in oppo&longs;ition to the Sun, and farthe&longs;t off <lb/>when they are towards the conjunction, and this approximatian <lb/>and rece&longs;&longs;ion importeth thus much that <emph type="italics"/>Mars<emph.end type="italics"/> neer at hand, ap­ <lb/>peareth very neer 60 times greater than when it is remote. </s><s>As to <lb/><arrow.to.target n="marg522"></arrow.to.target> <lb/><emph type="italics"/>Venus<emph.end type="italics"/> in the next place, and to <emph type="italics"/>Mercury,<emph.end type="italics"/> we are certain that <lb/>they revolve about the Sun, in that they never move far from <lb/>him, and in that we &longs;ee them one while above and another while <lb/><arrow.to.target n="marg523"></arrow.to.target> <lb/>below it, as the mutations of figure in <emph type="italics"/>Venus<emph.end type="italics"/> nece&longs;&longs;arily argueth. <lb/></s><s>Tonchiug the Moon it is certain, that &longs;he cannot in any way <pb xlink:href="040/01/316.jpg" pagenum="296"/>&longs;eperate from the Earth, for the rea&longs;ons that &longs;hall be more di&longs;tinct­ <lb/>ly alledged hereafter.</s></p><p type="margin"><s><margin.target id="marg522"></margin.target><emph type="italics"/>The mutation <lb/>of figure in<emph.end type="italics"/> Venus <lb/><emph type="italics"/>argueth its motion <lb/>to be about the Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg523"></margin.target><emph type="italics"/>The Moon can­ <lb/>not &longs;eperate from <lb/>the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I expect that I &longs;hall hear more admirable things that <lb/>depend upon this annual motion of the Earth, than were tho&longs;e <lb/>dependant upon the diurnal revolution. <lb/><arrow.to.target n="marg524"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg524"></margin.target><emph type="italics"/>The annual mo­ <lb/>tion of the Earth <lb/>mixing with the <lb/>motions of the o­ <lb/>ther Planets pro­ <lb/>duce extravagant <lb/>appearances.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You do not therein erre: For as to the operation of <lb/>the diurnal motion upon the Cele&longs;tial bodies, it neither was, nor <lb/>can be other, than to make the Univer&longs;e &longs;eem to run precipitately <lb/>the contrary way; but this annual motion intermixing with the <lb/>particular motions of all the planets, produceth very many ex­ <lb/>travagancies, which have di&longs;armed and non-plu&longs;t all the greate&longs;t <lb/>Scholars in the World. </s><s>But returning to our fir&longs;t general appre­ <lb/>hen&longs;ions, I reply that the centre of the Cele&longs;tial conver&longs;ions of <lb/>the five planets <emph type="italics"/>Saturn, Jupiter, Mars, Venus<emph.end type="italics"/> and <emph type="italics"/>Mercury,<emph.end type="italics"/> is <lb/>the Sun; and &longs;hall be likewi&longs;e the centre of the motion of the <lb/>Earth, if we do but &longs;ucceed in our attempt of placing it in Hea­ <lb/>ven. </s><s>And as for the Moon, this hath a circular motion about the <lb/>Earth, from which (as I &longs;aid before) it can by no means alienate <lb/>it &longs;elf, but yet doth it not cea&longs;e to go about the Sun together with <lb/>the Earth in an annual motion.</s></p><p type="main"><s>SIMP. </s><s>I do not as yet very well apprehend this &longs;tructure, but <lb/>it may be, that with making a few draughts thereof, one may bet­ <lb/>ter and more ea&longs;ily di&longs;cour&longs;e concerning the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>Tis very true: yea for your greater &longs;atisfaction and ad­ <lb/>miration together, I de&longs;ire you, that you would take the pains <lb/>to draw the &longs;ame; and to &longs;ee that although you think you do not <lb/>apprehend it, yet you very perfectly under&longs;tand it; And onely <lb/>by an&longs;wering to my interrogations you &longs;hall de&longs;igne it punctually. </s></p><p type="main"><s><arrow.to.target n="marg525"></arrow.to.target> <lb/>Take therefore a &longs;heet of paper and Compa&longs;les; And let this <lb/>white paper be the immen&longs;e expan&longs;ion of the Univer&longs;e; in which <lb/>you are to di&longs;tribute and di&longs;po&longs;e its parts in order, according as <lb/>rea&longs;on &longs;hall direct you. </s><s>And fir&longs;t, in regard that without my in­ <lb/>&longs;truction you verily believe that the Earth is placed in this Uni­ <lb/>ver&longs;e, therefore note a point at plea&longs;ure, about which you in­ <lb/>tend it to to be placed, and mark it with &longs;ome characters.</s></p><p type="margin"><s><margin.target id="marg525"></margin.target><emph type="italics"/>The Sy&longs;teme of <lb/>the Univer&longs;e de­ <lb/>&longs;igned from the ap­ <lb/>pearances.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Let this mark A be the place of the Terre&longs;trial Globe.</s></p><p type="main"><s>SALV. </s><s>Very well. </s><s>I know &longs;econdly, that you under&longs;tand per­ <lb/>fectly that the &longs;aid Earth is not within the body of the Sun, nor <lb/>&longs;o much as contiguous to it, but di&longs;tant for &longs;ome &longs;pace from the <lb/>&longs;ame, and therefore a&longs;&longs;ign to the Sun what other place you be&longs;t <lb/>like, as remote from the Earth as you plea&longs;e, and mark this in <lb/>like manner.</s></p><p type="main"><s>SIMP. </s><s>Here it is done: Let the place of the Solar body <lb/>be O.</s></p><p type="main"><s>SALV. </s><s>The&longs;e two being con&longs;tituted, I de&longs;ire that we may <pb xlink:href="040/01/317.jpg" pagenum="297"/>think of accomodating the body of <emph type="italics"/>Venus<emph.end type="italics"/> in &longs;uch a manner that <lb/>its &longs;tate and motion may agree with what &longs;en&longs;ible experiments do <lb/>&longs;hew us; and therefore recall to mind that. </s><s>which either by the <lb/>pa&longs;t di&longs;cour&longs;es, or your own ob&longs;ervations you have learnt to be­ <lb/>fal that &longs;tar, and afterwards a&longs;&longs;ign unto it that &longs;tate which you <lb/>think agreeth with the &longs;ame.</s></p><p type="main"><s>SIMP. </s><s>Suppo&longs;ing tho&longs;e <emph type="italics"/>Phænomena<emph.end type="italics"/> expre&longs;&longs;ed by you, and <lb/>which I have likewi&longs;e read in the little treati&longs;e of Conclu&longs;ions, to <lb/><figure id="id.040.01.317.1.jpg" xlink:href="040/01/317/1.jpg"/> <lb/>be true, namely, that that &longs;tar never recedes from the Sun beyond <lb/>&longs;uch a determinate &longs;pace of 40 degrees or thereabouts, &longs;o as that <lb/>it never cometh either to appo&longs;ition with the Sun, or &longs;o much as <lb/>to quadrature, or yet to the &longs;extile a&longs;pect; and more than that, <lb/><arrow.to.target n="marg526"></arrow.to.target> <lb/>&longs;uppo&longs;ing that it &longs;heweth at one time almo&longs;t 40 times greater than <lb/>at another; namely, very great, when being retrograde, it goeth to <lb/>the ve&longs;pertine conjnnction of the Sun, and very &longs;mall when with a <pb xlink:href="040/01/318.jpg" pagenum="298"/>motion &longs;traight forwards, it goeth to the matutine conjunction; <lb/>and moreover it being true, that when it appeareth bigge it &longs;hews <lb/>with a corniculate figure, and when it appeareth little, it &longs;eems <lb/>perfectly round, the&longs;e appearances, I &longs;ay, being true, I do not &longs;ee <lb/>how one can choo&longs;e but affirm the &longs;aid &longs;tar to revolve in a circle a­ <lb/><arrow.to.target n="marg527"></arrow.to.target> <lb/>bout the Sun, for that the &longs;aid circle cannot in any wi&longs;e be &longs;aid <lb/>to encompa&longs;&longs;e or to contain the Earth within it, nor to be inferi­ <lb/>our to the Sun, that is between it and the Earth, nor yet &longs;upe­ <lb/>riour to the Sun. </s><s>That circle cannot incompa&longs;&longs;e the Earth, be­ <lb/>cau&longs;e <emph type="italics"/>Venus<emph.end type="italics"/> would then &longs;ometimes come to oppofition with the <lb/>Sun; it cannot be inferiour, for then <emph type="italics"/>Venus<emph.end type="italics"/> in both its conjuncti­ <lb/>ons with the Sun would &longs;eem horned; nor can it be &longs;uperiour, <lb/>for then it would alwayes appear round, and never cornicular; <lb/>and therefore for receit of it I will draw the circle CH, about <lb/>the Sun, without encompa&longs;&longs;ing the Earth.</s></p><p type="margin"><s><margin.target id="marg526"></margin.target>Venus <emph type="italics"/>very greas <lb/>towards the re&longs;pe­ <lb/>ctive conjunction <lb/>and very &longs;mall to­ <lb/>wards the matu­ <lb/>tine.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg527"></margin.target>Venus <emph type="italics"/>nece&longs;&longs;a­ <lb/>rily proved to move <lb/>about the Sun.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Having placed <emph type="italics"/>Venus,<emph.end type="italics"/> it is requi&longs;ite that you think of <lb/><emph type="italics"/>Mercury,<emph.end type="italics"/> which, as you know, alwayes keeping about the Sun, <lb/>doth recede le&longs;&longs;e di&longs;tance from it than <emph type="italics"/>Venus<emph.end type="italics"/>; therefore con&longs;ider <lb/>with your &longs;elf, what place is mo&longs;t convenient to a&longs;&longs;ign it. <lb/><arrow.to.target n="marg528"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg528"></margin.target><emph type="italics"/>The revolution of<emph.end type="italics"/> <lb/>Mercury <emph type="italics"/>concluded <lb/>to be about the Sun, <lb/>within the Orb of<emph.end type="italics"/> <lb/>Venus.</s></p><p type="main"><s>SIMP. </s><s>It is not to be que&longs;tioned, but that this Planet imitat­ <lb/>ing <emph type="italics"/>Venus,<emph.end type="italics"/> the mo&longs;t commodious place for it will be, a le&longs;&longs;er cir­ <lb/>cle within this of <emph type="italics"/>Venus,<emph.end type="italics"/> in like manner about the Sun, being <lb/>that of its greate&longs;t vicinity to the Sun, an argument, an evidence <lb/>&longs;ufficiently proving the vigour of its illumination, above that of <lb/><emph type="italics"/>Venus,<emph.end type="italics"/> and of the other Planets, we may therefore upon the&longs;e <lb/>con&longs;iderations draw its Circle, marking it with the Characters <lb/>BG.</s></p><p type="main"><s><arrow.to.target n="marg529"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg529"></margin.target>Mars <emph type="italics"/>nece&longs;&longs;arily <lb/>includeth within its <lb/>Orb the Earth, and <lb/>al&longs;o the Sun.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>But <emph type="italics"/>Mars,<emph.end type="italics"/> Where &longs;hall we place it?</s></p><p type="main"><s>SIMP. <emph type="italics"/>Mars,<emph.end type="italics"/> Becau&longs;e it comes to an oppo&longs;ition with the Sun, <lb/>its Circle mu&longs;t of nece&longs;&longs;ity encompa&longs;s the Earth; But I &longs;ee that it <lb/>mu&longs;t nece&longs;&longs;arily encompa&longs;s the Sun al&longs;o, for coming to conjuncti­ <lb/>on with the Sun, if it did not move over it, but were below it, it <lb/>would appear horned, as <emph type="italics"/>Venus<emph.end type="italics"/> and the Moon; but it &longs;hews al­ <lb/>wayes round, and therefore it is nece&longs;&longs;ary, that it no le&longs;s includ­</s></p><p type="main"><s><arrow.to.target n="marg530"></arrow.to.target> <lb/>eth the Sun within its circle than the Earth. </s><s>And becau&longs;e I re­ <lb/>member that you did &longs;ay, that when it is in oppo&longs;ition with the <lb/>Sun, it &longs;eems 60 times bigger than when it is in the conjunction, <lb/>me thinks that a Circle about the Centre of the Sun, and that tak­ <lb/>eth in the earth, will very well agree with the&longs;e <emph type="italics"/>Phænomena,<emph.end type="italics"/> <lb/>which I do note and mark D I, where <emph type="italics"/>Mars<emph.end type="italics"/> in the point D, is near <lb/>to the earth, and oppo&longs;ite to the Sun; but when it is in the point <lb/>I, it is at Conjuction with the Sun, but very far from the Earth. <lb/><arrow.to.target n="marg531"></arrow.to.target> <lb/>And becau&longs;e the &longs;ame appearances are ob&longs;erved in <emph type="italics"/>Jupiter<emph.end type="italics"/> and <lb/><emph type="italics"/>Saturn,<emph.end type="italics"/> although with much le&longs;&longs;er difference in <emph type="italics"/>Jupiter<emph.end type="italics"/> than in <lb/><emph type="italics"/>Mars,<emph.end type="italics"/> and with yet le&longs;&longs;e in <emph type="italics"/>Saturn<emph.end type="italics"/> than in <emph type="italics"/>Jupiter<emph.end type="italics"/>; me thinks I <pb xlink:href="040/01/319.jpg" pagenum="299"/>under&longs;tand that we &longs;hould very commodiou&longs;ly &longs;alve all the <emph type="italics"/>Phæ­ <lb/>nomena<emph.end type="italics"/> of the&longs;e two Planets, with two Circles, in like manner, <lb/>drawn about the Sun, and this fir&longs;t for <emph type="italics"/>Jupiter,<emph.end type="italics"/> marking it E L, and <lb/>another above that for <emph type="italics"/>Saturn<emph.end type="italics"/> marked F M. <lb/><arrow.to.target n="marg532"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg530"></margin.target>Mars <emph type="italics"/>at its oppo­ <lb/>&longs;ition to the Sun <lb/>&longs;hews to be &longs;ixty <lb/>times bigger than <lb/>towards the con­ <lb/>junction.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg531"></margin.target>Jupiter <emph type="italics"/>and<emph.end type="italics"/> Sa­ <lb/>turn <emph type="italics"/>do likewi&longs;e en­ <lb/>compa&longs;&longs;e the Earth, <lb/>and the Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg532"></margin.target><emph type="italics"/>The approxima­ <lb/>tion and rece&longs;&longs;ion of <lb/>the three &longs;uperiour <lb/>Planets, importeth <lb/>double the Suns di­ <lb/>&longs;tance.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You have behaved your &longs;elf bravely hitherto. </s><s>And <lb/>becau&longs;e (as you &longs;ee) the approach and rece&longs;&longs;ion of the three Su­ <lb/>periour Planets is mea&longs;ured with double the di&longs;tance between the <lb/>Earth and Sun, this maketh greater difference in <emph type="italics"/>Mars<emph.end type="italics"/> than in <emph type="italics"/>Ju-<emph.end type="italics"/></s></p><p type="main"><s><arrow.to.target n="marg533"></arrow.to.target> <lb/><emph type="italics"/>piter,<emph.end type="italics"/> the Circle D I, of <emph type="italics"/>Mars,<emph.end type="italics"/> being le&longs;&longs;er than the Circle E L, <lb/>of <emph type="italics"/>Jupiter,<emph.end type="italics"/> and likewi&longs;e becau&longs;e this E L, is le&longs;&longs;e than this Circle <lb/>F M, of <emph type="italics"/>Saturn,<emph.end type="italics"/> the &longs;aid difference is al&longs;o yet le&longs;&longs;er in <emph type="italics"/>Saturn<emph.end type="italics"/> than <lb/>in <emph type="italics"/>Jupiter,<emph.end type="italics"/> and that punctually an&longs;wereth the <emph type="italics"/>Phænomena.<emph.end type="italics"/> <lb/>It remains now that you a&longs;&longs;ign a place to the Moon.</s></p><p type="margin"><s><margin.target id="marg533"></margin.target><emph type="italics"/>The difference of <lb/>the apparent mag­ <lb/>nitude le&longs;&longs;e in<emph.end type="italics"/> Sa­ <lb/>turn, <emph type="italics"/>than in<emph.end type="italics"/> Jupi­ <lb/>ter, <emph type="italics"/>an dn<emph.end type="italics"/> Jupiter <lb/><emph type="italics"/>than in<emph.end type="italics"/> Mars, <emph type="italics"/>and <lb/>why.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Following the &longs;ame Method (which &longs;eems to me very <lb/><arrow.to.target n="marg534"></arrow.to.target> <lb/>conclu&longs;ive) in regard we &longs;ee that the Moon cometh to conjunction <lb/>and oppo&longs;ition with the Sun, it is nece&longs;&longs;ary to &longs;ay, that its circle <lb/>encompa&longs;&longs;eth the Earth, but yet doth it not follow, that it mu&longs;t <lb/>environ the Sun, for then at that time towards its conjunction, it <lb/>would not &longs;eem horned, but alwayes round and full of Light. <lb/></s><s>Moreover it could never make, as it often doth, the Eclip&longs;e of the <lb/>Sun, by interpo&longs;ing betwixt it and us; It is nece&longs;&longs;ary therefore <lb/>to a&longs;&longs;ign it a circle about the Earth, which &longs;hould be this N P, &longs;o <lb/>that being con&longs;tituted in P, it will appear from the Earth A, to be <lb/>in conjunction with the Sun, and placed in N, it appeareth oppo&longs;ite <lb/>to the Sun, and in that po&longs;ition it may fall under the Earths &longs;ha­ <lb/>dow, and be ob&longs;cured.</s></p><p type="margin"><s><margin.target id="marg534"></margin.target><emph type="italics"/>The Moons Orb <lb/>invironeth the <lb/>Earth, but not the <lb/>Sun.<emph.end type="italics"/></s></p><p type="main"><s>SALV. Now, <emph type="italics"/>Simplicius,<emph.end type="italics"/> what &longs;hall we do with the fixed <lb/>&longs;tars? </s><s>Shall we &longs;uppo&longs;e them &longs;cattered through the immen&longs;e abi&longs;­ <lb/>&longs;es of the Univer&longs;e, at different di&longs;tances, from any one determi­ <lb/>nate point; or el&longs;e placed in a &longs;uperficies &longs;pherically di&longs;tended a­ <lb/>bout a centre of its own, &longs;o that each of them may be equi­ <lb/>di&longs;tant from the &longs;aid centre? <lb/><arrow.to.target n="marg535"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg535"></margin.target><emph type="italics"/>The probable <lb/>&longs;ituation of the <lb/>fixed &longs;tars.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I would rather take a middle way; and would a&longs;&longs;ign <lb/>them an Orb de&longs;cribed about a determinate centre and comprized <lb/>within two &longs;pherical &longs;uperficies, to wit, one very high, and con­ <lb/>cave, and the other lower, and convex, betwixt which I would </s></p><p type="main"><s><arrow.to.target n="marg536"></arrow.to.target> <lb/>con&longs;titute the innumerable multitude of &longs;tars, but yet at divers al­ <lb/>titudes, and this might be called the Sphere of the Univer&longs;e, contein­ <lb/>ing within it the Orbs of the planets already by us de&longs;cribed.</s></p><p type="margin"><s><margin.target id="marg536"></margin.target><emph type="italics"/>Which ought to <lb/>be accounted the <lb/>&longs;phere of the Vm­ <lb/>ver&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>But now we have all this while, <emph type="italics"/>Simplicius,<emph.end type="italics"/> di&longs;po&longs;ed the <lb/>mundane bodies exactly, according to the order of <emph type="italics"/>Copernicus,<emph.end type="italics"/> <lb/>and we have done it with your hand; and moreover to each of <lb/>them you have a&longs;&longs;igned peculiar motions of their own, except to <lb/>the Sun, the Earth, and &longs;tarry Sphere; and to <emph type="italics"/>Mercury<emph.end type="italics"/> with <lb/><emph type="italics"/>Venus,<emph.end type="italics"/> you have a&longs;cribed the circular motion about the Sun, <pb xlink:href="040/01/320.jpg" pagenum="300"/>without encompa&longs;&longs;ing the Earth; about the &longs;ame Sun you make <lb/>the three &longs;uperiour Planets <emph type="italics"/>Mars, Jupiter,<emph.end type="italics"/> and <emph type="italics"/>Saturn,<emph.end type="italics"/> to move, <lb/>comprehending the Earth within their circles. </s><s>The Moon in the <lb/>next place can move in no other manner than about the Earth, <lb/>without taking in the Sun, and in all the&longs;e motions you agree al&longs;o <lb/>with the &longs;ame <emph type="italics"/>Copernicus.<emph.end type="italics"/> There remains now three things to be <lb/>decided between the Sun, the Earth, and fixed &longs;tars, namely, <lb/><arrow.to.target n="marg537"></arrow.to.target> <lb/>Re&longs;t, which &longs;eemeth to belong to the Earth; the annual motion <lb/>under the Zodiack, which appeareth to pertain to the Sun; and the <lb/>diurnal motion, which &longs;eems to belong to the Starry Sphere, and <lb/>to be by that imparted to all the re&longs;t of the Univer&longs;e, the Earth <lb/>excepted, And it being true that all the Orbs of the Planets, I <lb/><arrow.to.target n="marg538"></arrow.to.target> <lb/>mean of <emph type="italics"/>Mercury, Venus, Mars, Jupiter,<emph.end type="italics"/> and <emph type="italics"/>Saturn,<emph.end type="italics"/> do move <lb/>about the Sun as their centre; re&longs;t &longs;eemeth with &longs;o much more <lb/>rea&longs;on to belong to the &longs;aid Sun, than to the Earth, in as much <lb/>as in a moveable Sphere, it is more rea&longs;onable that the centre <lb/>&longs;tand &longs;till, than any other place remote from the &longs;aid centre; to <lb/>the Earth therefore, which is con&longs;tituted in the mid&longs;t of move­ <lb/>able parts of the Univer&longs;e, I mean between <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mars,<emph.end type="italics"/> one <lb/>of which maketh its revolution in nine moneths, and the other in <lb/>two years, may the motion of a year very commodiou&longs;ly be a&longs;­ <lb/><arrow.to.target n="marg539"></arrow.to.target> <lb/>&longs;igned, leaving re&longs;t to the Sun. </s><s>And if that be &longs;o, it followeth <lb/>of nece&longs;&longs;ary con&longs;equence, that likewi&longs;e the diurnal motion be­ <lb/>longeth to the Earth; for, if the Sun &longs;tanding &longs;till, the Earth <lb/>&longs;hould not revolve about its &longs;elf, but have onely the annual mo­ <lb/>tion about the Sun, our year would be no other than one day and <lb/>one night, that is &longs;ix moneths of day, and &longs;ix moneths of night, <lb/>as hath already been &longs;aid. </s><s>You may con&longs;ider withal how commo­ <lb/>diou&longs;ly the precipitate motion of 24 hours is taken away from <lb/>the Univer&longs;e, and the fixed &longs;tars that are &longs;o many Suns, are made <lb/>in conformity to our Sun to enjoy a perpetual re&longs;t. </s><s>You &longs;ee more­ <lb/>over what facility one meets with in this rough draught to render <lb/>the rea&longs;on of &longs;o great appearances in the Cele&longs;tial bodies.</s></p><p type="margin"><s><margin.target id="marg537"></margin.target><emph type="italics"/>Re&longs;t, the annual <lb/>motion and the di­ <lb/>urnal ought to be <lb/>di&longs;tributed be­ <lb/>twixt the Sun, <lb/>Earth, and Fir­ <lb/>mament.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg538"></margin.target><emph type="italics"/>In a moveable <lb/>&longs;phere, it &longs;eemeth <lb/>more vea&longs;onable <lb/>that its centre be <lb/>&longs;table, than any o­ <lb/>ther of its parts.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg539"></margin.target><emph type="italics"/>Granting to the <lb/>Earth the annual, <lb/>it mu&longs;t of nece&longs;&longs;ity <lb/>al&longs;o have the diur­ <lb/>nal motion a&longs;&longs;ign­ <lb/>ed to it.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I very well perceive that facility, but as you from this <lb/>&longs;implicity collect great probabilities for the truth of that Sy&longs;tem, <lb/>others haply could make thence contrary deductions; doubting, <lb/>not without rea&longs;on, why that &longs;ame being the ancient Sy&longs;teme of <lb/><emph type="italics"/>Pythagoreans,<emph.end type="italics"/> and &longs;o well accommodated to the <emph type="italics"/>Phænomena,<emph.end type="italics"/> <lb/>hath in the &longs;ucce&longs;&longs;ion of &longs;o many thou&longs;and years had &longs;o few fol­ <lb/>lowers, and hath been even by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf refuted, and <lb/>&longs;ince that <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf hath had no better fortune.</s></p><p type="main"><s>SALV. </s><s>If you had at any time been a&longs;&longs;aulted, as I have been, <lb/>many and many a time, with the relation of &longs;uch kind of frivolous <lb/>rea&longs;ons, as &longs;erve to make the vulgar contumacious, and difficult to <lb/>be per&longs;waded to hearken, (I will not &longs;ay to con&longs;ent) to this novel­ <pb xlink:href="040/01/321.jpg" pagenum="301"/>ty, I believe that you wonder at the paucity of tho&longs;e who are fol­ <lb/>lowers of that opinion would be much dimini&longs;hed. </s><s>But &longs;mall re­ <lb/><arrow.to.target n="marg540"></arrow.to.target> <lb/>gard in my judgement, ought to be had of &longs;uch thick &longs;culs, as think <lb/>it a mo&longs;t convincing proof to confirm, and &longs;teadfa&longs;tly &longs;ettle them <lb/>in the belief of the earths immobility, to &longs;ee that if this day they <lb/>cannot Dine at <emph type="italics"/>Con&longs;tantinople,<emph.end type="italics"/> nor Sup in <emph type="italics"/>Jappan,<emph.end type="italics"/> that then the <lb/>Earth as being a mo&longs;t grave body cannot clamber above the Sun, <lb/>and then &longs;lide headlong down again; Of &longs;uch as the&longs;e I &longs;ay, <lb/>who&longs;e number is infinite, we need not make any reckoning, nor <lb/>need we to record their foolieries, or to &longs;trive to gain to our &longs;ide <lb/>as our partakers in &longs;ubtil and &longs;ublime opinions, men in who&longs;e de­ <lb/>finition the kind onely is concerned, and the difference is wanting. <lb/></s><s>Moreover, what ground do you think you could be able to gain, <lb/>with all the demon&longs;trations of the World upon brains &longs;o &longs;tupid, <lb/>as are not able of them&longs;elves to know their down right follies? </s><s>But <lb/>my admiration, <emph type="italics"/>Sagredus,<emph.end type="italics"/> is very different from yours, you won­ <lb/>der that &longs;o few are followers of the <emph type="italics"/>Pythagorean<emph.end type="italics"/> Opinion; and I <lb/>am amazed how there could be any yet left till now that do em­ <lb/>brace and follow it: Nor can I &longs;ufficiently admire the eminencie of <lb/><arrow.to.target n="marg541"></arrow.to.target> <lb/>tho&longs;e mens wits that have received and held it to be true, and with <lb/>the &longs;prightline&longs;&longs;e of their judgements offered &longs;uch violence to their <lb/>own &longs;ences, as that they have been able to prefer that which their <lb/>rea&longs;on dictated to them, to that which &longs;en&longs;ible experiments re­ <lb/>pre&longs;ented mo&longs;t manife&longs;tly on the contrary. </s><s>That the rea&longs;ons again&longs;t <lb/>the Diurnal virtiginous revolution of the Earth by you already ex­ <lb/>amined, do carry great probability with them, we have already <lb/>&longs;een; as al&longs;o that the <emph type="italics"/>Ptolomaicks,<emph.end type="italics"/> and <emph type="italics"/>Ari&longs;totelicks,<emph.end type="italics"/> with all their <lb/>Sectators did receive them for true, is indeed a very great argument <lb/>of their efficacie; but tho&longs;e experiments which apertly contradict <lb/>the annual motion, are of yet &longs;o much more manife&longs;tly repugnant, <lb/><arrow.to.target n="marg542"></arrow.to.target> <lb/>that (I &longs;ay it again) I cannot find any bounds for my admiration, <lb/>how that rea&longs;on was able in <emph type="italics"/>Ari&longs;tarchus<emph.end type="italics"/> and <emph type="italics"/>Copernicus,<emph.end type="italics"/> to com­ <lb/>mìt &longs;uch a rape upon their Sences, as in de&longs;pight thereof, to make <lb/>her &longs;elf mi&longs;tre&longs;s of their credulity.</s></p><p type="margin"><s><margin.target id="marg540"></margin.target><emph type="italics"/>Di&longs;cour&longs;es more <lb/>than childi&longs;h, &longs;erve <lb/>to keep fools in the <lb/>opinion of the <lb/>Earths &longs;tability.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg541"></margin.target><emph type="italics"/>A declaration <lb/>of the improbabi­ <lb/>lity of<emph.end type="italics"/> Copernicus <lb/><emph type="italics"/>his opinion.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg542"></margin.target><emph type="italics"/>Rea&longs;ons and di&longs;­ <lb/>cour&longs;e in<emph.end type="italics"/> Ari&longs;tar­ <lb/>cus <emph type="italics"/>and<emph.end type="italics"/> Coperni­ <lb/>cus <emph type="italics"/>prevailed over <lb/>manife&longs;t &longs;ence.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Are we then to have &longs;till more of the&longs;e &longs;trong oppo&longs;iti­ <lb/>ons again&longs;t this annual motion?</s></p><p type="main"><s>SALV. </s><s>We are, and they be &longs;o evident and &longs;en&longs;ible, that if a <lb/>&longs;ence more &longs;ublime and excellent than tho&longs;e common and vulgar, <lb/>did not take part with rea&longs;on, I much fear, that I al&longs;o &longs;hould have <lb/>been much more aver&longs;e to the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teem than I have been <lb/>&longs;ince the time that a clearer lamp than ordinary hath enlightned <lb/>me.</s></p><p type="main"><s>SAGR. </s><s>Now therefore <emph type="italics"/>Salviatus,<emph.end type="italics"/> let us come to joyn battail <lb/>for every word that is &longs;pent on any thing el&longs;e, I take to be ca&longs;t a­ <lb/>way.</s></p> <pb xlink:href="040/01/322.jpg" pagenum="302"/><p type="main"><s>SALV. </s><s>I am ready to &longs;erve you. </s><s>You have already &longs;een me <lb/>draw the form of the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme; again&longs;t the truth of <lb/><arrow.to.target n="marg543"></arrow.to.target> <lb/>which <emph type="italics"/>Mars<emph.end type="italics"/> him&longs;elf, in the fir&longs;t place, makes an hot charge; who, in <lb/>ca&longs;e it were true, that its di&longs;tances from the earth &longs;hould &longs;o much <lb/>vary, as that from the lea&longs;t di&longs;tance to the greate&longs;t, there were <lb/>twice as much difference, as from the earth to the Sun; it would be <lb/>nece&longs;&longs;ary, that when it is neare&longs;t unto us, its <emph type="italics"/>di&longs;cus<emph.end type="italics"/> would &longs;hew <lb/>more than 60. times bigger than it &longs;eems, when it is farthe&longs;t from <lb/>us; neverthele&longs;s that diver&longs;ity of apparent magnitude is not to be <lb/>&longs;een, nay in its oppo&longs;ition with the Sun, when its neare&longs;t to the <lb/>Earth, it doth not &longs;hew &longs;o much as quadruple and quintuple in <lb/>bigne&longs;s, to what it is, when towards the conjunction it cometh to <lb/>be occulted under the Suns rayes. </s><s>Another and greater difficulty <lb/>doth <emph type="italics"/>Venus<emph.end type="italics"/> exhibit; For if revolving about the Sun, as <emph type="italics"/>Copernicus<emph.end type="italics"/> <lb/><arrow.to.target n="marg544"></arrow.to.target> <lb/>affirmeth, it were one while above, & another while below the &longs;ame, <lb/>receding and approaching to us &longs;o much as the Diameter of the cir­ <lb/>cle de&longs;cribed would be, at &longs;uch time as it &longs;hould be below the Sun, <lb/>and neare&longs;t to us, its <emph type="italics"/>di&longs;cus<emph.end type="italics"/> would &longs;hew little le&longs;s than 40 times big­ <lb/>ger than when it is above the Sun, near to its other conjunction; yet <lb/>neverthele&longs;&longs;e, the difference is almo&longs;t imperceptible Let us add an­ <lb/><arrow.to.target n="marg545"></arrow.to.target> <lb/>other difficulty, that in ca&longs;e the body of <emph type="italics"/>Venus<emph.end type="italics"/> be of it &longs;elf dark, and <lb/>onely &longs;hineth as the Moon, by the illumination of the Sun, which <lb/>&longs;eemeth mo&longs;t rea&longs;onable; it would &longs;hew forked or horned at &longs;uch <lb/>time as it is under the Sun, as the Moon doth when &longs;he is in like <lb/>manner near the Sun; an accident that is not to be di&longs;covered in <lb/>her. </s><s>Whereupon <emph type="italics"/>Copernicus<emph.end type="italics"/> affirmeth, that either &longs;he is light of <lb/><arrow.to.target n="marg546"></arrow.to.target> <lb/>her &longs;elf, or el&longs;e that her &longs;ub&longs;tance is of &longs;uch a nature, that it can <lb/>imbue the Solar light, and tran&longs;mit the &longs;ame through all its whole <lb/>depth, &longs;o as to be able to appear to us alwayes &longs;hining; and in this <lb/>manner <emph type="italics"/>Copernicus<emph.end type="italics"/> excu&longs;eth the not changing figure in <emph type="italics"/>Venus<emph.end type="italics"/>: but <lb/>of her &longs;mall variation of Magnitude, he maketh no mention at all; <lb/><arrow.to.target n="marg547"></arrow.to.target> <lb/>and much le&longs;s of <emph type="italics"/>Mars<emph.end type="italics"/> than was needful; I believe as being una­ <lb/>ble &longs;o well as he de&longs;ired to &longs;alve a <emph type="italics"/>Phænomenon<emph.end type="italics"/> &longs;o contrary to his <lb/>Hypothe&longs;is, and yet being convinced by &longs;o many other occurrences <lb/>and rea&longs;ons he maintained, and held the &longs;ame Hypothe&longs;is to be true. <lb/></s><s>Be&longs;ides the&longs;e things, to make the Planets, together with the Earth, <lb/>to move above the Sun as the Centre of their conver&longs;ions, and the <lb/><arrow.to.target n="marg548"></arrow.to.target> <lb/>Moon onely to break that order, and to have a motion by it &longs;elf <lb/>about the earth; and to make both her, the Earth, and the whole <lb/>Elementary <emph type="italics"/>Sphere,<emph.end type="italics"/> to move all together about the Sun in a year, <lb/>this &longs;eemeth to pervert the order of this Sy&longs;teme, which rendreth <lb/>it unlikely and fal&longs;e. </s><s>The&longs;e are tho&longs;e difficulties that make me <lb/>wonder how <emph type="italics"/>Aristarchus<emph.end type="italics"/> and <emph type="italics"/>Copernicus,<emph.end type="italics"/> who mu&longs;t needs have ob­ <lb/>&longs;erved them, not having been able for all that to &longs;alve them, have <lb/>yet notwith&longs;tanding by other admirable occurrences been induced <pb xlink:href="040/01/323.jpg" pagenum="303"/>to con&longs;ide &longs;o much in that which rea&longs;on dictated to them, as that <lb/>they have con&longs;idently affirmed that the &longs;tructure of the Univer&longs;e <lb/>could have no other figure than that which they de&longs;igned to them­ <lb/>&longs;elves. </s><s>There are al&longs;o &longs;everal other very &longs;erious and curious doubts, <lb/>not &longs;o ea&longs;ie to be re&longs;olved by the middle &longs;ort of wits, but yet pe­ <lb/>netrated and declared by <emph type="italics"/>Coperninus,<emph.end type="italics"/> which we &longs;hall defer till by <lb/>and by, after we have an&longs;wered to other objections that &longs;eem to <lb/>make again&longs;t this opinion. </s><s>Now coming to the declarations and <lb/>an&longs;wers to tho&longs;e three before named grand Objections, I &longs;ay, that <lb/>the two fir&longs;t not onely contradict not the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme, but <lb/><arrow.to.target n="marg549"></arrow.to.target> <lb/>greatly and ab&longs;olutely favour it; For both <emph type="italics"/>Mars<emph.end type="italics"/> and <emph type="italics"/>Venus<emph.end type="italics"/> &longs;eems <lb/>unequal to them&longs;elves, according to the proportions a&longs;&longs;igned; and <lb/><emph type="italics"/>Venus<emph.end type="italics"/> under the Sun &longs;eemeth horned, and goeth changing figures <lb/>in it &longs;elf exactly like the Moon.</s></p><p type="margin"><s><margin.target id="marg543"></margin.target>Mars <emph type="italics"/>makes an <lb/>hot a&longs;&longs;ault upon the<emph.end type="italics"/> <lb/>Copernican <emph type="italics"/>Sy­ <lb/>&longs;teme.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg544"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Phænome­ <lb/>na <emph type="italics"/>of<emph.end type="italics"/> Venus <emph type="italics"/>appear <lb/>contrary to the Sy­ <lb/>&longs;teme of<emph.end type="italics"/> Coperni­ <lb/>cus.</s></p><p type="margin"><s><margin.target id="marg545"></margin.target><emph type="italics"/>Another diffi­ <lb/>culty rai&longs;ed by<emph.end type="italics"/> Ve­ <lb/>nus <emph type="italics"/>again&longs;t<emph.end type="italics"/> Coper­ <lb/>nicus.</s></p><p type="margin"><s><margin.target id="marg546"></margin.target>Venus, <emph type="italics"/>according <lb/>to<emph.end type="italics"/> Copernicus, <emph type="italics"/>ei­ <lb/>ther lucid in it <lb/>&longs;elf, or el&longs;e of a <lb/>tran&longs;parent &longs;ub­ <lb/>&longs;tance.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg547"></margin.target>Copernicus <emph type="italics"/>&longs;peak­ <lb/>eth nothing of the <lb/>&longs;mall variation of <lb/>bigne&longs;s in<emph.end type="italics"/> Venus <lb/><emph type="italics"/>and in<emph.end type="italics"/> Mars.</s></p><p type="margin"><s><margin.target id="marg548"></margin.target><emph type="italics"/>The moon much <lb/>di&longs;turbeth the or­ <lb/>der of the other <lb/>Planets.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg549"></margin.target><emph type="italics"/>An&longs;wers to the <lb/>three first objecti­ <lb/>ons again&longs;t the<emph.end type="italics"/> Co­ <lb/>pernican <emph type="italics"/>Sy&longs;teme.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>But how came this to be concealed from <emph type="italics"/>Copernicus,<emph.end type="italics"/> <lb/>and revealed to you?</s></p><p type="main"><s>SALV. </s><s>The&longs;e things cannot be comprehended, &longs;ave onely by <lb/>the &longs;en&longs;e of &longs;eeing, the which by nature was not granted to man <lb/>&longs;o perfect, as that it was able to attain to the di&longs;covery of &longs;uch dif­ <lb/>ferences; nay even the very in&longs;trument of &longs;ight is an impediment <lb/>to it &longs;elf: But &longs;ince that it hath plea&longs;ed God in our age to vouch­ <lb/>&longs;afe to humane ingenuity, &longs;o admirable an invention of perfecting <lb/>our &longs;ight, by multiplying it four, &longs;ix, ten, twenty, thirty, and four­ <lb/>ty times, infinite objects, that either by rea&longs;on of their di&longs;tance, or <lb/>for their extream &longs;mallne&longs;&longs;e were invi&longs;ible unto us, have by help <lb/>of the Tele&longs;cope been rendered vi&longs;ible.</s></p><p type="main"><s>SAGR. </s><s>But <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mars<emph.end type="italics"/> are none of the objects invi&longs;ible <lb/>for their di&longs;tance or &longs;mallne&longs;&longs;e, yea, we do di&longs;cern them with our <lb/>bare natural &longs;ight; why then do we not di&longs;tingui&longs;h the differences <lb/>of their magnitudes and figures?</s></p><p type="main"><s>SALV. </s><s>In this, the impediment of our very eye it &longs;elf hath a <lb/><arrow.to.target n="marg550"></arrow.to.target> <lb/>great &longs;hare, as but even now I hinted, by which the re&longs;plendent and <lb/>remote objects are not repre&longs;ented to us &longs;imple and pure; but gives <lb/>them us fringed with &longs;trange and adventitious rayes, &longs;o long and <lb/>den&longs;e, that their naked body &longs;heweth to us agrandized ten, twen­ <lb/>ty, an hundred, yea a thou&longs;and times more than it would appear, if <lb/>the capillitious rayes were taken away.</s></p><p type="margin"><s><margin.target id="marg550"></margin.target><emph type="italics"/>Therea&longs;on whence <lb/>it happens that<emph.end type="italics"/> Ve­ <lb/>nus <emph type="italics"/>and<emph.end type="italics"/> Mars <emph type="italics"/>do <lb/>not appear to vary <lb/>magnitude &longs;o much <lb/>as is requi&longs;ite.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Now I remember that I have read &longs;omething on this <lb/>&longs;ubject, I know not whether in the Solar Letters, or in the <emph type="italics"/>Sag­ <lb/>giatore<emph.end type="italics"/> of our common Friend, but it would be very good, a&longs;well <lb/>for recalling it into my memory, as for the information of <emph type="italics"/>Simpli­ <lb/>cius,<emph.end type="italics"/> who it may be never &longs;aw tho&longs;e writings, that you would de­ <lb/>clare unto us more di&longs;tinctly how this bu&longs;ine&longs;&longs;e &longs;tands, the know­ <lb/>ledge whereof I think to be very nece&longs;&longs;ary for the a&longs;&longs;i&longs;ting of us to <lb/>under&longs;tand that of which we now &longs;peak.</s></p> <pb xlink:href="040/01/324.jpg" pagenum="304"/><p type="main"><s>SIMP. </s><s>I mu&longs;t confe&longs;&longs;e that all that which <emph type="italics"/>Salviatus<emph.end type="italics"/> hath &longs;po­ <lb/>ken is new unto me, for truth is, I never have had the curio&longs;ity to <lb/>read tho&longs;e Books, nor have I hitherto given any great credit to <lb/>the Tele&longs;cope newly introduced; rather treading in the &longs;teps of o­ <lb/><arrow.to.target n="marg551"></arrow.to.target> <lb/>ther <emph type="italics"/>Peripatetick<emph.end type="italics"/> Philo&longs;ophers my companions, I have thought <lb/>tho&longs;e things to be fallacies and delu&longs;ions of the Chry&longs;tals, which <lb/>others have &longs;o much admired for &longs;tupendious operations: and <lb/>therefore if I have hitherto been in an errour, I &longs;hall be glad to be <lb/>freed from it, and allured by the&longs;e novelties already heard from <lb/>you, I &longs;hall the more attentively hearken to the re&longs;t.</s></p><p type="margin"><s><margin.target id="marg551"></margin.target><emph type="italics"/>The operations of <lb/>the Tele&longs;cope ac­ <lb/>counted fallacies by <lb/>the<emph.end type="italics"/> Peripateticks.</s></p><p type="main"><s>SALV. </s><s>The confidence that the&longs;e men have in their own ap­ <lb/>prehen&longs;ivene&longs;&longs;e, is no le&longs;s unrea&longs;onable than the &longs;mall e&longs;teem they <lb/>have of the judgment of others: yet its much that they &longs;hould e­ <lb/>&longs;teem them&longs;elves able to judge better of &longs;uch an in&longs;trument, with­ <lb/>out ever having made trial of it, than tho&longs;e who have made, and <lb/>daily do make a thou&longs;and experiments of the &longs;ame: But I pray <lb/>you, let us leave this kind of pertinacious men, whom we can­ <lb/>not &longs;o much as tax without doing them too great honour. </s><s>And re­ <lb/><arrow.to.target n="marg552"></arrow.to.target> <lb/>turning to our purpo&longs;e, I &longs;ay, that re&longs;plendent objects, whether <lb/>it is that their light doth refract on the humidity that is upon the <lb/>pupils, or that it doth reflect on the edges of the eye-browes, dif­ <lb/>fu&longs;ing its reflex rayes upon the &longs;aid pupils, or whether it is for &longs;ome <lb/>other rea&longs;on, they do appear to our eye, as if they were environ'd <lb/>with new rayes, and therefore much bigger than their bodies <lb/>would repre&longs;ent them&longs;elves to us, were they dive&longs;ted of tho&longs;e ir­ <lb/><arrow.to.target n="marg553"></arrow.to.target> <lb/>radiations. </s><s>And this aggrandizement is made with a greater and <lb/>greater proportion, by how much tho&longs;e lucid objects are le&longs;&longs;er and <lb/>le&longs;&longs;er; in the &longs;ame manner for all the world, as if we &longs;hould &longs;up­ <lb/>po&longs;e that the augmentation of &longs;hining locks were <emph type="italics"/>v.g.<emph.end type="italics"/> four inches, <lb/>which addition being made about a circle that hath four inches di­ <lb/>ameter would increa&longs;e its appearance to nine times its former big­ <lb/>ne&longs;&longs;e: but---------</s></p><p type="margin"><s><margin.target id="marg552"></margin.target><emph type="italics"/>Shining objects <lb/>&longs;eem environed <lb/>with adventitious <lb/>rayes.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg553"></margin.target><emph type="italics"/>The rea&longs;on why <lb/>luminous bodies ap­ <lb/>pear enlarged <lb/>much the more, by <lb/>how much they are <lb/>le&longs;&longs;er.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I believe you would have &longs;aid three times; for adding <lb/>four inches to this &longs;ide, and four inches to that &longs;ide of the diame­ <lb/>ter of a circle, which is like wi&longs;e four inches, its quantity is there­ <lb/>by tripled, and not made nine times bigger.</s></p><p type="main"><s>SALV. </s><s>A little more <emph type="italics"/>Geometry<emph.end type="italics"/> would do well, <emph type="italics"/>Simplicius.<emph.end type="italics"/> <lb/><arrow.to.target n="marg554"></arrow.to.target> <lb/>True it is, that the diameter is tripled, but the &longs;uperficies, which is <lb/>that of which we &longs;peak, increa&longs;eth nine times: for you mu&longs;t know, <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> that the &longs;uperficies of circles are to one another, as <lb/>the &longs;quares of their diameters; and a circle that hath four inches <lb/>diameter is to another that hath twelve, as the &longs;quare of four to <lb/>the &longs;quare of twelve; that is, as 16. is to 144 and therefore it &longs;hall <lb/>be increa&longs;ed nine times, and not three; this, by way of adverti&longs;e­ <lb/>ment to <emph type="italics"/>Simplicius.<emph.end type="italics"/> And proceeding forwards, if we &longs;hould add <pb xlink:href="040/01/325.jpg" pagenum="305"/>the &longs;aid irradiation of four inches to a circle that hath but two in­ <lb/>ches of diameter onely, the diameter of the irradiation or Gar­ <lb/>land would be ten inches, and the &longs;uperficial content of the circle <lb/>would be to the <emph type="italics"/>area<emph.end type="italics"/> of the naked body, as 100. to 4. for tho&longs;e <lb/>are the &longs;quares of 10. and of 2. the agrandizement would there­ <lb/>fore be 25. times &longs;o much; and la&longs;tly, the four inches of hair or <lb/>fringe, added to a &longs;mall circle of an inch in diameter, the &longs;ame <lb/>would be increa&longs;ed 81. times; and &longs;o continually the augmenta­ <lb/>tions are made with a proportion greater and greater, according <lb/>as the real objects that increa&longs;e, are le&longs;&longs;er and le&longs;&longs;er.</s></p><p type="margin"><s><margin.target id="marg554"></margin.target><emph type="italics"/>Superficial fi­ <lb/>gures encrea&longs;ing <lb/>proportion double to <lb/>their lines.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The doubt which puzzled <emph type="italics"/>Simplicius<emph.end type="italics"/> never troubled <lb/>me, but certain other things indeed there are, of which I de&longs;ire <lb/>a more di&longs;tinct under&longs;tanding; and in particular, I would know up­ <lb/>on what ground you affirm that the &longs;aid agrandizement is alwayes <lb/>equal in all vi&longs;ible objects. <lb/><arrow.to.target n="marg555"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg555"></margin.target><emph type="italics"/>Objects the more <lb/>vigorous they are <lb/>in light, the more <lb/>they do &longs;eem to in­ <lb/>crea&longs;e.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I have already declared the &longs;ame in part, when I &longs;aid, <lb/>that onely lucid objects &longs;o increa&longs;ed, and not the ob&longs;cure; now I <lb/>adde what remaines, that of the re&longs;plendent objects tho&longs;e that are <lb/>of a more bright light, make the reflection greater and more re­ <lb/>&longs;plendent upon our pupil; whereupon they &longs;eem to augment <lb/>much more than the le&longs;&longs;e lucid: and that I may no more inlarge <lb/>my &longs;elf upon this particular, come we to that which the true Mi­ <lb/>&longs;tris of <emph type="italics"/>Astronomy,<emph.end type="italics"/> Experience, teacheth us. </s><s>Let us this evening, <lb/>when the air is very ob&longs;cure, ob&longs;erve the &longs;tar of <emph type="italics"/>Jupiter<emph.end type="italics"/>; we <lb/>&longs;hall &longs;ee it very glittering, and very great; let us afterwards look </s></p><p type="main"><s><arrow.to.target n="marg556"></arrow.to.target> <lb/>through a tube, or el&longs;e through a &longs;mall trunk, which clutching the <lb/>hand clo&longs;e, and acco&longs;ting it to the eye, we lean between the palm <lb/>of the hands and the fingers, or el&longs;e by an hole made with a &longs;mall <lb/>needle in a paper; and we &longs;hall &longs;ee the &longs;aid &longs;tar dive&longs;ted of its <lb/>beams, but &longs;o &longs;mall, that we &longs;hall judge it le&longs;&longs;e, even than a &longs;ixti­ <lb/>eth part of its great glittering light &longs;een with the eye at liberty: <lb/>we may afterwards behold the <emph type="italics"/>Dog-&longs;tars<emph.end type="italics"/> beautiful and bigger than <lb/><arrow.to.target n="marg557"></arrow.to.target> <lb/>any of the other fixed &longs;tars, which &longs;eemeth to the bare eye no <lb/>great matter le&longs;&longs;e than <emph type="italics"/>Jupiter<emph.end type="italics"/>; but taking from it, as before, the <lb/>irradiation, its <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> will &longs;hew &longs;o little, that it will not be <lb/>thought the twentieth part of that of <emph type="italics"/>Jupiter,<emph.end type="italics"/> nay, he that hath not <lb/>very good eyes, will very hardly di&longs;cern it; from whence it may <lb/>be rationally inferred, that the &longs;aid &longs;tar, as having a much more <lb/>lively light than <emph type="italics"/>Jupiter,<emph.end type="italics"/> maketh its irradiation greater than <emph type="italics"/>Jupi­ <lb/>ter<emph.end type="italics"/> doth his. </s><s>In the next place, as to the irradiation of the Sun <lb/>and Moon, it is as nothing, by means of their magnitude, which <lb/><arrow.to.target n="marg558"></arrow.to.target> <lb/>po&longs;&longs;e&longs;&longs;eth of it &longs;elf alone &longs;o great a &longs;pace in our eye, that it lea­ <lb/>veth no place for the adventitious rayes; &longs;o that their faces &longs;eem <lb/>clo&longs;e clipt, and terminate. </s><s>We may a&longs;&longs;ure our &longs;elves of the &longs;ame <lb/>truth by another experiment which I have often made triall of; <pb xlink:href="040/01/326.jpg" pagenum="306"/><arrow.to.target n="marg559"></arrow.to.target> <lb/>we may a&longs;&longs;ure our &longs;elves, I &longs;ay, that bodies &longs;hining with mo&longs;t| live­ <lb/>ly light do irradiate, or beam forth rayes more by far than tho&longs;e <lb/>that are of a more langui&longs;hing light. </s><s>I have many times &longs;een <emph type="italics"/>Ju­ <lb/>piter<emph.end type="italics"/> and <emph type="italics"/>Venus<emph.end type="italics"/> together twenty or thirty degrees di&longs;tant from the <lb/>Sun, and the air being very dark, <emph type="italics"/>Venus<emph.end type="italics"/> appeared eight or ten <lb/>times bigger than <emph type="italics"/>Jupiter,<emph.end type="italics"/> being both beheld by the eye at liber­ <lb/>ty; but being beheld afterwards with the Tele&longs;cope, the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> <lb/>of <emph type="italics"/>Jupiter<emph.end type="italics"/> di&longs;covered it &longs;elf to be four or more times greater than <lb/>that of <emph type="italics"/>Venus,<emph.end type="italics"/> but the vivacity of the &longs;plendour of <emph type="italics"/>Venus<emph.end type="italics"/> was in­ <lb/>comparably bigger than the langui&longs;hing light of <emph type="italics"/>Jupiter<emph.end type="italics"/>; which <lb/>was only becau&longs;e of <emph type="italics"/>Jupiters<emph.end type="italics"/> being far from the Sun, and from us; <lb/>and <emph type="italics"/>Venus<emph.end type="italics"/> neer to us, and to the Sun. </s><s>The&longs;e things premi&longs;ed, it <lb/>will not be difficult to comprehend, how Mars, when it is in oppo­ <lb/>&longs;ition to the Sun, and therefore neerer to the Earth by &longs;even times, <lb/>and more, than it is towards the conjunction, cometh to appear <lb/>&longs;carce four or five times bigger in that &longs;tate than in this, when as it <lb/>&longs;hould appear more than fifty times &longs;o much; of which the only <lb/>irradiation is the cau&longs;e; for if we dive&longs;t it of the adventitious <lb/>rayes, we &longs;hall find it exactly augmented with the due proportion: <lb/>but to take away the capillitious border, the Tele&longs;cope is the be&longs;t <lb/><arrow.to.target n="marg560"></arrow.to.target> <lb/>and only means, which inlarging its <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> nine hundred or a <lb/>thou&longs;and times, makes it to be &longs;een naked and terminate, as that <lb/>of the Moon, and different from it &longs;elf in the two po&longs;itions, ac­ <lb/><arrow.to.target n="marg561"></arrow.to.target> <lb/>cording to its due proportions to an hair. </s><s>Again, as to <emph type="italics"/>Venus,<emph.end type="italics"/> <lb/>that in its ve&longs;pertine conjunction, when it is below the Sun, ought <lb/>to &longs;hew almo&longs;t fourty times bigger than in the other matutine con­ <lb/>junction, and yet doth not appear &longs;o much as doubled; it happen­ <lb/>eth, be&longs;ides the effect of the irradiation, that it is horned; and its <lb/>cre&longs;cents, be&longs;ides that they are &longs;harp, they do receive the Suns light <lb/>obliquely, and therefore emit but a faint &longs;plendour; &longs;o that as <lb/>being little and weak, its irradiation becometh the le&longs;&longs;e ample <lb/>and vivacious, than when it appeareth to us with its Hemi&longs;phere all <lb/>&longs;hining: but now the Tele&longs;cope manife&longs;tly &longs;hews its hornes to <lb/>have been as terminate and di&longs;tinct as tho&longs;e of the Moon, and <lb/>appear, as it were, with a great circle, and in a proportion tho&longs;e <lb/>well neer fourty times greater than its &longs;ame <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> at &longs;uch time <lb/>as it is &longs;uperiour to the Sun in its ultimate matutine apparition.</s></p><p type="margin"><s><margin.target id="marg556"></margin.target><emph type="italics"/>An ea&longs;ie expe­ <lb/>riment that &longs;hew­ <lb/>eth the increa&longs;e in <lb/>the &longs;tars, by means <lb/>of the adventitious <lb/>rays.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg557"></margin.target>Jupiter <emph type="italics"/>augments <lb/>le&longs;&longs;e than the<emph.end type="italics"/> Dog­ <lb/>&longs;tar.</s></p><p type="margin"><s><margin.target id="marg558"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Sun <emph type="italics"/>and<emph.end type="italics"/> <lb/>Moon <emph type="italics"/>increa&longs;e lis­ <lb/>tle.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg559"></margin.target><emph type="italics"/>It is &longs;een by ma­ <lb/>nife&longs;t experience, <lb/>that the more <lb/>&longs;plendid bodies do <lb/>much more irradi­ <lb/>ate than the le&longs;&longs;e <lb/>lucid.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg560"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Tele&longs;cope <lb/><emph type="italics"/>is the be&longs;t means to <lb/>take away the ir­ <lb/>radiations of the <lb/>Stars.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg561"></margin.target><emph type="italics"/>Another &longs;econd <lb/>rea&longs;on of the &longs;mall <lb/>apparent increa&longs;e <lb/>of<emph.end type="italics"/> Venus.</s></p><p type="main"><s>SAGR. Oh, <emph type="italics"/>Nicholas Copernicus,<emph.end type="italics"/> how great would have been <lb/>thy joy to have &longs;een this part of thy Sy&longs;teme, confirmed with &longs;o <lb/>manife&longs;t experiments! <lb/><arrow.to.target n="marg562"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg562"></margin.target>Copernicus <emph type="italics"/>per­ <lb/>&longs;waded by rea&longs;ons <lb/>contrary to &longs;en&longs;ible <lb/>experiments.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Tis true. </s><s>But how much le&longs;&longs;e the fame of his &longs;ublime <lb/>wit among&longs;t the intelligent? </s><s>when as it is &longs;een, as I al&longs;o &longs;aid before, <lb/>that he did con&longs;tantly continue to affirm (being per&longs;waded thereto <lb/>by rea&longs;on) that which &longs;en&longs;ible experiments &longs;eemed to contradict; <lb/>for I cannot cea&longs;e to wonder that he &longs;hould con&longs;tantly per&longs;i&longs;t in <lb/>&longs;aying, that <emph type="italics"/>Venus<emph.end type="italics"/> revolveth about the Sun, and is more than &longs;ix <pb xlink:href="040/01/327.jpg" pagenum="307"/>times farther from us at one time, than at another; and al&longs;o &longs;eem­ <lb/>eth to be alwayes of an equal bigne&longs;s, although it ought to &longs;hew <lb/>forty times bigger when neare&longs;t to us, than when farthe&longs;t off.</s></p><p type="main"><s>SAGR. </s><s>But in <emph type="italics"/>Jupiter, Saturn<emph.end type="italics"/> and <emph type="italics"/>Mercury,<emph.end type="italics"/> I believe that <lb/>the differences of their apparent magnitudes, &longs;hould &longs;eem punctu­ <lb/>ally to an&longs;wer to their different di&longs;tances.</s></p><p type="main"><s>SALV. </s><s>In the two Superiour ones, I have made preci&longs;e ob­ <lb/>&longs;ervations yearly for this twenty two years la&longs;t pa&longs;t: In <emph type="italics"/>Mercury<emph.end type="italics"/></s></p><p type="main"><s><arrow.to.target n="marg563"></arrow.to.target> <lb/>there can be no ob&longs;ervation of moment made, by rea&longs;on it &longs;uf­ <lb/>fers not it &longs;elf to be &longs;een, &longs;ave onely in its greate&longs;t digr&longs;&longs;ieons <lb/>from the Sun, in which its di&longs;tances from the earth are in&longs;en&longs;ibly <lb/>unequal, and tho&longs;e differences con&longs;equently not to be ob&longs;erved; <lb/>as al&longs;o its mutations of figures which mu&longs;t ab&longs;olutely happen in <lb/>it, as in <emph type="italics"/>Venus.<emph.end type="italics"/> And if we do &longs;ee it, it mu&longs;t of nece&longs;&longs;ity appear <lb/>in form of a Semicircle, as <emph type="italics"/>Venus<emph.end type="italics"/> likewi&longs;e doth in her greate&longs;t <lb/>digre&longs;&longs;ions; but its <emph type="italics"/>di&longs;cus<emph.end type="italics"/> is &longs;o very &longs;mall, and its &longs;plendor &longs;o <lb/>very great, by rea&longs;on of its vicinity to the Sun, that the virtue <lb/>of the Tele&longs;cope doth not &longs;uffice to clip its tre&longs;&longs;es or adventitious <lb/>rayes, &longs;o as to make them appear &longs;haved round about. </s><s>It re­ <lb/><arrow.to.target n="marg564"></arrow.to.target> <lb/>mains, that we remove that which &longs;eemed a great inconvenience <lb/>in the motion of the Earth, namely that all the Planets moving <lb/>about the Sun, it alone, not &longs;olitary as the re&longs;t, but in company <lb/>with the Moon, and the whole Elementary Sphear, &longs;hould move <lb/>round about the Sun in a year; and that the &longs;aid Moon withal <lb/>&longs;hould move every moneth about the earth. </s><s>Here it is nece&longs;&longs;ary <lb/>once again to exclaim and extol the admirable per&longs;picacity of <emph type="italics"/>Co­ <lb/>pernicus,<emph.end type="italics"/> and withal to condole his misfortune, in that he is not <lb/>now alive in our dayes, when for removing of the &longs;eeming ab­ <lb/>&longs;urdity of the Earth and Moons motion in con&longs;ort we &longs;ee <emph type="italics"/>Jupi­ <lb/>ter,<emph.end type="italics"/> as if it were another Earth, not in con&longs;ort with the Moon, <lb/>but accompanied by four Moons to rovolve about the Sun in 12. <lb/>years together, with what ever things the Orbs of the four Medi­ <lb/>cæan Stars can contain within them.</s></p><p type="margin"><s><margin.target id="marg563"></margin.target>Mercury <emph type="italics"/>admit­ <lb/>teth not of clear <lb/>ob&longs;ervations.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg564"></margin.target><emph type="italics"/>The difficulties <lb/>removed that ari&longs;e <lb/>from the Earths <lb/>moving about the <lb/>Sun, not &longs;olitarily, <lb/>but in con&longs;ort with <lb/>the Moon.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Why do you call the four jovial Planets, Moons?</s></p><p type="main"><s>SAGR. </s><s>Such they would &longs;eem to be to one that &longs;tanding in <lb/><arrow.to.target n="marg565"></arrow.to.target> <lb/><emph type="italics"/>Jupiter<emph.end type="italics"/> &longs;hould behold them; for they are of them&longs;elves dark, and <lb/>receive their light from the Sun, which is manife&longs;t from their be­ <lb/>ing eclip&longs;ed, when they enter into the cone of <emph type="italics"/>Jupiters<emph.end type="italics"/> &longs;hadow: <lb/>and becau&longs;e onely tho&longs;e their Hemi&longs;pheres, that look towards the <lb/>Sun are illuminated, to us that are without their Orbs, and near­ <lb/>er to the Sun, they &longs;eem alwayes <emph type="italics"/>lucid,<emph.end type="italics"/> but to one that &longs;hould be <lb/>in <emph type="italics"/>Jupiter,<emph.end type="italics"/> they would &longs;hew all illuminated, at &longs;uch time as they <lb/>were in the upper parts of their circles; but in the parts inferi­ <lb/>our, that is between <emph type="italics"/>Jupiter<emph.end type="italics"/> and the Sun, they would from <emph type="italics"/>Ju­ <lb/>piter<emph.end type="italics"/> be ob&longs;erved to be horned; and in a word they would, to <pb xlink:href="040/01/328.jpg" pagenum="308"/>the ob&longs;ervators &longs;tanding in <emph type="italics"/>Jupiter,<emph.end type="italics"/> make the &longs;elf &longs;ame changes <lb/>of Figure, that to us upon the Earth, the Moon doth make. </s><s>You <lb/>&longs;ee now how the&longs;e three things, which at &longs;ir&longs;t &longs;eémed di&longs;&longs;onant, <lb/>do admirably accord with the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme. </s><s>Here al&longs;o by <lb/>the way may <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;ee, with what probability one may con­ <lb/>clude, that the Sun and not the Earth, is in the Centre of the <lb/><emph type="italics"/>Planetary<emph.end type="italics"/> conver&longs;ions. </s><s>And &longs;ince the Earth is now placed a­ <lb/>mong&longs;t mundane Bodies, that undoubtedly move about the Sun, <lb/>to wit, above <emph type="italics"/>Mercury<emph.end type="italics"/> and <emph type="italics"/>Venus,<emph.end type="italics"/> and below <emph type="italics"/>Saturn, Jupiter,<emph.end type="italics"/> <lb/>and <emph type="italics"/>Mars<emph.end type="italics"/>; &longs;hall it not be in like manner probable, and perhaps <lb/>nece&longs;&longs;ary to grant, that it al&longs;o moveth round?</s></p><p type="margin"><s><margin.target id="marg565"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Medicean <lb/><emph type="italics"/>Stars areas it were <lb/>four Moons about<emph.end type="italics"/> <lb/>Jupiter.</s></p><p type="main"><s>SIMP. </s><s>The&longs;e accidents are &longs;o notable and con&longs;picuous, that <lb/>it is not po&longs;&longs;ible, but that <emph type="italics"/>Ptolomy<emph.end type="italics"/> and others his Sectators, &longs;hould <lb/>have had knowledge of them, and having &longs;o, it is likewi&longs;e nece&longs;­ <lb/>&longs;ary, that they have found a way to render rea&longs;ons of &longs;uch, and <lb/>&longs;o &longs;en&longs;ible appearances that were &longs;ufficient, and al&longs;o congruous <lb/>and probable, &longs;eeing that they have for &longs;o long a time been re­ <lb/>ceived by &longs;uch numbers of learned men. <lb/><arrow.to.target n="marg566"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg566"></margin.target><emph type="italics"/>The Principal <lb/>&longs;cope of A&longs;trono­ <lb/>mers, is to give a <lb/>rea&longs;on of appear­ <lb/>ances.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You argue very well; but you know that the principal <lb/>&longs;cope of <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> is to render only rea&longs;on for the appearances <lb/>in the Cæle&longs;tial Bodies, and to them, and to the motions of the <lb/>Stars, to accomodate &longs;uch &longs;tructures and compo&longs;itions of Circles, <lb/>that the motions following tho&longs;e calculations, an&longs;wer to the &longs;aid <lb/>appearances, little &longs;crupling to admit of &longs;ome exorbitances, that <lb/>indeed upon other accounts they would much &longs;tick at. </s><s>And <emph type="italics"/>Co-<emph.end type="italics"/></s></p><p type="main"><s><arrow.to.target n="marg567"></arrow.to.target> <lb/><emph type="italics"/>pernic us<emph.end type="italics"/> him&longs;elf writes, that he had in his fir&longs;t &longs;tudies re&longs;tored the <lb/>Science of <emph type="italics"/>A&longs;tronomy<emph.end type="italics"/> upon the very &longs;uppo&longs;itions of <emph type="italics"/>Ptolomy,<emph.end type="italics"/> and <lb/>in &longs;uch manner corrected the motions of the Planets, that the <lb/>computations did very exactly agree with the <emph type="italics"/>Phænomena,<emph.end type="italics"/> and <lb/>the <emph type="italics"/>Phænomena<emph.end type="italics"/> with the &longs;upputations, in ca&longs;e that he took the <lb/>Planets &longs;everally one by one. </s><s>But he addeth, that in going a­ <lb/>bout to put together all the &longs;tructures of the particular Fabricks, <lb/>there re&longs;ulted thence a Mon&longs;ter and <emph type="italics"/>Chimæra,<emph.end type="italics"/> compo&longs;ed of mem­ <lb/>bers mo&longs;t di&longs;proportionate to one another, and altogether incom­ <lb/>patible; So that although it &longs;atisfied an <emph type="italics"/>A&longs;tronomer<emph.end type="italics"/> meerly <emph type="italics"/>A­ <lb/>rithmetical,<emph.end type="italics"/> yet did it not afford &longs;atisfaction or content to the <lb/><arrow.to.target n="marg568"></arrow.to.target> <lb/><emph type="italics"/>A&longs;tronomer Phylo&longs;ophical.<emph.end type="italics"/> And becau&longs;e he very well under­ <lb/>&longs;tood, that if one might &longs;alve the Cæle&longs;tial appearances with fal&longs;e <lb/>a&longs;&longs;umptions in nature, it might with much more ea&longs;e be done by <lb/>true &longs;uppo&longs;itions, he &longs;et him&longs;elf diligently to &longs;earch whether a­ <lb/>ny among&longs;t the antient men of fame, had a&longs;cribed to the World <lb/>any other &longs;tructure, than that commonly received by <emph type="italics"/>Ptolomy<emph.end type="italics"/>; <lb/>and finding that &longs;ome <emph type="italics"/>Pythagoreans<emph.end type="italics"/> had in particular a&longs;&longs;igned <lb/>the Diurnal conver&longs;ion to the Earth, and others the annual mo­ <lb/>tion al&longs;o, he began to compare the appearances, and particulari­ <pb xlink:href="040/01/329.jpg" pagenum="309"/>ties of the Planets motions, with the&longs;e two new &longs;uppo&longs;itions, all <lb/>which things jumpt exactly with his purpo&longs;e; and &longs;eeing the whole <lb/>corre&longs;pond, with admirable facility to its parts, he imbraced this <lb/>new Sy&longs;teme, and it took up his re&longs;t.</s></p><p type="margin"><s><margin.target id="marg567"></margin.target>Copernicus <emph type="italics"/>re­ <lb/>&longs;tored A&longs;tronomy <lb/>upon the &longs;uppo&longs;iti­ <lb/>ous of<emph.end type="italics"/> Ptolomy:</s></p><p type="margin"><s><margin.target id="marg568"></margin.target><emph type="italics"/>What moved<emph.end type="italics"/> Co­ <lb/>pernicus <emph type="italics"/>to e&longs;ta­ <lb/>bli&longs;h his Sy&longs;teme.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>But what great exorbitancies are there in the <emph type="italics"/>Ptolo­ <lb/>maick<emph.end type="italics"/> Sy&longs;teme, for which there are not greater to be found in this <lb/>of <emph type="italics"/>Copernicus<emph.end type="italics"/>?</s></p><p type="main"><s>SALV. </s><s>In the <emph type="italics"/>Ptolomaick Hypothe&longs;is<emph.end type="italics"/> there are di&longs;ea&longs;es, and in <lb/><arrow.to.target n="marg569"></arrow.to.target> <lb/>the <emph type="italics"/>Copernican<emph.end type="italics"/> their cures. </s><s>And fir&longs;t will not all the Sects of <lb/><emph type="italics"/>Phylo&longs;ophers,<emph.end type="italics"/> account it a great inconvenience, that a body na­ <lb/>turally moveable in circumgyration, &longs;hould move irregularly upon <lb/>its own Centre, and regularly upon another point? </s><s>And yet <lb/>there are &longs;uch deformed motions as the&longs;e in the <emph type="italics"/>Ptolomæan<emph.end type="italics"/> Hypo­ <lb/>the&longs;is, but in the <emph type="italics"/>Copernican<emph.end type="italics"/> all move evenly about their own <lb/>Centres. </s><s>In the <emph type="italics"/>Ptolomaick,<emph.end type="italics"/> it is nece&longs;&longs;ary to a&longs;&longs;ign to the Cæ­ <lb/>le&longs;tial bodies, contrary motions, and to make them all to move, <lb/>from Ea&longs;t to We&longs;t, and at the &longs;ame time, from We&longs;t to Ea&longs;t; <lb/>But in the <emph type="italics"/>Copernican,<emph.end type="italics"/> all the Cæle&longs;tial revolutions are towards <lb/>one onely way, from We&longs;t to Ea&longs;t. </s><s>But what &longs;hall we &longs;ay of <lb/>the apparent motion of the Planets, &longs;o irregular, that they not on­ <lb/>ly go one while &longs;wift, and another while &longs;low, but &longs;ometimes <lb/>wholly &longs;eace to move; and then after a long time return back a­ <lb/>gain? </s><s>To &longs;alve which appearances <emph type="italics"/>Ptolomie<emph.end type="italics"/> introduceth very great <lb/><emph type="italics"/>Epicicles,<emph.end type="italics"/> accommodating them one by one to each Planet, with <lb/>&longs;ome rules of incongruous motions, which are all with one &longs;in­ <lb/>gle motion of the Earth taken away. </s><s>And would not you, <emph type="italics"/>Sim­ <lb/>plicius,<emph.end type="italics"/> call it a great ab&longs;urditie, if in the <emph type="italics"/>Ptolomaick<emph.end type="italics"/> Hypothe­ <lb/>&longs;is, in which the particular Planets, have their peculiar Orbs a&longs;­ <lb/>&longs;igned them one above another, one mu&longs;t be frequently forced <lb/>to &longs;ay, that <emph type="italics"/>Mars,<emph.end type="italics"/> con&longs;tituted above the Sphære of the Sun, doth <lb/>&longs;o de&longs;cend, that breaking the Solar Orb, it goeth under it, and <lb/>approacheth neaer to the Earth, than to the Body of the Sun, <lb/>and by and by immea&longs;urably a&longs;cendeth above the &longs;ame? </s><s>And <lb/>yet this, and other exorbitancies are remedied by the Soul and <lb/>fingle annual motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg569"></margin.target><emph type="italics"/>Inconveniencies <lb/>that are in the Sy­ <lb/>&longs;teme of<emph.end type="italics"/> Ptolomy.</s></p><p type="main"><s>SAGR. </s><s>I would gladly be bettter informed how the&longs;e &longs;tations, <lb/>and retrograde and direct motions, which did ever &longs;eem to me <lb/>great improbalities, do accord in this <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme. <lb/><arrow.to.target n="marg570"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg570"></margin.target><emph type="italics"/>Its a great Ar­ <lb/>gument in favour <lb/>of<emph.end type="italics"/> Copernicus, <emph type="italics"/>that <lb/>he obviates the &longs;ta­ <lb/>tions & retrograda­ <lb/>tions of the motions <lb/>of the Planets.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>You &longs;hall &longs;ee them &longs;o to accord, <emph type="italics"/>Sagredus,<emph.end type="italics"/> that <lb/>this onely conjecture ought to be &longs;ufficient to make one that <lb/>is not more than pertinacious or &longs;tupid, yield, a&longs;&longs;ent to all the <lb/>re&longs;t of this Doctrine. </s><s>I tell you therefore, that nothing being <lb/>altered in the motion of <emph type="italics"/>Saturn,<emph.end type="italics"/> which is 30 years, in that <lb/>of <emph type="italics"/>Jupiter,<emph.end type="italics"/> which is 12, in that of <emph type="italics"/>Mars,<emph.end type="italics"/> which is 2, in that of <lb/><emph type="italics"/>Venus,<emph.end type="italics"/> which is 9. moneths, in that of <emph type="italics"/>Mercury,<emph.end type="italics"/> which is 80. <pb xlink:href="040/01/330.jpg" pagenum="310"/>dayes, or thereabouts, the &longs;ole annual motion of the Earth be­ <lb/>tween <emph type="italics"/>Mars<emph.end type="italics"/> and <emph type="italics"/>Venus,<emph.end type="italics"/> cau&longs;eth the apparent inequalities in all </s></p><p type="main"><s><arrow.to.target n="marg571"></arrow.to.target> <lb/>the five &longs;tars before named. </s><s>And for a facile and full under­ <lb/>&longs;tanding of the whole, I will de&longs;cribe this figure of it. </s><s>There­ <lb/>fore &longs;uppo&longs;e the Sun to be placed in the centre O, about which <lb/>we will draw the Orb de&longs;cribed by the Earth, with the an­ <lb/>nual motion B G M, and let the circle de&longs;cribed, <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> by <lb/><emph type="italics"/>Jupiter<emph.end type="italics"/> about the Sun in 12. years, be this BGM, and in the <lb/><figure id="id.040.01.330.1.jpg" xlink:href="040/01/330/1.jpg"/> <lb/><arrow.to.target n="marg572"></arrow.to.target> <lb/>&longs;tarry &longs;phere let us imagine the Zodiack Y V S. Again, in the <lb/>annual Orb of the Earth let us take certain equal arches, B C, <lb/>C D, E F, F G, G H, H I, I K, K L, L M, and in the Sphere <lb/>of <emph type="italics"/>Jupiter<emph.end type="italics"/> let us make certain other arches, pa&longs;&longs;ed in the &longs;ame <lb/>times in which the Earth pa&longs;&longs;eth hers, which let be B C, C D, <lb/>D E, E F, F G, G H, H I, I K, K L, L M, which &longs;hall each be <lb/>proportionally le&longs;&longs;e than the&longs;e marked in the Earths Orb, like <lb/>as the motion of <emph type="italics"/>Jupiter<emph.end type="italics"/> under the Zodiack is &longs;lower than the <lb/>annual. </s><s>Suppo&longs;ing now, that when the Earth is in B, <emph type="italics"/>Jupiter<emph.end type="italics"/> is <lb/>in B, it &longs;hall appear to us in the Zodiack to be in P, de&longs;cribing <pb xlink:href="040/01/331.jpg" pagenum="311"/>the right line B B P. </s><s>Next &longs;uppo&longs;e the Earth to be moved from <lb/>B to C, and <emph type="italics"/>Jupiter<emph.end type="italics"/> from B to C, in the &longs;ame time; <emph type="italics"/>Iupiter<emph.end type="italics"/> <lb/>&longs;hall appear to have pa&longs;&longs;ed in the Zodiack to Q, and to have <lb/>moved &longs;traight forwards, according to the order of the &longs;ignes <lb/>P <expan abbr="q.">que</expan> In the next place, the Earth pa&longs;&longs;ing to D, and <emph type="italics"/>Iupiter<emph.end type="italics"/> <lb/>to D, it &longs;hall be &longs;een in the Zodiack in R, and from E, <emph type="italics"/>Iupi­ <lb/>ter<emph.end type="italics"/> being come to E; will appear in the Zodiack in S, having <lb/>all this while moved right forwards. </s><s>But the Earth afterwards <lb/>beginning to interpo&longs;e more directly between <emph type="italics"/>Iupiter<emph.end type="italics"/> and the <lb/>Sun, &longs;he being come to F, and <emph type="italics"/>Iupiter<emph.end type="italics"/> to F, he will appear in <lb/>T, to have already begun to return apparently back again un­ <lb/>der the Zodiack, and in that time that the Earth &longs;hall have pa&longs;­ <lb/>ed the arch E F, <emph type="italics"/>Iupiter<emph.end type="italics"/> &longs;hall have entertained him&longs;elf between <lb/>the points S T, and &longs;hall have appeared to us almo&longs;t motion­ <lb/>le&longs;&longs;e and &longs;tationary. </s><s>The Earth being afterwards come to G, <lb/>and <emph type="italics"/>Iupiter<emph.end type="italics"/> to G, in oppo&longs;ition to the Sun, it &longs;hall be vi&longs;ible in <lb/>the Zodiack at V, and much returned backwards by all the arch <lb/>of the Zodiack T V; howbeit that all the way pur&longs;uing its even <lb/>cour&longs;e it hath really gone forwards not onely in its own circle, <lb/>but in the Zodiack al&longs;o in re&longs;pect to the centre of the &longs;aid Zodi­ <lb/>ack, and to the Sun placed in the &longs;ame. </s><s>The Earth and <emph type="italics"/>Iupiter<emph.end type="italics"/> <lb/>again continuing their motions, when the Earth is come to H, <lb/>and <emph type="italics"/>Iupiter<emph.end type="italics"/> to H, it &longs;hall &longs;eem very much gone backward in the <lb/>Zodiack by all the arch V X. </s><s>The Earth being come to I, and <lb/><emph type="italics"/>Iupiter<emph.end type="italics"/> to I, it &longs;hall be apparently moved in the Zodiack by the lit­ <lb/>tle &longs;pace X Y, and there it will &longs;eem &longs;tationary. </s><s>When after­ <lb/>wards the Earth &longs;hall be come to K, and <emph type="italics"/>Iupiter<emph.end type="italics"/> to K; in the <lb/>Zodiack he &longs;hall have pa&longs;&longs;ed the arch Y N in a direct motion; <lb/>and the Earth pur&longs;uing its cour&longs;e to L, &longs;hall &longs;ee <emph type="italics"/>Iupiter<emph.end type="italics"/> in L, in <lb/>the point Z. </s><s>And la&longs;tly <emph type="italics"/>Iupiter<emph.end type="italics"/> in M &longs;hall be &longs;een from the Earth <lb/>M, to have pa&longs;&longs;ed to A, with a motion &longs;till right forwards; and <lb/>its whole apparent retrogadation in the Zodiack &longs;hall an&longs;wer to <lb/>the arch S Y, made by <emph type="italics"/>Iupiter,<emph.end type="italics"/> whil&longs;t that he in his own circle <lb/>pa&longs;&longs;eth the arch E I, and the Earth in hers the arch E I. </s><s>And <lb/><arrow.to.target n="marg573"></arrow.to.target> <lb/>this which hath been &longs;aid, is intended of <emph type="italics"/>Saturn<emph.end type="italics"/> and of <emph type="italics"/>Mars<emph.end type="italics"/> <lb/>al&longs;o; and in <emph type="italics"/>Saturn<emph.end type="italics"/> tho&longs;e retrogradations are &longs;omewhat more <lb/>frequent than in <emph type="italics"/>Jupiter,<emph.end type="italics"/> by rea&longs;on that its motion is a little <lb/>&longs;lower than that of <emph type="italics"/>Jupiter,<emph.end type="italics"/> &longs;o that the Earth overtaketh it <lb/>it in a &longs;horter &longs;pace of time; in <emph type="italics"/>Mars<emph.end type="italics"/> again they are more <lb/>rare, for that its motion is more &longs;wift than that of <emph type="italics"/>Jupiter.<emph.end type="italics"/> <lb/>Whereupon the Earth con&longs;umeth more time in recovering it. </s><s>Next <lb/>as to <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mercury,<emph.end type="italics"/> who&longs;e Circles are comprehended by that <lb/><arrow.to.target n="marg574"></arrow.to.target> <lb/>of the Earth, their &longs;tations and regre&longs;&longs;ions appear to be occa&longs;i­ <lb/>oned, not by their motions that really are &longs;uch, but by the anual <lb/>motion of the &longs;aid Earth, as <emph type="italics"/>Copernicus<emph.end type="italics"/> exellently demon&longs;trateth, <pb xlink:href="040/01/332.jpg" pagenum="312"/>together with <emph type="italics"/>Appollonius Pergæus<emph.end type="italics"/> in <emph type="italics"/>lib.<emph.end type="italics"/> 5. of his Revolutions, <lb/><emph type="italics"/>Chap.<emph.end type="italics"/> 35.</s></p><p type="margin"><s><margin.target id="marg571"></margin.target><emph type="italics"/>The &longs;ole annual <lb/>motion of the <lb/>Earth cau&longs;eth <lb/>great inequality of <lb/>motions in the five <lb/>Planets.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg572"></margin.target><emph type="italics"/>A demon&longs;tration of <lb/>the inequalities of <lb/>the three &longs;uperiour <lb/>Planets dependent <lb/>on the annual mo­ <lb/>tion of the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg573"></margin.target><emph type="italics"/>Retrogradations <lb/>more frequent in<emph.end type="italics"/> <lb/>Saturn, <emph type="italics"/>le&longs;&longs;e in<emph.end type="italics"/> Ju­ <lb/>piter, <emph type="italics"/>and yet le&longs;&longs;e <lb/>in<emph.end type="italics"/> Mars, <emph type="italics"/>and why.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg574"></margin.target><emph type="italics"/>The Retrograda­ <lb/>tion of<emph.end type="italics"/> Venus <emph type="italics"/>and<emph.end type="italics"/> <lb/>Mercury <emph type="italics"/>demon­ <lb/>&longs;trated by<emph.end type="italics"/> Apollo­ <lb/>nius <emph type="italics"/>and<emph.end type="italics"/> Coperni­ <lb/>cus.</s></p><p type="main"><s>You &longs;ee, Gentlemen, with what facility and &longs;implicity the annu­ <lb/><arrow.to.target n="marg575"></arrow.to.target> <lb/>al motion, were it appertaining to the Earth, is accommodated <lb/>to render a rea&longs;on of the apparent exorbitances, that are ob&longs;erved <lb/>in the motions of the five Planets, <emph type="italics"/>Saturn, Jupiter, Mars, Ve­ <lb/>nus<emph.end type="italics"/> and <emph type="italics"/>Mercury,<emph.end type="italics"/> taking them all away, and reducing them to <lb/><arrow.to.target n="marg576"></arrow.to.target> <lb/>equal and regular motions. </s><s>And of this admirable effect, <emph type="italics"/>Ni­ <lb/>cholas Copernicus,<emph.end type="italics"/> hath been the fir&longs;t that hath made the rea&longs;on <lb/>plain unto us. </s><s>But of another effect, no le&longs;&longs;e admirable than <lb/>this, and that with a knot, perhaps more difficult to unknit, <lb/>bindeth the wit of man, to admit this annual conver&longs;ion, and to <lb/>leave it to our Terre&longs;trial Globe; a new and unthought of con­ <lb/>jecture ari&longs;eth from the Sun it &longs;elf, which &longs;heweth that it is unwil­ <lb/>ling to be &longs;ingular in &longs;hifting, of this atte&longs;tation of &longs;o eminent a <lb/>conclu&longs;ion, rather as a te&longs;timony beyond all exception, it hath <lb/>de&longs;ired to be heard apart. </s><s>Hearken then to this great and new <lb/>wonder. <lb/><arrow.to.target n="marg577"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg575"></margin.target><emph type="italics"/>The annual mo­ <lb/>tion of the Earth <lb/>mo&longs;t apt to render <lb/>a rea&longs;on of the ex­ <lb/>orbttances of the <lb/>five Planets.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg576"></margin.target><emph type="italics"/>The Sun it &longs;elf <lb/>te&longs;tifieth the annu­ <lb/>al motion to belong <lb/>to the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg577"></margin.target><emph type="italics"/>The Lyncæan <lb/>Academick the <lb/>fir&longs;t di&longs;coverer of <lb/>the Solar &longs;pots, and <lb/>all the other cele­ <lb/>&longs;tial novelties.<emph.end type="italics"/></s></p><p type="main"><s>The fir&longs;t di&longs;coverer and ob&longs;erver of the <emph type="italics"/>Solar<emph.end type="italics"/> &longs;pots, as al&longs;o of <lb/>all the other Cœle&longs;tial novelties, was our <emph type="italics"/>Academick Lincæus<emph.end type="italics"/>; and <lb/>he di&longs;covered them <emph type="italics"/>anno<emph.end type="italics"/> 1610. being at that time Reader of the <lb/><emph type="italics"/>Mathematicks,<emph.end type="italics"/> in the Colledge of <emph type="italics"/>Padua,<emph.end type="italics"/> and there, and in <emph type="italics"/>Ve­ <lb/>nice,<emph.end type="italics"/> he di&longs;cour&longs;ed thereof with &longs;everal per&longs;ons, of which &longs;ome </s></p><p type="main"><s><arrow.to.target n="marg578"></arrow.to.target> <lb/>are yet living: And the year following, he &longs;hewed them in <emph type="italics"/>Rome<emph.end type="italics"/> <lb/>to many great per&longs;onages, as he relates in the fir&longs;t of his Letters <lb/>to <emph type="italics"/>Marcus Vel&longs;erus,<emph.end type="italics"/> ^{*} Sheriffe of <emph type="italics"/>Augu&longs;ta.<emph.end type="italics"/> He was the <lb/>fir&longs;t that again&longs;t the opinions of the too timorous and too jealous <lb/><arrow.to.target n="marg579"></arrow.to.target> <lb/>a&longs;&longs;ertors of the Heavens inalterability, affirmed tho&longs;e &longs;pots to be <lb/>matters, that in &longs;hort times were produced and di&longs;&longs;olved: for as <lb/>to place, they were contiguous to the body of the Sun, and re­ <lb/>volved about the &longs;ame; or el&longs;e being carried about by the &longs;aid <lb/>Solar body, which revolveth in it &longs;elfe about its own Centre, in <lb/>the &longs;pace almo&longs;t of a moneth, do fini&longs;h their cour&longs;e in that time; <lb/>which motion he judged at fir&longs;t to have been made by the Sun a­ <lb/>bout an Axis erected upon the plane of the Ecliptick; in regard <lb/>that the arches de&longs;cribed by the &longs;aid &longs;pots upon the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> of the <lb/>Sun appear unto our eye right lines, and parallels to the plane of <lb/>the Ecliptick: which therefore come to be altered, in part, with <lb/>&longs;ome accidental, wandring, and irregular motions, to which they <lb/>are &longs;ubject, and whereby tumultuarily, and without any order <lb/>they &longs;ucce&longs;&longs;ively change &longs;ituations among&longs;t them&longs;elves, one <lb/>while crouding clo&longs;e together, another while di&longs;&longs;evering, and <lb/>&longs;ome dividing them&longs;elves into many and very much changing fi­ <lb/>gures, which, for the mo&longs;t part, are very unu&longs;ual. </s><s>And albeit <lb/>tho&longs;e &longs;o incon&longs;tant mutations did &longs;omewhat alter the primary pe­ <pb xlink:href="040/01/333.jpg" pagenum="313"/>riodick cour&longs;e of the &longs;aid &longs;pots, yet did they not alter the opini­ <lb/>on of our friend, &longs;o as to make him believe, that they were any <lb/>e&longs;&longs;ential and fixed cau&longs;e of tho&longs;e deviations, but he continued to <lb/>hold, that all the apparent alterations derived them&longs;elves from <lb/>tho&longs;e accidental mutations: in like manner, ju&longs;t as it would hap­ <lb/>pen to one that &longs;hould from far di&longs;tant Regions ob&longs;erve the mo­ <lb/>tion of our Clouds; which would be di&longs;covered to move with a <lb/>mo&longs;t &longs;wift, great, and con&longs;tant motion, carried round by the di­ <lb/>urnal <emph type="italics"/>Vertigo<emph.end type="italics"/> of the Earth (if haply that motion belong to the <lb/>&longs;ame) in twenty four hours, by circles parallel to the Equinocti­ <lb/>al, but yet altered, in part, by the accidental motions cau&longs;ed by <lb/>the winds, which drive them, at all adventures, towards different <lb/>quarters of the World. </s><s>While this was in agitation, it came to <lb/>pa&longs;s that <emph type="italics"/>Vel&longs;erus<emph.end type="italics"/> &longs;ent him two Letters, written by a certain per­ <lb/><arrow.to.target n="marg580"></arrow.to.target> <lb/>&longs;on, under the feigned name of ^{*} <emph type="italics"/>Apelles,<emph.end type="italics"/> upon the &longs;ubject of <lb/>the&longs;e Spots, reque&longs;ting him, with importunity, to declare his <lb/>thoughts freely upon tho&longs;e Letters, and withall to let him know <lb/>what his opinion was touching the e&longs;&longs;ence of tho&longs;e &longs;pots; which his <lb/>reque&longs;t he &longs;atisfied in 3 Letters, &longs;hewing fir&longs;t of all howvain the <lb/>conjectures of <emph type="italics"/>Apelles<emph.end type="italics"/> were; & di&longs;covering, &longs;econdly, his own opi­ <lb/>nions; withal foretelling to him, that <emph type="italics"/>Apelles<emph.end type="italics"/> would undoubtedly <lb/>be better advi&longs;ed in time, and turn to his opinion, as it afterwards <lb/>came to pa&longs;s. </s><s>And becau&longs;e that our Academian (as it was al&longs;o <lb/>the judgment of many others that were intelligent in Natures &longs;e­ <lb/>crets) thought he had in tho&longs;e three Letters inve&longs;tigated and de­ <lb/>mon&longs;trated, if not all that could be de&longs;ired, or required by hu­ <lb/>mane curio&longs;ity, at lea&longs;t all that could be attained by humane <lb/>rea&longs;on in &longs;uch a matter, he, for &longs;ome time (being bu&longs;ied in other <lb/>&longs;tudies) intermitted his continual ob&longs;ervations, and onely in com­ <lb/>placency to &longs;ome friend, joyned with him, in making now and <lb/>then an abrupt ob&longs;ervation: till that he, and after &longs;ome years, <lb/><arrow.to.target n="marg581"></arrow.to.target> <lb/>we, being then at my ^{*} Country-&longs;eat, met with one of the &longs;olita­ <lb/>ry Solar &longs;pots very big, and thick, invited withal by a clear and <lb/>con&longs;tant &longs;erenity of the Heavens, he, at my reque&longs;t, made ob&longs;er­ <lb/>vations of the whole progre&longs;&longs;e of the &longs;aid &longs;pot, carefully marking <lb/>upon a &longs;heet of paper the places that it was in every day at the <lb/>time of the Suns coming into the Meridian; and we having found <lb/>that its cour&longs;e was not in a right line, but &longs;omewhat incurvated, <lb/>we came to re&longs;olve, at la&longs;t, to make other ob&longs;ervations from time <lb/>to time; to which undertaking we were &longs;trongly induced by a <lb/>conceit, that accidentally came into the minde of my Gue&longs;t, <lb/>which he imparted to me in the&longs;e or the like words.</s></p><p type="margin"><s><margin.target id="marg578"></margin.target><emph type="italics"/>The hi&longs;tory of <lb/>the proceedings of <lb/>the Academian <lb/>for a long time a­ <lb/>bout the ob&longs;ervati­ <lb/>on of the Solar <lb/>&longs;pots.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg579"></margin.target>* Duumviro.</s></p><p type="margin"><s><margin.target id="marg580"></margin.target>* This Authors <lb/>true name is <emph type="italics"/>Chri­ <lb/>&longs;topher Scheiner us<emph.end type="italics"/> <lb/>a Je&longs;uit, and his <lb/>Book here meant <lb/>is intituled, <emph type="italics"/>Apel­ <lb/>les po&longs;t tabulam.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg581"></margin.target>* La mia villa <lb/>delle Selue.</s></p><p type="main"><s>In my opinion, <emph type="italics"/>Philip,<emph.end type="italics"/> there is a way opened to a bu&longs;ine&longs;s of <lb/>very great con&longs;equence. </s><s>For if the Axis about which the Sun <lb/>turneth be not erect perpendicularly to the plane of the Eclip­ <pb xlink:href="040/01/334.jpg" pagenum="314"/><arrow.to.target n="marg582"></arrow.to.target> <lb/>tick, but is inclined upon the &longs;ame, as its crooked cour&longs;e, but e­ <lb/>ven now ob&longs;erved, makes me believe, we &longs;hall be able to make <lb/>&longs;uch conjectures of the &longs;tates of the Sun and Earth, as neither &longs;o <lb/>&longs;olid or &longs;o rational have been hitherto deduced from any other ac­ <lb/>cident what&longs;oever. </s><s>I being awakened at &longs;o great a promi&longs;e, im­ <lb/>portun'd him to make a free di&longs;covery of his conceit unto me. <lb/></s><s>And he continued his di&longs;cour&longs;e to this purpo&longs;e. </s><s>If the Earths <lb/><arrow.to.target n="marg583"></arrow.to.target> <lb/>motion were along the Ecliptique about the Sun; and the Sun <lb/>were con&longs;tituted in the centre of the &longs;aid Ecliptick, and therein <lb/>revolved in its &longs;elf, not about the Axis of the &longs;aid Ecliptique <lb/>(which would be the Axis of the Earths annual motion) but up­ <lb/>on one inclined, it mu&longs;t needs follow, that &longs;trange changes will <lb/>repre&longs;ent them&longs;elves to us in the apparent motions of the Solar <lb/>&longs;pots, although the &longs;aid Axis of the Sun &longs;hould be &longs;uppo&longs;ed to <lb/>per&longs;i&longs;t perpetually and immutably in the &longs;ame inclination, and in <lb/>one and the &longs;ame direction towards the &longs;elf-&longs;ame point of the <lb/>Univer&longs;e. </s><s>Therefore the Terre&longs;trial Globe in the annual motion <lb/>moving round it, it will fir&longs;t follow, that to us, carried about by <lb/>the &longs;ame, the cour&longs;es of the &longs;pots &longs;hall &longs;ometimes &longs;eem to be <lb/>made in right lines, but this only twice a year, and at all other <lb/>times &longs;hall appear to be made by arches in&longs;en&longs;ibly incurvated. <lb/></s><s>Secondly, the curvity of tho&longs;e arches for one half of the year, <lb/>will &longs;hew inclined the contrary way to what they will appear in <lb/>the other half; that is, for &longs;ix moneths the convexity of the ar­ <lb/>ches &longs;hall be towards the upper part of the Solar <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> and for <lb/>the other &longs;ix moneths towards the inferiour. </s><s>Thirdly, the &longs;pots be­ <lb/>ginning to appear, and (if I may &longs;o &longs;peak) to ri&longs;e to our eye from <lb/>the left &longs;ide of the Solar <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> and going to hide them&longs;elves <lb/>and to &longs;et in the right &longs;ide, the Oriental termes, that is, of their <lb/>fir&longs;t appearings for &longs;ix moneths, &longs;hall be lower than the oppo&longs;ite <lb/>termes of their occultations; and for other &longs;ix moneths it &longs;hall <lb/>happen contrarily, to wit, that the &longs;aid &longs;pots ri&longs;ing from more e­ <lb/>levated points, and from them de&longs;cending, they &longs;hall, in their <lb/>cour&longs;es, go and hide them&longs;elves in lower points; and onely for <lb/>two dayes in all the year &longs;hall tho&longs;e termes of ri&longs;ings and &longs;et­ <lb/>tings be equilibrated: after which freely beginning by &longs;mall de­ <lb/>grees the inclination of the cour&longs;es of the &longs;pots, and day by day <lb/>growing bigger, in three moneths, it &longs;hall arrive at its greate&longs;t <lb/>obliquity, and from thence beginning to dimini&longs;h, in &longs;uch another <lb/>time it &longs;hall reduce it &longs;elf to the other <emph type="italics"/>Æquilibrium.<emph.end type="italics"/> It &longs;hall hap­ <lb/>pen, for a fourth wonder, that the cour&longs;e of the greate&longs;t obli­ <lb/>quity &longs;hall be the &longs;ame with the cour&longs;e made by the right line, <lb/>and in the day of the Libration the arch of the cour&longs;e &longs;hall &longs;eem <lb/>more than ever incurvated. </s><s>Again, in the other times, accord­ <lb/>ing as the pendency &longs;hall &longs;ucce&longs;&longs;ively dimini&longs;h, and make its ap­ <pb xlink:href="040/01/335.jpg" pagenum="315"/>proach towards the <emph type="italics"/>Æquilibrium,<emph.end type="italics"/> the incurvation of the arches <lb/>of the cour&longs;es on the contrary &longs;hall, by degrees, increa&longs;e.</s></p><p type="margin"><s><margin.target id="marg582"></margin.target><emph type="italics"/>A concipt that <lb/>came &longs;uddenly in­ <lb/>to the minde of <lb/>the Academian<emph.end type="italics"/> <lb/>Lyncæus <emph type="italics"/>concern­ <lb/>ing the great con­ <lb/>&longs;equence that fol­ <lb/>lowed upon the mo­ <lb/>tion of the Solar <lb/>&longs;pots.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg583"></margin.target><emph type="italics"/>Extravagant mu­ <lb/>tations to be ob&longs;er­ <lb/>ved in the motions <lb/>of the &longs;pots, fore­ <lb/>&longs;een by the Aca­ <lb/>demick, in ca&longs;e <lb/>the Earth had the <lb/>annual motion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I confe&longs;&longs;e, <emph type="italics"/>Salviatus,<emph.end type="italics"/> that to interrupt you in your <lb/>Di&longs;cour&longs;e is ill manners, but I e&longs;teem it no le&longs;&longs;e rudene&longs;s to per­ <lb/>mit you to run on any farther in words, whil&longs;t they are, as the <lb/>&longs;aying is, ca&longs;t into the air: for, to &longs;peak freely, I know not how <lb/>to form any di&longs;tinct conceit of &longs;o much as one of the&longs;e conclu&longs;i­ <lb/>ons, that you have pronounced; but becau&longs;e, as I thus general­ <lb/>ly and confu&longs;edly apprehend them, they hold forth things of ad­ <lb/>mirable con&longs;equence, I would gladly, &longs;ome way or other, be <lb/>made to under&longs;tand the &longs;ame.</s></p><p type="main"><s>SALV. </s><s>The &longs;ame that befalls you, befell me al&longs;o, whil&longs;t my <lb/>Gue&longs;t tran&longs;ported me with bare words; who afterwards a&longs;&longs;i&longs;ted <lb/>my capacity, by de&longs;cribing the bu&longs;ine&longs;&longs;e upon a material In&longs;tru­ <lb/><arrow.to.target n="marg584"></arrow.to.target> <lb/>ment, which was no other than a &longs;imple Sphere, making u&longs;e of <lb/>&longs;ome of its circles, but to a different purpo&longs;e from that, to which <lb/>they are commonly applied. </s><s>Now I will &longs;upply the defect of <lb/>the Sphere, by drawing the &longs;ame upon a piece of paper, as need <lb/>&longs;hall require. </s><s>And to repre&longs;ent the fir&longs;t accident by me propoun­ <lb/>ded, which was, that the cour&longs;es or journeys of the &longs;pots, twice <lb/>a year, and no more, might be &longs;een to be made in right lines, let <lb/>us &longs;uppo&longs;e this point O [<emph type="italics"/>in Fig.<emph.end type="italics"/> 4.] to be the centre of the grand <lb/>Orb, or, if you will, of the Ecliptick, and likewi&longs;e al&longs;o of the <lb/>Globe of the Sun it &longs;elf; of which, by rea&longs;on of the great di­ <lb/>&longs;tance that is between it and the Earth, we that live upon the <lb/>Earth, may &longs;uppo&longs;e that we &longs;ee the one half: we will therefore <lb/>de&longs;cribe this circle A B C D about the &longs;aid centre O, which repre­ <lb/>&longs;enteth unto us the extream term that divideth and &longs;eparates the <lb/>Hemi&longs;phere of the Sun that is apparent to us, from the other that <lb/>is occult. </s><s>And becau&longs;e that our eye, no le&longs;&longs;e than the centre of <lb/>the Earth, is under&longs;tood to be in the plane of the Ecliptick, in <lb/>which is likewi&longs;e the centre of the Sun, therefore, if we &longs;hould <lb/>fancy to our &longs;elves the body of the Sun to be cut thorow by the <lb/>&longs;aid plane, the &longs;ection will appear to our eye a right line, which <lb/>let be B O D, and upon that a perpendicular being let fall AOC, <lb/>it &longs;hall be the Axis of the &longs;aid Ecliptick, and of the annual mo­ <lb/>tion of the Terre&longs;trial Globe. </s><s>Let us next &longs;uppo&longs;e the Solar body <lb/>(without changing centre) to revolve in it &longs;elf, not about the <lb/>Axis A O C (which is the erect Axis upon the plane of the E­ <lb/>cliptick) but about one &longs;omewhat inclined, which let be this <lb/>E O I, the which fixed and unchangeable Axis maintaineth it &longs;elf <lb/>perpetually in the &longs;ame inclination and direction towards the <lb/>&longs;ame points of the Firmament, and of the Univer&longs;e. </s><s>And be­ <lb/>cau&longs;e, in the revolutions of the Solar Globe, each point of its &longs;u­ <lb/>perficies (the Poles excepted) de&longs;cribeth the circumference of a <pb xlink:href="040/01/336.jpg" pagenum="316"/>circle, either bigger or le&longs;&longs;er, according as it is more or le&longs;&longs;e re­ <lb/>mote from the &longs;aid Poles, let us take the point F, equally di&longs;tant <lb/>from them, and draw the diameter F O G, which &longs;hall be perpen­ <lb/>dicular to the Axis E I, and &longs;hall be the diameter of the grand <lb/>circle de&longs;cribed about the Poles E I. </s><s>Suppo&longs;ing not that the <lb/>Earth, and we with her be in &longs;uch a place of the Ecliptick, that <lb/>the Hemi&longs;phere of the Sun to us apparent is determin'd or bound­ <lb/>ed by the circle A B C D, which pa&longs;&longs;ing (as it alwayes doth) by <lb/>the Poles A C, pa&longs;&longs;eth al&longs;o by E I. </s><s>It is manife&longs;t, that the grand <lb/>circle, who&longs;e diameter is FG, &longs;hall be erect to the circle A B C D, <lb/>to which the ray that from our eye falleth upon the centre O, is <lb/>perpendicular; &longs;o that the &longs;aid ray falleth upon the plane of <lb/>the circle, who&longs;e diameter is F G, and therefore its circumference <lb/>will appear to us a right line, and the &longs;elf &longs;ame with F G, where­ <lb/>upon if there &longs;hould be in the point F, a &longs;pot, it comming after­ <lb/>wards to be carried about by the Solar conver&longs;ion, would, upon <lb/>the &longs;urface of the Sun, trace out the circumference of that cir­ <lb/>cle, which &longs;eems to us a right line. </s><s>Its cour&longs;e or pa&longs;&longs;age will <lb/>therefore &longs;eem &longs;traight. </s><s>And &longs;traight al&longs;o will the motion of the <lb/>other &longs;pots appear, which in the &longs;aid revolution &longs;hall de&longs;cribe le&longs;­ <lb/>&longs;er circles, as being all parallel to the greater, and to our eye <lb/>placed at an immen&longs;e di&longs;tance from them. </s><s>Now, if you do but <lb/>con&longs;ider, how that after the Earth &longs;hall in &longs;ix moneths have run <lb/>thorow half the grand Orb, and &longs;hall be &longs;ituate oppo&longs;ite to that <lb/>Hemi&longs;phere of the Sun, which is now occult unto us, &longs;o as that <lb/>the boundary of the part that then &longs;hall be &longs;een, may be the &longs;elf <lb/>&longs;ame A B C D, which al&longs;o &longs;hall pa&longs;&longs;e by the Poles E I; you <lb/>&longs;hall under&longs;tand that the &longs;ame will evene in the cour&longs;es of the <lb/>&longs;pots, as before, to wit, that all will appear to be made by right <lb/>lines. </s><s>But becau&longs;e that that accident takes not place, &longs;ave one­ <lb/>ly when the terminator or boundary pa&longs;&longs;eth by the Poles E I, <lb/>and the &longs;aid terminator from moment to moment, by meanes of <lb/>the Earths annual motion, continually altereth, therefore its pa&longs;­ <lb/>&longs;age by the fixed Poles E I, &longs;hall be momentary, and con&longs;equent­ <lb/>ly momentary &longs;hall be the time, in which the motions of tho&longs;e <lb/>&longs;pots &longs;hall appear &longs;traight. </s><s>From what hath been hitherto &longs;poken <lb/>one may comprehend al&longs;o how that the apparition and beginning <lb/>of the motion of the &longs;pots from the part F, proceeding towards <lb/>G, their pa&longs;&longs;ages or cour&longs;es are from the left hand, a&longs;cending to­ <lb/>wards the right; but the Earth being placed in the part diame­ <lb/>trically oppo&longs;ite the appearance of the &longs;pots about G, &longs;hall &longs;till <lb/>be to the left hand of the beholder, but the pa&longs;&longs;age &longs;hall be de&longs;­ <lb/>cending towards the right hand F. </s><s>Let us now de&longs;cribe the Earth <lb/>te be &longs;ituate one fourth part farther di&longs;tant from its pre&longs;ent &longs;tate, <lb/>and let us draw, as in the other figure, the terminator A B C D, <pb xlink:href="040/01/337.jpg" pagenum="317"/>[<emph type="italics"/>as in Fig.<emph.end type="italics"/> 5.] and the Axis, as before A C, by which the plane <lb/>of our Meridian would pa&longs;&longs;e, in which plane &longs;hould al&longs;o be the <lb/>Axis of the Suns revolution, with its Poles, one towards us, that <lb/>is, in the apparent Hemi&longs;phere, which Pole we will repre&longs;ent by <lb/>the point E, and the other &longs;hall fall in the occult Hemi&longs;phere, <lb/>and I mark it I. </s><s>Inclining therefore the Axis E I, with the &longs;upe­ <lb/>riour part E, towards us, the great circle de&longs;cribed by the Suns <lb/>conver&longs;ion, &longs;hall be this B F D G, who&longs;e half by us &longs;een, name­ <lb/>ly B F D, &longs;hall no longer &longs;eem unto us a right line, by rea&longs;on the <lb/>Poles E I are not in the circumference A B C D, but &longs;hall appear <lb/>incurvated, and with its convexity towards the inferiour part C. <lb/></s><s>And it is manife&longs;t, that the &longs;ame will appear in all the le&longs;&longs;er cir­ <lb/>cles parallel to the &longs;ame B F D. </s><s>It is to be under&longs;tood al&longs;o, that <lb/>when the Earth &longs;hall be diametrically oppo&longs;ite to this &longs;tate, &longs;o <lb/>that it &longs;eeth the other Hemi&longs;phere of the Sun, which now is hid, <lb/>it &longs;hall of the &longs;aid great circle behold the part D G B incurved, <lb/>with its convexity towards the &longs;uperiour part A; and the cour­ <lb/>&longs;es of the &longs;pots in the&longs;e con&longs;titutions &longs;hall be fir&longs;t, by the arch <lb/>B F D, and afterwards by the other D G B, and the fir&longs;t appari­ <lb/>tions and ultimate occultations made about the points B and D, <lb/>&longs;hall be equilibrated, and not tho&longs;e that are more or le&longs;&longs;e eleva­ <lb/>ted than the&longs;e. </s><s>But if we con&longs;titute the Earth in &longs;uch a place <lb/>of the Ecliptick, that neither the boundary A B C D, nor the <lb/>Meridian A C, pa&longs;&longs;eth by the Poles of the Axis E I, as I will &longs;hew <lb/>you anon, drawing this other Figure [<emph type="italics"/>viz. </s><s>Fig.<emph.end type="italics"/> 6.] wherein the <lb/>apparent or vi&longs;ible Pole E falleth between the arch of the termi­ <lb/>nator A B, and the &longs;ection of the Meridian A C; the diameter <lb/>of the great circle &longs;hall be F O G, and the apparent &longs;emicircle <lb/>F N G, and the occult &longs;emicircle G S F, the one incurvated with <lb/>its convexity N towards the inferiour part, and the other al&longs;o <lb/>bending with its convexity S towards the upper part of the Sun. <lb/></s><s>The ingre&longs;&longs;ions and exitions of the &longs;pots, that is, the termes F <lb/>and G &longs;hall not be librated, as the two others B and D; but F <lb/>&longs;hall be lower, and G higher: but yet with le&longs;&longs;er difference <lb/>than in the fir&longs;t Figure. </s><s>The arch al&longs;o F N G &longs;hall be incurva­ <lb/>ted, but not &longs;o much as the precedent B F D; &longs;o that in this po­ <lb/>&longs;ition the pa&longs;&longs;ages or motions of the &longs;pots &longs;hall be a&longs;cendent <lb/>from the left &longs;ide F, towards the right G, and &longs;hall be made by <lb/>curved lines. </s><s>And imagining the Earth to be con&longs;tituted in the <lb/>po&longs;ition diametrically oppo&longs;ite; &longs;o that the Hemi&longs;phere of the <lb/>Sun, which was before the occult, may be the apparent, and ter­ <lb/>minated by the &longs;ame boundary A B C D, it will be manife&longs;tly <lb/>di&longs;cerned, that the cour&longs;e of the &longs;pots &longs;hall be by the arch G S F, <lb/>beginning from the upper point G, which &longs;hall then be likewi&longs;e <lb/>from the left hand of the beholder, and going to determine, de&longs;­ <pb xlink:href="040/01/338.jpg" pagenum="318"/>&longs;cending towards the right, in the point F. </s><s>What I have hi­ <lb/>therto &longs;aid, being under&longs;tood, I believe that there remains no <lb/>difficulty in conceiving how &longs;rom the pa&longs;&longs;ing of the terminator of <lb/>the Solar Hemi&longs;pheres by the Poles of the Suns conver&longs;ion, or <lb/>neer or far from the &longs;ame, do ari&longs;e all the differences in the appa­ <lb/>rent cour&longs;es of the &longs;pots; &longs;o that by how much the more tho&longs;e Poles <lb/>&longs;hall be remote from the &longs;aid terminator, by &longs;o much the more &longs;hall <lb/>tho&longs;e cour&longs;es be incurvated, and le&longs;&longs;e oblique; whereupon at <lb/>the &longs;ame di&longs;tance, that is, when tho&longs;e Poles are in the &longs;ection of <lb/>the Meridian, the incurvation is reduced to the greate&longs;t, but the <lb/>obliquity to the lea&longs;t, that is to <emph type="italics"/>Æquilibrium,<emph.end type="italics"/> as the &longs;econd of <lb/>the&longs;e three la&longs;t figures [<emph type="italics"/>viz. </s><s>Fig.<emph.end type="italics"/> 5.] demon&longs;trateth. </s><s>On the <lb/>contrary, when the Poles are in the terminator, as the fir&longs;t of <lb/>the&longs;e three figures [<emph type="italics"/>viz. </s><s>Fig.<emph.end type="italics"/> 4.] &longs;heweth the inclination is at <lb/>the greate&longs;t, but the incurvation at the lea&longs;t, and reduced to <lb/>rectitude. </s><s>The terminator departing from the Poles, the curvity <lb/>begins to grow &longs;en&longs;ible, the obliquity all the way encrea&longs;ing, <lb/>and the inclination growing le&longs;&longs;er.</s></p><p type="margin"><s><margin.target id="marg584"></margin.target><emph type="italics"/>The fir&longs;t Ac­ <lb/>cident to be ob&longs;er­ <lb/>ved in the motion <lb/>of the Solar &longs;pots; <lb/>and con&longs;equently <lb/>all the re&longs;t explai­ <lb/>ned.<emph.end type="italics"/></s></p><p type="main"><s>The&longs;e are tho&longs;e admirable and extravagant mutations, that my <lb/>Gue&longs;t told me would from time to time appear in the progre&longs;&longs;es <lb/>of the Solar &longs;pots, if &longs;o be it &longs;hould be true that the annual mo­ <lb/>tion belonged to the Earth, and that the Sun being con&longs;tituted <lb/>in the centre of the Ecliptick, were revolved in it &longs;elf upon an <lb/>Axis, not erect, but inclined to the Plane of the &longs;aid Eclip­ <lb/>tick.</s></p><p type="main"><s>SAGR. </s><s>I do now very well apprehend the&longs;e con&longs;equences, <lb/>and believe that they will be better imprinted in my fancy, when <lb/>I &longs;hall come to reflect upon them, accommodating a Globe to <lb/>tho&longs;e inclinations, and then beholding them from &longs;everal pla­ <lb/>ces. </s><s>It now remains that you tell us what followed afterwards <lb/>touching the event of the&longs;e imaginary con&longs;equences. <lb/><arrow.to.target n="marg585"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg585"></margin.target><emph type="italics"/>The events be­ <lb/>ing ob&longs;erved, were <lb/>an&longs;werable to the <lb/>predictions.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>It came to pa&longs;&longs;e thereupon, that continuing many &longs;e­ <lb/>veral moneths to make mo&longs;t accurate ob&longs;ervations, noting down <lb/>with great exactne&longs;&longs;e the cour&longs;es or tran&longs;itions of &longs;undry &longs;pots at <lb/>divers times of the year, we found the events punctually to cor­ <lb/>re&longs;pond to the predictions.</s></p><p type="main"><s>SAGR. <emph type="italics"/>Simplicius,<emph.end type="italics"/> if this which <emph type="italics"/>Salviatus<emph.end type="italics"/> &longs;aith be true; (nor <lb/>can we di&longs;tru&longs;t him upon his word) the <emph type="italics"/>Ptolomeans<emph.end type="italics"/> and <emph type="italics"/>Aristo­ <lb/>teleans<emph.end type="italics"/> hadneed of &longs;olid arguments, &longs;trong conjectures, and <lb/>well grounded experiments to counterpoi&longs;e an objection of &longs;o <lb/>much weight, and to &longs;upport their opinion from its final over­ <lb/>throw.</s></p><p type="main"><s>SIMP. </s><s>Fair and &longs;oftly good Sir, for haply you may not yet <lb/>be got &longs;o far as you per&longs;wade your &longs;elf you are gone. </s><s>And <lb/>though I am not an ab&longs;olute ma&longs;ter of the &longs;ubject of that narra­ <pb xlink:href="040/01/339.jpg" pagenum="319"/>tion given us by <emph type="italics"/>Salviatus<emph.end type="italics"/>; yet do I not find that my Logick, </s></p><p type="main"><s><arrow.to.target n="marg586"></arrow.to.target> <lb/>whil&longs;t I have a regard to form, teacheth me, that that kind of ar­ <lb/>gumentation affords me any nece&longs;&longs;ary rea&longs;on to conclude in fa­ <lb/>vour of the <emph type="italics"/>Copernican<emph.end type="italics"/> Hypothe&longs;is, that is, of the &longs;tability of <lb/>the Sun in the centre of the Zodiack, and of the mobility of <lb/>the Earth under its circumference. </s><s>For although it be true, that <lb/>the &longs;aid conver&longs;ion of the Sun, and cirnition of the Earth being <lb/>granted, there be a nece&longs;&longs;ity of di&longs;cerning &longs;uch and &longs;uch &longs;trange <lb/>extravagancies as the&longs;e in the &longs;pots of the Sun, yet doth it not <lb/>follow that arguing <emph type="italics"/>per conver&longs;um,<emph.end type="italics"/> from finding &longs;uch like un­ <lb/>u&longs;ual accidents in the Sun, one mu&longs;t of nec&longs;&longs;ity conclude the <lb/>Earth to move by the circumference, and the Sun to be placed <lb/>in the centre of the Zodiack. </s><s>For who &longs;hall a&longs;&longs;ertain me that the <lb/>like irregularities may not as well be vi&longs;ible in the Sun, it being <lb/>moveable by the Ecliptick, to the inhabitants of the Earth, it <lb/>being al&longs;o immoveable in the centre of the &longs;ame? </s><s>Unle&longs;&longs;e you <lb/>demon&longs;trate to me, that there can be no rea&longs;on given for that ap­ <lb/>pearance, when the Sun is made moveable, and the Earth &longs;table, <lb/>I will not alter my opinion and belief that the Sun moveth, and <lb/>the Earth &longs;tandeth &longs;till.</s></p><p type="margin"><s><margin.target id="marg586"></margin.target><emph type="italics"/>Though the an­ <lb/>nual motion a&longs;&longs;ign­ <lb/>ed to the Earth an­ <lb/>&longs;werth to the<emph.end type="italics"/> Phæ­ <lb/>nomena <emph type="italics"/>of the &longs;o­ <lb/>lar &longs;pots, yet doth <lb/>it not follow by con­ <lb/>ver&longs;ion that from <lb/>the<emph.end type="italics"/> Phænomena <emph type="italics"/>of <lb/>the &longs;pots one may <lb/>infor the annual <lb/>motion to belong to <lb/>the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. <emph type="italics"/>Simplicius<emph.end type="italics"/> behaveth him&longs;elf very bravely, and argueth <lb/>very &longs;ubtilly in defence of the cau&longs;e of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy<emph.end type="italics"/>; <lb/>and if I may &longs;peak the truth, mythinks that the conver&longs;ation of <lb/><emph type="italics"/>Salviatus,<emph.end type="italics"/> though it have been but of &longs;mall continuance, hath <lb/>much farthered him in di&longs;cour&longs;ing &longs;ilogi&longs;tically. </s><s>An effect which <lb/>I know to be wrought in others as well as him. </s><s>But as to finding <lb/>and judging whether competent rea&longs;on may be rendered of the <lb/>apparent exorbitancies and irregularities in the motions of the <lb/>&longs;pots, &longs;uppo&longs;ing the Earth to be immoveable, and the Sun <lb/>moveable, I &longs;hall expect that <emph type="italics"/>Salviatus<emph.end type="italics"/> manife&longs;t his opinion to <lb/>us, for it is very probable that he he hath con&longs;idered of the <lb/>&longs;ame, and collected together whatever may be &longs;aid upon the <lb/>point.</s></p><p type="main"><s>SALV. </s><s>I have often thought thereon, and al&longs;o di&longs;cour&longs;ed <lb/>thereof with my Friend and Gue&longs;t afore-named; and touching <lb/>what is to be produced by Philo&longs;ophers and A&longs;tronomers, in de­ <lb/>fence of the ancient Sy&longs;teme, we are on one hand certain, cer­ <lb/>tain I &longs;ay, that the true and pure <emph type="italics"/>Peripateticks<emph.end type="italics"/> laughing at &longs;uch <lb/><arrow.to.target n="marg587"></arrow.to.target> <lb/>as employ them&longs;elves in &longs;uch, to their thinking, in&longs;ipid foole­ <lb/>ries, will cen&longs;ure all the&longs;e <emph type="italics"/>Phænomena<emph.end type="italics"/> to be vain illu&longs;ions of the <lb/>Chri&longs;tals; and in this manner will with little trouble free them­ <lb/>&longs;elves from the obligation of &longs;tudying any more upon the &longs;ame. <lb/></s><s>Again, as to the A&longs;tronomical Philo&longs;ophers, after we have with <lb/>&longs;ome diligence weighed that which may be alledged as a mean <lb/>between tho&longs;e two others, we have not been able to find out an <pb xlink:href="040/01/340.jpg" pagenum="320"/>an&longs;wer that &longs;ufficeth to &longs;atis&longs;ie at once the cour&longs;e of the &longs;pots, <lb/>and the di&longs;cour&longs;e of the Mind. </s><s>I will explain unto you &longs;o much <lb/>as I remember thereof, that &longs;o you may judge thereon as &longs;eems <lb/>be&longs;t unto you.</s></p><p type="margin"><s><margin.target id="marg587"></margin.target><emph type="italics"/>The Pure<emph.end type="italics"/> Peri­ <lb/>patetick <emph type="italics"/>Philo&longs;o­ <lb/>phers will laugh at <lb/>the &longs;pots and their<emph.end type="italics"/> <lb/>Phænomena, <emph type="italics"/>as <lb/>illu&longs;ions of the <lb/>Chry&longs;tals in the <lb/>Tele&longs;cope.<emph.end type="italics"/></s></p><p type="main"><s>Suppo&longs;ing that the apparent motions of the Solar &longs;pots are the <lb/>&longs;ame with tho&longs;e that have been above declared, and &longs;uppo&longs;ing the <lb/>Earth to be immoveable in the centre of the Ecliptick, in who&longs;e <lb/>circumference let the center of the Sun be placed; it is nece&longs;&longs;ary <lb/>that of all the differences that are &longs;een in tho&longs;e motions, the cau­ <lb/>&longs;es do re&longs;ide in the motions that are in the body of the Sun: <lb/>Which in the fir&longs;t place mu&longs;t nece&longs;&longs;arily revolve in it &longs;elf (<emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> <lb/><arrow.to.target n="marg588"></arrow.to.target> <lb/>about its own axis) carrying the &longs;pots along therewith; which <lb/>&longs;pots have been &longs;uppo&longs;ed, yea and proved to adhere to the So­ <lb/>lar &longs;uperficies. </s><s>It mu&longs;t &longs;econdly be confe&longs;t, that the Axis of the <lb/>Solar conver&longs;ion is not parallel to the Axis of the Ecliptick, that <lb/>is as much as to &longs;ay, that it is not perpendicularly erected upon <lb/>the Plane of the Ecliptick, becau&longs;e if it were &longs;o, the cour&longs;es and <lb/>exitions of tho&longs;e &longs;pots would &longs;eem to be made by right lines pa­ <lb/>rallel to the Ecliptick. </s><s>The &longs;aid Axis therefore is inclining, in <lb/>regard the &longs;aid cour&longs;es are for the mo&longs;t part made by curve lines. <lb/></s><s>It will be nece&longs;&longs;ary in the third place to grant that the inclinati­ <lb/>on of this Axis is not fixed, and continually extended towards <lb/>one and the &longs;ame point of the Univer&longs;e, but rather that it doth <lb/>alwayes from moment to moment go changing its direction; for <lb/>if the pendency &longs;hould always look towards the &longs;elf &longs;ame point, <lb/>the cour&longs;es of the &longs;pots would never change appearance; but <lb/>appearing at one time either right or curved, bending upwards <lb/>or downwards, a&longs;cending or de&longs;cending, they would appear <lb/>the &longs;ame at all times. </s><s>It is therefore nece&longs;&longs;ary to &longs;ay, that the <lb/>&longs;aid Axis is convertible; and is &longs;ometimes found to be in the <lb/>Plane of the circle that is extreme, terminate, or of the vi&longs;ible <lb/>Hemi&longs;phere, I mean at &longs;uch time as the cour&longs;es of the &longs;pots <lb/>&longs;eem to be made in right lines, and more than ever pendent, <lb/>which happeneth twice a year; and at other times found to be in <lb/>the Plane of the Meridian of the Ob&longs;ervator, in &longs;uch &longs;ort that <lb/>one of its Poles falleth in the vi&longs;ible Hemi&longs;phere of the Sun, and <lb/>the other in the occult; and both of them remote from the ex­ <lb/>treme points, or we may &longs;ay, from the poles of another Axis of <lb/>the Sun, which is parallel to the Axis of the Ecliptick; (which <lb/>&longs;econd Axis mu&longs;t nece&longs;&longs;arily be a&longs;&longs;igned to the Solar Globe) re­ <lb/>mote, I &longs;ay, as far as the inclination of the Axis of the revolution <lb/>of the &longs;pots doth import; and moreover that the Pole falling in <lb/>the apparent Hemi&longs;phere, is one while in the &longs;uperiour, another <lb/>while in the inferiour part thereof; for that it mu&longs;t be &longs;o, the <lb/>cour&longs;es them&longs;elves do manife&longs;tly evince at &longs;uch time as they are <pb xlink:href="040/01/341.jpg" pagenum="321"/>equilibrated, and in their greate&longs;t curvity, one while with <lb/>their convexity towards the upper part, and another while <lb/>towards the lower part of the Solar <emph type="italics"/>Di&longs;cus.<emph.end type="italics"/> And becau&longs;e <lb/>tho&longs;e po&longs;itions are in continuall alteration, making the in­ <lb/>clinations and incurvations now greater, now le&longs;&longs;er, and &longs;ome­ <lb/>times reduce them&longs;elves, the fir&longs;t &longs;ort to perfect libration, and <lb/>the &longs;econd to perfect perpendicularity, it is nece&longs;&longs;ary to a&longs;&longs;ert that <lb/>the &longs;elf &longs;ame Axis of the monethly revolution of the &longs;pots hath <lb/>a particular revolution of its own, whereby its Poles de&longs;cribe <lb/>two circles about the Poles of another Axis, which for that rea­ <lb/>&longs;on ought (as I have &longs;aid) to be a&longs;&longs;igned to the Sun, the &longs;emidi­ <lb/>ameter of which circles an&longs;wereth to the quantity of the incli­ <lb/>nation of the &longs;aid Axis. </s><s>And it is nece&longs;&longs;ary, that the time of its <lb/>Period be a year; for that &longs;uch is the time in which all the ap­ <lb/>pearances and differences in the cour&longs;es of the &longs;pots do return. <lb/></s><s>And that the revolution of this Axis, is made about the Poles of <lb/>the other Axis parallel to that of the Ecliptick, & not about other <lb/>points, the greate&longs;t inclinations and greate&longs;t incurvations, which <lb/>are always of the &longs;ame bigne&longs;s, do clearly prove. </s><s>So that finally, to <lb/>maintain the Earth fixed in the centre, it will be nece&longs;&longs;ary to a&longs;­ <lb/>&longs;ign to the Sun, two motions about its own centre, upon two &longs;eve­ <lb/>ral Axes, one of which fini&longs;heth its conver&longs;ion in a year, and the <lb/>other in le&longs;&longs;e than a moneth; which a&longs;&longs;umption &longs;eemeth, to my <lb/>under&longs;tanding, very hard, and almo&longs;t impo&longs;&longs;ible; and this de­ <lb/>pendeth on the nece&longs;&longs;ity of a&longs;cribing to the &longs;aid Solar body two <lb/>other motions about the Earth upon different Axes, de&longs;cribing <lb/>with one the Ecliptick in a year, and with the other forming &longs;pi­ <lb/>rals, or circles parallel to the Equinoctial one every day: <lb/>whereupon that third motion which ought to be a&longs;&longs;igned to the <lb/>Solar Clobe about its own centre (I mean not that almo&longs;t <lb/>monethly, which carrieth the &longs;pots about, but I &longs;peak of that o­ <lb/>ther which ought to pa&longs;&longs;e thorow the Axis and Poles of this <lb/>monethly one) ought not, for any rea&longs;on that I &longs;ee, to fini&longs;h its <lb/>Period rather in a year, as depending on the annual motion by <lb/>the Ecliptick, than in twenty four hours, as depending on the <lb/>diurnal motion upon the Poles of the Equinoctial. </s><s>I know, that <lb/>what I now &longs;peak is very ob&longs;cure, but I &longs;hall make it plain unto <lb/>you, when we come to &longs;peak of the third motion annual, a&longs;&longs;ign­ <lb/>ed by <emph type="italics"/>Copernicus,<emph.end type="italics"/> to the Earth. </s><s>Now if the&longs;e four motions, &longs;o <lb/>incongruous with each other, (all which it would be nece&longs;&longs;ary to <lb/>a&longs;&longs;ign to the &longs;elf &longs;ame body of the Sun) may be reduced to one <lb/>&longs;ole and &longs;imple motion, a&longs;&longs;igned the Sun upon an Axis that never <lb/>changeth po&longs;ition, and that without innovating any thing in the <lb/>motions for &longs;o many other cau&longs;es a&longs;&longs;igned to the Terre&longs;trial <lb/>Globe, may &longs;o ea&longs;ily &longs;alve &longs;o many extravagant appearances in <pb xlink:href="040/01/342.jpg" pagenum="322"/>the motions of the Solar &longs;pots, it &longs;eemeth really that &longs;uch an <lb/>Hypothe&longs;is ought not to be rejected.</s></p><p type="margin"><s><margin.target id="marg588"></margin.target><emph type="italics"/>If the Earth be <lb/>immoveable in the <lb/>centre of the Zodi­ <lb/>ack, there mu&longs;t be <lb/>a&longs;cribed to the Sun <lb/>four &longs;everal moti­ <lb/>ons, as is declared <lb/>at length.<emph.end type="italics"/></s></p><p type="main"><s>This, <emph type="italics"/>Simplicius,<emph.end type="italics"/> is all that came into the minds of our friend, <lb/>and my &longs;elf, that could be alledged in explanation of this <emph type="italics"/>Phæno­ <lb/>menon<emph.end type="italics"/> by the <emph type="italics"/>Copernicans,<emph.end type="italics"/> and by the <emph type="italics"/>Ptolomæans,<emph.end type="italics"/> in defence <lb/>of their opinions. </s><s>Do you inferre from thence what your judg­ <lb/>ment per&longs;wades you.</s></p><p type="main"><s>SIMP. </s><s>I acknowledge my &longs;elf unable to interpo&longs;e in &longs;o im­ <lb/>portant a deci&longs;ion: And, as to my particular thoughts, I will <lb/>&longs;tand neutral; and yet neverthele&longs;&longs;e I hope that a time will <lb/>come, when our minds being illumin'd by more lofty contempla­ <lb/>tions than the&longs;e our humane rea&longs;onings, we &longs;hall be awakened <lb/>and freed from that mi&longs;t which now is &longs;o great an hinderance to <lb/>our &longs;ight.</s></p><p type="main"><s>SAGR. </s><s>Excellent and pious is the coun&longs;el taken by <emph type="italics"/>Simpli­ <lb/>cius,<emph.end type="italics"/> and worthy to be entertained and followed by all, as that <lb/>which being derived from the highe&longs;t wi&longs;dome and &longs;upreame&longs;t <lb/>authority, may onely, with &longs;ecurity be received. </s><s>But yet &longs;o far <lb/>as humane rea&longs;on is permitted to penetrate, confining my &longs;elf <lb/>within the bounds of conjectures, and probable rea&longs;ons, I will <lb/>&longs;ay a little more re&longs;olutely than <emph type="italics"/>Simplicius<emph.end type="italics"/> doth, that among&longs;t <lb/>all the ingenuous &longs;ubtilties I ever heard, I have never met with <lb/>any thing of greater admiration to my intellect, nor that hath <lb/>more ab&longs;olutely captivated my judgment, (alwayes excepting <lb/>pure Geometrical and Arithmetical Demon&longs;trations) than the&longs;e <lb/>two conjectures taken, the one from the &longs;tations and retrograda­ <lb/>tions of the five Planets, and the other from the&longs;e irregularities of <lb/>the motions of the Solar &longs;pots: and becau&longs;e they &longs;eem to me &longs;o <lb/>ea&longs;ily and clearly to a&longs;&longs;ign the true rea&longs;on of &longs;o extravagant ap­ <lb/>pearances, &longs;hewing as if they were but one &longs;ole &longs;imple motion, <lb/>mixed with &longs;o many others, &longs;imple likewi&longs;e, but different from <lb/>each other, without introducing any difficulty, rather with obvi­ <lb/>ating tho&longs;e that accompany the other Hypothe&longs;is; I am think­ <lb/>ing that I may rationally conclude, that tho&longs;e who contumaci­ <lb/>ou&longs;ly with&longs;tand this Doctrine, either never heard, or never un­ <lb/>der&longs;tood, the&longs;e &longs;o convincing arguments.</s></p><p type="main"><s>SALV. </s><s>I will not a&longs;cribe unto them the title either of con­ <lb/>vincing, or non-convincing; in regard my intention is not, as I <lb/>have &longs;everal times told you, to re&longs;olve any thing upon &longs;o high a <lb/>que&longs;tion, but onely to propo&longs;e tho&longs;e natural and A&longs;tronomicall <lb/>rea&longs;ons, which, for the one and other Sy&longs;teme, may be produced <lb/>by me, leaving the determination to others; which determinati­ <lb/>on cannot at la&longs;t, but be very manife&longs;t: for one of the two po&longs;i­ <lb/>tions being of nece&longs;&longs;ity to be true, and the other of nece&longs;&longs;ity to <lb/>be fal&longs;e, it is a thing impo&longs;&longs;ible that (alwayes confining our &longs;elves <pb xlink:href="040/01/343.jpg" pagenum="323"/>within the limits of humane doctrine) the rea&longs;ons alledged for <lb/>the true Hypothe&longs;is &longs;hould not manife&longs;t them&longs;elves as concludent <lb/>as tho&longs;e for the contrary vain and ineffectual.</s></p><p type="main"><s>SAGR. </s><s>It will be time therefore, that we hear the objections <lb/>of the little Book of^{*} <emph type="italics"/>Conclu&longs;ions,<emph.end type="italics"/> or Di&longs;qui&longs;itions which <emph type="italics"/>Simpli-<emph.end type="italics"/> <lb/><arrow.to.target n="marg589"></arrow.to.target> <lb/><emph type="italics"/>cius<emph.end type="italics"/> did bring with him.</s></p><p type="margin"><s><margin.target id="marg589"></margin.target>* I &longs;hould have <lb/>told you, that the <lb/>true name of this <lb/>concealed Au­ <lb/>thour is <emph type="italics"/>Chri&longs;to­ <lb/>pher Scheinerus,<emph.end type="italics"/> <lb/>and its title <emph type="italics"/>Di&longs;­ <lb/>qui&longs;itiones Ma­ <lb/>thematicæ.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Here is the Book, and this is the place where the Au­ <lb/>thor fir&longs;t briefly de&longs;cribeth the Sy&longs;teme of the world, according <lb/>to the Hypothe&longs;is of <emph type="italics"/>Copernicus,<emph.end type="italics"/> &longs;aying, <emph type="italics"/>Terram igitur unà cum <lb/>Luna, totoque hoc elementari mundo<emph.end type="italics"/> Copernicus, &c.</s></p><p type="main"><s>SALV. </s><s>Forbear a little, <emph type="italics"/>Simplicius,<emph.end type="italics"/> for methinks that this <lb/>Authour, in this fir&longs;t entrance, &longs;hews him&longs;elf to be but very ill <lb/>ver&longs;t in the Hypothe&longs;is which he goeth about to confute, in re­ <lb/>gard, he &longs;aith that <emph type="italics"/>Copernicus<emph.end type="italics"/> maketh the Earth, together with <lb/>the Moon, to de&longs;cribe the ^{*} grand Orb in a year moving from <lb/>Ea&longs;t to We&longs;t; a thing that as it is fal&longs;e and impo&longs;&longs;ible, &longs;o was it <lb/><arrow.to.target n="marg590"></arrow.to.target> <lb/>never affirmed by <emph type="italics"/>Copernicus,<emph.end type="italics"/> who rather maketh it to move the <lb/>contrary way, I mean from We&longs;t to Ea&longs;t, that is, according to <lb/>the order of the Signes; whereupon we come to think the &longs;ame <lb/>to be the annual motion of the Sun, con&longs;tituted immoveable in <lb/>the centre of the Zodiack. </s><s>See the too adventurous confidence <lb/>of this man; to undertake the confutation of anothers Doctrine, <lb/>and yet to be ignorant of the primary fundamentals; upon which <lb/>his adver&longs;ary layeth the greate&longs;t and mo&longs;t important part of all <lb/>the Fabrick. </s><s>This is a bad beginning to gain him&longs;elf credit <lb/>with his Reader; but let us go on.</s></p><p type="margin"><s><margin.target id="marg590"></margin.target>* I.e. the Ecliptick</s></p><p type="main"><s>SIMP. </s><s>Having explained the Univer&longs;al Sy&longs;teme, he beginneth <lb/>to propound his objections again&longs;t this annual motion: and <lb/>the fir&longs;t are the&longs;e, which he citeth Ironically, and in deri&longs;ion of <lb/><arrow.to.target n="marg591"></arrow.to.target> <lb/><emph type="italics"/>Copernicus,<emph.end type="italics"/> and of his followers, writing that in this phanta&longs;tical <lb/>Hypothe&longs;is of the World one mu&longs;t nece&longs;&longs;arily maintain very <lb/>gro&longs;&longs;e ab&longs;urdities; namely, that the Sun, <emph type="italics"/>Venus,<emph.end type="italics"/> and <emph type="italics"/>Mercury<emph.end type="italics"/> <lb/>are below the Earth; and that grave matters go naturally up­ <lb/>wards, and the light downwards; and that <emph type="italics"/>Chri&longs;t,<emph.end type="italics"/> our Lord and <lb/>Redeemer, a&longs;cended into Hell, and de&longs;cended into Heaven, when <lb/>he approached towards the Sun, and that when <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> com­ <lb/>manded the Sun to &longs;tand &longs;till, the Earth &longs;tood &longs;till, or the Sun <lb/>moved a contrary way to that of the Earth; and that when the <lb/>Sun is in <emph type="italics"/>Cancer,<emph.end type="italics"/> the Earth runneth through <emph type="italics"/>Capricorn<emph.end type="italics"/>; and that <lb/>the <emph type="italics"/>Hyemal<emph.end type="italics"/> (or Winter) Signes make the Summer, and the <lb/><emph type="italics"/>Æ&longs;tival<emph.end type="italics"/> Winter; and that the Stars do not ri&longs;e and &longs;et to <lb/>the Earth, but the Earth to the Stars; and that the Ea&longs;t begin­ <lb/>neth in the We&longs;t, and the We&longs;t in the Ea&longs;t; and, in a word, <lb/>that almo&longs;t the whole cour&longs;e of the World is inverted.</s></p><p type="margin"><s><margin.target id="marg591"></margin.target><emph type="italics"/>In&longs;tances of a <lb/>certain Book Iro­ <lb/>nically propounded <lb/>again&longs;t<emph.end type="italics"/> Coperni­ <lb/>cus.</s></p><p type="main"><s>SALV. </s><s>Every thing plea&longs;eth me, except it be his having inter­ <pb xlink:href="040/01/344.jpg" pagenum="324"/>mixed places out of the &longs;acred Scriptures (alwayes venerable, and <lb/>to be rever'd) among&longs;t the&longs;e, but two &longs;currilous fooleries, and <lb/>attempting to wound with holy Weapons, tho&longs;e who Philo&longs;o­ <lb/>phating in je&longs;t, and for diverti&longs;ement, neither affirm nor deny, <lb/>but, &longs;ome pre&longs;uppo&longs;als and po&longs;itions being a&longs;&longs;umed, do famili­ <lb/>arly argue.</s></p><p type="main"><s>SIMP. </s><s>Truth is, he hath di&longs;plea&longs;ed me al&longs;o, and that not a <lb/>little; and e&longs;pecially, by adding pre&longs;ently after that, howbeit, <lb/>the <emph type="italics"/>Copernichists<emph.end type="italics"/> an&longs;wer, though but very impertinently to the&longs;e <lb/>and &longs;uch like other rea&longs;ons, yet can they not reconcile nor an&longs;wer <lb/>tho&longs;e things that follow.</s></p><p type="main"><s>SALV. </s><s>This is wor&longs;e than all the re&longs;t; for he pretendeth to <lb/>have things more efficacious and concludent than the Authorities <lb/>of the &longs;acred Leaves; But I pray you, let us reverence them, <lb/>and pa&longs;&longs;e on to natural and humane rea&longs;ons: and yet if he give <lb/>us among&longs;t his natural arguments, things of no more &longs;olidity, <lb/>than tho&longs;e hitherto alleadged, we may wholly decline this under­ <lb/>taking, for I as to my own parricular, do not think it fit to &longs;pend <lb/>words in an&longs;wering &longs;uch trifling impertinencies. </s><s>And as to what <lb/>he &longs;aith, that the <emph type="italics"/>Copernicans<emph.end type="italics"/> an&longs;wer to the&longs;e objections, it is <lb/>mo&longs;t fal&longs;e, nor may it be thought, that any man &longs;hould &longs;et him <lb/>&longs;elf to wa&longs;t his time &longs;o unprofitably. <lb/><arrow.to.target n="marg592"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg592"></margin.target><emph type="italics"/>Suppo&longs;ing the <lb/>annual motion to <lb/>belong to the Earth, <lb/>it followeth, that <lb/>one fixed Star, is <lb/>bigger than the <lb/>whole grand Orb.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I concur with you in the &longs;ame judgment; therefore <lb/>let us hear the other in&longs;tances that he brings, as much &longs;tronger. <lb/></s><s>And ob&longs;erve here, how he with very exact computations conclud­ <lb/>eth, that if the grand Orb of the Earth, or the ecliptick, in which <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> maketh it to run in a year round the Sun, &longs;hould be <lb/>as it were, in&longs;en&longs;ible, in re&longs;pect of the immen&longs;itie of the Starry <lb/>Sphære, according as the &longs;aid <emph type="italics"/>Copernicus,<emph.end type="italics"/> &longs;aith it is to be &longs;up­ <lb/>po&longs;ed, it would be nece&longs;&longs;ary to grant and confirm, that the fixed <lb/>Stars were remote from us, an unconceivable di&longs;tance, and that <lb/>the le&longs;&longs;er of them, were bigger than the whole grand Orb afore­ <lb/>&longs;aid, and &longs;ome other much bigger than the whole Sphære of <emph type="italics"/>Sa­ <lb/>turn<emph.end type="italics"/>; Ma&longs;&longs;es certainly too exce&longs;&longs;ively va&longs;t, unimaginable, and <lb/>incredible.</s></p><p type="main"><s><arrow.to.target n="marg593"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg593"></margin.target>Tycho <emph type="italics"/>his Ar­ <lb/>gument grounded <lb/>upon a fal&longs;e Hypo­ <lb/>the&longs;is.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I have heretofore &longs;een &longs;uch another objection brought <lb/>by <emph type="italics"/>Tycho<emph.end type="italics"/> again&longs;t <emph type="italics"/>Copernicus,<emph.end type="italics"/> and this is not the fir&longs;t time that I <lb/>have di&longs;covered the fallacy, or, to &longs;ay better, the fallacies of this <lb/>Argumemtation, founded upon a mo&longs;t fal&longs;e Hypothe&longs;is, and upon </s></p><p type="main"><s><arrow.to.target n="marg594"></arrow.to.target> <lb/>a Piopo&longs;ition of the &longs;aid <emph type="italics"/>Copernicus,<emph.end type="italics"/> under&longs;tood by his adver&longs;a­ <lb/>ries, with too punctual a nicity, according to the practi&longs;e of tho&longs;e <lb/>pleaders, who finding the flaw to be in the very merit of their <lb/>cau&longs;e, keep to &longs;ome one word, fallen unawares from the contra­ <lb/>ry partie, and fly out into loud and tedious de&longs;cants upon that. <lb/></s><s>But for your better information; <emph type="italics"/>Copernicus<emph.end type="italics"/> having declared <pb xlink:href="040/01/345.jpg" pagenum="325"/>tho&longs;e admirable con&longs;equences which are derived from the Earths <lb/><arrow.to.target n="marg595"></arrow.to.target> <lb/>annual motion, to the other Planets, that is to &longs;ay, of the ^{*} directi­ <lb/><arrow.to.target n="marg596"></arrow.to.target> <lb/>ons and retrogradations of the three uppermo&longs;t in particular; he <lb/>&longs;ubjoyneth, that this apparent mutation (which is di&longs;cerned more <lb/>in <emph type="italics"/>Mars<emph.end type="italics"/> than in <emph type="italics"/>Jupiter,<emph.end type="italics"/> by rea&longs;on <emph type="italics"/>Jupiter<emph.end type="italics"/> is more remote, and <lb/>yet le&longs;&longs;e in <emph type="italics"/>Saturn,<emph.end type="italics"/> by rea&longs;on it is more remote than <emph type="italics"/>Jupiter<emph.end type="italics"/>) in <lb/>the fixed Stars, did remain imperceptible, by rea&longs;on of their <lb/>immen&longs;e remotene&longs;&longs;e from us, in compari&longs;on of the di&longs;tances of <lb/><emph type="italics"/>Jupiter<emph.end type="italics"/> or <emph type="italics"/>Saturn.<emph.end type="italics"/> Here the Adver&longs;aries of this opinion ri&longs;e up, <lb/>and &longs;uppo&longs;ing that fore-named imperceptibility of <emph type="italics"/>Copernicus,<emph.end type="italics"/> as <lb/>if it had been taken by him, for a real and ab&longs;olute thing of no­ <lb/>thing, and adding, that a fixed Star of one of the le&longs;&longs;er magni­ <lb/>tudes, is notwith&longs;tanding perceptible, &longs;eeing that it cometh un­ <lb/>der the &longs;ence of &longs;eeing, they go on to calculate with the inter­ <lb/>vention of other fal&longs;e a&longs;&longs;umptions, and concluding that it is nece&longs;­ <lb/>&longs;ary by the <emph type="italics"/>Copernican<emph.end type="italics"/> Doctrine, to admit, that a fixed Star is much <lb/>bigger than the whole grand Orb. </s><s>Now to di&longs;cover the vanity <lb/><arrow.to.target n="marg597"></arrow.to.target> <lb/>of this their whole proceeding, I &longs;hall &longs;hew that a fixed Star of the <lb/>&longs;ixth magnitude, being &longs;uppo&longs;ed to be no bigger than the Sun, <lb/>one may thence conclude with true demon&longs;trations, that the di­ <lb/>&longs;tance of the &longs;aid fixed Stars from us, cometh to be &longs;o great, that <lb/>the annual motion of the Earth, which cau&longs;eth &longs;o great and <lb/>notable variations in the Planets, appears &longs;carce ob&longs;ervable in <lb/>them; and at the &longs;ame time, I will di&longs;tinctly &longs;hew the gro&longs;s <lb/>fallacies, in the a&longs;&longs;umptions of <emph type="italics"/>Copernicus<emph.end type="italics"/> his Adver&longs;aries.</s></p><p type="margin"><s><margin.target id="marg594"></margin.target><emph type="italics"/>Litigious Lawyers <lb/>that are entertain­ <lb/>ed in an ill cau&longs;e, <lb/>keep clo&longs;e to &longs;ome <lb/>expre&longs;&longs;ion fallen <lb/>from the adver&longs;e <lb/>party at unawares.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg595"></margin.target>* Or progre&longs;&longs;ions.</s></p><p type="margin"><s><margin.target id="marg596"></margin.target><emph type="italics"/>The apparent <lb/>diver&longs;ity of motion <lb/>in the Planets, is <lb/>in&longs;en&longs;ible in the <lb/>fixed Start.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg597"></margin.target><emph type="italics"/>Suppo&longs;ing that a <lb/>fixed Star of the <lb/>&longs;ixth magnitude is <lb/>no bigger than the<emph.end type="italics"/> <lb/>Sun, <emph type="italics"/>the diver&longs;itie <lb/>which is &longs;o great <lb/>in the Planets, in <lb/>the fixed Stars is <lb/>almost in&longs;en&longs;ible.<emph.end type="italics"/></s></p><p type="main"><s>And fir&longs;t of all, I &longs;uppo&longs;e with the &longs;aid <emph type="italics"/>Copernicus,<emph.end type="italics"/> and al&longs;o <lb/><arrow.to.target n="marg598"></arrow.to.target> <lb/>with his oppo&longs;ers, that the Semidiameter of the grand Orb, which <lb/>is the di&longs;tance of the Earth from the Sun, containeth 1208 Semi­ <lb/>diameters of the &longs;aid Earth. </s><s>Secondly, I premi&longs;e with the allow­ <lb/>ance afore&longs;aid, and of truth, that the ^{*} apparent diameter of the <lb/><arrow.to.target n="marg599"></arrow.to.target> <lb/>Sun in its mean di&longs;tance, to be about half a degree, that is, 30. <lb/><emph type="italics"/>min. </s><s>prim.<emph.end type="italics"/> which are 1800. &longs;econds, that is, 108000. thirds. <lb/></s><s>And becau&longs;e the apparent Diameter of a fixed Star of the fir&longs;t <lb/><arrow.to.target n="marg600"></arrow.to.target> <lb/>magnitude, is no more than 5. &longs;econds, that is, 300. thirds, and <lb/>the Diameter of a fixed Star of the &longs;ixth magnitude, 50. thirds, <lb/>(and herein is the greate&longs;t errour of the <emph type="italics"/>Anti-Copernicans<emph.end type="italics"/>) There­ <lb/><arrow.to.target n="marg601"></arrow.to.target> <lb/>fore the Diameter of the Sun, containeth the Diameter of a <lb/>fixed Star of the &longs;ixth magnitude 2160 times. </s><s>And therefore <lb/>if a fixed Star of the &longs;ixth magnitude, were &longs;uppo&longs;ed to be really <lb/>equal to the Sun, and not bigger, which is the &longs;ame as to &longs;ay, if <lb/>the Sun were &longs;o far removed, that its Diameter &longs;hould &longs;eem to <lb/>be one of the 2160. parts of what it now appeareth, its di&longs;tance <lb/>ought of nece&longs;&longs;ity to be 2160. times greater than now in effect it <lb/>is, which is as much as to &longs;ay, that the di&longs;tance of the fixed Stars <lb/>of the &longs;ixth magnitude, is 2160. Semidiameters of the grand <pb xlink:href="040/01/346.jpg" pagenum="326"/>Orb. </s><s>And becau&longs;e the di&longs;tance of the Sun from the Earth, con­ <lb/><arrow.to.target n="marg602"></arrow.to.target> <lb/>tains by common con&longs;ent 1208. Semidiameters of the &longs;aid Earth, <lb/>and the di&longs;tance of the fixed Stars (as hath been &longs;aid) 2160. <lb/>Semediameters of the grand Orb, therefore the Semediameter of <lb/>the Earth is much greater (that is almo&longs;t double) in compari&longs;on <lb/>of the grand Orb, than the Semediameter of the grand Orb, in <lb/><arrow.to.target n="marg603"></arrow.to.target> <lb/>relation to the di&longs;tance of the Starry Sphære; and therefore the <lb/>variation of a&longs;pect in the fixed Stars, cau&longs;ed by the Diameter of <lb/>the grand Orb, can be but little more ob&longs;ervable, than that which <lb/>is ob&longs;erved in the Sun, occa&longs;ioned by the Semediameter of the <lb/>Earth.</s></p><p type="margin"><s><margin.target id="marg598"></margin.target><emph type="italics"/>The di&longs;tance of <lb/>the Sun, containeth<emph.end type="italics"/> <lb/>1208 <emph type="italics"/>Semid. </s><s>of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg599"></margin.target>* The Diameter <lb/>of the Sun, half a <lb/>degree.</s></p><p type="margin"><s><margin.target id="marg600"></margin.target><emph type="italics"/>The Diameter <lb/>of a fixed Star, of <lb/>the fir&longs;t magni­ <lb/>tude, and of one of <lb/>the &longs;ixth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg601"></margin.target><emph type="italics"/>The apparent <lb/>Diameter of the <lb/>Sun, how much it <lb/>is bigger than that <lb/>of a fixed &longs;tar.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg602"></margin.target><emph type="italics"/>The di&longs;tance of <lb/>a fixed &longs;tar of the <lb/>&longs;ixth magnitude, <lb/>how much it is, the <lb/>&longs;tar being &longs;uppo&longs;ed <lb/>to be equal to the <lb/>Sun.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg603"></margin.target><emph type="italics"/>In the fixed &longs;tars <lb/>the diver&longs;itie of a­ <lb/>&longs;pect, cau&longs;ed by <lb/>the grand Orb, is <lb/>little more then <lb/>that cau&longs;ed by the <lb/>Earth in the Snn.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This is a great fall for the fir&longs;t &longs;tep.</s></p><p type="main"><s>SALV. </s><s>It is doubtle&longs;&longs;e an errour; for a fixed Star of the &longs;ixth <lb/><arrow.to.target n="marg604"></arrow.to.target> <lb/>magnitude, which by the computation of this Authour, ought, <lb/>for the upholding the propo&longs;ition of <emph type="italics"/>Copernicus,<emph.end type="italics"/> to be as big as <lb/>the whole grand Orb, onely by &longs;uppo&longs;ing it equal to the Sun, <lb/>which Sun is le&longs;&longs;e by far, than the hundred and &longs;ix milionth part <lb/>of the &longs;aid grand Orb, maketh the &longs;tarry Sphære &longs;o great and high <lb/>as &longs;ufficeth to overthrow the in&longs;tance brought again&longs;t the &longs;aid <emph type="italics"/>Co­ <lb/>pernicus.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg604"></margin.target><emph type="italics"/>A &longs;tar of the <lb/>&longs;ixth magnitude, <lb/>&longs;uppo&longs;ed by<emph.end type="italics"/> Tycho <lb/><emph type="italics"/>and the Authour <lb/>of the Book of Con­ <lb/>clu&longs;ions, an hun­ <lb/>dred and &longs;ix mili­ <lb/>ons of times bigger <lb/>than needs.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Favour me with this computation.</s></p><p type="main"><s>SALV. </s><s>The &longs;upputation is ea&longs;ie and &longs;hort. </s><s>The Diameter of <lb/>the Sun, is eleven &longs;emediameters of the Earth, and the Diameter <lb/><arrow.to.target n="marg605"></arrow.to.target> <lb/>of the grand Orb, contains 2416. of tho&longs;e &longs;ame &longs;emediameters, <lb/>by the a&longs;cent of both parties; &longs;o that the Diameter of the &longs;aid <lb/>Orb, contains the Suns Diameter 220. times very near. </s><s>And <lb/>becau&longs;e the Spheres are to one another, as the Cubes of their Di­ <lb/>ameters, let us make the Cube of 220. which is 106480000. and <lb/>we &longs;hall have the grand Orb, an hundred and &longs;ix millions, four <lb/>hundred and eighty thou&longs;and times bigger than the Sun, to which <lb/>grand Orb, a &longs;tar of the fixth magnitude, ought to be equal, ac­ <lb/>cording to the a&longs;&longs;ertion of this Authour.</s></p><p type="margin"><s><margin.target id="marg605"></margin.target><emph type="italics"/>The computati­ <lb/>on of the magni­ <lb/>tude of the fixed <lb/>Stars, in re&longs;pect to <lb/>the grand Orb.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The errour then of the&longs;e men, con&longs;i&longs;teth in being ex­ <lb/>treamly mi&longs;taken, in taking the apparent Diameter of the fixed <lb/>Stars.</s></p><p type="main"><s>SALV. </s><s>This is one, but not the onely errour of them; and <lb/><arrow.to.target n="marg606"></arrow.to.target> <lb/>indeed, I do very much admire how &longs;o many <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> and <lb/>tho&longs;e very famous, as are <emph type="italics"/>Alfagranus, Albategnus, Tebizius,<emph.end type="italics"/> and <lb/>much more modernly the <emph type="italics"/>Tycho's<emph.end type="italics"/> and <emph type="italics"/>Clavius's,<emph.end type="italics"/> and in &longs;umm, <lb/>all the predece&longs;&longs;ors of our <emph type="italics"/>Academian,<emph.end type="italics"/> &longs;hould have been &longs;o gro&longs;ly <lb/>mi&longs;taken, in determining the magnitudes of all the Stars, as well <lb/>&longs;ixed as moveable, the two Luminaries excepted out of that num­ <lb/>ber; and that they have not taken any heed to the adventitious <lb/>irradiations that deceitfully repre&longs;ent them an hundred and more <lb/>times bigger, than when they are beheld, without tho&longs;e capilli­ <pb xlink:href="040/01/347.jpg" pagenum="327"/>ous rayes, nor can this their inadvertency be excu&longs;ed, in regard <lb/>that it was in their power to have beheld them at their plea&longs;ure <lb/>without tho&longs;e tre&longs;&longs;es, which is done, by looking upon them at <lb/>their fir&longs;t appearance in the evening, or their la&longs;t occultation in <lb/><arrow.to.target n="marg607"></arrow.to.target> <lb/>the comming on of day; and if none of the re&longs;t, yet <emph type="italics"/>Venus,<emph.end type="italics"/> <lb/>which oft times is &longs;een at noon day, &longs;o &longs;mall, that one mu&longs;t &longs;har­ <lb/>pen the &longs;ight in di&longs;cerning it; and again, in the following night, <lb/>&longs;eemeth a great flake of light, might adverti&longs;e them of their fal­ <lb/>lacy; for I will not believe that they thought the true <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> to <lb/>be that which is &longs;een in the ob&longs;cure&longs;t darkne&longs;&longs;es, and not that <lb/>which is di&longs;cerned in the luminous <emph type="italics"/>Medium<emph.end type="italics"/>: for our lights, which <lb/>&longs;een by night afar off appear great, and neer at hand &longs;hew their <lb/>true lu&longs;tre to be terminate and &longs;mall, might have ea&longs;ily have <lb/>made them cautious; nay, if I may freely &longs;peak my thoughts, I <lb/>ab&longs;olutely believe that none of them, no not <emph type="italics"/>Tycho<emph.end type="italics"/> him&longs;elf, &longs;o <lb/>accurate in handling A&longs;tronomical In&longs;truments, and that &longs;o great <lb/>and accurate, without &longs;paring very great co&longs;t in their con&longs;tru­ <lb/>ction, did ever go about to take and mea&longs;ure the apparent dia­ <lb/>meter of any Star, the Sun and Moon excepted; but I think, <lb/>that arbitrarily, and as we &longs;ay, with the eye, &longs;ome one of the <lb/>more antient of them pronounced the thing to be &longs;o and &longs;o, and <lb/>that all that followed him afterwards, without more ado, kept <lb/>clo&longs;e to what the fir&longs;t had &longs;aid; for if any one of them had ap­ <lb/>plied him&longs;elf to have made &longs;ome new proof of the &longs;ame, he would <lb/>doubtle&longs;&longs;e have di&longs;covered the fraud.</s></p><p type="margin"><s><margin.target id="marg606"></margin.target><emph type="italics"/>A common er­ <lb/>rour of all the<emph.end type="italics"/> A­ <lb/>&longs;tronomers, <emph type="italics"/>touch­ <lb/>ing the magnitude <lb/>of the &longs;tars.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg607"></margin.target>Venus <emph type="italics"/>renders the <lb/>errour of A&longs;trono­ <lb/>mers in determin­ <lb/>ing the magnitudes <lb/>of &longs;tars inexcu&longs;a­ <lb/>ble.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>But if they wanted the Tele&longs;cope, and you have al­ <lb/>ready &longs;aid, that our <emph type="italics"/>Friend<emph.end type="italics"/> with that &longs;ame In&longs;trument came to <lb/>the knowledge of the truth, they ought to be excu&longs;ed, and not <lb/>accu&longs;ed of ignorance.</s></p><p type="main"><s>SALV. </s><s>This would hold good, if without the Tele&longs;cope the <lb/>bu&longs;ine&longs;&longs;e could not be effected. </s><s>Its true, that this In&longs;trument by <lb/>&longs;hewing the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> of the Star naked, and magnified an hun­ <lb/>dred or a thou&longs;and times, rendereth the operation much more ea­ <lb/>&longs;ie, but the &longs;ame thing may be done, although not altogether &longs;o <lb/>exactly, without the In&longs;trument, and I have many times done <lb/>the &longs;ame, and my method therein was this. </s><s>I have cau&longs;ed a rope <lb/><arrow.to.target n="marg608"></arrow.to.target> <lb/>to be hanged towards &longs;ome Star, and I have made u&longs;e of the <lb/>Con&longs;tellation, called the <emph type="italics"/>Harp,<emph.end type="italics"/> which ri&longs;eth between the North <lb/>and ^{*} North-ea&longs;t, and then by going towards, and from <lb/><arrow.to.target n="marg609"></arrow.to.target> <lb/>the &longs;aid rope, interpo&longs;ed between me and the Star, I have found <lb/>the place from whence the thickne&longs;&longs;e of the rope hath ju&longs;t hid <lb/>the Star from me: this done, I have taken the di&longs;tance from the <lb/>eye to the rope, which was one of the &longs;ides including the angle <lb/>that was compo&longs;ed in the eye, and ^{*} which in&longs;i&longs;teth upon the <lb/><arrow.to.target n="marg610"></arrow.to.target> <lb/>thickne&longs;&longs;e of the rope, and which is like, yea the &longs;ame with the <pb xlink:href="040/01/348.jpg" pagenum="328"/>angle in the Starry Sphere, that in&longs;i&longs;teth upon the diameter of <lb/>the Star, and by the proportion of the ropes thickne&longs;&longs;e to the <lb/>di&longs;tance from the eye to the rope, by the table of Arches and <lb/>Chords, I have immediately found the quantity of the angle; u­ <lb/>&longs;ing all the while the wonted caution that is ob&longs;erved in taking <lb/>angles &longs;o acute, not to forme the concour&longs;e of the vi&longs;ive rayes <lb/>in the centre of the eye, where they are onely refracted, but <lb/>beyond the eye, where really the pupils greatne&longs;&longs;e maketh them <lb/>to concur.</s></p><p type="margin"><s><margin.target id="marg608"></margin.target><emph type="italics"/>A way to mea­ <lb/>&longs;ure the apparent <lb/>diameter of a &longs;tar.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg609"></margin.target>* Rendred in <lb/>Latine <emph type="italics"/>Corum,<emph.end type="italics"/> that <lb/>is to &longs;ay, North­ <lb/>we&longs;t.</s></p><p type="margin"><s><margin.target id="marg610"></margin.target>* <emph type="italics"/>i.e.<emph.end type="italics"/> Is &longs;ubten­ <lb/>ded by.</s></p><p type="main"><s>SAGR. </s><s>I apprehend this your cautelous procedure, albeit I <lb/>have a kind of hæ&longs;itancy touching the &longs;ame, but that which mo&longs;t <lb/>puzzleth me is, that in this operation, if it be made in the dark <lb/>of night, methinks that you mea&longs;ure the diameter of the irradia­ <lb/>ted <emph type="italics"/>Di&longs;cus,<emph.end type="italics"/> and not the true and naked face of the Star.</s></p><p type="main"><s>SALV. </s><s>Not &longs;o, Sir, for the rope in covering the naked body <lb/>of the Star, taketh away the rayes, which belong not to it, but <lb/>to our eye, of which it is deprived &longs;o &longs;oon as the true <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> <lb/>thereof is hid; and in making the ob&longs;ervation, you &longs;hall &longs;ee, how <lb/>unexpectedly a little cord will cover that rea&longs;onable big body of <lb/>light, which &longs;eemed impo&longs;&longs;ible to be hid, unle&longs;&longs;e it were with a <lb/>much broader Screene: to mea&longs;ure, in the next place, and exa­ <lb/>ctly to find out, how many of tho&longs;e thickne&longs;&longs;es of the rope inter­ <lb/>po&longs;e in the di&longs;tance between the &longs;aid rope and the eye, I take not <lb/>onely one diameter of the rope, but laying many pieces of the <lb/>&longs;ame together upon a Table, &longs;o that they touch, I take with a <lb/>pair of Compa&longs;&longs;es the whole &longs;pace occupied by fifteen, or twen­ <lb/>ty of them, and with that mea&longs;ure I commen&longs;urate the di&longs;tance <lb/>before with another &longs;maller cord taken from the rope to the con­ <lb/>cour&longs;e of the vi&longs;ive rayes. </s><s>And with this &longs;ufficiently-exact ope­ <lb/>ration I finde the apparent diameter of a fixed Star of the fir&longs;t <lb/>magnitude, commonly e&longs;teemed to be 2 <emph type="italics"/>min. </s><s>pri.<emph.end type="italics"/> and al&longs;o 3 <emph type="italics"/>min. <lb/></s><s>prim.<emph.end type="italics"/> by <emph type="italics"/>Tycho<emph.end type="italics"/> in his <emph type="italics"/>A&longs;tronomical Letters, cap.<emph.end type="italics"/> 167. to be no <lb/><arrow.to.target n="marg611"></arrow.to.target> <lb/>more than 5 <emph type="italics"/>&longs;econds,<emph.end type="italics"/> which is one of the 24. or 36. parts of what <lb/>they have held it: &longs;ee now upon what gro&longs;&longs;e errours their Do­ <lb/>ctrines are founded.</s></p><p type="margin"><s><margin.target id="marg611"></margin.target><emph type="italics"/>The diameter of <lb/>a fixed &longs;tar of the <lb/>fir&longs;t magnitude not <lb/>more than five &longs;ec. <lb/></s><s>min.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I &longs;ee and comprehend this very well, but before we <lb/>pa&longs;&longs;e any further, I would propound the doubt that ari&longs;eth in <lb/>me in the finding the concour&longs;e [or inter&longs;ection] of the vi&longs;ual <lb/>rayes beyond the eye, when ob&longs;ervation is made of objects com­ <lb/>prehended between very acute angles; and my &longs;cruple proceeds <lb/>from thinking, that the &longs;aid concour&longs;e may be &longs;ometimes more <lb/>remote, and &longs;ometimes le&longs;&longs;e; and this not &longs;o much, by meanes <lb/>of the greater or le&longs;&longs;er magnitude of the object that is beheld, as <lb/>becau&longs;e that in ob&longs;erving objects of the &longs;ame bigne&longs;&longs;e, it &longs;eems <lb/>to me that the concour&longs;e of the rayes, for certain other re­ <pb xlink:href="040/01/349.jpg" pagenum="329"/>&longs;pects ought to be made more and le&longs;&longs;e remote from the eye.</s></p><p type="main"><s>SALV. </s><s>I &longs;ee already, whither the apprehen&longs;ion of <emph type="italics"/>Sagredus,<emph.end type="italics"/> <lb/>a mo&longs;t diligent ob&longs;erver of Natures &longs;ecrets, tendeth; and I <lb/><arrow.to.target n="marg612"></arrow.to.target> <lb/>would lay any wager, that among&longs;t the thou&longs;ands that have ob­ <lb/>&longs;erved Cats to contract and inlarge the pupils of their eyes very <lb/>much, there are not two, nor haply one that hath ob&longs;erved the <lb/>like effect to be wrought by the pupils of men in &longs;eeing, whil&longs;t <lb/>the <emph type="italics"/>medium<emph.end type="italics"/> is much or little illumin'd, and that in the open light <lb/>the circlet of the pupil dimini&longs;heth con&longs;iderably: &longs;o that in loo­ <lb/>king upon the face or <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> of the Sun, it is reduced to a &longs;mall­ <lb/>ne&longs;&longs;e le&longs;&longs;er than a grain of ^{*} <emph type="italics"/>Panick,<emph.end type="italics"/> and in beholding objects <lb/><arrow.to.target n="marg613"></arrow.to.target> <lb/>that do not &longs;hine, and are in a le&longs;&longs;e luminous <emph type="italics"/>medium,<emph.end type="italics"/> it is inlar­ <lb/>god to the bigne&longs;&longs;e of a Lintel or more; and in &longs;umme this <lb/>expan&longs;ion and contraction differeth in more than decuple pro­ <lb/>portion: From whence it is manife&longs;t, that when the pupil is <lb/>much dilated, it is nece&longs;&longs;ary that the angle of the rayes con­ <lb/>cour&longs;e be more remote from the eye; which happeneth in be­ <lb/>holding objects little luminated. </s><s>This is a Doctrine which <emph type="italics"/>Sa­ <lb/>gredus<emph.end type="italics"/> hath, ju&longs;t now, given me the hint of, whereby, if we <lb/>were to make a very exact ob&longs;ervation, and of great con&longs;e­ <lb/>quence, we are advertized to make the ob&longs;ervation of that con­ <lb/>cour&longs;e in the act of the &longs;ame, or ju&longs;t &longs;uch another operation; but <lb/>in this our ca&longs;e, wherein we are to &longs;hew the errour of <emph type="italics"/>Astrono­ <lb/>mers,<emph.end type="italics"/> this accuratene&longs;&longs;e is not nece&longs;&longs;ary: for though we &longs;hould, <lb/>in favour of the contrary party, &longs;uppo&longs;e the &longs;aid concour&longs;e to be <lb/>made upon the pupil it &longs;elf, it would import little, their mi&longs;take <lb/>being &longs;o great. </s><s>I am not certain, <emph type="italics"/>Sagredus,<emph.end type="italics"/> that this would have <lb/>been your objection.</s></p><p type="margin"><s><margin.target id="marg612"></margin.target><emph type="italics"/>The circle of the <lb/>pupil of the eye en­ <lb/>largeth and con­ <lb/>tracteth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg613"></margin.target>+ <emph type="italics"/>Panicum,<emph.end type="italics"/> a <lb/>&longs;mall grain like to <lb/>Mill, I take it to be <lb/>the &longs;ame with that <lb/>called Bird Seed.</s></p><p type="main"><s>SAGR. </s><s>It is the very &longs;ame, and I am glad that it was not al­ <lb/>together without rea&longs;on, as your concurrence in the &longs;ame a&longs;&longs;u­ <lb/>reth me; but yet upon this occa&longs;ion I would willingly hear what <lb/>way may be taken to finde out the di&longs;tance of the concour&longs;e of <lb/>the vi&longs;ual rayes.</s></p><p type="main"><s>SALV. </s><s>The method is very ea&longs;ie, and this it is, I take two <lb/>long^{*} labels of paper, one black, and the other white, and make <lb/><arrow.to.target n="marg614"></arrow.to.target> <lb/>the black half as broad as the white; then I &longs;tick up the white a­ <lb/>gain&longs;t a wall, and far from that I place the other upon a &longs;tick, or <lb/>other &longs;upport, at a di&longs;tance of fifteen or twenty yards, and rece­ <lb/>ding from this, &longs;econd another &longs;uch a &longs;pace in the &longs;ame right line, <lb/>it is very manife&longs;t, that at the &longs;aid di&longs;tance the right lines will <lb/>concur, that departing from the termes of the breadth of the <lb/>white piece, &longs;hall pa&longs;&longs;e clo&longs;e by the edges of the other label pla­ <lb/>ced in the mid-way; whence it followeth, that in ca&longs;e the eye <lb/>were placed in the point of the &longs;aid concour&longs;e or inter&longs;ection, <lb/>the black &longs;lip of paper in the mid&longs;t would preci&longs;ely hide the op­ <pb xlink:href="040/01/350.jpg" pagenum="330"/>po&longs;ite blank, if the &longs;ight were made in one onely point; but if we <lb/>&longs;hould find, that the edges of the white cartel appear di&longs;covered, <lb/>it &longs;hall be a nece&longs;&longs;ary argument that the vi&longs;ual rayes do not i&longs;&longs;ue <lb/>from one &longs;ole point. </s><s>And to make the white label to be hid by <lb/>the black, it will be requi&longs;ite to draw neerer with the eye: <lb/>Therefore, having approached &longs;o neer, that the intermediate la­ <lb/>bel covereth the other, and noted how much the required ap­ <lb/>proximation was, the quantity of that approach &longs;hall be the cer­ <lb/>tain mea&longs;ure, how much the true concour&longs;e of the vi&longs;ive rayes, is <lb/>remote from the eye in the &longs;aid operation, and we &longs;hall moreover <lb/>have the diameter of the pupil, or of that circlet from whence <lb/>the vi&longs;ive rayes proceed: for it &longs;hall be to the breadth of the <lb/>black paper, as is the di&longs;tance from the concour&longs;e of the lines, <lb/>that are produced by the edges of the papers to the place where <lb/>the eye &longs;tandeth, when it fir&longs;t &longs;eeth the remote paper to be hid <lb/>by the intermediate one, as that di&longs;tance is, I &longs;ay, to the di&longs;tance <lb/>that is between tho&longs;e two papers. </s><s>And therefore when we <lb/>would, with exactne&longs;&longs;e, mea&longs;ure the apparent diameter of a Star, <lb/>having made the ob&longs;ervation in manner, as afore&longs;aid, it would be <lb/>nece&longs;&longs;ary to compare the diameter of the rope to the diameter of <lb/>the pupil; and having found <emph type="italics"/>v.g.<emph.end type="italics"/> the diameter of the rope to be <lb/>quadruple to that of the pupil, and the di&longs;tance of the eye from <lb/>the rope to be, for example, thirty yards, we would &longs;ay, that the <lb/>true concour&longs;e of the lines produced from the ends or extremi­ <lb/>ties of the diameter of the &longs;tar, by the extremities of the dia­ <lb/>meter of the rope, doth fall out to be fourty yards remote from <lb/>the &longs;aid rope, for &longs;o we &longs;hall have ob&longs;erved, as we ought, the pro­ <lb/>portion between the di&longs;tance of the rope from the concour&longs;e of <lb/>the &longs;aid lines, and the di&longs;tance from the &longs;aid concour&longs;e to the <lb/>place of the eye, which ought to be the &longs;ame that is between <lb/>the diameter of the rope, and diameter of the pupil.</s></p><p type="margin"><s><margin.target id="marg614"></margin.target>* Stri&longs;ce. <lb/><emph type="italics"/>How to find the <lb/>di&longs;tance of the rays <lb/>concour&longs;e from the <lb/>pupil.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I have perfectly under&longs;tood the whole bu&longs;ine&longs;&longs;e, and <lb/>therefore let us hear what <emph type="italics"/>Simplicius<emph.end type="italics"/> hath to alledge in defence of <lb/>the <emph type="italics"/>Anti-Copernicans.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Albeit that grand and altogether incredible inconve­ <lb/>nience in&longs;i&longs;ted upon by the&longs;e adver&longs;aries of <emph type="italics"/>Copernicus<emph.end type="italics"/> be much <lb/>moderated and abated by the di&longs;cour&longs;e of <emph type="italics"/>Salviatus,<emph.end type="italics"/> yet do I <lb/>not think it weakened &longs;o, as that it hath not &longs;trength enough left <lb/>to foil this &longs;ame opinion. </s><s>For, if I have rightly apprehended the <lb/>chief and ultimate conclu&longs;ion, in ca&longs;e, the &longs;tars of the &longs;ixth mag­ <lb/>nitude were &longs;uppo&longs;ed to be as big as the Sun, (which yet I can <lb/>hardly think) yet it would &longs;till be true, that the grand Orb [or <lb/>Ecliptick] would occa&longs;ion a mutation and variation in the &longs;tarry <lb/>Sphere, like to that which the &longs;emidiameter of the Earth produ­ <lb/>ceth in the Sun, which yet is ob&longs;ervable; &longs;o that neither that, no <pb xlink:href="040/01/351.jpg" pagenum="331"/>nor a le&longs;&longs;e mutation being di&longs;cerned in the fixed Stars, methinks <lb/>that by this means the annual motion of the Earth is de&longs;troyed <lb/>and overthrown.</s></p><p type="main"><s>SALV. </s><s>You might very well &longs;o conclude, <emph type="italics"/>Simplicius,<emph.end type="italics"/> if we <lb/>had nothing el&longs;e to &longs;ay in behalf of <emph type="italics"/>Copernicus<emph.end type="italics"/>: but we have <lb/>many things to alledge that yet have not been mentioned; and <lb/>as to that your reply, nothing hindereth, but that we may &longs;up­ <lb/>po&longs;e the di&longs;tance of the fixed Stars to be yet much greater than <lb/>that which hath been allowed them, and you your &longs;elf, and who­ <lb/>ever el&longs;e will not derogate from the propo&longs;itions admitted by <lb/><emph type="italics"/>Piolomy<emph.end type="italics"/>'s &longs;ectators, mu&longs;t needs grant it as a thing mo&longs;t requi&longs;ite <lb/>to &longs;uppo&longs;e the Starry Sphere to be very much bigger yet than <lb/>that which even now we &longs;aid that it ought to be e&longs;teemed. </s><s>For <lb/><arrow.to.target n="marg615"></arrow.to.target> <lb/>all A&longs;tronomers agreeing in this, that the cau&longs;e of the greater <lb/>tardity of the Revolutions of the Planets is, the majority of <lb/>their Spheres, and that therefore <emph type="italics"/>Saturn<emph.end type="italics"/> is more flow than <emph type="italics"/>Ju­ <lb/>piter,<emph.end type="italics"/> and <emph type="italics"/>Jupiter<emph.end type="italics"/> than the Sun, for that the fir&longs;t is to de&longs;cribe a <lb/>greater circle than the &longs;econd, and that than this later, &c. </s><s>con­ <lb/>&longs;idering that <emph type="italics"/>Saturn v.g.<emph.end type="italics"/> the altitude of who&longs;e Orb is nine times <lb/>higher than that of the Sun, and that for that cau&longs;e the time of <lb/>one Revolution of <emph type="italics"/>Saturn,<emph.end type="italics"/> is thirty times longer than that of a <lb/>conver&longs;ion of the Sun, in regard that according to the Doctrine <lb/>of <emph type="italics"/>Ptolomy,<emph.end type="italics"/> one conver&longs;ion of the &longs;tarry Sphere is fini&longs;hed in <lb/>36000. years, whereas that of <emph type="italics"/>Saturn<emph.end type="italics"/> is con&longs;ummate in thirty, <lb/>and that of the Sun in one, arguing with a like proportion, and <lb/><arrow.to.target n="marg616"></arrow.to.target> <lb/>&longs;aying, if the Orb of <emph type="italics"/>Saturn,<emph.end type="italics"/> by rea&longs;on it is nine times bigger <lb/>than that of the Sun, revolves in a time thirty times longer, by <lb/>conver&longs;ion, how great ought that Orb to be, which revolves <lb/>36000. times more &longs;lowly? </s><s>it &longs;hall be found that the di&longs;tance of <lb/>the &longs;tarry Sphere ought to be 10800 &longs;emidiameters of the grand <lb/>Orb, which &longs;hould be full five times bigger than that, which even <lb/>now we computed it to be, in ca&longs;e that a fixed Star of the &longs;ixth <lb/>magnitude were equal to the Sun. </s><s>Now &longs;ee how much le&longs;&longs;er yet, <lb/>upon this account, the variation occa&longs;ioned in the &longs;aid Stars, by <lb/>the annual motion of the Earth, ought to appear. </s><s>And if at the <lb/>&longs;ame rate we would argue the di&longs;tance of the &longs;tarry Sphere from <lb/><arrow.to.target n="marg617"></arrow.to.target> <lb/><emph type="italics"/>Jupiter,<emph.end type="italics"/> and from <emph type="italics"/>Mars,<emph.end type="italics"/> that would give it us to be 15000. and <lb/>this 27000 &longs;emidiameters of the grand Orb, to wit, the fir&longs;t <lb/>&longs;even, and the &longs;econd twelve times bigger than what the mag­ <lb/>nitude of the fixed Star, &longs;uppo&longs;ed equal to the Sun, did make <lb/>it.</s></p><p type="margin"><s><margin.target id="marg615"></margin.target><emph type="italics"/>All Astrono­ <lb/>mers agree that <lb/>the greater magni­ <lb/>tudes of the Orbes <lb/>is the cau&longs;e of the <lb/>tardity of the con­ <lb/>ver&longs;ions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg616"></margin.target><emph type="italics"/>By another &longs;up­ <lb/>po&longs;ition taken from <lb/>A&longs;tronomers, the <lb/>di&longs;tance of the fix­ <lb/>ed Stars is calcu­ <lb/>lated to be 10800 <lb/>&longs;emidiameters of <lb/>the grand Orb.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg617"></margin.target><emph type="italics"/>By the proportion <lb/>of<emph.end type="italics"/> Jupiter <emph type="italics"/>and of<emph.end type="italics"/> <lb/>Mais, <emph type="italics"/>the &longs;tarry <lb/>Sphere is found to <lb/>be yet more remote.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Methinks that to this might be an&longs;wered, that the mo­ <lb/>tion of the &longs;tarry Sphere hath, &longs;ince <emph type="italics"/>Ptolomy,<emph.end type="italics"/> been ob&longs;erved not <lb/>to be &longs;o &longs;low as he accounted it; yea, if I mi&longs;take. </s><s>not, I have <lb/>heard that <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf made the Ob&longs;ervation.</s></p> <pb xlink:href="040/01/352.jpg" pagenum="332"/><p type="main"><s>SALV. </s><s>You &longs;ay very well; but you alledge nothing in that <lb/>which may favour the cau&longs;e of the <emph type="italics"/>Ptolomœans<emph.end type="italics"/> in the lea&longs;t, who <lb/>did never yet reject the motion of 36000. years in the &longs;tarry <lb/>Sphere, for that the &longs;aid tardity would make it too va&longs;t and im­ <lb/>men&longs;e. </s><s>For if that the &longs;aid immen&longs;ity was not to be &longs;uppo&longs;ed in <lb/>Nature, they ought before now to to have denied a conver&longs;ion <lb/>&longs;o &longs;low as that it could not with good proportion adapt it &longs;elf, <lb/>&longs;ave onely to a Sphere of mon&longs;trous magnitude.</s></p><p type="main"><s>SAGR. </s><s>Pray you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> let us lo&longs;e no more time in pro­ <lb/>ceeding, by the way of the&longs;e proportions with people that are apt <lb/>to admit things mo&longs;t di&longs;-proportionate; &longs;o that its impo&longs;&longs;ible <lb/>to win any thing upon them this way: and what more di&longs;propor­ <lb/>tionate proportion can be imagined than that which the&longs;e men <lb/>&longs;wallow down, and admit, in that writing, that there cannot be a <lb/>more convenient way to di&longs;po&longs;e the Cœle&longs;tial Spheres, in order, <lb/>than to regulate them by the differences of the times of their pe­ <lb/>riods, placing from one degree to another the more flow above <lb/>the more &longs;wift, when they have con&longs;tituted the Starry Sphere <lb/>higher than the re&longs;t, as being the &longs;lowe&longs;t, they frame another <lb/>higher &longs;till than that, and con&longs;equently greater, and make it re­ <lb/>volve in twenty four hours, whil&longs;t the next below, it moves not <lb/>round under 36000. years?</s></p><p type="main"><s>SALV. </s><s>I could wi&longs;h, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that &longs;u&longs;pending for a time <lb/>the affection rhat you bear to the followers of your opinion, you <lb/>would &longs;incerely tell me, whether you think that they do in their <lb/>minds comprehend that magnitude, which they reject afterwards <lb/>as uncapable for its immen&longs;ity to be a&longs;cribed to the Univer&longs;e. <lb/></s><s>For I, as to my own part, think that they do not; But believe, <lb/><arrow.to.target n="marg618"></arrow.to.target> <lb/>that like as in the apprehen&longs;ion of numbers, when once a man <lb/>begins to pa&longs;&longs;e tho&longs;e millions of millions, the imagination is con­ <lb/>founded, and can no longer form a conceipt of the &longs;ame, &longs;o it <lb/>happens al&longs;o in comprehending immen&longs;e magnitudes and di&longs;tan­ <lb/>ces; &longs;o that there intervenes to the comprehen&longs;ion an effect like <lb/>to that which befalleth the &longs;en&longs;e; For while&longs;t that in a &longs;erene <lb/>night I look towards the Stars, I judge, according to &longs;en&longs;e, that <lb/>their di&longs;tance is but a few miles, and that the fixed Stars are not a <lb/>jot more remote than <emph type="italics"/>Jupiter<emph.end type="italics"/> or <emph type="italics"/>Saturn,<emph.end type="italics"/> nay than the Moon. <lb/></s><s>But without more ado, con&longs;ider the controver&longs;ies that have pa&longs;t <lb/>between the A&longs;tronomers and Peripatetick Philo&longs;ophers, upon <lb/>occa&longs;ion of the new Stars of <emph type="italics"/>Ca&longs;&longs;iopeia<emph.end type="italics"/> and of <emph type="italics"/>Sagittary,<emph.end type="italics"/> the A­ <lb/>&longs;tronomers placing them among&longs;t the fixed Stars, and the Philo­ <lb/>&longs;ophers believing them to be below the Moon. </s><s>So unable is our <lb/>&longs;en&longs;e to di&longs;tingui&longs;h great di&longs;tances from the greate&longs;t, though the&longs;e <lb/>be in reality many thou&longs;and times greater than tho&longs;e. </s><s>In a word, <lb/>I ask of thee, O fooli&longs;h man! Doth thy imagination comprehend <pb xlink:href="040/01/353.jpg" pagenum="333"/>that va&longs;t magnitude of the Univer&longs;e, which thou afterwards judg­ <lb/>e&longs;t to be too immen&longs;e? </s><s>If thou comprehende&longs;t it; wilt thou <lb/>hold that thy apprehen&longs;ion extendeth it &longs;elf farther than the Di­ <lb/>vine Power? </s><s>wilt thou &longs;ay, that thou can&longs;t imagine greater <lb/>things than tho&longs;e which God can bring to pa&longs;&longs;e? </s><s>But if thou <lb/>apprehende&longs;t it not, why wilt thou pa&longs;&longs;e thy verdict upon things <lb/>beyond thy comprehen&longs;ion?</s></p><p type="margin"><s><margin.target id="marg618"></margin.target><emph type="italics"/>Immen&longs;e mag­ <lb/>nitudes and num­ <lb/>bers are incompre­ <lb/>hen&longs;ible by our un­ <lb/>der&longs;tanding.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>All this is very well, nor can it be denied, but that <lb/>Heaven may in greatne&longs;&longs;e &longs;urpa&longs;&longs;e our imagination, as al&longs;o that <lb/>God might have created it thou&longs;ands of times va&longs;ter than now it <lb/>is; but we ought not to grant any thing to have been made in <lb/>vain, and to be idle in the Univer&longs;e. </s><s>Now, in that we &longs;ee this ad­ <lb/>mirable order of the Planets, di&longs;po&longs;ed about the Earth in di&longs;tan­ <lb/>ces proportionate for producing their effects for our advantage, <lb/>to what purpo&longs;e is it to interpo&longs;e afterwards between the &longs;ublime <lb/>Orb of <emph type="italics"/>Saturn<emph.end type="italics"/> and the &longs;tarry Sphere, a va&longs;t vacancy, without any <lb/>&longs;tar that is &longs;uperfluous, and to no purpo&longs;e? </s><s>To what end? </s><s>For <lb/>who&longs;e profit and advantage?</s></p><p type="main"><s>SALV. </s><s>Methinks we arrogate too much to our &longs;elves, <emph type="italics"/>Simpli­ <lb/>cius,<emph.end type="italics"/> whil&longs;t we will have it, that the onely care of us, is the ad­ <lb/>æquate work, and bound, beyond which the Divine Wi&longs;dome <lb/>and Power doth, or di&longs;po&longs;eth of nothing. </s><s>But I will not con­ <lb/>&longs;ent, that we &longs;hould &longs;o much &longs;horten its hand, but de&longs;ire that we <lb/>may content our &longs;elves with an a&longs;&longs;urance that God and Nature <lb/><arrow.to.target n="marg619"></arrow.to.target> <lb/>are &longs;o imployed in the governing of humane affairs, that they <lb/>could not more apply them&longs;elves thereto, although they had no <lb/>other care than onely that of mankind; and this, I think, I am <lb/>able to make out by a mo&longs;t pertinent and mo&longs;t noble example, <lb/>taken from the operation of the Suns light, which while&longs;t it at­ <lb/><arrow.to.target n="marg620"></arrow.to.target> <lb/>tracteth the&longs;e vapours, or &longs;corcheth that plant, it attracteth, it <lb/>&longs;corcheth them, as if it had no more to do; yea, in ripening that <lb/>bunch of grapes, nay that one &longs;ingle grape, it doth apply it &longs;elf <lb/>&longs;o, that it could not be more inten&longs;e if the &longs;um of all its bu&longs;ine&longs;s <lb/>had been the only maturation of that grape. </s><s>Now if this grape <lb/>receiveth all that it is po&longs;&longs;ible for it to receive from the Sun, not <lb/>&longs;uffering the lea&longs;t injury by the Suns production of a thou&longs;and <lb/>other effects at the &longs;ame time; it would be either envy or folly <lb/>to blame that grape, if it &longs;hould think or wi&longs;h that the Sun would <lb/>onely appropriate its rayes to its advantage. </s><s>I am confident that <lb/>nothing is omitted by the Divine Providence, of what concernes <lb/>the government of humane affairs; but that there may not be <lb/>other things in the Univer&longs;e, that depend upon the &longs;ame infinite <lb/>Wi&longs;dome, I cannot, of my &longs;elf, by what my rea&longs;on holds forth <lb/>to me, bring my &longs;elf to believe. </s><s>However, if it were not &longs;o, <lb/>yet &longs;hould I not forbear to believe the rea&longs;ons laid before me by <pb xlink:href="040/01/354.jpg" pagenum="334"/>&longs;ome more &longs;ublime intelligence. </s><s>In the mean time, if one <lb/>&longs;hould tell me, that an immen&longs;e &longs;pace interpo&longs;ed between the <lb/>Orbs of the Planets and the Starry Sphere, deprived of &longs;tars and <lb/>idle, would be vain and u&longs;ele&longs;&longs;e, as likewi&longs;e that &longs;o great an <lb/>immen&longs;ity for receipt of the fixed &longs;tars, as exceeds our utmo&longs;t <lb/>comprehen&longs;ion would be &longs;uperfluous, I would reply, that it is <lb/>ra&longs;hne&longs;&longs;e to go about to make our &longs;hallow rea&longs;on judg of the <lb/>Works of God, and to call vain and &longs;uperfluous, what&longs;oever <lb/>thing in the Univer&longs;e is not &longs;ub&longs;ervient to us.</s></p><p type="margin"><s><margin.target id="marg619"></margin.target><emph type="italics"/>God & Nature <lb/>do imploy them­ <lb/>&longs;elves in caring <lb/>for men, as if they <lb/>minded nothing <lb/>el&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg620"></margin.target><emph type="italics"/>An example of <lb/>Gods care of man­ <lb/>kind taken from <lb/>the Sun.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Say rather, and I believe you would &longs;ay better, that <lb/><arrow.to.target n="marg621"></arrow.to.target> <lb/>we know not what is &longs;ub&longs;ervient to us; and I hold it one of the <lb/>greate&longs;t vanities, yea follies, that can be in the World, to &longs;ay, <lb/>becau&longs;e I know not of what u&longs;e <emph type="italics"/>Jupiter<emph.end type="italics"/> or <emph type="italics"/>Saturn<emph.end type="italics"/> are to me, that <lb/>therefore the&longs;e Planets are &longs;uperfluous, yea more, that there are <lb/>no &longs;uch things <emph type="italics"/>in rerum natura<emph.end type="italics"/>; when as, oh fooli&longs;h man! I <lb/>know not &longs;o much as to what purpo&longs;e the arteries, the gri&longs;tles, <lb/>the &longs;pleen, the gall do &longs;erve; nay I &longs;hould not know that I have <lb/>a gall, &longs;pleen, or kidneys, if in many de&longs;ected Corps, they were <lb/>not &longs;hewn unto me; and then onely &longs;hall I be able to know what <lb/>the &longs;pleen worketh in me, when it comes to be taken from me. <lb/></s><s>To be able to know what this or that Cœle&longs;tial body worketh in <lb/><arrow.to.target n="marg622"></arrow.to.target> <lb/>me (&longs;eeing you will have it that all their influences direct them­ <lb/>&longs;elves to us) it would be requi&longs;ite to remove that body for &longs;ome <lb/>time; and then what&longs;oever effect I &longs;hould find wanting in me, I <lb/>would &longs;ay that it depended on that &longs;tar. </s><s>Moreover, who will pre­ <lb/>&longs;ume to &longs;ay that the &longs;pace which they call too va&longs;t and u&longs;ele&longs;&longs;e <lb/>between <emph type="italics"/>Saturn<emph.end type="italics"/> and the fixed &longs;tars, is void of other mundane bo­ <lb/>dies? </s><s>Mu&longs;t it be &longs;o, becau&longs;e we do not &longs;ee them? </s><s>Then the four <lb/><arrow.to.target n="marg623"></arrow.to.target> <lb/>Medicean Planets, and the companions of <emph type="italics"/>Saturn<emph.end type="italics"/> came fir&longs;t in­ <lb/>to Heaven, when we began to &longs;ee them, and not before? </s><s>And <lb/>by this rule the innumerable other fixed &longs;tars had no exi&longs;tence <lb/>before that men did look on them? </s><s>and the cloudy con&longs;tellati­ <lb/>ons called <emph type="italics"/>Nebulo&longs;œ<emph.end type="italics"/> were at fir&longs;t only white flakes, but afterwards <lb/>with the Tele&longs;cope we made them to become con&longs;tellations of <lb/>many lucid and bright &longs;tars. </s><s>Oh pre&longs;umptious, rather oh ra&longs;h <lb/>ignorance of man!</s></p><p type="margin"><s><margin.target id="marg621"></margin.target><emph type="italics"/>It is great ra&longs;h­ <lb/>ne&longs;&longs;e to cen&longs;ure <lb/>that to be &longs;uperflu­ <lb/>ous in the Univer&longs;e, <lb/>which we do not <lb/>perceive to be made <lb/>for us.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg622"></margin.target><emph type="italics"/>By depriving <lb/>Heaven of &longs;ome <lb/>&longs;tar, one might <lb/>come to know what <lb/>influence it hath <lb/>upon us.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg623"></margin.target><emph type="italics"/>Many things <lb/>may be in Heauen, <lb/>that are invi&longs;ible <lb/>to us<emph.end type="italics"/></s></p><p type="main"><s>SALV. It's to no purpo&longs;e <emph type="italics"/>Sagredus,<emph.end type="italics"/> to &longs;ally out any more into <lb/>the&longs;e unprofitable exaggerations: Let us pur&longs;ue our intended <lb/>de&longs;igne of examining the validity of the rea&longs;ons alledged on ei­ <lb/>ther &longs;ide, without determining any thing, remitting the judg­ <lb/>ment thereof when we have done, to &longs;uch as are more knowing. <lb/></s><s>Returning therefore to our natural and humane di&longs;qui&longs;itions, I <lb/><arrow.to.target n="marg624"></arrow.to.target> <lb/>&longs;ay, that great, little, immen&longs;e, &longs;mall, <emph type="italics"/>&c.<emph.end type="italics"/> are not ab&longs;olute, <lb/>but relative terms, &longs;o that the &longs;elf &longs;ame thing compared with <lb/>divers others, may one while be called immen&longs;e, and another <pb xlink:href="040/01/355.jpg" pagenum="335"/>while imperceptible, not to &longs;ay &longs;mall. </s><s>This being &longs;o, I demand <lb/>in relation to what the Starry Sphere of <emph type="italics"/>Copernicus<emph.end type="italics"/> may be cal­ <lb/>led over va&longs;t. </s><s>In my judgment it cannot be compared, or &longs;aid <lb/>to be &longs;uch, unle&longs;&longs;e it be in relation to &longs;ome other thing of the <lb/>&longs;ame kind; now let us take the very lea&longs;t of the &longs;ame kind, <lb/><arrow.to.target n="marg625"></arrow.to.target> <lb/>which &longs;hall be the Lunar Orb; and if the Starry Orb may be &longs;o <lb/>cen&longs;ured to be too big in re&longs;pect to that of the Moon, every o­ <lb/>ther magnitude that with like or greater proportion exceedeth <lb/>another of the &longs;ame kind, ought to be adjudged too va&longs;t, and <lb/>for the &longs;ame rea&longs;on to be denied that they are to be found in the <lb/>World; and thus an Elephant, and a Whale, &longs;hall without more <lb/>ado be condemned for <emph type="italics"/>Chymæra's,<emph.end type="italics"/> and Poetical fictions, be­ <lb/>cau&longs;e that the one as being too va&longs;t in relation to an Ant, which <lb/>is a Terre&longs;trial animal, and the other in re&longs;pect to the ^{*}Gudgeon, <lb/><arrow.to.target n="marg626"></arrow.to.target> <lb/>which is a Fi&longs;h, and are certainly &longs;een to be <emph type="italics"/>in rerum natura,<emph.end type="italics"/> <lb/>would be too immea&longs;urable; for without all di&longs;pute, the Ele­ <lb/>phant and Whale exceed the Ant and Gudgeon in a much great­ <lb/>er proportion than the Starry Sphere doth that of the Moon, <lb/>although we &longs;hould fancy the &longs;aid Sphere to be as big as the <emph type="italics"/>Co­ <lb/>pernican<emph.end type="italics"/> Sy&longs;teme maketh it. </s><s>Moreover, how hugely big is the <lb/><arrow.to.target n="marg627"></arrow.to.target> <lb/>Sphere of <emph type="italics"/>Jupiter,<emph.end type="italics"/> or that of <emph type="italics"/>Saturn,<emph.end type="italics"/> defigned for a receptacle <lb/>but for one &longs;ingle &longs;tar; and that very &longs;mall in compari&longs;on of one <lb/>of the fixed? </s><s>Certainly if we &longs;hould a&longs;&longs;ign to every one of the <lb/>fixed &longs;tars for its receptacle &longs;o great a part of the Worlds &longs;pace, <lb/>it would be nece&longs;&longs;ary to make the Orb wherein &longs;uch innumerable <lb/>multitudes of them re&longs;ide, very many thou&longs;ands of times big­ <lb/>ger than that which &longs;erveth the purpo&longs;e of <emph type="italics"/>Copernicus.<emph.end type="italics"/> Be&longs;ides, <lb/><arrow.to.target n="marg628"></arrow.to.target> <lb/>do not you call a fixed &longs;tar very &longs;mall, I mean even one of the <lb/>mo&longs;t apparent, and not one of tho&longs;e which &longs;hun our &longs;ight; and <lb/>do we not call them &longs;o in re&longs;pect of the va&longs;t &longs;pace circumfu&longs;ed? <lb/></s><s>Now if the whole Starry Sphere were one entire lucid body; who <lb/><arrow.to.target n="marg629"></arrow.to.target> <lb/>is there, that doth not know that in an infinite &longs;pace there might be <lb/>a&longs;&longs;igned a di&longs;tance &longs;o great, as that the &longs;aid lucid Sphere might <lb/>from thence &longs;hew as little, yea le&longs;&longs;e than a fixed &longs;tar, now ap­ <lb/>peareth beheld from the Earth? </s><s>From thence therefore we <lb/>&longs;hould <emph type="italics"/>then<emph.end type="italics"/> judg that &longs;elf &longs;ame thing to be little, which <emph type="italics"/>now<emph.end type="italics"/> from <lb/>hence we e&longs;teem to be immea&longs;urably great.</s></p><p type="margin"><s><margin.target id="marg624"></margin.target><emph type="italics"/>Great, &longs;mall, <lb/>immen&longs;e,<emph.end type="italics"/> &c. <emph type="italics"/>are <lb/>relative terms.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg625"></margin.target><emph type="italics"/>Vanity of tho&longs;e <lb/>mens di&longs;cour &longs;ewho <lb/>judg the &longs;tarry <lb/>&longs;phere too va&longs;t in <lb/>the<emph.end type="italics"/> Copernican <lb/><emph type="italics"/>Hypothe&longs;is.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg626"></margin.target>* <emph type="italics"/>Spilloncola,<emph.end type="italics"/> which <lb/>is here put for the <lb/>lea&longs;t of Fi&longs;hes.</s></p><p type="margin"><s><margin.target id="marg627"></margin.target><emph type="italics"/>The &longs;pace a&longs;­ <lb/>&longs;igned to a fixed <lb/>&longs;tar, is much ie&longs;&longs;e <lb/>than that of a Pla­ <lb/>net.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg628"></margin.target><emph type="italics"/>A &longs;tar is cal­ <lb/>led in re&longs;pect of the <lb/>&longs;pace that environs <lb/>it.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg629"></margin.target><emph type="italics"/>The whole &longs;tar­ <lb/>ry &longs;phere beheld <lb/>from a great di­ <lb/>&longs;tance might ap­ <lb/>pear as &longs;mall as <lb/>one &longs;ingle &longs;tar.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Great in my judgment, is the folly of tho&longs;e who <lb/>would have had God to have made the World more proportinal <lb/>to the narrow capacities of their rea&longs;on, than to his immen&longs;e, <lb/>rather infinite power.</s></p><p type="main"><s>SIMP. </s><s>All this that you &longs;ay is very true; but that upon <lb/>which the adver&longs;ary makes a &longs;cruple, is, to grant that a fixed <lb/>&longs;tar &longs;hould be not onely equal to, but &longs;o much bigger than the <lb/>Sun; when as they both are particular bodies &longs;ituate within the <pb xlink:href="040/01/356.jpg" pagenum="336"/>Starry Orb: “And indeed in my opinion this Authour very <lb/>pertinently que&longs;tioneth and asketh: To what end, and <lb/>for who&longs;e &longs;ake are &longs;uch huge machines made? </s><s>Were they <lb/><arrow.to.target n="marg630"></arrow.to.target> <lb/>produced for the Earth, for an incon&longs;iderable point? </s><s>And <lb/>why &longs;o remote? </s><s>To the end they might &longs;eem &longs;o very &longs;mall, <lb/>and might have no influence at all upon the Earth? </s><s>To <lb/><arrow.to.target n="marg631"></arrow.to.target> <lb/>what purpo&longs;e is &longs;uch a needle&longs;&longs;e mon&longs;trous ^{*} immen&longs;ity be­ <lb/>tween them and <emph type="italics"/>Saturn<emph.end type="italics"/>? </s><s>All tho&longs;e a&longs;&longs;ertions fall to the <lb/>ground that are not upheld by probable rea&longs;ons.”</s></p><p type="margin"><s><margin.target id="marg630"></margin.target><emph type="italics"/>In&longs;tances of the <lb/>Authour of the <lb/>Conclu&longs;ions by way <lb/>of interrogation.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg631"></margin.target>Or Gulph.</s></p><p type="main"><s>SALV. </s><s>I conceive by the que&longs;tions which this per&longs;on asketh, <lb/><arrow.to.target n="marg632"></arrow.to.target> <lb/>that one may collect, that in ca&longs;e the Heavens, the Stars, and <lb/>the quantity of their di&longs;tances and magnitudes which he hath <lb/>hitherto held, be let alone, (although he never certainly fancied <lb/>to him&longs;elf any conceivable magnitude thereof) he perfectly di&longs;­ <lb/>cerns and comprehends the benefits that flow from thence to the <lb/>Earth, which is no longer an incon&longs;iderable thing; nor are they <lb/>any longer &longs;o remote as to appear &longs;o very &longs;mall, but big enough to <lb/>be able to operate on the Earth; and that the di&longs;tance between <lb/>them and <emph type="italics"/>Saturn<emph.end type="italics"/> is very well proportioned, and that he, for all <lb/>the&longs;e things, hath very probable rea&longs;ons; of which I would glad­ <lb/>ly have heard &longs;ome one: but being that in the&longs;e few words he <lb/><arrow.to.target n="marg633"></arrow.to.target> <lb/>confounds and contradicts him&longs;elf, it maketh me think that he <lb/>is very poor and ill furni&longs;hed with tho&longs;e probable rea&longs;ons, and <lb/>that tho&longs;e which he calls rea&longs;ons, are rather fallacies, or dreams <lb/>of an over-weening fancy. </s><s>For I ask of him, whether the&longs;e Ce­ <lb/><arrow.to.target n="marg634"></arrow.to.target> <lb/>le&longs;tial bodies truly operate on the Earth, and whether for the <lb/>working of tho&longs;e effects they were produced of &longs;uch and &longs;uch <lb/>magnitudes, and di&longs;po&longs;ed at &longs;uch and &longs;uch di&longs;tances, or el&longs;e <lb/>whether they have nothing at all to do with Terrene mattets. </s><s>If <lb/>they have nothing to do with the Earth; it is a great folly for us <lb/>that are Earth-born, to offer to make our &longs;elves arbitrators of <lb/>their magnitudes, and regulators of their local di&longs;po&longs;itions, &longs;ee­ <lb/>ing that we are altogether ignorant of their whole bu&longs;ine&longs;&longs;e and <lb/>concerns; but if he &longs;hall &longs;ay that they do operate, and that they <lb/>are directed to this end, he doth affirm the &longs;ame thing which a <lb/>little before he denied, and prai&longs;eth that which even now he <lb/>condemned, in that he &longs;aid, that the Cele&longs;tial bodies &longs;ituate &longs;o <lb/>far remote as that they appear very &longs;mall, cannot have any in­ <lb/>fluence at all upon the Earth. </s><s>But, good Sir, in the Starry Sphere <lb/>pre-e&longs;tabli&longs;hed at its pre&longs;ent di&longs;tance, and which you did ac­ <lb/>knowledg to be in your judgment, well proportioned to have an <lb/>influence upon the&longs;e Terrene bodies, many &longs;tars appear very <lb/>&longs;mall, and an hundred times as many more are wholly invi&longs;ible <lb/>unto us (which is an appearing yet le&longs;&longs;e than very &longs;mall) <lb/>therefore it is nece&longs;&longs;ary that (contradicting your &longs;elf) you do <pb xlink:href="040/01/357.jpg" pagenum="337"/>now deny their operation upon the the Earth; or el&longs;e that (&longs;till <lb/>contradicting your &longs;elf) you grant that their appearing very &longs;mall <lb/>doth not in the lea&longs;t le&longs;&longs;en their influence; or el&longs;e that (and this <lb/>&longs;hall be a more &longs;incere and mode&longs;t conce&longs;&longs;ion) you acknowledg <lb/>and freely confe&longs;&longs;e, that our pa&longs;&longs;ing judgment upon their mag­ <lb/>nitudes and di&longs;tances is a vanity, not to &longs;ay pre&longs;umption or <lb/>ra&longs;hne&longs;&longs;e.</s></p><p type="margin"><s><margin.target id="marg632"></margin.target><emph type="italics"/>An&longs;wers to the <lb/>interrogatories of <lb/>the &longs;aid Authour.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg633"></margin.target><emph type="italics"/>The Auihour <lb/>of the Conclu&longs;i­ <lb/>ons confound and <lb/>contradicts him­ <lb/>&longs;elfin his interro­ <lb/>gations.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg634"></margin.target><emph type="italics"/>Inter ogatories <lb/>put to the Au­ <lb/>thour of the Con­ <lb/>clu&longs;ions, by which <lb/>the weakne&longs;&longs;e of <lb/>his is made appear.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Truth is, I my &longs;elf did al&longs;o, in reading this pa&longs;&longs;age <lb/>perceive the manife&longs;t contradiction, in &longs;aying, that the Stars. (if <lb/>one may &longs;o &longs;peak) of <emph type="italics"/>Copernicus<emph.end type="italics"/> appearing &longs;o very &longs;mall, could <lb/>not operate on the Earth, and not perceiving that he had granted <lb/>an influence upon the Earth to tho&longs;e of <emph type="italics"/>Ptolomy,<emph.end type="italics"/> and his &longs;ecta­ <lb/>tors, which appear not only very &longs;mall, but are, for the mo&longs;t <lb/>part, very invi&longs;ible.</s></p><p type="main"><s>SALV. </s><s>But I proceed to another con&longs;ideration: What is the <lb/>rea&longs;on, doth he &longs;ay, why the &longs;tars appear &longs;o little? </s><s>Is it haply, <lb/>becau&longs;e they &longs;eem &longs;o to us? </s><s>Doth not he know, that this com­ <lb/><arrow.to.target n="marg635"></arrow.to.target> <lb/>meth from the In&longs;trument that we imploy in beholding them, to <lb/>wit, from our eye? </s><s>And that this is true, by changing In&longs;tru­ <lb/>ment, we &longs;hall &longs;ee them bigger and bigger, as much as we will. <lb/></s><s>And who knows but that to the Earth, which beholdeth them <lb/>without eyes, they may not &longs;hew very great, and &longs;uch as in reali­ <lb/>ty they are? </s><s>But it's time that, omitting the&longs;e trifles, we come <lb/>to things of more moment; and therefore I having already de­ <lb/>mon&longs;trated the&longs;e two things: Fir&longs;t, how far off the Firmament <lb/>ought to be placed to make, that the grand Orb cau&longs;eth no grea­ <lb/>ter difference than that which the Terre&longs;trial Orb occa&longs;ioneth in <lb/>the remotene&longs;&longs;e of the Sun; And next, how likewi&longs;e to make <lb/>that a &longs;tar of the Firmament appear to us of the &longs;ame bigne&longs;&longs;e, <lb/>as now we &longs;ee it, it is not nece&longs;&longs;ary to &longs;uppo&longs;e it bigger than the <lb/>Sun; I would know whether <emph type="italics"/>Tycho,<emph.end type="italics"/> or any of his adherents hath <lb/>ever attempted to find out, by any means, whether any appea­ <lb/>rance be to be di&longs;covered in the &longs;tarry Sphere, upon which one <lb/>may the more re&longs;olutely deny or admit the annual motion of <lb/>the Earth.</s></p><p type="margin"><s><margin.target id="marg635"></margin.target><emph type="italics"/>That remote ol­ <lb/>jects appeare &longs;o <lb/>&longs;mall, is the defect <lb/>of the eye, as is <lb/>demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I would an&longs;wer for them, that there is not, no nor is <lb/><arrow.to.target n="marg636"></arrow.to.target> <lb/>there any need there &longs;hould; &longs;eeing that it is <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf <lb/>that &longs;aith, that no &longs;uch diver&longs;ity is there: and they, arguing <emph type="italics"/>ad <lb/>hominem,<emph.end type="italics"/> admit him the &longs;ame; and upon this a&longs;&longs;umption they <lb/>demon&longs;trate the improbability that followeth thereupon, name­ <lb/>ly, that it would be nece&longs;&longs;ary to make the Sphere &longs;o immen&longs;e, <lb/>that a fixed &longs;tar, to appear unto us as great as it now &longs;eems, ought <lb/>of nece&longs;&longs;ity to be of &longs;o immen&longs;e a magnitude, as that it would <lb/>exceed the bigne&longs;&longs;e of the whole grand Orb, a thing, which not­ <lb/>with&longs;tanding, as they &longs;ay, is altogether incredible.</s></p> <pb xlink:href="040/01/358.jpg" pagenum="338"/><p type="margin"><s><margin.target id="marg636"></margin.target>Tycho <emph type="italics"/>nor his <lb/>followers ever at­ <lb/>tempted to &longs;ee whe­ <lb/>ther there are any <lb/>appearances in the <lb/>Firmament for or <lb/>against the annual <lb/>motion.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I am of the &longs;ame judgment, and verily believe that <lb/>they argue <emph type="italics"/>contra hominem,<emph.end type="italics"/> &longs;tudying more to defend another <lb/>man, than de&longs;iring to come to the knowledge of the truth. </s><s>And <lb/><arrow.to.target n="marg637"></arrow.to.target> <lb/>I do not only believe, that none of them ever applied them&longs;elves <lb/>to make any &longs;uch ob&longs;ervation, but I am al&longs;o uncertain, whether <lb/>any of them do know what alteration the Earths annual motion <lb/>ought to produce in the fixed &longs;tars, in ca&longs;e the &longs;tarry Sphere were <lb/>not &longs;o far di&longs;tant, as that in them the &longs;aid diver&longs;ity, by rea&longs;on of <lb/>its minuity di&longs;-appeareth; for their &longs;urcea&longs;ing that inqui&longs;ition, <lb/>and referring them&longs;elves to the meer a&longs;&longs;ertion of <emph type="italics"/>Copernicus,<emph.end type="italics"/> <lb/>may very well &longs;erve to convict a man, but not to acquit him of <lb/>the fact: For its po&longs;&longs;ible that &longs;uch a diver&longs;ity may be, and yet <lb/><arrow.to.target n="marg638"></arrow.to.target> <lb/>not have been &longs;ought for; or that either by rea&longs;on of its minui­ <lb/>ty, or for want of exact In&longs;truments it was not di&longs;covered by <emph type="italics"/>Co­ <lb/>pernicus<emph.end type="italics"/>; for though it were &longs;o, this would not be the fir&longs;t thing, <lb/>that he either for want of In&longs;truments, or for &longs;ome other defect <lb/>hath not known; and yet he proceeding upon other &longs;olid and <lb/>rational conjectures, affirmeth that, which the things by him not <lb/>di&longs;covered do &longs;eem to contradict: for, as hath been &longs;aid already, <lb/>without the Tele&longs;cope, neither could <emph type="italics"/>Mars<emph.end type="italics"/> be di&longs;cerned to in­ <lb/>crea&longs;e 60. times; nor <emph type="italics"/>Venus<emph.end type="italics"/> 40. more in that than in this po&longs;iti­ <lb/>on; yea, their differences appear much le&longs;&longs;e than really they are: <lb/>and yet neverthele&longs;&longs;e it is certainly di&longs;covered at length, that <lb/>tho&longs;e mutations are the &longs;ame, to an hair that the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy­ <lb/><arrow.to.target n="marg639"></arrow.to.target> <lb/>&longs;teme required. </s><s>Now it would be very well, if with the greate&longs;t <lb/>accuratene&longs;&longs;e po&longs;&longs;ible one &longs;hould enquire whether &longs;uch a muta­ <lb/>tion as ought to be di&longs;coverable in the fixed &longs;tars, &longs;uppo&longs;ing the <lb/>annual motion of the Earth, would be ob&longs;erved really and in <lb/>effect, a thing which I verily believe hath never as yet been done <lb/>by any; done, &longs;aid I? no, nor haply (as I &longs;aid before) by many <lb/>well under&longs;tood how it ought to be done. </s><s>Nor &longs;peak I this at <lb/>randome, for I have heretofore &longs;een a certain Manu&longs;cript of <lb/>one of the&longs;e <emph type="italics"/>Anti-Copernicans,<emph.end type="italics"/> which &longs;aid, that there would ne­ <lb/>ce&longs;&longs;arily follow, in ca&longs;e that opinion were true, a continual ri­ <lb/>&longs;ing and falling of the Pole from &longs;ix moneths to &longs;ix moneths, ac­ <lb/>cording as the Earth in &longs;uch a time, by &longs;uch a &longs;pace as is the dia­ <lb/>meter of the grand Orb, retireth one while towards the North, and <lb/>another while towards the South; and yet it &longs;eemed to him rea&longs;o­ <lb/>nable, yea nece&longs;&longs;ary, that we, following the Earth, when we were <lb/>towards the North &longs;hould have the Pole more elevated than when <lb/>we are towards the South. </s><s>In this very error did one fall that was <lb/>otherwi&longs;e a very skilful Mathematician, & a follower of <emph type="italics"/>Copernic.<emph.end type="italics"/> <lb/><arrow.to.target n="marg640"></arrow.to.target> <lb/>as <emph type="italics"/>Tycho<emph.end type="italics"/> relateth in his ^{*}<emph type="italics"/>Progymna&longs;ma. </s><s>pag<emph.end type="italics"/> 684. which &longs;aid, that he <lb/>had ob&longs;erved the Polar altitude to vary, and to differ in Summer <lb/>from what it is in Winter: and becau&longs;e <emph type="italics"/>Tycho<emph.end type="italics"/> denieth the merit <pb xlink:href="040/01/359.jpg" pagenum="339"/>of the cau&longs;e, but findeth no fault with the method of it; that <lb/>is, denieth that there is any mutation to be &longs;een in the altitude of <lb/>the Pole, but doth not blame the inqui&longs;ition, for not being adap­ <lb/>ted to the finding of what is &longs;ought, he thereby &longs;heweth, that he <lb/>al&longs;o e&longs;tecemed the Polar altitude varied, or not varied every &longs;ix <lb/>moneths, to be a good te&longs;timony to di&longs;prove or inferre the annual <lb/>motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg637"></margin.target><emph type="italics"/>A &longs;tronomeys, <lb/>perhaps, have not <lb/>known what ap­ <lb/>pearances ought to <lb/>follow upon the an­ <lb/>nual motion of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg638"></margin.target>Copernicus <emph type="italics"/>un­ <lb/>der&longs;tood not &longs;ome <lb/>things for want of <lb/>In&longs;truments.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg639"></margin.target>Tycho <emph type="italics"/>and o­ <lb/>thers argue a­ <lb/>gain&longs;t the annual <lb/>motion, from the <lb/>invariable eleva­ <lb/>tion of the Pole.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg640"></margin.target>* Chri&longs;iophoius <lb/>Rothmannus.</s></p><p type="main"><s>SIMP. </s><s>In truth, <emph type="italics"/>Salviatus,<emph.end type="italics"/> my opinion al&longs;o tells me, that the <lb/>&longs;ame mu&longs;t nece&longs;&longs;arily en&longs;ue: for I do not think that you will de­ <lb/>ny me, but that if we walk only 60. miles towards the North, <lb/>the Pole will ri&longs;e unto us a degree higher, and that if we move <lb/>60. miles farther Northwards, the Pole will be elevated to us a <lb/>degree more, &c. </s><s>Now if the approaching or receding 60. miles <lb/>onely, make &longs;o notable a change in the Polar altitudes, what <lb/>alteration would follow, if the Earth and we with it, &longs;hould <lb/>be tran&longs;ported, I will not &longs;ay 60. miles, but 60. thou&longs;and miles <lb/>that way.</s></p><p type="main"><s>SALV. </s><s>It would follow (if it &longs;hould proceed in the &longs;ame <lb/>proportion) that the Pole &longs;hall be elevated a thou&longs;and degrees. <lb/></s><s>See, <emph type="italics"/>Simplicius,<emph.end type="italics"/> what a long rooted opinion can do. </s><s>Yea, by <lb/>rea&longs;on you have fixed it in your mind for &longs;o many years, that it <lb/>is Heaven, that revolveth in twenty four hours, and not the <lb/>Earth, and that con&longs;equently the Poles of that Revolution are in <lb/>Heaven, and not in the Terre&longs;trial Globe, cannot now, in an <lb/>hours time &longs;hake off this habituated conceipt, and take up the <lb/>contrary, fancying to your &longs;elf, that the Earth is that which mo­ <lb/>veth, only for &longs;o long time as may &longs;uffice to conceive of what <lb/>would follow, thereupon &longs;hould that lye be a truth. </s><s>If the Earth <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> be that which moveth in its &longs;elf in twenty four hours, <lb/>in it are the Poles, in it is the Axis, in it is the Equinoctial, that <lb/>is, the grand Circle, de&longs;cribed by the point, equidi&longs;tant from the <lb/>Poles, in it are the in&longs;inite Parallels bigger and le&longs;&longs;er de&longs;cribed by <lb/>the points of the &longs;uperficies more and le&longs;&longs;e di&longs;tant from the Poles, <lb/>in it are all the&longs;e things, and not in the &longs;tarry Sphere, which, as <lb/>being immoveable, wants them all, and can only by the imagina­ <lb/>tion be conceived to be therein, prolonging the Axis of the Earth <lb/>&longs;o far, till that determining, it &longs;hall mark out two points placed <lb/>right over our Poles, and the plane of the Equinoctial being ex­ <lb/>tended, it &longs;hall de&longs;cribe in Heaven a circle like it &longs;elf. </s><s>Now if the <lb/>true Axis, the true Poles, the true Equinoctial, do not change <lb/>in the Earth &longs;o long as you continue in the &longs;ame place of the <lb/>Earth, and though the Earth be tran&longs;ported, as you do plea&longs;e, <lb/>yet you &longs;hall not change your habitude either to the Poles, or to <lb/>the circles, or to any other Earthly thing; and this becau&longs;e, that <lb/>that tran&longs;po&longs;ition being common to you and to all Terre&longs;trial <pb xlink:href="040/01/360.jpg" pagenum="340"/>things; and that motion where it is common, is as if it never <lb/><arrow.to.target n="marg641"></arrow.to.target> <lb/>were; and as you change not habitude to the Terre&longs;trial Poles <lb/>(habitude I &longs;ay, whether that they ri&longs;e, or de&longs;cend) &longs;o neither <lb/>&longs;hall you change po&longs;ition to the Poles imagined in Heaven; al­ <lb/>wayes provided that by Cele&longs;tial Poles we under&longs;tand (as hath <lb/>been already defined) tho&longs;e two points that come to be marked <lb/>out by the prolongation of the Terre&longs;trial Axis unto that length. <lb/></s><s>Tis true tho&longs;e points in Heaven do change, when the Earths tran­ <lb/>&longs;portment is made after &longs;uch a manner, that its Axis cometh to <lb/>pa&longs;&longs;e by other and other points of the immoveable Cele&longs;tial <lb/>Sphere, but our habitude thereunto changeth not, &longs;o as that the <lb/>&longs;econd &longs;hould be more elevated to us than the fir&longs;t. </s><s>If any one <lb/>will have one of the points of the Firmament, which do an&longs;wer <lb/>to the Poles of the Earth to a&longs;cend, and the other to de&longs;cend, <lb/>he mu&longs;t walk along the Earth towards the one, receding from the <lb/>other, for the tran&longs;portment of the Earth, and with it us our <lb/>&longs;elves, (as I told you before) operates nothing at all.</s></p><p type="margin"><s><margin.target id="marg641"></margin.target><emph type="italics"/>Motion where <lb/>it is common, is as <lb/>if it never were.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Permit me, I be&longs;eech you <emph type="italics"/>Salviatus,<emph.end type="italics"/> to make this a <lb/>little more clear by an example, which although gro&longs;&longs;e, is a­ <lb/>commodated to this purpo&longs;e. </s><s>Suppo&longs;e your &longs;elf, <emph type="italics"/>Simplicius,<emph.end type="italics"/> to <lb/><arrow.to.target n="marg642"></arrow.to.target> <lb/>be aboard a Ship, and that &longs;tanding in the Poope, or Hin-deck; <lb/>you have directed a Quadrant, or &longs;ome other A&longs;tronomical In­ <lb/>&longs;trument, towards the top of the Top-gallant-Ma&longs;t, as if you <lb/>would take its height, which &longs;uppo&longs;e it were <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> 40. degrees, <lb/><arrow.to.target n="marg643"></arrow.to.target> <lb/>there is no doubt, but that if you walk along the ^{*} Hatches to­ <lb/>wards the Ma&longs;t 25. or 30. paces; and then again direct the &longs;aid <lb/>In&longs;trument to the &longs;ame Top-Gallant-Top. </s><s>You &longs;hall find its ele­ <lb/>vation to be greater, and to be encrea&longs;ed <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> 10. degrees; but <lb/>if in&longs;tead of walking tho&longs;e 25. or 30. paces towards the Ma&longs;t, <lb/>you &longs;tand &longs;till at the Sterne, and make the whole Ship to move <lb/>thitherwards, do you believe that by rea&longs;on of the 25. or 30. <lb/>paces that it had pa&longs;t, the elevation of the Top-Gallant-Top <lb/>would &longs;hew 10. degrees encrea&longs;ed?</s></p><p type="margin"><s><margin.target id="marg642"></margin.target><emph type="italics"/>An example fit­ <lb/>ted to prove that <lb/>the altitude of the <lb/>Pole ought not to <lb/>vary by means of <lb/>the Earths annual <lb/>motion.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg643"></margin.target>* <emph type="italics"/>Cor&longs;ia,<emph.end type="italics"/> the bank <lb/>or bench on which <lb/>&longs;laves &longs;it in a Gal­ <lb/>ly.</s></p><p type="main"><s>SIMP. </s><s>I believe and know that it would not gain an hairs <lb/>breadth in the pa&longs;&longs;ing of 30. paces, nor of a thou&longs;and, no nor of <lb/>an hundred thou&longs;and miles; but yet I believe withal that look­ <lb/>ing through the &longs;ights at the Top and Top-Gallant, if I &longs;hould <lb/>find a fixed Star that was in the &longs;ame elevation, I believe I &longs;ay, <lb/>that, holding &longs;till the Quadrant, after I had &longs;ailed towards the <lb/>&longs;tar 60. miles, the eye would meet with the top of the &longs;aid <lb/>Ma&longs;t, as before, but not with the &longs;tar, which would be eleva­ <lb/>ted to me one degree.</s></p><p type="main"><s>SAGR. </s><s>Then you do not think that the &longs;ight would fall upon <lb/>that point of the Starry Sphere, that an&longs;wereth to the direction <lb/>of the Top-Gallant Top?</s></p> <pb xlink:href="040/01/361.jpg" pagenum="341"/><p type="main"><s>SIMP. No: For the point would be changed, and would be <lb/>beneath the &longs;tar fir&longs;t ob&longs;erved.</s></p><p type="main"><s>SAGR. </s><s>You are in the right. </s><s>Now like as that which in this <lb/>example an&longs;wereth to the elevation of the Top-Gallant-Top, is <lb/>not the &longs;tar, but the point of the Firmament that lyeth in a right <lb/>line with the eye, and the &longs;aid top of the Ma&longs;t, &longs;o in the ca&longs;e <lb/>exemplified, that which in the Firmament an&longs;wers to the Pole <lb/>of the Earth, is not a &longs;tar, or other fixed thing in the Firma­ <lb/>ment; but is that point in which the Axis of the Earth continu­ <lb/>ed &longs;treight out, till it cometh thither doth determine, which point <lb/>is not fixed, but obeyeth the mutations that the Pole of the <lb/>Earth doth make. </s><s>And therefore <emph type="italics"/>Tycho,<emph.end type="italics"/> or who ever el&longs;e that <lb/><arrow.to.target n="marg644"></arrow.to.target> <lb/>did alledg this objection, ought to have &longs;aid that upon that <lb/>&longs;ame motion of the Earth, were it true, one might ob&longs;erve &longs;ome <lb/>difference in the elevation and depre&longs;&longs;ion (not of the Pole, but) <lb/>of &longs;ome fixed &longs;tar toward that part which an&longs;wereth to our Pole.</s></p><p type="margin"><s><margin.target id="marg644"></margin.target><emph type="italics"/>Upon the annu­ <lb/>al motion of the <lb/>Earth, alteration <lb/>may en&longs;ue in <lb/>&longs;ome fixed &longs;tar, <lb/>not in the Pole.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I already very well under&longs;tand the mi&longs;take by them <lb/>committed; but yet therefore (which to me &longs;eems very great) of <lb/>the argument brought on the contrary is not le&longs;&longs;ened, &longs;uppo­ <lb/>&longs;ing relation to be had to the variation of the &longs;tars, and not of <lb/>the Pole; for if the moving of the Ship but 60. miles, make a <lb/>fixed &longs;tar ri&longs;e to me one degree, &longs;hall I not find alike, yea and <lb/>very much greater mutation, if the Ship &longs;hould &longs;ail towards the <lb/>&longs;aid &longs;tar for &longs;o much &longs;pace as is the Diameter of the Grand <lb/>Orb, which you affirm to be double the di&longs;tance that is between <lb/>the Earth and Sun?</s></p><p type="main"><s>SAGR. </s><s>Herein <emph type="italics"/>Simplicius,<emph.end type="italics"/> there is another fallacy, which, <lb/><arrow.to.target n="marg645"></arrow.to.target> <lb/>truth is, you under&longs;tand, but do not upon the &longs;udden think of <lb/>the &longs;ame, but I will try to bring it to your remembrance: Tell <lb/>me therefore; if when after you have directed the Quadrant to <lb/>a fixed &longs;tar, and found <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> its elevation to be 40. degrees, <lb/>you &longs;hould without &longs;tirring from the place, incline the &longs;ide of <lb/>the Ouadrant, &longs;o as that the &longs;tar might remain elevated above <lb/>that direction, would you thereupon &longs;ay that the &longs;tar had acqui­ <lb/>red greater elevation?</s></p><p type="margin"><s><margin.target id="marg645"></margin.target><emph type="italics"/>The equivoke of <lb/>tho&longs;e who believe <lb/>that in the annual <lb/>motion great mu­ <lb/>tations are to be <lb/>made about the <lb/>elevation of a fix­ <lb/>ed &longs;tar, is confu­ <lb/>ted.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Certainly no: For the mutation was made in the In­ <lb/>&longs;trument and not in the Ob&longs;erver, that did change place, mo­ <lb/>ving towards the &longs;ame.</s></p><p type="main"><s>SAGR. </s><s>But if you &longs;ail or walk along the &longs;urface of the Terre­ <lb/>&longs;trial Globe, will you &longs;ay that there is no alteration made in the <lb/>&longs;aid Quadrant, but that the &longs;ame elevarion is &longs;till retained in re­ <lb/>&longs;pect of the Heavens, &longs;o long as you your &longs;elf do not incline it, <lb/>but let it &longs;tand at its fir&longs;t con&longs;titution?</s></p><p type="main"><s>SIMP. </s><s>Give me leave to think of it. </s><s>I would &longs;ay without <lb/>more ado, that it would not retain the &longs;ame, in regard the pro­ <pb xlink:href="040/01/362.jpg" pagenum="342"/>gre&longs;&longs;e I make is not <emph type="italics"/>in plano,<emph.end type="italics"/> but about the circumference of the <lb/>Terre&longs;trial Globe, which at every &longs;tep changeth inclination in <lb/>re&longs;pect to Heaven, and con&longs;equently maketh the &longs;ame change <lb/>in the In&longs;trument which is erected upon the &longs;ame.</s></p><p type="main"><s>SAGR. </s><s>You &longs;ay very well: And you know withal, that by <lb/>how much the bigger that circle &longs;hall be upon which you move, <lb/>&longs;o many more miles you are to walk, to make the &longs;aid &longs;tar to <lb/>ri&longs;e that &longs;ame degree higher; and that &longs;inally if the motion to­ <lb/>wards the &longs;tar &longs;hould be in a right line, you ought to move yet <lb/>farther, than if it were about the circumference of never &longs;o <lb/>great a circle? <lb/><arrow.to.target n="marg646"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg646"></margin.target><emph type="italics"/>The right line, <lb/>and circumference <lb/>of an infinite cir­ <lb/>cle, are the &longs;ame <lb/>thing.<emph.end type="italics"/></s></p><p type="main"><s>SALV. True: For in &longs;hort the circumference of an infinite <lb/>circle, and a right line are the &longs;ame thing.</s></p><p type="main"><s>SAGR. </s><s>But this I do not under&longs;tand, nor as I believe, doth <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> apprehend the &longs;ame; and it mu&longs;t needs be concealed <lb/>from us under &longs;ome mi&longs;tery, for we know that <emph type="italics"/>Salviatus<emph.end type="italics"/> never <lb/>&longs;peaks at random, nor propo&longs;eth any Paradox, which doth not <lb/>break forth into &longs;ome conceit, not trivial in the lea&longs;t. </s><s>Therefore <lb/>in due time and place I will put you in mind to demon&longs;trate this, <lb/>that the right line is the &longs;ame with the circumference of an infi­ <lb/>nite circle, but at pre&longs;ent I am unwilling that we &longs;hould inter­ <lb/>rupt the di&longs;cour&longs;e in hand. </s><s>Returning then to the ca&longs;e, I pro­ <lb/>po&longs;e to the con&longs;ideration of <emph type="italics"/>Simplicius,<emph.end type="italics"/> how the acce&longs;&longs;ion and <lb/>rece&longs;&longs;ion that the Earth makes from the &longs;aid fixed &longs;tar which is <lb/>neer the Pole can be made as it were by a right line, for &longs;uch is <lb/>the Diameter of the Grand Orb, &longs;o that the attempting to re­ <lb/>gulate the elevation and depre&longs;&longs;ion of the Polar &longs;tar by the mo­ <lb/>tion along the &longs;aid Diameter, as if it were by the motion about <lb/>the little circle of the Earth, is a great argument of but little <lb/>judgment.</s></p><p type="main"><s>SIMP. </s><s>But we continue &longs;till un&longs;atisfied, in regard that the <lb/>&longs;aid &longs;mall mutation that &longs;hould be therein, would not be di&longs;cer­ <lb/>ned; and if this be <emph type="italics"/>null,<emph.end type="italics"/> then mu&longs;t the annual motion about <lb/>the Grand Orb a&longs;cribed to the Earth, be <emph type="italics"/>null<emph.end type="italics"/> al&longs;o.</s></p><p type="main"><s>SAGR. </s><s>Here now I give <emph type="italics"/>Salviatus<emph.end type="italics"/> leave to go on, who as I <lb/>believe will not overpa&longs;&longs;e the elevation and depre&longs;&longs;ion of the <lb/>Polar &longs;tar or any other of tho&longs;e that are fixed as <emph type="italics"/>null,<emph.end type="italics"/> although <lb/>not di&longs;covered by any one, and affirmed by <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf <lb/>to be, I will not &longs;ay <emph type="italics"/>null,<emph.end type="italics"/> but unob&longs;ervable by rea&longs;on of its <lb/>minuity.</s></p><p type="main"><s>SALV. </s><s>I have already &longs;aid above, that I do not think that </s></p><p type="main"><s><arrow.to.target n="marg647"></arrow.to.target> <lb/>any one did ever &longs;et him&longs;elf to ob&longs;erve, whether in different times <lb/>of the year there is any mutation to be &longs;een in the fixed &longs;tars, that <lb/>may have a dependance on the annual motion of the Earth, and <lb/>added withal, that I doubted lea&longs;t haply &longs;ome might never have <pb xlink:href="040/01/363.jpg" pagenum="343"/>under&longs;tood what tho&longs;e mutations are, and among&longs;t what &longs;tars <lb/>they &longs;hould be di&longs;cerned; therefore it would be nece&longs;&longs;ary that <lb/>we in the next place narrowly examine this particular. </s><s>My ha­ <lb/><arrow.to.target n="marg648"></arrow.to.target> <lb/>ving onely found written in general terms that the annual moti­ <lb/>on of the Earth about the Grand Orb, ought not to be admit­ <lb/>ted, becau&longs;e it is not probable but that by means of the &longs;ame <lb/>there would be di&longs;coverd &longs;ome apparent mutation in the fixed <lb/>&longs;tars, and not hearing &longs;ay what tho&longs;e apparent mutations ought to <lb/>be in particular, and in what &longs;tars, maketh me very rea&longs;onably <lb/>to infer that they who rely upon that general po&longs;ition, have not <lb/>under&longs;tood, no nor po&longs;&longs;ibly endeavoured to under&longs;tand, how <lb/>the bu&longs;ine&longs;&longs;e of the&longs;e mutations goeth, nor what things tho&longs;e <lb/>are which they &longs;ay ought to be &longs;een. </s><s>And to this judgment I am <lb/><arrow.to.target n="marg649"></arrow.to.target> <lb/>the rather induced, knowing that the annual motion a&longs;cribed <lb/>by <emph type="italics"/>Copernicus<emph.end type="italics"/> to the Earth, if it &longs;hould appear &longs;en&longs;ible in the <lb/>Starry Sphere, is not to make apparent mutations equal in re­ <lb/>&longs;pect to all the &longs;tars, but tho&longs;e appearances ought to be made <lb/>in &longs;ome greater, in others le&longs;&longs;er, and in others yet le&longs;&longs;er; and <lb/>la&longs;tly, in others ab&longs;olutely nothing at all, by rea&longs;on of the <lb/>va&longs;t magnitude that the circle of this annual motion is &longs;uppo&longs;ed <lb/>to be of. </s><s>As for the mutations that &longs;hould b &longs;een, they are of <lb/>two kinds, one is the &longs;aid &longs;tars changing apparent magnitude, <lb/>and the other their variation of altitudes in the Meridian. </s><s>Upon <lb/>which nece&longs;&longs;arily followeth the mutation of ri&longs;ings and &longs;ettings, <lb/>and of their di&longs;tances from the Zenith, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg647"></margin.target><emph type="italics"/>Enquiry is made <lb/>what mutations, & <lb/>in what &longs;tars, are to <lb/>be di&longs;covered, by <lb/>means of the an­ <lb/>nual motion of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg648"></margin.target><emph type="italics"/>A&longs;tronomers ha­ <lb/>ving omitted to in­ <lb/>&longs;tance what alte­ <lb/>rations tho&longs;e are <lb/>that may be deri­ <lb/>ved from the an­ <lb/>nual motion of the <lb/>Earth, do thereby <lb/>te&longs;tifie that they <lb/>never rightly un­ <lb/>der&longs;tood the &longs;ame.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg649"></margin.target><emph type="italics"/>The mutations <lb/>of the fixed &longs;tars <lb/>ought to be in &longs;ome <lb/>greater, in others <lb/>le&longs;&longs;er, and in others <lb/>nothing at all.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Methinks I &longs;ee preparing for me &longs;uch a skean of the&longs;e <lb/>revolutions, that I wi&longs;h it may never be my task to di&longs;-intangle <lb/>them, for to confe&longs;&longs;e my infirmity to <emph type="italics"/>Salviatus,<emph.end type="italics"/> I have &longs;ome­ <lb/>times thought thereon, but could never find the ^{*} Lay-band of <lb/><arrow.to.target n="marg650"></arrow.to.target> <lb/>it, and I &longs;peak not &longs;o much of this which pertains to the fixed <lb/>&longs;tars, as of another more terrible labour which you bring to my <lb/>remembrance by maintaining the&longs;e Meridian Altitudes, Ortive <lb/>Latitudes and di&longs;tances from the Vertex, <emph type="italics"/>&c.<emph.end type="italics"/> And that which <lb/><arrow.to.target n="marg651"></arrow.to.target> <lb/>puzzleth my brains, ari&longs;eth from what I am now about to tell <lb/>you. <emph type="italics"/>Copernicus<emph.end type="italics"/> &longs;uppo&longs;eth the Starry Sphere immoveable, and <lb/>the Sun in the centre thereof immoveable al&longs;o. </s><s>Therefore eve­ <lb/>ry mutation which &longs;eemeth unto us to be made in the Sun or in <lb/>the fixed &longs;tars, mu&longs;t of nece&longs;&longs;ity befall the Earth and be ous. <lb/></s><s>But the Sun ri&longs;eth and declineth in our Meridian by a very great <lb/>arch of almo&longs;t 47. degrees, and by arches yet greater and <lb/>greatet, varieth its Ortive and Occidual Latitudes in the oblique <lb/><arrow.to.target n="marg652"></arrow.to.target> <lb/>Horizons. </s><s>Now how can the Earth ever incline and elevate &longs;o <lb/>notably to the Sun, and nothing at all to the fixed &longs;tars, or &longs;o <lb/>little, that it is not to be perceived? </s><s>This is that knot which <lb/>could never get thorow my ^{*} Loom-Combe; and if you &longs;hall <pb xlink:href="040/01/364.jpg" pagenum="344"/>untie it, I &longs;hall hold you for more than an <emph type="italics"/>Alexander.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg650"></margin.target>* <emph type="italics"/>Bandola<emph.end type="italics"/> that <lb/>end of a skeen <lb/>where with hou&longs;e­ <lb/>wives fa&longs;ten their <lb/>hankes of yarn, <lb/>thread or &longs;ilk.</s></p><p type="margin"><s><margin.target id="marg651"></margin.target><emph type="italics"/>The grand dif­ <lb/>ficulty in<emph.end type="italics"/> Coper­ <lb/>nicus <emph type="italics"/>his Doctrine, <lb/>is that which con­ <lb/>cerns the<emph.end type="italics"/> Phæno­ <lb/>mena <emph type="italics"/>of the Sun <lb/>and fixed &longs;tars.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg652"></margin.target>* <emph type="italics"/>Pettine,<emph.end type="italics"/> it is <lb/>the &longs;tay in a Wea­ <lb/>vets Loom, that <lb/>permitteth no knot <lb/>or &longs;narle to pa&longs;&longs;e <lb/>it, called by them <lb/>the Combe of the <lb/>Loom.</s></p><p type="main"><s>SALV. </s><s>The&longs;e are &longs;cruples worthy of the ingenuity of <emph type="italics"/>Sagre­ <lb/>dus,<emph.end type="italics"/> and this doubt is &longs;o intricate, that even <emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf <lb/>almo&longs;t de&longs;paired of being able to explain the &longs;ame, &longs;o as to <lb/>render it intelligible, which we &longs;ee as well by his own confe&longs;&longs;ion <lb/>of its ob&longs;curity, as al&longs;o by his, at two &longs;everal times, taking two <lb/>different wayes to make it out. </s><s>And, I ingenuou&longs;ly confe&longs;&longs;e that <lb/>I under&longs;tood not his explanation, till &longs;uch time as another me­ <lb/>thod more plain and manife&longs;t, had rendred it intelligible; and <lb/>yet neither was that done without a long and laborious applica­ <lb/>tion of my thoughts to the &longs;ame.</s></p><p type="main"><s>SIMP. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aw the &longs;ame &longs;cruple, and makes u&longs;e there­ <lb/><arrow.to.target n="marg653"></arrow.to.target> <lb/>of to oppo&longs;e certain of the Ancients, who held that the Earth <lb/>was a Planet; again&longs;t whom he argueth, that if it were &longs;o, it <lb/>would follow that it al&longs;o, as the re&longs;t of the Planets, &longs;hould have a <lb/>plurality of motions, from whence would follow the&longs;e variati­ <lb/>ons in the ri&longs;ings and &longs;ettings of the fixed &longs;tars, and likewi&longs;e in <lb/>the Meridian Altitudes. </s><s>And in regard that he propoundeth the <lb/>difficulty, and doth not an&longs;wer it, it mu&longs;t needs be, if not im­ <lb/>po&longs;&longs;ible, at lea&longs;t very difficult to be re&longs;olved.</s></p><p type="margin"><s><margin.target id="marg653"></margin.target>Ari&longs;totles <emph type="italics"/>argu­ <lb/>ment again&longs;t the <lb/>Ancients, who held <lb/>that the Earth <lb/>was a Planet.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The &longs;tre&longs;&longs;e and &longs;trength of the knot rendereth the <lb/>&longs;olution thereof more commendable and admirable; but I do <lb/>not promi&longs;e you the &longs;ame at this time, and pray you to di&longs;pen&longs;e <lb/>with me therein till too morrow, and for the pre&longs;ent we will go <lb/>con&longs;idering and explaining tho&longs;e mutations and differences that <lb/>by means of the annual motion ought to be di&longs;cerned in the fix­ <lb/>ed &longs;tars, like as even now we &longs;aid, for the explication whereof <lb/>certain preparatory points offer them&longs;elves, which may facili­ <lb/>tate the an&longs;wer to the grand objection. </s><s>Now rea&longs;&longs;uming the <lb/>two motions a&longs;cribed to the Earth (two I &longs;ay, for the third is <lb/>no motion, as in its place I will declare) that is the annual and <lb/><arrow.to.target n="marg654"></arrow.to.target> <lb/>diurnal, the fir&longs;t is to be under&longs;tood to be made by the centre of <lb/>the Earth in or about the circumference of the grand Orb, that <lb/>is of a very great circle de&longs;cribed in the plain of the fixed and <lb/>immutable Ecliptick; the other, namely the diurnal, is made <lb/>by the Globe of the Earth in it &longs;elf about its own centre, and <lb/>own Axis, not erect, but inclined to the Plane of the Ecliptick, <lb/>with the inclination of 23. degrees and an half, or thereabouts, <lb/>the which inclination is maintained all the year about, and that <lb/>which ought e&longs;pecially to be ob&longs;erved, is alwayes &longs;ituate to­ <lb/>wards the &longs;ame point of Heaven: in &longs;o much that the Axis of the <lb/><arrow.to.target n="marg655"></arrow.to.target> <lb/>diurnal motion doth alwayes remain parallel to it &longs;elf; &longs;o that <lb/>if we imagine that &longs;ame Axis to be continued out until it reach <lb/>the fixed &longs;tars, whil&longs;t the centre of the Earth is encircling the <lb/>whole Ecliptick in a year, the &longs;aid Axis de&longs;cribeth the &longs;uper­ <pb xlink:href="040/01/365.jpg" pagenum="345"/>ficies of an oblique Cylinder, which hath for one of its ba&longs;es <lb/>the &longs;aid annual circle, and for the other a like circle imagina­ <lb/>rily de&longs;cribed by its extremity, or, (if you will) Pole, among&longs;t <lb/>the fixed &longs;tars. </s><s>And this &longs;ame cylinder is oblique to the Plane of <lb/>the Ecliptick, according to the inclination of the Axis that de­ <lb/>&longs;cribeth it, which we have &longs;aid to be 23 degrees and an half, <lb/>the which continuing perpetually the &longs;ame (&longs;ave onely, that in <lb/>many thou&longs;ands of years it maketh &longs;ome very &longs;mall mutation, <lb/>which nothing importeth in our pre&longs;ent bu&longs;ine&longs;&longs;e) cau&longs;eth that <lb/><arrow.to.target n="marg656"></arrow.to.target> <lb/>the Terre&longs;trial Globe doth never more incline or elevate, but <lb/>&longs;till con&longs;erveth the &longs;ame &longs;tate without mutation. </s><s>From whence <lb/>en&longs;ueth, that as to what pertaineth to the mutations to be ob­ <lb/>&longs;erved in the fixed &longs;tars dependant on the &longs;ole annual motion, <lb/>the &longs;ame &longs;hall happen to any point what&longs;oever of the Earths <lb/>&longs;urface, as befalleth unto the centre of the Earth it &longs;elf; and <lb/>therefore in the pre&longs;ent explanations we will make u&longs;e of the <lb/>centre, as if it were any what&longs;oever point of the &longs;uperficies. <lb/></s><s>And for a more facile under&longs;tanding of the whole, let us de&longs;ign <lb/><arrow.to.target n="marg657"></arrow.to.target> <lb/>the &longs;ame in lineal figures: And fir&longs;t of all let us de&longs;cribe in the <lb/>Plane of the Ecliptick the circle A N B O [<emph type="italics"/>in Fig.<emph.end type="italics"/> 7.] and let <lb/>us under&longs;tand the points A and B, to be the extreams towards <lb/>the North and South; that is, the beginning of [<emph type="italics"/>or entrance into<emph.end type="italics"/>] <lb/><emph type="italics"/>Cancer<emph.end type="italics"/> or <emph type="italics"/>Capricorn,<emph.end type="italics"/> and let us prolong the Diameter A B, in­ <lb/>determinately by D and C towards the Starry Sphere. </s><s>I &longs;ay <lb/>now in the fir&longs;t place, that none of the fixed &longs;tars placed in the <lb/>Ecliptick, &longs;hall ever vary elevation, by rea&longs;on of any what&longs;o­ <lb/>ever mutation made by the Earth along the &longs;aid Plane of the <lb/>Ecliptick, but &longs;hall alwayes appear in the &longs;ame &longs;uperficies, al­ <lb/>though the Earth &longs;hall approach and recede as great a &longs;pace as is <lb/>that of the diameter of the Grand Orb, as may plainly be <lb/>&longs;een in the &longs;aid figure. </s><s>For whether the Earth be in the point <lb/>A or in B, the &longs;tar C alwayes appeareth in the &longs;ame line A B C; <lb/>although the di&longs;tance B C, be le&longs;&longs;e than A C, by the whole <lb/>diameter A B. </s><s>The mo&longs;t therefore that can be di&longs;covered in the <lb/>&longs;tar C, and in any other placed in the Ecliptick, is the aug­ <lb/>mented or dimini&longs;hed apparent magnitude, by rea&longs;on of the ap­ <lb/>proximation or rece&longs;&longs;ion of the Earth.</s></p><p type="margin"><s><margin.target id="marg654"></margin.target><emph type="italics"/>The annual mo­ <lb/>tion made by the <lb/>centre of the Earth <lb/>under the Eclip­ <lb/>tick and the diur­ <lb/>nal motion made <lb/>by the Earth about <lb/>its own centre.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg655"></margin.target><emph type="italics"/>The axis of the <lb/>Earth continueth <lb/>alwayes parallel to <lb/>it &longs;elf, and de&longs;cri­ <lb/>beth a Cylindrai­ <lb/>cal &longs;uperficies, in­ <lb/>clining to the <lb/>grand Orb.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg656"></margin.target><emph type="italics"/>The Orb of the <lb/>Earth never incli­ <lb/>neth, but is im­ <lb/>mutably the &longs;ame.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg657"></margin.target><emph type="italics"/>The fixed &longs;tars <lb/>placed in the E­ <lb/>cliptick never ele­ <lb/>vate nor de&longs;cend, <lb/>on account of the <lb/>annual motion, but <lb/>yet approach and <lb/>recede.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Stay a while I pray you, for I meet with a certain <lb/>&longs;cruple, which much troubleth me, and it is this: That the &longs;tar <lb/>C may be &longs;een by the &longs;ame line A B C, as wel when the Earth <lb/>is in A, as when it is in B, I under&longs;tand very well, as al&longs;o fur­ <lb/>thermore I apprehend that the &longs;ame would happen in all the <lb/><arrow.to.target n="marg658"></arrow.to.target> <lb/>points of the line A B, &longs;o long as the Earth &longs;hould pa&longs;&longs;e from A <lb/>to B by the &longs;aid line; but it pa&longs;&longs;ing thither, as is to be &longs;uppo&longs;ed, <lb/>by the arch A N B, it is manife&longs;t that when it &longs;hall be in the <pb xlink:href="040/01/366.jpg" pagenum="346"/>point N, and in any other except tho&longs;e two A and B, the &longs;aid <lb/>&longs;tar &longs;hall no longer be ob&longs;erved in the line A B; but in others. <lb/></s><s>So that, if the appearing under &longs;everal lines ought to cau&longs;e <lb/>apparent mutations, &longs;ome difference mu&longs;t needs appear in <lb/>this ca&longs;e. </s><s>Nay more, I will &longs;peak it with that Philo&longs;ophical <lb/>freedom, which ought to be allowed among&longs;t Philo&longs;ophick <lb/>friends, methinks that you, contradicting your &longs;elf, deny that <lb/>now, which but even now to our admiration, you proved to be <lb/>really true, and con&longs;iderable; I mean that which happeneth in <lb/>the Planets, and particularly in the three &longs;uperiour ones, that <lb/>being con&longs;tantly in the Ecliptick, or very near unto it, do not <lb/>onely &longs;hew them&longs;elves one while near unto us, and another <lb/>while remote, but &longs;o deformed in their regular motions, that <lb/>they &longs;eem &longs;ometimes immoveable, and &longs;ometimes many de­ <lb/>grees retrograde; and all upon no other occa&longs;ion than the an­ <lb/>nual motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg658"></margin.target><emph type="italics"/>Objections again&longs;t <lb/>the Earths annual <lb/>motion taken from <lb/>the fixed stars <lb/>placed in the E­ <lb/>cliptick.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Though by a thou&longs;and accidents I have been hereto­ <lb/>fore a&longs;&longs;ured of the wittine&longs;&longs;e of <emph type="italics"/>Sagredus,<emph.end type="italics"/> yet I had a de&longs;ire by <lb/>this one experiment more to a&longs;certain me of what I may expect <lb/>from his ingenuity, and all this for my own intere&longs;t, for in ca&longs;e <lb/>my Propo&longs;itions &longs;tand but proof again&longs;t the hammer and fur­ <lb/>nace of his judgment, I &longs;hall be confident that they will abide <lb/><arrow.to.target n="marg659"></arrow.to.target> <lb/>the ^{*} te&longs;t of all Touch-&longs;tones. </s><s>I &longs;ay therefore that I had pur­ <lb/>po&longs;ely di&longs;&longs;embled this objection, but yet not with any intent to <lb/>deceive you, and to put any fal&longs;hood upon you, as it might <lb/>have happened if the objection by me di&longs;gui&longs;ed, and by you o­ <lb/>ver-lookt, had been the &longs;ame in effect as it &longs;eemed to be in ap­ <lb/>pearance, that is, really valid and conclu&longs;ive; but it is not &longs;o; <lb/>nay I rather &longs;u&longs;pect that to try me, you make as if you did not <lb/>&longs;ee its nullity. </s><s>But I will herein be too hard for you, and force <lb/>from your tongue, that which you would &longs;o artificially conceal; <lb/>and therefore tell me, what that thing &longs;hould be, whereby you <lb/>come to know the &longs;tation and retrogradation of the Planets, <lb/>which is derived from the annual motion, aud which is &longs;o great, <lb/>that at lea&longs;t &longs;ome foot-&longs;teps of &longs;uch an effect ought to appear in <lb/>the &longs;tars of the Ecliptick?</s></p><p type="margin"><s><margin.target id="marg659"></margin.target>* Or will prove <lb/>of good alloy.</s></p><p type="main"><s>SAGR. </s><s>This demand of yours containeth two que&longs;tions, to <lb/>which it is nece&longs;&longs;ary that I make reply; the fir&longs;t relates to the <lb/>imputation which you lay upon me of a Di&longs;&longs;embler; the other <lb/>concerneth that which may appear in the &longs;tars, <emph type="italics"/>&c.<emph.end type="italics"/> As to the <lb/>fir&longs;t, I will &longs;ay with your permi&longs;&longs;ion, that it is not true, that I <lb/>have di&longs;&longs;embled my knowing the nullity of that objection; and <lb/>to a&longs;&longs;ure you of the &longs;ame, I now tell you that I very well under­ <lb/>&longs;tand the nullity thereof.</s></p><p type="main"><s>SALV. </s><s>But yet I do not under&longs;tand how it can be, that you <pb xlink:href="040/01/367.jpg" pagenum="347"/>&longs;pake not friendly, when you &longs;aid you did not know that &longs;ame <lb/>fallacy which you now confe&longs;&longs;e that you know very well.</s></p><p type="main"><s>SAGR. </s><s>The very confe&longs;&longs;ion of knowing it may a&longs;&longs;ure you <lb/>that I did not di&longs;&longs;emble, when I &longs;aid that I did not under&longs;tand it; <lb/>for if I had had a mind, and would di&longs;&longs;emble, who could hin­ <lb/>der me from continuing in the &longs;ame &longs;imulation, and denying &longs;till <lb/>that I under&longs;tand the fallacy? </s><s>I &longs;ay therefore that I under&longs;tood <lb/>not the &longs;ame, at that time, but that I do now at this pre&longs;ent ap­ <lb/>prehend it, for that you have prompted my intellect, fir&longs;t by <lb/>telling me re&longs;olutely that it is <emph type="italics"/>null,<emph.end type="italics"/> and then by beginning to <lb/>que&longs;tion me &longs;o at large what thing that might be, whereby I <lb/>might come to know the &longs;tation and retrogradation of the Pla­ <lb/><arrow.to.target n="marg660"></arrow.to.target> <lb/>nets; and becau&longs;e this is known by comparing them with the fix­ <lb/>ed &longs;tars, in relation to which, they are &longs;een to vary their mo­ <lb/>tions, one while towards the We&longs;t, and another towards the <lb/>Ea&longs;t, and &longs;ometimes to abide immoveable; and becau&longs;e there <lb/>is not any thing above the Starry Sphere, immen&longs;ely more remote <lb/>from us, and vi&longs;ible unto us, wherewith we may compare our <lb/>fixed &longs;tars, therefore we cannot di&longs;cover in the fixed &longs;tars any <lb/>foot-&longs;teps of what appeareth to us in the Planets. </s><s>This I believe <lb/>is the &longs;ub&longs;tance of that which you would force from me.</s></p><p type="margin"><s><margin.target id="marg660"></margin.target><emph type="italics"/>The &longs;tation, di­ <lb/>rection and retro­ <lb/>gradation of the <lb/>Planets is known, <lb/>in relation to the <lb/>fixed &longs;tars.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>It is &longs;o, with the addition moreover of your admi­ <lb/><arrow.to.target n="marg661"></arrow.to.target> <lb/>rable ingenuity; and if with half a word I did open your eyes, <lb/>you by the like have remembred me that it is not altogether im­ <lb/>po&longs;&longs;ible, but that &longs;ometime or other &longs;omething ob&longs;ervable may <lb/>be found among&longs;t the fixed &longs;tars, by which it may be gathered <lb/>wherein the annual conver&longs;ion re&longs;ides, &longs;o as that they al&longs;o no <lb/>le&longs;&longs;e than the Planets and Sun it &longs;elf, may appear in judgment to <lb/>bear witne&longs;&longs;e of that motion, in favour of the Earth; for I do not <lb/>think that the &longs;tas are &longs;pread in a &longs;pherical &longs;uperficies equally re­ <lb/>mote from a common centre, but hold, that their di&longs;tances from <lb/>us are &longs;o various, that &longs;ome of them may be twice and thrice as <lb/>remote as others; &longs;o that if with the Tele&longs;cope one &longs;hould ob­ <lb/>&longs;erve a very &longs;mall &longs;tar neer to one of the bigger, and which <lb/>therefore was very exceeding high, it might happen that &longs;ome <lb/>&longs;en&longs;ible mutation might fall out between them, corre&longs;pondent <lb/>to that of the &longs;uperiour Planets. </s><s>And &longs;o much &longs;hall &longs;erve to have <lb/>&longs;poken at this time touching the &longs;tars placed in the Ecliptick. <lb/><arrow.to.target n="marg662"></arrow.to.target> <lb/>Let us now come to the fixed &longs;tars, placed out of the Ecliptick, <lb/>and let us &longs;uppo&longs;e a great circle erect upor [<emph type="italics"/>i. </s><s>e. </s><s>at right angles <lb/>to<emph.end type="italics"/>] the Plane of the ^{*} &longs;ame; and let it, for example, be a cir­ <lb/>cle that in the Starry Sphere an&longs;wers to the Sol&longs;titial Colure, <lb/><arrow.to.target n="marg663"></arrow.to.target> <lb/>and let us mark it C E H [<emph type="italics"/>in Fig.<emph.end type="italics"/> 8.] which &longs;hall happen to be <lb/>withal a Meridian, and in it we will take a &longs;tar without the Eclip­ <lb/>tick, which let be E. </s><s>Now this &longs;tar will indeed vary its elevati­ <pb xlink:href="040/01/368.jpg" pagenum="348"/>on upon the Earths motion; for from the Earth in A it &longs;hall be <lb/>&longs;een according to the ray A E, with the elevation of the angle <lb/>E A C; but from the Earth placed in B, it &longs;hall be &longs;een ac­ <lb/>cording to the ray B E, with the elevation of the angle E B C, <lb/>bigger than the other E A C, that being extern, and this in­ <lb/>tern and oppo&longs;ite in the triangle E A B, the di&longs;tance therefore <lb/>of the &longs;tar E from the Ecliptick, &longs;hall appear changed; and <lb/>likewi&longs;e its altitude in the Meridian &longs;hall become greater in the <lb/>po&longs;ition B, than in the place A, according as the angle E B C <lb/>exceeds the angle E A C, which exce&longs;&longs;e is the quantity of the <lb/>angle A E B: For in the triangle E A B, the &longs;ide A B being <lb/>continued to C, the exteriour angle E B C (as being equal to <lb/>the two interiour and oppo&longs;ite E and A) exceedeth the &longs;aid an­ <lb/>gle A, by the quantity of the angle <emph type="italics"/>E.<emph.end type="italics"/> And if we &longs;hould take <lb/>another &longs;tar in the &longs;ame Meridian, more remote from the Ecli­ <lb/>ptick, as for in&longs;tance the &longs;tar H, the diver&longs;ity in it &longs;hall be <lb/>greater by being ob&longs;erved from the two &longs;tations A and B, accor­ <lb/>ding as the angle A H B is greater than the other <emph type="italics"/>E<emph.end type="italics"/>; which an­ <lb/>gle &longs;hall encrea&longs;e continually according as the ob&longs;erved &longs;tar &longs;hall <lb/>be farther and farther from the Ecliptick, till that at la&longs;t the <lb/>greate&longs;t mutation will appear in that &longs;tar that &longs;hould be placed in <lb/>the very Pole of the Ecliptick. </s><s>As for a full under&longs;tanding there­ <lb/>of we thus demon&longs;trate. </s><s>Suppo&longs;e the diameter of the Grand <lb/>Orb to be A B, who&longs;e centre [<emph type="italics"/>in the &longs;ame Figure<emph.end type="italics"/>] is G, and <lb/>let it be &longs;uppo&longs;ed to be continued out as far as the Starry Sphere <lb/>in the points D and C, and from the centre G let there be erected <lb/>the Axis of the Ecliptick G F, prolonged till it arrive at the &longs;aid <lb/>Sphere, in which a Meridian D F C is &longs;uppo&longs;ed to be de&longs;cribed, <lb/>that &longs;hall be perpendicular to the Plane of the Ecliptick; and <lb/>in the arch F C any points H and <emph type="italics"/>E,<emph.end type="italics"/> are imagined to be taken, <lb/>as places of fixed &longs;tars: Let the lines F A, F B, A H, H G, <lb/>H B, A <emph type="italics"/>E,<emph.end type="italics"/> G <emph type="italics"/>E,<emph.end type="italics"/> B <emph type="italics"/>E,<emph.end type="italics"/> be conjoyned. </s><s>And let the angle of dif­ <lb/>ference, or, if you will, the Parallax of the &longs;tar placed in the <lb/>Pole F, be A F B, and let that of the &longs;tar placed in H, be the <lb/>angle A H <emph type="italics"/>B,<emph.end type="italics"/> and let that of the &longs;tar in <emph type="italics"/>E,<emph.end type="italics"/> be the angle <lb/>A <emph type="italics"/>E<emph.end type="italics"/> B. </s><s>I &longs;ay, that the angle of difference of the Polar &longs;tar F, is <lb/>the greate&longs;t, and that of the re&longs;t, tho&longs;e that are nearer to the <lb/>greate&longs;t are bigger than the more remote; that is to &longs;ay, that the <lb/>angle F is bigger than the angle H, and this bigger than the angle <lb/><emph type="italics"/>E.<emph.end type="italics"/> Now about the triangle F A B, let us &longs;uppo&longs;e a circle to be de­ <lb/>&longs;cribed. </s><s>And becau&longs;e the angle F is acute, (by rea&longs;on that its ba&longs;e <lb/>AB is le&longs;&longs;e than the diameter DC, of the &longs;emicircle D F C) it &longs;hall <lb/>be placed in the greater portion of the circum&longs;cribed circle cut <lb/>by the ba&longs;e A B. </s><s>And becau&longs;e the &longs;aid A B is divided in the <lb/>mid&longs;t, and at right angles by F G, the centre of the circum&longs;cri­ <pb xlink:href="040/01/369.jpg" pagenum="349"/>bed circle &longs;hall be in the line F G, which let be the point I; and <lb/>becau&longs;e that of &longs;uch lines as are drawn from the point G, which <lb/>is not the centre, unto the circumference of the circum&longs;cribed <lb/>circle, the bigge&longs;t is that which pa&longs;&longs;eth by the centre, G F &longs;hall <lb/>be bigger than any other that is drawn from the point G, to the <lb/>circumference of the &longs;aid circle; and therefore that circumfe­ <lb/>rence will cut the line G H (which is equal to the line G F) and <lb/>cutting G H, it will al&longs;o cut A H. </s><s>Let it cut it in L, and con­ <lb/>joyn the line L B. </s><s>The&longs;e two angles, therefore, A F B and A L B <lb/>&longs;hall be equal, as being in the &longs;ame portion of the circle cir­ <lb/>cum&longs;cribed. </s><s>But A L B external, is bigger than the internal H; <lb/>therefore the angle F is bigger than the angle H. </s><s>And by the <lb/>&longs;ame method we might demon&longs;trate the angle H to be bigger <lb/>than the angle E, becau&longs;e that of the circle de&longs;cribed about the <lb/>triangle A H B, the centre is in the perpendicular G F, to which <lb/>the line G H is nearer than the line G E, and therefore the cir­ <lb/>cumference of it cutteth G E, and al&longs;o A E, whereupon the pro­ <lb/>po&longs;ition is manife&longs;t. </s><s>We will conclude from hence, that the dif­ <lb/>ference of appearance, (which with the proper term of art, we <lb/>might call the Parallax of the fixed &longs;tars) is greater, or le&longs;&longs;e, ac­ <lb/>cording as the Stars ob&longs;erved are more or le&longs;&longs;e adjacent to the <lb/>Pole of the Ecliptick, &longs;o that, in conclu&longs;ion of tho&longs;e Stars that <lb/>are in the Ecliptick it &longs;elf, the &longs;aid diver&longs;ity is reduced to nothing. <lb/></s><s>In the next place, as to the Earths acce&longs;&longs;ion by that motion to, <lb/><arrow.to.target n="marg664"></arrow.to.target> <lb/>or rece&longs;&longs;ion from the Stars, it appeareth to, and recedeth from <lb/>tho&longs;e that are in the Ecliptick, the quantity of the whole diame­ <lb/>ter of the grand Orb, as we did &longs;ee even now, but that acce&longs;&longs;ion <lb/>or rece&longs;&longs;ion to, or from the &longs;tars about the Pole of the Ecliptick, <lb/>is almo&longs;t nothing; and in going to and from others, this diffe­ <lb/>rence groweth greater, according as they are neerer to the Eclip­ <lb/>tick. </s><s>We may, in the third place, know, that the &longs;aid difference <lb/><arrow.to.target n="marg665"></arrow.to.target> <lb/>of A&longs;pect groweth greater or le&longs;&longs;er, according as the Star ob&longs;er­ <lb/>ved &longs;hall be neerer to us, or farther from us. </s><s>For if we draw a­ <lb/>nother Meridian, le&longs;&longs;e di&longs;tant from the Earth; as for example, <lb/>this D F I [<emph type="italics"/>in Fig.<emph.end type="italics"/> 7.] a Star placed in F, and &longs;een by the &longs;ame <lb/>ray A F E, the Earth being in A, would, in ca&longs;e it &longs;hould be ob­ <lb/>&longs;erved from the Earth in B, appear according to the ray B F, and <lb/>would make the angle of difference, namely, B F A, bigger <lb/>than the former A E B, being the exteriour angle of the trian­ <lb/>gle B F E.</s></p><p type="margin"><s><margin.target id="marg661"></margin.target><emph type="italics"/>An Indice in <lb/>the fixed &longs;tars like <lb/>to that which is <lb/>&longs;een in the Pla­ <lb/>nets, is an argu­ <lb/>ment of the Earths <lb/>annual motion.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg662"></margin.target><emph type="italics"/>The fixed &longs;tars <lb/>without the Eclip­ <lb/>tick elevate and <lb/>de&longs;cend more or <lb/>le&longs;&longs;e, according to <lb/>their di&longs;tance from <lb/>the &longs;aid Ecliptick.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg663"></margin.target>* <emph type="italics"/>i. </s><s>e.<emph.end type="italics"/> of the E­ <lb/>cliptick.</s></p><p type="margin"><s><margin.target id="marg664"></margin.target><emph type="italics"/>The Earth ap­ <lb/>proacheth or rece­ <lb/>deth from the fix­ <lb/>ed &longs;tars of the E­ <lb/>cliptick, the quan­ <lb/>tity of the Dinme­ <lb/>ter of the Grand <lb/>Orb.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg665"></margin.target><emph type="italics"/>The &longs;tars near­ <lb/>er to us make <lb/>greater differences <lb/>than the more re­ <lb/>more.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>With great delight, and al&longs;o benefit have I heard <lb/>your di&longs;cour&longs;e; and that I may be certain, whether I have right­ <lb/><arrow.to.target n="marg666"></arrow.to.target> <lb/>ly under&longs;tood the &longs;ame, I &longs;hall give you the &longs;umme of the Con­ <lb/>clu&longs;ions in a few words. </s><s>As I take it, you have explained to us <lb/>the different appearances, that by means of the Earths annual mo­ <pb xlink:href="040/01/370.jpg" pagenum="350"/>tion, may be by us ob&longs;erved in the fixed &longs;tars to be of two <lb/>kinds: The one is, that of their apparent magnitudes varied, ac­ <lb/>cording as we, tran&longs;ported by the Earth, approach or recede <lb/>from the &longs;ame: The other (which likewi&longs;e dependeth on the <lb/>&longs;ame acce&longs;&longs;ion and reee&longs;&longs;ion) their appearing unto us in the <lb/>&longs;ame Meridian, one while more elevated, and another while le&longs;&longs;e. <lb/></s><s>Moreover, you tell us (and I under&longs;tand it very well) that the <lb/>one and other of the&longs;e mutations are not made alike in all the <lb/>&longs;tars, but in &longs;ome greater, and in others le&longs;&longs;er, and in others not <lb/>at all. </s><s>The acce&longs;&longs;ion and rece&longs;&longs;ion whereby the &longs;ame &longs;tar ought <lb/>to appear, one while bigger, and another while le&longs;&longs;er, is in&longs;en&longs;i­ <lb/>ble, and almo&longs;t nothing in the &longs;tars neer unto the pole of the E­ <lb/>cliptick, but is greate&longs;t in the &longs;tars placed in the Ecliptick it &longs;elf, <lb/>and indifferent in the intermediate: the contrary happens in the <lb/>other difference, that is, the elevation or depre&longs;&longs;ion of the &longs;tars <lb/>placed in the Ecliptick is nothing at all, greate&longs;t in tho&longs;e neere&longs;t <lb/>to the Pole of the &longs;aid Ecliptick, and indifferent in the interme­ <lb/>diate. </s><s>Be&longs;ides, both the&longs;e differences are more &longs;en&longs;ible in the <lb/>Stars neere&longs;t to us, in the more remote le&longs;&longs;e &longs;en&longs;ible, and in <lb/>tho&longs;e that are very far di&longs;tant wholly di&longs;appear. </s><s>This is, as to <lb/>what concerns my &longs;elf; it remaineth now, as I conceive, that <lb/>&longs;omething be &longs;aid for the &longs;atisfaction of <emph type="italics"/>Simplicius,<emph.end type="italics"/> who, as I <lb/>believe, will not ea&longs;ily be made to over-pa&longs;&longs;e tho&longs;e differences, <lb/>as in&longs;en&longs;ible that are derived from a motion of the Earth &longs;o va&longs;t, <lb/>and from a mutation that tran&longs;ports the Earth into places twice <lb/>as far di&longs;tant from us as the Sun.</s></p><p type="margin"><s><margin.target id="marg666"></margin.target><emph type="italics"/>The Epilogue of <lb/>the<emph.end type="italics"/> Phænomena <lb/><emph type="italics"/>of the fixed &longs;tars <lb/>cau&longs;ed by the an­ <lb/>nual motion of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Truth is, to &longs;peak freely, I am very loth to confe&longs;&longs;e, that <lb/>the di&longs;tance of the fixed Stars ought to be &longs;uch, that in them the <lb/>fore-mentioned differences &longs;hould be wholly imperceptible.</s></p><p type="main"><s>SALV. </s><s>Do notthrow your &longs;elf into ab&longs;olute de&longs;pair, <emph type="italics"/>Simpli­ <lb/>cius,<emph.end type="italics"/> for there may perhaps yet &longs;ome qualification be found for <lb/>your difficulties. </s><s>And fir&longs;t, that the apparent magnitude of the <lb/>&longs;tars is not &longs;een to make any &longs;en&longs;ible alteration, ought not to be <lb/>judged by you a thing improbable, in regard you &longs;ee the gue&longs;&longs;es <lb/>of men in this particular to be &longs;o gro&longs;&longs;ely erroneous, e&longs;pecially in <lb/>looking upon &longs;plendid objects; and you your &longs;elf beholding <lb/><emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> a lighted Torch at the di&longs;tance of 200 paces, if it ap­ <lb/><arrow.to.target n="marg667"></arrow.to.target> <lb/>proach nearer to you 3. or 4. yards, do you think that it will <lb/>&longs;hew any whit encrea&longs;ed in magnitude? </s><s>I for my part &longs;hould <lb/>not perceive it certainly, although it &longs;hould approach 20. or <lb/>30. yards nearer; nay it hath &longs;ometimes happened that in &longs;eeing <lb/>&longs;uch a light at that di&longs;tance I know not how to re&longs;olve whether <lb/>it came towards me, or retreated from me, when as it did in <lb/>reality approach nearer to me. </s><s>But what need I &longs;peak of this? <lb/></s><s>If the &longs;elf &longs;ame acce&longs;&longs;ion and rece&longs;&longs;ion (I &longs;peak of a di&longs;tance <pb xlink:href="040/01/371.jpg" pagenum="351"/>twice as great as that from the Sun to us) in the &longs;tar of <emph type="italics"/>Saturn<emph.end type="italics"/> is <lb/>almo&longs;t totally imperceptible, and in <emph type="italics"/>Jupiter<emph.end type="italics"/> not very ob&longs;erva­ <lb/>ble, what &longs;hall we think of the fixed &longs;tars, which I believe you <lb/>will not &longs;cruple to place twice as far off as <emph type="italics"/>Saturn<emph.end type="italics"/>? </s><s>In <emph type="italics"/>Mars,<emph.end type="italics"/> <lb/>which for that it is nearer to us -------</s></p><p type="margin"><s><margin.target id="marg667"></margin.target><emph type="italics"/>In objects far <lb/>remote, and lumi­ <lb/>nous, a &longs;mall ap­ <lb/>proach or rece&longs;&longs;ion <lb/>is imperceptible.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Pray Sir, put your &longs;elf to no farther trouble in this <lb/>particular, for I already conceive that what hath been &longs;poken <lb/>touching the unaltered apparent magnitude of the fixed &longs;tars may <lb/>very well come to pa&longs;&longs;e, but what &longs;hall we &longs;ay of the other dif­ <lb/>ficulty that proceeds from not perceiving any variation in the <lb/>mutation of a&longs;pect?</s></p><p type="main"><s>SALV. </s><s>We will &longs;ay that which peradventure may &longs;atisfie <lb/>you al&longs;o in this particular. </s><s>And to make &longs;hort, would you not <lb/>be &longs;atisfied if there &longs;hould be di&longs;covered in the &longs;tars face muta­ <lb/>tions that you think ought to be di&longs;covered, in ca&longs;e the annual <lb/>motion belonged to the Earth?</s></p><p type="main"><s>SIMP. </s><s>I &longs;hould &longs;o doubtle&longs;&longs;e, as to what concerns this par­ <lb/>ticular.</s></p><p type="main"><s>SALV. </s><s>I could wi&longs;h you would &longs;ay that in ca&longs;e &longs;uch a diffe­ <lb/><arrow.to.target n="marg668"></arrow.to.target> <lb/>rence were di&longs;covered, nothing more would remain behind, that <lb/>might render the mobility of the Earth que&longs;tionable. </s><s>But al­ <lb/>though yet that &longs;hould not &longs;en&longs;ibly appear, yet is not its mo­ <lb/>bility removed, nor its immobility nece&longs;&longs;arily proved, it being <lb/>po&longs;&longs;ible, (as <emph type="italics"/>Copernicus<emph.end type="italics"/> affirmeth) that the immen&longs;e di&longs;tance of <lb/>the Starry Sphere rendereth &longs;uch very &longs;mall <emph type="italics"/>Phænomena<emph.end type="italics"/> unob&longs;er­ <lb/>vable; the which as already hath been &longs;aid, may po&longs;&longs;ibly not <lb/>have been hitherto &longs;o much as &longs;ought for, or if &longs;ought for, yet <lb/>not &longs;ought for in &longs;uch a way as they ought, to wit, with that <lb/><arrow.to.target n="marg669"></arrow.to.target> <lb/>exactne&longs;&longs;e which to &longs;o minute a punctuality would be nece&longs;&longs;ary; <lb/>which exactne&longs;&longs;e is very difficult to obtain, as well by rea&longs;on of the <lb/>deficiency of A&longs;ttonomical In&longs;truments, &longs;ubject to many altera­ <lb/>tions, as al&longs;o through the fault of tho&longs;e that manage them with le&longs;s <lb/>diligence then is requi&longs;ite. </s><s>A nece&longs;&longs;ary argument how little cre­ <lb/>dit is to be given to tho&longs;e ob&longs;ervations may be deduced from the <lb/>differences which we find among&longs;t A&longs;tronomers in a&longs;&longs;igning the <lb/>places, I will not &longs;ay, of the new Stars or Comets, but of the fixed <lb/>&longs;tars them&longs;elves, even to the altitudes of the very Poles, in <lb/>which, mo&longs;t an end, they are found to differ from one another <lb/>many minutes. </s><s>And to &longs;peak the truth, who can in a Quadrant, <lb/>or Sextant, that at mo&longs;t &longs;hall have its &longs;ide ^{*} 3. or 4. yards long, <lb/><arrow.to.target n="marg670"></arrow.to.target> <lb/>a&longs;certain him&longs;elf in the incidence of the perpendicular, or in the <lb/>direction of the &longs;ights, not to erre two or three minutes, which <lb/>in its circumference &longs;hall not amount to the breadth of a grain of <lb/>^{*}<emph type="italics"/>Mylet<emph.end type="italics"/>? </s><s>Be&longs;ides that, it is almo&longs;t impo&longs;&longs;ible, that the In&longs;trument <lb/><arrow.to.target n="marg671"></arrow.to.target> <lb/>&longs;hould be made, and kept with ab&longs;olute exactne&longs;&longs;e. <emph type="italics"/>Ptolomey<emph.end type="italics"/> <pb xlink:href="040/01/372.jpg" pagenum="352"/><arrow.to.target n="marg672"></arrow.to.target> <lb/>&longs;heweth his di&longs;tru&longs;t of a Spherical In&longs;trument compo&longs;ed by <emph type="italics"/>Ar­ <lb/>chimedes<emph.end type="italics"/> hi&longs;melf to take the Suns ingre&longs;&longs;ion into the Æqui­ <lb/>noctial. <lb/><arrow.to.target n="marg673"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg668"></margin.target><emph type="italics"/>If in the fixed <lb/>&longs;tars one &longs;hould <lb/>di&longs;cover any an­ <lb/>nual mutation, the <lb/>motion of the <lb/>Earth would be <lb/>undeniable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg669"></margin.target><emph type="italics"/>It is proved what <lb/>&longs;mall credit is to be <lb/>given to A&longs;trono­ <lb/>mical In&longs;truments <lb/>in minute ob&longs;erva­ <lb/>tions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg670"></margin.target>* Braceia Italian.</s></p><p type="margin"><s><margin.target id="marg671"></margin.target>* Or Mill.</s></p><p type="margin"><s><margin.target id="marg672"></margin.target>Ptolomy <emph type="italics"/>did not <lb/>tru&longs;t to an In&longs;tru­ <lb/>ment made by<emph.end type="italics"/> Ar­ <lb/>chimedes.</s></p><p type="margin"><s><margin.target id="marg673"></margin.target><emph type="italics"/>In&longs;truments of<emph.end type="italics"/> <lb/>Tycho <emph type="italics"/>made with <lb/>great expence.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>But if the In&longs;truments be &longs;o &longs;u&longs;pitious, and the ob&longs;er­ <lb/>vations &longs;o dubious, how can we ever come to any certainty of <lb/>things, or free our &longs;elves from mi&longs;takes? </s><s>I have heard &longs;trange <lb/>things of the In&longs;truments of <emph type="italics"/>Tycho<emph.end type="italics"/> made with extraordinary co&longs;t, <lb/>and of his &longs;ingular diligence in ob&longs;ervations.</s></p><p type="main"><s>SALV. </s><s>All this I grant you; but neither one nor other of <lb/>the&longs;e is &longs;ufficient to a&longs;certain us in a bu&longs;ine&longs;&longs;e of this importance. </s></p><p type="main"><s><arrow.to.target n="marg674"></arrow.to.target> <lb/>I de&longs;ire that we may make u&longs;e of In&longs;truments greater by far, and <lb/>by far certainer than tho&longs;e of <emph type="italics"/>Tycho,<emph.end type="italics"/> made with a very &longs;mall <lb/>charge; the &longs;ides of which are of 4. 6. 20. 30. and 50. miles, &longs;o <lb/><arrow.to.target n="marg675"></arrow.to.target> <lb/>as that a degree is a mile broad, a minute prim. </s><s>50 ^{*} yards, a <lb/>&longs;econd but little le&longs;&longs;e than a yard, and in &longs;hort we may without <lb/>a farthing expence procure them of what bigne&longs;&longs;e we plea&longs;e. </s><s>I <lb/><arrow.to.target n="marg676"></arrow.to.target> <lb/>being in a Countrey Seat of mine near to <emph type="italics"/>Florence,<emph.end type="italics"/> did plainly <lb/>ob&longs;erve the Suns arrival at, and departure from the Summer <lb/>Sol&longs;tice, whil&longs;t one Evening at the time of its going down it ap­ <lb/>peared upon the top of a Rock on the Mountains of <emph type="italics"/>Pictrapana,<emph.end type="italics"/> <lb/>about 60. miles from thence, leaving di&longs;covered of it a &longs;mall <lb/>&longs;treak or filament towards the North, who&longs;e breadth was not <lb/>the hundredth part of its Diameter; and the following Evening <lb/>at the like &longs;etting, it &longs;hew'd &longs;uch another part of it, but notably <lb/>more &longs;mall, a nece&longs;&longs;ary argument, that it had begun to recede <lb/>from the Tropick; and the regre&longs;&longs;ion of the Sun from the fir&longs;t to <lb/>the &longs;econd ob&longs;ervation, doth not import doubtle&longs;&longs;e a &longs;econd mi­ <lb/><arrow.to.target n="marg677"></arrow.to.target> <lb/>nute in the Ea&longs;t. </s><s>The ob&longs;ervation made afterwards with an ex­ <lb/>qui&longs;ite Tele&longs;cope, and that multiplyeth the <emph type="italics"/>Di&longs;cus<emph.end type="italics"/> of the Sun <lb/>more than a thou&longs;and times, would prove ea&longs;ie, and with all <lb/>delightful. </s><s>Now with &longs;uch an In&longs;trument as this, I would have <lb/>ob&longs;ervations to be made in the fixed &longs;tars, making u&longs;e of &longs;ome <lb/>of tho&longs;e wherein the mutation ought to appear more con&longs;picu­ <lb/>ous, &longs;uch as are (as hath already been declared) the more re­ <lb/>mote from the Ecliptick, among&longs;t which the Harp a very great <lb/>&longs;tar, and near to the Pole of the Ecliptick, would be very pro­ <lb/>per in Countries far North, proceeding according to the man­ <lb/>ner that I &longs;hall &longs;hew by and by, but in the u&longs;e of another &longs;tar; <lb/>and I have already fancied to my &longs;elf a place very well adapted <lb/>for &longs;uch an ob&longs;ervation. </s><s>The place is an open Plane, upon <lb/>which towards the North there ri&longs;eth a very eminent Mountain, <lb/>in the apex or top whereof is built a little Chappel, &longs;ituate Ea&longs;t <lb/>and We&longs;t, &longs;o as that the ridg of its Roof may inter&longs;ect at right <lb/>angles, the meridian of &longs;ome building &longs;tanding in the Plane. </s><s>I <lb/>will place a beam parallel to the &longs;aid ridg, or top of the Roof, <pb xlink:href="040/01/373.jpg" pagenum="353"/>and di&longs;tant from it a yard or thereabouts. </s><s>This being placed, I <lb/>will &longs;eek in the Plain the place from whence one of the &longs;tars of <lb/><emph type="italics"/>Charls's<emph.end type="italics"/> Waine, in pa&longs;&longs;ing by the Meridian, cometh to hide it <lb/>&longs;elf behind the beam &longs;o placed, or in ca&longs;e the beam &longs;hould not <lb/>be &longs;o big as to hide the &longs;tar, I will finde a &longs;tation where one <lb/>may &longs;ee the &longs;aid beam to cut the &longs;aid &longs;tar into two equal parts; <lb/>an effect that with an ^{*} exqui&longs;ite Tele&longs;cope may be perfectly <lb/>di&longs;cerned. </s><s>And if in the place where the &longs;aid accident is di&longs;cover­ <lb/>ed, there were &longs;ome building, it will be the more commodious; <lb/>but if not, I will cau&longs;e a Pole to be &longs;tuck very fa&longs;t in the <lb/>ground, with &longs;ome &longs;tanding mark to direct where to place the <lb/>eye anew, when ever I have a mind to repeat the ob&longs;ervation. <lb/></s><s>The fir&longs;t of which ob&longs;ervations I will make about the Summer <lb/>Sol&longs;tice, to continue afterwards from Moneth to Moneth, or <lb/>when I &longs;hall &longs;o plea&longs;e, to the other Sol&longs;tice; with which ob&longs;er­ <lb/>vation one may di&longs;cover the elevation and depre&longs;&longs;ion of the &longs;tar, <lb/>though it be very &longs;mall. </s><s>And if in that operation it &longs;hall hap­ <lb/>pen, that any mutation &longs;hall di&longs;cover it &longs;elf, what and how great <lb/>benefit will it bring to A&longs;tronomy? </s><s>Seeing that thereby, be&longs;ides <lb/>our being a&longs;&longs;ured of the annual motion, we may come to know <lb/>the grandure and di&longs;tance of the &longs;ame &longs;tar.</s></p><p type="margin"><s><margin.target id="marg674"></margin.target><emph type="italics"/>What In&longs;tru­ <lb/>ments are apt for <lb/>mo&longs;t exact ob&longs;er­ <lb/>vation.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg675"></margin.target>* Italian braces.</s></p><p type="margin"><s><margin.target id="marg676"></margin.target><emph type="italics"/>An exqui&longs;ite <lb/>ob&longs;ervation of the <lb/>approach and de­ <lb/>parture of the Sun <lb/>from the Summer <lb/>Sol&longs;tice.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg677"></margin.target><emph type="italics"/>A place aecom­ <lb/>modated for the <lb/>ob&longs;ervation of the <lb/>fixed &longs;tars, as to <lb/>what concers the <lb/>annual motion of <lb/>the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I very well comprehend your whole proceedings; <lb/>and the operation &longs;eems to me &longs;o ea&longs;ie, and &longs;o commodious for <lb/>the purpo&longs;e, that it may very rationally be thought, that either <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> him&longs;elf, or &longs;ome other A&longs;tronomer had made trial <lb/>of it.</s></p><p type="main"><s>SALV. </s><s>But I judg the quite contrary, for it is not probable, <lb/>that if any one had experimented it, he would not have men­ <lb/>tioned the event, whether it fell out in favour of this, or that <lb/>opinion; be&longs;ides that, no man that I can find, either for this, <lb/>or any other end, did ever go about to make &longs;uch an Ob&longs;ervati­ <lb/>on; which al&longs;o without an exact Tele&longs;cope could but badly be <lb/>effected.</s></p><p type="main"><s>SIMP. </s><s>I am fully &longs;atisfied with what you &longs;ay. </s><s>But &longs;eeing <lb/>that it is a great while to night, if you defire that I &longs;hall pa&longs;&longs;e <lb/>the &longs;ame quietly, let it not be a trouble to you to explain unto <lb/>us tho&longs;e Problems, the declaration whereof you did even now <lb/>reque&longs;t might be deferred until too morrow. </s><s>Be plea&longs;ed to grant <lb/>us your promi&longs;ed indulgence, and, laying a&longs;ide all other di&longs;cour­ <lb/>&longs;es, proceed to &longs;hew us, that the motions which <emph type="italics"/>Copernicus<emph.end type="italics"/> a&longs;&longs;igns <lb/>to the Earth being taken for granted, and &longs;uppo&longs;ing the Sun <lb/>and fixed &longs;tars immoveable, there may follow the &longs;ame acci­ <lb/>dents touching the elevations and depre&longs;&longs;ions of the Sun, touch­ <lb/>ing the mutations of the Sea&longs;ons, and the inequality of dayes <lb/>and nights, <emph type="italics"/>&c.<emph.end type="italics"/> in the &longs;elf &longs;ame manner, ju&longs;t as they are with <pb xlink:href="040/01/374.jpg" pagenum="345[354]"/>facility apprehended in the <emph type="italics"/>Prolomaick<emph.end type="italics"/> Sy&longs;teme.</s></p><p type="main"><s>SALV. </s><s>I neither ought, nor can deny any thing that <emph type="italics"/>Sagredus<emph.end type="italics"/> <lb/>&longs;hall reque&longs;t: And the delay by me de&longs;ired was to no other end, <lb/>&longs;ave only that I might have time once again to methodize tho&longs;e <lb/>prefatory points, in my fancy, that &longs;erve for a large and plain de­ <lb/>claration of the manner how the forenamed accidents follow, as <lb/>well in the <emph type="italics"/>Copernican<emph.end type="italics"/> po&longs;ition, as in the <emph type="italics"/>Ptolomaick<emph.end type="italics"/>: nay, with <lb/><arrow.to.target n="marg678"></arrow.to.target> <lb/>much greater facility and &longs;implicity in that than in this. </s><s>Whence <lb/>one may manife&longs;tly conceive that Hypothe&longs;is to be as ea&longs;ie to be <lb/>effected by nature, as difficult to be apprehended by the under­ <lb/>&longs;tanding: yet neverthele&longs;&longs;e, I hope by making u&longs;e of another <lb/><arrow.to.target n="marg679"></arrow.to.target> <lb/>kind of explanation, than that u&longs;ed by <emph type="italics"/>Copernicus,<emph.end type="italics"/> to render like­ <lb/>wi&longs;e the apprehending of it &longs;omewhat le&longs;&longs;e ob&longs;cure. </s><s>Which <lb/>that I may do, I will propo&longs;e certain &longs;uppo&longs;itions of them&longs;elves <lb/>known and manife&longs;t, and they &longs;hall be the&longs;e that follow.</s></p><p type="margin"><s><margin.target id="marg678"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Coperni­ <lb/>can <emph type="italics"/>Sy&longs;teme diffi­ <lb/>cult to be under­ <lb/>&longs;tood, but ea&longs;ie to <lb/>be effected.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg679"></margin.target><emph type="italics"/>Nece&longs;&longs;ary pre­ <lb/>po&longs;itions for the <lb/>better conceiving <lb/>of the con&longs;equences <lb/>of the Earths mo­ <lb/>tion.<emph.end type="italics"/></s></p><p type="main"><s>Fir&longs;t, I &longs;uppo&longs;e that the Earth is a &longs;pherical body, turning <lb/>round upon its own Axis and Poles, and that each point a&longs;&longs;igned <lb/>in its &longs;uperficies, de&longs;cribeth the circumference of a circle, great­ <lb/>er or le&longs;&longs;er, according as the point a&longs;&longs;igned &longs;hall be neerer or <lb/>farther from the Poles: And that of the&longs;e circles the greate&longs;t is <lb/>that which is de&longs;cribed by a point equidi&longs;tant from the &longs;aid Poles; <lb/>and all the&longs;e circles are parallel to each other; and <emph type="italics"/>Parallels<emph.end type="italics"/> we <lb/>will call them.</s></p><p type="main"><s>Secondly, The Earth being of a Spherical Figure, and of an o­ <lb/>pacous &longs;ub&longs;tance, it is continually illuminated by the Sun, accor­ <lb/>ding to the half of its &longs;urface, the other half remaining ob&longs;cure, <lb/>and the boundary that di&longs;tingui&longs;heth the illuminated part from <lb/>the dark being a grand circle, we will call that circle the <emph type="italics"/>termi­ <lb/>nator of the light.<emph.end type="italics"/></s></p><p type="main"><s>Thirdly, If the Circle that is terminator of the light &longs;hould <lb/>pa&longs;&longs;e by the Poles of the Earth, it would cut (being a grand <lb/>and principal circle) all the parallels into equal parts; but not <lb/>pa&longs;&longs;ing by the Poles, it would cut them all in parts unequal, ex­ <lb/>cept only the circle in the middle, which, as being a grand circle <lb/>will be cut into equal parts.</s></p><p type="main"><s>Fourthly, The Earth turning round upon its own Poles, the <lb/>quantities of dayes and nights are termined by the arches of the <lb/>Parallels, inter&longs;ected by the circle, that is, the terminator of the <lb/>light, and the arch that is &longs;cituate in the illuminated Hemi&longs;phere <lb/>pre&longs;cribeth the length of the day, and the remainer is the quan­ <lb/>tity of the night.</s></p><p type="main"><s>The&longs;e things being pre&longs;uppo&longs;ed, for the more clear under­ <lb/><arrow.to.target n="marg680"></arrow.to.target> <lb/>&longs;tanding of that which remaines to be &longs;aid, we will lay it down <lb/>in a Figure. </s><s>And fir&longs;t, we will draw the circumference of a <lb/>circle, that &longs;hall repre&longs;ent unto us that of the grand Orb de&longs;cri­ <pb xlink:href="040/01/375.jpg" pagenum="355"/>bed in the plain of the Ecliptick, and this we will divide into <lb/>four equal parts with the two diameters <emph type="italics"/>Capricorn Cancer,<emph.end type="italics"/> and <lb/><emph type="italics"/>Libra Aries,<emph.end type="italics"/> which, at the &longs;ame time, &longs;hall repre&longs;ent unto us the <lb/>four Cardinal points, that is, the two Sol&longs;tices, and the two E­ <lb/>quinoctials; and in the centre of that circle we will place the <lb/>Sun O, fixed and immoveable.</s></p><p type="margin"><s><margin.target id="marg680"></margin.target><emph type="italics"/>A plain Scheme <lb/>repre&longs;enting the<emph.end type="italics"/> <lb/>Copernican <emph type="italics"/>Hypo­ <lb/>the&longs;is, and its con­ <lb/>&longs;equences.<emph.end type="italics"/></s></p><figure id="id.040.01.375.1.jpg" xlink:href="040/01/375/1.jpg"/><p type="main"><s>Let us next draw about the four points, Capricorn, Cancer, <lb/>Libra and Aries, as centres, four equal circles, which repre&longs;ent <lb/>unto us the Earth placed in them at four &longs;everal times of the <lb/>year. </s><s>The which, with its centre, in the &longs;pace of a year, pa&longs;&longs;eth <lb/>through the whole circumference, Capricorn, Aries, Cancer, Li­ <lb/>bra, moving from Ea&longs;t to We&longs;t, that is, according to the order <lb/>of the Signes. </s><s>It is already manife&longs;t, that whil&longs;t the Earth is in <lb/>Capricorn, the Sun will appear in Cancer, and the Earth moving <lb/><arrow.to.target n="marg681"></arrow.to.target> <lb/>along the arch Capricorn Aries, the Sun will &longs;eem to move along <lb/>the arch Cancer Libra, and in &longs;hort, will run thorow the Zodiack <lb/>according to the order of the Signes, in the &longs;pace of a year; and <lb/>by this fir&longs;t a&longs;&longs;umption, without all que&longs;tion, full &longs;atisfaction is <lb/>given for the Suns apparent annual motion under the Ecliptick. <lb/></s><s>Now, coming to the other, that is, the diurnal motion of the <lb/>Earth in it &longs;elf, it is nece&longs;&longs;ary to e&longs;tabli&longs;h its Poles and its Axis, <lb/>the which mu&longs;t be under&longs;tood not to be erect perpendicularly <lb/>upon the plain of the Ecliptick, that is, not to be parallel to the <lb/>Axis of the grand Orb, but declining from a right angle 23 de­ <lb/>grees and an half, or thereabouts, with its North Pole towards <pb xlink:href="040/01/376.jpg" pagenum="356"/>the Axis of the grand Orb, the Earths centre being in the Sol&longs;ti­ <lb/>tial point of Capricorn. </s><s>Suppo&longs;ing therefore the Terre&longs;trial <lb/>Globe to have its centre in the point Capricorn, we will de&longs;cribe <lb/>its Poles and Axis A B, inclined upon the diameter Capricorn <lb/>Cancer 23 degrees and an half; &longs;o that the angle A Capricorn <lb/>Cancer cometh to be the complement of a Quadrant or Radius, <lb/>that is, 66 degrees and an half; and this inclination mu&longs;t be un­ <lb/>der&longs;tood to be immutable, and we will &longs;uppo&longs;e the &longs;uperiour <lb/>Pole A to be Boreal, or North, and the other Au&longs;tral, or South. <lb/></s><s>Now imagining the Earth to revolve in it &longs;elf about the Axis A B <lb/>in twenty four hours, from We&longs;t to Ea&longs;t, there &longs;hall by all the <lb/>points a&longs;&longs;igned in its &longs;uper&longs;icies, be circles de&longs;cribed parallel to <lb/>each other. </s><s>We will draw, in this fir&longs;t po&longs;ition of the Earth, <lb/>the greate&longs;t C D, and tho&longs;e two di&longs;tant from it <emph type="italics"/>gr.<emph.end type="italics"/> 23. and an <lb/>half, E F above, and G M beneath, and the other two extream <lb/>ones I K and L M remote, by tho&longs;e intervals from the Poles A <lb/>and B; and as we have marked the&longs;e five, &longs;o we may imagine in­ <lb/>numerable others, parallel to the&longs;e, de&longs;cribed by the innumera­ <lb/>ble points of the Terre&longs;trial &longs;urface. </s><s>Next let us &longs;uppo&longs;e the <lb/>Earth, with the annual motion of its centre, to transferre it &longs;elf <lb/>into the other places already marked; but to pa&longs;&longs;e thither in &longs;uch <lb/>a manner, that its own Axis A B &longs;hall not only not change incli­ <lb/>nation upon the plain of the Ecliptick, but &longs;hall al&longs;o never vary <lb/>direction; &longs;o that alwayes keeping parallel to it &longs;elf, it may <lb/>continually tend towards the &longs;ame part of the Univer&longs;e, or, if <lb/>you will, of the Firmament, whereas, if we do but &longs;uppo&longs;e it <lb/>prolonged, it will, with its extream termes, de&longs;igne a Circle pa­ <lb/>rallel and equal to the grand Orb, Libra Capricorn Aries Cancer, <lb/>as the &longs;uperiour ba&longs;e of a Cylinder de&longs;cribed by it &longs;elf in the an­ <lb/>nual motion above the inferiour ba&longs;e, Libra Capricorn Aries <lb/>Cancer. </s><s>And therefore this immutability of inclination conti­ <lb/>nuing, we will de&longs;ign the&longs;e other three figures about the centres <lb/>Aries, Cancer, and Libra, alike in every thing to that fir&longs;t de­ <lb/>&longs;cribed about the centre Capricorn. </s><s>Now we will con&longs;ider the <lb/>fir&longs;t figure of the Earth, in which, in regard the Axis A B is de­ <lb/>clined from perpendicularity upon the diameter Capricorn Can­ <lb/>cer 23 degrees and an half towards the Sun O, and the arch A I <lb/>being al&longs;o 23 degrees and an half, the illumination of the Sun <lb/>will illu&longs;trate the Hemi&longs;phere of the Terre&longs;trial Globe expo&longs;ed <lb/>towards the Sun (of which, in this place, half is to be &longs;een) di­ <lb/>vided from the ob&longs;cure part by the Terminator of the light <lb/>I M, by which the parallel C D, as being a grand circle, &longs;hall <lb/>come to be divided into equal parts, but all the re&longs;t into parts un­ <lb/>equal; being that the terminator of the light I M pa&longs;&longs;eth not <lb/>by their Poles A B, and the parallel I K, together with all the re&longs;t <pb xlink:href="040/01/377.jpg" pagenum="357"/>de&longs;cribed within the &longs;ame, and neerer to the pole A, &longs;hall wholly <lb/>be included in the illuminated part; as on the contrary, the op­ <lb/>po&longs;ite ones towards the Pole B, contained within the paral­ <lb/>lel L M, &longs;hall remain in the dark. </s><s>Moreover, the arch A I be­ <lb/>ing equal to the arch F D, and the arch A F, common to them <lb/>both, the two arches I K F and A F D &longs;hall be equal, and each <lb/>a quadrant or 90 degrees. </s><s>And becau&longs;e the whole arch I F M <lb/>is a &longs;emicircle, the arch F M &longs;hall be a quadrant, and equal to <lb/>the other F K I; and therefore the Sun O &longs;hall be in this &longs;tate <lb/>of the Earth vertical to one that &longs;tands in the point F. </s><s>But by <lb/>the revolution diurnal about the &longs;tanding Axis A B, all the points <lb/>of the parallel E F pa&longs;&longs;e by the &longs;ame point F: and therefore in <lb/>that &longs;ame day the Sun, at noon, &longs;hall be vertical to all the inha­ <lb/>bitants of the Parallel E F, and will &longs;eem to them to de&longs;cribe in its <lb/>apparent motion the circle which we call the Tropick of Cancer. <lb/></s><s>But to the inhabitants of all the Parallels that are above the pa­ <lb/>rallel E F, towards the North pole A, the Sun declineth from <lb/>their <emph type="italics"/>Vertex<emph.end type="italics"/> or Zenith towards the South; and on the contrary, <lb/>to all the inhabitants of the Parallels that are beneath E F, to­ <lb/>wards the Equinoctial C D, and the South Pole B, the Meridian <lb/>Sun is elevated beyond their <emph type="italics"/>Vertex<emph.end type="italics"/> towards the North Pole A. <lb/>Next, it is vi&longs;ible that of all the Parallels, only the greate&longs;t C D <lb/>is cut in equal parts by the Terminator of the light I M. </s><s>But <lb/>the re&longs;t, that are beneath and above the &longs;aid grand circle, are all <lb/>inter&longs;ected in parts unequal: and of the &longs;uperiour ones, the &longs;e­ <lb/>midiurnal arches, namely tho&longs;e of the part of the Terre&longs;trial &longs;ur­ <lb/>face, illu&longs;trated by the Sun, are bigger than the &longs;eminocturnal <lb/>ones that remain in the dark: and the contrary befalls in the <lb/>remainder, that are under the great one C D, towards the pole B, <lb/>of which the &longs;emidiurnal arches are le&longs;&longs;er than the &longs;eminocturnal, <lb/>It is likewi&longs;e apparently manife&longs;t, that the differences of the &longs;aid <lb/>arches go augmenting, according as the Parallels are neerer to <lb/>the Poles, till &longs;uch time as the parallel I K comes to be wholly in <lb/>the part illuminated, and the inhabitants thereof have a day of <lb/>twenty four hours long, without any night; and on the contrary, <lb/>the Parallel L M, remaining all in ob&longs;curity, hath a night of <lb/>twenty four hours, without any day. </s><s>Come we next to the <lb/>third Figure of the Earth, placed with its centre in the point <lb/>Cancer, where the Sun &longs;eemeth to be in the fir&longs;t point of Ca­ <lb/>pricorn. </s><s>We have already &longs;een very manife&longs;tly, that by rea&longs;on <lb/>the Axis A B doth not change inclination, but continueth paral­ <lb/>lel to it &longs;elf, the a&longs;pect and &longs;ituation of the Earth is the &longs;ame to <lb/>an hair with that in the fir&longs;t Figure; &longs;ave onely that that Hemi­ <lb/>&longs;phere which in the fir&longs;t was illuminated by the Sun, in this re­ <lb/>maineth obtenebrated, and that cometh to be luminous, which in <pb xlink:href="040/01/378.jpg" pagenum="358"/>the fir&longs;t was tenebrous: whereupon that which happened before <lb/>concerning the differences of dayes and nights, touching the <lb/>dayes being greater or le&longs;&longs;er than the nights, now falls out quite <lb/>contrary. </s><s>And fir&longs;t, we &longs;ee, that whereas in the fir&longs;t Figure the <lb/>circle I K was wholly in the light, it is now wholly in the dark; <lb/>and the oppo&longs;ite arch L M is now wholly in the light, which <lb/>was before wholly in the dark. </s><s>Of the parallels between the <lb/>grand circle C D, and the Pole A, the &longs;emidiurnal arches are now <lb/>le&longs;&longs;er than the &longs;eminocturnal, which before were the contrary. <lb/></s><s>Of the others likewi&longs;e towards the Pole B, the &longs;emidiurnal arch­ <lb/>es are now bigger than the &longs;eminocturnal, the contrary to what <lb/>happened in the other po&longs;ition of the Earth. </s><s>We now &longs;ee the <lb/>Sun made vertical to the inhabitants of the Tropick G N, and to <lb/>be depre&longs;&longs;ed towards the South, with tho&longs;e of the Parallel E F, <lb/>by all the arch E C G, that is, 47 degrees; and in &longs;umme, to have <lb/>pa&longs;&longs;ed from one to the other Tropick, traver&longs;ing the Equinoctial, <lb/>elevating and declining in the Meridians the &longs;aid &longs;pace of 47 de­ <lb/>grees. </s><s>And all this mutation is derived not from the inclination <lb/>or elevation of the Earth, but on the contrary, from its not in­ <lb/>clining or elevating at all; and in a word, by continuing always <lb/>in the &longs;ame po&longs;ition, in re&longs;pect of the Univer&longs;e, onely with turn­ <lb/>ing about the Sun &longs;ituate iu the mid&longs;t of the &longs;aid plane, in which <lb/>it moveth it &longs;elf about circularly with its annual motion. </s><s>And <lb/><arrow.to.target n="marg682"></arrow.to.target> <lb/>here is to be noted an admirable accident, which is, that like as <lb/>the Axis of the Earth con&longs;erving the &longs;ame direction towards the <lb/>Univer&longs;e, or we may &longs;ay, towards the highe&longs;t Sphere of the fixed <lb/>&longs;tars, cau&longs;eth the Sun to appear to elevate and incline &longs;o great a <lb/>&longs;pace, namely, for 47 degrees, and the fixed Stars to incline or e­ <lb/>levate nothing at all; &longs;o, on the contrary, if the &longs;ame Axis of <lb/>the Earth &longs;hould maintain it &longs;elf continually in the &longs;ame inclina­ <lb/>tion towards the Sun, or, if you will, towards the Axis of the <lb/>Zodiack, no mutation would appear to be made in the Sun about <lb/>its elevating or declining, whereupon the inhabitants of one and <lb/>the &longs;ame place would alwayes have one and the &longs;ame difference <lb/>of dayes and nights, and one and the &longs;ame con&longs;titution of Sea­ <lb/>&longs;ons, that is, &longs;ome alwayes Winter, others alwayes Summer, <lb/>others Spring, &c. </s><s>but, on the contrary, the alterations in the <lb/>fixed Stars would appear very great, as touching their elevation, <lb/>and inclination to us, which would amount to the &longs;ame 47 de­ <lb/>grees. </s><s>For the under&longs;tanding of which let us return to con&longs;ider <lb/>the po&longs;ition of the Earth, in its fir&longs;t Figure, where we &longs;ee the <lb/>Axis A B, with the &longs;uperiour Pole A, to incline towards the Sun; <lb/>but in its third Figure, the &longs;ame Axis having kept the &longs;ame dire­ <lb/>ction towards the highe&longs;t Sphere, by keeping parallel to it &longs;elf, <lb/>inclines no longer towards the Sun with its &longs;uperiour Pole A, but <pb xlink:href="040/01/379.jpg" pagenum="359"/>on the contrary reclines from its former po&longs;ition <emph type="italics"/>gr.<emph.end type="italics"/> 47. and in­ <lb/>clineth towards the oppo&longs;ite part, &longs;o that to re&longs;tore the &longs;ame in­ <lb/>clination of the &longs;aid Pole A towards the Sun, it would be requi­ <lb/>&longs;ite by turning round the Terre&longs;trial Globe, according to the <lb/>circumference A C B D, to tran&longs;port it towards E tho&longs;e &longs;ame <lb/><emph type="italics"/>gr.<emph.end type="italics"/> 47. and for &longs;o many degrees, any what&longs;oever fixed &longs;tar ob­ <lb/>&longs;erved in the Meridian, would appear to be elevated, or inclined. <lb/></s><s>Let us come now to the explanation of that which remains, and <lb/>let us con&longs;ider the Earth placed in the fourth Figure, that is, <lb/>with its centre in the fir&longs;t point of Libra; upon which the Sun <lb/>will appear in the beginning of Aries. </s><s>And becau&longs;e the Axis of <lb/><figure id="id.040.01.379.1.jpg" xlink:href="040/01/379/1.jpg"/> <lb/>the Earth, which in the fir&longs;t Figure is &longs;uppo&longs;ed to be inclined up­ <lb/>on the diameter Capricorn Cancer, and therefore to be in that <lb/>&longs;ame plane, which cutting the plane of the grand Orb, accor­ <lb/>ding to the line Capricorn Cancer, was erected perpendicularly <lb/>upon the &longs;ame, tran&longs;po&longs;ed into the fourth Figure, and maintai­ <lb/>ned, as hath alwayes been &longs;aid, parallel to it &longs;elf, it &longs;hall come <lb/>to be in a plane in like manner erected to the &longs;uperficies of <lb/>the Grand Orbe, and parallel to the plane, which at right <lb/>angles cuts the &longs;ame &longs;uperficies, according to the diameter Ca­ <lb/>pricorn Cancer. </s><s>And therefore the line which goeth from <lb/>the centre of the Sunne to the centre of the Earth, that is, <lb/>O Libra, &longs;hall be perpendicular to the Axis BA: but the <lb/>&longs;ame line which goeth from the centre of the Sunne to the <lb/>centre of the Earth, is al&longs;o alwayes perpendicular to the <pb xlink:href="040/01/380.jpg" pagenum="360"/>circle that is the Terminator of the light; therefore this &longs;ame <lb/>circle &longs;hall pa&longs;&longs;e by the Poles A B in the fourth figure, and <lb/>in its plain the Axis A B &longs;hall fall, but the greate&longs;t circle pa&longs;&longs;ing <lb/>by the Poles of the Parallels, divideth them all in equal parts; <lb/>therefore the arches I K, E F, C D, G N, L M, &longs;hall be all <lb/>&longs;emicircles, and the illumin'd Hemi&longs;phere &longs;hall be this which <lb/>looketh towards us, and the Sun, and the Terminator of the <lb/>light &longs;hall be one and the &longs;ame circle A C B D, and the Earth <lb/>being in this place &longs;hall make it Equinoctial to all its Inhabitants. <lb/></s><s>And the &longs;ame happeneth in the &longs;econd figure, where the Earth <lb/>having its illuminated Hemi&longs;phere towards the Sun, &longs;heweth us <lb/>the other that is ob&longs;cure, with its nocturnal arches, which in <lb/>like manner are all &longs;emicircles, and con&longs;equently, here al&longs;o it <lb/>maketh the Equinoctial. </s><s>And la&longs;tly in regard that the line pro­ <lb/>duced from the centre of the Sun to the centre of the Earth, is <lb/>perpendicular to the Axis A B, to which the greate&longs;t circle of <lb/>the parallels C D, is likewi&longs;e erect, the &longs;aid line O <emph type="italics"/>Libra<emph.end type="italics"/> &longs;hall <lb/>pa&longs;&longs;e of nece&longs;&longs;ity by the &longs;ame Plain of the parallel C D, cutting <lb/>its circumference in the mid&longs;t of the diurnal arch C D; and <lb/>therefore the Snn &longs;hall be vertical to any one that &longs;hall &longs;tand <lb/>where that inter&longs;ection is made; but all the Inhabitants of that <lb/>Parallel &longs;hall pa&longs;&longs;e the &longs;ame, as being carried about by the <lb/>Earths diurnal conver&longs;ion; therefore all the&longs; upon that day <lb/>&longs;hall have the Meridian Sun in their vertex. </s><s>And the Sun at the <lb/>&longs;ame time to all the Inhabitants of the Earth &longs;hall &longs;eem to de­ <lb/>&longs;cribe the Grand Parallel called the Equinoctial. </s><s>Furthermore, <lb/>fora&longs;much as the Earth being in both the Sol&longs;titial points of the <lb/>Polar circles I K and L M, the one is wholly in the light, and <lb/>the other wholly in the dark; but when the Earth is in the Equi­ <lb/>noctial points, the halves of tho&longs;e &longs;ame polar circles are in the <lb/>light, the remainder of them being in the dark; it &longs;hould not <lb/>be hard to under&longs;tand, how that the Earth <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> from <emph type="italics"/>Cancer<emph.end type="italics"/> <lb/>(where the parallel I K is wholly in the dark) to <emph type="italics"/>Leo,<emph.end type="italics"/> one part of <lb/>the parallel towards the point I, beginneth to enter into the light, <lb/>and that the Terminator of the light I M beginneth to retreat to­ <lb/>wards the Pole AB, inter&longs;ecting the circle ACBD nolonger in IM, <lb/>but in two other points falling between the terms I A and MB, of <lb/>the arches IA and M B; whereupon the Inhabitants of the circle <lb/>begin to enjoy the light, and the other Inhabitants of the circle <lb/>L M to partake of night. </s><s>And thus you &longs;ee that by two &longs;imple <lb/>motions made in times proportionate to their bigne&longs;&longs;es, and not <lb/>contrary to one another, but performed, as all others that be­ <lb/>long to moveable mundane bodies, from We&longs;t to Ea&longs;t a&longs;&longs;igned <lb/>to the Terre&longs;trial Globe, adequate rea&longs;ons are rendred of all <lb/>tho&longs;e <emph type="italics"/>Phænomena<emph.end type="italics"/> or appearances, for the accommodating of <pb xlink:href="040/01/381.jpg" pagenum="361"/>which to the &longs;tability of the Earth it is nece&longs;&longs;ary (for&longs;aking that <lb/>Symetry which is ob&longs;erved to be between the velocities and mag­ <lb/>nitudes of moveables) to a&longs;cribe to a Sphere, va&longs;t above all <lb/>others, an unconceiveable celerity, whil&longs;t the other le&longs;&longs;er <lb/>Spheres move extream &longs;lowly; and which is more, to make that <lb/>motion contrary to all their motions; and, yet again to adde to <lb/>the improbability, to make that &longs;uperiour Sphere forcibly to <lb/>tran&longs;port all the inferionr ones along with it contrary to their <lb/>proper inclination. </s><s>And here I refer it to your judgment to de­ <lb/>termine which of the two is the mo&longs;t probable.</s></p><p type="margin"><s><margin.target id="marg681"></margin.target><emph type="italics"/>The Suns an­ <lb/>nual motion, how <lb/>it comes to pa&longs;&longs;e, <lb/>according to<emph.end type="italics"/> Co­ <lb/>pernicus.</s></p><p type="margin"><s><margin.target id="marg682"></margin.target><emph type="italics"/>An admirable <lb/>accident depending <lb/>on the not inclining <lb/>of the Earths axis<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>To me, as far as concerneth &longs;en&longs;e, there appeareth <lb/>no &longs;mall difference betwixt the &longs;implicity and facility of opera­ <lb/>ting effects by the means a&longs;&longs;igned in this new con&longs;titution, and <lb/>the multiplicity, con&longs;ufion, and difficulty, that is found in the <lb/>ancient and commonly received Hypothe&longs;is. </s><s>For if the Univer&longs;e <lb/>were di&longs;po&longs;ed according to this multiplicity, it would be ne­ <lb/>ce&longs;&longs;ary to renounce many Maximes in Philo&longs;ophy commonly re­ <lb/><arrow.to.target n="marg683"></arrow.to.target> <lb/>ceived by Philo&longs;ophers, as for in&longs;tance, That Nature doth <lb/>not multiply things without nece&longs;&longs;ity; and, That She makes u&longs;e <lb/>of the mo&longs;t facile and &longs;imple means in producing her effects; <lb/>and, That She doth nothing in vain, and the like. </s><s>I do confe&longs;&longs;e <lb/>that I never heard any thing more admirable than this, nor can I <lb/>believe that Humane Under&longs;tanding ever penetrated a more <lb/>&longs;ublime &longs;peculation. </s><s>I know not what <emph type="italics"/>Simplicius<emph.end type="italics"/> may think <lb/>of it.</s></p><p type="margin"><s><margin.target id="marg683"></margin.target><emph type="italics"/>Axiomes com­ <lb/>monly admitted by <lb/>all Philo&longs;ophers.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>The&longs;e (if I may &longs;peak my judgment freely) do &longs;eem <lb/><arrow.to.target n="marg684"></arrow.to.target> <lb/>to me &longs;ome of tho&longs;e Geometrical &longs;ubtilties which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> finds <lb/>fault with in <emph type="italics"/>Plato,<emph.end type="italics"/> when he accu&longs;eth him that by his too <lb/>much &longs;tudying of Geometry he for&longs;ook &longs;olid Philo&longs;ophy; and I <lb/>have known and heard very great <emph type="italics"/>Peripatetick<emph.end type="italics"/> Philo&longs;ophers to <lb/>di&longs;&longs;wade their Scholars from the Study of the Mathematicks, as <lb/>tho&longs;e that render the wit cavilous, and unable to philo&longs;ophate <lb/>well; an In&longs;titute diametrically contrary to that of <emph type="italics"/>Plato,<emph.end type="italics"/> who <lb/>admitted uone to Philo&longs;ophy, unle&longs;&longs;e he was fir&longs;t well entered in <lb/>Geometry.</s></p><p type="margin"><s><margin.target id="marg684"></margin.target>Ari&longs;totle <emph type="italics"/>tax­ <lb/>eth<emph.end type="italics"/> Plato <emph type="italics"/>for being <lb/>too &longs;tudious of Ge­ <lb/>ometry.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I commend the policy of the&longs;e your <emph type="italics"/>Peripateticks,<emph.end type="italics"/> in <lb/><arrow.to.target n="marg685"></arrow.to.target> <lb/>dehorting their Di&longs;ciples from the Study of Geometry, for that <lb/>there is no art more commodious for detecting their fallacies; but <lb/>&longs;ee how they differ from the Mathematical Philo&longs;ophers, who <lb/>much more willingly conver&longs;e with tho&longs;e that are well ver&longs;t in <lb/>the commune Peripatetick Philo&longs;ophy, than with tho&longs;e that are <lb/>de&longs;titute of that knowledg, who for want thereof cannot di­ <lb/>&longs;tingui&longs;h between doctrine and doctrine. </s><s>But pa&longs;&longs;ing by this, tell <lb/>me I be&longs;eech you, what are tho&longs;e extravagancies and tho&longs;e too <lb/>affected &longs;ubtilties that make you think this <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme <lb/>the le&longs;&longs;e plau&longs;ible?</s></p> <pb xlink:href="040/01/382.jpg" pagenum="362"/><p type="margin"><s><margin.target id="marg685"></margin.target>Peripatetick <emph type="italics"/>Phi­ <lb/>lo&longs;ophers condemn <lb/>the Study of Geo­ <lb/>metry, and why.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>To tell you true, I do not very well know; perhaps, <lb/>becau&longs;e I have not &longs;o much as learnt the rea&longs;ons that are by <emph type="italics"/>Ftolo­ <lb/>my<emph.end type="italics"/> produced, of tho&longs;e effects, I mean of tho&longs;e &longs;tations, retrogra­ <lb/>dations, acce&longs;&longs;ions, rece&longs;&longs;ions of the Planets; lengthenings and <lb/>&longs;hortnings of dayes, changes of &longs;ea&longs;ons, &c. </s><s>But omitting the <lb/>con&longs;equences that depend on the fir&longs;t &longs;uppo&longs;itions, I find in the <lb/>&longs;uppo&longs;itions them&longs;elves no &longs;mall difficulties; which &longs;uppo&longs;itions, <lb/>if once they be overthrown, they draw along with them the ruine <lb/>of the whole fabrick. </s><s>Now fora&longs;much as becau&longs;e the whole <lb/>module of <emph type="italics"/>Copernicus<emph.end type="italics"/> &longs;eemeth in my opinion to be built upon in­ <lb/>firm foundations, in that it relyeth upon the mobility of the earth, <lb/>if this &longs;hould happen to be di&longs;proved, there would be no need of <lb/>farther di&longs;pute. </s><s>And to di&longs;prove this, the Axiom of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>is in my judgment mo&longs;t &longs;ufficient, That of one &longs;imple body, <lb/>one &longs;ole &longs;imple motion can be natural: but here in this ca&longs;e, to <lb/><arrow.to.target n="marg686"></arrow.to.target> <lb/>the Earth, a &longs;imple body, there are a&longs;&longs;igned 3. if not 4. motions, <lb/>and all very different from each other. </s><s>For be&longs;ides the light <lb/>motion, as a grave body towards its centre, which cannot be de­ <lb/>nied it, there is a&longs;&longs;igned to it a circular motion in a great circle <lb/>about the Sun in a year, and a vertiginous conver&longs;ion about its <lb/>own centre in twenty four hours. </s><s>And that in the next place <lb/>which is more exorbitant, & which happly for that rea&longs;on you pa&longs;s <lb/>over in &longs;ilence, there is a&longs;cribed to it another revolution about <lb/>its own centre, contrary to the former of twenty four hours, <lb/>and which fini&longs;heth its period in a year. </s><s>In this my under&longs;tand­ <lb/>ing apprehendeth a very great contradiction. <lb/><arrow.to.target n="marg687"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg686"></margin.target><emph type="italics"/>Four &longs;everal <lb/>motions a&longs;&longs;igned to <lb/>the Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg687"></margin.target><emph type="italics"/>The motion of <lb/>de&longs;cent belongs not <lb/>to the terre&longs;trial <lb/>Globe, but to its <lb/>parts.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>As to the motion of de&longs;cent, it hath already been con­ <lb/>cluded not to belong to the Terre&longs;trial Globe which did never <lb/>move with any &longs;uch motion, nor never &longs;hall do; but is (if there be <lb/>&longs;uch a thing) that propen&longs;ion of its parts to reunite them&longs;elves <lb/>to their whole. </s><s>As, in the next place, to the Annual motion, </s></p><p type="main"><s><arrow.to.target n="marg688"></arrow.to.target> <lb/>and the Diurnal, the&longs;e being both made towards one way, are <lb/>very compatible, in the &longs;ame manner ju&longs;t as if we &longs;hould let a <lb/>Ball trundle downwards upon a declining &longs;uperficies, it would in <lb/>its de&longs;cent along the &longs;ame &longs;pontaneou&longs;ly revolve in it &longs;elf. </s><s>As <lb/>to the third motion a&longs;&longs;igned it by <emph type="italics"/>Copernicus,<emph.end type="italics"/> namely about it <lb/>&longs;elf in a year, onely to keep its Axis inclined and directed <lb/>towards the &longs;ame part of the Firmament, I will tell you a thing <lb/>worthy of great con&longs;ideration: namely <emph type="italics"/>ut tantum abe&longs;t<emph.end type="italics"/> (although <lb/>it be made contrary to the other annual) it is &longs;o far from having <lb/>any repugnance or difficulty in it, that naturally and without any <lb/><arrow.to.target n="marg689"></arrow.to.target> <lb/>moving cau&longs;e, it agreeth to any what&longs;oever &longs;u&longs;pended and libra­ <lb/>ted body, which if it &longs;hall be carried round in the circumference <lb/>of a circle, immediate of it &longs;elf, it acquireth a conver&longs;ion about <lb/>its own centre, contrary to that which carrieth it about, and of <pb xlink:href="040/01/383.jpg" pagenum="363"/>&longs;uch velocity, that they both fini&longs;h one revolution in the &longs;ame <lb/>time preci&longs;ely. </s><s>You may &longs;ee this admirable, and to our pur­ <lb/><arrow.to.target n="marg690"></arrow.to.target> <lb/>po&longs;e accommodate experience, if putting in a Ba&longs;on of water a <lb/>Ball that will &longs;wim; and holding the Ba&longs;on in your hand, you <lb/>turn round upon your toe, for you &longs;hall immediatly &longs;ee the Ball <lb/>begin to revolve in it &longs;elf with a motion, contrary to that of the <lb/>Ba&longs;on, and it &longs;hall fini&longs;h its revolution, when that of the Ba&longs;on it <lb/>&longs;hall fini&longs;h. </s><s>Now what other is the Earth than a pen&longs;il Globe <lb/>librated in tenuous and yielding aire, which being carried a­ <lb/>bout in a year along the circumference of a great circle, mu&longs;t <lb/><arrow.to.target n="marg691"></arrow.to.target> <lb/>needs acquire, without any other mover, a revolution about its <lb/>own centre, annual, and yet contrary to the other motion in like <lb/>manner annual? </s><s>You &longs;hall &longs;ee this effect I &longs;ay, but if afterwards <lb/>you more narrowly con&longs;ider it, you &longs;hall find this to be no real <lb/>thing, but a meer appearance; and that which you think to be <lb/>a revolution in it &longs;elf, you will find to be a not moving at all, <lb/>but a continuing altogether immoveable in re&longs;pect of all that <lb/>which without you, and without the ve&longs;&longs;el is immoveable: for if in <lb/>that Ball you &longs;hall make &longs;ome mark, and con&longs;ider to what part of <lb/>the Room where you are, or of the Field, or of Heaven it is <lb/>&longs;ituate, you &longs;hall &longs;ee that mark in yours, and the ve&longs;&longs;els revolu­ <lb/>tion to look alwayes towards that &longs;ame part; but comparing it to <lb/>the ve&longs;&longs;el and to your &longs;elf that are moveable, it will appear to go <lb/>altering its direction, and with a motion contrary to yours, and <lb/>that of the ve&longs;&longs;el, to go &longs;eeking all the points of its circumgyra­ <lb/>tion; &longs;o that with more rea&longs;on you and the ba&longs;on may be &longs;aid <lb/>to turn round the immoveable Ball, than that it moveth round <lb/>in the ba&longs;on. </s><s>In the &longs;ame manner the Earth &longs;u&longs;pended and li­ <lb/>brated in the circumference of the Grand Orbe, and &longs;cituate in <lb/>&longs;uch &longs;ort that one of its notes, as for example, its North Pole, loo­ <lb/>keth towards &longs;uch a Star or other part of the Firmament, it always <lb/>keepeth directed towards the &longs;ame, although carried round by <lb/>the annual motion about the circumference of the &longs;aid Grand <lb/>Orbe. </s><s>This alone is &longs;ufficient to make the Wonder cea&longs;e, and <lb/>to remove all difficulties. </s><s>But what will <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;ay, if to <lb/>this non-indigence of the co-operating cau&longs;e we &longs;hould adde <lb/>an admirable intrin&longs;ick vertue of the Terre&longs;trial Globe, of look­ <lb/><arrow.to.target n="marg692"></arrow.to.target> <lb/>ing with its determinate parts towards determinate parts of the <lb/>Firmament, I &longs;peak of the Magnetick vertue con&longs;tantly partici­ <lb/>pated by any what&longs;oever piece of Loade-&longs;tone. </s><s>And if every <lb/>minute particle of that S one have in it &longs;uch a vertue, who will <lb/><arrow.to.target n="marg693"></arrow.to.target> <lb/>que&longs;tion but that the &longs;ame more powerfully re&longs;ides in this whole <lb/>Terre&longs;trial Globe, abounding in that Magnetick matter, and <lb/>which happily it &longs;elf, as to its internal and primary &longs;ub&longs;tance, is <lb/>nothing el&longs;e but a huge ma&longs;&longs;e of Loade-&longs;tone.</s></p> <pb xlink:href="040/01/384.jpg" pagenum="364"/><p type="margin"><s><margin.target id="marg688"></margin.target><emph type="italics"/>The annual and <lb/>diurnal motion are <lb/>compatible in the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg689"></margin.target><emph type="italics"/>Every pen&longs;il and <lb/>librated, body car­ <lb/>ryed round in the <lb/>circumference of a <lb/>circle, acquireth of <lb/>it &longs;elf a motion in <lb/>it &longs;elf contrary to <lb/>that.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg690"></margin.target><emph type="italics"/>An Experiment <lb/>which &longs;en&longs;ibly <lb/>&longs;hews that two con­ <lb/>trary motions may <lb/>naturally agree in <lb/>the &longs;ame move­ <lb/>able.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg691"></margin.target><emph type="italics"/>The third motion <lb/>a&longs;cribed to the <lb/>Earth is rather <lb/>re&longs;ting immove­ <lb/>able.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg692"></margin.target><emph type="italics"/>An admirable <lb/>intern vertœe of the <lb/>terre&longs;trial Globe of <lb/>alwayes beholding <lb/>the &longs;ame part of <lb/>Heaven.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg693"></margin.target><emph type="italics"/>The terre&longs;triæl <lb/>Globe made of <lb/>Loade-&longs;tone.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>Then you are one of tho&longs;e it &longs;eems that hold the Mag­ <lb/><arrow.to.target n="marg694"></arrow.to.target> <lb/>netick Phylo&longs;ophy <emph type="italics"/>William<emph.end type="italics"/> ^{*} <emph type="italics"/>Gilbert.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg694"></margin.target>An eminent <lb/>Doctor of Phy&longs;ick, <lb/>our Countreyman, <lb/>born at <emph type="italics"/>Colohe&longs;ter,<emph.end type="italics"/> <lb/>and famous for this <lb/>his learned Trea­ <lb/>ti&longs;e, publi&longs;hed a­ <lb/>bout 60 years &longs;ince <lb/>at <emph type="italics"/>London, The <lb/>Magnetick Phi­ <lb/>lo&longs;ophy of<emph.end type="italics"/> William <lb/>Gilbert.</s></p><p type="main"><s>SALV. </s><s>I am for certain, and think that all tho&longs;e that have <lb/>&longs;eriou&longs;ly read his Book, and tried his experiments, will bear me <lb/>company therein; nor &longs;hould I de&longs;pair, that what hath befallen <lb/>me in this ca&longs;e, might po&longs;&longs;ibly happen to you al&longs;o, if &longs;o be a cu­ <lb/>rio&longs;ity, like to mine, and a notice that infinite things in Nature <lb/>are &longs;till conceal'd from the wits of mankind, by delivering you <lb/>from being captivated by this or that particular writer in natural <lb/>things, &longs;hould but &longs;lacken the reines of your Rea&longs;on, and mol­ <lb/>lifie the contumacy and tenaceou&longs;ne&longs;&longs;e of your &longs;en&longs;e; &longs;o as that <lb/>they would not refu&longs;e to hearken &longs;ometimes to novelties never <lb/><arrow.to.target n="marg695"></arrow.to.target> <lb/>before &longs;poken of. </s><s>But (permit me to u&longs;e this phra&longs;e) the pu&longs;illa­ <lb/>nimity of vulgar Wits is come to that pa&longs;&longs;e, that not only like <lb/>blind men, they make a gift, nay tribute of their own a&longs;&longs;ent to <lb/>what&longs;oever they find written by tho&longs;e Authours, which in the <lb/>infancy of their Studies were laid before them, as authentick by <lb/>their Tutors, but refu&longs;e to hear (not to &longs;ay examine) any new <lb/>Propo&longs;ition or Probleme, although it not only never hath been <lb/>confuted, but not &longs;o much as examined or con&longs;idered by their <lb/>Authours. </s><s>Among&longs;t which, one is this, of inve&longs;tigating what is <lb/>the true, proper, primary, interne, and general matter and &longs;ub­ <lb/>&longs;tance of this our Terre&longs;trial Globe; For although it never came <lb/>into the mind either of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> or of any one el&longs;e, before <emph type="italics"/>Wil­ <lb/>liam Gilbert<emph.end type="italics"/> to think that it might be a Magnet, &longs;o far are <emph type="italics"/>Ari­ <lb/>&longs;totle<emph.end type="italics"/> and the re&longs;t from confuting this opinion, yet neverthele&longs;&longs;e <lb/>I have met with many, that at the very fir&longs;t mention of it, as a <lb/>Hor&longs;e at his own &longs;hadow, have &longs;tart back, and refu&longs;ed to di&longs;­ <lb/>cour&longs;e thereof, and cen&longs;ured the conceipt for a vain <emph type="italics"/>Chymæra,<emph.end type="italics"/> <lb/>yea, for a &longs;olemn madne&longs;&longs;e: and its po&longs;&longs;ible the Book of <emph type="italics"/>Gilbert<emph.end type="italics"/> <lb/>had never come to my hands, if a Peripatetick Philo&longs;opher, of great <lb/>fame, as I believe, to free his Library from its contagion, had not <lb/>given it me.</s></p><p type="margin"><s><margin.target id="marg695"></margin.target><emph type="italics"/>The Pu&longs;illani­ <lb/>mity of Popular <lb/>Wits.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. I, who ingenuou&longs;ly confe&longs;&longs;e my &longs;elf to be one of <lb/>tho&longs;e vulgar Wits, and never till within the&longs;e few dayes that I <lb/>have been admitted to a &longs;hare in your conferences, could I pre­ <lb/>tend to have in the lea&longs;t withdrawn from tho&longs;e trite and popu­ <lb/>lar paths, yet, for all that, I think I have advantaged my &longs;elf &longs;o <lb/>much, as that I could without much trouble or difficulty, ma&longs;ter <lb/>the roughne&longs;&longs;es of the&longs;e novel and fanta&longs;tical opinions.</s></p><p type="main"><s>SALV. </s><s>If that which <emph type="italics"/>Gilbert<emph.end type="italics"/> writeth be true, then is it no o­ <lb/>pinion, but the &longs;ubject of Science; nor is it new, but as antient <lb/>as the Earth it &longs;elf; nor can it (being true) be rugged or diffi­ <lb/>cult, but plain and ea&longs;ie; and when you plea&longs;e I &longs;hall make you <lb/>feel the &longs;ame in your hand, for that you of your &longs;elf fancy it to <pb xlink:href="040/01/385.jpg" pagenum="365"/>be a Gho&longs;t, and &longs;tand in fear of that which hath nothing in it of <lb/>dreadfull, like as a little child doth fear the Hobgoblin, without <lb/>knowing any more of it, &longs;ave the name; as that which be&longs;ides <lb/>the name is nothing.</s></p><p type="main"><s>SIMP. </s><s>I &longs;hould be glad to be informed, and reclaimed from <lb/>an errour.</s></p><p type="main"><s>SALV. </s><s>An&longs;wer me then to the que&longs;tions that I &longs;hall ask you. <lb/></s><s>And fir&longs;t of all, Tell me whether you believe, that this our Globe, <lb/>which we inhabit and call Earth, con&longs;i&longs;teth of one &longs;ole and &longs;im­ <lb/>ple matter, or el&longs;e that it is an aggregate of matters different <lb/>from each other.</s></p><p type="main"><s>SIMP. </s><s>I &longs;ee it to be compo&longs;ed of &longs;ub&longs;tances and bodies very <lb/><arrow.to.target n="marg696"></arrow.to.target> <lb/>different; and fir&longs;t, for the greate&longs;t parts of the compo&longs;ition, <lb/>I &longs;ee the Water and the Earth, which extreamly differ from one <lb/>another.</s></p><p type="margin"><s><margin.target id="marg696"></margin.target><emph type="italics"/>The<emph.end type="italics"/> Terre&longs;trial <lb/>Globe <emph type="italics"/>compo&longs;ed of <lb/>&longs;undry matters.<emph.end type="italics"/></s></p><p type="main"><s>SAIV. </s><s>Let us, for this once, lay a&longs;ide the Seas and other Wa­ <lb/>ters, and let us con&longs;ider the &longs;olid parts, and tell me, if you think <lb/>them one and the &longs;ame thing, or el&longs;e different.</s></p><p type="main"><s>SIMP. </s><s>As to appearance, I &longs;ee that they are different things, <lb/>there being very great heaps of unfruitful &longs;ands, and others of <lb/>fruitful &longs;oiles; There are infinite &longs;harp and &longs;teril mountains, full <lb/>of hard &longs;tones and quarries of &longs;everal kinds, as Porphyre, Ala­ <lb/>bla&longs;ter, Ja&longs;per, and a thou&longs;and other kinds of Marbles: There <lb/>are va&longs;t Minerals of &longs;o many kinds of metals; and in a word, <lb/>&longs;uch varieties of matters, that a whole day would not &longs;uffice on­ <lb/>ly to enumerate them.</s></p><p type="main"><s>SALV. </s><s>Now of all the&longs;e different matters, do you think, <lb/>that in the compo&longs;ition of this grand ma&longs;&longs;e, there do concur por­ <lb/>tions, or el&longs;e that among&longs;t them all there is one part that far ex­ <lb/>ceeds the re&longs;t, and is as it were the matter and &longs;ub&longs;tance of the <lb/>immen&longs;e lump?</s></p><p type="main"><s>SIMP. </s><s>I believe that the Stones, Marbles, Metals, Gems, and <lb/>the &longs;o many other &longs;everal matters are as it were Jewels, and ex­ <lb/>teriour and &longs;uperficial Ornaments of the primary Globe, which <lb/>in gro&longs;&longs;e, as I believe, doth without compare exceed all the&longs;e <lb/>things put together.</s></p><p type="main"><s>SALV. </s><s>And this principal and va&longs;t ma&longs;&longs;e, of which tho&longs;e <lb/>things above named are as it were excre&longs;&longs;ences and ornaments, of <lb/>what matter do you think that it is compo&longs;ed?</s></p><p type="main"><s>SIMP. </s><s>I think that it is the &longs;imple, or le&longs;&longs;e impure element of <lb/>Earth.</s></p><p type="main"><s>SALV. </s><s>But what do you under&longs;tand by Earth? </s><s>Is it haply <lb/>that which is di&longs;per&longs;ed all over the fields, which is broke up with <lb/>Mattocks and Ploughs, wherein we &longs;owe corne, and plant fruits, <lb/>and in which great bo&longs;cages grow up, without the help of cul­ <pb xlink:href="040/01/386.jpg" pagenum="366"/>ture, and which is, in a word, the habitation of all animals, and <lb/>the womb of all vegetables?</s></p><p type="main"><s>SIMP. </s><s>Tis this that I would affirm to be the &longs;ub&longs;tance of this <lb/>our Globe.</s></p><p type="main"><s>SALV. </s><s>But in this you do, in my judgment, affirm that which <lb/>is not right: for this Earth which is broke up, is &longs;owed, and is <lb/>fertile, is but one part, and that very &longs;mall of the &longs;urface of the <lb/>Globe, which doth not go very deep, yea, its depth is very &longs;mall, <lb/>in compari&longs;on of the di&longs;tance to the centre: and experience <lb/>&longs;heweth us, that one &longs;hall not dig very low, but one &longs;hall finde <lb/>matters very different from this exteriour &longs;curf, more &longs;olid, and <lb/>not good for the production of vegetables. </s><s>Be&longs;ides the interne <lb/>parts, as being compre&longs;&longs;ed by very huge weights that lie upon <lb/>them, are, in all probability, &longs;lived, and made as hard as any <lb/>hard rock. </s><s>One may adde to this, that fecundity would be in <lb/>vain conferred upon tho&longs;e matters which never were de&longs;igned to <lb/>bear fruit, but to re&longs;t eternally buried in the profound and dark <lb/>aby&longs;&longs;es of the Earth.</s></p><p type="main"><s>SIMP. </s><s>But who &longs;hall a&longs;&longs;ure us, that the parts more inward <lb/>and near to the centre are unfruitful? </s><s>They al&longs;o may, perhaps, <lb/>have their productions of things unknown to us?</s></p><p type="main"><s>SALV. </s><s>You may a&longs;well be a&longs;&longs;ured thereof, as any man el&longs;e, <lb/>as being very capable to comprehend, that if the integral bodies <lb/>of the Univer&longs;e be produced onely for the benefit of Mankind, <lb/>this above all the re&longs;t ought to be de&longs;tin d to the &longs;ole convenien­ <lb/>ces of us its inhabitants. </s><s>But what bene&longs;it can we draw from <lb/>matters &longs;o hid and remote from us, as that we &longs;hall never be a­ <lb/><arrow.to.target n="marg697"></arrow.to.target> <lb/>ble to make u&longs;e of them? </s><s>Therefore the interne &longs;ub&longs;tance of <lb/>this our Globe cannot be a matter frangible, di&longs;&longs;ipable, and non­ <lb/>coherent, like this &longs;uperficial part which we call ^{*} EARTH: but <lb/><arrow.to.target n="marg698"></arrow.to.target> <lb/>it mu&longs;t, of nece&longs;&longs;ity, be a mo&longs;t den&longs;e and &longs;olid body, and in a <lb/>word, a mo&longs;t hard &longs;tone. </s><s>And, if it ought to be &longs;o, what rea&longs;on <lb/>is there that &longs;hould make you more &longs;crupulous to believe that it <lb/>is a Load&longs;tone than a Porphiry, a Ja&longs;per, or other hard Mar­ <lb/>ble? </s><s>Happily if <emph type="italics"/>Gilbert<emph.end type="italics"/> had written, that this Globe is all com­ <lb/><arrow.to.target n="marg699"></arrow.to.target> <lb/>pounded within of ^{*} <emph type="italics"/>Pietra Serena,<emph.end type="italics"/> or of <emph type="italics"/>Chalcedon,<emph.end type="italics"/> the paradox <lb/>would have &longs;eemed to you le&longs;&longs;e exorbitant?</s></p><p type="margin"><s><margin.target id="marg697"></margin.target><emph type="italics"/>The interne parts <lb/>of the terre&longs;trial <lb/>Globe mu&longs;t of ne­ <lb/>ce&longs;&longs;ity be &longs;olid.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg698"></margin.target>* Or MOULD.</s></p><p type="margin"><s><margin.target id="marg699"></margin.target>Of which with <lb/>the Latin tran&longs;la­ <lb/>tour, I mu&longs;t once <lb/>more profe&longs;&longs;e my <lb/>&longs;elf ignorant.</s></p><p type="main"><s>SIMP. </s><s>That the parts of this Globe more intern are more <lb/>compre&longs;&longs;ed, and &longs;o more &longs;lived together and &longs;olid, and more <lb/>and more &longs;o, according as they lie lower, I do grant, and &longs;o <lb/>likewi&longs;e doth <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> but that they degenerate and become <lb/>other than Earth, of the &longs;ame &longs;ort with this of the &longs;uperficial <lb/>parts, I &longs;ee nothing that obliege h me to believe.</s></p><p type="main"><s>SALV. </s><s>I undertook not this di&longs;cour&longs;e with an intent to prove <lb/>demon&longs;tratively that the primary and real &longs;ub&longs;tance of this our <pb xlink:href="040/01/387.jpg" pagenum="367"/>Globe is Load-&longs;tone; but onely to &longs;hew that no rea&longs;on could be <lb/>given why one &longs;hould be more unwilling to grant that it is of <lb/>Load-&longs;tone, than of &longs;ome other matter. </s><s>And if you will but <lb/><arrow.to.target n="marg700"></arrow.to.target> <lb/>&longs;eriou&longs;ly con&longs;ider, you &longs;hall find that it is not improbable, that <lb/>one &longs;ole, pure, and arbitrary name, hath moved men to think <lb/>that it con&longs;i&longs;ts of Earth; and that is their having made u&longs;e com­ <lb/>monly from the beginning of this word Earth, as well to &longs;igni­ <lb/>&longs;ie that matter which is plowed and &longs;owed, as to name this our <lb/>Globe. </s><s>The denomination of which if it had been taken from <lb/>&longs;tone, as that it might as well have been taken from that as <lb/>from the Earth; the &longs;aying that its primary &longs;ub&longs;tance was &longs;tone, <lb/>would doubtle&longs;&longs;e have found no &longs;cruple or oppo&longs;ition in any <lb/>man. </s><s>And is &longs;o much the more probable, in that I verily be­ <lb/>lieve, that if one could but pare off the &longs;curf of this great Globe, <lb/>taking away but one full thou&longs;and or two thou&longs;and yards; and <lb/>afterwards &longs;eperate the Stones from the Earth, the accumulati­ <lb/>on of the &longs;tones would be very much biger than that of the fer­ <lb/>tile Mould. </s><s>But as for the rea&longs;ons which concludently prove <emph type="italics"/>de <lb/>facto,<emph.end type="italics"/> that is our Globe is a Magnet, I have mentioned none of <lb/>them, nor is this a time to alledg them, and the rather, for that <lb/>to your benefit you may read them in <emph type="italics"/>Gilbert<emph.end type="italics"/>; onely to encou­ <lb/>rage you to the peru&longs;al of them, I will &longs;et before you, in a &longs;imi­ <lb/><arrow.to.target n="marg701"></arrow.to.target> <lb/>litude of my own, the method that he ob&longs;erved in his Philo&longs;o­ <lb/>phy. </s><s>I know you under&longs;tand very well how much the know­ <lb/>ledg of the accidents is &longs;ub&longs;ervient to the inve&longs;tigation of the <lb/>&longs;ub&longs;tance and e&longs;&longs;ence of things; therefore I de&longs;ire that you <lb/>would take pains to informe your &longs;elf well of many accidents and <lb/>properties that are found in the Magnet, and in no other &longs;tone, <lb/><arrow.to.target n="marg702"></arrow.to.target> <lb/>or body; as for in&longs;tance of attracting Iron, of conferring up­ <lb/>on it by its &longs;ole pre&longs;ence the &longs;ame virtue, of communicating <lb/>likewi&longs;e to it the property of looking towards the Poles, as it <lb/>al&longs;o doth it &longs;elf; and moreover endeavour to know by trial, <lb/>that it containeth in it a virtue of conferring upon the magnetick <lb/>needle not onely the direction under a Meridian towards the <lb/>Poles, with an Horizontal motion, (a property a long time ago <lb/>known) but a new found accident, of declining (being ballanced <lb/>under the Meridian before marked upon a little &longs;pherical Mag­ <lb/>net) of declining I &longs;ay to determinate marks more or le&longs;&longs;e, ac­ <lb/>cording as that needle is held nearer or farther from the Pole, <lb/>till that upon the Pole it &longs;elf it erecteth perpendicularly, where­ <lb/>as in the middle parts it is parallel to the Axis. </s><s>Furthermore pro­ <lb/>cure a proof to be made, whether the virtue of attracting Iron, <lb/>re&longs;iding much more vigorou&longs;ly about the Poles, than about the <lb/>middle parts, this force be not notably more vigorous in one <lb/>Pole than in the other, and that in all pieces of Magnet; the <pb xlink:href="040/01/388.jpg" pagenum="368"/>&longs;tronger of which Poles is that which looketh towards the South. <lb/></s><s>Ob&longs;erve, in the next place, that in a little Magnet this South and <lb/>more vigorous Pole, becometh weaker, when ever it is to take <lb/>up an iron in pre&longs;ence of the North Pole, of another much big­ <lb/>ger Magnet: and not to make any tedious di&longs;cour&longs;e of it, a&longs;&longs;er­ <lb/>tain your &longs;elf, by experience, of the&longs;e and many other properties <lb/>de&longs;cribed by <emph type="italics"/>Gilbert,<emph.end type="italics"/> which are all &longs;o peculiar to the Magnet, as <lb/><arrow.to.target n="marg703"></arrow.to.target> <lb/>that none of them agree with any other matter. </s><s>Tell me now, <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> if there were laid before you a thou&longs;and pieces of <lb/>&longs;everal matters, but all covered and concealed in a cloth, under <lb/>which it is hid, and you were required, without uncovering them, <lb/>to make a gue&longs;&longs;e, by external &longs;ignes, at the matter of each of <lb/>them, and that in making trial, you &longs;hould hit upon one that <lb/>&longs;hould openly &longs;hew it &longs;elf to have all the properties by you alrea­ <lb/>dy acknowledged to re&longs;ide onely in the Magnet, and in no other <lb/>matter, what judgment would you make of the e&longs;&longs;ence of &longs;uch a <lb/>body? </s><s>Would you &longs;ay, that it might be a piece of Ebony, or <lb/>Alabla&longs;ter, or Tin.</s></p><p type="margin"><s><margin.target id="marg700"></margin.target><emph type="italics"/>Our Globe would <lb/>have been called <lb/>&longs;tone, in &longs;tead of <lb/>Earth, if that <lb/>name had been gi­ <lb/>uen it in the be­ <lb/>ginning.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg701"></margin.target><emph type="italics"/>The method of<emph.end type="italics"/> <lb/>Gilbert <emph type="italics"/>in his Phi­ <lb/>lo&longs;ophy.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg702"></margin.target><emph type="italics"/>Many proper­ <lb/>ties in the Mag­ <lb/>net.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg703"></margin.target><emph type="italics"/>An Argument <lb/>proving the terre­ <lb/>&longs;trial Globe to be <lb/>a<emph.end type="italics"/> Magnet.</s></p><p type="main"><s>SIMP. </s><s>I would &longs;ay, without the lea&longs;t hæ&longs;itation, that it was a <lb/>piece of Load-&longs;tone.</s></p><p type="main"><s>SALV. </s><s>If it be &longs;o, &longs;ay re&longs;olutely, that under this cover and <lb/>&longs;curf of Earth, &longs;tones, metals, water, &c. </s><s>there is hid a great <lb/>Magnet, fora&longs;much as about the &longs;ame there may be &longs;een by any <lb/>one that will heedfully ob&longs;erve the &longs;ame, all tho&longs;e very accidents <lb/>that agree with a true and vi&longs;ible Globe of Magnet; but if no <lb/>more were to be &longs;een than that of the Declinatory Needle, which <lb/>being carried about the Earth, more and more inclineth, as it ap­ <lb/>proacheth to the North Pole, and declineth le&longs;&longs;e towards the E­ <lb/>quinoctial, under which it finally is brought to an <emph type="italics"/>Æquilibrium,<emph.end type="italics"/> <lb/>it might &longs;erve to per&longs;wade even the mo&longs;t &longs;crupulous judgment. </s><s>I <lb/>forbear to mention that other admirable effect, which is &longs;en&longs;ibly <lb/>ob&longs;erved in every piece of Magnet, of which, to us inhabitants <lb/>of the Northern Hemi&longs;phere, the Meridional Pole of the &longs;aid Mag­ <lb/>net is more vigorous than the other; and the difference is found <lb/>greater, by how much one recedeth from the Equinoctial; and <lb/>under the Equinoctial both the parts are of equal &longs;trength, but <lb/>notably weaker. </s><s>But, in the Meridional Regions, far di&longs;tant <lb/>from the Equinoctial, it changeth nature, and that part which to <lb/>us was more weak, acquireth more &longs;trength than the other: and <lb/>all this I confer with that which we &longs;ee to be done by a &longs;mall <lb/>piece of Magnet, in the pre&longs;ence of a great one, the vertue of <lb/>which &longs;uperating the le&longs;&longs;er, maketh it to become obedient to it, <lb/>and according as it is held, either on this or on that &longs;ide the Equi­ <lb/>noctial of the great one, maketh the &longs;elf &longs;ame mutations, <lb/>which I have &longs;aid are made by every Magnet, carried on this <pb xlink:href="040/01/389.jpg" pagenum="369"/>&longs;ide, or that &longs;ide of the Equinoctiall of the Earth.</s></p><p type="main"><s>SAGR. </s><s>I was per&longs;waded, at the very fir&longs;t reading of the Book <lb/>of <emph type="italics"/>Gilbertus<emph.end type="italics"/>; and having met with a mo&longs;t excellent piece of <lb/><arrow.to.target n="marg704"></arrow.to.target> <lb/>Magnet, I, for a long time, made many Ob&longs;ervations, and all <lb/>worthy of extream wonder; but above all, that &longs;eemeth to me <lb/>very &longs;tupendious of increa&longs;ing the faculty of taking up Iron &longs;o <lb/>much by arming it, like as the &longs;aid Authour teacheth; and with <lb/>arming that piece of mine, I multiplied its force in octuple propor­ <lb/>tion; and whereas unarmed it &longs;carce took up nine ounces of <lb/>Iron, it being armed did take up above &longs;ix pounds: And, it <lb/>may be, you have &longs;een this Load&longs;tone in the ^{*} Gallery of your <lb/><arrow.to.target n="marg705"></arrow.to.target> <lb/><emph type="italics"/>Mo&longs;t Serene Grand Duke<emph.end type="italics"/> (to whom I pre&longs;ented it) upholding <lb/>two little Anchors of Iron.</s></p><p type="margin"><s><margin.target id="marg704"></margin.target><emph type="italics"/>|The Magnet <lb/>armed takes up <lb/>much more Iron, <lb/>than when unar­ <lb/>med.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg705"></margin.target>+ Or Clo&longs;et of <lb/>rarities.</s></p><p type="main"><s>SALV. </s><s>I &longs;aw it many times, and with great admiration, till <lb/>that a little piece of the like &longs;tone gave me greater cau&longs;e of won­ <lb/>der, that is in the keeping of our Academick, which being no <lb/>more than of &longs;ix ounces weight, and &longs;u&longs;taining, when unarmed, <lb/>hardly two ounces, doth, when armed, take up 160. ounces, &longs;o <lb/>as that it is of 80. times more force armed than unarmed, and <lb/>takes up a weight 26. times greater than its own; a much greater <lb/>wonder than <emph type="italics"/>Gilbert<emph.end type="italics"/> could ever meet with, who writeth, that he <lb/>could never get any Load&longs;tone that could reach to take up four <lb/>times its own weight.</s></p><p type="main"><s>SAGR. </s><s>In my opinion, this Stone offers to the wit of man a <lb/>large Field to Phylo&longs;ophate in; and I have many times thought <lb/>with my &longs;elf, how it can be that it conferreth on that Iron, which <lb/>armeth it, a &longs;trength &longs;o &longs;uperiour to its own; and finally, I finde <lb/>nothing that giveth me &longs;atisfaction herein; nor do I find any <lb/>thing extraordinary in that which <emph type="italics"/>Gilbert<emph.end type="italics"/> writes about this parti­ <lb/>cular; I know not whether the &longs;ame may have befallen <lb/>you.</s></p><p type="main"><s>SALV. </s><s>I extreamly prai&longs;e, admire, and envy this Authour, <lb/>for that a conceit &longs;o &longs;tupendious &longs;hould come into his minde, <lb/>touching a thing handled by infinite &longs;ublime wits, and hit upon <lb/>by none of them: I think him moreover worthy of extraordi­ <lb/>nary applau&longs;e for the many new and true Ob&longs;ervations that he <lb/>made, to the di&longs;grace of &longs;o many fabulous Authours, that write <lb/>not only what they do not know, but what ever they hear &longs;po­ <lb/>ken by the fooli&longs;h vulgar, never &longs;eeking to a&longs;&longs;ure them&longs;elves of <lb/>the &longs;ame by experience, perhaps, becau&longs;e they are unwilling to <lb/>dimini&longs;h the bulk of their Books. </s><s>That which I could have de­ <lb/>&longs;ired in <emph type="italics"/>Gilbert,<emph.end type="italics"/> is, that he had been a little greater Mathematici­ <lb/>an, and particularly well grounded in <emph type="italics"/>Geometry,<emph.end type="italics"/> the practice <lb/>whereof would have rendered him le&longs;s re&longs;olute in accepting tho&longs;e <lb/>rea&longs;ons for true Demon&longs;trations, which he produceth for true <pb xlink:href="040/01/390.jpg" pagenum="370"/>cau&longs;es of the true conclu&longs;ions ob&longs;erved by him&longs;elf. </s><s>Which rea­ <lb/>&longs;ons (freely &longs;peaking) do not knit and bind &longs;o fa&longs;t, as tho&longs;e un­ <lb/>doubtedly ought to do, in that of natural, nece&longs;&longs;ary, and la&longs;ting <lb/>conclu&longs;ions may be alledged. </s><s>And I doubt not, but that in pro­ <lb/>ce&longs;&longs;e of time this new Science will be perfected with new ob&longs;er­ <lb/>vations, and, which is more, with true and nece&longs;&longs;ary Demon&longs;tra­ <lb/><arrow.to.target n="marg706"></arrow.to.target> <lb/>tions. </s><s>Nor ought the glory of the fir&longs;t Inventor to be thereby <lb/>dimini&longs;hed, nor do I le&longs;&longs;e e&longs;teem, but rather more admire, the <lb/>Inventor of the Harp (although it may be &longs;uppo&longs;ed that the In­ <lb/>&longs;trument at fir&longs;t was but rudely framed, and more rudely finger­ <lb/>ed) than an hundred other Arti&longs;ts, that in the in&longs;uing Ages redu­ <lb/>ced that profe&longs;&longs;ion to great perfection. </s><s>And methinks, that An­ <lb/>tiquity had very good rea&longs;on to enumerate the fir&longs;t Inventors of <lb/>the Noble Arts among&longs;t the Gods; &longs;eeing that the common wits <lb/>have &longs;o little curio&longs;ity, and are &longs;o little regardful of rare and ele­ <lb/>gant things, that though they &longs;ee and hear them exercirated by <lb/>the exquifite profe&longs;&longs;ors of them, yet are they not thereby per­ <lb/>&longs;waded to a de&longs;ire of learning them. </s><s>Now judge, whether Capa­ <lb/>cities of this kind would ever have attempted to have found out <lb/>the making of the Harp, or the invention of Mu&longs;ick, upon the <lb/>hint of the whi&longs;tling noi&longs;e of the dry &longs;inews of a Tortois, or <lb/>from the &longs;triking of four Hammers. </s><s>The application to great <lb/>inventions moved by &longs;mall hints, and the thinking that under a <lb/>primary and childi&longs;h appearance admirable Arts may lie hid, is <lb/>not the part of a trivial, but of a &longs;uper-humane &longs;pirit. </s><s>Now an­ <lb/>&longs;wering to your demands, I &longs;ay, that I al&longs;o have long thought <lb/>upon what might po&longs;&longs;ibly be the cau&longs;e of this &longs;o tenacious and <lb/>potent union, that we &longs;ee to be made between the one Iron that <lb/>armeth the Magnet, and the other that conjoyns it &longs;elf unto it. <lb/><arrow.to.target n="marg707"></arrow.to.target> <lb/>And fir&longs;t, we are certain, that the vertue and &longs;trength of the &longs;tone <lb/>doth not augment by being armed, for it neither attracts at <lb/>greater di&longs;tance, nor doth it hold an Iron the fa&longs;ter, if between it, <lb/>and the arming or cap, a very fine paper, or a leaf of beaten gold, <lb/>be interpo&longs;ed; nay, with that interpo&longs;ition, the naked &longs;tone <lb/>takes up more Iron than the armed. </s><s>There is therefore no alte­ <lb/>ration in the vertue, and yet there is an innovation in the effect. <lb/><arrow.to.target n="marg708"></arrow.to.target> <lb/>And becau&longs;e its nece&longs;&longs;ary, that a new effect have a new cau&longs;e, if <lb/>it be inquired what novelty is introduced in the act of taking up <lb/>with the cap or arming, there is no mutation to be di&longs;covered, but <lb/>in the different contact; for whereas before Iron toucht Load­ <lb/>&longs;tone, now Iron toucheth Iron. </s><s>Therefore it is nece&longs;&longs;ary to con­ <lb/>clude, that the diver&longs;ity of contacts is the cau&longs;e of the diver&longs;ity <lb/><arrow.to.target n="marg709"></arrow.to.target> <lb/>of effects. </s><s>And for the difference of contacts it cannot, as I &longs;ee, <lb/>be derived from any thing el&longs;e, &longs;ave from that the &longs;ub&longs;tance of <lb/>the Iron is of parts more &longs;ubtil, more pure, and more compact­ <pb xlink:href="040/01/391.jpg" pagenum="371"/>ed than tho&longs;e of the Magnet, which are more gro&longs;&longs;e, impure, and <lb/>rare. </s><s>From whence it followeth, that the &longs;uperficies of two I­ <lb/>rons that are to touch, by being exqui&longs;itely plained, filed, and <lb/>burni&longs;hed, do &longs;o exactly conjoyn, that all the infinite points of <lb/>the one meet with the infinite points of the other; &longs;o that the <lb/>filaments, if I may &longs;o &longs;ay, that collegate the two Irons, are many <lb/>more than tho&longs;e that collegate the Magnet to the Iron, by rea&longs;on <lb/>that the &longs;ub&longs;tance of the Magnet is more porous, and le&longs;&longs;e com­ <lb/>pact, which maketh that all the points and filaments of the Load­ <lb/>&longs;tone do not clo&longs;e with that which it unites unto. </s><s>In the next <lb/>place, that the &longs;ub&longs;tance of Iron (e&longs;pecially the well refined, as <lb/>namely, the pure&longs;t &longs;teel) is of parts much more den&longs;e, &longs;ubtil, <lb/>and pure than the matter of the Load&longs;tone, is &longs;een, in that one <lb/>may bring its edge to an extraordinary &longs;harpne&longs;&longs;e, &longs;uch as is that <lb/>of the Ra&longs;or, which can never be in any great mea&longs;ure effected in <lb/>a piece of Magnet. </s><s>Then, as for the impurity of the Magnet, and <lb/><arrow.to.target n="marg710"></arrow.to.target> <lb/>its being mixed with other qualities of &longs;tone, it is fir&longs;t &longs;en&longs;ibly <lb/>di&longs;covered by the colour of &longs;ome little &longs;pots, for the mo&longs;t part <lb/>white; and next by pre&longs;enting a needle to it, hanging in a <lb/>thread, which upon tho&longs;e &longs;tonyne&longs;&longs;es cannot find repo&longs;e, but <lb/>being attracted by the parts circumfu&longs;ed, &longs;eemeth to fly from <lb/><arrow.to.target n="marg711"></arrow.to.target> <lb/>^{*} <emph type="italics"/>tho&longs;e,<emph.end type="italics"/> and to leap upon the Magnet contiguous to <emph type="italics"/>them:<emph.end type="italics"/> and <lb/>as &longs;ome of tho&longs;e Heterogeneal parts are for their magnitude ve­ <lb/>ry vi&longs;ible, &longs;o we may believe, that there are others, in great a­ <lb/>bundance, which, for their &longs;mallne&longs;&longs;e, are imperceptible, that are <lb/>di&longs;&longs;eminated throughout the whole ma&longs;&longs;e. </s><s>That which I &longs;ay, <lb/>(namely, that the multitude of contacts that are made between <lb/>Iron and Iron, is the cau&longs;e of the &longs;o &longs;olid conjunction) is con­ <lb/>firmed by an experiment, which is this, that if we pre&longs;ent the <lb/>&longs;harpned point of a needle to the cap of a Magnet, it will &longs;tick <lb/>no fa&longs;ter to it, than to the &longs;ame &longs;tone unarmed: which can <lb/>proceed from no other cau&longs;e, than from the equality of the con­ <lb/>tacts that are both of one &longs;ole point. </s><s>But what then? </s><s>Let a <lb/>^{*} Needle be taken and placed upon a Magnet, &longs;o that one of its <lb/><arrow.to.target n="marg712"></arrow.to.target> <lb/>extremities hang &longs;omewhat over, and to that pre&longs;ent a Nail; to <lb/>which the Needle will in&longs;tantly cleave, in&longs;omuch that withdraw­ <lb/>ing the Nail, the Needle will &longs;tand in &longs;u&longs;pen&longs;e, and with its two <lb/>ends touching the Magnet and the Iron; and withdrawing the <lb/>Nail yet a little further, the Needle will for&longs;ake the Magnet; <lb/>provided that the eye of the Needle be towards the Nail, and <lb/>the point towards the Magnet; but if the eye be towards the <lb/>Load&longs;tone, in withdrawing the Nail the Needle will cleave to <lb/>the Magnet; and this, in my judgment, for no other rea&longs;on, <lb/>&longs;ave onely that the Needle, by rea&longs;on it is bigger towards the <lb/>eye, toucheth in much more points than its &longs;harp point doth.</s></p> <pb xlink:href="040/01/392.jpg" pagenum="372"/><p type="margin"><s><margin.target id="marg706"></margin.target><emph type="italics"/>The fir&longs;t ob&longs;er­ <lb/>vers and inventers <lb/>of things ought to <lb/>be admired.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg707"></margin.target><emph type="italics"/>The true cau&longs;e <lb/>of the multiplica­ <lb/>tion of vertue in <lb/>the Magnet, by <lb/>means of the ar­ <lb/>ming.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg708"></margin.target><emph type="italics"/>Of a new effect <lb/>its nece&longs;&longs;ary that <lb/>the cau&longs;e be like­ <lb/>wi&longs;e new.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg709"></margin.target><emph type="italics"/>It is proved, <lb/>that Iron con&longs;ists <lb/>of parts more &longs;ub­ <lb/>til, pure, and com­ <lb/>pact than the mag­ <lb/>net.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg710"></margin.target><emph type="italics"/>A &longs;en&longs;ible proof <lb/>of the impurity of <lb/>the Magnet.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg711"></margin.target>* The Author <lb/>hereby meaneth <lb/>that the &longs;tone <lb/>doth not all con­ <lb/>&longs;i&longs;t of magnetick <lb/>matter, but that <lb/>the whiter &longs;pecks <lb/>being weak, tho&longs;e <lb/>other parts of the <lb/>Load&longs;tone of a <lb/>more dark & con­ <lb/>&longs;tant colour, con­ <lb/>tain all that vertue <lb/>wherewith bodies <lb/>are attracted.</s></p><p type="margin"><s><margin.target id="marg712"></margin.target>* A common <lb/>&longs;ewing needle.</s></p><p type="main"><s>SAGR. </s><s>Your whole di&longs;cour&longs;e hath been in my judgment very <lb/>concluding, and this experiment of the Needle hath made me <lb/>think it little inferiour to a Mathematical Demon&longs;tration; and <lb/>I ingenuou&longs;ly confe&longs;&longs;e, that in all the Magnetick Philo&longs;ophy, I <lb/>never heard or read any thing, that with &longs;uch &longs;trong rea&longs;ons <lb/>gave account of its &longs;o many admirable accidents, of which, if the <lb/>cau&longs;es were with the &longs;ame per&longs;picuity laid open, I know not <lb/>what &longs;weeter food our Intellects could de&longs;ire.</s></p><p type="main"><s>SALV. </s><s>In &longs;eeking the rea&longs;ons of conclu&longs;ions unknown unto <lb/>us, it is requi&longs;ite to have the good fortune to direct the di&longs;­ <lb/>cour&longs;e from the very beginning towards the way of truth; in <lb/>which if any one walk, it will ea&longs;ily happen, that one &longs;hall meet <lb/>with &longs;everal other Propo&longs;itions known to be true, either by di&longs;­ <lb/>putes or experiments, from the certainty of which the truth of <lb/>ours acquireth &longs;trength and evidence; as it did in every re&longs;pect <lb/>happen to me in the pre&longs;ent Probleme, for being de&longs;irous to a&longs;­ <lb/>&longs;ure my &longs;elf, by &longs;ome other accident, whether the rea&longs;on of the <lb/>Propo&longs;ition, by me found, were true; namely, whether the &longs;ub­ <lb/>&longs;tance of the Magnet were really much le&longs;&longs;e continuate than that <lb/>of Iron or of Steel, I made the Arti&longs;ts that work in the Gallery <lb/>of my Lord the Grand Duke, to &longs;mooth one &longs;ide of that piece <lb/>of Magnet, which formerly was yours, and then to poli&longs;h and <lb/>burni&longs;h it; upon which to my &longs;atisfaction I found what I de&longs;ired. <lb/></s><s>For I di&longs;covered many &longs;pecks of colour different from the re&longs;t, <lb/>but as &longs;plendid and bright, as any of the harder &longs;ort of &longs;tones; <lb/>the re&longs;t of the Magnet was polite, but to the tact onely, not <lb/>being in the lea&longs;t &longs;plendid; but rather as if it were &longs;meered over <lb/>with &longs;oot; and this was the &longs;ub&longs;tance of the Load &longs;tone, and <lb/>the &longs;hining part was the fragments of other &longs;tones intermixt <lb/>therewith, as was &longs;en&longs;ibly made known by pre&longs;enting the face <lb/>thereof to filings of Iron, the which in great number leapt to <lb/>the Load-&longs;tone, but not &longs;o much as one grain did &longs;tick to the <lb/>&longs;aid &longs;pots, which were many, &longs;ome as big as the fourth part of <lb/>the nail of a mans finger, others &longs;omewhat le&longs;&longs;er, the lea&longs;t of <lb/>all very many, and tho&longs;e that were &longs;carce vi&longs;ible almo&longs;t innu­ <lb/>merable. </s><s>So that I did a&longs;&longs;ure my &longs;elf, that my conjecture was <lb/>true, when I fir&longs;t thought that the &longs;ub&longs;tance of the Magnet <lb/>was not clo&longs;e and compact, but porous, or to &longs;ay better, &longs;pon­ <lb/>gy; but with this difference, that whereas the &longs;ponge in its <lb/>cavities and little cels conteineth Air or Water, the Magnet hath <lb/>its pores full of hard and heavy &longs;tone, as appears by the exqui­ <lb/>&longs;ite lu&longs;tre which tho&longs;e &longs;pecks receive. </s><s>Whereupon, as I have &longs;aid <lb/>from the beginning, applying the &longs;urface of the Iron to the &longs;u­ <lb/>perficies of the Magnet the minute particles of the Iron, though <lb/>perhaps more continuate than the&longs;e of any other body (as its <pb xlink:href="040/01/393.jpg" pagenum="373"/>&longs;hining more than any other matter doth &longs;hew) do not all, nay <lb/>but very few of them incounter pure Magnet; and the contacts <lb/>being few, the union is but weak. </s><s>But becau&longs;e the cap of the <lb/>Load-&longs;tone, be&longs;ides the contact of a great part of its &longs;uperficies, <lb/>inve&longs;ts its &longs;elf al&longs;o with the virtue of the parts adjoyning, al­ <lb/>though they touch not; that &longs;ide of it being exactly &longs;moothed <lb/>to which the other face, in like manner well poli&longs;ht of the Iron to <lb/>be attracted, is applyed, the contact is made by innumera­ <lb/>ble minute particles, if not haply by the infinite points of both <lb/>the &longs;uperficies, whereupon the union becometh very &longs;trong. <lb/></s><s>This ob&longs;ervation of &longs;moothing the &longs;urfaces of the Irons that are <lb/>to touch, came not into the thoughts of <emph type="italics"/>Gilbert,<emph.end type="italics"/> for he makes <lb/>the Irons convex, &longs;o that their contact is very &longs;mall; and there­ <lb/>upon it cometh to pa&longs;&longs;e that the tenacity, wherewith tho&longs;e Irons <lb/>conjoyn, is much le&longs;&longs;er.</s></p><p type="main"><s>SAGR. </s><s>I am, as I told you before, little le&longs;&longs;e &longs;atisfied with <lb/>this rea&longs;on, that if it were a pure Geometrical Demon&longs;tration; <lb/>and becau&longs;e we &longs;peak of a Phy&longs;ical Problem, I believe that al&longs;o <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> will find him&longs;elf &longs;atisfied as far as natural &longs;cience ad­ <lb/>mits, in which he knows that Geometrical evidence is not to be <lb/>required.</s></p><p type="main"><s>SIMP. </s><s>I think indeed, that <emph type="italics"/>Salviatus<emph.end type="italics"/> with a fine circumlo­ <lb/><arrow.to.target n="marg713"></arrow.to.target> <lb/>cution hath &longs;o manife&longs;tly di&longs;played the cau&longs;e of this effect, that <lb/>any indifferent wit, though not ver&longs;t in the Sciences, may ap­ <lb/>prehend the &longs;ame; but we, confining our &longs;elves to the terms of <lb/>Art, reduce the cau&longs;e of the&longs;e and other the like natural effects <lb/>to <emph type="italics"/>Sympathy,<emph.end type="italics"/> which is a certain agreement and mutual appetite <lb/>which ari&longs;eth between things that are &longs;emblable to one another <lb/>in qualities; as likewi&longs;e on the contrary that hatred & enmity for <lb/>which other things &longs;hun & abhor one another we call <emph type="italics"/>Antipathy.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg713"></margin.target>Sympathy <emph type="italics"/>and<emph.end type="italics"/> <lb/>Antipathy, <emph type="italics"/>terms <lb/>u&longs;ed by Philo&longs;o­ <lb/>phers to give a rea­ <lb/>&longs;on ea&longs;ily of ma­ <lb/>ny narural effests.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>And thus with the&longs;e two words men come to render <lb/>rea&longs;ons of a great number of accidents and effects which we &longs;ee <lb/>not without admiration to be produced in nature. </s><s>But this kind <lb/>of philo&longs;ophating &longs;eems to me to have great &longs;ympathy with a <lb/><arrow.to.target n="marg714"></arrow.to.target> <lb/>certain way of Painting that a Friend of mine u&longs;ed, who writ <lb/>upon the <emph type="italics"/>Tele<emph.end type="italics"/> or Canva&longs;&longs;e in chalk, here I will have the Foun­ <lb/>tain with <emph type="italics"/>Diana<emph.end type="italics"/> and her Nimphs, there certain Hariers, in this <lb/>corner I will have a Hunt&longs;-man with the Head of a Stag, the re&longs;t <lb/>&longs;hall be Lanes, Woods, and Hills; and left the remainder for <lb/>the Painter to &longs;et forth with Colours; and thus he per&longs;waded <lb/>him&longs;elf that he had painted the Story of <emph type="italics"/>Acteon,<emph.end type="italics"/> when as he had <lb/>contributed thereto nothing of his own more than the names. <lb/></s><s>But whether are we wandred with &longs;o long a digre&longs;&longs;ion, contrary <lb/>to our former re&longs;olutions? </s><s>I have almo&longs;t forgot what the point <lb/>was that we were upon when we fell into this magnetick di&longs;­ <pb xlink:href="040/01/394.jpg" pagenum="374"/>cour&longs;e; and yet I had &longs;omething in my mind that I intended to <lb/>have &longs;poken upon that &longs;ubject.</s></p><p type="margin"><s><margin.target id="marg714"></margin.target><emph type="italics"/>A plea&longs;ant ex­ <lb/>ampleaeclaring the <lb/>invalidity of &longs;ome <lb/>Phylo&longs;ophical ar­ <lb/>gumentations.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>We were about to demon&longs;trate that third motion a­ <lb/>&longs;cribed by <emph type="italics"/>Copernicus<emph.end type="italics"/> to the Earth to be no motion but a quie­ <lb/>&longs;cence and maintaining of it &longs;elf immutably directed with its de­ <lb/>terminate parts towards the &longs;ame & determinate parts of the Uni­ <lb/>ver&longs;e, that is a perpetual con&longs;ervation of the Axis of its diurnal <lb/>revolution parallel to it &longs;elf, and looking towards &longs;uch and &longs;uch <lb/>fixed &longs;tars; which mo&longs;t con&longs;tant po&longs;ition we &longs;aid did naturally <lb/>agree with every librated body &longs;u&longs;pended in a fluid and yielding <lb/><emph type="italics"/>medium,<emph.end type="italics"/> which although carried about, yet did it not change di­ <lb/>rectionin re&longs;pect of things external, but onely &longs;eemed to revolve in <lb/>its &longs;elf, in re&longs;pect of that which carryed it round, and to the <lb/>ve&longs;&longs;el in which it was tran&longs;ported. </s><s>And then we added to this <lb/>&longs;imple and natural accident the magnetick virtue, whereby the <lb/>&longs;elf Terre&longs;trial Globe might &longs;o much the more con&longs;tantly keep it <lb/>immutable, -----</s></p><p type="main"><s>SAGR. </s><s>Now I remember the whole bu&longs;ine&longs;&longs;e; and that which <lb/>then came into my minde, & which I would have intimated, was a <lb/>certain con&longs;ideration touching the &longs;cruple and objection of <emph type="italics"/>Sim­ <lb/>plicius,<emph.end type="italics"/> which he propounded again&longs;t the mobility of the Earth, <lb/><arrow.to.target n="marg715"></arrow.to.target> <lb/>taken from the multiplicity of motions, impo&longs;&longs;ible to be a&longs;&longs;igned <lb/>to a &longs;imple body, of which but one &longs;ole and &longs;imple motion, ac­ <lb/>cording to the doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> can be natural; and that <lb/>which I would have propo&longs;ed to con&longs;ideration, was the Magnet, <lb/>to which we manife&longs;tly &longs;ee three motions naturally to agree: <lb/>one towards the centre of the Earth, as a <emph type="italics"/>Grave<emph.end type="italics"/>; the &longs;econd is <lb/>the circular Horizontal Motion, whereby it re&longs;tores and con­ <lb/>&longs;erves its Axis towards determinate parts of the Univer&longs;e; and <lb/>the third is this, newly di&longs;covered by <emph type="italics"/>Gilbert,<emph.end type="italics"/> of inclining its <lb/>Axis, being in the plane of a Meridian towards the &longs;urface of the <lb/>Earth, and this more and le&longs;&longs;e, according as it &longs;hall be di&longs;tant <lb/>from the Equinoctial, under which it is parallel to the Axis of <lb/>the Earth. </s><s>Be&longs;ides the&longs;e three, it is not perhaps improbable, <lb/>but that it may have a fourth, of revolving upon its own Axis, in <lb/>ca&longs;e it were librated and &longs;u&longs;pended in the air or other fluid and <lb/>yielding <emph type="italics"/>Medium,<emph.end type="italics"/> &longs;o that all external and accidental impediments <lb/>were removed, and this opinion <emph type="italics"/>Gilbert<emph.end type="italics"/> him&longs;elf &longs;eemeth al&longs;o to <lb/>applaud. </s><s>So that, <emph type="italics"/>Simplicius,<emph.end type="italics"/> you &longs;ee how tottering the Axiome <lb/>of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> is.</s></p><p type="margin"><s><margin.target id="marg715"></margin.target><emph type="italics"/>The &longs;everal na­ <lb/>tural motions of <lb/>the Magnet.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>This doth uot only not make again&longs;t the Maxime, but <lb/>not &longs;o much as look towards it: for that he &longs;peaketh of a fimple <lb/>body, and of that which may naturally con&longs;i&longs;t therewith; but <lb/>you propo&longs;e that which befalleth a mixt body; nor do you tell <lb/>us of any thing that is new to the doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> for that <pb xlink:href="040/01/395.jpg" pagenum="375"/>he likewi&longs;e granteth to mixt bodies compound motions by -----</s></p><p type="main"><s>SAGR. </s><s>Stay a little, <emph type="italics"/>Simplicius,<emph.end type="italics"/> & an&longs;wer me to the que&longs;tions <lb/>I &longs;hall ask you. </s><s>You &longs;ay that the Load-&longs;tone is no &longs;imple body, <lb/><arrow.to.target n="marg716"></arrow.to.target> <lb/>now I defire you to tell me what tho&longs;e &longs;imple bodies are, that <lb/>mingle in compo&longs;ing the Load-&longs;tone.</s></p><p type="margin"><s><margin.target id="marg716"></margin.target>Ari&longs;tole <emph type="italics"/>grants <lb/>a compound motion <lb/>to mixt bodies.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I know not how to tell you th'ingredients nor &longs;imples <lb/>preci&longs;ely, but it &longs;ufficeth that they are things elementary.</s></p><p type="main"><s>SALV. </s><s>So much &longs;ufficeth me al&longs;o. </s><s>And of the&longs;e &longs;imple ele­ <lb/>mentary bodies, what are the natural motions?</s></p><p type="main"><s>SIMP. </s><s>They are the two right and &longs;imple motions, <emph type="italics"/>&longs;ur&longs;um<emph.end type="italics"/> <lb/>and <emph type="italics"/>deor&longs;um.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Tell me in the next place? </s><s>Do you believe that the <lb/>motion, that &longs;hall remain natural to that &longs;ame mixed body, &longs;hould <lb/>be one that may re&longs;ult from the compo&longs;ition of the two &longs;imple <lb/>natural motions of the &longs;imple bodies compounding, or that it <lb/>may be a motion impo&longs;&longs;ible to be compo&longs;ed of them. <lb/><arrow.to.target n="marg717"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg717"></margin.target><emph type="italics"/>The motion of <lb/>mixt bodies ought <lb/>to be &longs;uch as may <lb/>re&longs;ult from the <lb/>compo&longs;ition of the <lb/>motions of the &longs;im­ <lb/>ple bodies com­ <lb/>pounding.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I believe that it &longs;hall move with the motion re&longs;ulting <lb/>from the compo&longs;ition of the motions of the &longs;imple bodies com­ <lb/>pounding, and that with a motion impo&longs;&longs;ible to be compo&longs;ed of <lb/>the&longs;e, it is impo&longs;&longs;ible that it &longs;hould move.</s></p><p type="main"><s>SAGR. But, <emph type="italics"/>Simplicius,<emph.end type="italics"/> with two right and &longs;imple motions, you <lb/>&longs;hall never be able to compo&longs;e a circular motion, &longs;uch as are the </s></p><p type="main"><s><arrow.to.target n="marg718"></arrow.to.target> <lb/>two, or three circular motions that the magnet hath: you &longs;ee <lb/>then into what ab&longs;urdities evil grounded Principles, or, to &longs;ay <lb/><arrow.to.target n="marg719"></arrow.to.target> <lb/>better, the ill-inferred con&longs;equences of good Principles carry a <lb/>man; for you are now forced to &longs;ay, that the Magnet is a mix­ <lb/>ture compounded of &longs;ub&longs;tances elementary and cœle&longs;tial, if you <lb/>will maintain that the &longs;traight motion is a peculiar to the Ele­ <lb/>ments, and the circular to the cœle&longs;tial bodies. </s><s>Therefore if <lb/>you will more &longs;afely argue, you mu&longs;t &longs;ay, that of the integral <lb/>bodies of the Univer&longs;e, tho&longs;e that are by nature moveable, do all <lb/>move circularly, and that therefore the Magnet, as a part of the <lb/><arrow.to.target n="marg720"></arrow.to.target> <lb/>true primary, and integral &longs;ub&longs;tance of our Globe, pertaketh of <lb/>the &longs;ame qualities with it. </s><s>And take notice of this your fallacy, <lb/>in calling the Magnet a mixt body, and the Terre&longs;trial Globe a <lb/>&longs;imple body, which is &longs;en&longs;ibly perceived to be a thou&longs;and times <lb/>more compound: for, be&longs;ides that it containeth an hundred an <lb/>hundred matters, exceeding different from one another, it con­ <lb/>taineth great abundance of this which you call mixt, I mean <lb/>of the Load-&longs;tone. </s><s>This &longs;eems to me ju&longs;t as if one &longs;hould call <lb/><arrow.to.target n="marg721"></arrow.to.target> <lb/>bread a mixt body, and ^{*} <emph type="italics"/>Pannada<emph.end type="italics"/> a &longs;imple body, in which there <lb/>is put no &longs;mall quantity of bread, be&longs;ides many other things edi­ <lb/>ble. </s><s>This &longs;eemeth to me a very admirable thing, among&longs;t others <pb xlink:href="040/01/396.jpg" pagenum="376"/><arrow.to.target n="marg722"></arrow.to.target> <lb/>of the Peripateticks, who grant (nor can it be denied) that our <lb/>Terre&longs;trial Globe is, <emph type="italics"/>de facto,<emph.end type="italics"/> a compound of infinite different <lb/>matters; and grant farther that of compound bodies the motion <lb/>ought to be compound: now the motions that admit of compo­ <lb/>&longs;ition are the right and circular: For the two right motions, as <lb/>being contrary, are incompatible together, they affirm, that the <lb/>pure Element of Earth is no where to be found; they confe&longs;&longs;e, <lb/>that it never hath been moved with a local motion; and yet they <lb/>will introduce in Nature that body which is not to be found, and <lb/>make it move with that motion which it never exerci&longs;ed, nor ne­ <lb/>ver &longs;hall do, and to that body which hath, and ever had a being, <lb/>they deny that motion, which before they granted, ought natu­ <lb/>rally to agree therewith.</s></p><p type="margin"><s><margin.target id="marg718"></margin.target><emph type="italics"/>With two right <lb/>motions one cannot <lb/>compo&longs;e circular <lb/>motions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg719"></margin.target><emph type="italics"/>Philo&longs;ophers are <lb/>forced to confe&longs;&longs;e <lb/>that the Magnet <lb/>is compounded of <lb/>cœle&longs;tial &longs;ub&longs;tan­ <lb/>ces, and of elemen­ <lb/>tary.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg720"></margin.target><emph type="italics"/>The errour of <lb/>tho&longs;e who call the <lb/>Magnet a mixt <lb/>body, and the ter­ <lb/>re&longs;trial Globe <lb/>&longs;imble body.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg721"></margin.target>* Ogliopotrida <lb/><emph type="italics"/>a Spani&longs;h di&longs;h of <lb/>many ingredients <lb/>boild together.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg722"></margin.target><emph type="italics"/>The Di&longs;cour&longs;es <lb/>of Peripateticks, <lb/>full of errours and <lb/>contradictions.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I be&longs;eech you, <emph type="italics"/>Sagredus,<emph.end type="italics"/> let us not weary our &longs;elves <lb/>any more about the&longs;e particulars, and the rather, becau&longs;e you <lb/>know that our purpo&longs;e was not to determine re&longs;olutely, or to <lb/>accept for true, this or that opinion, but only to propo&longs;e for our <lb/>diverti&longs;ement &longs;uch rea&longs;ons, and an&longs;wers as may be alledged on <lb/>the one &longs;ide, or on the other; and <emph type="italics"/>Simplicius<emph.end type="italics"/> maketh this an­ <lb/>&longs;wer, in defence of his Peripateticks, therefore let us leave the <lb/>judgment in &longs;u&longs;pen&longs;e, and remit the determination into the <lb/>hands of &longs;uch as are more known than we. </s><s>And becau&longs;e I think <lb/>that we have, with &longs;ufficient prolixity, in the&longs;e three dayes, di&longs;­ <lb/>cour&longs;ed upon the Sy&longs;teme of the Univer&longs;e, it will now be &longs;ea&longs;o­ <lb/>nable, that we proceed to the grand accident, from whence our <lb/>Di&longs;putations took beginning, I mean, of the ebbing and flowing <lb/>of the Sea, the cau&longs;e whereof may, in all probability, be referred <lb/>to the motion of the Earth. </s><s>But that, if you &longs;o plea&longs;e, we will <lb/>re&longs;erve till to morrow. </s><s>In the mean time, that I may not forget <lb/>it, I will &longs;peak to one particular, to which I could have wi&longs;hed, <lb/>that <emph type="italics"/>Gilbert<emph.end type="italics"/> had not lent an ear; I mean that of admitting, that <lb/><arrow.to.target n="marg723"></arrow.to.target> <lb/>in ca&longs;e a little Sphere of Load&longs;tone might be exactly librated, it <lb/>would revolve in it &longs;elf; becau&longs;e there is no rea&longs;on why it &longs;hould <lb/>do &longs;o; For if the whole Terre&longs;trial Globe hath a natural facul­ <lb/>ty of revolving about its own centre in twenty four hours, and <lb/>that all its parts ought to have the &longs;ame, I mean, that faculty of <lb/>turning round together with their <emph type="italics"/>whole,<emph.end type="italics"/> about its centre in twen­ <lb/>ty four hours; they already have the &longs;ame in effect, whil&longs;t that, <lb/>being upon the Earth, they turn round along with it: And the <lb/>a&longs;&longs;igning them a revolution about their particular centres, would <lb/>be to a&longs;cribe unto them a &longs;econd motion much different from the <lb/>fir&longs;t; for &longs;o they would have two, namely, the revolving in twen­ <lb/>ty four hours about the centre of their <emph type="italics"/>whole<emph.end type="italics"/>; and the turning <lb/>about their own: now this &longs;econd is arbitrary, nor is there any <pb xlink:href="040/01/397.jpg" pagenum="377"/>rea&longs;on for the introducing of it: If by pluoking away a piece <lb/>of Load&longs;tone from the whole natural ma&longs;&longs;d, it were deprived of <lb/>the faculty of following it, as it did, whil&longs;t it was unitedy thereto, <lb/>&longs;o that it is thereby deprived of the revodution about the univer­ <lb/>&longs;al centre of the Terre&longs;trial Globe, it might Chaply, with &longs;ome­ <lb/>what greater probability be thought by &longs;ome, that the &longs;aid Mag­ <lb/>net was to appropriate to it &longs;elf a new conver&longs;ion about its parti­ <lb/>cular centre; but if it do no le&longs;&longs;e, when &longs;eparated, than when <lb/>conjoyned, continue always to pur&longs;ue its fir&longs;t, eternal, and natu­ <lb/>ral cour&longs;e, to what purpo&longs;e &longs;hould we go about to obtrude upon <lb/>it another new one?</s></p><p type="margin"><s><margin.target id="marg723"></margin.target><emph type="italics"/>An improba­ <lb/>ble effect admired <lb/>by<emph.end type="italics"/> Gilbertus <emph type="italics"/>in the <lb/>Load&longs;tone.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I under&longs;tand you very well, and this puts me in mind <lb/>of a Di&longs;cour&longs;e very like to this for the vanity of it, falling from <lb/><arrow.to.target n="marg724"></arrow.to.target> <lb/>certain Writers upon the Sphere, and I think, if I well remem­ <lb/>ber, among&longs;t others from <emph type="italics"/>Sacrobo&longs;co,<emph.end type="italics"/> who, to &longs;hew how the E­ <lb/>lement of Water, doth, together with the Earth, make a com­ <lb/>pleat Spherical Figure, and &longs;o between them both compo&longs;e this <lb/>our Globe, writeth, that the &longs;eeing the &longs;mall ^{*} particles of water <lb/>&longs;hape them&longs;elves into rotundity, as in the drops, and in the dew <lb/>daily apparent upon the leaves of &longs;everal herbs, is a &longs;trong ar­ <lb/>gument; and becau&longs;e, according to the trite Axiome, there is <lb/>the &longs;ame rea&longs;on for the whole, as for the parts, the parts affecting <lb/>that &longs;ame figure, it is nece&longs;&longs;ary that the &longs;ame is proper to the <lb/>whole Element: and truth is, methinks it is a great over&longs;ight <lb/>that the&longs;e men &longs;hould not perceive &longs;o apparent a vanity, and con­ <lb/>&longs;ider that if their argument had run right, it would have follow­ <lb/>ed, that not only the &longs;mall drops, but that any what&longs;oever greater <lb/>quantity of water &longs;eparated from the whole Element, &longs;hould be re­ <lb/>duced into a Globe: Which is not &longs;een to happen; though indeed <lb/>the Sen&longs;es may &longs;ee, and the Under&longs;tanding perceive that the E­ <lb/>lement of Water loving to form it &longs;elf into a Spherical Figure <lb/>about the common centre of gravity, to which all grave bo­ <lb/>dies tend (that is, the centre of the Terre&longs;trial Globe) it <lb/>therein is followed by all its parts, according to the Axiome; <lb/>&longs;o that all the &longs;urfaces of Seas, Lakes, Pools, and in a word, <lb/>of all the parts of Waters conteined in ve&longs;&longs;els, di&longs;tend <lb/>them&longs;elves into a Spherical Figure, but that Figure is an arch <lb/>of that Sphere that hath for its centre the centre of the Ter­ <lb/>re&longs;trial Globe, and do not make particular Spheres of them­ <lb/>&longs;elves.</s></p><p type="margin"><s><margin.target id="marg724"></margin.target><emph type="italics"/>The vain argu­ <lb/>mentation of &longs;ome <lb/>to prove the Ele­ <lb/>ment of Water to <lb/>be of a Spherical <lb/>&longs;uper ficies.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>The errour indeed is childi&longs;h; and if it had <lb/>been onely the &longs;ingle mi&longs;take of <emph type="italics"/>Sacrobo&longs;co,<emph.end type="italics"/> I would ea&longs;ily <lb/>have allowed him in it; but to pardon it al&longs;o to his Com­ <lb/>mentators, and to other famous men, and even to <emph type="italics"/>Ptolomy<emph.end type="italics"/> <pb xlink:href="040/01/398.jpg" pagenum="378"/>him&longs;elfe; this I cannot do, without blu&longs;hing for their repu­ <lb/>tation. </s><s>But it is high time to take leave, it row being <lb/>very late, and we being to meet again to morrow, <lb/>at the u&longs;ual hour, to bring all the foregoing <lb/>Di&longs;cour&longs;es to a final conclu&longs;ion. <lb/></s></p><pb xlink:href="040/01/399.jpg"/><figure id="id.040.01.399.1.jpg" xlink:href="040/01/399/1.jpg"/><figure id="id.040.01.399.2.jpg" xlink:href="040/01/399/2.jpg"/><figure id="id.040.01.399.3.jpg" xlink:href="040/01/399/3.jpg"/><figure id="id.040.01.399.4.jpg" xlink:href="040/01/399/4.jpg"/><figure id="id.040.01.399.5.jpg" xlink:href="040/01/399/5.jpg"/><figure id="id.040.01.399.6.jpg" xlink:href="040/01/399/6.jpg"/><figure id="id.040.01.399.7.jpg" xlink:href="040/01/399/7.jpg"/><figure id="id.040.01.399.8.jpg" xlink:href="040/01/399/8.jpg"/><p type="caption"><s><emph type="italics"/>Place this Plate <lb/>at the end of <lb/>the third<emph.end type="italics"/>Dialogue</s></p><pb xlink:href="040/01/400.jpg"/></chap><chap> <pb xlink:href="040/01/401.jpg" pagenum="379"/><p type="head"><s>GALILÆUS <lb/>Gailæus Lyncæus, <lb/>HIS <lb/>SYSTEME <lb/>OF THE <lb/>WORLD.</s></p><p type="head"><s>The Fourth Dialogue.</s></p><p type="head"><s><emph type="italics"/>INTERLOCVTORS.<emph.end type="italics"/></s></p><p type="head"><s>SALVIATUS, SAGREDUS, & SIMPLICIUS.</s></p><p type="main"><s>SAGR. </s><s>I know not whether your return to our <lb/>accu&longs;tomed conferences hath really been <lb/>later than u&longs;ual, or whether the de&longs;ire <lb/>of hearing the thoughts of <emph type="italics"/>Salviatus,<emph.end type="italics"/> <lb/>touching a matter &longs;o curious, hath <lb/>made me think it &longs;o: But I have tar­ <lb/>ried a long hour at this window, expe­ <lb/>cting every moment when the <emph type="italics"/>Gondola<emph.end type="italics"/> <lb/>would appear that I &longs;ent to fetch you.</s></p><p type="main"><s>SALV. </s><s>I verily believe that your imagination more than our <lb/>tarriance hath prolonged the time: and to make no longer de­ <lb/><arrow.to.target n="marg725"></arrow.to.target> <lb/>murre, it would be well, if without interpo&longs;ing more words, we <lb/>came to the matter it &longs;elf; and did &longs;hew, that nature hath per­ <lb/>mitted (whether the bu&longs;ine&longs;s <emph type="italics"/>in rei veritate<emph.end type="italics"/> be &longs;o, or el&longs;e to play <pb xlink:href="040/01/402.jpg" pagenum="380"/>and &longs;port with our Fancies) hath, I &longs;ay, hath permitted that the <lb/><arrow.to.target n="marg726"></arrow.to.target> <lb/>motions for every other re&longs;pect, except to re&longs;olve the ebbing and <lb/>flowing of the Sea, a&longs;&longs;igned long &longs;ince to the earth, &longs;hould be found <lb/>now at la&longs;t to an&longs;wer exactly to the cau&longs;e thereof; and, as it <lb/><arrow.to.target n="marg727"></arrow.to.target> <lb/>were, with mutual a emulation, the &longs;aid ebbing and flowing <lb/>to appear in confirmation of the Terre&longs;trial motion: the <emph type="italics"/>judices<emph.end type="italics"/> <lb/>whereof have hitherto been taken from the cœle&longs;tial Phænomena, <lb/>in regard that of tho&longs;e things that happen on Earth, not any one <lb/>was of force to prove one opinion more than another, as we al­ <lb/>ready have at large proved, by &longs;hewing that all the terrene occur­ <lb/>rences upon which the &longs;tability of the Earth and mobility of the <lb/>Sun and Firmament is commonly inferred, are to &longs;eem to us per­ <lb/>formed in the &longs;ame manner, though we &longs;uppo&longs;ed the mobility of <lb/>the Earth, and the immobility of them. </s><s>The Element of Wa­ <lb/>ter onely, as being mo&longs;t va&longs;t, and which is not annexed and con­ <lb/>catenated to the Terre&longs;trial Globe as all its other &longs;olid parts are; <lb/>yea, rather which by rea&longs;on of its fluidity remaineth apart <emph type="italics"/>&longs;ui <lb/>juris,<emph.end type="italics"/> and free, is to be ranked among&longs;t tho&longs;e &longs;ublunary things, <lb/>from which we may collect &longs;ome hinte and intimation of what the <lb/>Earth doth in relation to motion and re&longs;t. </s><s>After I had many <lb/>and many a time examined with my &longs;elf the effects and accidents, <lb/>partly &longs;een and partly under&longs;tood from others, thar are to be ob­ <lb/>&longs;erved in the motions of waters: and moreover read and heard <lb/>the great vanities produced by many, as the cau&longs;es of tho&longs;e acci­ <lb/>dents, I have been induced upon no &longs;light rea&longs;ons to omit the&longs;e <lb/><arrow.to.target n="marg728"></arrow.to.target> <lb/>two conclu&longs;ions (having made withal the nece&longs;&longs;ary pre&longs;uppo­ <lb/>&longs;als) that in ca&longs;e the terre&longs;trial Globe be immoveable, the flux <lb/>and reflux of the Sea cannot be natural; and that, in ca&longs;e tho&longs;e <lb/>motions be conferred upon the &longs;aid Globe, which have been long <lb/>&longs;ince a&longs;&longs;igned to it, it is nece&longs;&longs;ary that the Sea be &longs;ubject to eb­ <lb/>bing and flowing, according to all that which we ob&longs;erve to hap­ <lb/>pen in the &longs;ame.</s></p><p type="margin"><s><margin.target id="marg725"></margin.target><emph type="italics"/>Nature in &longs;port <lb/>maketh the ebbing <lb/>and flowing of the <lb/>Sea, to approve the <lb/>Earths mobility.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg726"></margin.target><emph type="italics"/>The tide, and <lb/>mobility of the <lb/>Earth mutually <lb/>confirm each other<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg727"></margin.target><emph type="italics"/>All terrene ef­ <lb/>fects, indifferently <lb/>confirm the motion <lb/>or re&longs;t of the <lb/>Earth, except the <lb/>ebbing and flowing <lb/>of the Sea.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg728"></margin.target><emph type="italics"/>The fir&longs;t gene­ <lb/>ral conclu&longs;ion of <lb/>the impo&longs;&longs;ibility of <lb/>the ebbing and <lb/>flowing the immo­ <lb/>bility of the terre­ <lb/>&longs;trial Globe being <lb/>granted.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>The Propo&longs;ition is very con&longs;iderable, as well for it <lb/>&longs;elf as for what followeth upon the &longs;ame by way of con&longs;equence, <lb/>&longs;o that I &longs;hall the more inten&longs;ly hearken to the explanation and <lb/>confirmation of it. <lb/><arrow.to.target n="marg729"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg729"></margin.target><emph type="italics"/>The knowledge <lb/>of the offests con­ <lb/>tributes to the in­ <lb/>ve&longs;tigation of the <lb/>cau&longs;es.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>Becau&longs;e in natural que&longs;tions, of which number this <lb/>which we have in hand is one, the knowledge of the effects is a <lb/>means to guide us to the inve&longs;tigation and di&longs;covery of the cau­ <lb/>&longs;es, and without which we &longs;hould walk in the dark, nay with <lb/>more uncertainty, for that we know not whither we would go, <lb/>whereas the blind, at lea&longs;t, know where they de&longs;ire to arrive; there­ <lb/>fore fir&longs;t of all it is nece&longs;&longs;ary to know the effects whereof we en­ <lb/>quire the cau&longs;es: of which effects you, <emph type="italics"/>Sagredus,<emph.end type="italics"/> ought more <lb/>abundantly and more certainly to be informed than I am, <pb xlink:href="040/01/403.jpg" pagenum="381"/>as one, that be&longs;ides your being born, and having, for a long <lb/>time, dwelt in <emph type="italics"/>Venice,<emph.end type="italics"/> where the Tides are very notable for their <lb/>greatne&longs;&longs;e, have al&longs;o &longs;ailed into <emph type="italics"/>Syria,<emph.end type="italics"/> and, as an ingenuous and <lb/>apprehen&longs;ive wit, mu&longs;t needs have made many Ob&longs;ervations up­ <lb/>on this &longs;ubject: whereas I, that could onely for a time, and that <lb/>very &longs;hort, ob&longs;erve what happened in the&longs;e extream parts of the <lb/><emph type="italics"/>Adriatick<emph.end type="italics"/> Gulph, and in our Seas below about the <emph type="italics"/>Tyrrhene<emph.end type="italics"/> <lb/>&longs;hores, mu&longs;t needs take many things upon the relation of o­ <lb/>thers, who, for the mo&longs;t part, not very well agreeing, and con­ <lb/>&longs;equently being very uncertain, contribute more of confu&longs;ion <lb/>than confirmation to our &longs;peculations. </s><s>Neverthele&longs;&longs;e, from tho&longs;e <lb/>that we are &longs;ure of, and which are the principal, I think I am a­ <lb/>ble to attain to the true and primary cau&longs;es; not that I pretend <lb/>to be able to produce all the proper and adequate rea&longs;ons of <lb/>tho&longs;e effects that are new unto me, and which con&longs;equently I <lb/>could never have thought upon. </s><s>And that which I have to &longs;ay, <lb/>I propo&longs;e only, as a key that openeth the door to a path never <lb/>yet trodden by any, in certain hope, that &longs;ome wits more &longs;pecu­ <lb/>lative than mine, will make a further progre&longs;&longs;e herin, and pene­ <lb/>trate much farther than I &longs;hall have done in this my fir&longs;t Di&longs;co­ <lb/>very: And although that in other Seas, remote from us, there may <lb/>happen &longs;everal accidents, which do not happen in our Mediter­ <lb/>ranean Sea, yet doth not this invalidate the rea&longs;on and cau&longs;e that <lb/>I &longs;hall produce, if &longs;o be that it veri&longs;ie and fully re&longs;olve the ac­ <lb/>cidents which evene in our Sea: for that in conclu&longs;ion there can <lb/>be but one true and primary cau&longs;e of the effects that are of the <lb/>&longs;ame kind. </s><s>I will relate unto you, therefore, the effects that I <lb/>know to be true, and a&longs;&longs;igne the cau&longs;es thereof that I think <lb/>to be true, and you al&longs;o, Gentlemen, &longs;hall produce &longs;uch <lb/>others as are known to you, be&longs;ides mine, and then we will <lb/>try whether the cau&longs;e, by me alledged, may &longs;atisfie them <lb/>al&longs;o.</s></p><p type="main"><s><arrow.to.target n="marg730"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg730"></margin.target><emph type="italics"/>Three Periods <lb/>of ebbings and <lb/>flowings, diurnal, <lb/>monethly, and an­ <lb/>nual.<emph.end type="italics"/></s></p><p type="main"><s>I therefore affirm the periods that are ob&longs;erved in the fluxes <lb/>and refluxes of the Sea-waters to be three: the fir&longs;t and princi­ <lb/>pal is this great and mo&longs;t obvious one; namely, the diurnal, accor­ <lb/>ding to which the intervals of &longs;ome hours with the waters flow and <lb/>ebbe; and the&longs;e intervals are, for the mo&longs;t part, in the Mediter­ <lb/>rane from &longs;ix hours to &longs;ix hours, or thereabouts, that is, they for <lb/>&longs;ix hours flow, and for &longs;ix hours ebbe. </s><s>The &longs;econd period is <lb/>monethly, and it &longs;eemes to take its origen from the motion of <lb/>the Moon, not that it introduceth other motions, but only al­ <lb/>tereth the greatne&longs;&longs;e of tho&longs;e before mentioned, with a notable <lb/>difference, according as it &longs;hall wax or wane, or come to the <lb/>Quadrature with the Sun. </s><s>The third Period is annual, and is <lb/>&longs;een to depend on the Sunne, and onely altereth the diurnal <pb xlink:href="040/01/404.jpg" pagenum="382"/>motions, by making them different in the times of the Sol­ <lb/>&longs;tices, as to greatne&longs;&longs;e, from what they are in the Equinoxes.</s></p><p type="main"><s>We will &longs;peak (in the fir&longs;t place, of the diurnal motion, as <lb/>being the principal, and upon which the Moon and Sun &longs;eem to <lb/>exerci&longs;e their power &longs;econdarily, in their monethly and annual </s></p><p type="main"><s><arrow.to.target n="marg731"></arrow.to.target> <lb/>alterations. </s><s>Three differences are ob&longs;ervable in the&longs;e horary <lb/>mutations; for in &longs;ome places the waters ri&longs;e and fall, without <lb/>making any progre&longs;&longs;ive motion; in others, without ri&longs;ing or fal­ <lb/>ling they run one while towards the Ea&longs;t, and recur another <lb/>while towards the We&longs;t; and in others they vary the heights <lb/>and cour&longs;e al&longs;o, as happeneth here in <emph type="italics"/>Venice,<emph.end type="italics"/> where the Tides in <lb/>coming in ri&longs;e, and in going out fall; and this they do in the ex­ <lb/>termities of the lengths of Gulphs that di&longs;tend from We&longs;t to <lb/>Ea&longs;t, and terminate in open &longs;hores, up along which &longs;hores the <lb/>Tide at time of flood hath room to extend it &longs;elf: but if the <lb/>courfe of the Tide were iutercepted by Cliffes and Banks of <lb/>great height and &longs;teepne&longs;&longs;e, there it will flow and ebbe without <lb/>any progre&longs;&longs;ive motion. </s><s>Again, it runs to and again, without <lb/>changing height in the middle parts of the Mediterrane, as nota­ <lb/><arrow.to.target n="marg732"></arrow.to.target> <lb/>bly happeneth in the ^{*} <emph type="italics"/>Faro de Me&longs;&longs;ina,<emph.end type="italics"/> between <emph type="italics"/>Scylla<emph.end type="italics"/> and <emph type="italics"/>Ca­ <lb/>rybdis,<emph.end type="italics"/> where the Currents, by rea&longs;on of the narrowne&longs;&longs;e of <lb/>the Channel, are very &longs;wift; but in the more open Seas, and <lb/>about the I&longs;les that &longs;tand farther into the Mediterranean Sea, as <lb/><arrow.to.target n="marg733"></arrow.to.target> <lb/>the <emph type="italics"/>Baleares, Cor&longs;ica, Sardignia, ^{*} Elba, Sicily<emph.end type="italics"/> towards the <emph type="italics"/>Affrican<emph.end type="italics"/> <lb/><arrow.to.target n="marg734"></arrow.to.target> <lb/>Coa&longs;ts, <emph type="italics"/>Malta, ^{*} Candia, &c.<emph.end type="italics"/> the changes of watermark are <lb/>very &longs;mall; but the currents indeed are very notable, and e&longs;pe­ <lb/>cially when the Sea is pent between I&longs;lands, or between them <lb/>and the Continent.</s></p><p type="margin"><s><margin.target id="marg731"></margin.target><emph type="italics"/>Varieties that <lb/>happen in the diur­ <lb/>nal period.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg732"></margin.target>* A Strait, &longs;o <lb/>called.</s></p><p type="margin"><s><margin.target id="marg733"></margin.target>* Or Ilva.</s></p><p type="margin"><s><margin.target id="marg734"></margin.target>* Or Creta.</s></p><p type="main"><s>Now the&longs;e onely true and certain effects, were there no more <lb/>to be ob&longs;erved, do, in my judgment, very probably per&longs;wade <lb/>any man, that will contain him&longs;elf within the bounds of natu­ <lb/>ral cau&longs;es, to grant the mobility of the Earth: for to make the <lb/>ve&longs;&longs;el (as it may be called) of the Mediterrane &longs;tand &longs;till, and to <lb/>make the water contained therein to do, as it doth, exceeds my <lb/>imagination, and perhaps every mans el&longs;e, who will but pierce <lb/>beyond the rinde in the&longs;e kind of inquiries.</s></p><p type="main"><s>SIMP. </s><s>The&longs;e accidents, <emph type="italics"/>Salviatus,<emph.end type="italics"/> begin not now, they are <lb/>mo&longs;t ancient, and have been ob&longs;erved by very many, and &longs;everal <lb/>have attempted to a&longs;&longs;igne, &longs;ome one, &longs;ome another cau&longs;e for the <lb/>&longs;ame: and there dwelleth not many miles from hence a famous <lb/>Peripatetick, that alledgeth a cau&longs;e for the &longs;ame newly fi&longs;hed out <lb/><arrow.to.target n="marg735"></arrow.to.target> <lb/>of a certain Text of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> not well under&longs;tood by his Ex­ <lb/>po&longs;itors, from which Text he collecteth, that the true cau&longs;e of <lb/>the&longs;e motions doth only proceed from the different profundities <lb/>of Seas: for that the waters of greate&longs;t depth being greater in <pb xlink:href="040/01/405.jpg" pagenum="383"/>abundance, and therefore more grave, drive back the Waters <lb/>of le&longs;&longs;e depth, which being afterwards rai&longs;ed, de&longs;ire to de­ <lb/>&longs;cend, and from this continual colluctation or conte&longs;t proceeds <lb/><arrow.to.target n="marg736"></arrow.to.target> <lb/>the ebbing and flowing. </s><s>Again tho&longs;e that referre the &longs;ame to the <lb/>Moon are many, &longs;aying that &longs;he hath particular Dominion over <lb/>the Water; and at la&longs;t a certain Prelate hath publi&longs;hed a little <lb/>Treati&longs;e, wher in he &longs;aith that the Moon wandering too and <lb/>fro in the Heavens attracteth and draweth towards it a Ma&longs;&longs;e of <lb/>Water, which goeth continually following it, &longs;o that it is full Sea <lb/>alwayes in that part which lyeth under the Moon; and becau&longs;e, <lb/>that though &longs;he be under the Horizon, yet neverthele&longs;&longs;e the Tide <lb/>returneth, he &longs;aith that no more can be &longs;aid for the &longs;alving of that <lb/>particular, &longs;ave onely, that the Moon doth not onely naturally <lb/>retain this faculty in her &longs;elf; but in this ca&longs;e hath power to con­ <lb/>fer it upon that degree of the Zodiack that is oppo&longs;ite unto it. <lb/></s><s>Others, as I believe you know, do &longs;ay that the Moon is able <lb/><arrow.to.target n="marg737"></arrow.to.target> <lb/>with her temperate heat to rarefie the Water, which being ra­ <lb/>refied, doth thereupon flow. </s><s>Nor hath there been wanting &longs;ome <lb/>that ----</s></p><p type="margin"><s><margin.target id="marg735"></margin.target><emph type="italics"/>The cau&longs;e of the <lb/>abbing and flowing <lb/>alledged by a cer­ <lb/>tain modern Phi­ <lb/>lo&longs;opher.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg736"></margin.target><emph type="italics"/>The cau&longs;e of <lb/>the ebbing and <lb/>flowing a&longs;cribed to <lb/>the Moon by a <lb/>certain Prelate.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg737"></margin.target>Hieronymus Bor­ <lb/>rius <emph type="italics"/>and other<emph.end type="italics"/> Pe­ <lb/>ripateticks <emph type="italics"/>refer it <lb/>to the temperate <lb/>heat of the Moon.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I pray you <emph type="italics"/>Simplicius<emph.end type="italics"/> let us hear no more of them, <lb/>for I do not think it is worth the while to wa&longs;t time in relating <lb/>them, or to &longs;pend our breath in confuting them; and for your <lb/>part, if you gave your a&longs;&longs;ent to any of the&longs;e or the like foole­ <lb/>ries, you did a great injury to your judgment, which neverthe­ <lb/>le&longs;&longs;e I acknowledg to be very piercing.</s></p><p type="main"><s>SALV. </s><s>But I that am a little more flegmatick than you, <emph type="italics"/>Sagre-<emph.end type="italics"/> <lb/><arrow.to.target n="marg738"></arrow.to.target> <lb/><emph type="italics"/>dus,<emph.end type="italics"/> will &longs;pend a few words in favour of <emph type="italics"/>Simplicius,<emph.end type="italics"/> if haply <lb/>he thinks that any probability is to be found in tho&longs;e things that <lb/>he hath related. </s><s>I &longs;ay therefore: The Waters, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that <lb/>have their exteriour &longs;uperficies higher, repel tho&longs;e that are infe­ <lb/>riour to them, and lower; but &longs;o do not tho&longs;e Waters that are <lb/>of greate&longs;t profundity; and the higher having once driven back <lb/>the lower, they in a &longs;hort time grow quiet and ^{*} level. </s><s>This <lb/><arrow.to.target n="marg739"></arrow.to.target> <lb/>your <emph type="italics"/>Peripatetick<emph.end type="italics"/> mu&longs;t needs be of an opinion, that all the Lakes <lb/>in the World that are in a calme, and that all the Seas where <lb/>the ebbing and flowing is in&longs;en&longs;ible, are level in their bottoms; <lb/>but I was &longs;o &longs;imple, that I per&longs;waded my &longs;elf that had we no o­ <lb/><arrow.to.target n="marg740"></arrow.to.target> <lb/>ther plummet to &longs;ound with, the I&longs;les that advance &longs;o high a­ <lb/>bove Water, had been a &longs;ufficient evidence of the unevenne&longs;&longs;e <lb/>of their bottomes. </s><s>To that Prelate I could &longs;ay that the Moon <lb/>runneth every day along the whole Mediterrane, and yet its <lb/>Waters do not ri&longs;e thereupon &longs;ave onely in the very extream <lb/>bounds of it Ea&longs;tward, and here to us at <emph type="italics"/>Venice.<emph.end type="italics"/> And for tho&longs;e <lb/>that make the Moons temperate heat able to make the Water <lb/>&longs;well, bid them put fire under a Kettle full of Water, and hold <pb xlink:href="040/01/406.jpg" pagenum="384"/>their right hand therein till that the Water by rea&longs;on of the heat <lb/>do ri&longs;e but one &longs;ole inch, and then let them take it out, and <lb/>write off the tumefaction of the Sea. </s><s>Or at lea&longs;t de&longs;ire them to <lb/>&longs;hew you how the Moon doth to rarefie a certain part of the <lb/>Waters, and not the remainder; as for in&longs;tance, the&longs;e here of <lb/><emph type="italics"/>Venice,<emph.end type="italics"/> and not tho&longs;e of <emph type="italics"/>Ancona, Naples, Genova<emph.end type="italics"/>: the truth is <lb/><arrow.to.target n="marg741"></arrow.to.target> <lb/>Poetick Wits are of two kinds, &longs;ome are ready and apt to <lb/>invent Fables, and others di&longs;po&longs;ed and inclined to believe them.</s></p><p type="margin"><s><margin.target id="marg738"></margin.target><emph type="italics"/>An&longs;wers to the <lb/>vanities alledged <lb/>as cau&longs;es of the eb­ <lb/>bing and flowing.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg739"></margin.target>+ Or rather <lb/>&longs;mooth.</s></p><p type="margin"><s><margin.target id="marg740"></margin.target><emph type="italics"/>The I&longs;les are to­ <lb/>kens of the une­ <lb/>venne&longs;&longs;e of the <lb/>bottomes of Seas.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg741"></margin.target><emph type="italics"/>Poetick wits of <lb/>two kinds.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I believe that no man believeth Fables, &longs;o long as he <lb/>knows them to be &longs;o; and of the opinions concerning the cau&longs;es <lb/>of ebbing and flowing, which are many, becau&longs;e I know that of <lb/>one &longs;ingle effect there is but one &longs;ingle cau&longs;e that is true and pri­ <lb/>mary, I under&longs;tand very well, and am certain that but one alone <lb/>at the mo&longs;t can be true, and for all the re&longs;t I am &longs;ure that they are <lb/>fabulous, and fal&longs;e; and its po&longs;&longs;ible that the true one may not be <lb/>among tho&longs;e that have been hitherto produced; nay I verily be­ <lb/>lieve that it is not, for it would be very &longs;trange that the truth <lb/><arrow.to.target n="marg742"></arrow.to.target> <lb/>&longs;hould have &longs;o little light, as that it &longs;hould not be vi&longs;ible among&longs;t <lb/>the umbrages of &longs;o many fal&longs;hoods. </s><s>But this I &longs;hall &longs;ay with the <lb/>liberty that is permitted among&longs;t us, that the introduction of the <lb/>Earths motion, and the making it the cau&longs;e of the ebbing and <lb/>flowing of Tides, &longs;eemeth to me as yet a conjecture no le&longs;&longs;e fa­ <lb/>bulous than the re&longs;t of tho&longs;e that I have heard; and if there <lb/>&longs;hould not be propo&longs;ed to me rea&longs;ons more conformable to natu­ <lb/>ral matters, I would without any more ado proceed to believe <lb/>this to be a &longs;upernatural effect, and therefore miraculous, and <lb/>un&longs;earchable to the under&longs;tandings of men, as infinite others there <lb/>are, that immediately depend on the Omnipotent hand of God. <lb/><arrow.to.target n="marg743"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg742"></margin.target><emph type="italics"/>Truth hath not <lb/>&longs;o little light as <lb/>not to be di&longs;cover­ <lb/>ed amid&longs;t the um­ <lb/>brages of fal­ <lb/>&longs;hoods.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg743"></margin.target>Ari&longs;totle <emph type="italics"/>holdeth <lb/>tho&longs;e effects to be <lb/>miraculous, of <lb/>which the cau&longs;es <lb/>are unknown.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>You argue very prudently, and according to the <lb/>Doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who you know in the beginning of his <lb/>mechanical que&longs;tions referreth tho&longs;e things to a Miracle, the <lb/>cau&longs;es whereof are occult. </s><s>But that the cau&longs;e of the ebbing and <lb/>flowing is one of tho&longs;e that are not to be found out, I believe <lb/>you have no greater proof than onely that you &longs;ee, that among&longs;t <lb/>all tho&longs;e that have hitherto been produced for true cau&longs;es there­ <lb/>of, there is not one wherewith, working by what artifice you <lb/>will, we are able to repre&longs;ent &longs;uch an effect; in regard that nei­ <lb/>ther with the light of the Moon nor of the Sun, nor with <lb/>temperate heats, nor with different profundities, &longs;hall one ever <lb/>artificially make the Water conteined in an immoveable Ve&longs;&longs;el <lb/>to run one way or another, and to ebbe and flow in one place, <lb/>and not in another. </s><s>But if without any other artifice, but with <lb/>the onely moving of the Ve&longs;&longs;el, I am able punctually to repre­ <lb/>&longs;ent all tho&longs;e mutations that are ob&longs;erved in the Sea Water, why <lb/>will you refu&longs;e this rea&longs;on and run to a Miracle?</s></p> <pb xlink:href="040/01/407.jpg" pagenum="385"/><p type="main"><s>SIMP. </s><s>I will run to a Miracle &longs;till, if you do not with &longs;ome <lb/>other natural cau&longs;es, be&longs;ides that of the motion of the Ve&longs;&longs;els of <lb/>the Sea-water di&longs;&longs;wade me from it; for I know that tho&longs;e Ve&longs;&longs;els <lb/>move not, in regard that all the entire Terre&longs;trial Globe is natu­ <lb/>rally immoveable.</s></p><p type="main"><s>SALV. </s><s>But do not you think, that the Terre&longs;trial Globe might <lb/>&longs;upernaturally, that is, by the ab&longs;olute power of God, be made <lb/>moveable? </s><s>SIMP. </s><s>Who doubts it?</s></p><p type="main"><s>SALV. </s><s>Then <emph type="italics"/>Simplicius,<emph.end type="italics"/> &longs;eeing that to make the flux and <lb/>reflux of the Sea, it is nece&longs;&longs;ary to introduce a Miracle, let us <lb/>&longs;uppo&longs;e the Earth to move miraculou&longs;ly, upon the motion of <lb/>which the Sea moveth naturally: and this effect &longs;hall be al&longs;o the <lb/>more &longs;imple, and I may &longs;ay natural, among&longs;t the miraculous o­ <lb/>perations, in that the making a Globe to move round, of which <lb/>kind we &longs;ee many others to move, is le&longs;&longs;e difficult than to make <lb/>an immen&longs;e ma&longs;&longs;e of water go forwards and backwards, in one <lb/>place more &longs;wiftly, and in another le&longs;&longs;e, and to ri&longs;e and fall in <lb/>&longs;ome places more; in &longs;ome le&longs;&longs;e, and in &longs;ome not at all: and to <lb/>work all the&longs;e different effects in one and the &longs;ame Ve&longs;&longs;el that <lb/>containeth it: be&longs;ides, that the&longs;e are &longs;everal Miracles, and that <lb/>is but one onely. </s><s>And here it may be added, that the Miracle <lb/>of making the water to move is accompanied with another, <lb/>namely, the holding of the Earth &longs;tedfa&longs;t again&longs;t impetuosities <lb/>of the water, able to make it &longs;wage &longs;ometimes one way, and <lb/>&longs;ometimes another, if it were not miraculou&longs;ly kept to rights.</s></p><p type="main"><s>SAGR. </s><s>Good <emph type="italics"/>Simplicius,<emph.end type="italics"/> let us for the pre&longs;ent &longs;u&longs;pend our <lb/>judgement about &longs;entencing the new opinion to be vain that <emph type="italics"/>Sal­ <lb/>viatus<emph.end type="italics"/> is about to explicate unto us, nor let us &longs;o ha&longs;tily flye out <lb/>into pa&longs;&longs;ion like the &longs;colding overgrown Haggs: and as for the <lb/>Miracle, we may as well recurre to it when we have done hea­ <lb/>ring the Di&longs;cour&longs;es contained within the bounds of natural cau­ <lb/>&longs;es: though to &longs;peak freely, all the Works of nature, or rather <lb/>of God, are in my judgement miraculous.</s></p><p type="main"><s>SALV. </s><s>And I am of the &longs;ame opinion; nor doth my &longs;aying, <lb/>that the motion of the Earth is the Natural cau&longs;e of the ebbing <lb/>and flowing, hinder, but that the &longs;aid motion of the Earth may <lb/>be miraculous. </s><s>Now rea&longs;&longs;uming our Argument, I apply, and <lb/>once again affirm, that it hath been hitherto unknown how it <lb/>might be that the Waters contained in our Mediterranean <lb/>Straights &longs;hould make tho&longs;e motions, as we &longs;ee it doth, if &longs;o be <lb/>the &longs;aid Straight, or containing Ve&longs;&longs;el were immoveable. </s><s>And <lb/>that which makes the difficulty, and rendreth this matter inextri­ <lb/>cable, are the things which I am about to &longs;peak of, and which <lb/>are daily ob&longs;erved. </s><s>Therefore lend me your attention.</s></p><p type="main"><s>We are here in <emph type="italics"/>Venice,<emph.end type="italics"/> where at this time the Waters are low, </s></p> <pb xlink:href="040/01/408.jpg" pagenum="386"/><p type="main"><s><arrow.to.target n="marg744"></arrow.to.target> <lb/>the Sea calm, the Air tranquil; &longs;uppo&longs;e it to be young flood, <lb/>and that in the term of five or &longs;ix hours the water do ri&longs;e ten <lb/>^{*} hand breadths and more; that ri&longs;e is not made by the fir&longs;t <lb/>water, which was &longs;aid to be rarefied, but it is done by the acce&longs;­ <lb/>&longs;ion of new Water: Water of the &longs;ame &longs;ort with the former, <lb/><arrow.to.target n="marg745"></arrow.to.target> <lb/>of the &longs;ame bracki&longs;hne&longs;s, of the &longs;ame den&longs;ity, of the &longs;ame <lb/>weight: Ships, <emph type="italics"/>Simplicius,<emph.end type="italics"/> float therein as in the former, with­ <lb/>out drawing an hairs breadth more water; a Barrel of this &longs;econd <lb/>doth not weigh one &longs;ingle grain more or le&longs;s than &longs;uch another <lb/>quantity of the other, and retaineth the &longs;ame coldne&longs;s without <lb/>the lea&longs;t alteration: And it is, in a word, Water newly and vi&longs;i­ <lb/><arrow.to.target n="marg746"></arrow.to.target> <lb/>bly entred by the Channels and Mouth of the ^{*} <emph type="italics"/>Lio.<emph.end type="italics"/> Con&longs;ider <lb/>now, how and from whence it came thither. </s><s>Are there happly <lb/>hereabouts any Gulphs or Whirle pools in the bottom of the <lb/>Sea, by which the Earth drinketh in and &longs;pueth out the Water, <lb/>breathing as it were a great and mon&longs;truous Whale? </s><s>But if this <lb/>be &longs;o, how comes it that the Water doth not flow in the &longs;pace of <lb/>&longs;ix hours in <emph type="italics"/>Ancona,<emph.end type="italics"/> in ^{*} <emph type="italics"/>Ragu&longs;a,<emph.end type="italics"/> in <emph type="italics"/>Corfu,<emph.end type="italics"/> where the Tide is ve­ <lb/>ry &longs;mall, and happly unob&longs;ervable? </s><s>Who will invent a way to <lb/>pour new Water into an immoveable Ve&longs;&longs;el, and to make that <lb/>it ri&longs;e onely in one determinate part of it, and in other places <lb/>not? </s><s>Will you &longs;ay, that this new Water is borrowed from the <lb/>Ocean, being brought in by the Straight of <emph type="italics"/>Gibraltar<emph.end type="italics"/>? </s><s>This <lb/>will not remove the doubt afore&longs;aid, but will beget a greater. <lb/></s><s>And fir&longs;t tell me what ought to be the current of that Water, <lb/>that entering at the Straights mouth, is carried in &longs;ix hours to <lb/>the remote&longs;t Creeks of the Mediterrane, at a di&longs;tance of two <lb/>or three thou&longs;and Miles, and that returneth the &longs;ame &longs;pace again <lb/>in a like time at its going back? </s><s>What would Ships do that lye out <lb/>at Sea? </s><s>What would become of tho&longs;e that &longs;hould be in the <lb/>Straights-mouth in a continual precipice of a va&longs;t accumulation of <lb/>Waters, that entering in at a Channel but eight Mile, broad, is to <lb/>give admittance to &longs;o much Water as in &longs;ix hours over-floweth a <lb/>tract of many hundred Miles broad, & thou&longs;ands in length? </s><s>What <lb/>Tygre, what Falcon runneth or flyeth with &longs;o much &longs;wiftne&longs;s? <lb/></s><s>With the &longs;wiftne&longs;s, I &longs;ay, of above 400 Miles an hour. </s><s>The cur­ <lb/>rents run (nor can it be denied) the long-wayes of the Gulph, but <lb/>&longs;o &longs;lowly, as that a Boat with Oars will out-go them, though in­ <lb/>deed not without defalking for their wanderings. </s><s>Moreover, if this <lb/>Water come in at the Straight, the other doubt yet remaineth, <lb/>namely, how it cometh to flow here &longs;o high in a place &longs;o remote, <lb/>without fir&longs;t ri&longs;ing a like or greater height in the parts more adja­ <lb/>cent? </s><s>In a word, I cannot think that either ob&longs;tinacy, or &longs;harpne&longs;s <lb/>of wit can ever find an an&longs;wer to the&longs;e Objections, nor con&longs;e­ <lb/>quently to maintain the &longs;tability of the Earth again&longs;t them, keep­ <lb/>ing within the bounds of Nature.</s></p> <pb xlink:href="040/01/409.jpg" pagenum="387"/><p type="margin"><s><margin.target id="marg744"></margin.target><emph type="italics"/>It is proved <lb/>impo&longs;&longs;ible that <lb/>there &longs;hould natu­ <lb/>rally be any ebbing <lb/>and flowing, the <lb/>Earth being im­ <lb/>moveable.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg745"></margin.target>* Palms.</s></p><p type="margin"><s><margin.target id="marg746"></margin.target>+ <emph type="italics"/>Lio<emph.end type="italics"/> is a fair <lb/>Port in the Vene­ <lb/>tian Gulph, lying <lb/>N. E. from the <lb/>City.</s></p><p type="main"><s>SAGR. </s><s>I have all the while perfectly apprehended you in this; <lb/>and I &longs;tand greedily attending to hear in what manner the&longs;e won­ <lb/>ders may occur without ob&longs;truction from the motion already a&longs;­ <lb/>&longs;igned to the Earth.</s></p><p type="main"><s>SALV. </s><s>The&longs;e effects being to en&longs;ue in con&longs;equence of the mo­ <lb/>tions that naturally agree with the Earth, it is nece&longs;&longs;ary that they <lb/>not onely meet with no impediment or ob&longs;tacle, but that they do <lb/>follow ea&longs;ily, & not onely that they follow with facility, but with <lb/>nece&longs;&longs;ity, &longs;o as that it is impo&longs;&longs;ible that it &longs;hould &longs;ucceed otherwi&longs;e, <lb/>for &longs;uch is the property & condition of things natural & true. </s><s>Ha­ <lb/><arrow.to.target n="marg747"></arrow.to.target> <lb/>ving therefore &longs;hewen the impo&longs;&longs;ibility of rendring a rea&longs;on of the <lb/>motions di&longs;cerned in the Waters, & at the &longs;ame time to maintain <lb/>the immobility of the ve&longs;&longs;el that containeth them: we may proceed <lb/>to enquire, whether the mobility of the Container may produce <lb/>the required effect, in the manner that it is ob&longs;erved to evene.</s></p><p type="margin"><s><margin.target id="marg747"></margin.target><emph type="italics"/>True and natu­ <lb/>ral effects follow <lb/>without difficulty.<emph.end type="italics"/></s></p><p type="main"><s>Two kinds of motions may be conferred upon a Ve&longs;&longs;el, where­ <lb/><arrow.to.target n="marg748"></arrow.to.target> <lb/>by the Water therein contained, may acquire a faculty of flu­ <lb/>ctuating in it, one while towards one &longs;ide, and another while <lb/>towards another; and there one while to ebbe, and another <lb/>while to flow. </s><s>The fir&longs;t is, when fir&longs;t one, and then another of <lb/>tho&longs;e &longs;ides is declined, for then the Water running towards the <lb/>inclining &longs;ide, will alternately be higher and lower, &longs;ometimes <lb/>on one &longs;ide, and &longs;ometimes on another. </s><s>But becau&longs;e that this <lb/>ri&longs;ing and abating is no other than a rece&longs;&longs;ion and acce&longs;&longs;ion to the <lb/>centre of the Earth, &longs;uch a motion cannot be a&longs;cribed to the Cavi­ <lb/>ties of the &longs;aid Earth, that are the Ve&longs;&longs;els which contain the Wa­ <lb/>ters; the parts of which Ve&longs;&longs;el cannot by any what&longs;oever motion <lb/>a&longs;&longs;igned to the Earth, be made to approach or recede from the <lb/><arrow.to.target n="marg749"></arrow.to.target> <lb/>centre of the &longs;ame: The other &longs;ort of motion is, when the <lb/>Ve&longs;&longs;el moveth (without inclining in the lea&longs;t) with a progre&longs;&longs;ive <lb/>motion, not uniform, but that changeth velocity, by &longs;ometimes <lb/>accellerating, and other times retarding: from which di&longs;parity <lb/><arrow.to.target n="marg750"></arrow.to.target> <lb/>it would follow, that the Water contained in the Ve&longs;&longs;el its true, <lb/>but not fixed fa&longs;t to it, as its other &longs;olid parts, but by rea&longs;on of <lb/>its fluidity, as if it were &longs;eparated and at liberty, and not obli­ <lb/>ged to follow all the mutations of its Container, in the retardation <lb/>of the Ve&longs;&longs;el, it keeping part of the <emph type="italics"/>impetus<emph.end type="italics"/> before conceived, <lb/>would run towards the the preceding part, whereupon it would <lb/>of nece&longs;&longs;ity come to ri&longs;e; and on the contrary, if new velocity <lb/>&longs;hould be added to the Ve&longs;&longs;el, with retaining parts of its tardity, <lb/>&longs;taying &longs;omewhat behind, before it could habituate it &longs;elf to the <lb/>new <emph type="italics"/>impetus,<emph.end type="italics"/> it would hang back towards the following part, <lb/>where it would come to ri&longs;e &longs;omething. </s><s>The which effects we <lb/>may plainly declare and make out to the Sen&longs;e by the example of <lb/>one of tho&longs;e &longs;ame Barks yonder, which continually come from <pb xlink:href="040/01/410.jpg" pagenum="388"/><arrow.to.target n="marg751"></arrow.to.target> <lb/>^{*} <emph type="italics"/>Lizza-Fu&longs;ina,<emph.end type="italics"/> laden with fre&longs;h water, for the &longs;ervice of the City. <lb/></s><s>Let us therefore fancy one of tho&longs;e Barks, to come from thence <lb/>with moderate velocity along the Lake, carrying the water gently, <lb/>of which it is full: and then either by running a ground, or by <lb/>&longs;ome other impediment that it &longs;hall meet with, let it be notably <lb/>retarded. </s><s>The water therein contained &longs;hall not, by that means, <lb/>lo&longs;e, as the Bark doth, its pre-conceived <emph type="italics"/>impetus,<emph.end type="italics"/> but retaining <lb/>the &longs;ame, &longs;hall run forwards towards the prow, where it &longs;hall <lb/>ri&longs;e notably, falling as much a &longs;tern. </s><s>But if, on the contrary, <lb/>the &longs;aid Bark, in the mid&longs;t of its &longs;mooth cour&longs;e, &longs;hall have a new <lb/>velocity, with notable augmentation added to it, the water con­ <lb/>tained before it can habituate it &longs;elf thereto, continuing in its <lb/>tardity, &longs;hall &longs;tay behinde, namely a &longs;tern, where of con&longs;e­ <lb/>quence it &longs;hall mount, and abate for the &longs;ame at the prow. </s><s>This <lb/>effect is undoubted and manife&longs;t, and may hourly be experimen­ <lb/>ted; in which I de&longs;ire that for the pre&longs;ent three particulars may <lb/>be noted. </s><s>The flr&longs;t is, that to make the water to ri&longs;e on one <lb/>&longs;ide of the ve&longs;&longs;el, there is no need of new water, nor that it run <lb/>thither, for&longs;aking the other &longs;ide. </s><s>The &longs;econd is, that the water <lb/>in the middle doth not ri&longs;e or fall notably, unle&longs;&longs;e the cour&longs;e of <lb/>the Bark were not before that very &longs;wift, and the &longs;hock or other <lb/>arre&longs;t that held it exceeding &longs;trong and &longs;udden, in which ca&longs;e its <lb/>po&longs;&longs;ible, that not only all the water might run forwards, but <lb/>that the greater part thereof might i&longs;&longs;ue forth of the Bark: and <lb/>the &longs;ame al&longs;o would en&longs;ue, whil&longs;t that being under &longs;ail in a <lb/>&longs;mooth cour&longs;e, a mo&longs;t violent <emph type="italics"/>impetus<emph.end type="italics"/> &longs;hould, upon an in&longs;tant, <lb/>overtake it: But when to its calme motion there is added a mo­ <lb/>derate retardation or incitation, the middle parts (as I &longs;aid) un­ <lb/>ob&longs;ervedly ri&longs;e and fall: and the other parts, according as they <lb/>are neerer to the middle, ri&longs;e the le&longs;&longs;e; and the more remote, <lb/>more. </s><s>The third is, that whereas the parts about the mid&longs;t do <lb/>make little alteration in ri&longs;ing and falling, in re&longs;pect of the wa­ <lb/>ters of the &longs;ides; on the contrary, they run forwards and back­ <lb/>wards very much, in compari&longs;on of the extreams. </s><s>Now, my <lb/>Ma&longs;ters, that which the Bark doth, in re&longs;pect of the water by it <lb/>contained, and that which the water contained doth, in re­ <lb/>&longs;pect of the Bark its container, is the &longs;elf-&longs;ame, to an hair, with <lb/>that which the Mediterranean Ve&longs;&longs;el doth, in re&longs;pect of the wa­ <lb/>ters in it contained, and that which the waters contained do, in <lb/><arrow.to.target n="marg752"></arrow.to.target> <lb/>re&longs;pect of the Mediterranean Ve&longs;&longs;el their container. </s><s>It follow­ <lb/>eth now that we demon&longs;trate how, and in what manner it is true, <lb/>that the Mediterrane, and all the other Straits; and in a word, <lb/>all the parts of the Earth do all move, with a motion notably <lb/>uneven, though no motion that is not regular and uniforme, is <lb/>thereby a&longs;&longs;igned to all the &longs;aid Globe taken collectively.</s></p> <pb xlink:href="040/01/411.jpg" pagenum="389"/><p type="margin"><s><margin.target id="marg748"></margin.target><emph type="italics"/>Two &longs;orts of <lb/>motions of the con­ <lb/>taining Ve&longs;&longs;el, may <lb/>make the contai­ <lb/>ned water to ri&longs;e <lb/>and fall.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg749"></margin.target><emph type="italics"/>The Cavities of <lb/>the Earth cannot <lb/>approach or go far­ <lb/>ther from the cen­ <lb/>tre of the &longs;ame.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg750"></margin.target><emph type="italics"/>The progpe&longs;&longs;ive <lb/>and uneven motion <lb/>may make the wa­ <lb/>ter contained in a <lb/>Ve&longs;&longs;el to run to <lb/>and fro.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg751"></margin.target>+ A Town ly­ <lb/>ing S. E. of <emph type="italics"/>Venice<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg752"></margin.target><emph type="italics"/>The parts of the <lb/>terre&longs;trial Globe <lb/>accelerate and re­ <lb/>tard in their moti­ <lb/>on.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>This Propo&longs;ition, at fir&longs;t &longs;ight to me, that am neither <lb/>Geometrician nor A&longs;tronomer, hath the appearance of a very <lb/>great Paradox; and if it &longs;hould be true, that the motion of the <lb/><emph type="italics"/>whole,<emph.end type="italics"/> being regular, that of the parts, which are all united to <lb/>their <emph type="italics"/>whole,<emph.end type="italics"/> may be irregular, the Paradox will overthrow the <lb/>Axiome that affirmeth, <emph type="italics"/>Eandem e&longs;&longs;e rationem totius & par­ <lb/>tium.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I will demon&longs;trate my Paradox, and leave it to your <lb/>care, <emph type="italics"/>Simplicius,<emph.end type="italics"/> to defend the Axiome from it, or el&longs;e to re­ <lb/>concile them; and my demon&longs;tration &longs;hall be &longs;hort and fa­ <lb/>miliar, depending on the things largely handled in our prece­ <lb/>dent conferences, without introducing the lea&longs;t &longs;yllable, in fa­ <lb/>vour of the flux and reflux.</s></p><p type="main"><s>We have &longs;aid, that the motions a&longs;&longs;igned to the Terre&longs;trial <lb/><arrow.to.target n="marg753"></arrow.to.target> <lb/>Globe are two, the fir&longs;t Annual, made by its centre about the <lb/>circumference of the Grand Orb, under the Ecliptick, according <lb/>to the order of the Signes, that is, from We&longs;t to Ea&longs;t; the other <lb/>made by the &longs;aid Globe revolving about its own centre in twenty <lb/>four hours; and this likewi&longs;e from We&longs;t to Ea&longs;t: though a­ <lb/>bout an Axis &longs;omewhat inclined, and not equidi&longs;tant from that <lb/>of the Annual conver&longs;ion. </s><s>From the mixture of the&longs;e two mo­ <lb/>tions, each of it &longs;elf uniform, I &longs;ay, that there doth re&longs;ult an <lb/>uneven and deformed motion in the parts of the Earth. </s><s>Which, <lb/>that it may the more ea&longs;ily be under&longs;tood, I will explain, by <lb/>drawing a Scheme thereof. </s><s>And fir&longs;t, about the centre A [<emph type="italics"/>in <lb/>Fig. </s><s>1. of this Dialogue<emph.end type="italics"/>] I will de&longs;cribe the circumference of <lb/><arrow.to.target n="marg754"></arrow.to.target> <lb/>the Grand Orb B C, in which any point being taken, as B, <lb/>about it as a centre we will de&longs;cribe this le&longs;&longs;er circle D E F G, <lb/>repre&longs;enting the Terre&longs;trial Globe; the which we will &longs;uppo&longs;e <lb/>to run thorow the whole circumference of the Grand Orb, with <lb/>its centre B, from the We&longs;t towards the Ea&longs;t, that is, from the <lb/>part B towards C; and moreover we will &longs;uppo&longs;e the Terre­ <lb/>&longs;trial Globe to turn about its own centre B likewi&longs;e from We&longs;t <lb/>to Ea&longs;t, that is, according to the &longs;ucce&longs;&longs;ion of the points <lb/>D E F G, in the &longs;pace of twenty four hours. </s><s>But here we <lb/>ought carefully to note, that a circle turning round upon its <lb/>own centre, each part of it mu&longs;t, at different times, move with <lb/>contrary motions: the which is manife&longs;t, con&longs;idering that whil&longs;t <lb/>the parts of the circumference, about the point D move to the <lb/>left hand, that is, towards E, the oppo&longs;ite parts that are about F, <lb/>approach to the right hand, that is, towards G; &longs;o that when <lb/>the parts D &longs;hall be in F, their motion &longs;hall be contrary to what <lb/>it was before. </s><s>when it was in D. Furthermore, the &longs;ame time <lb/>that the parts E de&longs;cend, if I may &longs;o &longs;peak, towards F, tho&longs;e in <lb/>G a&longs;cend towards D. </s><s>It being therefore pre&longs;uppo&longs;ed, that <pb xlink:href="040/01/412.jpg" pagenum="390"/><arrow.to.target n="marg755"></arrow.to.target> <lb/>there are &longs;uch contrarieties of motions in the parts of the Terre­ <lb/>&longs;trial Surface, whil&longs;t it turneth round upon its own centre, it is <lb/>nece&longs;&longs;ary, that in conjoyning this Diurnal Motion, with the other <lb/>Annual, there do re&longs;ult an ab&longs;olute motion for the parts of the <lb/>&longs;aid Terre&longs;trial Superficies, one while very accelerate, and ano­ <lb/>ther while as &longs;low again. </s><s>The which is manife&longs;t, con&longs;idering <lb/>fir&longs;t the parts about D, the ab&longs;olute motion of which &longs;hall be <lb/>extream &longs;wift, as that which proceedeth from two motions made <lb/>both one way, namely, towards the left hand; the fir&longs;t of <lb/>which is part of the Annual Motion, common to all the parts of <lb/>the Globe, the other is that of the &longs;aid point D., carried likewi&longs;e <lb/>to the left, by the Diurnal Revolution; &longs;o that, in this ca&longs;e, the <lb/>Diurnal motion increa&longs;eth and accelerateth the Annual. </s><s>The <lb/>contrary to which happeneth in the oppo&longs;ite part F, which, whil&longs;t <lb/>it is by the common annual motion carried, together with the <lb/>whole Globe, towards the left, it happeneth to be carried by the <lb/>Diurnal conver&longs;ion al&longs;o towards the right: &longs;o that the Diur­ <lb/>nal motion by that means detracteth from the Annual, where­ <lb/>upon the ab&longs;olute motion, re&longs;ulting from the compo&longs;ition of both <lb/>the other, is much retarded. </s><s>Again, about the points E and G, <lb/>the ab&longs;olute motion becometh in a manner equal to the &longs;imple <lb/>Annual one, in regard that little or nothing increa&longs;eth or dimi­ <lb/>ni&longs;heth it, as not tending either to the left hand, or to the right, <lb/>but downwards and upwards. </s><s>We will conclude therefore, that <lb/>like as it is true, that the motion of the whole Globe, and of <lb/>each of its parts, would be equal and uniforme, in ca&longs;e they did <lb/>move with one &longs;ingle motion, whether it were the meer Annual, <lb/>or the &longs;ingle Diurnal Revolution, &longs;o it is requi&longs;ite, that mixing <lb/>tho&longs;e two motions together, there do re&longs;ult thence for the parts <lb/>of the &longs;aid Globe irregular motions, one while accelerated, and <lb/>another while retarded, by means of the additions or &longs;ub&longs;tracti­ <lb/>ons of the Diurnal conver&longs;ion from the annual circulation. </s><s>So <lb/>that, if it be true (and mo&longs;t true it is, as experience proves) that <lb/>the acceleration and retardation of the motion of the Ve&longs;­ <lb/>&longs;el, makes water contained therein to run to and again the long <lb/>waves of it, and to ri&longs;e and fall in its extreames, who will make <lb/>&longs;cruple of granting, that the &longs;aid effect may, nay ought to &longs;uc­ <lb/>ceed in the Sea-waters, contained within their Ve&longs;&longs;els, &longs;ubject to <lb/>&longs;uch like alterations, and e&longs;pecially in tho&longs;e that di&longs;tend them­ <lb/>&longs;elves long-wayes from We&longs;t to Ea&longs;t, which is the cour&longs;e that <lb/><arrow.to.target n="marg756"></arrow.to.target> <lb/>the motion of tho&longs;e &longs;ame Ve&longs;&longs;els &longs;teereth? </s><s>Now this is the <lb/>mo&longs;t potent and primary cau&longs;e of the ebbing and flowing, with­ <lb/>out the which no &longs;uch effect would en&longs;ue. </s><s>But becau&longs;e the par­ <lb/>ticular accidents are many and various, that in &longs;everal places and <lb/>times are ob&longs;erved, which mu&longs;t of nece&longs;&longs;ity have dependance <pb xlink:href="040/01/413.jpg" pagenum="391"/>on other different concomitant cau&longs;es, although they ought all <lb/>to have connexion with the primary; therefore it is convenient <lb/>that we propound and examine the &longs;everal accidents that may <lb/>be the cau&longs;es of &longs;uch different effects.</s></p><p type="margin"><s><margin.target id="marg753"></margin.target><emph type="italics"/>Demon&longs;trations <lb/>how the parts of <lb/>the terre&longs;triall <lb/>Globe accelerats <lb/>and ratard.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg754"></margin.target><emph type="italics"/>The parts of a <lb/>Circle regularly <lb/>moved about its <lb/>own centre move in <lb/>divers times with <lb/>contrary motions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg755"></margin.target><emph type="italics"/>The mixture of <lb/>the two motions <lb/>annnal and diur­ <lb/>nal, cau&longs;eth the <lb/>inequality in the <lb/>motion of the parts <lb/>of the terre&longs;trial <lb/>Globe.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg756"></margin.target><emph type="italics"/>The mo&longs;t potent <lb/>and primary cau&longs;e <lb/>of the ebbing and <lb/>flowing.<emph.end type="italics"/></s></p><p type="main"><s>The fir&longs;t of which is, that when ever the water, by means of a <lb/><arrow.to.target n="marg757"></arrow.to.target> <lb/>notable retardation or acceleration of the motion of the Ve&longs;&longs;el, <lb/>its container, &longs;hall have acquired a cau&longs;e of running towards this <lb/><arrow.to.target n="marg758"></arrow.to.target> <lb/>or that extream, and &longs;hall be rai&longs;ed in the one, and abated in the <lb/><arrow.to.target n="marg759"></arrow.to.target> <lb/>other, it &longs;hall not neverthele&longs;&longs;e continue, for any time in that <lb/>&longs;tate, when once the primary cau&longs;e is cea&longs;ed: but by vertue of <lb/>its own gravity and natural inclination to level and grow, even it <lb/>&longs;hall &longs;peedily return backwards of its own accord, and, as being <lb/>grave and fluid, &longs;hall not only move towards <emph type="italics"/>Æquilibrium<emph.end type="italics"/>; but <lb/>being impelled by its own <emph type="italics"/>impetus,<emph.end type="italics"/> &longs;hall go beyond it, ri&longs;ing in <lb/>the part, where before it was lowe&longs;t; nor &longs;hall it &longs;tay here, but <lb/>returning backwards anew, with more reiterated reciprocations of <lb/>its undulations, it &longs;hall give us to know, that it will not from a <lb/>velocity of motion, once conceived, reduce it &longs;elf, in an in&longs;tant, <lb/>to the privation thereof, and to the &longs;tate of re&longs;t, but will &longs;ucce&longs;­ <lb/>&longs;ively, by decrea&longs;ing a little and a little, reduce it &longs;elf unto the <lb/>&longs;ame, ju&longs;t in the &longs;ame manner as we &longs;ee a weight hanging at a <lb/>cord, after it hath been once removed from its &longs;tate of re&longs;t, that <lb/>is, from its perpendicularity, of its own accord, to return thither <lb/>and &longs;ettle it &longs;elf, but not till &longs;uch time as it &longs;hall have often <lb/>pa&longs;t to one &longs;ide, and to the other, with its reciprocall vi­ <lb/>brations.</s></p><p type="margin"><s><margin.target id="marg757"></margin.target><emph type="italics"/>Sundry accidents <lb/>that happen in the <lb/>ebbings & flowings<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg758"></margin.target><emph type="italics"/>The first acci­ <lb/>dent.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg759"></margin.target><emph type="italics"/>The Water rai­ <lb/>&longs;ed in one end of <lb/>the Ve&longs;&longs;el return­ <lb/>eth of its &longs;elf to<emph.end type="italics"/> <lb/>Æquilibrium.</s></p><p type="main"><s>The &longs;econd accident to be ob&longs;erved is, that the before­ <lb/><arrow.to.target n="marg760"></arrow.to.target> <lb/>declared reciprocations of motion come to be made and repeated <lb/>with greater or le&longs;&longs;er frequency, that is, under &longs;horter or longer <lb/>times, according to the different lengths of the Ve&longs;&longs;els contain­ <lb/>ing the waters; &longs;o that in the &longs;horter &longs;paces the reciprocati­ <lb/>ons are more frequent, and in the longer more rare: ju&longs;t as in <lb/>the former example of pendent bodies, the vibrations of tho&longs;e <lb/>that are hanged to longer cords are &longs;een to be le&longs;&longs;e frequent, <lb/>than tho&longs;e of them that hang at &longs;horter &longs;trings.</s></p><p type="margin"><s><margin.target id="marg760"></margin.target><emph type="italics"/>In the &longs;horter <lb/>Vi&longs;&longs;els the undula­ <lb/>tions of waters are <lb/>more frequent.<emph.end type="italics"/></s></p><p type="main"><s>And here, for a third ob&longs;ervation, it is to be noted, that not <lb/><arrow.to.target n="marg761"></arrow.to.target> <lb/>onely the greater or le&longs;&longs;er length of the Ve&longs;&longs;el is a cau&longs;e that <lb/>the water maketh its reciprocations under different times; but <lb/>the greater or le&longs;&longs;er profundity worketh the &longs;ame effect. </s><s>And <lb/>it happeneth, that of waters contained in receptacles of equall <lb/>length, but of unequal depth, that which &longs;hall be the deepe&longs;t, <lb/>maketh its undulations under &longs;horter times, and the reciprocati­ <lb/>ons of the &longs;hallower waters are le&longs;&longs;e frequent.</s></p><p type="margin"><s><margin.target id="marg761"></margin.target><emph type="italics"/>The greater <lb/>profundity maketh <lb/>the undulations of <lb/>waters more fre­ <lb/>quent.<emph.end type="italics"/></s></p><p type="main"><s>Fourthly, there are two effects worthy to be noted, and di­ <lb/>ligently ob&longs;erved, which the water worketh in tho&longs;e its vibra­ <pb xlink:href="040/01/414.jpg" pagenum="392"/><arrow.to.target n="marg762"></arrow.to.target> <lb/>tions; the one is its ri&longs;ing and falling alternately towards the <lb/>one and other extremity; the other is its moving and running, to <lb/>&longs;o &longs;peak, Horizontally forwards and backwards. </s><s>Which two dif­ <lb/>ferent motions differently re&longs;ide in divers parts of the Water: <lb/>for its extream parts are tho&longs;e which mo&longs;t eminently ri&longs;e and fall; <lb/>tho&longs;e in the middle never ab&longs;olutely moving upwards and down­ <lb/>wards, of the re&longs;t &longs;ucce&longs;&longs;ively tho&longs;e that are neere&longs;t to the ex­ <lb/>treams ri&longs;e and fall proportionally more than the remote: but on <lb/>the contrary, touching the other progre&longs;&longs;ive motion forwards <lb/>and backwards, the middle parts move notably, going and re­ <lb/>turning, and the waters that are in the extream parts gain no <lb/>ground at all; &longs;ave onely in ca&longs;e that in their ri&longs;ing they over­ <lb/>flow their banks, and break forth of their fir&longs;t channel and re­ <lb/>ceptacle; but where there is the ob&longs;tacle of banks to keep them <lb/>in, they onely ri&longs;e and fall; which yet hindereth not the waters <lb/>in the middle from fluctuating to and again; which likewi&longs;e <lb/>the other parts do in proportion, undulating more or le&longs;&longs;e, <lb/>according as they are neerer or more remote from the middle. <lb/><arrow.to.target n="marg763"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg762"></margin.target><emph type="italics"/>Water ri&longs;eth & <lb/>falleth in the ex­ <lb/>tream parts of the <lb/>Ve&longs;&longs;el, and runneth <lb/>to and fro in the <lb/>midst.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg763"></margin.target><emph type="italics"/>An accident of <lb/>the Earths motions <lb/>impo&longs;&longs;ible to be re­ <lb/>duced to practice <lb/>by art.<emph.end type="italics"/></s></p><p type="main"><s>The fifth particular accident ought the more attentively to be <lb/>con&longs;idered, in that it is impo&longs;&longs;ible to repre&longs;ent the effect there­ <lb/>of by an experiment or example; and the accident is this. </s><s>In <lb/>the ve&longs;&longs;els by us framed with art, and moved, as the above­ <lb/>named Bark, one while more, and another while le&longs;&longs;e &longs;wiftly, <lb/>the acceleration and retardation is imparted in the &longs;ame manner <lb/>to all the ve&longs;&longs;el, and to every part of it; &longs;o that whil&longs;t <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> the <lb/>Bark forbeareth to move, the parts precedent retard no more <lb/>than the &longs;ub&longs;equent, but all equally partake of the &longs;ame re­ <lb/>tardment; and the &longs;elf-&longs;ame holds true of the acceleration, <lb/>namely, that conferring on the Bark a new cau&longs;e of grea­ <lb/>ter velocity, the Prow and Poop both accelerate in one and <lb/>the &longs;ame manner. </s><s>But in huge great ve&longs;&longs;els, &longs;uch as are the very <lb/>long bottomes of Seas, albeit they al&longs;o are no other than cer­ <lb/>tain cavities made in the &longs;olidity of the Terre&longs;trial Globe, <lb/>it alwayes admirably happeneth, that their extreams do not <lb/>unitedly equall, and at the &longs;ame moments of time increa&longs;e <lb/>and dimini&longs;h their motion, but it happeneth that when one of its <lb/>extreames hath, by vertue of the commixtion of the two <lb/>Motions, Diurnal, and Annual, greatly retarded its velocity, <lb/>the other extream is animated with an extream &longs;wift motion. <lb/></s><s>Which for the better under&longs;tanding of it we will explain, rea&longs;­ <lb/>&longs;uming a Scheme like to the former; in which if we do but &longs;up­ <lb/>po&longs;e a tract of Sea to be long, <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> a fourth part, as is the arch <lb/>B C [<emph type="italics"/>in Fig.<emph.end type="italics"/> 2.] becau&longs;e the parts B are, as hath been already <lb/>declared, very &longs;wift in motion, by rea&longs;on of the union of the <lb/>two motions diurnal and annual, towards one and the &longs;ame way, <pb xlink:href="040/01/415.jpg" pagenum="393"/>but the part C at the &longs;ame time is retarded in its motion, as be <lb/>ing deprived of the progre&longs;&longs;ion dependant on the diurnal motion: <lb/>If we &longs;uppo&longs;e, I &longs;ay, a tract of Sea as long as the arch B C, we <lb/>have already &longs;een, that its extreams &longs;hall move in the &longs;ame time <lb/>with great inequality. </s><s>And extreamly different would the velo­ <lb/>cities of a tract of Sea be that is in length a &longs;emicircle, and pla­ <lb/>ced in the po&longs;ition B C D, in regard that the extream B would <lb/>be in a mo&longs;t accelerate motion, and the other D, in a mo&longs;t &longs;low <lb/>one; and the intermediate parts towards C, would be in a <lb/>moderate motion. </s><s>And according as the &longs;aid tracts of Sea &longs;hall <lb/>be &longs;horter, they &longs;hall le&longs;&longs;e participate of this extravagant acci­ <lb/>dent, of being in &longs;ome hours of the day with their parts diver&longs;ly <lb/>affected by velocity and tardity of motion. </s><s>So that, if, as in the fir&longs;t <lb/>ca&longs;e, we &longs;ee by experience that the acceleration and retardation, <lb/>though equally imparted to all the parts of the conteining Ve&longs;&longs;el, <lb/>is the cau&longs;e that the water contained, fluctuates too and again, what <lb/>may we think would happen in a Ve&longs;&longs;el &longs;o admirably di&longs;po&longs;ed, <lb/>that retardation and acceleration of motion is very unequally <lb/>contributed to its parts? </s><s>Certainly we mu&longs;t needs grant that <lb/>greater and more wonderful cau&longs;es of the commotions in the <lb/>Water ought to be looked for. </s><s>And though it may &longs;eem im­ <lb/>po&longs;&longs;ible to &longs;ome, that in artificial Machines and Ve&longs;&longs;els we &longs;hould <lb/>be able to experiment the effects of &longs;uch an accident; yet ne­ <lb/>verthele&longs;&longs;e it is not ab&longs;olutely impo&longs;&longs;ible to be done; and I have <lb/>by me the model of an Engine, in which the effect of the&longs;e admi­ <lb/>rable commixtions of motions may be particularly ob&longs;erved. </s><s>But <lb/>as to what concerns our pre&longs;ent purpo&longs;e, that which you may <lb/>have hitherto comprehended with your imagination may &longs;uf­ <lb/>fice.</s></p><p type="main"><s>SAGR. </s><s>I for my own particular very well conceive that this <lb/>admirable accident ought nece&longs;&longs;arily to evene in the Straights of <lb/>Seas, and e&longs;pecially in tho&longs;e that di&longs;tend them&longs;elves for a great <lb/>length from We&longs;t to Ea&longs;t; namely according to the cour&longs;e of <lb/>the motions of the Terre&longs;trial Globe; and as it is in a certain <lb/>manner unthought of, and without a pre&longs;ident among the moti­ <lb/>ons po&longs;&longs;ible to be made by us, &longs;o it is not hard for me to believe, <lb/>that effects may be derived from the &longs;ame, which are not to be i­ <lb/>mitated by our artificial experiments.</s></p><p type="main"><s>SALV. </s><s>The&longs;e things being declared, it is time that we pro­ <lb/>ceed to examine the particular accidents, which, together with <lb/>their diver&longs;ities, are ob&longs;erved by experience in the ebbing and <lb/>flowing of the waters. </s><s>And fir&longs;t we need not think it hard to </s></p><p type="main"><s><arrow.to.target n="marg764"></arrow.to.target> <lb/>gue&longs;&longs;e whence it happeneth, that in Lakes, Pooles, and al&longs;o in the <lb/>le&longs;&longs;er Seas there is no notable flux and reflux; the which hath <lb/>two very &longs;olid rea&longs;ons. </s><s>The one is, that by rea&longs;on of the &longs;hort­ <pb xlink:href="040/01/416.jpg" pagenum="394"/><arrow.to.target n="marg765"></arrow.to.target> <lb/>ne&longs;&longs;e of the Ve&longs;&longs;el, in its acquiring in &longs;everal hours of the day <lb/>&longs;everal degrees of velocity, they are with very little difference <lb/>acquired by all its parts; for as well the precedent as the &longs;ub&longs;e­ <lb/>quent, that is to &longs;ay, both the Ea&longs;tern and We&longs;tern parts, do <lb/>accelerate and retard almo&longs;t in the &longs;ame manner; and withal <lb/>making that alteration by little and little, and not by giving the <lb/>motion of the conteining Ve&longs;&longs;el a &longs;udden check, and retard­ <lb/>ment, or a &longs;udden and great impul&longs;e or acceleration; both it <lb/>and all its parts, come to be gently and equally impre&longs;&longs;ed with <lb/>the &longs;ame degrees of velocity; from which uniformity it follow­ <lb/>eth, that al&longs;o the conteined water with but &longs;mall re&longs;i&longs;tance and <lb/>oppo&longs;ition, receiveth the &longs;ame impre&longs;&longs;ions, and by con&longs;equence <lb/>doth give but very ob&longs;cure &longs;ignes of its ri&longs;ing or falling, or of its <lb/>running towards one part or another. </s><s>The which effect is likewi&longs;e <lb/>manife&longs;tly to be &longs;een in the little artificial Ve&longs;&longs;els, wherein the <lb/>contained water doth receive the &longs;elf &longs;ame impre&longs;&longs;ions of veloci­ <lb/>ty; when ever the acceleration and retardation is made by gentle <lb/>and uniform proportion. </s><s>But in the Straights and Bays that for a <lb/>great length di&longs;tend them&longs;elves from Ea&longs;t to We&longs;t, the accele­ <lb/>ration and retardation is more notable and more uneven, for <lb/>that one of its extreams &longs;hall be much retarded in motion, and <lb/>the other &longs;hall at the &longs;ame time move very &longs;wiftly: The reci­ <lb/>procal libration or levelling of the water proceeding from the <emph type="italics"/>im­ <lb/>petus<emph.end type="italics"/> that it had conceived from the motion of its container. <lb/></s><s>The which libration, as hath been noted, hath its undulations <lb/>very frequent in &longs;mall Ve&longs;&longs;els; from whence en&longs;ues, that though <lb/>there do re&longs;ide in the Terre&longs;trial motions the cau&longs;e of confer­ <lb/>ring on the waters a motion onely from twelve hours to twelve <lb/>hours, for that the motion of the conteining Ve&longs;&longs;els do ex­ <lb/>treamly accelerate and extreamly retard but once every day, <lb/>and no more; yet neverthele&longs;&longs;e this &longs;ame &longs;econd cau&longs;e depend­ <lb/>ing on the gravity of the water which &longs;triveth to reduce it &longs;elf to <lb/>equilibration, and that according to the &longs;hortne&longs;&longs;e of the Ve&longs;­ <lb/>&longs;el hath its reciprocations of one, two, three, or more hours, this <lb/>intermixing with the fir&longs;t, which al&longs;o it &longs;elf in &longs;mall Ve&longs;&longs;els is <lb/>very little, it becommeth upon the whole altogether in&longs;en&longs;ible. <lb/></s><s>For the primary cau&longs;e, which hath the periods of twelve hours, <lb/>having not made an end of imprinting the precedent commoti­ <lb/>on, it is overtaken and oppo&longs;ed by the other &longs;econd, depen­ <lb/>dant on the waters own weight, which according to the brevity <lb/>and profundity of the Ve&longs;&longs;el, hath the time of its undulations of <lb/>one, two, three, four, or more hours; and this contending <lb/>with the other former one, di&longs;turbeth and removeth it, not per­ <lb/>mitting it to come to the height, no nor to the half of its moti­ <lb/>on; and by this conte&longs;tation the evidence of the ebbing and <pb xlink:href="040/01/417.jpg" pagenum="395"/>flowing is wholly annihilated, or at lea&longs;t very much ob&longs;cured. <lb/></s><s>I pa&longs;&longs;e by the continual alteration of the air, which di&longs;quieting <lb/>the water, permits us not to come to a certainty, whether any, <lb/>though but &longs;mall, encrea&longs;e or abatement of half an inch, or <lb/>le&longs;&longs;e, do re&longs;ide in the Straights, or receptacles of water not a­ <lb/>bove a degree or two in length.</s></p><p type="margin"><s><margin.target id="marg764"></margin.target><emph type="italics"/>Rea&longs;ons renew­ <lb/>ed of the particu­ <lb/>lar accidents ob­ <lb/>&longs;erved in the eb­ <lb/>bings and flowings.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg765"></margin.target><emph type="italics"/>Second cau&longs;es <lb/>why in &longs;mall Seas <lb/>and in Lakes there <lb/>are no ebbings and <lb/>flowings.<emph.end type="italics"/></s></p><p type="main"><s>I come in the &longs;econd place to re&longs;olve the que&longs;tion, why, there <lb/><arrow.to.target n="marg766"></arrow.to.target> <lb/>not re&longs;iding any vertue in the primary principle of commoving <lb/>the waters, &longs;ave onely every twelve hours, that is to &longs;ay, once <lb/>by the greate&longs;t velocity, and once by the greate&longs;t tardity of <lb/>motion; the ebbings and flowings &longs;hould yet neverthele&longs;&longs;e ap­ <lb/>pear to be every &longs;ix hours. </s><s>To which is an&longs;wered, that this de­ <lb/>termination cannot any wayes be taken from the primary cau&longs;e <lb/>onely; but there is a nece&longs;&longs;ity of introducing the &longs;econdary cau­ <lb/>&longs;es, as namely the greater or le&longs;&longs;e length of the Ve&longs;&longs;els, and <lb/>the greater or le&longs;&longs;e depth of the waters in them conteined. <lb/></s><s>Which cau&longs;es although they have not any operation in the moti­ <lb/>ons of the waters, tho&longs;e operations belonging to the &longs;ole prima­ <lb/>ry cau&longs;e, without which no ebbing or flowing would happen, <lb/>yet neverthele&longs;&longs;e they have a principal &longs;hare in determining the <lb/>times or periods of the reciprocations, and herein their influ­ <lb/>ence is &longs;o powerful, that the primary cau&longs;e mu&longs;t of force give <lb/>way unto them. </s><s>The period of &longs;ix hours therefore is no more <lb/>proper or natural than tho&longs;e of other intervals of times, though <lb/>indeed its the mo&longs;t ob&longs;erved, as agreeing with our Mediterrane, <lb/>which was the onely Sea that for many Ages was navigated: <lb/>though neither is that period ob&longs;erved in all its parts; for <lb/>that in &longs;ome more angu&longs;t places, &longs;uch as are the <emph type="italics"/>Helle­ <lb/>&longs;pont,<emph.end type="italics"/> and the <emph type="italics"/>Ægean<emph.end type="italics"/> Sea, the periods are much &longs;horter, <lb/>and al&longs;o very divers among&longs;t them&longs;elves; for which diver­ <lb/>&longs;ities, and their cau&longs;es incomprehen&longs;ible to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> &longs;ome <lb/>&longs;ay, that after he had a long time ob&longs;erved it upon &longs;ome <lb/>cliffes of <emph type="italics"/>Negropont,<emph.end type="italics"/> being brought to de&longs;peration, he threw <lb/>him&longs;elf into the adjoyning <emph type="italics"/>Euripus,<emph.end type="italics"/> and voluntarily drowned <lb/>him&longs;elf.</s></p><p type="margin"><s><margin.target id="marg766"></margin.target><emph type="italics"/>The rea&longs;on gi­ <lb/>ven, why the eb­ <lb/>bings and flowings, <lb/>for the mo&longs;t part, <lb/>are every &longs;ix <lb/>hours.<emph.end type="italics"/></s></p><p type="main"><s>In the third place we have the rea&longs;on ready at hand, whence <lb/><arrow.to.target n="marg767"></arrow.to.target> <lb/>it commeth to pa&longs;&longs;e, that &longs;ome Seas, although very long, as is <lb/>the Red Sea, are almo&longs;t altogether exempt from Tides, which <lb/>happeneth becau&longs;e their length extendeth not from Ea&longs;t to <lb/>We&longs;t, but rather tran&longs;ver&longs;ly from the Southea&longs;t to the North­ <lb/>we&longs;t; but the motions of the Earth going from We&longs;t to Ea&longs;t; <lb/>the impul&longs;es of the water, by that means, alwayes happen to fall <lb/>in the Meridians, and do not move from parallel to parallel; <lb/>in&longs;omuch that in the Seas that extend them&longs;elves athwart to­ <lb/>wards the Poles, and that the contrary way are narrow, there is <pb xlink:href="040/01/418.jpg" pagenum="396"/>no cau&longs;e of ebbing and flowing, &longs;ave onely by the participation <lb/>of another Sea, wherewith it hath communication, that is &longs;ub­ <lb/>ject to great commotions. <lb/><arrow.to.target n="marg768"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg767"></margin.target><emph type="italics"/>The cau&longs;e why <lb/>&longs;ome Seas, though <lb/>very long, &longs;uffer <lb/>no ebbing and <lb/>flowing.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg768"></margin.target><emph type="italics"/>Ebbings and <lb/>flowings why grea­ <lb/>te&longs;t in the extre­ <lb/>mities of gulphs, <lb/>and lea&longs;t in the <lb/>middle parts.<emph.end type="italics"/></s></p><p type="main"><s>In the fourth place we &longs;hall very ea&longs;ily find out the rea&longs;on <lb/>why the fluxes and refluxes are greate&longs;t, as to the waters ri&longs;ing <lb/>and falling in the utmo&longs;t extremities of Gulphs, and lea&longs;t in the <lb/>intermediate parts; as daily experience &longs;heweth here in <emph type="italics"/>Venice,<emph.end type="italics"/> <lb/>lying in the farther end of the <emph type="italics"/>Adriatick<emph.end type="italics"/> Sea, where that diffe­ <lb/>rence commonly amounts to five or &longs;ix feet; but in the places <lb/>of the Mediterrane, far di&longs;tant from the extreams, that mutati­ <lb/>on is very &longs;mall, as in the I&longs;les of <emph type="italics"/>Cor&longs;ica<emph.end type="italics"/> and <emph type="italics"/>Sardinnia,<emph.end type="italics"/> and <lb/>in the Strands of <emph type="italics"/>Rome<emph.end type="italics"/> and <emph type="italics"/>Ligorne,<emph.end type="italics"/> where it exceeds not half a <lb/>foot; we &longs;hall under&longs;tand al&longs;o, why on the contrary, where <lb/>the ri&longs;ings and fallings are &longs;mall, the cour&longs;es and recour&longs;es are <lb/>great: I &longs;ay it is an ea&longs;ie thing to under&longs;tand the cau&longs;es of the&longs;e <lb/>accidents, &longs;eeing that we meet with many manife&longs;t occurrences <lb/>of the &longs;ame nature in every kind of Ve&longs;&longs;el by us artificially com­ <lb/>po&longs;ed, in which the &longs;ame effects are ob&longs;erved naturally to fol­ <lb/>low upon our moving it unevenly, that is, one while fa&longs;ter, and <lb/>another while &longs;lower.</s></p><p type="main"><s><arrow.to.target n="marg769"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg769"></margin.target><emph type="italics"/>Why in narrow <lb/>places the cour&longs;e <lb/>of the waters is <lb/>more &longs;wift than in <lb/>larger.<emph.end type="italics"/></s></p><p type="main"><s>Moreover, con&longs;idering in the fifth place, that the &longs;ame <lb/>quantity of Water being moved, though but gently, in a &longs;patious <lb/>Channel, comming afterwards to go through a narrow pa&longs;&longs;age, <lb/>will of nece&longs;&longs;ity run, with great violence, we &longs;hall not finde it hard <lb/>to comprehend the cau&longs;e of the great Currents that are made <lb/>in the narrow Channel that &longs;eparateth <emph type="italics"/>Calabria<emph.end type="italics"/> from <emph type="italics"/>Sicilia:<emph.end type="italics"/> <lb/>for that all the Water that, by the &longs;paciou&longs;ne&longs;&longs;e of the I&longs;le, <lb/>and by the <emph type="italics"/>Ionick<emph.end type="italics"/> Gulph, happens to be pent in the Ea&longs;tern <lb/>part of the Sea, though it do in that, by rea&longs;on of its largene&longs;s, <lb/>gently de&longs;cend towards the We&longs;t, yet neverthele&longs;&longs;e, in that it <lb/>is pent up in the <emph type="italics"/>Bo&longs;phorus,<emph.end type="italics"/> it floweth with great violence be­ <lb/>tween <emph type="italics"/>Scilla<emph.end type="italics"/> and <emph type="italics"/>Caribdis,<emph.end type="italics"/> and maketh a great agitation. </s><s>Like to <lb/>which, and much greater, is &longs;aid to be betwixt <emph type="italics"/>Africa<emph.end type="italics"/> and the <lb/>great I&longs;le of St. <emph type="italics"/>Lorenzo,<emph.end type="italics"/> where the Waters of the two va&longs;t <lb/>Seas, <emph type="italics"/>Indian<emph.end type="italics"/> and <emph type="italics"/>Ethiopick,<emph.end type="italics"/> that lie round it, mu&longs;t needs be <lb/>&longs;traightned into a le&longs;&longs;e Channel between the &longs;aid I&longs;le and the <lb/><emph type="italics"/>Ethiopian<emph.end type="italics"/> Coa&longs;t. </s><s>And the Currents mu&longs;t needs be very great <lb/>in the Straights of <emph type="italics"/>Magellanes,<emph.end type="italics"/> which joyne together the <lb/>va&longs;t Oceans of <emph type="italics"/>Ethiopia,<emph.end type="italics"/> and <emph type="italics"/>Del Zur,<emph.end type="italics"/> called al&longs;o the <emph type="italics"/>Pacifick<emph.end type="italics"/> <lb/>Sea.</s></p><p type="main"><s><arrow.to.target n="marg770"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg770"></margin.target><emph type="italics"/>A di&longs;cu&longs;&longs;ion of <lb/>&longs;ome more ab&longs;tru&longs;e <lb/>accidents ob&longs;erved <lb/>in the ebbing and <lb/>flowing.<emph.end type="italics"/></s></p><p type="main"><s>It follows now, in the &longs;ixth place, that to render a rea&longs;on of <lb/>&longs;ome more ab&longs;tru&longs;e and incredible accidents, which are ob&longs;er­ <lb/>ved upon this occa&longs;ion, we make a con&longs;iderable reflection upon <lb/>the two principal cau&longs;es of ebbings and flowings, afterwards <lb/>compounding and mixing them together. </s><s>The fir&longs;t and &longs;imple&longs;t <pb xlink:href="040/01/419.jpg" pagenum="397"/>of which is (as hath often been &longs;aid) the determinate accelera­ <lb/>tion and retardation of the parts of the Earth, from whence <lb/>the Waters have a determinate period put to their decur&longs;ions <lb/>towards the Ea&longs;t, and return towards the We&longs;t, in the time of <lb/>twenty &longs;our hours. </s><s>The other is that which dependeth on the pro­ <lb/>per gravity of the Water, which being once commoved by the <lb/>primary cau&longs;e, &longs;eeketh, in the next place, to reduce it &longs;elf to <emph type="italics"/>Æ­ <lb/>quilibrium,<emph.end type="italics"/> with iterated reciprocations; which are not deter­ <lb/>mined by one &longs;ole and prefixed time; but have as many varie­ <lb/>ties of times as are the different lengths and profundities of the <lb/>receptacles, and Straights of Seas; and by what dependeth on <lb/>this &longs;econd principle, they would ebbe. </s><s>and flow, &longs;ome in one <lb/>hour, others in two, in four, in &longs;ix, in eight, in ten, &c. </s><s>Now if <lb/>we begin to put together the fir&longs;t cau&longs;e, which hath its &longs;et Period <lb/>from twelve hours to twelve hours, with &longs;ome one of the &longs;econ­ <lb/>dary, that hath its Period <emph type="italics"/>verb. </s><s>grat.<emph.end type="italics"/> from five hours to five <lb/>hours, it would come to pa&longs;&longs;e, that at &longs;ometimes the primary <lb/>cau&longs;e and &longs;econdary would accord to make impul&longs;es both one <lb/>and the &longs;ame way; and in this concurrency, and (as one may call <lb/>it) unanimous con&longs;piration the flowings &longs;hall be great. </s><s>At other <lb/>times it happening that the primary impul&longs;e doth, in a certain <lb/>manner, oppo&longs;e that which the &longs;econdary Period would make, <lb/>and in this conte&longs;t one of the Principles being taken away, that <lb/>which the other would give, will weaken the commotion of the <lb/>Waters, and the Sea will return to a very tranquil State, and <lb/>almo&longs;t immoveable. </s><s>And at other times, according as the two <lb/>afore&longs;aid Principles &longs;hall neither altogether conte&longs;t, nor altoge­ <lb/>ther concur, there &longs;hall be other kinds of alterations made in <lb/>the increa&longs;e and diminution of the ebbing and flowing. </s><s>It may <lb/>likewi&longs;e fall out that two Seas, con&longs;iderably great and which <lb/>communicate by &longs;ome narrow Channel, may chance to have, by <lb/>rea&longs;on of the mixtion of the two Principles of motion, one <lb/>cau&longs;e to flow at the time that the other hath cau&longs;e to move a <lb/>contrary way; in which ca&longs;e in the Channel, whereby they di&longs;­ <lb/>imbogue them&longs;elves into each other, there do extraordinary <lb/>conturbations in&longs;ue, with oppo&longs;ite and vortick motions, and <lb/>mo&longs;t dangerous boilings and breakings, as frequent relations <lb/>and experiences do a&longs;&longs;ure us. </s><s>From &longs;uch like di&longs;cordant moti­ <lb/>ons, dependent not onely on the differenr po&longs;itions and longi­ <lb/>tudes, but very much al&longs;o upon the different profundities of the <lb/>Seas, which have the &longs;aid intercour&longs;e there do happen at &longs;ome­ <lb/>times different commotions in the Waters, irregular, and that <lb/>can be reduced to no rules of ob&longs;ervation, the rea&longs;ons of which <lb/>have much troubled, and alwayes do trouble Mariners, for that <lb/>they meet with them without &longs;eeing either impul&longs;e of winds, or <pb xlink:href="040/01/420.jpg" pagenum="398"/>other eminent aereal alteration that might occa&longs;ion the &longs;ame; of <lb/>which di&longs;turbance of the Air we ought to make great account <lb/>in other accidents, and to take it for a third and accidental <lb/>cau&longs;e, able to alter very much the ob&longs;ervation of the effects de­ <lb/>pending on the &longs;econdary and more e&longs;&longs;ential cau&longs;es. </s><s>And it is <lb/>not to be doubted, but that impetuous windes, continuing to <lb/>blow, for example, from the Ea&longs;t, they &longs;hall retein the Waters <lb/>and prohibit the reflux or ebbing; whereupon the &longs;econd and <lb/>third reply of the flux or tide overtaking the former, at the <lb/>hours prefixed, they will &longs;well very high; and being thus born <lb/>up for &longs;ome dayes, by the &longs;trength of the Winds, they &longs;hall ri&longs;e <lb/>more than u&longs;ual, making extraordinary inundations.</s></p><p type="main"><s>We ought al&longs;o, (and this &longs;hall &longs;erve for a &longs;eventh Probleme) <lb/>to take notice of another cau&longs;e of motion dependant on the <lb/>great abundance of the Waters of great Rivers that di&longs;charge </s></p><p type="main"><s><arrow.to.target n="marg771"></arrow.to.target> <lb/>them&longs;elves into Seas of no great capacity, whereupon in the <lb/>Straits or <emph type="italics"/>Bo&longs;phori<emph.end type="italics"/> that communicate with tho&longs;e Seas, the Waters <lb/>are &longs;een to run always one way: as it happeneth in the <emph type="italics"/>Thraci­ <lb/>an Bo&longs;phorus<emph.end type="italics"/> below <emph type="italics"/>Con&longs;tantinople,<emph.end type="italics"/> where the water alwayes <lb/>runneth from the <emph type="italics"/>Black-Sea,<emph.end type="italics"/> towards the <emph type="italics"/>Propontis<emph.end type="italics"/>: For in the <lb/>&longs;aid <emph type="italics"/>Black-Sea<emph.end type="italics"/> by rea&longs;on of its &longs;hortne&longs;&longs;e, the principal cau&longs;es <lb/>of ebbing and flowing are but of &longs;mall force. </s><s>But, on the con­ <lb/>trary, very great Rivers falling into the &longs;ame, tho&longs;e huge de­ <lb/>fluxions of water being to pa&longs;&longs;e and di&longs;gorge them&longs;elves by the <lb/><arrow.to.target n="marg772"></arrow.to.target> <lb/>the Straight, the ^{*}cour&longs;e is there very notable and alwayes to­ <lb/>wards the South. </s><s>Where moreover we ought to take notice, that <lb/>the &longs;aid Straight or Channel, albeit very narrow, is not &longs;ubject <lb/>to perturbations, as the Straight of <emph type="italics"/>Soilla<emph.end type="italics"/> and <emph type="italics"/>Carybdis<emph.end type="italics"/>; for that <lb/>that hath the <emph type="italics"/>Black-Sea<emph.end type="italics"/> above towards the North, and the <emph type="italics"/>Pro­ <lb/>pontis,<emph.end type="italics"/> the <emph type="italics"/>Ægean,<emph.end type="italics"/> and the <emph type="italics"/>Mediterranean<emph.end type="italics"/> Seas joyned unto it, <lb/>though by a long tract towards the South; but now, as we have <lb/>ob&longs;erved, the Seas, though of never &longs;o great length, lying North <lb/>and South, are not much &longs;ubject to ebbings and flowings; but <lb/>becau&longs;e the <emph type="italics"/>Sicilian<emph.end type="italics"/> Straight is &longs;ituate between the parts of the <lb/>Mediterrane di&longs;tended for a long tract or di&longs;tance from We&longs;t to <lb/>Ea&longs;t, that is, according to the cour&longs;e of the fluxes and refluxes, <lb/>therefore in this the agitations are very great; and would be <lb/>much more violent between <emph type="italics"/>Hercules Pillars,<emph.end type="italics"/> in ca&longs;e the <lb/>Straight of <emph type="italics"/>Gibraltar<emph.end type="italics"/> did open le&longs;&longs;e; and tho&longs;e of the Straight of <lb/><emph type="italics"/>Magellanes<emph.end type="italics"/> are reported to be extraordinary violent.</s></p><p type="margin"><s><margin.target id="marg771"></margin.target><emph type="italics"/>The cau&longs;e why, <lb/>in &longs;ome narrow <lb/>Channels, we &longs;ee <lb/>the Sea-waters run <lb/>alwayes one way.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg772"></margin.target>* Or current.</s></p><p type="main"><s>This is what, for the pre&longs;ent, cometh into my mind to &longs;ay unto <lb/>you about the cau&longs;es of this fir&longs;t period diurnal of the Tide, and <lb/>its various accidents, touching which, if you have any thing to <lb/>offer, you may let us hear it, that &longs;o we may afterwards pro­ <lb/>ceed to the other two periods, monethly and annual.</s></p> <pb xlink:href="040/01/421.jpg" pagenum="399"/><p type="main"><s>SIMP. </s><s>In my opinion, it cannot be denied, but that your di&longs;­ <lb/>cour&longs;e carrieth with it much of probability, arguing, as we &longs;ay, <lb/><emph type="italics"/>ex &longs;uppo&longs;itione,<emph.end type="italics"/> namely, granting that the Earth moveth with <lb/>the two motions a&longs;&longs;igned it by <emph type="italics"/>Copernicus<emph.end type="italics"/>: but if that motion <lb/><arrow.to.target n="marg773"></arrow.to.target> <lb/>be di&longs;proved, all that you have &longs;aid is vain, and in&longs;ignificant: <lb/>and for the di&longs;proval of that <emph type="italics"/>Hypothe&longs;is,<emph.end type="italics"/> it is very manife&longs;tly <lb/>hinted by your Di&longs;cour&longs;e it &longs;elf. </s><s>You, with the &longs;uppo&longs;ition of <lb/>the two Terre&longs;trial motions, give a rea&longs;on of the ebbing and <lb/>flowing; and then again, arguing circularly, from the ebbing <lb/>and flowing, draw the rea&longs;on and confirmation of tho&longs;e very <lb/>motions; aud &longs;o proceeding to a more &longs;pecious Di&longs;cour&longs;e, you <lb/>&longs;ay that the Water, as being a fluid body, and not tenaciou&longs;ly <lb/>annexed to the Earth, is not con&longs;trained punctually to obey eve­ <lb/>ry of its motions, from which you afterwards infer its ebbing <lb/>and flowing, Now I, according to your own method, argue <lb/>the quite contrary, and &longs;ay; the Air is much more tenuous, and <lb/>fluid than the Water, and le&longs;&longs;e annexed to the Earths &longs;uperfici­ <lb/>es, to which the Water, if it be for nothing el&longs;e, yet by rea&longs;on <lb/>of its gravity that pre&longs;&longs;eth down upon the &longs;ame more than the <lb/>light Air, adhereth; therefore the Air is much obliged to fol­ <lb/>low the motions of the Earth: and therefore were it &longs;o, that the <lb/>Earth did move in that manner, we the inhabitants of it, and <lb/>carried round with like velocity by it, ought perpetually to feel <lb/>a Winde from the Ea&longs;t that beateth upon us with intolerable <lb/>force. </s><s>And that &longs;o it ought to fall out, quotidian experience a&longs;­ <lb/>&longs;ureth us: for if with onely riding po&longs;t, at the &longs;peed of eight or <lb/>ten miles an hour in the tranquil Air, the incountering of it with <lb/>our face &longs;eemeth to us a Winde that doth not lightly blow upon <lb/>us, what &longs;hould we expect from our rapid cour&longs;e of 800. or a <lb/>thou&longs;and miles an hour, again&longs;t the Air, that is, free from that <lb/>motion? </s><s>And yet, notwith&longs;tanding we cannot perceive any <lb/>thing of that nature.</s></p><p type="margin"><s><margin.target id="marg773"></margin.target><emph type="italics"/>The Hypothe&longs;ir <lb/>of the Earths mo­ <lb/>bility taken in fa­ <lb/>vour of the Tide, <lb/>oppo&longs;ed.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>To this objection that hath much of likelihood in it, I <lb/><arrow.to.target n="marg774"></arrow.to.target> <lb/>reply, that its true, the Air is of greater tenuity and levity; and, <lb/>by rea&longs;on of its levity, le&longs;&longs;e adherent to the Earth than Water &longs;o <lb/>much more grave and ^{*}bulky; but yet the con&longs;equence is fal&longs;e <lb/>that you infer from the&longs;e qualities; namely, that upon account <lb/><arrow.to.target n="marg775"></arrow.to.target> <lb/>of that its levity, tenuity, and le&longs;&longs;e adherence to the Earth, it <lb/>&longs;hould be more exempt than the Water from following the <lb/>Terre&longs;trial Motions; &longs;o as that to us, who ab&longs;olutely pertake of <lb/>of them, the &longs;aid exemption &longs;hould be &longs;en&longs;ible and manife&longs;t; <lb/>nay, it happeneth quite contrary; for, if you well remember, the <lb/>cau&longs;e of the ebbing and flowing of the Water a&longs;&longs;igned by us, <lb/>con&longs;i&longs;teth in the Waters not following the unevenne&longs;&longs;e of the <lb/>motion of its Ve&longs;&longs;el, but retaining the <emph type="italics"/>impetus<emph.end type="italics"/> conceived before, <pb xlink:href="040/01/422.jpg" pagenum="400"/>without dimini&longs;hing or increa&longs;ing it according to the preci&longs;e rate <lb/>of its dimini&longs;hing or increa&longs;ing in its Ve&longs;&longs;el. </s><s>Becau&longs;e therefore <lb/><arrow.to.target n="marg776"></arrow.to.target> <lb/>that in the con&longs;ervation and retention of the <emph type="italics"/>impetus<emph.end type="italics"/> before con­ <lb/>ceived, the di&longs;obedience to a new augmentation or diminution of <lb/>motion con&longs;i&longs;teth, that moveable that &longs;hall be mo&longs;t apt for &longs;uch <lb/>a retention, &longs;hall be al&longs;o mo&longs;t commodious to demon&longs;trate the <lb/>effect that followeth in con&longs;equence of that retention. </s><s>Now how <lb/>much the Water is di&longs;po&longs;ed to maintain &longs;uch a conceived agita­ <lb/>tion; though the cau&longs;es cea&longs;e that impre&longs;s the &longs;ame, the experi­ <lb/>ence of the Seas extreamly di&longs;turbed by impetuous Winds &longs;hew­ <lb/>eth us; the Billows of which, though the Air be grown calm, and <lb/>the Wind laid, for a long time after continue in motion: As the <lb/>Sacred Poet plea&longs;antly &longs;ings,</s></p><p type="margin"><s><margin.target id="marg774"></margin.target><emph type="italics"/>The an&longs;wer to <lb/>the objections <lb/>made again&longs;t the <lb/>motion of the Ter­ <lb/>re&longs;trial Globe.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg775"></margin.target>+ Corpulenta.</s></p><p type="margin"><s><margin.target id="marg776"></margin.target><emph type="italics"/>The Water more <lb/>apt to con&longs;erve an<emph.end type="italics"/> <lb/>impetus <emph type="italics"/>conceived, <lb/>then the Air.<emph.end type="italics"/></s></p><p type="head"><s><emph type="italics"/>Qual l'alto Egeo,<emph.end type="italics"/> &c.----------</s></p><p type="main"><s>And that long continuing rough after a &longs;torm, dependeth on <lb/><arrow.to.target n="marg777"></arrow.to.target> <lb/>the gravity of the water: For, as I have el&longs;ewhere &longs;aid, light bo­ <lb/>dies are much ea&longs;ier to be moved than the more grave, but yet <lb/>are &longs;o much the le&longs;s apt to con&longs;erve the motion imparted, when <lb/>once the moving cau&longs;e cea&longs;eth. </s><s>Whence it comes that the Aire, <lb/>as being of it &longs;elf very light and thin, is ea&longs;ily mov'd by any very <lb/>&longs;mall force, yet it is withall very unable to hold on its motion, <lb/>the Mover once cea&longs;ing. </s><s>Therefore, as to the Aire which envi­ <lb/>rons the Terre&longs;trial Globe, I would fay, that by rea&longs;on of its <lb/>adherence, it is no le&longs;&longs;e carried about therewith then the Water; <lb/>and e&longs;pecially that part which is contained in its ve&longs;&longs;els; which <lb/><arrow.to.target n="marg778"></arrow.to.target> <lb/>ve&longs;&longs;els are the valleys enclo&longs;ed with Mountains. </s><s>And we may <lb/>with much more rea&longs;on affirm that this &longs;ame part of the Air is <lb/>carried round, and born forwards by the rugged parts of the <lb/>Earth, than that the higher is whirl'd about by the motion of the <lb/>Heavens, as ye <emph type="italics"/>Peripateticks<emph.end type="italics"/> maintain.</s></p><p type="margin"><s><margin.target id="marg777"></margin.target><emph type="italics"/>Light bodies ea&longs;ier <lb/>to be moved than <lb/>beavy, but le&longs;s aut <lb/>to con&longs;erve the mo­ <lb/>tion.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg778"></margin.target><emph type="italics"/>Its more rational <lb/>that the Air be <lb/>commoved by the <lb/>rugged &longs;urface of <lb/>the Earth than <lb/>by the Cele&longs;tial <lb/>motion.<emph.end type="italics"/></s></p><p type="main"><s>What hath been hitherto &longs;poken, &longs;eems to me a &longs;ufficient an­ <lb/><arrow.to.target n="marg779"></arrow.to.target> <lb/>&longs;wer to the allega ion of <emph type="italics"/>Simputius<emph.end type="italics"/>; yet neverthele&longs;s with a new <lb/>in&longs;tance and &longs;olution, founded upon an admirable experiment, I <lb/>will &longs;uperabundantly &longs;atisfie him, and confirm to <emph type="italics"/>Sagredus<emph.end type="italics"/> the <lb/>mobility of the Earth. </s><s>I have told you that the Air, and in par­ <lb/>ticular that part of it which a&longs;cendeth not above the tops of the <lb/>highe&longs;t Mountains, is carried round by the uneven parts of the <lb/>Earths &longs;urface: from whence it &longs;hould &longs;eem, that it mu&longs;t of con­ <lb/>&longs;equence come to pa&longs;&longs;e, that in ca&longs;e the &longs;uperficies of the Earth <lb/>were not uneven, but &longs;mooth and plain, no cau&longs;e would remain <lb/>for drawing the Air along with it, or at lea&longs;t for revolving it with <lb/>&longs;o much uniformity. </s><s>Now the &longs;urface of this our Globe, is not <lb/>all craggy and rugged, but there are exceeding great tracts very <pb xlink:href="040/01/423.jpg" pagenum="401"/>even, to wit, the &longs;urfaces of very va&longs;t Seas, which being al&longs;o far <lb/>remote from the continuate ledges of Mountains which environ <lb/>it, &longs;eem to have no faculty of carrying the &longs;uper-ambient Air <lb/>along therewith: and not carrying it about, we may perceive what <lb/>will of con&longs;equence en&longs;ue in tho&longs;e places.</s></p><p type="margin"><s><margin.target id="marg779"></margin.target><emph type="italics"/>The revolution of <lb/>the Earth con­ <lb/>firmed by a new <lb/>argument taken <lb/>from the Air.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I was about to propo&longs;e the very &longs;ame difficulty, which <lb/>I think is of great validity.</s></p><p type="main"><s>SALV. </s><s>You &longs;ay very well <emph type="italics"/>Simplicius,<emph.end type="italics"/> for from the not finding <lb/>in the Air that which of con&longs;equence would follow, did this our <lb/>Globe move round; you argue its immoveablene&longs;&longs;e. </s><s>But in ca&longs;e <lb/>that this which you think ought of nece&longs;&longs;ary con&longs;equence to be <lb/>found, be indeed by experience proved to be &longs;o; will you accept <lb/>it for a &longs;ufficient te&longs;timony and an argument for the mobility of <lb/>the &longs;aid Globe?</s></p><p type="main"><s>SIMP. </s><s>In this ca&longs;e it is not requi&longs;ite to argue with me alone, <lb/>for if it &longs;hould &longs;o fall out, and that I could not comprehend the <lb/>cau&longs;e thereof, yet haply it might be known by others.</s></p><p type="main"><s>SALV. </s><s>So that by playing with you, a man &longs;hall never get, but <lb/>be alwayes on the lo&longs;ing hand; and therefore it would be better <lb/>to give over: Neverthele&longs;s, that we may not cheat our third man <lb/>we will play on. </s><s>We &longs;aid even now, and with &longs;ome addition we <lb/>reitterate it, that the Ayr as if it were a thin and fluid body, and <lb/>not &longs;olidly conjoyned with the Earth, &longs;eem'd not to be nece&longs;&longs;i­ <lb/>tated to obey its motion; unle&longs;&longs;e &longs;o far as the craggine&longs;s of the <lb/>terre&longs;trial &longs;uperficies, tran&longs;ports and carries with it a part there­ <lb/>of contigious thereunto; which doth not by any great &longs;pace ex­ <lb/>ceed the greate&longs;t altitude of Mountains: the which portion of Air <lb/>ought to be &longs;o much le&longs;s repugnant to the terre&longs;trial conver&longs;ion, <lb/><arrow.to.target n="marg780"></arrow.to.target> <lb/>by how much it is repleat with vapours, fumes, and exhalations, <lb/>matters all participating of terrene qualities, and con&longs;equently <lb/>apt of their own nature to the &longs;ame motions. </s><s>But where there are <lb/>wanting the cau&longs;es of motion, that is, where the &longs;urface of the <lb/>Globe hath great levels, and where there is le&longs;s mixture of the <lb/>terrene vapours, there the cau&longs;e whereby the ambient Air is con­ <lb/>&longs;trained to give entire obedience to the terre&longs;trial conver&longs;ion will <lb/>cea&longs;e in part; &longs;o that in &longs;uch places, whil&longs;t the Earth revolveth to­ <lb/>wards the Ea&longs;t, there will be continually a wind perceived which <lb/>will beat upon us, blowing from the Ea&longs;t towards the We&longs;t: <lb/>and &longs;uch gales will be the more &longs;en&longs;ible, where the revolution of <lb/>the Globe is mo&longs;t &longs;wift; which will be in places more remote from <lb/>the Poles, and approaching to the greate&longs;t Circle of the diurnal <lb/>conver&longs;ion. </s><s>But now <emph type="italics"/>de facto<emph.end type="italics"/> experience much confi meth this <lb/>Phylo&longs;ophical argumentation; for in the &longs;patious Seas, and in their <lb/>parts mo&longs;t remote from Land, and &longs;ituate under the Torrid Zone, <lb/>that is bounded by the Tropicks, where there are none of tho&longs;e <pb xlink:href="040/01/424.jpg" pagenum="402"/><arrow.to.target n="marg781"></arrow.to.target> <lb/>&longs;ame terre&longs;trial evaporations, we finde a perpetual gale move <lb/>from the Ea&longs;t with &longs;o con&longs;tant a bla&longs;t, that &longs;hips by favour there­ <lb/>of &longs;ail pro&longs;perou&longs;ly to the <emph type="italics"/>West-India's.<emph.end type="italics"/> And from the &longs;ame <lb/>coa&longs;ting along the <emph type="italics"/>Mexican<emph.end type="italics"/> &longs;hore, they with the &longs;ame felicity pa&longs;s <lb/>the <emph type="italics"/>Pacifick<emph.end type="italics"/> Ocean towards the <emph type="italics"/>India's<emph.end type="italics"/>; which to us are Ea&longs;t, but <lb/><arrow.to.target n="marg782"></arrow.to.target> <lb/>to them are We&longs;t. </s><s>Whereas on the contrary the Cour&longs;e from <lb/>thence towards the Ea&longs;t is difficult and uncertain, and not to be <lb/>made by the &longs;ame Rhumb, but mu&longs;t vere more to Land-ward, to <lb/>recover other Winds, which we may call accidentary and tumul­ <lb/>tuary, produced from other Principles, as tho&longs;e that inhabit the <lb/>continent find by experience. </s><s>Of which productions of Winds, <lb/>the Cau&longs;es are many and different, which &longs;hall not at this time be <lb/><arrow.to.target n="marg783"></arrow.to.target> <lb/>mentioned. </s><s>And the&longs;e accidentary Winds are tho&longs;e which blow <lb/>indifferently from all parts of the Eatth, and make rough the Seas <lb/>remote from the Equinoctial, and environed by the rugged Sur­ <lb/>face of the Earth; which is as much as to &longs;ay environ'd with <lb/>tho&longs;e perturbations of Air, that confound that primary Gale. <lb/></s><s>The which, in ca&longs;e the&longs;e accidental impediments were removed, <lb/>would be continually felt, and e&longs;pecially upon the Sea. </s><s>Now <lb/>&longs;ee how the effect of the Water and Air &longs;eem wonderfully to ac­ <lb/>cord with the Cele&longs;tial ob&longs;ervations, to confirm the mobility of <lb/>our Terre&longs;trial Globe. <lb/><arrow.to.target n="marg784"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg780"></margin.target><emph type="italics"/>The vaporous <lb/>parts of the earth, <lb/>partake of its mo­ <lb/>tions.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg781"></margin.target><emph type="italics"/>Con&longs;tant gales <lb/>within the Tro­ <lb/>pieks blow towards <lb/>the We&longs;t.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg782"></margin.target><emph type="italics"/>The cour&longs;e to the <lb/>We&longs;t<emph.end type="italics"/>-India's <emph type="italics"/>ea­ <lb/>&longs;ie, the return dif­ <lb/>ficult.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg783"></margin.target><emph type="italics"/>Winds from Land <lb/>make rough the <lb/>Seas.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg784"></margin.target><emph type="italics"/>Another ob&longs;erva­ <lb/>tion taken from the <lb/>Air in confirmati­ <lb/>on of the motion of <lb/>the Earth.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I al&longs;o for a final clo&longs;e will relate to you one particular, <lb/>which as I believe is unknown unto you, and which likewi&longs;e may <lb/>&longs;erve to confirm the &longs;ame conclu&longs;ion: You <emph type="italics"/>Salviatus<emph.end type="italics"/> alledged, <lb/>That Accident which Sailers meet with between the Tropicks; <lb/>I mean that perpetual Gale of Winde that beats upon them from <lb/>the Ea&longs;t, of which I have an account from tho&longs;e that have many <lb/>times made the Voyage: And moreover (which is very ob&longs;er­ <lb/>vable) I under&longs;tand that the Mariners do not call it a <emph type="italics"/>Wind,<emph.end type="italics"/> but </s></p><p type="main"><s><arrow.to.target n="marg785"></arrow.to.target> <lb/>by another ^{*} name, which I do not now remember, taken haply <lb/>from its &longs;o fixed and con&longs;tant Tenor; which when they have met <lb/>with, they tie up their &longs;hrouds and other cordage belonging to <lb/>the Sails, and without any more need of touching them, though <lb/>they be in a &longs;leep, they can continue their cour&longs;e. </s><s>Now this con&longs;tant <lb/>Trade-wind was known to be &longs;uch by its continual blowing with­ <lb/>out interruptions; for if it were interrupted by other Windes, it <lb/>would not have been acknowledged for a &longs;ingular Effect, and <lb/>different from the re&longs;t: from which I wlll infer, That it may be <lb/>that al&longs;o our Mediterranean Sea doth partake of the like accident; <lb/>but it is not ob&longs;erved, as being frequently altered by the conflu­ <lb/>ence of other windes. </s><s>And this I &longs;ay, not without good grounds, <lb/>yea upon very probable conjectures whch came unto my know­ <lb/>ledge, from that which tendred it &longs;elf to my notice on occa&longs;ion of <lb/>the voyage that I made into <emph type="italics"/>Syria,<emph.end type="italics"/> going Con&longs;ul for this Nation <pb xlink:href="040/01/425.jpg" pagenum="403"/>to <emph type="italics"/>Aleppo,<emph.end type="italics"/> and this it is: That keeping a particular account and <lb/><arrow.to.target n="marg786"></arrow.to.target> <lb/>memorial of the dayes of the departure and arrival of the Ships in <lb/>the Ports of <emph type="italics"/>Alexandria,<emph.end type="italics"/> of <emph type="italics"/>Alexandretta,<emph.end type="italics"/> and this of <emph type="italics"/>Venice<emph.end type="italics"/>; in <lb/>comparing &longs;undry of them, which I did for my curio&longs;ity, I found <lb/>that in exactne&longs;s of account the returns hither, that is the voiages <lb/>from Ea&longs;t to We&longs;t along the Mediterrane, are made in le&longs;s time <lb/>then the contrary cour&longs;es by 25. in the Hundred: So that we &longs;ee <lb/>that one with another, the Ea&longs;tern windes are &longs;tronger then the <lb/>We&longs;tern.</s></p><p type="margin"><s><margin.target id="marg785"></margin.target>Which Wind <lb/>with our Engli&longs;h <lb/>Mariners is called <lb/>the <emph type="italics"/>Trade-wind.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg786"></margin.target><emph type="italics"/>The voiages in the <lb/>Mediterrane from <lb/>Ea&longs;t to We&longs;t are <lb/>made in &longs;horter <lb/>times than from <lb/>We&longs;t to Ea&longs;t.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>I am very glad I know this particular, which doth not <lb/>a little make for the confirmation of the Earths mobility. </s><s>And <lb/>although it may be alledged, That all the Water of the Mediter­ <lb/>rane runs perpetually towards the Straits-mouth, as being to <lb/>di&longs;imbogue into the Ocean, the waters of as many Rivers, as do <lb/>di&longs;charge them&longs;elves into the &longs;ame; I do not think that that cur­ <lb/>rent can be &longs;o great, as to be able of it &longs;elf alone to make &longs;o no­ <lb/>table a difference: which is al&longs;o manife&longs;t by ob&longs;erving that the <lb/>water in the Pharo of <emph type="italics"/>Sicily<emph.end type="italics"/> runneth back again no le&longs;s towards <lb/>the Ea&longs;t, than it runneth forwards towards the We&longs;t.</s></p><p type="main"><s>SAGR. I, that have not as <emph type="italics"/>Simplicius,<emph.end type="italics"/> an inclination to &longs;ati&longs;­ <lb/>fie any one be&longs;ides my &longs;elf, am &longs;atisfied with what hath been &longs;aid <lb/>as to this fir&longs;t particular: Therefore <emph type="italics"/>Salviatus,<emph.end type="italics"/> when you think <lb/>it fit to proceed forward, I am prepared to hear you.</s></p><p type="main"><s>SALV. </s><s>I &longs;hall do as you command me, but yet I would fain <lb/>hear the opinion al&longs;o of <emph type="italics"/>Simplicius,<emph.end type="italics"/> from who&longs;e judgement I can <lb/>argue how much I may promi&longs;e to my &longs;elf touching the&longs;e di&longs;­ <lb/>cour&longs;es from the <emph type="italics"/>Peripatetick<emph.end type="italics"/> Schools, if ever they &longs;hould come <lb/>to their ears.</s></p><p type="main"><s>SIMP. </s><s>I de&longs;ire not that my opinion &longs;hould &longs;erve or &longs;tand for <lb/>a mea&longs;ure, whereby you &longs;hould judge of others thoughts; for <lb/>as I have often &longs;aid, I am incon&longs;iderable in the&longs;e kinde of &longs;tudies, <lb/>and &longs;uch things may come into the mindes of tho&longs;e that are enter­ <lb/>ed into the deepe&longs;t pa&longs;&longs;ages of Philo&longs;ophy, as I could never think <lb/>of; as having (according to the Proverb) &longs;carce ki&longs;t her Maid: <lb/>yet neverthele&longs;s, to give you my &longs;udden thoughts, I &longs;hall tell <lb/>you, That of tho&longs;e effects by you recounted, and particularly the <lb/>la&longs;t, there may in my judgement very &longs;ufficient Rea&longs;ons be given <lb/>without the Earths mobility, by the mobility of the Heavens one­ <lb/>ly; never introducing any novelty more, than the inver&longs;ion of <lb/>that which you your &longs;elf propo&longs;e unto us. </s><s>It hath been received <lb/><arrow.to.target n="marg787"></arrow.to.target> <lb/>by the <emph type="italics"/>Peripatetick<emph.end type="italics"/> Schools, that the Element of Fire, and al&longs;o a <lb/>great part of the Aire is carried about according to the Diurnal <lb/>conver&longs;ion from Ea&longs;t to We&longs;t, by the contact of the Concave of <lb/>the Lunar Orb, as by the Ve&longs;&longs;el their container. </s><s>Now without <lb/>going out of your track, I will that we determine the Quantity of <pb xlink:href="040/01/426.jpg" pagenum="404"/><arrow.to.target n="marg788"></arrow.to.target> <lb/>the Aire which partaketh of that motion to di&longs;tend &longs;o low as to <lb/>the Tops of the highe&longs;t Hills, and that likewi&longs;e they would reach <lb/>to the Earth, if tho&longs;e Mountains did not impede them, which <lb/>agreeth with what you &longs;ay: For as you affirm, the Air, which is <lb/>invironed by ledges of Mountains, to be carried about by the <lb/>a&longs;perity of the moveable Earth; we on the contrary &longs;ay, That <lb/>the whole Element of Air is carried about by the motion of <lb/>Heaven, that part only excepted which lyeth below tho&longs;e bodies, <lb/>which is hindred by the a&longs;perity of the immoveable Earth. </s><s>And <lb/>whereas you &longs;aid, That in ca&longs;e that a&longs;perity &longs;hould be removed, <lb/>the Air would al&longs;o cea&longs;e to be whirld about; we may &longs;ay, <lb/>That the &longs;aid a&longs;perity being removed, the whole Aire would con­ <lb/>tinue its motion. </s><s>Whereupon, becau&longs;e the &longs;urfaces of &longs;pacious <lb/>Seas are &longs;mooth, and even; the Airs motion &longs;hall continue upon <lb/>tho&longs;e, alwaies blowing from the Ea&longs;t: And this is more &longs;en&longs;ibly <lb/>perceived in Climates lying under the Line, and within the Tro­ <lb/>picks, where the motion of Heaven is &longs;wifter; and like as that <lb/>Cele&longs;tial motion is able to bear before it all the Air that is at <lb/>liberty, &longs;o we may very rationally affirm that it contributeth the <lb/>&longs;ame motion to the Water moveable, as being fluid and not con­ <lb/>nected to the immobility of the Earth: And with &longs;o much the <lb/><arrow.to.target n="marg789"></arrow.to.target> <lb/>more confidence may we affirm the &longs;ame, in that by your con­ <lb/>fe&longs;&longs;ion, that motion ought to be very &longs;mall in re&longs;ect of the efficient <lb/>Cau&longs;e; which begirting in a natural day the whole Terre&longs;trial <lb/>Globe, pa&longs;&longs;eth many hundreds of miles an hour, and e&longs;pecially <lb/>towards the Equinoctial; whereas in the currents of the open Sea, <lb/>it moveth but very few miles an hour. </s><s>And thus the voiages to­ <lb/>wards the We&longs;t &longs;hall come to be commodious and expeditious, <lb/>not onely by rea&longs;on of the perpetual Ea&longs;tern Gale, but of the <lb/>cour&longs;e al&longs;o of the Waters; from which cour&longs;e al&longs;o perhaps the <lb/>Ebbing and Flowing may come, by rea&longs;on of the different &longs;citu­ <lb/><arrow.to.target n="marg790"></arrow.to.target> <lb/>ation of the Terre&longs;trial Shores: again&longs;t which the Water coming <lb/>to beat, may al&longs;o return backwards with a contrary motion, like <lb/>as experience &longs;heweth us in the cour&longs;e of Rivers; for according as <lb/>the Water in the unevenne&longs;s of the Banks, meeteth with &longs;ome <lb/>parts that &longs;tand out, or make with their Meanders &longs;ome Reach or <lb/>Bay, here the Water turneth again, and is &longs;een to retreat back <lb/>a con&longs;iderable &longs;pace. </s><s>Upon this I hold, That of tho&longs;e effects <lb/>from which you argue the Earths mobility, and alledge it as a <lb/>cau&longs;e of them, there may be a&longs;&longs;igned a cau&longs;e &longs;ufficiently valid, <lb/>retaining the Earth &longs;tedfa&longs;t, and re&longs;toring the mobility of <lb/>Heaven.</s></p><p type="margin"><s><margin.target id="marg787"></margin.target><emph type="italics"/>It is demon&longs;tra­ <lb/>ted inverting the <lb/>argument, that <lb/>the perpetual mo­ <lb/>tion of the Air <lb/>from Ea&longs;t to We&longs;t <lb/>cometh from the <lb/>motion of Heaven?<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg788"></margin.target><emph type="italics"/>It is demon&longs;trated <lb/>inverting the ar­ <lb/>gument, that the <lb/>perpetual motion of <lb/>the Air from Ea&longs;t <lb/>to We&longs;t, cometh <lb/>from the motion of <lb/>Heaven.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg789"></margin.target><emph type="italics"/>The motion of the <lb/>Water dependeth <lb/>on the motion of <lb/>Heaven.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg790"></margin.target><emph type="italics"/>The flux and re­ <lb/>flux may depend <lb/>on the diurual mo­ <lb/>tion of Heaven.<emph.end type="italics"/></s></p><p type="main"><s>SALV. </s><s>It cannot be denied, but that your di&longs;cour&longs;e is ingenious, <lb/>& hath much of probability, I mean probability in appearance, but <lb/>not in reality & exi&longs;tence: It con&longs;i&longs;teth of two parts: In the fir&longs;t it <pb xlink:href="040/01/427.jpg" pagenum="405"/>a&longs;&longs;ignes a rea&longs;on of the continual motion of the Ea&longs;tern Winde, <lb/>and al&longs;o of a like motion in the Water. </s><s>In the &longs;econd, It would <lb/>draw from the &longs;ame Sour&longs;e the cau&longs;e of the Ebbing and Flowing. <lb/></s><s>The fir&longs;t part hath (as I have &longs;aid) &longs;ome appearance of probabi­ <lb/>lity, but yet extreamly le&longs;s then that which we take from the <lb/>Terre&longs;trial motion. </s><s>The &longs;econd is not onely wholly improbable, <lb/>but altogether impo&longs;&longs;ible and fal&longs;e. </s><s>And coming to the fir&longs;t, <lb/><arrow.to.target n="marg791"></arrow.to.target> <lb/>whereas it is &longs;aid that the Concave of the Moon carrieth about <lb/>the element of Fire, and the whole Air, even to the tops of the <lb/>higher Mountains. </s><s>I an&longs;wer fir&longs;t, that it is dubious whether <lb/>there be any element of Fire: But &longs;uppo&longs;e there be, it is much <lb/>doubted of the Orbe of the Moon, as al&longs;o of all the re&longs;t; that is, <lb/>Whether there be any &longs;uch &longs;olid bodies and va&longs;t, or el&longs;s, Whether <lb/>beyond the Air there be extended a continuate expan&longs;ion of a <lb/>&longs;ub&longs;tance of much more tenuity and purity than our Air, up and <lb/>down which the Planets go wandring, as now at la&longs;t a good part <lb/>of tho&longs;e very Phylo&longs;ophers begin to think: But be it in this or in <lb/><arrow.to.target n="marg792"></arrow.to.target> <lb/>that manner, there is no rea&longs;on for which the Fire, by a &longs;imple <lb/>contract to a &longs;uperficies, which you your &longs;elf grant to be &longs;mooth <lb/>and ter&longs;e, &longs;hould be according to its whole depth carried round in <lb/>a motion different from its natural inclination; as hath been de­ <lb/>fu&longs;ely proved, and with &longs;en&longs;ible rea&longs;ons demon&longs;trated by^{+} <emph type="italics"/>Il Sag-<emph.end type="italics"/> <lb/><arrow.to.target n="marg793"></arrow.to.target> <lb/><emph type="italics"/>giatore<emph.end type="italics"/>: Be&longs;ides the other improbability of the &longs;aid motions <lb/>transfu&longs;ing it &longs;elf from the &longs;ubtile&longs;t Fire throughout the Air, much <lb/>more den&longs;e; and from that al&longs;o again to the Water. </s><s>But that <lb/>a body of rugged and mountainous &longs;urface, by revolving in it <lb/>&longs;elf, &longs;hould carry with it the Air contiguous to it, and again&longs;t <lb/>which its promontaries beat, is not onely probable but nece&longs;&longs;ary, <lb/>and experience thereof may be daily &longs;een; though without &longs;ee­ <lb/>ing it, I believe that there is no judgement that doubts thereof. <lb/></s><s>As to the other part, &longs;uppo&longs;ing that the motion of Heaven did <lb/>carry round the Air, and al&longs;o the Water; yet would that motion <lb/>for all that have nothing to do with the Ebbing and Flowing. <lb/></s><s>For being that from one onely and uniform cau&longs;e, there can fol­ <lb/><arrow.to.target n="marg794"></arrow.to.target> <lb/>low but one &longs;ole and uniform effect; that which &longs;hould be di&longs;co­ <lb/>vered in the Water, would be a continuate and uniform cour&longs;e <lb/>from Ea&longs;t to We&longs;t; and in that a Sea onely, which running com­ <lb/>pa&longs;s environeth the whole Globe. </s><s>But in determinate Seas, &longs;uch <lb/>as is the Mediterrane &longs;hut up in the Ea&longs;t, there could be no &longs;uch <lb/>motion. </s><s>For if its Water might be driven by the cour&longs;e of <lb/>Heaven towards the We&longs;t, it would have been dry many ages <lb/>&longs;ince: Be&longs;ides that our Water runneth not onely towards the <lb/>We&longs;t, But returneth backwards towards the Ea&longs;t, and that in or­ <lb/>dinal Periods: And whereas you &longs;ay by the example of Rivers, <lb/>that though the cour&longs;e of the Sea were Originally that onely <pb xlink:href="040/01/428.jpg" pagenum="406"/>from Ea&longs;t to We&longs;t, yet neverthele&longs;s the different Po&longs;ition of the <lb/>Shores may make part of the Water regurgitate, and return <lb/>backwards: I grant it you, but it is nece&longs;&longs;ary that you take no­ <lb/>tice my <emph type="italics"/>Simplicius,<emph.end type="italics"/> that where the Water upon that account <lb/>returneth backwards, it doth &longs;o there perpetually; and where <lb/>it runneth &longs;traight forwards, it runneth there alwayes in the &longs;ame <lb/>manner; for &longs;o the example of the Rivers &longs;hewes you: But in the <lb/>ca&longs;e of the ebbing and flowing, you mu&longs;t finde and give us &longs;ome <lb/>rea&longs;on why it doth in the &longs;elf &longs;ame place run one while one way, <lb/>and another while another; Effects that being contrary & irregular, <lb/>can never be deduced from any uniform and con&longs;tant Cau&longs;e: <lb/>And this Argument, that overthrows the Hypothe&longs;is of the mo­ <lb/>tion contributed to the Sea from the Heavens diurnal motion, <lb/>doth al&longs;o confute that Po&longs;ition of tho&longs;e who would admit the &longs;ole <lb/>diurnal motion of the Earth, and believe that they are able with <lb/>that alone to give a rea&longs;on of the Flux and Reflux: Of which <lb/>effect &longs;ince it is irregular, the cau&longs;e mu&longs;t of nece&longs;&longs;ity be irregular <lb/>and alterable.</s></p><p type="margin"><s><margin.target id="marg791"></margin.target><emph type="italics"/>A rea&longs;on of the <lb/>continual motion of <lb/>the Air and Wa­ <lb/>ter may be given, <lb/>making the Earth <lb/>moveable, then by <lb/>making it immove­ <lb/>able.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg792"></margin.target><emph type="italics"/>Its improbable that <lb/>the element of Fire <lb/>&longs;hould be carried <lb/>round by the Con­ <lb/>cave of the Moon.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg793"></margin.target>+ A Treati&longs;e of our <lb/>Author formerly <lb/>cited.</s></p><p type="margin"><s><margin.target id="marg794"></margin.target><emph type="italics"/>The Ebbing and <lb/>Flowing cannot de­ <lb/>pend on the motion <lb/>of Heaven.<emph.end type="italics"/></s></p><p type="main"><s>SIMP. </s><s>I have nothing to reply, neither of my own, by rea&longs;on <lb/>of the weakne&longs;s of my under&longs;tanding; nor of that of others, for <lb/>that the Opinion is &longs;o new: But I could believe that if it were <lb/>&longs;pread among&longs;t the Schools, there would not want Phylo&longs;ophers <lb/>able to oppo&longs;e it.</s></p><p type="main"><s>SAGR. </s><s>Expect &longs;uch an occa&longs;ion; and we in the mean time <lb/>if it &longs;eem good to <emph type="italics"/>Salviatus,<emph.end type="italics"/> will proceed forward.</s></p><p type="main"><s>SALV. </s><s>All that which hath been &longs;aid hitherto, pertaineth to <lb/>the diurnal period of the ebbing and flowing; of which we have in <lb/>the fir&longs;t place demon&longs;trated in general the primary and univer&longs;al <lb/>Cau&longs;e, without which, no &longs;uch effect would follow: Afterw ds <lb/>pa&longs;&longs;ing to the particular Accidents, various, and in a certain &longs;ort <lb/>irregular, that are ob&longs;erved therein: We have handled the &longs;econ­ <lb/>dary and concommitant Cau&longs;es upon which they depend. </s><s>Now <lb/>follow the two other Periods, Monethly, and Annual, which do <lb/>not bring with them new and different Accidents, other than <lb/>tho&longs;e already con&longs;idered in the diurnal Period; but they ope­ <lb/>rate on the &longs;ame Accidents, by rendring them greater and le&longs;&longs;er <lb/>in &longs;everal parts of the Lunar Moneth, and in &longs;everal times of <lb/>the Solar Year; as if that the Moon and Sun did each conceive <lb/>it &longs;elf apart in operating and producing of tho&longs;e Effects; a thing <lb/>that totally cla&longs;heth with my under&longs;tanding, which &longs;eeing how <lb/>that this of Seas is a local and &longs;en&longs;ible motion, made in an im­ <lb/>men&longs;e ma&longs;s of Water, it cannot be brought to &longs;ub&longs;cribe to <lb/>Lights, to temperate Heats, to predominacies by occult Quali­ <lb/>ties, and to &longs;uch like vain Imaginations, that are &longs;o far from be­ <lb/>ing, or being po&longs;&longs;ible to be Cau&longs;es of the Tide; that on the con­ <pb xlink:href="040/01/429.jpg" pagenum="407"/>trary, the Tide is the cau&longs;e of them, that is, of bringing them <lb/>into the brains more apt for loquacity and o&longs;tentation, than for <lb/>the &longs;peculation and di&longs;covering of the more ab&longs;tru&longs;e &longs;ecrets of <lb/>Nature; which kind of people, before they can be brought to <lb/>prononnce that wi&longs;e, ingenious, and mode&longs;t &longs;entence, <emph type="italics"/>I know it <lb/>not,<emph.end type="italics"/> &longs;uffer to e&longs;cape from their mouths and pens all manner of ex­ <lb/>travagancies. </s><s>And the onely ob&longs;erving, that the &longs;ame Moon, and <lb/>the &longs;ame Sun operate not with their light with their motion, with <lb/>great heat, or with temperate, on the le&longs;&longs;er reeeptaces of Water, <lb/>but that to effect their flowing by heat, they mu&longs;t be reduced to <lb/>little le&longs;&longs;e than boiling, and in &longs;hort, we not being able artificially <lb/>to imitate any way the motions of the Tide, &longs;ave only by the mo­ <lb/>tion of the Ve&longs;&longs;el, ought it not to &longs;atisfie every one, that all <lb/>the other things alledged, as cau&longs;es of tho&longs;e e&longs;&longs;ects, are <lb/>vaine fancies, and altogether e&longs;tranged from the Truth. </s><s>I <lb/><arrow.to.target n="marg795"></arrow.to.target> <lb/>&longs;ay, therefore, that if it be true, that of one effect there is but <lb/>one &longs;ole primary cau&longs;e, and that between the cau&longs;e and effect, <lb/>there is a firm and con&longs;tant connection; it is nece&longs;&longs;ary that when­ <lb/>&longs;oever there is &longs;een a firm and con&longs;tant alteration in the effect, <lb/>there be a firm and con&longs;tant alteration in the cau&longs;e. </s><s>And be­ <lb/>cau&longs;e the alterations that happen in the ebbing and flowing in <lb/>&longs;everal parts of the Year and Moneths, have their periods firm and <lb/>con&longs;tant, it is nece&longs;&longs;ary to &longs;ay, that a regular alteration in tho&longs;e <lb/>&longs;ame times happeneth in the primary cau&longs;e of the ebbings and <lb/>flowings. </s><s>And as for the alteration that in tho&longs;e times happens <lb/><arrow.to.target n="marg796"></arrow.to.target> <lb/>in the ebbings and flowings con&longs;i&longs;teth onely in their greatne&longs;s; <lb/>that is, in the Waters ri&longs;ing and falling more or le&longs;&longs;e, and in <lb/>running with greater or le&longs;&longs;e <emph type="italics"/>impetus<emph.end type="italics"/>; therefore it is nece&longs;&longs;ary, <lb/>that that which is the primary cau&longs;e of the ebbing and flowing, <lb/>doth in tho&longs;e &longs;ame determinate times increa&longs;e and dimini&longs;h its <lb/>force. </s><s>But we have already concluded upon the inequality and <lb/>irregularity of the motion of the Ve&longs;&longs;els containing the Water to <lb/>be the primary cau&longs;e of the ebbings and flowings. </s><s>Therefore <lb/>it is nece&longs;&longs;ary, that that irregularity, from time to time, corre­ <lb/>&longs;pondently grow more irregular, that is, grow greater and le&longs;&longs;er. <lb/></s><s>Now it is requi&longs;ite, that we call to minde, that the irregularity, <lb/>that is, the different velocity of the motions of the Ve&longs;&longs;els, to <lb/>wit, of the parts of the Terre&longs;trial Superficies, dependeth on <lb/>their moving with a compound motion, re&longs;ulting from the com­ <lb/>mixtion of the two motions, Annual and Diurnal, proper to the <lb/>whole Terre&longs;trial Globe; of which the Diurnal conver&longs;ion, by <lb/>one while adding to, and another while &longs;ub&longs;tracting from, the <lb/>Annual motion, is that which produceth the irregularity in the <lb/>compound motion; &longs;o that, in the additions and &longs;ub&longs;tractions, <lb/>that the Diurnal revolution maketh from the Annual motion, <pb xlink:href="040/01/430.jpg" pagenum="408"/>con&longs;i&longs;teth the original cau&longs;e of the irregular motion of the Ve&longs;­ <lb/>&longs;els, and con&longs;equently of the Ebbing and Flowing: in&longs;omuch <lb/><arrow.to.target n="marg797"></arrow.to.target> <lb/>that if the&longs;e additions and &longs;ub&longs;tractions &longs;hould alwayes proceed <lb/>in the &longs;ame proportion, in re&longs;pect of the Annual motion, the <lb/>cau&longs;e of the Ebbing and Flowing would indeed continue, but <lb/>yet &longs;o as that they would perpetually return in the &longs;elf &longs;ame man­ <lb/>ner: But we are to finde out the cau&longs;e of making the &longs;ame Eb­ <lb/>bings and Flowings in divers times greater and le&longs;&longs;er: There­ <lb/>fore we mu&longs;t (if we will retain the identity of the cau&longs;e) find the <lb/>alteration in the&longs;e additions and &longs;ub&longs;tractions, that make them <lb/>more & le&longs;s potent, in producing tho&longs;e effects which depend there­ <lb/>upon. </s><s>But I &longs;ee not how that potency and impotence can be intro­ <lb/>duced, unle&longs;&longs;e by making the &longs;ame additions and &longs;ub&longs;tractions, <lb/>one while greater, and another while le&longs;&longs;er; &longs;o that the accelera­ <lb/>tion and the retardment of the compound motion, may be made, <lb/>&longs;ometimes in greater, and &longs;ometimes in le&longs;&longs;er proportion.</s></p><p type="margin"><s><margin.target id="marg795"></margin.target><emph type="italics"/>The alterations <lb/>in the effects argue <lb/>alteration in the <lb/>cau&longs;e.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg796"></margin.target><emph type="italics"/>The cau&longs;es at <lb/>large a&longs;&longs;igned of <lb/>the Periods Mo­ <lb/>nethly and Annu­ <lb/>al of the ebbing <lb/>and flowing.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg797"></margin.target><emph type="italics"/>The monethly <lb/>and annual altera­ <lb/>tions of the tide can <lb/>depend upon no­ <lb/>thing, &longs;ave on the <lb/>alteration of the <lb/>additions & &longs;ub­ <lb/>&longs;tractions of the <lb/>diurnal period from <lb/>the annual.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I feel my &longs;elf very gently led, as it were, by the hand, <lb/>and though I finde no rubs in the way, yet neverthele&longs;&longs;e, like a <lb/>blind man, I &longs;ee not whether your Clue leadeth me, nor can I <lb/>imagine where &longs;uch a Journey will end.</s></p><p type="main"><s>SALV. </s><s>Though there be a great difference between my &longs;low <lb/>pac't Philo&longs;ophy, and your more nimble Rea&longs;on, yet neverthe­ <lb/>le&longs;&longs;e, in this particular which we are now upon, I do not much <lb/>wonder, if the apprehen&longs;ivene&longs;&longs;e of your wit be a little ob&longs;cu­ <lb/>red by the dark and thick mi&longs;t that hides the mark, at which we <lb/>aime: and that which le&longs;&longs;eneth my admiration is, the remem­ <lb/>brance of the many hours, many dayes, yea more, many nights <lb/>that I have con&longs;umed in this contemplation, and of the many <lb/>times that, de&longs;pairing to bring it to a period, I have, for an in­ <lb/>couragement of my &longs;elf, indeavoured to believe, by the exam­ <lb/>ple of the unfortunate <emph type="italics"/>Orlando,<emph.end type="italics"/> that that might not po&longs;&longs;ibly be <lb/>true, which yet the te&longs;timony of &longs;o many credible men &longs;et be­ <lb/>fore my eyes: wonder not, therefore, if this once, contrary to <lb/>your cu&longs;tome, you do not fore&longs;ee what I intend: and if you will <lb/>needs admire, I believe that the event, as far as I can judge un­ <lb/>expected, will make you cea&longs;e your wonderment.</s></p><p type="main"><s>SAGR. </s><s>I thank God, that he did not permit that de&longs;peration <lb/>of yours to end in the <emph type="italics"/>Exit<emph.end type="italics"/> that is fabled of the mi&longs;erable <emph type="italics"/>Or­ <lb/>lando,<emph.end type="italics"/> nor in that which haply is no le&longs;&longs;e fabulou&longs;ly related of <lb/><emph type="italics"/>Ari&longs;totle,,<emph.end type="italics"/> that &longs;o neither my &longs;elf nor others &longs;hould be deprived <lb/>of the di&longs;covery of a thing, as ab&longs;tru&longs;e as it was de&longs;irable: I <lb/>be&longs;eech you, therefore, to &longs;atisfie my eager appetite as &longs;oon as <lb/>you can.</s></p><p type="main"><s>SALV. </s><s>I am ready to &longs;erve you: We were upon an inquiry <lb/>in what manner the additions and &longs;ub&longs;tractions of the Terre&longs;tri­ <pb xlink:href="040/01/431.jpg" pagenum="409"/>all conver&longs;ion from the Annual motion, could be made, one <lb/>while in a greater, and another while in a le&longs;&longs;er proportion; <lb/>which diver&longs;ity, and no other thing, could be a&longs;&longs;igned for the <lb/>cau&longs;e of the alterations, Monethly and Annual, that are &longs;een in <lb/>the greatne&longs;&longs;e of the Ebbings and Flowings. </s><s>I will now con­ <lb/>&longs;ider how this proportion of the additions and &longs;ub&longs;tractions of <lb/><arrow.to.target n="marg798"></arrow.to.target> <lb/>the Diurnal Revolution, and Annual motion may grow greater <lb/>and le&longs;&longs;er three &longs;everal wayes. </s><s>One is by increa&longs;ing and dimi­ <lb/>ni&longs;hing the velocity of the Annual motion, retaining the additi­ <lb/>ons and &longs;ub&longs;tractions made by the Diurnal conver&longs;ion in the <lb/>&longs;ame greatne&longs;&longs;e, becau&longs;e the Annual motion being about three <lb/>times greater, that is, more velocious than the Diurnal motion <lb/>(con&longs;idered likewi&longs;e in the Grand Circle) if we increa&longs;e it <lb/>anew, the additions and &longs;ub&longs;tractions of the Diurnal motion <lb/>will occa&longs;ion le&longs;&longs;e alteration therein: but, on the other &longs;ide, <lb/>making it more &longs;low, it will be altered in greater proportion, by <lb/>that &longs;ame diurnal motion, ju&longs;t as the adding or &longs;ub&longs;tracting <lb/>four degrees of velocity from one that moveth with twenty de­ <lb/>grees, altereth his cour&longs;e le&longs;&longs;e, than tho&longs;e very four degrees would <lb/>do, added or &longs;ub&longs;tracted from one that &longs;hould move onely with <lb/>ten degrees. </s><s>The &longs;econd way would be, by making the additi­ <lb/>ons and &longs;ub&longs;tractions greater and le&longs;&longs;er, retaining the annual mo­ <lb/>tion in the &longs;ame velocity; which is as ea&longs;ie to be under&longs;tood, as it <lb/>is manife&longs;t, that a velocity <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> of 20. degr. </s><s>is more altered by the <lb/>addition or &longs;ub&longs;traction of 10. deg. </s><s>than by the addition or &longs;ub&longs;tra­ <lb/>ction of 4. The third way would be, in ca&longs;e the&longs;e two were joyned <lb/>together, dimini&longs;hing the annual motion, & increa&longs;ing the diurnal <lb/>additions and &longs;ub&longs;tractions. </s><s>Hitherto, as you &longs;ee, it was no <lb/>hard matter to attain, but yet it proved to me very hard to find <lb/>by what means this might be effected in Nature. </s><s>Yet in the end, <lb/><arrow.to.target n="marg799"></arrow.to.target> <lb/>I finde that &longs;he doth admirably make u&longs;e thereof, and in wayes <lb/>almo&longs;t incredible: I mean, admirable and incredible to us, but <lb/>not to her, who worketh even tho&longs;e very things, which, to our <lb/>capacity, are of infinite wonder, with extraordinary facility and <lb/>&longs;implicity: and that which it is hard for us to under&longs;tand, is ea­ <lb/>&longs;ie for her to effect. </s><s>Now to proceed, having &longs;hewn that the <lb/>proportion between the additions and &longs;ub&longs;tractions of the Diur­ <lb/>nal conver&longs;ion and Annual motion may be made greater and le&longs;­ <lb/>&longs;er, two wayes, (and I &longs;ay two, becau&longs;e the third is comprized in <lb/>the two fir&longs;t) I adde, that Nature maketh u&longs;e of them both: <lb/>and farthermore, I &longs;ubjoyn, that if &longs;he did make u&longs;e but of one <lb/>alone, it would be nece&longs;&longs;ary to take away one of the two Perio­ <lb/>dical alterations. </s><s>That of the Monethly Period would cea&longs;e, if <lb/><arrow.to.target n="marg800"></arrow.to.target> <lb/>the annual motion &longs;hould not alter. </s><s>And in ca&longs;e the additions <lb/>and &longs;ub&longs;tractions of the diurnal revolution &longs;hould continually <pb xlink:href="040/01/432.jpg" pagenum="410"/>be equal, the alterations of the annual Period would fail.</s></p><p type="margin"><s><margin.target id="marg798"></margin.target><emph type="italics"/>Three wayes of <lb/>altering the pro­ <lb/>portion of the ad­ <lb/>ditions of the diur­ <lb/>nal Revolution to <lb/>the annual motion.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg799"></margin.target><emph type="italics"/>That which to <lb/>us is hard to be un­ <lb/>der&longs;tood, is with <lb/>Nature ea&longs;ie to be <lb/>effected.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg800"></margin.target><emph type="italics"/>If the Diurnal <lb/>motion &longs;hould not <lb/>alter, the annual <lb/>Period would cea&longs;e<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>It &longs;eems then, that the Monethly alteration of eb­ <lb/>bings and flowings dependeth on the alteration of the annual <lb/>motion of the Earth? </s><s>And the annual alteration of tho&longs;e eb­ <lb/>bings and flowings do, it &longs;eems, depend on the additions and <lb/>&longs;ub&longs;tractions of the diurnal conver&longs;ion? </s><s>And here now I finde <lb/>my &longs;elf wor&longs;e puzzled than before, and more out of hope of <lb/>being able to comprehend how this intricacy may be, which is <lb/>more inextricable, in my judgment, than the Gordian knot. </s><s>And <lb/>I envy <emph type="italics"/>Simplicius,<emph.end type="italics"/> from who&longs;e &longs;ilence I argue that he doth ap­ <lb/>prehend the whole bu&longs;ine&longs;&longs;e, and is acquit of that confu&longs;ion <lb/>which greatly puzzleth my brains.</s></p><p type="main"><s>SIMP. </s><s>I believe verily, <emph type="italics"/>Sagredus,<emph.end type="italics"/> that you are put to a <lb/>a &longs;tand; and I believe that I know al&longs;o the cau&longs;e of your con­ <lb/>fu&longs;ion, which, if I mi&longs;take not, ri&longs;eth from your under&longs;tanding <lb/>part of tho&longs;e particulars but even now alledged by <emph type="italics"/>Salviatus,<emph.end type="italics"/> <lb/>and but a part. </s><s>It is true likewi&longs;e that I find my &longs;elf free from the <lb/>like confu&longs;ion; but not for that cau&longs;e as you think, to wit, be­ <lb/>cau&longs;e I apprehend the whole, nay it happens upon the quite <lb/>contrary account; namely, from my not comprehending any <lb/>thing; and confu&longs;ion is in the plurality of things, and not in <lb/>nothing.</s></p><p type="main"><s>SAGR. </s><s>You &longs;ee <emph type="italics"/>Salviatus,<emph.end type="italics"/> how a few checks given to <emph type="italics"/>Simpli­ <lb/>cius<emph.end type="italics"/> in the dayes preceding, have rendered him gentle, and <lb/>brought him from the <emph type="italics"/>capriol<emph.end type="italics"/> to the <emph type="italics"/>amble.<emph.end type="italics"/> But I be&longs;eech you <lb/>without farther delay, put us both out of &longs;u&longs;pence.</s></p><p type="main"><s>SALV. </s><s>I will endeavour it to the utmo&longs;t of my har&longs;h way of <lb/>expre&longs;&longs;ing my &longs;elf, the obtu&longs;ene&longs;&longs;e of which, the acutene&longs;&longs;e of <lb/>your wit &longs;hall &longs;upply. </s><s>The accidents of which we are to enquire <lb/>the cau&longs;es are two: The fir&longs;t re&longs;pecteth the varieties that happen <lb/>in the ebbings and flowings in the Monethly Period; and the o­ <lb/>thr relateth to the Annual. </s><s>We will fir&longs;t &longs;peak of the Moneth­ <lb/>ly, and then treat of the Annual; and it is convenient that we <lb/>re&longs;olve them all according to the Fundamentals and Hypothe&longs;is <lb/>already laid down, without introducing any novelty either in A­ <lb/>&longs;tronomy, or in the Univer&longs;e, in favour of the ebbings and flow­ <lb/>ings; therefore let us demon&longs;trate that of all the &longs;everal acci­ <lb/>dents in them ob&longs;erved, the cau&longs;es re&longs;ide in the things already <lb/><arrow.to.target n="marg801"></arrow.to.target> <lb/>known, and received for true and undoubted. </s><s>I &longs;ay therefore, <lb/>that it is a truly natural, yea nece&longs;&longs;ary thing, that one and the &longs;ame <lb/>moveable made to move round by the &longs;ame moving virtue in a <lb/>longer time, do make its cour&longs;e by a greater circle, rather than <lb/>by a le&longs;&longs;er; and this is a truth received by all, and con­ <lb/>firmed by all experiments, of which we will produce a few. <lb/><arrow.to.target n="marg802"></arrow.to.target> <lb/>In the wheel-clocks, and particularly in the great ones, to mo­ <pb xlink:href="040/01/433.jpg" pagenum="411"/>derate the time, the Artificers that make them accomodate a cer­ <lb/>tain voluble &longs;taffe horozontally, and at each end of it they fa­ <lb/>&longs;ten two Weights of Lead, and when the time goeth too &longs;low, <lb/>by the onely removing tho&longs;e Leads a little nearer to the centre <lb/>of the &longs;taffe, they render its vibrations more frequent; and on <lb/>the contrary to retard it, it is but drawing tho&longs;e Weights more <lb/>towards the ends; for &longs;o the vibrations are made more &longs;eldome, <lb/>and con&longs;equently the intervals of the hours are prolonged.</s></p><p type="margin"><s><margin.target id="marg801"></margin.target><emph type="italics"/>The true Hypo­ <lb/>the&longs;is may di&longs;patch <lb/>its revolutions in a <lb/>&longs;horter time, in <lb/>le&longs;&longs;er circles than <lb/>in greater; the <lb/>which is proved by <lb/>two examples.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg802"></margin.target><emph type="italics"/>The fir&longs;t ex­ <lb/>ample.<emph.end type="italics"/></s></p><p type="main"><s>Here the movent vertue is the &longs;ame, namely the counterpoi&longs;e, <lb/><arrow.to.target n="marg803"></arrow.to.target> <lb/>the moveables are tho&longs;e &longs;ame Weights of lead, and their vi­ <lb/>brations are more frequent when they are neerer to the centre, <lb/>that is, when they move by le&longs;&longs;er circles. </s><s>Hanging equal <lb/>Weights at unequal cords, and being removed from their per­ <lb/>pendicularity, letting them go; we &longs;hall &longs;ee tho&longs;e that are pen­ <lb/>dent at the &longs;horter cords, to make their vibrations under &longs;horter <lb/>times, as tho&longs;e that move by le&longs;&longs;er circles. </s><s>Again, let &longs;uch a <lb/>kind of Weight be fa&longs;tened to a cord, which cord let play upon <lb/>a &longs;taple fa&longs;tened in the Seeling, and do you hold the other end <lb/>of the cord in your hand, and having given the motion to the <lb/>pendent Weight, whil&longs;t it is making its vibrations, pull the <lb/>end of the cord that you hold in your hand, &longs;o that the Weight <lb/>may ri&longs;e higher and higher: In its ri&longs;ing you &longs;hall &longs;ee the fre­ <lb/>quency of its vibrations encrea&longs;e, in regard that they are made <lb/>&longs;ucce&longs;&longs;ively by le&longs;&longs;er and le&longs;&longs;er circies. </s><s>And here I de&longs;ire you to <lb/><arrow.to.target n="marg804"></arrow.to.target> <lb/>take notice of two particulars worthy to be ob&longs;erved. </s><s>One is <lb/>that the vibrations of one of tho&longs;e plummets are made with &longs;uch <lb/>a nece&longs;&longs;ity under &longs;uch determinate times, that it is altogether <lb/>impo&longs;&longs;ible to cau&longs;e them to be made under other times, unle&longs;&longs;e <lb/>it be by prolonging, or abreviating the cord; of which you <lb/>may al&longs;o at this very in&longs;tant a&longs;certain your &longs;elves by experience, <lb/>tying a &longs;tone to a pack-threed, and holding the other end in <lb/>your hand, trying whether you can ever by any artifice be able <lb/>to &longs;wing it this way and that way in other than one determinate <lb/>time, unle&longs;&longs;e by lengthening or &longs;hortening the &longs;tring, which <lb/>you will find to be ab&longs;olutely impo&longs;&longs;ible. </s><s>The other particular <lb/>truly admirable is, that the &longs;elf &longs;ame <emph type="italics"/>pendulum<emph.end type="italics"/> makes its vibra­ <lb/>tions with one and the &longs;ame frequency, or very little, and as it <lb/>were in&longs;en&longs;ibly different, whether they be made by very great, <lb/>or very &longs;mall arches of the &longs;elf-&longs;ame circumference. </s><s>I mean that <lb/>whether we remove the <emph type="italics"/>pendulum<emph.end type="italics"/> from perpendicularity one, two, <lb/>or three degrees onely, or whether we remove it 70. 80. nay to <lb/>an entire quadrant, it being let go, will in the one ca&longs;e and in <lb/>the other make its vibrations with the &longs;ame frequency, as well <lb/>the former where it is to move by an arch of but four or &longs;ix de­ <lb/>grees, as the &longs;econd, where it is to pa&longs;&longs;e arches of 160. or more <pb xlink:href="040/01/434.jpg" pagenum="412"/>degrees. </s><s>Which may the better be &longs;een, by hanging two weights <lb/>at two &longs;trings of equal length, and then removing them from per­ <lb/>pendicularity, one a little way, and the other very far; the which <lb/>being &longs;et at liberty, will go & return under the &longs;ame times, the one <lb/>by arches very &longs;mall, & the other by very great ones, from whence <lb/>followeth the conclu&longs;ion of an admirable Problem; which is, <lb/><arrow.to.target n="marg805"></arrow.to.target> <lb/>That a Quadrant of a Circle being given (take a little diagram of <lb/>the &longs;ame, [in <emph type="italics"/>Fig.<emph.end type="italics"/> 3.]) as for in&longs;tance: A B erect to the Hori­ <lb/>zon, &longs;o as that it re&longs;t upon the plain touching in the point B. and <lb/>an Arch being made with a Hoop well plained and &longs;moothed in <lb/>the concave part, bending it according to the curvity of the Cir­ <lb/>cumference A D B. </s><s>So that a Bullet very round and &longs;mooth <lb/>may freely run to and again within it (the rim of a Sieve is very <lb/>proper for the experiment) I &longs;ay, that the Bullet being put in any <lb/>what ever place, neer or far from the lowe&longs;t term B. </s><s>As for in­ <lb/>&longs;tance, putting it in the point C, or here in D, or in E; and then <lb/>let go, it will in equal times, or in&longs;en&longs;ibly different arrive at the <lb/>term B, departing from C, or from D, or from E, or from what­ <lb/>ever other place; an accident truly wonderfull. </s><s>We may add <lb/>another accident no le&longs;s &longs;trange than this, which is, That more­ <lb/>over by all the cords drawn from the point B to the points C, <lb/>D, E; and to any other what&longs;oever, taken not onely in the Qua­ <lb/>drant B A, but in all the whole circumference of the Circle the <lb/>&longs;aid moveable &longs;hall de&longs;cend in times ab&longs;olutely equal; in&longs;omuch <lb/>that it &longs;hall be no longer in de&longs;cending by the whole Diameter <lb/>erect perpendicularly upon the point B, then it &longs;hall in de&longs;cend­ <lb/>ing by B. C. although it do &longs;ublend but one &longs;ole degree, or a le&longs;­ <lb/>&longs;er Arch. </s><s>Let us add the other wonder, which is, That the mo­ <lb/>tions of the falling bodies made by the Arches of the Quadrant <lb/>A B; are made in &longs;horter times than tho&longs;e that are made by the <lb/>cords of tho&longs;e &longs;ame Arches; &longs;o that the &longs;wifte&longs;t motion, and <lb/>made by a moveable in the &longs;horte&longs;t time, to arrive from the <lb/>point A, to the term B, &longs;hall be that which is made, not by the <lb/>right line A, B, (although it be the &longs;horte&longs;t of all tho&longs;e that can <lb/>de drawn between the points A. B.) but by the circumference <lb/>A D B. </s><s>And any point being taken in the &longs;aid Arch; as for <lb/>example: The point D. and two cords drawn A D, and D. B. <lb/>the moveable departing from the qoint A, &longs;hall in a le&longs;s time <lb/>come to B, moving by the two cords A D and D B. than by the <lb/>&longs;ole cord A, B. </s><s>But the &longs;horte&longs;t of all the times &longs;hall be that of <lb/>the fall by the Arch A D B. </s><s>And the &longs;elf &longs;ame accidents are <lb/>to be under&longs;tood of all the other le&longs;&longs;er Arches taken from the <lb/>lowermo&longs;t term B. upwards.</s></p><p type="margin"><s><margin.target id="marg803"></margin.target><emph type="italics"/>The &longs;econd ex­ <lb/>ample.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg804"></margin.target><emph type="italics"/>Two particular <lb/>notable accidents <lb/>in the<emph.end type="italics"/> penduli <emph type="italics"/>and <lb/>their vibrations.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg805"></margin.target><emph type="italics"/>Admirable Pro­ <lb/>blems of movea­ <lb/>bles de&longs;cending by <lb/>the Quadrant of a <lb/>Circle, and of tho&longs;e <lb/>de&longs;cending by all <lb/>the cords of the <lb/>whole Circle.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>No more, no more; for you &longs;o confund and fill me <lb/>with Wonders, and di&longs;tract my thoughts &longs;o many &longs;everal wayes, <pb xlink:href="040/01/435.jpg" pagenum="413"/>that I fear I &longs;hall have but a &longs;mall part of it left free and di&longs;in­ <lb/>gaged, to apply to the principal matter that is treated of, and <lb/>which of it &longs;elf is but even too ob&longs;cure and intricate: So that <lb/>I intreat you to vouch&longs;afe me, having once di&longs;patcht the bu&longs;ine&longs;s <lb/>of the ebbings and flowings, to do this honour to my hou&longs;e (and <lb/>yours) &longs;ome other dayes, and to di&longs;cour&longs;e upon the &longs;o many other <lb/>Problems that we have left in &longs;u&longs;pence; and which perhaps are <lb/>no le&longs;s curious and admirable, than this that hath been di&longs;cu&longs;&longs;ed <lb/>the&longs;e dayes pa&longs;t, and that now ought to draw to a con­ <lb/>clu&longs;ion.</s></p><p type="main"><s>SALV. </s><s>I &longs;hall be ready to &longs;erve you, but we mu&longs;t make more <lb/>than one or two Se&longs;&longs;ions; if be&longs;ides the other que&longs;tions re&longs;erved <lb/>to be handled apart, we would di&longs;cu&longs;&longs;e tho&longs;e many that pertain <lb/>to the local motion, as well of natural moveables, as of the reject­ <lb/>ed: an Argument largely treated of by our <emph type="italics"/>Lyncean Accade­ <lb/>mick.<emph.end type="italics"/> But turning to our fir&longs;t purpo&longs;e, where we were about to <lb/>declare, That the bodies moving circularly by a movent virtue, <lb/>which continually remaineth the &longs;ame, the times of the circula­ <lb/>tions were prefixt and determined, and impo&longs;&longs;ible to be made <lb/>longer or &longs;horter, having given examples, and produced experi­ <lb/>ments thereof, &longs;en&longs;ible, and fea&longs;ible, we may confirm the &longs;ame <lb/>truth by the experiences of the Cele&longs;tial motions of the Planets; <lb/>in which we &longs;ee the &longs;ame rule ob&longs;erved; for tho&longs;e that move by <lb/>greater Circles, confirm longer times in pa&longs;&longs;ing them. </s><s>A mo&longs;t <lb/>pertinent ob&longs;ervation of this we have from the <emph type="italics"/>Medicæan<emph.end type="italics"/> Pla­ <lb/>nets, which in &longs;hort times make their revolutions about <emph type="italics"/>Jupiter<emph.end type="italics"/>: <lb/>In&longs;omuch that it is not to be que&longs;tioned, nay we may hold it for <lb/>&longs;ure and certain, that if for example, the Moon continuing to be <lb/>moved by the &longs;ame movent faculty, &longs;hould retire by little and <lb/>little in le&longs;&longs;er Circles, it would acquire a power of abreviating <lb/>the times of its Periods, according to that <emph type="italics"/>Pendulum,<emph.end type="italics"/> of which in <lb/>the cour&longs;e of its vibrations, we by degrees &longs;hortned the cord, that <lb/>is contracted the Semidiameter of the circumferences by it pa&longs;&longs;ed. <lb/></s><s>Know now that this that I have alledged an example of it in the <lb/>Moon, is &longs;een and verified e&longs;&longs;entially in fact. </s><s>Let us call to mind, <lb/>that it hath been already concluded by us, together with <emph type="italics"/>Coperni-<emph.end type="italics"/> <lb/><arrow.to.target n="marg806"></arrow.to.target> <lb/><emph type="italics"/>cus,<emph.end type="italics"/> That it is not po&longs;&longs;ible to &longs;eparate the Moon from the Earth, <lb/>about which it without di&longs;pute revolveth in a Moneth: Let us <lb/>remember al&longs;o that the Terre&longs;trial Globe, accompanyed alwayes <lb/>by the Moon, goeth along the circumference of the Grand Orb <lb/>about the Sun in a year, in which time the Moon revolveth about <lb/>the Earth almo&longs;t thirteen times; from which revolution it follow­ <lb/>eth, that the &longs;aid Moon &longs;ometimes is found near the Sun; that is, <lb/>when it is between the Sun and the Earth, and &longs;ometimes <lb/>much more remote, that is, when the Earth is &longs;ituate between <pb xlink:href="040/01/436.jpg" pagenum="414"/>the Moon and Sun; neer, in a word, at the time of its conjun <lb/>ction and change; remote, in its Full and Oppo&longs;ition; and the <lb/>greate&longs;t vicinity differ the quantity of the Diameter of the Lu­ <lb/>nar Orb. </s><s>Now if it be true that the virtue which moveth the <lb/>Earth and Moon, about the Sun, be alwayes maintained in <lb/>the &longs;ame vigour; and if it be true that the &longs;ame moveable <lb/>moved by the &longs;ame virtue, but in circles unequal, do in &longs;horter <lb/>times pa&longs;&longs;e like arches of le&longs;&longs;er circles, it mu&longs;t needs be granted, <lb/>that the Moon when it is at a le&longs;&longs;e di&longs;tance from the Sun, that is <lb/>in the time of conjunction, pa&longs;&longs;eth greater arches of the Grand <lb/>Orb, than when it is at a greater di&longs;tance, that is in its Oppp&longs;ition <lb/>and Full. </s><s>And this Lunar inequality mu&longs;t of nece&longs;&longs;ity be imparted <lb/>to the Earth al&longs;o; for if we &longs;hall &longs;uppo&longs;e a right line produced from <lb/>the centre of the Sun by the centre of the Terre&longs;trial Globe, and <lb/>prolonged as far as the Orb of the Moon, this &longs;hall be the &longs;emi­ <lb/>diameter of the Grand Orb, in which the Earth, in ca&longs;e it were <lb/>alone, would move uniformly, but if in the &longs;ame &longs;emidiameter we <lb/>&longs;hould place another body to be carried about, placing it one <lb/>while between the Earth and Sun, and another while beyond <lb/>the Earth, at a greater di&longs;tance from the Sun, it is nece&longs;&longs;ary, <lb/>that in this &longs;econd ca&longs;e the motion common to both, according <lb/>to the circumference of the great Orb by means of the di&longs;tance <lb/>of the Moon, do prove a little &longs;lower than in the other ca&longs;e, <lb/>when the Moon is between the Earth and Sun, that is at a le&longs;&longs;er <lb/>di&longs;tance. </s><s>So that in this bu&longs;ine&longs;&longs;e the very &longs;ame happeneth that <lb/>befals in the time of the clock; that lead which is placed one <lb/>while farther &longs;rom the centre, to make the vibrations of the <lb/>&longs;taffe or ballance le&longs;&longs;e frequent, and another while nearer, to <lb/>make them thicker, repre&longs;enting the Moon. </s><s>Hence it may be <lb/>manife&longs;t, that the annual motion of the Earth in the Grand <lb/>Orb, and under the Ecliptick, is not uniform, and that its ir­ <lb/>regularity proceedeth from the Moon, and hath its Monethly <lb/>Periods and Returns. </s><s>And becau&longs;e it hath been concluded, that <lb/>the Monethly and Annual Periodick alterations of the ebbings <lb/>and flowings, cannot be deduced from any other cau&longs;e than <lb/>from the altered proportion between the annual motion and the <lb/>additions and &longs;ub&longs;tractions of the diurnal conver&longs;ion; and that <lb/>tho&longs;e alterations might be made two wayes, that is by altering <lb/>the annual motion, keeping the quantity of the additions un­ <lb/>altered, or by changing of the bigne&longs;&longs;e of the&longs;e, reteining the <lb/>uniformity of annual motion. </s><s>We have already found the fir&longs;t <lb/>of the&longs;e, depending on the irregularity of the annual motion <lb/>occa&longs;ioned by the Moon, and which hath its Monethly Periods. <lb/></s><s>It is therefore nece&longs;&longs;ary, that upon that account the ebbings <lb/>and flowings have a Monethly Period in which they do grow <pb xlink:href="040/01/437.jpg" pagenum="415"/>greater and le&longs;&longs;er. </s><s>Now you &longs;ee that the cau&longs;e of the Monethly <lb/>Period re&longs;ideth in the annual motion; and withal you &longs;ee how <lb/>much the Moon is concerned in this bu&longs;ine&longs;s, and how it is there­ <lb/>with interrupted apart, without having any thing to do with either, <lb/>with Seas or Waters.</s></p><p type="margin"><s><margin.target id="marg806"></margin.target><emph type="italics"/>The Earths an­ <lb/>nual motion by the <lb/>Ecliptick, unequal <lb/>by means of the <lb/>Moons motion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>If one that never had &longs;een any kinde of Stairs or La­ <lb/>der, were &longs;hewed a very high Tower, and asked if ever he hoped <lb/>to climb to the top of it, I verily believe that he would an&longs;wer he <lb/>did not, not conceiving how one &longs;hould come thither any way <lb/>except by flying; but &longs;hewing him a &longs;tone of but a foot high, and <lb/>asking him whether he thought he could get to the top of that, <lb/>I am certain that he would an&longs;wer he could; and farther, that he <lb/>would not deny, but that it was not onely one, but ten, twenty, <lb/>and an hundred times ea&longs;ier to climb that: But now if he &longs;hould <lb/>be &longs;hewed the Stairs, by means whereof, with the facility by him <lb/>granted, it is po&longs;&longs;ible to get thither, whither he a little before had <lb/>affirmed it was impo&longs;&longs;ible to a&longs;cend, I do think that laughing at <lb/>him&longs;elf he would confe&longs;s his dulne&longs;s of apprehen&longs;ion. </s><s>Thus, <lb/><emph type="italics"/>Salviatus,<emph.end type="italics"/> have you &longs;tep by &longs;tep &longs;o gently lead me, that, not <lb/>without wonder, I finde that I am got with &longs;mall pains to that <lb/>height which I de&longs;paired of arriving at. 'Tis true; that the Stair­ <lb/>ca&longs;e having been dark, I did not perceive that I was got nearer <lb/>to, or arrived at the top, till that coming into the open Air I di&longs;­ <lb/>covered a great Sea, and &longs;pacious Country: And as in a&longs;cending <lb/>one &longs;tep, there is no labour; &longs;o each of your propo&longs;itions by it <lb/>&longs;elf &longs;eemed to me &longs;o plain, that thinking I heard but little or no­ <lb/>thing that was new unto me, I conceived that my benefit thereby <lb/>had been little or none at all: Whereupon I was the more ama­ <lb/>zed at the unexpected <emph type="italics"/>exit<emph.end type="italics"/> of this di&longs;cour&longs;e, that hath guided me <lb/>to the knowledge of a thing which I held impo&longs;&longs;ible to be de­ <lb/>mon&longs;trated. </s><s>One doubt onely remains, from which I de&longs;ire to <lb/>be freed, and this it is; Whether that if the motion of the Earth <lb/>together with that of the Moon under the Zodiack are irregular <lb/>motions, tho&longs;e irregularities ought to have been ob&longs;erved and ta­ <lb/>ken notice of by <emph type="italics"/>A&longs;tronomers,<emph.end type="italics"/> which I do not know that they <lb/>are: Therefore I pray you, who are better acquainted with the&longs;e <lb/>things than I, to free me from this doubt, and tell me how the <lb/>ca&longs;e &longs;tands.</s></p><p type="main"><s>SALV. </s><s>You ask a rational que&longs;tion, and an&longs;wering to the Ob­ <lb/><arrow.to.target n="marg807"></arrow.to.target> <lb/>jection, I &longs;ay; That although <emph type="italics"/>A&longs;tronomy<emph.end type="italics"/> in the cour&longs;es of many <lb/>ages hath made a great progre&longs;s in di&longs;covering the con&longs;titution <lb/>and motions of the Cele&longs;tial bodies, yet is it not hitherto arrived <lb/>at that height, but that very many things remain undecided, and <lb/>haply many others al&longs;o undi&longs;covered. </s><s>It is to be &longs;uppo&longs;ed that the <lb/>fir&longs;t ob&longs;ervers of Heaven knew no more but one motion common <pb xlink:href="040/01/438.jpg" pagenum="416"/>to all the Stars, as is this diurnal one: yet I believe that in few <lb/>dayes they perceived that the Moon was incon&longs;tant in keeping <lb/>company with the other Stars; but yet withal, that many years <lb/>pa&longs;t, before that they di&longs;tingui&longs;hed all the Planets: And in par­ <lb/>ticular, I conceit that <emph type="italics"/>Saturn<emph.end type="italics"/> by its &longs;lowne&longs;s, and <emph type="italics"/>Mercury<emph.end type="italics"/> by rea­ <lb/><arrow.to.target n="marg808"></arrow.to.target> <lb/>&longs;on of its &longs;eldom appearing, were the la&longs;t that were ob&longs;erved to <lb/>be wandring and errant. </s><s>It is to be thought that many more <lb/>years run out before the &longs;tations and retrogradations of the three <lb/>&longs;uperiour Planets were known, as al&longs;o their approximations and <lb/>rece&longs;&longs;ions from the Earth, nece&longs;&longs;ary occa&longs;ions of introducing the <lb/>Eccentrix and Epicicles, things unknown even to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> for <lb/>that he makes no mention thereof. <emph type="italics"/>Mercury,<emph.end type="italics"/> and <emph type="italics"/>Venus,<emph.end type="italics"/> with <lb/>their admirable apparitions; how long did they keep A&longs;trono­ <lb/>mers in &longs;u&longs;pence, before that they could re&longs;olve (not to &longs;peak of <lb/>any other of their qualities) upon their &longs;ituation? </s><s>In&longs;omuch <lb/>that the very order onely of the Mundane bodies, and the inte­ <lb/>gral &longs;tructure of the parts of the Univer&longs;e by us known, hath been <lb/>doubted of untill the time of <emph type="italics"/>Copernicus,<emph.end type="italics"/> who hath at la&longs;t given <lb/>us notice of the true con&longs;titution, and real &longs;y&longs;teme, according to <lb/>which tho&longs;e parts are di&longs;po&longs;ed; &longs;o that at length we are certain <lb/>that <emph type="italics"/>Mercury, Venus,<emph.end type="italics"/> and the other Planets do revolve about <lb/>the Sun; and that the Moon revolveth about the Earth. </s><s>But <lb/><arrow.to.target n="marg809"></arrow.to.target> <lb/>how each Planet governeth it &longs;elf in its particular revolution, and <lb/>how preci&longs;ely the &longs;tructure of its Orb is framed; which is that <lb/>which is vulgarly called the <emph type="italics"/>Theory<emph.end type="italics"/> of the <emph type="italics"/>Planets,<emph.end type="italics"/> we cannot as <lb/>yet undoubtedly re&longs;olve. <emph type="italics"/>Mars,<emph.end type="italics"/> that hath &longs;o much puzled our <lb/>Modern A&longs;tronomers, is a proof of this: And to the Moon her <lb/>&longs;elf there have been a&longs;&longs;igned &longs;everal Theories, after that the &longs;aid <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> had much altered it from that of <emph type="italics"/>Ptolomy.<emph.end type="italics"/> And to <lb/>de&longs;cend to our particular ca&longs;e, that is to &longs;ay, to the apparent mo­ <lb/>tion of the Sun and Moon; touching the former, there hath been <lb/>ob&longs;erved a certain great irregularity, whereby it pa&longs;&longs;eth the two <lb/><arrow.to.target n="marg810"></arrow.to.target> <lb/>&longs;emicircles of the Ecliptick, divided by the points of the Equi­ <lb/>noxes in very different times; in pa&longs;&longs;ing one of which, it &longs;pend­ <lb/>eth about nine dayes more than in pa&longs;&longs;ing the other; a difference, <lb/>as you &longs;ee, very great and notable. </s><s>But if in pa&longs;&longs;ing &longs;mall arches, <lb/>&longs;uch for example as are the twelve Signs, he maintain a mo&longs;t re­ <lb/>gular motion, or el&longs;e proceed with paces, one while a little more <lb/>&longs;wift, and another more &longs;low, as it is nece&longs;&longs;ary that it do, in ca&longs;e <lb/>the annual motion belong to the Sun onely in appearance, but <lb/>in reality to the Earth in company with the Moon, it is what hath <lb/>not hitherto been ob&longs;erved, nor it may be, &longs;ought. </s><s>Touching <lb/><arrow.to.target n="marg811"></arrow.to.target> <lb/>the Moon in the next place, who&longs;e re&longs;titutions have been prin­ <lb/>cipally lookt into an account of the Eclip&longs;es, for which it is &longs;uf­ <lb/>ficient to have an exact knowledge of its motion about the Earth, <pb xlink:href="040/01/439.jpg" pagenum="417"/>it hath not been likewi&longs;e with a perfect curio&longs;ity inquired, what <lb/>its cour&longs;e is thorow the particular arches of the Zodiack. </s><s>That <lb/>therefore the Earth and Moon in running through the Zodiack, <lb/>that is round the Grand Orb, do &longs;omewhat accellerate at the <lb/>Moons change, and retard at its full, ought not to be doubted; <lb/>for that the &longs;aid difference is not manife&longs;t, which cometh to be <lb/>unob&longs;erved upon two accounts; Fir&longs;t, Becau&longs;e it hath not been <lb/>lookt for. </s><s>Secondly, Becau&longs;e that its po&longs;&longs;ible it may not be very <lb/>great. </s><s>Nor is there any need that it &longs;hould be great, for the pro­ <lb/>ducing the effect that we &longs;ee in the alteration of the greatne&longs;s of <lb/>ebbings and flowings. </s><s>For not onely tho&longs;e alterations, but the <lb/><arrow.to.target n="marg812"></arrow.to.target> <lb/>Tides them&longs;elves are but &longs;mall matters in re&longs;pect of the grandure <lb/>of the &longs;ubjects on which they work; albeit that to us, and to our <lb/>littlene&longs;s they &longs;eem great. </s><s>For the addition or &longs;ubduction of <lb/>one degree of velocity where there are naturally 700, or 1000, <lb/>can be called no great alteration, either in that which conferreth <lb/>it, or in that Which receiveth it: the Water of our Mediterrane <lb/>carried about by the diurnal revolution, maketh about 700 miles <lb/>an hour, (which is the motion common to the Earth and to it, and <lb/>therefore not perceptible to us) & that which we &longs;en&longs;ibly di&longs;cern <lb/>to be made in the &longs;treams or currents, is not at the rate of full one <lb/>mile an hour, (I &longs;peak of the main Seas, and not of the Straights) <lb/>and this is that which altereth the fir&longs;t, naturall, and grand mo­ <lb/>tion; and this motion is very great in re&longs;pect of us, and of Ships: <lb/>for a Ve&longs;&longs;el that in a &longs;tanding Water by the help of Oares can <lb/>make <emph type="italics"/>v. </s><s>g.<emph.end type="italics"/> three miles an hour, in that &longs;ame current will row <lb/>twice as far with the &longs;tream as again&longs;t it: A notable difference <lb/>in the motion of the Boat, though but very &longs;mall in the motion <lb/>of the Sea, which is altered but its &longs;even hundredth part. </s><s>The <lb/>like I &longs;ay of its ri&longs;ing, and falling one, two, or three feet; and <lb/>&longs;carcely four or five in the utmo&longs;t bounds of a &longs;treight, two thou­ <lb/>&longs;and, or more miles long, and where there are depths of hundreds <lb/>of feet; this alteration is much le&longs;s than if in one of the Boats <lb/>that bring us fre&longs;h Water, the &longs;aid Water upon the arre&longs;t of the <lb/>Boat &longs;hould ri&longs;e at the Prow the thickne&longs;s of a leaf. </s><s>I conclude <lb/>therefore that very &longs;mall alterations in re&longs;pect of the immen&longs;e <lb/>greatne&longs;s, and extraordinary velocity of the Seas, is &longs;ufficient to <lb/>make therein great mutations in relation to our &longs;mallne&longs;s, and to <lb/>our accidents.</s></p><p type="margin"><s><margin.target id="marg807"></margin.target><emph type="italics"/>Many things <lb/>may remain as yet <lb/>unob&longs;erved in A­ <lb/>&longs;tronomy.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg808"></margin.target>Saturn <emph type="italics"/>for its <lb/>&longs;lowne&longs;s, and<emph.end type="italics"/> Mer­ <lb/>cury <emph type="italics"/>for its rare­ <lb/>ne&longs;s of appearing <lb/>were among&longs;t tho&longs;e <lb/>that were la&longs;t ob­ <lb/>&longs;erved.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg809"></margin.target><emph type="italics"/>Particular &longs;tru­ <lb/>ctures of the Orbs <lb/>of the Planets not <lb/>yet well re&longs;olved.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg810"></margin.target><emph type="italics"/>The Sun pa&longs;&longs;­ <lb/>eth one half of the <lb/>Zodiack nine days <lb/>&longs;ooner than the <lb/>other.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg811"></margin.target><emph type="italics"/>The Moons mo­ <lb/>tion principally <lb/>&longs;ought in the ac­ <lb/>count of Eclip&longs;es.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg812"></margin.target><emph type="italics"/>Ebbings and <lb/>flowings are petty <lb/>things in compari­ <lb/>&longs;on of the va&longs;tne&longs;s <lb/>of Seas, and of the <lb/>velocity of the mo­ <lb/>tion of the Terre­ <lb/>&longs;trial Globe.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I am fully &longs;atisfied as to this particular; it remains to <lb/>declare unto us how tho&longs;e additions and &longs;ub&longs;tractions derived <lb/>from the diurnal <emph type="italics"/>Vertigo<emph.end type="italics"/> are made one while greater, and ano­ <lb/>ther while le&longs;&longs;er; from which alterations you hinted that the an­ <lb/>nual period of the augmentations and diminutions of the eb­ <lb/>bings and flowings did depend.</s></p> <pb xlink:href="040/01/440.jpg" pagenum="418"/><p type="main"><s>SALV. </s><s>I will u&longs;e my utmo&longs;t endeavours to render my &longs;elf <lb/><arrow.to.target n="marg813"></arrow.to.target> <lb/>intelligible, but the difficulty of the accident it &longs;elf, and the <lb/>great attention of mind requi&longs;ite for the comprehending of it, <lb/>con&longs;trains me to be ob&longs;cure. </s><s>The unequalities of the additions <lb/>and &longs;ub&longs;tractions, that the diurnal motion maketh to or from <lb/>the annual dependeth upon the inclination of the Axis of the di­ <lb/>urnal motion upon the plane of the Grand Orb, or, if you plea&longs;e, <lb/>of the Ecliptick; by means of which inclination the Equinoctial <lb/>inter&longs;ecteth the &longs;aid Ecliptick, remaining inclined and oblique <lb/>upon the &longs;ame according to the &longs;aid inclination of Axis. </s><s>And the <lb/>quantity of the additions importeth as much as the whole diame­ <lb/>ter of the &longs;aid Equinoctial, the Earths centre being at the &longs;ame <lb/>time in the Sol&longs;titial points; but being out of them it importeth <lb/>le&longs;&longs;e and le&longs;&longs;e, according as the &longs;aid centre &longs;ucce&longs;&longs;ively approa­ <lb/>cheth to the points of the Equinoxes, where tho&longs;e additions are <lb/>le&longs;&longs;er than in any other places. </s><s>This is the whole bu&longs;ine&longs;&longs;e, but <lb/>wrapt up in the ob&longs;curity that you &longs;ee.</s></p><p type="margin"><s><margin.target id="marg813"></margin.target><emph type="italics"/>The cau&longs;es of <lb/>the inequality of <lb/>the additions and <lb/>&longs;ub&longs;tractions of the <lb/>diurnal conver&longs;ion <lb/>from the annual <lb/>motion.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>Rather in that which I do no not &longs;ee; for hitherto I <lb/>comprehend nothing at all.</s></p><p type="main"><s>SALV. </s><s>I have already foretold it. </s><s>Neverthele&longs;&longs;e we will try <lb/>whether by drawing a Diagram thereof, we can give &longs;ome <lb/>&longs;mall light to the &longs;ame; though indeed it might better be &longs;et <lb/>forth by &longs;olid bodies than by bare Schemes; yet we will help our <lb/>&longs;elves with Per&longs;pective and fore-&longs;hortning. </s><s>Let us draw there­ <lb/>fore, as before, the circumference of the Grand Orb, [<emph type="italics"/>as in <lb/>Fig.<emph.end type="italics"/> 4.] in which the point A is under&longs;tood to be one of the <lb/>Sol&longs;titials, and the diameter A P the common Section of the <lb/>Sol&longs;titial Colure, and of the plane of the Grand Orb or Eclip­ <lb/>tick; and in that &longs;ame point A let us &longs;uppo&longs;e the centre of the <lb/>Terre&longs;trial Globe to be placed, the Axis of which C A B, in­ <lb/>clined upon the Plane of the Grand Orb, falleth on the plane of <lb/>the &longs;aid Colure that pa&longs;&longs;eth thorow both the Axis of the Equino­ <lb/>ctial, and of the Ecliptick. </s><s>And for to prevent confu&longs;ion, let <lb/>us only draw the Equinoctial circle, marking it with the&longs;e chara­ <lb/>cters D G E F, the common &longs;ection of which, with the plane of <lb/>the grand Orb, let be the line D E, &longs;o that half of the &longs;aid E­ <lb/>quinoctial D F E will remain inclined below the plane of the <lb/>Grand Orb, and the other half D G E elevated above. </s><s>Let <lb/>now the Revolution of the &longs;aid Equinoctial be made, according <lb/>to the order of the points D G E F, and the motion of the cen­ <lb/>tre from A towards E. </s><s>And becau&longs;e the centre of the Earth <lb/>being in A, the Axis C B (which is erect upon the diameter of <lb/>the Equinoctial D E) falleth, as hath been &longs;aid, in the Sol&longs;ti­ <lb/>tial Colure, the common Section of which and of the <lb/>Grand Orb, is the diameter P A, the &longs;aid line P A &longs;hall <pb xlink:href="040/01/441.jpg" pagenum="419"/>be perpendicular to the &longs;ame D E, by rea&longs;on that the Colure is <lb/>erect upon the grand Orb; and therefore the &longs;aid D E, <lb/>&longs;hall be the Tangent of the grand Orb in the point A. <lb/></s><s>So that in this Po&longs;ition the motion of the Centre by the arch <lb/>A E; that is, of one degree every day differeth very little; yea, <lb/>is as if it were made by the Tangent D A E. </s><s>And becau&longs;e by <lb/>means of the diurnal motion the point D, carried about by G, <lb/>unto E, encrea&longs;eth the motion of the Centre moved almo&longs;t in the <lb/>&longs;ame line D E, as much as the whole diameter D E amounts <lb/>unto; and on the other &longs;ide dimini&longs;heth as much, moving about <lb/>the other &longs;emicircle E F D. </s><s>The additions and &longs;ubductions <lb/>in this place therefore, that is in the time of the &longs;ol&longs;tice, &longs;hall be <lb/>mea&longs;ured by the whole diameter D E.</s></p><p type="main"><s>Let us in the next place enquire, Whether they be of the &longs;ame <lb/>bigne&longs;s in the times of the <emph type="italics"/>E<emph.end type="italics"/>quinoxes; and tran&longs;porting the <lb/>Centre of the Earth to the point I, di&longs;tant a Quadrant of a <lb/>Circle from the point A. </s><s>Let us &longs;uppo&longs;e the &longs;aid Equinoctial <lb/>to be G E F D, its common &longs;ection with the grand Orb D E, the <lb/>Axis with the &longs;ame inclination C B; but the Tangent of the grand <lb/>Orb in the point I &longs;hall be no longer D E, but another which <lb/>&longs;hall cut that at right Angles; and let it be this marked H I L, <lb/>according to which the motion of the Centre I, &longs;hall make its pro­ <lb/>gre&longs;s, proceeding along the circumference of this grand Orb. <lb/></s><s>Now in this &longs;tate the Additions and Sub&longs;tractions are no longer <lb/>mea&longs;ured by the diameter D E, as before was done; becau&longs;e that <lb/>diameter not di&longs;tending it &longs;elf according to the line of the annual <lb/>motion H L, rather cutting it at right angles, tho&longs;e terms D E, do <lb/>neither add nor &longs;ub&longs;tract any thing; but the Additions and <lb/>Sub&longs;tractons are to be taken from that diameter that falleth <lb/>in the plane that is errect upon the plane of the grand Orb, and <lb/>that inter&longs;ects it according to the line H L; which diameter in this <lb/>ca&longs;e &longs;hall be this G F and the Adjective, if I may &longs;o &longs;ay, &longs;hall <lb/>be that made by the point G, about the &longs;emicircle G E F, and the <lb/>Ablative &longs;hall be the re&longs;t made by the other &longs;emicircle F D G. <lb/></s><s>Now this diameter, as not being in the &longs;ame line H L of the <lb/>annual motion, but rather cutting it, as we &longs;ee in the point I, the <lb/>term G being elevated above, and E depre&longs;&longs;ed below the plane <lb/>of the grand Orb, doth not determine the Additions and Sub­ <lb/>&longs;tractions according to its whole length, but the quantity of tho&longs;e <lb/>fir&longs;t ought to be taken from the part of the line H L, that is in­ <lb/>tercepted between the perpendiculars drawn upon it from the <lb/>terms G F; namely, the&longs;e two G S, and F V: So that the mea­ <lb/>&longs;ure of the additions is the line S V le&longs;&longs;er then G F, or then D E; <lb/>which was the mea&longs;ure of the additions in the Sol&longs;tice A. </s><s>And <lb/>&longs;o &longs;ucce&longs;&longs;ively, according as the centre of the Earth &longs;hall be con­ <pb xlink:href="040/01/442.jpg" pagenum="420"/>&longs;tituted in other points of the Quadrant A I, drawing the Tan­ <lb/>gents in the &longs;aid points, and the perpndiculars upon the &longs;ame fal­ <lb/>ling from the terms of the diameters of the Equinoctial drawn <lb/>from the errect planes by the &longs;aid Tangents to the plane of the <lb/>grand Orb; the parts of the &longs;aid Tangents (which &longs;hall conti­ <lb/>nually be le&longs;&longs;er towards the Equinoctials, and greater towards the <lb/>Sol&longs;tices) &longs;hall give us the quantities of the additions and &longs;ub&longs;tra­ <lb/>ctions. </s><s>How much in the next place the lea&longs;t additions differ from <lb/>the greate&longs;t, is ea&longs;ie to be known, becau&longs;e there is the &longs;ame dif­ <lb/>ference betwixt them, as between the whole Axis or Diameter of <lb/>the Sphere, and the part thereof that lyeth between the Polar­ <lb/>Circles; the which is le&longs;s than the whole diameter by very near a <lb/>twelfth part, &longs;uppo&longs;ing yet that we &longs;peak of the additions and <lb/>&longs;ub&longs;tractions made in the Equinoctial; but in the other Paral­ <lb/>lels they are le&longs;&longs;er, according as their diameters do dimini&longs;h.</s></p><p type="main"><s>This is all that I have to &longs;ay upon this Argument, and all perhaps <lb/>that can fall under the comprehen&longs;ion of our knowledge, which, <lb/>as you well know, may not entertain any conclu&longs;ions, &longs;ave onely <lb/>tho&longs;e that are firm and con&longs;tant, &longs;uch as are the three kinds of Pe­ <lb/>riods of the ebbings and flowings; for that they depend on cau&longs;es <lb/>that are invariable, &longs;imple, and eternal. </s><s>But becau&longs;e that &longs;e­ <lb/>condary and particular cau&longs;es, able to make many alterations, in­ <lb/>termix with the&longs;e that are the primary and univer&longs;al; and the&longs;e <lb/>&longs;econdary cau&longs;es being part of them incon&longs;tant, and not to be <lb/>ob&longs;erved; as for example, The alteration of Winds, and part <lb/>(though terminate and fixed) unob&longs;erved for their multiplicity, <lb/>as are the lengths of the Straights, their various inclinations to­ <lb/>wards this or that part, the &longs;o many and &longs;o different depths of the <lb/>Waters, who &longs;hall be able, unle&longs;s after very long ob&longs;ervations, and <lb/>very certain relations, to frame &longs;o expeditious Hi&longs;tories thereof, as <lb/>that they may &longs;erve for Hypoth e&longs;es, and certain &longs;uppo&longs;itions to <lb/>&longs;uch as will by their combinations give adequate rea&longs;ons of all the <lb/>appearances, and as I may &longs;ay, Anomalie, and particular irregula­ <lb/>rities that may be di&longs;covered in the motions of the Waters? </s><s>I <lb/>will content my &longs;elf with adverti&longs;ing you, that the accidental <lb/>cau&longs;es are in nature, and are able to produce many alterations; <lb/>for the more minute ob&longs;ervations, I remit them to be made by <lb/>tho&longs;e that frequent &longs;everal Seas: and onely by way of a conclu­ <lb/>&longs;ion to this our conference, I will propo&longs;e to be con&longs;idered, how <lb/>that the preci&longs;e times of the fluxes and refluxes do not onely hap­ <lb/>pen to be altered by the length of Straights, and by the diffe­ <lb/>rence of depths; but I believe that a notable alteration may al&longs;o <lb/>proceed from the comparing together of &longs;undry tarcts of Sea, <lb/>different in greatne&longs;s; and in po&longs;ition, or, if you will, inclina­ <lb/>tion; which difference happeneth exactly here in the <emph type="italics"/>Adriatick<emph.end type="italics"/> <pb xlink:href="040/01/443.jpg" pagenum="421"/>Gulph, le&longs;&longs;e by far than the re&longs;t of the Mediterrane, and placed in <lb/>&longs;o different an inclination, that whereas that hath its bounds that <lb/>inclo&longs;eth it on the Ea&longs;tern part, as are the Coa&longs;ts of <emph type="italics"/>Syria,<emph.end type="italics"/> this is <lb/>&longs;hut up in its more We&longs;terly part: and becau&longs;e the ebbings and <lb/>flowings are much greater towards the extremities, yea, becau&longs;e <lb/>the Seas ri&longs;ings and fallings are there onely greate&longs;t, it may pro­ <lb/>bably happen that the times of Flood at <emph type="italics"/>Venice<emph.end type="italics"/> may be the time of <lb/>low Water in the other Sea, which, as being much greater, and <lb/>di&longs;tended more directly from We&longs;t to Ea&longs;t, cometh in a certain <lb/>&longs;ort to have dominion over the <emph type="italics"/>Adriatick:<emph.end type="italics"/> and therefore it <lb/>would be no wonder, in ca&longs;e the effects depending on the pri­ <lb/>mary cau&longs;es, &longs;hould not hold true in the times that they ought, <lb/>and that corre&longs;pond to the periods in the <emph type="italics"/>Adriatick,<emph.end type="italics"/> as it doth <lb/>in the re&longs;t of the Mediterrane. </s><s>But the&longs;e Particularities require <lb/>long Ob&longs;ervations, which I neither have made as yet, nor &longs;hall I <lb/>ever be able to make the &longs;ame for the future.</s></p><p type="main"><s>SAGR. </s><s>You have, in my opinion, done enough in opening us <lb/>the way to &longs;o lofty a &longs;peculation, of which, if you had given us <lb/>no more than that fir&longs;t general Propo&longs;ition that &longs;eemeth to me to <lb/>admit of no reply, where you declare very rationally, that the <lb/>Ve&longs;&longs;els containing the Sea-waters continuing &longs;tedfa&longs;t, it would <lb/>be impo&longs;&longs;ible, according to the common cour&longs;e of Nature, that <lb/>tho&longs;e motions &longs;hould follow in them which we &longs;ee do follow; <lb/>and that, on the other &longs;ide, granting the motions a&longs;cribed, for o­ <lb/>ther re&longs;pects, by <emph type="italics"/>Copernicus<emph.end type="italics"/> to the Terre&longs;trial Globe, the&longs;e &longs;ame <lb/>alterations ought to en&longs;ue in the Seas, if I &longs;ay you had told us no <lb/>more, this alone in my judgment, &longs;o far exceeds the vanities in­ <lb/>troduced by &longs;o many others, that my meer looking on them <lb/>makes me nau&longs;eate them, and I very much admire, that among <lb/>men of &longs;ublime wit, of which neverthele&longs;s there are not a few, <lb/>not one hath ever con&longs;idered the incompatibility that is between <lb/>the reciprocal motion of the Water contained, and the immobi­ <lb/>lity of the Ve&longs;&longs;el containing, which contradiction &longs;eemeth to me <lb/>now &longs;o manife&longs;t.</s></p><p type="main"><s>SALV. </s><s>It is more to be admired, that it having come into the <lb/><arrow.to.target n="marg814"></arrow.to.target> <lb/>thoughts of &longs;ome to refer the cau&longs;e of the Tide to the motion of <lb/>the Earth, therein &longs;hewing a more than common apprehen&longs;ion, <lb/>they &longs;hould, in afterwards driving home the motion clo&longs;e with <lb/>no &longs;ide; and all, becau&longs;e they did not &longs;ee that one &longs;imple and <lb/>uniform motion, as <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> the &longs;ole diurnal motion of the Terre­ <lb/>&longs;trial Globe, doth not &longs;uffice, but that there is required an une­ <lb/>ven motion, one while accelerated, and another while retarded: <lb/>for when the motion of the Ve&longs;&longs;els are uniforme, the waters <lb/>contained will habituate them&longs;elves thereto, without ever ma­ <lb/>king any alteration. </s><s>To &longs;ay al&longs;o (as it is related of an ancient <pb xlink:href="040/01/444.jpg" pagenum="422"/><arrow.to.target n="marg815"></arrow.to.target> <lb/>Mathematician) that the motion of the Earth meeting with the <lb/>motion of the Lunar Orb, the concurrence of them occa&longs;ioneth <lb/>the Ebbing and Flowing, is an ab&longs;olute vanity, not onely be­ <lb/>cau&longs;e it is not expre&longs;t, nor &longs;een how it &longs;hould &longs;o happen, but the <lb/>fal&longs;ity is obvious, for that the Revolution of the Earth is not con­ <lb/>trary to the motion of the Moon, but is towards the &longs;ame way. <lb/></s><s>So that all that hath been hitherto &longs;aid, and imagined by others, <lb/>is, in my judgment, altogether invalid. </s><s>But among&longs;t all the <lb/>famous men that have philo&longs;ophated upon this admirable effect <lb/><arrow.to.target n="marg816"></arrow.to.target> <lb/>of Nature, I more wonder at <emph type="italics"/>Kepler<emph.end type="italics"/> than any of the re&longs;t, who <lb/>being of a free and piercing wit, and having the motion a&longs;cri­ <lb/>bed to the Earth, before him, hath for all that given his ear and <lb/>a&longs;&longs;ent to the Moons predominancy over the Water, and to oc­ <lb/>cult properties, and &longs;uch like trifles.</s></p><p type="margin"><s><margin.target id="marg814"></margin.target><emph type="italics"/>One &longs;ingle moti­ <lb/>on of the terre&longs;tri­ <lb/>al Globe &longs;ufficeth <lb/>not to produce the <lb/>Ebbing & Flowing<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg815"></margin.target><emph type="italics"/>The opinion of<emph.end type="italics"/> <lb/>Seleucus <emph type="italics"/>the Ma­ <lb/>thematician cen&longs;u­ <lb/>red.<emph.end type="italics"/></s></p><p type="margin"><s><margin.target id="marg816"></margin.target>Kepler <emph type="italics"/>is with <lb/>ve&longs;pect blamed.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>I am of opinion, that to the&longs;e more &longs;paculative per­ <lb/>&longs;ons the &longs;ame happened, that at pre&longs;ent befalls me, namely, the <lb/>not under&longs;tanding the intricate commixtion of the three Periods <lb/>Annual, Monethly, and Diurnal; And how their cau&longs;es &longs;hould <lb/>&longs;eem to depend on the Sun, and on the Moon, without the Suns <lb/>or Moons having any thing to do with the Water; a bu&longs;ine&longs;&longs;e, <lb/>for the full under&longs;tanding of which I &longs;tand in need of a little <lb/>longer time to con&longs;ider thereof, which the novelty and difficulty <lb/>of it hath hitherto hindred me from doing: but I de&longs;pair not, but <lb/>that when I return in my &longs;olitude and &longs;ilence to ruminate that <lb/>which remaineth in my fancy, not very well dige&longs;ted, I &longs;hall <lb/>make it my own. </s><s>We have now, from the&longs;e four dayes Di&longs;­ <lb/>cour&longs;e, great atte&longs;tations, in favour of the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme, <lb/>among&longs;t which the&longs;e three taken: the fir&longs;t, from the Stations and <lb/>Retrogradations of the Planets, and from their approaches, and <lb/>rece&longs;&longs;ions from the Earth; the &longs;econd, from the Suns revolving <lb/>in it &longs;elf, and from what is ob&longs;erved in its &longs;pots; the third, from <lb/>the Ebbing and Flowing of the Sea do &longs;hew very rational and <lb/>concluding.</s></p><p type="main"><s>SALV. </s><s>To which al&longs;o haply, in &longs;hort, one might adde a <lb/>fourth, and peradventure a fifth; a fourth, I &longs;ay, taken from <lb/>the fixed &longs;tars, &longs;eeing that in them, upon exact ob&longs;ervations, tho&longs;e <lb/>minute mutations appear, that <emph type="italics"/>Copernicus<emph.end type="italics"/> thought to have been <lb/>in&longs;en&longs;ible. </s><s>There &longs;tarts up, at this in&longs;tant, a fifth novelty, from <lb/>which one may argue mobility in the Terre&longs;trial Globe, by <lb/><arrow.to.target n="marg817"></arrow.to.target> <lb/>means of that which the mo&longs;t Illu&longs;trious <emph type="italics"/>Signore Cæ&longs;are,<emph.end type="italics"/> of the <lb/>noble Family of the <emph type="italics"/>Mar&longs;ilii<emph.end type="italics"/> of <emph type="italics"/>Bologna,<emph.end type="italics"/> and a <emph type="italics"/>Lyncean<emph.end type="italics"/> Aca­ <lb/>demick, di&longs;covereth with much ingenuity, who in a very learned <lb/>Tract of his, &longs;heweth very particularly how that he had ob&longs;erved <lb/>a continual mutation, though very &longs;low in the Meridian line, <lb/>of which Treati&longs;e, at length, with amazement, peru&longs;ed by me, <pb xlink:href="040/01/445.jpg" pagenum="423"/>I hope he will communicate Copies to all tho&longs;e that are Students <lb/>of Natures Wonders.</s></p><p type="margin"><s><margin.target id="marg817"></margin.target>Sig. </s><s>Cæ&longs;are Mar­ <lb/>&longs;ilius <emph type="italics"/>ob&longs;erveth the <lb/>Meridian to be <lb/>moveable.<emph.end type="italics"/></s></p><p type="main"><s>SAGR. </s><s>This is not the fir&longs;t time that I have heard &longs;peak of <lb/>the exqui&longs;ite Learning of this Gentleman, and of his &longs;hewing <lb/>him&longs;elf a zealous Patron of all the Learned, and if this, or any <lb/>other of his Works &longs;hall come to appear in publique, we may be <lb/>aforehand a&longs;&longs;ured, that they will be received, as things of great <lb/>value.</s></p><p type="main"><s>SALV. </s><s>Now becau&longs;e it is time to put an end to our Di&longs;cour­ <lb/>&longs;es, it remaineth, that I intreat you, that if, at more lea&longs;ure go­ <lb/>ing over the things again that have been alledged you meet <lb/>with any doubts, or &longs;cruples not well re&longs;olved, you will excu&longs;e <lb/>my over&longs;ight, as well for the novelty of the Notion, as for the <lb/>weakne&longs;&longs;e of my wit, as al&longs;o for the grandure of the Subject, <lb/>as al&longs;o finally, becau&longs;e I do not, nor have pretended to that a&longs;­ <lb/>&longs;ent from others, which I my &longs;elf do not give to this conceit, <lb/>which I could very ea&longs;ily grant to be a <emph type="italics"/>Chymæra,<emph.end type="italics"/> and a meer <lb/>paradox; and you <emph type="italics"/>Sagredus,<emph.end type="italics"/> although in the Di&longs;cour&longs;es pa&longs;t <lb/>you have many times, with great applau&longs;e, declared, that you <lb/>were plea&longs;ed with &longs;ome of my conjectures, yet do I believe, that <lb/>that was in part more occa&longs;ioned by the novelty than by the cer­ <lb/>tainty of them, but much more by your courte&longs;ie, which did <lb/>think and de&longs;ire, by its a&longs;&longs;ent, to procure me that content which <lb/>we naturally u&longs;e to take in the approbation and applau&longs;e of our <lb/>own matters: and as your civility hath obliged me to you; &longs;o <lb/>am I al&longs;o plea&longs;ed with the ingenuity of <emph type="italics"/>Simplicius.<emph.end type="italics"/> Nay, his <lb/>con&longs;tancy in maintaining the Doctrine of his Ma&longs;ter, with &longs;o <lb/>much &longs;trength & undauntedne&longs;s, hath made me much to love him. <lb/></s><s>And as I am to give you thanks, <emph type="italics"/>Sagredus,<emph.end type="italics"/> for your courteous a&longs;­ <lb/>fection; &longs;o of <emph type="italics"/>Simplicius,<emph.end type="italics"/> I ask pardon, if I have &longs;ometimes <lb/>moved him with my too bold and re&longs;olute &longs;peaking: and let him <lb/>be a&longs;&longs;ured that I have not done the &longs;ame out of any inducement <lb/>of &longs;ini&longs;ter affection, but onely to give him occa&longs;ion to &longs;et before <lb/>us more lofty fancies that might make me the more knowing.</s></p><p type="main"><s>SIMP. </s><s>There is no rea&longs;on why you &longs;hould make all the&longs;e ex­ <lb/>cu&longs;es, that are needle&longs;&longs;e, and e&longs;pecially to me, that being accu­ <lb/>&longs;tomed to be at Conferences and publique Di&longs;putes, have an <lb/>hundred times &longs;een the Di&longs;putants not onely to grow hot and an­ <lb/>gry at one another, but likewi&longs;e to break forth into injurious <lb/>words, and &longs;ometimes to come very neer to blows. </s><s>As for the <lb/>pa&longs;t Di&longs;cour&longs;es, and particulatly in this la&longs;t, of the rea&longs;on of <lb/>the Ebbing and Flowing of the Sea, I do not, to &longs;peak the truth, <lb/>very well apprehend the &longs;ame, but by that &longs;light <emph type="italics"/>Idea,<emph.end type="italics"/> what e­ <lb/>ver it be, that I have formed thereof to my &longs;elf, I confe&longs;&longs;e that <lb/>your conceit &longs;eemeth to me far more ingenuous than any of all <pb xlink:href="040/01/446.jpg" pagenum="424"/>tho&longs;e that I ever heard be&longs;ides, but yet neverthele&longs;&longs;e I e&longs;teem it <lb/>not true and concluding: but keeping alwayes before the eyes <lb/>of my mind a &longs;olid Doctrine that I have learn't from a mo&longs;t <lb/>learned and ingenuous per&longs;on, and with which it is nece&longs;&longs;ary to <lb/>&longs;it down; I know that both you being asked, Whether God, by <lb/>his infinite Power and Wi&longs;dome might confer upon the Element <lb/>of Water the reciprocal motion which we ob&longs;erve in the &longs;ame in <lb/>any other way, than by making the containing Ve&longs;&longs;el to move; I <lb/>know, I &longs;ay, that you will an&longs;wer, that he might, and knew how <lb/>to have done the &longs;ame many wayes, and tho&longs;e unimaginable to <lb/>our &longs;hallow under&longs;tanding: upon which I forthwith conclude, <lb/>that this being granted, it would be an extravagant boldne&longs;&longs;e <lb/>for any one to goe about to limit and confine the Divine <lb/>Power and Wi&longs;dome to &longs;ome one particular conjecture of <lb/>his own.</s></p><p type="main"><s>SALV. </s><s>This of yours is admirable, and truly Angelical Do­ <lb/>ctrine, to which very exactly that other accords, in like manner <lb/>divine, which whil&longs;t it giveth us leave to di&longs;pute, touching the <lb/>con&longs;titution of the World, addeth withall (perhaps to the end, <lb/>that the exerci&longs;e of the minds of men might neither be di&longs;cou­ <lb/>raged, nor made bold) that we cannot find out the works made <lb/>by his hands. </s><s>Let therefore the Di&longs;qui&longs;ition permitted and or­ <lb/>dain'd us by God, a&longs;&longs;i&longs;t us in the knowing, and &longs;o much more <lb/>admiring his greatne&longs;&longs;e, by how much le&longs;&longs;e we finde our &longs;elves <lb/>too dull to penetrate the profound Aby&longs;&longs;es of his infinite Wi&longs;­ <lb/>dome.</s></p><p type="main"><s>SAGR. </s><s>And this may &longs;erve for a final clo&longs;e of our four dayes <lb/>Di&longs;putations, after which, if it &longs;eem good to <emph type="italics"/>Salviatus,<emph.end type="italics"/> to take <lb/>&longs;ome time to re&longs;t him&longs;elf, our curio&longs;ity mu&longs;t, of nece&longs;&longs;ity, grant <lb/>him the &longs;ame, yet upon condition, that when it is le&longs;&longs;e incommo­ <lb/>dious for him, he will return and &longs;atisfie my de&longs;ire in particular <lb/>concerning the Problemes that remain to be di&longs;cu&longs;t, and that I <lb/>have &longs;et down to be propounded at one or two other Conferen­ <lb/>ces, according to our agreement: and above all, I &longs;hall very <lb/>impatiently wait to hear the Elements of the new Science of our <lb/><emph type="italics"/>Academick<emph.end type="italics"/> about the natural and violent local Motions. </s><s>And <lb/>in the mean time, we may, according to our cu&longs;tome, &longs;pend an <lb/>hour in taking the Air in the <emph type="italics"/>Gondola<emph.end type="italics"/> that waiteth for us.</s></p><p type="head"><s><emph type="italics"/>FINIS.<emph.end type="italics"/></s></p><pb xlink:href="040/01/447.jpg"/><figure id="id.040.01.447.1.jpg" xlink:href="040/01/447/1.jpg"/><figure id="id.040.01.447.2.jpg" xlink:href="040/01/447/2.jpg"/><figure id="id.040.01.447.3.jpg" xlink:href="040/01/447/3.jpg"/><figure id="id.040.01.447.4.jpg" xlink:href="040/01/447/4.jpg"/><p type="caption"><s><emph type="italics"/>Place this Plate <lb/> at the end of <lb/>the fourth<emph.end type="italics"/><lb/>Dialogue</s></p></chap> <pb xlink:href="040/01/448.jpg"/><pb xlink:href="040/01/449.jpg"/><chap><p type="head"> <s>THE <lb/>Ancient and Modern <lb/>DOCTRINE <lb/>OF <lb/>Holy Fathers, <lb/>AND <lb/>Iudicious Divines,</s></p><p type="head"> <s>CONCERNING</s></p><p type="head"> <s>The ra&longs;h citation of the Te&longs;timony of SACRED <lb/>SCRIPTURE, in Conclu&longs;ions meerly Natural, and <lb/>that may be proved by Sen&longs;ible Experiments, and <lb/>Nece&longs;&longs;ary Demon&longs;trations.</s></p><p type="head"> <s>Written, &longs;ome years &longs;ince, to Gratifie The mo&longs;t SERENE <lb/>CHRISTINA LOTHARINGA, <emph type="italics"/>Arch­<lb/>Dutche&longs;s<emph.end type="italics"/> of <emph type="italics"/>TVSCANR<emph.end type="italics"/>;</s></p><p type="head"> <s>By GALILÆO GALILÆI, A Gentleman of <lb/><emph type="italics"/>Florence,<emph.end type="italics"/> and Chief Philo&longs;opher and Mathematician to <lb/>His mo&longs;t Serene Highne&longs;s the Grand <emph type="italics"/>DVKE.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>And now rendred into Engli&longs;h from the Italian,<emph.end type="italics"/><lb/>BY <lb/>THOMAS SALUSBURY.</s></p><p type="main"> <s><emph type="italics"/>Naturam Rerum invenire, difficile; & ubi inveneris, indicare <lb/>in vulgus, nefas.<emph.end type="italics"/> Plato.</s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, 1661.</s></p> </chap> <pb xlink:href="040/01/450.jpg"/><chap><pb xlink:href="040/01/451.jpg" pagenum="427"/><p type="head"> <s>TO <lb/>Her mo&longs;t Serene <lb/>HIGHNES <lb/>THE <lb/>Gran Duche&longs;s Mother.</s></p><p type="main"> <s>Some years &longs;ince, as Your mo&longs;t Serene Highne&longs;s well <lb/>knoweth, I did di&longs;cover many particulars in Hea­<lb/>ven that had been un&longs;een and unheard of untill <lb/>this our Age; which, as well for their Novelty, as <lb/>for certain con&longs;equences which depend upon <lb/>them, cla&longs;hing with &longs;ome Phy&longs;ical Propo&longs;itions commonly recei­<lb/>ved by the Schools, did &longs;tir up again&longs;t me no &longs;mall number of <lb/>&longs;uch as profe&longs;&longs;ed the vulgar Philo&longs;ophy in the Univer&longs;ities; as if <lb/>I had with my own hand newly placed the&longs;e things in Heaven to <lb/>ob&longs;cure and di&longs;turb Nature and the Sciences: who forgetting <lb/>that the multitude of Truths contribute, and concur to the inve­<lb/>&longs;tigation, augmentation, and e&longs;tabli&longs;hment of the Arts, and not to <lb/>their diminution, and de&longs;truction; and at the &longs;ame time &longs;hewing <lb/>them&longs;elves more affectionate to their own Opinions, than to <lb/>Truth, went about to deny, and to di&longs;prove tho&longs;e Novelties; of <lb/>which their very &longs;en&longs;e, had they but plea&longs;ed to have inten&longs;ly be­<lb/>held them, would have rendered them thorowly a&longs;&longs;ured. </s> <s>And <lb/>to this purpo&longs;e they alledged &longs;undry things, and publi&longs;hed cer­<lb/>tain Papers fraughted with vain di&longs;cour&longs;es; and which was a <lb/>more gro&longs;s errour, interwoven with the atte&longs;tations of the Sacred <lb/>Scriptures, taken from places by them not rightly under&longs;tood, <lb/>and which did not any thing concern the point for which they <lb/>were produced Into which errour perhaps they would not <lb/>have run, if they had but been adverti&longs;ed of a mo&longs;t profitable <lb/>Document which S. <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/> giveth us, concerning our pro­<lb/>ceeding warily, in making po&longs;itive determinations in points that <pb xlink:href="040/01/452.jpg" pagenum="428"/>are ob&longs;cure and hard to be under&longs;tood by the meer help of <lb/>ratiocination; where treating (as we) of a certain natural conclu­<lb/>&longs;ion concerning Cele&longs;tial Bodies, he thus writes: <emph type="italics"/>(a) But now<emph.end type="italics"/><lb/><arrow.to.target n="marg818"></arrow.to.target><lb/><emph type="italics"/>having evermore a re&longs;pect to the moderation of pious Gravity, <lb/>we ought to believe nothing unadvi&longs;edly in a doubtful point; le&longs;t <lb/>we conceive a prejudice again&longs;t that, in favour to our Errour, <lb/>which Truth hereafter may di&longs;cover to be no wi&longs;e contrary to the <lb/>Sacred Books either of the Old, or New Te&longs;tament.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg818"></margin.target><emph type="italics"/>(a) Nunc au­<lb/>tem, &longs;ervatâ &longs;em­<lb/>per moderatione piæ <lb/>gravitatis, nihil <lb/>credere de re ob­<lb/>&longs;curâ temerè de­<lb/>bemus, ne fortè, <lb/>quod po&longs;tea veritas <lb/>patefecerit, quam­<lb/>vis Libris Sanct is, <lb/>&longs;ive Te&longs;tamenti <lb/>Veteris, &longs;ive No­<lb/>vi, nisllo modo e&longs;&longs;e <lb/>po&longs;&longs;it adver&longs;um, <lb/>tamen propter a­<lb/>morem no&longs;tri erro­<lb/>ris, oderimus.<emph.end type="italics"/></s></p><p type="main"> <s>It hath &longs;ince come to pa&longs;s, that Time hath by degrees di&longs;co­<lb/>vered to every one the truths before by me indicated: and to­<lb/>gether with the truth of the fact, a di&longs;covery hath been made of <lb/>the difference of humours between tho&longs;e who &longs;imply and with­<lb/>out pa&longs;&longs;ion did refu&longs;e to admit &longs;uch like <emph type="italics"/>Phænomena<emph.end type="italics"/> for true, and <lb/>tho&longs;e who to their incredulity had added &longs;ome di&longs;compo&longs;ed af­<lb/>fection: For as tho&longs;e who were better grounded in the Science of <lb/><arrow.to.target n="marg819"></arrow.to.target><lb/>A&longs;tronomy, and Natural Philo&longs;ophy, became &longs;atisfied upon my <lb/>fir&longs;t ntimation of the news; &longs;o all tho&longs;e who &longs;tood not in the <lb/>Negative, or in doubt for any other rea&longs;on, but becau&longs;e it was <lb/>an unlookt-for-Novelty, and becau&longs;e they had not an occa&longs;ion of <lb/>&longs;eeing a &longs;ensible experiment thereof, did by degrees come to &longs;a­<lb/>risfie them&longs;elves: But tho&longs;e, who be&longs;ides the love they bore to <lb/>their fir&longs;t Errour, have I know not what imaginary intere&longs;s to <lb/>render them di&longs;affected; not &longs;o much towards the things, as to­<lb/>wards the Author of them, not being able any longer to deny <lb/>them, conceal them&longs;elves under an ob&longs;tinate &longs;ilence; and being <lb/>exa&longs;perated more than ever by that whereby tho&longs;e others were <lb/>&longs;atisfied and convinced, they divert their thoughts to other pro­<lb/>jects, and &longs;eek to prejudice me &longs;ome other wayes: of whom I <lb/>prore&longs;s that I would make no more account than I have done of <lb/>tho&longs;e who heretofore have contradicted me (at whom I alwaies <lb/>laugh, as being a&longs;&longs;ured of the i&longs;&longs;ue that the bu&longs;ine&longs;s is to have) <lb/>but that I &longs;ee that tho&longs;e new Calumnies and Per&longs;ecutions do not <lb/>determine in our greater or le&longs;ier Learning (in which I will &longs;carce <lb/>pretend to any thing) but extend &longs;o far as to attempt to a&longs;per&longs;e <lb/>me with Crimes which ought to be, and are more abhorred by me <lb/>than Death it &longs;elf: Nor ought I to content my &longs;elf that they <lb/>are known to be unju&longs;t by tho&longs;e onely who know me and them, <lb/>but by all men what&longs;oever. </s> <s>They per&longs;i&longs;ting therefore in their <lb/>fir&longs;t Re&longs;olution, Of ruining me and what&longs;oever is mine, by all <lb/>imaginable waies; and knowing how that I in my Studies of <lb/>A&longs;tronomy and Philo&longs;ophy hold, as to the Worlds Sy&longs;teme, <lb/>That the Sun, without changing place, is &longs;ituate in the Centre <lb/>of the Conver&longs;ion of the Cele&longs;tial Orbes; and that the Earth, <lb/>convertible about its own Axis, moveth it &longs;elf about the Sun: <lb/>And moreover under&longs;tanding, that I proceed to maintain this Po­<pb xlink:href="040/01/453.jpg" pagenum="429"/>&longs;ition, not onely by refuting the Rea&longs;ons of <emph type="italics"/>Ptolomy<emph.end type="italics"/> and <emph type="italics"/>Ari&longs;to­<lb/>tle,<emph.end type="italics"/> but by producing many on the contrary; and in particular, <lb/>&longs;ome Phy&longs;ical pertaining to Natural Effects, the cau&longs;es of which <lb/>perhaps can be by no other way a&longs;&longs;igned; and others A&longs;trono­<lb/>mical depending upon many circum&longs;tances and encounters of <lb/>new Di&longs;coveries in Heaven, which manife&longs;tly confute the Ptolo­<lb/>maick Sy&longs;teme, and admirably agree with and confirm this other <lb/>Hypothe&longs;is: and po&longs;&longs;ibly being a&longs;hamed to &longs;ee the known truth <lb/>of other Po&longs;itions by me a&longs;&longs;erted, different from tho&longs;e that have <lb/>been commonly received; and therefore di&longs;tru&longs;ting their de­<lb/>fence &longs;o long as they &longs;hould continue in the Field of Philo&longs;o­<lb/>phy: for the&longs;e re&longs;pects, I &longs;ay, they have re&longs;olved to try whe­<lb/>ther they could make a Shield for the fallacies of their Argu­<lb/>ments of the Mantle of a feigned Religion, and of the Autho­<lb/>rity of the Sacred Scriptures, applyed by them with little judg­<lb/>ment to the confutation of &longs;uch Rea&longs;ons of mine as they had <lb/>neither under&longs;tood, nor &longs;o much as heard.</s></p><p type="margin"> <s><margin.target id="marg819"></margin.target>Lib_{+} 2. Gene&longs;i <lb/>ad Literam in <lb/>fine.</s></p><p type="main"> <s>And fir&longs;t, they have indeavoured, as much as in them lay, to <lb/>divulge an opiniou thorow the Univer&longs;e, that tho&longs;e Propo&longs;itions <lb/>are contrary to the Holy Letters, and con&longs;equently Damnable <lb/>and Heretical: And thereupon perceiving, that for the mo&longs;t <lb/>part, the inclination of Mans Nature is more prone to imbrace <lb/>tho&longs;e enterprizes, whereby his Neighbour may, although un­<lb/>ju&longs;tly, be oppre&longs;&longs;ed, than tho&longs;e from whence he may receive <lb/>ju&longs;t incouragement; it was no hard matter to find tho&longs;e Com­<lb/>plices, who for &longs;uch (that is, for Damnable and Heretical) did <lb/>from their Pulpits with unwonted confidence preach it, with but <lb/>an unmerciful and le&longs;s con&longs;iderate injury, not only to this Do­<lb/>ctrine, and to its followers, but to all Mathematicks and Ma­<lb/>thematicians together. </s> <s>Hereupon a&longs;&longs;uming greater confidence, <lb/>and vainly hoping that that Seed which fir&longs;t took root in their un­<lb/>&longs;ound mindes, might &longs;pread its branches, and a&longs;cend towards <lb/>Heaven, they went &longs;cattering rumours up and down among the <lb/>People, That it would, ere long be condemned by Supreme Au­<lb/>thority: and knowing that &longs;uch a <emph type="italics"/>Cen&longs;ure<emph.end type="italics"/> would &longs;upplant <lb/>not onely the&longs;e two Conclu&longs;ions of the Worlds Sy&longs;teme, but <lb/>would make all other A&longs;tronomical and Phy&longs;ical Ob&longs;ervations <lb/>that have corre&longs;pondence and nece&longs;&longs;ary connection therewith to <lb/>become damnable, to facilitate the bu&longs;ine&longs;s they &longs;eek all they <lb/>can to make this opinion (at lea&longs;t among the vulgar) to &longs;eem new, <lb/>and peculiar to my &longs;elf, not owning to know that <emph type="italics"/>Nicholas Coper­<lb/>nicus<emph.end type="italics"/> was its Authour, or rather Re&longs;torer and Confirmer: a per­<lb/>&longs;on who was not only a Catholick, but a Prie&longs;t, Canonick, and <lb/>&longs;o e&longs;teemed, that there being a Di&longs;pute in the <emph type="italics"/>Lateran Council,<emph.end type="italics"/><lb/>under <emph type="italics"/>Leo<emph.end type="italics"/> X. touching the correction of the Eccle&longs;ia&longs;tick Ca­<pb xlink:href="040/01/454.jpg" pagenum="430"/>lendar, he was &longs;ent for to <emph type="italics"/>Rome<emph.end type="italics"/> from the remote&longs;t parts of <lb/><emph type="italics"/>Germany,<emph.end type="italics"/> for to a&longs;&longs;i&longs;t in this Reformation, which for that time <lb/>was left imperfect, onely becau&longs;e as then the true mea&longs;ure of <lb/>the Year and Lunar Moneth was not exactly known: whereupon <lb/>it was given him in charge by the Bi&longs;hop of <emph type="italics"/>Sempronia,<emph.end type="italics"/> at that <lb/>time Super-intendent in that Affair, to &longs;earch with reiterated <lb/>&longs;tudies and pains for greater light and certainty, touching tho&longs;e <lb/>Cœle&longs;tial Motions. </s> <s>Upon which, with a Labour truly <emph type="italics"/>Atlantick<emph.end type="italics"/><lb/>and with his admirable Wit, &longs;etting him&longs;elf again to that Study, <lb/>he made &longs;uch a progre&longs;s in the&longs;e Sciences, and reduced the <lb/>knowledge of the Cœle&longs;tial Motions to &longs;uch exactne&longs;&longs;e, that he <lb/>gained the title of an Excellent <emph type="italics"/>A&longs;tronomer.<emph.end type="italics"/> And, according <lb/>unto his Doctrine, not only the Calendar hath been &longs;ince regu­<lb/>lated, but the Tables of all the Motions of the Planets have al­<lb/>&longs;o been calculated: and having reduced the &longs;aid Doctrine into <lb/>&longs;ix Books, he publi&longs;hed them to the World at the in&longs;tance of <lb/>the Cardinal of <emph type="italics"/>Capua,<emph.end type="italics"/> and of the Bi&longs;hop of <emph type="italics"/>Culma.<emph.end type="italics"/> And in <lb/>regard that he had re-a&longs;&longs;umed this &longs;o laborious an enterprize by <lb/>the order of The Pope; he dedicated his Book <emph type="italics"/>De Revolutioni­<lb/>bus Cœle&longs;tibus<emph.end type="italics"/> to His Succe&longs;&longs;our, namely <emph type="italics"/>Paul<emph.end type="italics"/> III. which, being <lb/>then al&longs;o Printed, hath been received by The Holy Church, and <lb/>read and &longs;tudied by all the World, without any the lea&longs;t um­<lb/>brage of &longs;cruple that hath ever been conceived at his Doctrine; <lb/>The which, whil&longs;t it is now proved by manife&longs;t Experiments and <lb/>nece&longs;&longs;ary Demon&longs;trations to have been well grounded, there <lb/>want not per&longs;ons that, though they never &longs;aw that &longs;ame Book in­<lb/>tercept the reward of tho&longs;e many Labours to its Authour, by <lb/>cau&longs;ing him to be cen&longs;ured and pronounced an Heretick; and <lb/>this, only to &longs;atisfie a particular di&longs;plea&longs;ure conceived, without <lb/>any cau&longs;e, again&longs;t another man, that hath no other intere&longs;t in <lb/><emph type="italics"/>Copernicus,<emph.end type="italics"/> but only as he is an approver of his Doctrine.</s></p><p type="main"> <s>Now in regard of the&longs;e fal&longs;e a&longs;per&longs;ions, which they &longs;o unju&longs;tly <lb/>&longs;eek to throw upon me, I have thought it nece&longs;&longs;ary for my ju&longs;ti­<lb/>fication before the World (of who&longs;e judgment in matters of <lb/>Religion and Reputation I ought to make great e&longs;teem) to <lb/>di&longs;cour&longs;e concerning tho&longs;e Particulars, which the&longs;e men produce <lb/>to &longs;candalize and &longs;ubvert this Opinion, and in a word, to con­<lb/>demn it, not only as fal&longs;e, but al&longs;o as Heretical; continually <lb/>making an Hipocritical Zeal for Religion their Shield; going a­<lb/>bout moreover to intere&longs;t the Sacred Scriptures in the Di&longs;pute, <lb/>and to make them in a certain &longs;en&longs;e Mini&longs;ters of their deceiptful <lb/>purpo&longs;es: and farthermore de&longs;iring, if I mi&longs;take not, contrary to <lb/>the intention of them, and of the Holy Fathers to extend (that I <lb/>may not &longs;ay abu&longs;e) their Authority, &longs;o as that even in Conclu&longs;ions <lb/>meerly Natural, and not <emph type="italics"/>de Fide,<emph.end type="italics"/> they would have us altogether <pb xlink:href="040/01/455.jpg" pagenum="431"/>leave Sen&longs;e and Demon&longs;trative Rea&longs;ons, for &longs;ome place of Scri­<lb/>pture which &longs;ometimes under the apparent words may contain <lb/>a different &longs;en&longs;e. </s> <s>Now I hope to &longs;hew with how much <lb/>greater Piety and Religious Zeal I proceed, than they do, in that <lb/>I propo&longs;e not, that the Book of <emph type="italics"/>Copernicus<emph.end type="italics"/> is not to be condemn­<lb/>ed, but that it is not to be condemned, as they would have it; <lb/>without under&longs;tanding it, hearing it, or &longs;o much as &longs;eeing it; <lb/>and e&longs;pecially he being an Author that never treateth of matters <lb/>of Religion or Faith; nor by Rea&longs;ons any way depending on the <lb/>Authority of Sacred Scripoures whereupon he may have erroni­<lb/>ou&longs;ly interpreted them; but alwaies in&longs;i&longs;ts upon Natural Conclu­<lb/>&longs;ions belonging to the Cele&longs;tial Motions, handled with A&longs;trono­<lb/>mical and Geometrical Demon&longs;trations. </s> <s>Not that he had not a <lb/><arrow.to.target n="marg820"></arrow.to.target><lb/>re&longs;pect to the places of the Sacred Leaves, but becau&longs;e he knew <lb/>very well that his &longs;aid Doctrine being demon&longs;trated, it could <lb/>not contradict the Scriptures, rightly, and according to their true <lb/>meaning under&longs;tood. </s> <s>And therefore in the end of his Epi&longs;tle <lb/>Dedicatory, &longs;peaking to The Pope, he &longs;aith thus: <emph type="italics"/>(b) If there <lb/>&longs;hould chance to be any Matæologi&longs;ts, who though ignorant in all <lb/>the Mathematicks, yet pretending a skill in tho&longs;e Learnings, <lb/>&longs;hould dare, upon the authority of &longs;ome place of Scripture wre&longs;ted <lb/>to their purpo&longs;e, to condemn and cen&longs;ure this my Hypothe&longs;is, I <lb/>value them not, but &longs;hall &longs;light their incon&longs;iderate Judgement. </s> <s>For <lb/>it is not unknown, that<emph.end type="italics"/> Lactantius (<emph type="italics"/>otherwi&longs;e a Famous Author, <lb/>though mean Mathematician) writeth very childi&longs;hly touching the <lb/>Form of the Earth, when he &longs;coffs at tho&longs;e who affirm the Earth to <lb/>be in Form of a Globe. </s> <s>So that it ought not to &longs;eem &longs;trange to the <lb/>Ingenious, if any &longs;uch &longs;hould likewi&longs;e now deride us. </s> <s>The Ma­<lb/>thematicks are written for Mathematitians, to whom (if I deceive <lb/>not my &longs;elf) the&longs;e Labours of mine &longs;hall &longs;eem to add &longs;omething, <lb/>as al&longs;o to the Common-weale of the Church, who&longs;e Government is <lb/>now in the hands of Your Holine&longs;s.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg820"></margin.target><emph type="italics"/>(c) Si fort a&longs;&longs;eerunt <lb/>Matæologi, qui <lb/>cum omnium Ma­<lb/>thematicum igna­<lb/>ri &longs;int, tamen de tis <lb/>judicium a&longs;&longs;u­<lb/>munt, propter ali­<lb/>quem locum Scri­<lb/>ptur æ, malè ad &longs;u­<lb/>um propo&longs;itum, de­<lb/>tortum, au&longs;i fue­<lb/>rint hoc meum in­<lb/>&longs;titutum reprehen­<lb/>dere ac in&longs;ectari, <lb/>illos nihil moror, <lb/>adeò ut etiam illo­<lb/>rum judicium, tan­<lb/>guam temera ium <lb/>contemnam. </s> <s>Non <lb/>enim ob&longs;curum e&longs;t, <lb/>Lact antium, cele­<lb/>lebrem alioqui <lb/>Scriptorem, &longs;ed <lb/>Mathematicum <lb/>parvum, admodum <lb/>pueriliter de forma <lb/>Terræ loqui, cùm <lb/>deridet eos, qui <lb/>Terram, Globi for­<lb/>mam habere prodi­<lb/>derunt. </s> <s>Itaque non <lb/>debet mirum vide­<lb/>ri &longs;tudio&longs;is, &longs;i qui <lb/>tales, nos ettam ri­<lb/>debunt. </s> <s>Mathema­<lb/>ta Mathematicis <lb/>&longs;cribuntur; quibus <lb/>& hi no&longs;tri labo­<lb/>res, (&longs;i me non fal­<lb/>lit opinio) vide­<lb/>buntur etiam Rei­<lb/>publicæ Eccle&longs;ia­<lb/>&longs;ticæ conducere a­<lb/>liquid, cujus Prin­<lb/>cipatum Tua San­<lb/>ctitas nunc teness.<emph.end type="italics"/></s></p><p type="main"> <s>And of this kinde do the&longs;e appear to be who indeavour to <lb/>per&longs;wade that <emph type="italics"/>Copernicus<emph.end type="italics"/> may be condemned before his Book is <lb/>read; and to make the World believe that it is not onely lawfull <lb/>but commendable &longs;o to do, produce certain Authorities of the <lb/>Scripture, of Divines, and of Councils; which as they are by me <lb/>had in reverence, and held of Supream Authority, in&longs;omuch that <lb/>I &longs;hould e&longs;teem it high temerity for any one to contradict them <lb/>whil&longs;t they are u&longs;ed according to the In &longs;titutes of Holy Church, <lb/>&longs;o I believe that it is no errour to &longs;peak, &longs;o long as one hath rea­<lb/>&longs;on to &longs;u&longs;pect that a per&longs;on hath a de&longs;ire, for &longs;ome concern of <lb/>his own, to produce and alledge them, to purpo&longs;es different from <lb/>tho&longs;e that are in the mo&longs;t Sacred intention of The Holy Church. <lb/></s> <s>Therefore I not onely prote&longs;t (and my &longs;incerity &longs;hall manife&longs;t it <pb xlink:href="040/01/456.jpg" pagenum="432"/>&longs;elf) that I intend to &longs;ubmit my &longs;elf freely to renounce tho&longs;e et­<lb/>rors, into which, through ignorance, I may run in this Di&longs;cour&longs;e <lb/>of matters pertaining to Religion; but I farther declare, that I <lb/>de&longs;ire not in the&longs;e matters to engage di&longs;pute with any one, al­<lb/>though it &longs;hould be in points that are di&longs;putable: for my end <lb/>endeth onely to this, That if in the&longs;e con&longs;iderations, be&longs;ides my <lb/>own profe&longs;&longs;ion, among&longs;t the errours that may be in them, there <lb/>be any thing apt to give others an hint of &longs;ome Notion beneficial <lb/>to the Holy Church, touching the determining about the <emph type="italics"/>Coper­<lb/>nican<emph.end type="italics"/> Sy&longs;teme, it may be taken and improved as &longs;hall &longs;eem be&longs;t <lb/>to my Superiours: If not, let my Book be torn and burnt; for <lb/>that I do neither intend, nor pretend to gain to my &longs;elf any fruit <lb/>from my writings, that is not Pious and Catholick. </s> <s>And more­<lb/>over, although that many of the things that I ob&longs;erve have been <lb/>&longs;poken in my own hearing, yet I &longs;hall freely admit and grant to <lb/>tho&longs;e that &longs;pake them, that they never &longs;aid them, if &longs;o they <lb/>plea&longs;e, but confe&longs;s that I might have been mi&longs;taken: And <lb/>therefore what I &longs;ay, let it be &longs;uppo&longs;ed to be &longs;poken not by them, <lb/>but by tho&longs;e which were of this opinion.</s></p><p type="main"> <s>The motive therefore that they produce to condemn the Opi­<lb/>nion of the Mobility of the Earth, and Stability of the Sun, is, that <lb/>reading in the Sacred Leaves, in many places, that the Sun mo­<lb/>veth, that the Earth &longs;tandeth &longs;till; and the Scripture not being <lb/>capable of lying, or erring, it followeth upon nece&longs;&longs;ary con&longs;e­<lb/>quence, that the Po&longs;ition of tho&longs;e is Erronious and Heretical, who <lb/>maintain that the Sun of it &longs;elf is immoveable, and the Earth <lb/>moveable.</s></p><p type="main"> <s>Touching this Rea&longs;on I think it fit in the fir&longs;t place, to con­<lb/>&longs;ider, That it is both piou&longs;ly &longs;poken, and prudently affirmed, That <lb/>the Sacred Scripture can never lye, when ever its true meaning is <lb/>under&longs;tood: Which I believe none will deny to be many times <lb/>very ab&longs;truce, and very different from that which the bare &longs;ound <lb/>of the words &longs;ignifieth. </s> <s>Whence it cometh to pa&longs;s, that if ever <lb/>any one &longs;hould con&longs;tantly confine him&longs;elf to the naked Gram­<lb/>matical Sence, he might, erring him&longs;elf, make not only Contra­<lb/>dictions and Propo&longs;itions remote from Truth to appear in the <lb/>Scriptures, but al&longs;o gro&longs;s Here&longs;ies and Bla&longs;phemies: For that we <lb/>&longs;hould be forced to a&longs;&longs;ign to God feet, and hands, and eyes, yea <lb/>more corporal and humane affections, as of Anger, of Repen­<lb/>tance, of Hatred, nay, and &longs;ometimes the Forgetting of things <lb/>pa&longs;t, and Ignorance of tho&longs;e to come: Which Propo&longs;itions, like <lb/>as (&longs;o the Holy Gho&longs;t affirmeth) they were in that manner pro­<lb/>nounced by the Sacred Scriptures, that they might be accommo­<lb/>dated to the Capacity of the Vulgar, who are very rude and un­<lb/>learned; &longs;o likewi&longs;e, for the &longs;akes of tho&longs;e that de&longs;erve to be di­<pb xlink:href="040/01/457.jpg" pagenum="433"/>&longs;tingui&longs;hed from the Vulgar, it is nece&longs;&longs;ary that grave and skilful <lb/>Expo&longs;itors produce the true &longs;en&longs;es of them, and &longs;hew the parti­<lb/>cular Rea&longs;ons why they are dictated under &longs;uch and &longs;uch words. <lb/></s> <s>And this is a Doctrine &longs;o true and common among&longs;t Divines, <lb/>that it would be &longs;uperfluous to produce any atte&longs;tation <lb/>thereof.</s></p><p type="main"> <s>Hence methinks I may with much more rea&longs;on conclude, that <lb/>the &longs;ame holy Writ, when ever it hath had occa&longs;ion to pronounce <lb/>any natural Conclu&longs;ion, and e&longs;pecially, any of tho&longs;e which are <lb/>more ab&longs;truce, and difficult to be under&longs;tood, hath not failed to <lb/>ob&longs;erve this Rule, that &longs;o it might not cau&longs;e confu&longs;ion in the <lb/>mindes of tho&longs;e very people, and render them the more contu­<lb/>macious again&longs;t the Doctrines that were more &longs;ublimely my&longs;teri­<lb/>ous: For (like as we have &longs;aid, and as it plainly appeareth) out <lb/>of the &longs;ole re&longs;pect of conde&longs;cending to Popular Capacity, the <lb/>Scripture hath not &longs;crupled to &longs;hadow over mo&longs;t principal and <lb/>fundamental Truths, attributing, even to God him&longs;elf, qualities <lb/>extreamly remote from, and contrary unto his E&longs;&longs;ence. </s> <s>Who <lb/>would po&longs;itively affirm that the Scripture, laying a&longs;ide that re­<lb/>&longs;pect, in &longs;peaking but occa&longs;ionally of the Earth, of the Water, of <lb/>the Sun, or of any other Creature, hath cho&longs;en to confine it <lb/>&longs;elf, with all rigour, within the bare and narrow literal &longs;en&longs;e of <lb/>the words? </s> <s>And e&longs;pecially, in mentioning of tho&longs;e Crea­<lb/>tures, things not at all concerning the primary In&longs;titution of <lb/>the &longs;ame Sacred Volume, to wit, the Service of God, and the <lb/>&longs;alvation of Souls, and in things infinitely beyond the appre­<lb/>hen&longs;ion of the Vulgar?</s></p><p type="main"> <s>This therefore being granted, methinks that in the Di&longs;cu&longs;&longs;ion <lb/>of Natural Problemes, we ought not to begin at the authority <lb/>of places of Scripture; but at Sen&longs;ible Experiments and Ne­<lb/>ce&longs;&longs;ary Demon&longs;trations: For, from the Divine Word, the <lb/>Sacred Scripture and Nature did both alike proceed; the fir&longs;t, <lb/>as the Holy Gho&longs;ts In&longs;piration; the &longs;econd, as the mo&longs;t ob&longs;er­<lb/>vant Executrix of Gods Commands: And moreover it being <lb/>convenient in the Scriptures (by way of conde&longs;cen&longs;ion to the <lb/>under&longs;tanding of all men) to &longs;peak many things different, in <lb/>appearance; and &longs;o far as concernes the naked &longs;igni&longs;ication of <lb/>the words, from ab&longs;olute truth: But on the contrary, Nature <lb/>being inexorable and immutable, and never pa&longs;&longs;ing the bounds <lb/>of the Laws a&longs;&longs;igned her, as one that nothing careth whether <lb/>her ab&longs;tru&longs;e rea&longs;ons and methods of operating be, or be not ex­<lb/>po&longs;ed to the Capacity of Men; I conceive that that, concer­<lb/>ning Natural Effects, which either Sen&longs;ible Experience &longs;ets be­<lb/>fore our eyes, or Nece&longs;&longs;ary Demon&longs;trations do prove unto us, <lb/>ought not, upon any account, to be called into que&longs;tion, much <pb xlink:href="040/01/458.jpg" pagenum="434"/>le&longs;s condemned upon the te&longs;timony of Texts of Scripture, which <lb/>may, under their words, couch Sen&longs;es &longs;eemingly contrary there­<lb/>to; In regard that every Expre&longs;&longs;ion of Scripture is not tied to <lb/>&longs;o &longs;trict conditions, as every Effect of Nature: Nor doth God <lb/>le&longs;s admirably di&longs;cover him&longs;elf unto us in Nature's Actions, than <lb/>in the Scriptures Sacred Dictions. </s> <s>Which peradventure <emph type="italics"/>Tertul-<emph.end type="italics"/><lb/><arrow.to.target n="marg821"></arrow.to.target><lb/><emph type="italics"/>lian<emph.end type="italics"/> intended to expre&longs;s in tho&longs;e words<emph type="italics"/>: (c) We conclude, God <lb/>is known; fir&longs;t, by Nature, and then again more particularly <lb/>known by Doctrine: by Nature, in his Works; by Doctrine, in his <lb/>Word preached.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg821"></margin.target><emph type="italics"/>Nos definimus, <lb/>Deum, primò N.­<lb/>tura cogno&longs;cen­<lb/>dum; Deinde, Do­<lb/>ctrina recogno&longs;cen­<lb/>dum: Natura ex <lb/>operibus; Doctri­<lb/>na ex pr ædicatio­<lb/>nibus.<emph.end type="italics"/></s></p><p type="main"> <s>But I will not hence affirm, but that we ought to have an ex­<lb/>traordinary e&longs;teem for the Places of Sacred Scripture, nay, being <lb/><arrow.to.target n="marg822"></arrow.to.target><lb/>come to a certainty in any Natural Conclu&longs;ions, we ought <lb/>to make u&longs;e of them, as mo&longs;t appo&longs;ite helps to the true Expo­<lb/>&longs;ition of the &longs;ame Scriptures, and to the inve&longs;tigation of tho&longs;e <lb/>Sen&longs;es which are nece&longs;&longs;arily conteined in them, as mo&longs;t true, and <lb/>concordant with the Truths demon&longs;trated.</s></p><p type="margin"> <s><margin.target id="marg822"></margin.target>Tertul. </s> <s>adver. <lb/></s> <s>Marcion. </s> <s>lib. 1. <lb/>cap. 18.</s></p><p type="main"> <s>This maketh me to &longs;uppo&longs;e, that the Authority of the Sacred <lb/>Volumes was intended principally to per&longs;wade men to the be­<lb/>lief of tho&longs;e Articles and Propo&longs;itions, which, by rea&longs;on they <lb/>&longs;urpa&longs;s all humane di&longs;cour&longs;e, could not by any other Science, or <lb/>by any other means be made credible, than by the Mouth of <lb/>the Holy Spirit it &longs;elf. </s> <s>Be&longs;ides that, even in tho&longs;e Propo&longs;itions, <lb/>which are not <emph type="italics"/>de Fide,<emph.end type="italics"/> the Authority of the &longs;ame Sacred Leaves <lb/>ought to be preferred to the Authority of all Humane Sciences <lb/>that are not written in a Demon&longs;trative Method, but either with <lb/>bare Narrations, or el&longs;e with probable Rea&longs;ons; and this I hold <lb/>to be &longs;o far convenient and nece&longs;&longs;ary, by how far the &longs;aid Di­<lb/>vine Wi&longs;dome &longs;urpa&longs;&longs;eth all humane Judgment and Conjecture. <lb/></s> <s>But that that &longs;elf &longs;ame God who hath indued us with Sen&longs;es, <lb/>Di&longs;cour&longs;e, and Under&longs;tanding hath intended, laying a&longs;ide the <lb/>u&longs;e of the&longs;e, to give the knowledg of tho&longs;e things by other means, <lb/>which we may attain by the&longs;e, &longs;o as that even in tho&longs;e Natural <lb/>Conclu&longs;ions, which either by Sen&longs;ible Experiments or Nece&longs;&longs;ary <lb/>Demon&longs;trations are &longs;et before our eyes, or our Under&longs;tanding, we <lb/>ought to deny Sen&longs;e and Rea&longs;on, I do not conceive that I am <lb/>bound to believe it; and e&longs;pecially in tho&longs;e Sciences, of which <lb/>but a &longs;mall part, and that divided into Conclu&longs;ions is to be <lb/>found in the Scripture: Such as, for in&longs;tance, is that of <emph type="italics"/>A&longs;tro­<lb/>nomy,<emph.end type="italics"/> of which there is &longs;o &longs;mall a part in Holy Writ, that it doth <lb/>not &longs;o much as name any of the Planets, except the Sun and the <lb/>Moon, and once or twice onely <emph type="italics"/>Venus<emph.end type="italics"/> under the name of <emph type="italics"/>Luci­<lb/>fer.<emph.end type="italics"/> For if the Holy Writers had had any intention to per&longs;wade <lb/>People to believe the Di&longs;po&longs;itions and Motions of the Cœle&longs;tial <lb/>Bodies; and that con&longs;equently we are &longs;till to derive that know­<pb xlink:href="040/01/459.jpg" pagenum="435"/>ledge from the Sacred Books they would not, in my opinion, have <lb/>&longs;poken &longs;o little thereof, that it is as much as nothing, in compa­<lb/>ri&longs;on of the infinite admirable Conclu&longs;ions, which in that Sci­<lb/>ence are comprized and demon&longs;trated Nay, that the Authours <lb/>of the Holy Volumes did not only not pretend to teach us the <lb/>Con&longs;titutions and Motions of the Heavens and Stars, their Fi­<lb/>gures, Magnitudes, and Di&longs;tances, but that intentionally (al­<lb/>beit that all the&longs;e things were very well known unto them) they <lb/><arrow.to.target n="marg823"></arrow.to.target><lb/>forbore to &longs;peak of them, is the opinion of the Mo&longs;t Holy & Mo&longs;t <lb/>Learned Fathers: and in S. <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/> we read the following words. <lb/><emph type="italics"/>(c) It is likewi&longs;e commonly asked, of what Form and Figure <lb/>we may believe Heaven to be, according to the Scriptures: For <lb/>many contend much about tho&longs;e matters, which the greater pru­<lb/>dence of our Authors hath forborn to &longs;peak of, as nothing further­<lb/>ing their Learners in relation to able&longs;&longs;ed life; and, (which is <lb/>the chiefe&longs;t thing) taking up much of that time which &longs;hould be <lb/>&longs;pent in holy exerci&longs;es. </s> <s>For what is it to me whether Heaven, as <lb/>a Sphere, doth on all &longs;ides environ the Earth, a Ma&longs;s ballanced in <lb/>the middle of the World; or whether like a Di&longs;h it doth onely cover <lb/>or overca&longs;t the &longs;ame? </s> <s>But becau&longs;e belief of Scripture is urged for <lb/>that cau&longs;e, which we have oft mentioned, that is, That none through <lb/>ignorance of Divine Phra&longs;es, when they &longs;hall find any thing of this <lb/>nature in, or hear any thing cited out of our Bibles which may &longs;eem <lb/>to oppo&longs;e manife&longs;t Conclu&longs;ions, &longs;hould be induced to &longs;u&longs;pect their <lb/>truth, when they admoni&longs;h, relate, & deliver more profitable matters <lb/>Briefly be it &longs;poken, touching the Figure of Heaven, that our Au­<lb/>thors knew the truth: But the H. </s> <s>Spirit would not, that men &longs;hould <lb/>learn what is profitable to none for &longs;alvation.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg823"></margin.target><emph type="italics"/>(c) Quæri etiam<lb/>&longs;olet, quæ forma & <lb/>figura Cæli cre­<lb/>denda &longs;it &longs;ecun­<lb/>dum Scripturas <lb/>no&longs;tras: Multi e­<lb/>nim multum di&longs;­<lb/>put ant de iis rebus, <lb/>quas majori pru­<lb/>dentia no&longs;tri Auto­<lb/>res omi&longs;erunt, ad <lb/>beatam vitam non <lb/>profutur as di&longs;cen­<lb/>libus, & occupan­<lb/>tes (quod prius e&longs;t) <lb/>multum prolixa, <lb/>& rebus &longs;alubri­<lb/>bus impendenda <lb/>temporum &longs;patia. <lb/></s> <s>Quid enim ad me <lb/>pertinet, utrum <lb/>Cælum, &longs;icut Sphæ­<lb/>ra, undique conclu­<lb/>dat Terram, in <lb/>media. </s> <s>Mundi mo­<lb/>le libratam; an <lb/>eam ex una par­<lb/>te de&longs;uper, ve­<lb/>lut di&longs;cus, ope­<lb/>riat? </s> <s>Sed quia de Fide agitur S cripiurærum, propter illam cau&longs;am, quam non &longs;emel commemoravimus, Ne &longs;cilicet <lb/>qui&longs;quam eloquia divina non intelligens, cum de his rebus tale aliquid vel invenerit in Libris No&longs;tris, vel ex illis <lb/>audiverit, quod perceptis a&longs;&longs;ertionibus adver &longs;ari videatur, nullo modo eis, cetera utilia monentibus, vel narrantibus, <lb/>vel pranuntiantibus, credat: Breviter di&longs;cendum e&longs;t, de figura Cæli, hoc &longs;ci&longs;&longs;e Autores no&longs;tros, quod verit as ha­<lb/>bet: Sed Spiritum Dei, qui per ip&longs;os loquebstur, nolui&longs;&longs;e i&longs;ta docere homines, nulli ad &longs;alutem profutura.<emph.end type="italics"/> D. <lb/>Augu&longs;t. </s> <s>Lib. 2. De Gen. </s> <s>ad literam, Cap. </s> <s>9. Idem etiam legitur apud <emph type="italics"/>Petrum Lombardum<emph.end type="italics"/> Magi&longs;trum Sententiarum.</s></p><p type="main"> <s>And the &longs;ame intentional &longs;ilence of the&longs;e &longs;acred Penmen in <lb/>determining what is to be believed of the&longs;e accidents of the Ce­<lb/>le&longs;tial Bodies, is again hinted to us by the &longs;ame Father in the en­<lb/>&longs;uing 10. Chapter upon the Que&longs;tion, Whether we are to believe <lb/>that Heaven moveth, or &longs;tandeth &longs;till, in the&longs;e words: <emph type="italics"/>(d) There<emph.end type="italics"/><lb/><arrow.to.target n="marg824"></arrow.to.target><lb/><emph type="italics"/>are &longs;ome of the Brethren that &longs;tart a que&longs;tion concerning the motion <lb/>of Heaven, Whether it be fixed, or moved: For if it be moved <lb/>(&longs;ay they) how is it a Firmament? </s> <s>If it &longs;tand &longs;till, how do the&longs;e <lb/>Stars which are held to be fixed go round from Ea&longs;t to We&longs;t, the <lb/>more Norchern performing &longs;horter Circuits near the Pole; &longs;o that <lb/>Heaven, if there be another Pole, to us unknown, may &longs;eem to re­<lb/>volve upon &longs;ome other Axis; but if there be not another Pole, it <lb/>may be thought to move as a Di&longs;cus? </s> <s>To whom I reply, That<emph.end type="italics"/><pb xlink:href="040/01/460.jpg" pagenum="436"/><emph type="italics"/>the&longs;e points require many &longs;ubtil and profound Rea&longs;ons, for the <lb/>making out whether they be really &longs;o, or no; the undertakeing and <lb/>di&longs;eu&longs;&longs;ing of which is neither con&longs;i&longs;tent with my lea&longs;ure, nor their <lb/>duty, vvhom I de&longs;ire to in&longs;truct in the nece&longs;&longs;ary matters more di­<lb/>rectly conducing to their &longs;alvation, and to the benefit of The Holy <lb/>Church.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg824"></margin.target><emph type="italics"/>(d) De Motu <lb/>etiam Cæli, non­<lb/>nulli fratres quæ­<lb/>&longs;tionem movent, u­<lb/>trum &longs;tet, an mo­<lb/>veatur; quia &longs;i mo­<lb/>vetur, inquiunt, <lb/>quomodo Firma­<lb/>mentum e&longs;t? </s> <s>Si <lb/>autem &longs;tat, quomo­<lb/>do Sydera quæ in<lb/>ip&longs;o fixa credun­<lb/>tur, ab Oriente in <lb/>Occidentem circum<lb/>eunt, Septentrio­<lb/>nalibus breviores <lb/>gyros juxta cardi­<lb/>nem perag entibus; <lb/>ut Cælum, &longs;i est a­<lb/>lius nobis occultus <lb/>cardo, ex alio ver­<lb/>tice, &longs;icut Sphæra; <lb/>&longs;i autem nullus a­<lb/>lius cardo e&longs;t, vel <lb/>uti di&longs;cus rotari <lb/>videatur? </s> <s>Quibus <lb/>re&longs;pondeo, Multum <lb/>&longs;ubtilibus & labo­<lb/>rio&longs;is rationibus <lb/>i&longs;ta perquiri, ut ve­<lb/>re percipiatur, u­<lb/>trum ita, an non <lb/>ita &longs;it, quibus ine­<lb/>undis atque tra­<lb/>ctandis, nec mihi <lb/>jam tempus e&longs;t, nec <lb/>illis e&longs;&longs;e debet, quos <lb/>ad &longs;alutem &longs;uam, <lb/>è Sanctæ Eccle&longs;iæ <lb/>nece&longs;&longs;aria utilitate <lb/>cupimus informa­<lb/>ri:<emph.end type="italics"/></s></p><p type="main"> <s>From which (that we may come nearer to our particular ca&longs;e) <lb/>it nece&longs;&longs;arily followeth, that the Holy Gho&longs;t not having intend­<lb/>ed to teach us, whether Heaven moveth or &longs;tandeth &longs;till; nor <lb/>whether its Figure be in Form of a Sphere, or of a Di&longs;cus, or di­<lb/>&longs;tended <emph type="italics"/>in Planum<emph.end type="italics"/>: Nor whether the Earth be contained in the <lb/>Centre of it, or on one &longs;ide; he hath much le&longs;s had an intention <lb/>to a&longs;&longs;ure us of other Conclu&longs;ions of the &longs;ame kinde, and in &longs;uch <lb/>a manner, connected to the&longs;e already named, that without the <lb/>dedermination of them, one can neither affirm one or the other <lb/>part; which are, The determining of the Motion and Re&longs;t of the <lb/>&longs;aid Earth, and of the Sun. </s> <s>And if the &longs;ame Holy Spirit hath <lb/>purpo&longs;ely pretermitted to teach us tho&longs;e Propo&longs;itions, as nothing <lb/>concerning his intention, that is, our &longs;alvation; how can it be af­<lb/>firmed, that the holding of one part rather than the other, &longs;hould <lb/>be &longs;o nece&longs;&longs;ary, as that it is <emph type="italics"/>de Fide,<emph.end type="italics"/> and the other erronious? <lb/></s> <s>Can an Opinion be Heretical, and yet nothing concerning the <lb/>&longs;alvation of &longs;ouls? </s> <s>Or can it be &longs;aid that the Holy Gho&longs;t purpo­<lb/>&longs;ed not to teach us a thing that concerned our &longs;alvation? </s> <s>I might <lb/><arrow.to.target n="marg825"></arrow.to.target><lb/>here in&longs;ert the Opinion of an Eccle&longs;ia&longs;tical ^{*} Per&longs;on, rai&longs;ed to the <lb/><arrow.to.target n="marg826"></arrow.to.target><lb/>degree of <emph type="italics"/>Eminenti&longs;&longs;imo,<emph.end type="italics"/> to wit, <emph type="italics"/>That the intention of the Holy <lb/>Gho&longs;t, is to teach us how we &longs;hall go to Heaven, and not how Hea­<lb/>ven goeth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg825"></margin.target>* Card. </s> <s>Baronius.</s></p><p type="margin"> <s><margin.target id="marg826"></margin.target><emph type="italics"/>Spiritu &longs;ancti <lb/>mentem fui&longs;&longs;e, nos <lb/>docere, quomodo ad <lb/>Cælum eatur: non <lb/>autem, quomodo <lb/>Cælum gradiatur.<emph.end type="italics"/><lb/>Cardinal. </s> <s>Bar.</s></p><p type="main"> <s>But let us return to con&longs;ider how much nece&longs;&longs;ary Demon&longs;tra­<lb/>tions, and &longs;en&longs;ible Experiments ought to be e&longs;teemed in Natural <lb/>Conclu&longs;ions; and of what Authority Holy and Learned Divines <lb/>have accounted them, from whom among&longs;t an hundred other atte­<lb/><arrow.to.target n="marg827"></arrow.to.target><lb/>&longs;tations, we have the&longs;e that follow: <emph type="italics"/>(e) We must al&longs;o carefully <lb/>heed and altogether avoid in handling the Doctrine of<emph.end type="italics"/> Mo&longs;es, <emph type="italics"/>to <lb/>avouch or &longs;peak any thing affirmatively and confidently which <lb/>contradicteth the manife&longs;t Experiments and Rea&longs;ons of Philo&longs;o­<lb/>phy, or other Sciences. </s> <s>For &longs;ince all Truth is agreeable to Truth, <lb/>the Truth of Holy Writ cannot be contrary to the &longs;olid Rea&longs;ons <lb/>and Experiments of Humane Learning.<emph.end type="italics"/><lb/><arrow.to.target n="marg828"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg827"></margin.target><emph type="italics"/>(e) Illud etiam <lb/>diligenter caven­<lb/>dum, & emnino <lb/>fugiendum e&longs;t, ne <lb/>in tractanda<emph.end type="italics"/> Mo­<lb/>&longs;is <emph type="italics"/>Dectrina, quic­<lb/>quam affirmate & <lb/>a&longs;&longs;everanter &longs;en­<lb/>tiamus & dica­<lb/>mus, quod repug­<lb/>net manife&longs;tis ex­<lb/>perimentis & rationibus Philo&longs;ophiæ, vel aliarum Di&longs;ciplinarum. </s> <s>Namque cum Verum omne &longs;emper cum Vero <lb/>congruat, non pote&longs;t Verit as Sacrarum Litterarum, Veris Rationibus & Experimentis Humanarum Doctrina­<lb/>rum e&longs;&longs;e contraria.<emph.end type="italics"/> Perk. in Gen. circa Principium.</s></p><p type="margin"> <s><margin.target id="marg828"></margin.target><emph type="italics"/>(f) Si manife­<lb/>&longs;tæ certæque Rati­<lb/>oni, velut &longs;ancta­<lb/>rum Litterarum <lb/>objicitur autori­<lb/>ritas, non intelli­<lb/>git, qui hoc facit; <lb/>& non Scripturæ <lb/>&longs;en&longs;um (ad quem <lb/>penetrare non po­<lb/>tuit) &longs;ed &longs;uum po­<lb/>tius objicit verita­<lb/>ti: nec id quod in <lb/>sa, &longs;ed quod in &longs;e­<lb/>ip&longs;o velue pro ea<lb/>invenit, opponit.<emph.end type="italics"/></s></p><p type="main"> <s>And in St. <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/> we read: <emph type="italics"/>(f) If any one &longs;hall object <lb/>the Authority of Sacred Writ, again&longs;t clear and manife&longs;t Rea&longs;on, <lb/>he that doth &longs;o, knows not what he undertakes: For he objects<emph.end type="italics"/><pb xlink:href="040/01/461.jpg" pagenum="437"/><emph type="italics"/>again&longs;t the Truth, not the &longs;en&longs;e of the Scripture (which is be­<lb/>yond his comprehen&longs;ion) but rather his own; not what is in it, but <lb/>what, finding it in him&longs;elf, he fancyed to be in it.<emph.end type="italics"/></s></p><p type="main"> <s>This granted, and it being true, (as hath been &longs;aid) that two <lb/>Truths cannot be contrary to each other, it is the office of a <lb/>Judicious Expo&longs;itor to &longs;tudy to finde the true Sen&longs;es of Sacred <lb/>Texts, which undoubtedly &longs;hall accord with tho&longs;e Natural Con­<lb/>clu&longs;ions, of which manife&longs;t Sen&longs;e and Nece&longs;&longs;ary Demon&longs;trations </s></p><p type="main"> <s><arrow.to.target n="marg829"></arrow.to.target><lb/>had before made us &longs;ure and certain. </s> <s>Yea, in regard that the <lb/>Scriptures (as hath been &longs;aid) for the Rea&longs;ons alledged, admit in <lb/>many places Expo&longs;itions far from the Sen&longs;e of the words; and <lb/>moreover, we not being able to affirm, that all Interpreters <lb/>&longs;peak by Divine In&longs;piration; For (if it were &longs;o) then there <lb/>would be no difference between them about the Sen&longs;es of the <lb/>&longs;ame places; I &longs;hould think that it would be an act of great pru­<lb/>dence to make it unlawful for any one to u&longs;urp Texts of Scri­<lb/>pture, and as it were to force them to maintain this or that Natu­<lb/>rall Conclu&longs;ion for truth, of which Sence, & Demon&longs;trative, and <lb/>nece&longs;&longs;ary Rea&longs;ons may one time or other a&longs;&longs;ure us the contrary. <lb/></s> <s>For who will pre&longs;cribe bounds to the Wits of men? </s> <s>Who will <lb/>a&longs;&longs;ert that all that is &longs;en&longs;ible and knowable in the World is al­<lb/>ready di&longs;covered and known? </s> <s>Will not they that in other points <lb/>di&longs;agree with us, confe&longs;s this (and it is a great truth) that <emph type="italics"/>Ea <lb/>quæ &longs;cimus, &longs;int minima pars eorum quæ ignoramus<emph.end type="italics"/>? </s> <s>That tho&longs;e <lb/>Truths which we know, are very few, in compari&longs;on of tho&longs;e <lb/>which we know not? </s> <s>Nay more, if we have it from the Mouth <lb/><arrow.to.target n="marg830"></arrow.to.target><lb/>of the Holy Gho&longs;t, that <emph type="italics"/>Deus tradidit Mundum di&longs;putationi <lb/>eorum, ut non inveniat homo opus, quod operatus e&longs;t Deus ab <lb/>initio ad finem:<emph.end type="italics"/> One ought not, as I conceive, to &longs;top the way <lb/>to free Philo&longs;ophating, touching the things of the World, and of <lb/>Nature, as if that they were already certainly found, and all ma­<lb/>nife&longs;t: nor ought it to be counted ra&longs;hne&longs;s, if one do not fit <lb/>down &longs;atisfied with the opinions now become as it were com­<lb/>mune; nor ought any per&longs;ons to be di&longs;plea&longs;ed, if others do not <lb/>hold, in natural Di&longs;putes to that opinion which be&longs;t plea&longs;eth <lb/>them; and e&longs;pecially touching Problems that have, for thou&longs;ands <lb/>of years, been controverted among&longs;t the greate&longs;t Philo&longs;ophers, as is <lb/>the Stability of the Sun, and Mobility of the Earth, an opinion <lb/>held by <emph type="italics"/>Pythagoras,<emph.end type="italics"/> and by his whole Sect; by <emph type="italics"/>Heraclides Pon­<lb/>ticus,<emph.end type="italics"/> who was of the &longs;ame opininion; by <emph type="italics"/>Phylolaus,<emph.end type="italics"/> the Ma&longs;ter <lb/>of <emph type="italics"/>Plato<emph.end type="italics"/>; and by <emph type="italics"/>Plato<emph.end type="italics"/> him&longs;elf, as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> relateth, and of <lb/>which <emph type="italics"/>Plutarch<emph.end type="italics"/> writeth in the life of <emph type="italics"/>Numa,<emph.end type="italics"/> that the &longs;aid <emph type="italics"/>Plato,<emph.end type="italics"/><lb/>when he was grown old, &longs;aid, It is a mo&longs;t ab&longs;urd thing to think <lb/>otherwi&longs;e: The &longs;ame was believed by <emph type="italics"/>Ari&longs;tarchus Samius,<emph.end type="italics"/> as <lb/>we have it in <emph type="italics"/>Archimedes<emph.end type="italics"/>; and probably by <emph type="italics"/>Archimedes<emph.end type="italics"/> him­<pb xlink:href="040/01/462.jpg" pagenum="438"/>&longs;elf; by <emph type="italics"/>Nicetas<emph.end type="italics"/> the Philo&longs;opher, upon the te&longs;timony of <emph type="italics"/>Scicero,<emph.end type="italics"/><lb/>and by many others. </s> <s>And this opinion hath, finally, been am­<lb/>plified, and with many Ob&longs;ervations and Demon&longs;trations con­<lb/>firmed by <emph type="italics"/>Nicholaus Copernicus.<emph.end type="italics"/> And <emph type="italics"/>Seneca,<emph.end type="italics"/> a mo&longs;t eminent <lb/>Philo&longs;opher, in his Book <emph type="italics"/>De Cometis,<emph.end type="italics"/> advertizeth us that we <lb/>ought, with great diligence, &longs;eek for an a&longs;&longs;ured knowledge, <lb/>whether it be Heaven, or the Earth, in which the Diurnal Con­<lb/>ver&longs;ion re&longs;ides.</s></p><p type="margin"> <s><margin.target id="marg829"></margin.target>Epi&longs;t. </s> <s>7. ad Mar­<lb/>cellinum.</s></p><p type="margin"> <s><margin.target id="marg830"></margin.target>Eccle&longs;ia&longs;t. </s> <s>cap. 3.</s></p><p type="main"> <s>And for this cau&longs;e, it would probably be prudent and pro&longs;i­<lb/>table coun&longs;el, if be&longs;ides the Articles which concern our Salvati­<lb/>on, and the e&longs;tabli&longs;hment of our Faith (again&longs;t the &longs;tability of <lb/>which there is no fear that any valid and &longs;olid Doctrine can e­<lb/>ver ri&longs;e up) men would not aggregate and heap up more, with­<lb/>out nece&longs;&longs;ity: And if it be &longs;o, it would certainly be a prepo&longs;te­<lb/>rous thing to introduce &longs;uch Articles at the reque&longs;t of per&longs;ons <lb/>who, be&longs;ides that we know not that they &longs;peak by in&longs;piration <lb/>of Divine Grace, we plainly &longs;ee that there might be wi&longs;hed in <lb/>them the under&longs;tanding which would be nece&longs;&longs;ary fir&longs;t to enable <lb/>them to comprehend, and then to di&longs;cu&longs;s the Demon&longs;trations <lb/>wherewith the &longs;ubtiler Sciences proceed in confirming &longs;uch like <lb/>Conclu&longs;ions. </s> <s>Nay, more I &longs;hould &longs;ay, (were it lawful to &longs;peak <lb/>my judgment freely on this Argument) that it would haply <lb/>more &longs;uit with the <emph type="italics"/>Decorum<emph.end type="italics"/> and Maje&longs;ty of tho&longs;e Sacred Vo­<lb/>lumes, if care were taken that every &longs;hallow and vulgar Writer <lb/>might not authorize his Books (which are not &longs;eldome grounded <lb/>upon fooli&longs;h fancies) by in&longs;erting into them Places of Holy Scri­<lb/>pture, interpreted, or rather di&longs;torted to Sen&longs;es as remote from <lb/>the right meaning of the &longs;aid Scripture, as they are neer to deri­<lb/>ri&longs;ion, who not without o&longs;tentation flouri&longs;h out their Writings <lb/>therewith. </s> <s>Examples of &longs;uch like abu&longs;es there might many be <lb/>produced, but for this time I will confine my &longs;elf to two, not <lb/>much be&longs;ides the&longs;e matters of <emph type="italics"/>A&longs;tronomy:<emph.end type="italics"/> One of which, is that <lb/>of tho&longs;e Pamphlets which were publi&longs;hed again&longs;t the <emph type="italics"/>Medicean<emph.end type="italics"/><lb/>Planets, of which I had the fortune to make the di&longs;covery; a­<lb/>gain&longs;t the exi&longs;tence of which there were brought many places of <lb/>Sacred Sctipture: Now, that all the World &longs;eeth them to be <lb/>Planets, I would gladly hear with what new interpretations <lb/>tho&longs;e very Antagoni&longs;ts do expound the Scripture, and excu&longs;e their <lb/>own &longs;implicity. </s> <s>The other example is of him who but very <lb/>lately hath Printed again&longs;t <emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> and <emph type="italics"/>Philo&longs;ophers,<emph.end type="italics"/> that <lb/>the Moon doth not receive its light from the Sun, but is of its own <lb/>nature re&longs;plendent: which imagination he in the clo&longs;e confirm­<lb/>eth, or, to &longs;ay better, per&longs;wadeth him&longs;elf that he confirmeth by <lb/>&longs;undry Texts of Scripture, which he thinks cannot be reconciled <lb/>unle&longs;&longs;e his opinion &longs;hould be true and nece&longs;&longs;ary. </s> <s>Neverthele&longs;&longs;e, <pb xlink:href="040/01/463.jpg" pagenum="439"/>the Moon of it &longs;elf is Tenebro&longs;e, and yet it is no le&longs;&longs;e lucid than <lb/>the Splendor of the Sun.</s></p><p type="main"> <s>Hence it is manife&longs;t, that the&longs;e kinde of Authors, in regard they <lb/>did not dive into the true Sence of the Scriptures, would (in ca&longs;e <lb/>their authority were of any great moment) have impo&longs;ed a nece&longs;­<lb/>&longs;ity upon others to believe &longs;uch Conclu&longs;ions for true as were re­<lb/>pugnant to manife&longs;t Rea&longs;on, and to Sen&longs;e. </s> <s>Which abu&longs;e <emph type="italics"/>Deus <lb/>avertat,<emph.end type="italics"/> that it do not gain Countenance and Authority; for if it <lb/>&longs;hould, it would in a &longs;hort time be nece&longs;&longs;ary to pro&longs;cribe and in­<lb/>hibit all the Contemplative Sciences. </s> <s>For being that by nature <lb/>the number of &longs;uch as are very unapt to under&longs;tand perfectly <lb/>both the Sacred Scriptures, and the other Sciences is much great­<lb/>er than that of the skilfull and intelligene; tho&longs;e of the fir&longs;t &longs;ort <lb/>&longs;uperficially running over the Scriptures, would arrogate to them­<lb/>&longs;elves an Authority of decreeing upon all the Que&longs;tions in Na­<lb/>ture, by vertue of &longs;ome Word by them mi&longs;onder&longs;tood, and pro­<lb/>duced by the Sacred Pen-men to another purpo&longs;e: Nor would <lb/>the &longs;mall number of the Intelligent be able to repre&longs;s the furious <lb/>Torrent of tho&longs;e men, who would finde &longs;o many the more fol­<lb/>lowers, in that the gaining the reputation of Wi&longs;e men without <lb/>pains or Study, is far more grateful to humane Nature, than the <lb/>con&longs;uming our &longs;elves with re&longs;tle&longs;s contemplations about the mo&longs;t <lb/>painfull Arts. </s> <s>Therefore we ought to return infinite thanks to <lb/>Almighty God, who of his Goodne&longs;s freeth us from this fear, in <lb/>that he depriveth &longs;uch kinde of per&longs;ons of all Authority and, re­<lb/>po&longs;eth the Con&longs;ulting, Re&longs;olving, and Decreeing upon &longs;o im­<lb/>portant Determinations in the extraordinary Wi&longs;dom and Can­<lb/>dor of mo&longs;t Sacred Fathers; and in the Supream Authority of <lb/>tho&longs;e, who being guided by his Holy Spirit, cannot but determin <lb/>Holily: So ordering things, that of the levity of tho&longs;e other men, <lb/>there is no account made. </s> <s>This kinde of men are tho&longs;e, as I be­<lb/>lieve, again&longs;t whom, not without Rea&longs;on, Grave, and Holy Wri­<lb/>ters do &longs;o much inveigh; and of whom in particular S. <emph type="italics"/>Hierom<emph.end type="italics"/><lb/><arrow.to.target n="marg831"></arrow.to.target><lb/>writeth: <emph type="italics"/>(g) This<emph.end type="italics"/> (Scilicet <emph type="italics"/>the Sacred Scripture) the talking <lb/>old woman, the doting old man, the talkative Sophi&longs;ter, all venture <lb/>upon, lacerate, teach, and that before they have learnt it. </s> <s>Others <lb/>induced by Pride, diving into hard words, Philo&longs;ophate among&longs;t <lb/>Women, touching the Holy Scriptures. </s> <s>Others (Oh &longs;hame­<lb/>ful!) Learn of Women what they teach to Men; and, as if this <lb/>were nothiug, in a certain facility of words, I may &longs;ay of confi­<lb/>dence, expound to others what they under&longs;tand not them&longs;elves. </s> <s>I <lb/>forbear to &longs;peak of tho&longs;e of my own Profe&longs;&longs;ion, who, if after Hu­<lb/>mane Learning they chance to attain to the Holy Scriptures, and <lb/>tickle the ears of the people with affected and Studied expre&longs;&longs;ions, <lb/>they affirm that all they &longs;ay, is to be entertained as the Law of God<emph.end type="italics"/>; <pb xlink:href="040/01/464.jpg" pagenum="440"/><emph type="italics"/>and not &longs;tooping to learn what the Prophets and Apo&longs;tles held, <lb/>they force incongruous te&longs;timonies to their own Sen&longs;e: As if it <lb/>were the genuine, and not corrupt way of teaching to deprave Sen­<lb/>tences, and Wre&longs;t the Scripture according to their own &longs;ingular and <lb/>contradictory humour.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg831"></margin.target><emph type="italics"/>(g) Hanc (Sci­<lb/>licer Sacram Scri­<lb/>pturam) garrula <lb/>arus, hanc deli­<lb/>rus &longs;enex hanc So­<lb/>phi&longs;ta verbo&longs;us, <lb/>h<gap/> univer&longs;i præ­<lb/>&longs;umunt, lacerant, <lb/>docent, anteguans <lb/>di&longs;cant. </s> <s>Alij, <lb/>addacto &longs;upercilio, <lb/>grandia verba <lb/>trutinantes, inter <lb/>mulierculas, de <lb/>Sacris Litteris <lb/>Philo&longs;ophantur. <lb/></s> <s>Alij di&longs;cunt, prob <lb/>pudor! à fæminis, <lb/>quod viros docent, <lb/>& ne parum hoc <lb/>&longs;it, quadam faci­<lb/>litate verborum, <lb/>imo audaciâ, edi&longs;­<lb/>&longs;erunt aliis, quod <lb/>ip&longs;i non intelli­<lb/>gunt. </s> <s>Taceo de <lb/>mei &longs;imilibus, qui <lb/>&longs;i fortè ad Scriptu­<lb/>ras Sanctas, po&longs;t <lb/>&longs;eculares litteras <lb/>venerint, & &longs;er­<lb/>mone compo&longs;ito, <lb/>aurem populi mul­<lb/>&longs;erint; quicquid <lb/>dixerint, hoc le­<lb/>gem Dei putant: <lb/>nec &longs;cire dignan­<lb/>tur, quid Prophe­<lb/>tæ, quid Apo&longs;toli <lb/>&longs;en&longs;erint, &longs;ed ad <lb/>&longs;en&longs;um &longs;uum, in­<lb/>congrua aptant te­<lb/>&longs;timonia: Qua&longs;i <lb/>grande &longs;it, & non <lb/>vitioci&longs;&longs;imum do­<lb/>cendi genus, de­<lb/>pravare &longs;ententi­<lb/>as, & ad volun­<lb/>tatem &longs;uam Scri­<lb/>pturamtrahere re­<lb/>pugnantem.<emph.end type="italics"/> Je­<lb/>ron. </s> <s>Epi&longs;t. </s> <s>ad <lb/><emph type="italics"/>Paul.<emph.end type="italics"/> 103.</s></p><p type="main"> <s>I will not rank among the&longs;e &longs;ame &longs;ecular Writers any <emph type="italics"/>Theo­<lb/>logi&longs;ts,<emph.end type="italics"/> whom I repute to be men of profound Learning, and &longs;o­<lb/>ber Manners, and therefore hold them in great e&longs;teem and vene­<lb/>ration: Yet I cannot deny but that I have a certain &longs;cruple in <lb/>my mind, and con&longs;equently am de&longs;irous to have it removed, <lb/>whil&longs;t I hear that they pretend to a power of con&longs;training others <lb/>by Authority of the Scriptures to follow that opinion in Natu­<lb/>ral Di&longs;putations, which they think mo&longs;t agreeth with the Texts <lb/>of that: Holding withall, that they are not bound to an&longs;wer <lb/>the Rea&longs;ons and Experiments on the contrary: In Explication <lb/>and Confirmation of which their judgement they &longs;ay, That <emph type="italics"/>The­<lb/>ologie<emph.end type="italics"/> being the Queen of all the Sciences, &longs;he ought not upon <lb/>any account to &longs;toop to accomodate her &longs;elf to the Po&longs;itions of <lb/>the re&longs;t, le&longs;s worthy, and inferior to her: But that they ought <lb/>to refer them&longs;elves to her (as to their Supream Empere&longs;s) and <lb/>change and alter their Conclu&longs;ions, according to <emph type="italics"/>Theological<emph.end type="italics"/><lb/>Statutes and Decrees. </s> <s>And they further add, That if in the <lb/>inferior Science there &longs;hould be any Conclu&longs;ion certain by ver­<lb/>tue of Demon&longs;trations or experiments, to which there is found <lb/>in Scripture another Conclu&longs;ion repugnant; the very Profe&longs;&longs;ors <lb/>of that Science ought of them&longs;elves to re&longs;olve their Demon&longs;trati­<lb/>ons, and di&longs;cover the falacies of their own Experiments, without <lb/>repairing to Theologers and Textuaries, it not &longs;uiting (as hath <lb/>been &longs;aid) with the dignity of <emph type="italics"/>Theologie<emph.end type="italics"/> to &longs;toop to the inve&longs;tiga­<lb/>tion of the falacies of the inferior Sciences: But it &longs;ufficeth her, <lb/>to determine the truth of the Conclu&longs;ion with her ab&longs;olute Au­<lb/>thority, and by her infallibility. </s> <s>And then the Natural Conclu­<lb/>&longs;ions in which they &longs;ay that we ought to bide by the meer Au­<lb/>thority of the Scripture, without glo&longs;&longs;ing, or expounding it to <lb/>Sen&longs;es different from the Words, they affirm to be Tho&longs;e of <lb/>which the Scripture &longs;peaketh alwaies in the &longs;ame manner; and <lb/>the Holy Fathers all receive, and expound to the &longs;ame <lb/>Sen&longs;e.</s></p><p type="main"> <s>Now as to the&longs;e Determinations, I have had occa&longs;ion to con&longs;i­<lb/>der &longs;ome particulars (which I will purpo&longs;e) for that I was made <lb/>cautious thereof, by tho&longs;e who under&longs;tand more than I in the&longs;e <lb/>bu&longs;ine&longs;&longs;es, and to who&longs;e judgments I alwaies &longs;ubmit my &longs;elf. <lb/></s> <s>And fir&longs;t I could &longs;ay, that there might po&longs;&longs;ibly a certain kinde of <lb/>equivocation interpo&longs;e, in that they do not di&longs;tingui&longs;h the prehe­<lb/>minences whereby Sacred <emph type="italics"/>Theologie<emph.end type="italics"/> meriteth the Title of Queen. <pb xlink:href="040/01/465.jpg" pagenum="441"/>For it might be called &longs;o, either becau&longs;e that that which is taught <lb/>by all the other Sciences, is found to be comprized and demon&longs;tra­<lb/>ted in it, but with more excellent means, and with more &longs;ublime <lb/>Learning; in like manner, as for example; The Rules of mea&longs;uring <lb/>of Land, & of Accountant&longs;hip are much more excellently contain­<lb/>ed in the Arithmatick and Geometry of <emph type="italics"/>Euclid,<emph.end type="italics"/> than in the Practi­<lb/>&longs;es of Surveyours and Accomptants: Or becau&longs;e the Subject about <lb/>which <emph type="italics"/>Theologie<emph.end type="italics"/> is conver&longs;ant, excelleth in Dignity all the other <lb/>Subjects, that are the Matters of other Sciences: As al&longs;o becau&longs;e <lb/>its Documents are divulged by nobler waies. </s> <s>That the Title <lb/>and Authority of Queen belongeth to <emph type="italics"/>Theologie<emph.end type="italics"/> in the fir&longs;t <lb/>Sen&longs;e, I think that no Theologers will affirm, that have but any <lb/>in-&longs;ight into the other Sciences; of which there are none (as I be­<lb/>lieve) that will &longs;ay that Geometry, A&longs;tronomy Mu&longs;ick, and Me­<lb/>dicine are much more excellently and exactly contained in the <lb/>Sacred Volumes, than in the Books of <emph type="italics"/>Archimedes,<emph.end type="italics"/> in <emph type="italics"/>Ptolomy,<emph.end type="italics"/> in <lb/><emph type="italics"/>Boetius,<emph.end type="italics"/> and in <emph type="italics"/>Galen.<emph.end type="italics"/> Therefore it is probable that the Regal <lb/>Preheminence is given her upon the &longs;econd account, namely, By <lb/>rea&longs;on of the Subject, and the admirable communicating of the <lb/>Divine Revelations in tho&longs;e Conclu&longs;ions which by other means <lb/>could not be conceived by men, and which chiefly concern the <lb/>acqui&longs;t of eternal Beatitude. </s> <s>Now if <emph type="italics"/>Theologie<emph.end type="italics"/> being conver­<lb/>&longs;ant about the loftie&longs;t Divine Contemplation, and re&longs;iding for <lb/>Dignity in the Regal Throne of the Sciences, (whereby &longs;he be­<lb/>cometh of highe&longs;t Authority) de&longs;cendeth not to the more mean <lb/>and humble Speculations of the inferior Sciences: Nay; (as hath <lb/>been declared above) hath no regard to them, as not concerning <lb/>Bearitude; the Profe&longs;&longs;ors thereof ought not to arrogate to them­<lb/>&longs;elves the Authority to determin of Controver&longs;ies in tho&longs;e Pro­<lb/>fe&longs;&longs;ions which have been neither practi&longs;ed nor &longs;tudied by them. <lb/></s> <s>For this would be as if an Ab&longs;olute Prince, knowing that he <lb/>might freely command, and cau&longs;e him&longs;elf to be obeyed, &longs;hould <lb/>(being neither Phi&longs;itian nor Architect) undertake to admini&longs;ter <lb/>Medicines, and erect Buildings after his own fa&longs;hion, to the great <lb/>endangering af the lives of the poor Patients, and to the manife&longs;t <lb/>de&longs;truction of the Edifices.</s></p><p type="main"> <s>Again, to command the very Profe&longs;&longs;ors of <emph type="italics"/>A&longs;tronomy,<emph.end type="italics"/> that <lb/>they of them&longs;elves &longs;ee to the confuting of their own Ob&longs;erva­<lb/>tions and Demon&longs;trations, as tho&longs;e that can be no other but <lb/>Falacies and Sophi&longs;mes, is to enjoyn a thing beyond all po&longs;&longs;ibi­<lb/>lity of doing: For it is not onely to command them that they do <lb/>not &longs;ee that which they &longs;ee, and that they do not under&longs;tand <lb/>that which they under&longs;tand; but that in &longs;eeking, they finde the <lb/>contrary of that which they happen to meet with. </s> <s>Therefore be­<lb/>fore that this is to be done, it would be nece&longs;&longs;ary that they were <pb xlink:href="040/01/466.jpg" pagenum="442"/>&longs;hewed the way how to make the Powers of the Soul to command <lb/>one another, and the inferior the Superior; &longs;o that the imaginati­<lb/>on and will might, and &longs;hould believe contrary to what the Intel­<lb/>lect under&longs;tands: I &longs;till mean in Propo&longs;itions purely Natural, and <lb/>which are not <emph type="italics"/>de Fide,<emph.end type="italics"/> and not in the Supernatural, which are <lb/><emph type="italics"/>de Fide.<emph.end type="italics"/></s></p><p type="main"> <s>I would entreat the&longs;e Wi&longs;e and Prudent Fathers, that they <lb/>would withal diligence con&longs;ider the difference that is between <lb/>Opinable and Demon&longs;trative Doctrines: To the end, that well <lb/>weighing in their minds with what force Nece&longs;&longs;ary Illations ob­<lb/>lige, they might the better a&longs;certain them&longs;elves, that it is not in <lb/>the Power of the Profe&longs;&longs;ors of Demon&longs;trative Sciences to change <lb/>their Opinions at plea&longs;ure, and apply them&longs;elves one while to <lb/>one &longs;ide, and another while to another; and that there is a great <lb/>difference between commanding a Methametitian or a Philo&longs;o­<lb/>pher, and the di&longs;po&longs;ing of a Lawyer or a Merchant; and that the <lb/>demon&longs;trated Conclu&longs;ions touching the things of Nature and of <lb/>the Heavens cannot be changed with the &longs;ame facility, as the <lb/>Opinions are touching what is lawful or not in a Contract, Bar­<lb/>gain, or Bill of Exchange. </s> <s>This difference was well under&longs;tood <lb/>by the Learned and Holy Fathers, as their having been at great <lb/>pains to confute many Arguments, or to &longs;ay better, many Phi­<lb/><arrow.to.target n="marg832"></arrow.to.target><lb/>lo&longs;ophical Fallacies, doth prove unto us; and as may expre&longs;ly be <lb/>read in &longs;ome of them, and particularly we have in S. <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/><lb/>the following words: <emph type="italics"/>(g) This is to be held for an undoubt­<lb/>ed Truth, That we may be confident, that whatever the Sages of <lb/>this World have demon&longs;trated touching Natural Points, is no waies <lb/>contrary to our Bibles: And in ca&longs;e they teach any thing in their <lb/>Books that is contrary to the Holy Scriptures, we may without any <lb/>&longs;cruple conclude it to be mo&longs;t fal&longs;e; And aceording to our ability <lb/>let us make the &longs;ame appear: And let us &longs;o keep the Faith of our <lb/>Lord, in whom are hidden all the Trea&longs;ures of Wi&longs;dom; that we <lb/>be neither &longs;educed with the Loquacity of fal&longs;e Philo&longs;ophy, nor <lb/>&longs;cared by the &longs;uper&longs;tition of a counterfeit Religion.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg832"></margin.target><emph type="italics"/>(g) Hoc indu­<lb/>bitanter tenendum <lb/>e&longs;t, ut quicquid <lb/>Sapientes hujus <lb/>Mundi, de Natu­<lb/>ra rerum veraci­<lb/>ter demon&longs;trare <lb/>potuerint, o&longs;tenda­<lb/>mus, no&longs;tris libris <lb/>non e&longs;&longs;e contrari­<lb/>um: quicquid au­<lb/>tem illi, in &longs;uis vo­<lb/>lumintbus, contra­<lb/>rium Sacris Lit­<lb/>teris docent, &longs;ine <lb/>ulla dubitatione <lb/>credamus, id fal&longs;i&longs;­<lb/>&longs;imum e&longs;&longs;e, & quo­<lb/>quo modo po&longs;&longs;u­<lb/>mus, etiam o&longs;ten­<lb/>damus; atque it a <lb/>teneamus Fidem <lb/>Domini no&longs;tri, in <lb/>qua&longs;unt ab&longs;conditi <lb/>omnes the&longs;auri <lb/>Sapientiæ, ut ne­<lb/>que fal&longs;æ Philo&longs;o­<lb/>phiæ loquacitate <lb/>&longs;educamur, neque <lb/>&longs;imulata Religio­<lb/>nis &longs;uper&longs;titione <lb/>terreamur.<emph.end type="italics"/></s></p><p type="main"> <s>From which words, I conceive that I may collect this Do­<lb/>ctrine, namely, That in the Books of the Wi&longs;e of this World, <lb/>there are contained &longs;ome Natural truths that are &longs;olidly demon­<lb/>&longs;trated, and others again that are barely taught; and that as to <lb/>the fir&longs;t &longs;ort, it is the Office of wi&longs;e Divines to &longs;hew that they <lb/>are not contrary to the Sacred Scriptures; As to the re&longs;t, taught, <lb/>but not nece&longs;&longs;arily demon&longs;trated, if they &longs;hall contain any thing <lb/>contrary to the Sacred Leaves, it ought to be held undoubtedly <lb/>fal&longs;e, and &longs;uch it ought by all po&longs;&longs;ible waies to be demon­<lb/>&longs;trated.<lb/><arrow.to.target n="marg833"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg833"></margin.target>Gen. </s> <s>ad Litteram. <lb/><emph type="italics"/>lib<emph.end type="italics"/> I. Cap. 25.</s></p><p type="main"> <s>If therefore Natural Conclu&longs;ions veritably demon&longs;trated, are <pb xlink:href="040/01/467.jpg" pagenum="443"/>not to be po&longs;tpo&longs;ed to the Places of Scripture, but that it ought <lb/>to be &longs;hewn how tho&longs;e Places do not interfer with the &longs;aid Con­<lb/>clu&longs;ions; then its nece&longs;&longs;ary before a Phy&longs;ical Propo&longs;ition be <lb/>condemned, to &longs;hew that it is not nece&longs;&longs;arily demon&longs;trated; and <lb/>this is to be done not by them who hold it to be true, but by tho&longs;e <lb/>who judge it to be fal&longs;e. </s> <s>And this &longs;eemeth very rea&longs;onable, <lb/>and agreeable to Nature; that is to &longs;ay, that they may much <lb/>more ea&longs;ily find the fallacies in a Di&longs;cour&longs;e, who believe it to be <lb/>fal&longs;e, than tho&longs;e who account it true and concludent. </s> <s>Nay, in <lb/>this particular it will come to pa&longs;&longs;e, that the followers of this o­<lb/>pinion, the more that they &longs;hall turn over Books, examine the <lb/>Arguments, repeat the Ob&longs;ervations, and compare the Experi­<lb/>ments, the more &longs;hall they be confirmed in this belief. </s> <s>And your <lb/>Highne&longs;s knoweth what happened to the late Mathematick Pro­<lb/>fe&longs;&longs;or in the Univer&longs;ity of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> Who betook him&longs;elf in his old <lb/>age to look into the Doctrine of <emph type="italics"/>Copernicus,<emph.end type="italics"/> with hope that he <lb/>might be able &longs;olidly to confute it (for that he held it &longs;o far to <lb/>be fal&longs;e, as that he had never &longs;tudied it) but it was his fortune, <lb/>that as &longs;oon as he had under&longs;tood the grounds, proceedings, and <lb/>demon&longs;trations of <emph type="italics"/>Copernicus,<emph.end type="italics"/> he found him&longs;elf to be per&longs;waded, <lb/>and of an oppo&longs;er became his mo&longs;t confident Defender. </s> <s>I <lb/>might al&longs;o nominate other ^{*} Mathematicians, who being moved </s></p><p type="main"> <s><arrow.to.target n="marg834"></arrow.to.target><lb/>by my la&longs;t Di&longs;coveries, have confe&longs;&longs;ed it nece&longs;sary to change the <lb/>formerly received Con&longs;titution of the World, it not being able <lb/>by any means to &longs;ub&longs;i&longs;t any longer.</s></p><p type="margin"> <s><margin.target id="marg834"></margin.target>* P. </s> <s>Clavius the <lb/>Je&longs;uite.</s></p><p type="main"> <s>If for the bani&longs;hing this Opinion and Hypothe&longs;is out of the <lb/>World, it were enough to &longs;top the mouth of one alone, as it <lb/>may be they per&longs;wade them&longs;elves who mea&longs;uring others judge­<lb/>ments by their own, think it impo&longs;&longs;ible that this Doctrine &longs;hould <lb/>be able to &longs;ub&longs;i&longs;t and finde any followers, this would be very ea­<lb/>&longs;ie to be done, but the bu&longs;ine&longs;s &longs;tandeth otherwi&longs;e: For to <lb/>execute &longs;uch a determination, it would be nece&longs;&longs;ary to prohibite <lb/>not onely the Book of <emph type="italics"/>Copernicus,<emph.end type="italics"/> and the Writings of the o­<lb/>ther Authors that follow the &longs;ame opinion, but to interdict the <lb/>whole Science of <emph type="italics"/>A&longs;tronomy<emph.end type="italics"/>; and which is more, to forbid men <lb/>looking towards Heaven, that &longs;o they might not &longs;ee <emph type="italics"/>Mars<emph.end type="italics"/> and <lb/><emph type="italics"/>Venus<emph.end type="italics"/> at one time neer to the Earth, and at another farther off, <lb/>with &longs;uch a difference that the latter is found to be fourty times, <lb/>and the former &longs;ixty times bigger in &longs;urface at one time than at <lb/>another; and to the end, that the &longs;ame <emph type="italics"/>Venus<emph.end type="italics"/> might not be <lb/>di&longs;covered to be one while round, and another while forked, with <lb/>mo&longs;t &longs;ubtil hornes: and many other &longs;en&longs;ible Ob&longs;ervations which <lb/>can never by any means be reconciled to the <emph type="italics"/>Ptolomaick<emph.end type="italics"/> Sy&longs;teme, <lb/>but are unan&longs;werable Arguments for the <emph type="italics"/>Copernican.<emph.end type="italics"/></s></p><p type="main"> <s>But the prohibiting of <emph type="italics"/>Copernicus<emph.end type="italics"/> his Book, now that by many <pb xlink:href="040/01/468.jpg" pagenum="444"/>new Ob&longs;ervations, and by the application of many of the Lear­<lb/>ned to the reading of him, his Hypothe&longs;is and Doctrine doth <lb/>every day appear to be more true, having admitted and tolerated <lb/>it for &longs;o many years, whil&longs;t he was le&longs;&longs;e followed, &longs;tudied, and <lb/>confirmed, would &longs;eem, in my judgment, an affront to Truth, <lb/>and a &longs;eeking the more to ob&longs;cure and &longs;uppre&longs;&longs;e her, the more <lb/>&longs;he &longs;heweth her &longs;elf clear and per&longs;picuous.</s></p><p type="main"> <s>The aboli&longs;hing and cen&longs;uring, not of the whole Book, but <lb/>onely &longs;o much of it as concerns this particular opinion of the <lb/><emph type="italics"/>Earths Mobility,<emph.end type="italics"/> would, if I mi&longs;take not, be a greater detriment <lb/>to &longs;ouls, it being an occa&longs;ion of great &longs;candal, to &longs;ee a Po&longs;ition <lb/>proved, and to &longs;ee it afterwards made an Here&longs;ie to believe it.</s></p><p type="main"> <s>The prohibiting of the whole Science, what other would it <lb/>be but an open contempt of an hundred Texts of the Holy Scri­<lb/>ptures, which teach us, That the Glory, and the Greatne&longs;&longs;e of <lb/>Almighty God is admirably di&longs;cerned in all his Works, and di­<lb/>vinely read in the Open Book of Heaven? </s> <s>Nor let any one <lb/>think that the Lecture of the lofty conceits that are written in <lb/>tho&longs;e Leaves fini&longs;h in only beholding the Splendour of the Sun, <lb/>and of the Stars, and their ri&longs;ing and &longs;etting, (which is the term <lb/>to which the eyes of bruits and of the vulgar reach) but there <lb/>are couched in them my&longs;teries &longs;o profound, and conceipts &longs;o &longs;ub­<lb/>lime, that the vigils, labours, and &longs;tudies of an hundred and an <lb/>hundred acute Wits, have not yet been able thorowly to dive <lb/>into them after the continual di&longs;qui&longs;ition of &longs;ome thou&longs;ands of <lb/>years. </s> <s>But let the Unlearned believe, that like as that which <lb/>their eyes di&longs;cern in beholding the a&longs;pect of a humane body, is <lb/>very little in compari&longs;on of the &longs;tupendious Artifices, which an <lb/>exqui&longs;ite and curious Anatomi&longs;t or Philo&longs;opher finds in the &longs;ame <lb/>when he is &longs;earching for the u&longs;e of &longs;o many Mu&longs;cles, Tendons, <lb/>Nerves, and Bones; and examining the Offices of the Heart, <lb/>and of the other principal Members, &longs;eeking the &longs;eat of the vi­<lb/>tal Faculties, noting and ob&longs;erving the admirable &longs;tructures of <lb/>the In&longs;truments of the Sen&longs;es, and, without ever making an end <lb/>of &longs;atisfying his curio&longs;ity and wonder, contemplating the Re­<lb/>ceptacles of the Imagination, of the Memory, and of the Un­<lb/>der&longs;tanding; So that which repre&longs;ents it &longs;elf to the meer &longs;ight, <lb/>is as nothing in compari&longs;on and proportion to the &longs;trange Won­<lb/>ders, that by help of long and accurate Ob&longs;ervations the Wit <lb/>of Learned Men di&longs;covereth in Heaven. </s> <s>And this is the &longs;ub­<lb/>&longs;tance of what I had to con&longs;ider touching this particular.</s></p><p type="main"> <s>In the next place, as to tho&longs;e that adde, That tho&longs;e Natural <lb/>Propo&longs;itions of which the Scripture &longs;till &longs;peaks in one con&longs;tant <lb/>tenour, and which the Fathers all unanimou&longs;ly receive in the <lb/>&longs;ame &longs;en&longs;e, ought to be accepted according to the naked and <pb xlink:href="040/01/469.jpg" pagenum="445"/>literal &longs;en&longs;e of the Words, without glo&longs;&longs;es and interpretations; <lb/>and received and held for mo&longs;t certain and true; and that con­<lb/>&longs;equently the Mobility of the Sun, and Stability of the Earth, <lb/>as being &longs;uch, are <emph type="italics"/>de Fide<emph.end type="italics"/> to be held for true, and the contrary <lb/>opinion to be deemed Heretical: I &longs;hall propo&longs;e to con&longs;idera­<lb/>tion, in the fir&longs;t place, That of Natural Propo&longs;itions, &longs;ome there <lb/>are, of which all humane Science and Di&longs;cour&longs;e can furni&longs;h us <lb/>only with &longs;ome plau&longs;ible opinion, and probable conjecture ra­<lb/>ther than with any certain and demon&longs;trative knowledge; as for <lb/>example, whether the Stars be animated: Others there are, of <lb/>which we have, or may confidently believe that we may have, <lb/>by Experiments, long Ob&longs;ervations, and Nece&longs;&longs;ary Demon&longs;tra­<lb/>tions an undubitable a&longs;&longs;urance; as for in&longs;tance, whether the <lb/>Earth and Heavens move, or not; whether the Heavens are <lb/>Spherical, or otherwi&longs;e. </s> <s>As to the fir&longs;t &longs;ort, I doubt not in the <lb/>lea&longs;t, that if humane Ratiocinations cannot reach them, and <lb/>that con&longs;equently there is no Science to be had of them, but on­<lb/>ly an Opinion or Belief, we ought fully and ab&longs;olutely to com­<lb/>ply with the meer Verbal Sen&longs;e of the Scripture: But as to the <lb/>other Po&longs;itions, I &longs;hould think (as hath been &longs;aid above) That <lb/>we are fir&longs;t to a&longs;certain our &longs;elves of the fact it &longs;elf, which will <lb/>a&longs;&longs;i&longs;t us in finding out the true &longs;en&longs;es of the Scriptures; which <lb/>&longs;hall mo&longs;t certainly be found to accord with the fact demon&longs;tra­<lb/>ted, for two truths can never contradict each other. </s> <s>And <lb/>this I take to be a Doctrine orthodox and undoubted, for that I <lb/>&longs;inde it written in Saint <emph type="italics"/>Augu&longs;tine,<emph.end type="italics"/> who &longs;peaking to our point <lb/>of the Figure of Heaven, and what it is to be believed to be, in <lb/>regard that which A&longs;tronomers affirm concerning it &longs;eemeth to <lb/>be, contrary to the Scripture, (they holding it to be rotund, <lb/>and the Scripture calling it as it were a ^{*} Curtain, determi­<lb/><arrow.to.target n="marg835"></arrow.to.target><lb/>neth that we are not at all to regard that the Scripture contra­<lb/>dicts A&longs;tronomers; but to believe its Authority, if that which <lb/>they &longs;ay &longs;hall be fal&longs;e, and founded, only on the conjectures of <lb/>humane infirmity: but if that which which they affirm be pro­<lb/>ved by indubitable Rea&longs;ons, this Holy Father doth not &longs;ay, <lb/>that the A&longs;tronomers are to be enjoyned, that they them&longs;elves <lb/>re&longs;olving and renouncing their Demon&longs;trations do declare their <lb/>Conclu&longs;ion to be fal&longs;e, but &longs;aith, that it ought to be de­<lb/>mon&longs;trated, That what is &longs;aid in Scripture of a Curtain is not <lb/>contrary to their true Demon&longs;trations. </s> <s>The&longs;e are his words: <lb/><arrow.to.target n="marg836"></arrow.to.target><lb/><emph type="italics"/>(h) But &longs;ome object; How doth it appear, that the &longs;aying in our <lb/>Bibles,<emph.end type="italics"/> Who &longs;tretcheth out the Heaven as a Curtain, <emph type="italics"/>maketh <lb/>not again&longs;t tho&longs;e who maintain the Heavens to be in figure of a <lb/>Sphere? </s> <s>Let it be &longs;o, if that be fal&longs;e which they affirme: For <lb/>that is truth which is &longs;poke by Divine Authority, rather than<emph.end type="italics"/> <pb xlink:href="040/01/470.jpg" pagenum="446"/><emph type="italics"/>that which proceeds from Humane In&longs;irmity. </s> <s>But if peradven­<lb/>ture they &longs;hould be able to prove their Po&longs;ition by &longs;uch Experiments <lb/>as puts it out of que&longs;tion, it is to be proved, that what is &longs;aid in <lb/>Scripture concerning a Curtain, doth in no wi&longs;e contradict <lb/>their manife&longs;t Rea&longs;ons.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg835"></margin.target>* <emph type="italics"/>Pelle,<emph.end type="italics"/> a Skin in <lb/>the Original, out <lb/>in our Bibles a <lb/>Curtain.</s></p><p type="margin"> <s><margin.target id="marg836"></margin.target>(h) <emph type="italics"/>Sed ait ali­<lb/>quis, quomodo non <lb/>e&longs;t coutrarium iis, <lb/>qui figur am Sphæ­<lb/>ræ Cœlo tribunt, <lb/>quod &longs;criptum e&longs;t <lb/>en Libris No&longs;tris,<emph.end type="italics"/><lb/>Qui extendit Cœ­<lb/>lum, &longs;icut pellem? <lb/><emph type="italics"/>Stt &longs;ane contrari­<lb/>um, &longs;i fal&longs;um e&longs;t, <lb/>quod illi dicunt: <lb/>hoc enim verum <lb/>e&longs;t, quod Divina <lb/>dicit authoritas, <lb/>potius quans illud, <lb/>quod humana in­<lb/>firmitas conjicit. <lb/></s> <s>Sed &longs;i forte illud <lb/>talibus illi docu­<lb/>mentis probare po­<lb/>tuerint, at dubi­<lb/>tari inde non debe­<lb/>at; demon&longs;trandum <lb/>e&longs;t, hoc quod apud <lb/>nos e&longs;t de Pelle di­<lb/>ctum, veris illis <lb/>rationibus non e&longs;&longs;e <lb/>contrarium.<emph.end type="italics"/></s></p><p type="main"> <s>He proceedeth afterwards to admoni&longs;h us that we ought to be <lb/>no le&longs;s careful and ob&longs;ervant in reconciling a Text of Scripture <lb/>with a demon&longs;trated Natural Propo&longs;ition, than with another <lb/>Text of Scripture which &longs;hould &longs;ound to a contrary Sen&longs;e. </s> <s>Nay <lb/>methinks that the circum&longs;pection of this Saint is worthy to be ad­<lb/>mired and imitated, who even in ob&longs;cure Conclu&longs;ions, and of <lb/>which we may a&longs;&longs;ure our &longs;elves that we can have no knowledge <lb/>or Science by humane demon&longs;tration, is very re&longs;erved in deter­<lb/>mining what is to be believed, as we &longs;ee by that which he wri­<lb/>teth in the end of his &longs;econd Book, <emph type="italics"/>de Gene&longs;i ad Litteram,<emph.end type="italics"/> &longs;peak­<lb/>ing, whether the Stars are to be believed animate: <emph type="italics"/>(i) Which<emph.end type="italics"/><lb/><arrow.to.target n="marg837"></arrow.to.target><lb/><emph type="italics"/>particular, although (at pre&longs;ent) it cannot ea&longs;ily be comprehended, <lb/>yet I &longs;uppo&longs;e in our farther Progre&longs;s of bandling the Scriptures, <lb/>we may meet with &longs;ome more pertinent places, upon which it will <lb/>be permitted us (if not to determin any thing for certain, yet) to <lb/>&longs;ugge&longs;t &longs;omewhat concerning this matter, according to the dictates <lb/>of Sacred Authority. </s> <s>But now, the moderation of pious gravity <lb/>being alwaies ob&longs;erved, we ought to receive nothing ra&longs;hly in <lb/>a doubtful point, lea&longs;t perhaps we reject that out of re&longs;pect to <lb/>our Errour, which hereafter Truth may di&longs;cover, to be in no <lb/>wi&longs;e repugnant to the Sacred Volumes of the Old and New Te­<lb/>&longs;tament.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg837"></margin.target><emph type="italics"/>(i) Quod licet in <lb/>pra&longs;enti facile non <lb/>po&longs;&longs;it comprehendi; <lb/>arbitror tamen, in <lb/>proce&longs;&longs;is tract an­<lb/>dærum Scriptura­<lb/>rum, opportuntora <lb/>loca po&longs;&longs;e occurre­<lb/>re, ubinobis de hac <lb/>re, &longs;ecundum San­<lb/>ctæ auctoritatis <lb/>Litteras, et&longs;i non <lb/>o&longs;tendere certum <lb/>aliquid, tamen cre­<lb/>dere licebit. </s> <s>Nunc <lb/>autem, &longs;ervat â <lb/>&longs;emper moderatio­<lb/>ne piæ gravitatis, <lb/>nihil credere dere <lb/>ob&longs;cura temere <lb/>debemus; ne fortè, <lb/>quoà po&longs;tea verit as <lb/>patefecerit, quam­<lb/>vis Libris San­<lb/>ctis, &longs;ive Te&longs;ta­<lb/>menti veteris, &longs;ive, <lb/>novi nullo modo e&longs;­<lb/>&longs;e po&longs;&longs;it æever&longs;um, <lb/>tamen propter a­<lb/>morem no&longs;tri er­<lb/>roris, oderimus.<emph.end type="italics"/></s></p><p type="main"> <s>By this and other places (if I deceive not my &longs;elf) the intent <lb/>of the Holy Fathers appeareth to be, That in Natural que&longs;tions, <lb/>and which are not <emph type="italics"/>de Fide,<emph.end type="italics"/> it is fir&longs;t to be con&longs;idered, whether <lb/>they be indubitably demon&longs;trated, or by &longs;en&longs;ible Experiments <lb/>known; or whether &longs;uch a knowledge and demon&longs;tration is to be <lb/>had; which having obtained, and it being the gift of God, it <lb/>ought to be applyed to find out the true Sences of the Sacred Pa­<lb/>ges in tho&longs;e places, which in appearance might &longs;eem to &longs;peak to <lb/>a contrary meaning: Which will unque&longs;tionably be pierced into <lb/>by Prudent Divines, together with the occa&longs;ions that moved the <lb/><arrow.to.target n="marg838"></arrow.to.target><lb/>Holy Gho&longs;t, (for our exerci&longs;e, or for &longs;ome other rea&longs;on to me un­<lb/>known) to veil it &longs;elf &longs;ometimes under words of different &longs;igni­<lb/>fications.</s></p><p type="margin"> <s><margin.target id="marg838"></margin.target>Id. </s> <s>D Aug. </s> <s>in <lb/>Gen. <emph type="italics"/>ad Lute­<lb/>ram,<emph.end type="italics"/> lib. 1. <emph type="italics"/>in fine.<emph.end type="italics"/></s></p><p type="main"> <s>As to the other point, Of our regarding the Primary Scope of <lb/>tho&longs;e Sacred Volumes, I cannot think that their having &longs;poken <lb/>alwaies in the &longs;ame tenour, doth any thing at all di&longs;turb this <lb/>Rule. </s> <s>For if it hath been the Scope of the Scripture by way of <lb/>conde&longs;cention to the capacity of the Vulgar at any time, to ex­ <pb xlink:href="040/01/471.jpg" pagenum="447"/>pre&longs;s a Propo&longs;ition in words, that bear a &longs;en&longs;e different from the <lb/>E&longs;&longs;ence of the &longs;aid Propo&longs;ition; why might it not have ob&longs;erved <lb/>the &longs;ame, and for the &longs;ame re&longs;pect, as often as it had occa&longs;ion to <lb/>&longs;peak of the &longs;ame thing? </s> <s>Nay I conceive, that to have done <lb/>otherwi&longs;e, would but have encrea&longs;ed the confu&longs;ion, and dimi­<lb/>ni&longs;hed the credit that the&longs;e Sacred Records ought to have a­<lb/>mong&longs;t the Common People.</s></p><p type="main"> <s>Again, that touching the Re&longs;t and Motion of the Sun and <lb/>Earth, it was nece&longs;&longs;ary, for accommodation. </s> <s>to Popular Capa­<lb/>city, to a&longs;&longs;ert that which the Litteral &longs;en&longs;e of the Scripture im­<lb/>porteth, experience plainly proveth: For that even to our dayes <lb/>people far le&longs;s rude, do continue in the &longs;ame Opinion upon Rea­<lb/>&longs;ons, that if they were well weighed and examined, would be <lb/>found to be extream trivial, and upon Experiments, either whol­<lb/>ly fal&longs;e, or altogether be&longs;ides the purpo&longs;e. </s> <s>Nor is it worth <lb/>while to go about to remove them from it, they being incapable <lb/>of the contrary Rea&longs;ons that depend upon too exqui&longs;ite Ob&longs;er­<lb/>vations, and too &longs;ubtil Demon&longs;trations, grounded upon Ab&longs;tra­<lb/>ctions, which, for the comprehending of them, require too &longs;trong <lb/>an Imagination. </s> <s>Whereupon, although that the Stability of <lb/>Heaveu, and Motion of the Earth &longs;hould be more than certain <lb/>and demon&longs;trated to the Wi&longs;e; yet neverthele&longs;s it would be <lb/>nece&longs;&longs;ary, for the con&longs;ervation of credit among&longs;t the Vulgar, to <lb/>affirm the contrary: For that of a thou&longs;and ordinary men, that <lb/>come to be que&longs;tioned concerning the&longs;e particulars, its probab e <lb/>that there will not be found &longs;o much as one that will not an­<lb/>&longs;wer that he thinketh, and &longs;o certainly he doth, that the Sun <lb/>moveth, and the Earth &longs;tandeth &longs;till. </s> <s>But yet none ought to <lb/>take this common Popular A&longs;&longs;ent to be any Argument of the <lb/>truth of that which is affirmed: For if we &longs;hould examine <lb/>the&longs;e very men touching the grounds and motives by which they <lb/>are induced to believe in that manner; and on the other &longs;ide <lb/>&longs;hould hear what Experiments and Demon&longs;trationslper&longs;wade <lb/>tho&longs;e few others to believe the contrary, we &longs;hould finde the&longs;e <lb/>latter to be moved by mo&longs;t &longs;olid Rea&longs;ons, and the former by <lb/>&longs;imple appearances, and vain and ridiculous occurrences. </s> <s>That <lb/>therefore it was nece&longs;&longs;ary to a&longs;&longs;ign Motion to the Sun, and Re&longs;t <lb/>to the earth, le&longs;t the &longs;hallow capacity of the Vulgar &longs;hould be <lb/>confounded, amu&longs;ed, and rendred ob&longs;tinate and contumacious, <lb/>in giving credit to the principal Articles, and which are ab&longs;olute­<lb/>ly <emph type="italics"/>de fide,<emph.end type="italics"/> it is &longs;ufficiently obvious. </s> <s>And if it was nece&longs;&longs;ary &longs;o <lb/>to do, it is not at all to be wondred at, that it was with extraor­<lb/>dinary Wi&longs;dom &longs;o done, in the Divine Scriptures.</s></p><p type="main"> <s>But I will alledge further, That not onely a re&longs;pect to the <lb/>Incapacity of the Vulgar, but the current Opinion of tho&longs;e times <pb xlink:href="040/01/472.jpg" pagenum="448"/>made the Sacred Writers, in the points that were not nece&longs;&longs;ary <lb/>to &longs;alvation, to accommodate them&longs;elves more to the received <lb/>u&longs;e, than to the true E&longs;&longs;ence of things: Of which S. <emph type="italics"/>Hierom<emph.end type="italics"/><lb/>treating, writeth: <emph type="italics"/>(k) As if many things were not &longs;poken in<emph.end type="italics"/><lb/><arrow.to.target n="marg839"></arrow.to.target><lb/><emph type="italics"/>the Holy Scriptures according to the judgement of tho&longs;e times <lb/>in which they were acted, and not according to that which <lb/>truth contained.<emph.end type="italics"/> And el&longs;ewhere, the &longs;ame Saint: <emph type="italics"/>(l) It is the cu­<lb/>&longs;tome for the Pen-men of Scripture, to deliver their Judgments in <lb/>many things, according to the common received opinion that their <lb/>times had of them.<emph.end type="italics"/> And ^{*} S. <emph type="italics"/>Thomas Aquinas<emph.end type="italics"/> in <emph type="italics"/>Job<emph.end type="italics"/> upon tho&longs;e <lb/>words, <emph type="italics"/>Qui extendit Aquilonem &longs;uper vacuum, & appendit<emph.end type="italics"/><lb/><arrow.to.target n="marg840"></arrow.to.target><lb/><emph type="italics"/>Terram &longs;uper nihilum<emph.end type="italics"/>: Noteth that the Scripture calleth that <lb/>&longs;pace <emph type="italics"/>Vacuum<emph.end type="italics"/> and <emph type="italics"/>Nihilum,<emph.end type="italics"/> which imbraceth and invironeth the <lb/>Earth, and which we know, not to be empty, bat filled with Air; <lb/>Neverthele&longs;&longs;e, &longs;aith he, The Scripture to comply with the appre­<lb/>hen&longs;ion of the Vulgar, who think that in that &longs;ame &longs;pace there <lb/>is nothing, calleth it <emph type="italics"/>Vacuum<emph.end type="italics"/> and <emph type="italics"/>Nihilum.<emph.end type="italics"/> Here the words of <lb/><arrow.to.target n="marg841"></arrow.to.target><lb/>S. <emph type="italics"/>Thomas, Quod de &longs;uperiori Hæmi&longs;phærio Cœli nibil nobis ap­<lb/>paret, ni&longs;i &longs;patium aëre plenum, quod vulgares homines reputant <lb/>Vacnum; loquitur enim &longs;ecundum exi&longs;timationem vulgarium ho­<lb/>minum, prout e&longs;t mos in Sacra Scriptura.<emph.end type="italics"/> Now from this Place <lb/>I think one may very Logically argue, That the Sacred Scripture <lb/>for the &longs;ame re&longs;pect had much more rea&longs;on to phra&longs;e the Sun mo­<lb/>veable, and the Earth immoveable. </s> <s>For if we &longs;hould try the ca­<lb/>pacity of the Common People, we &longs;hould find them much more <lb/>unapt to be per&longs;waded of the &longs;tability of the Sun, and Motion <lb/>of the Earth, than that the &longs;pace that environeth it is full of Air. <lb/></s> <s>Therefore if the &longs;acred Authors, in this point, which had not &longs;o <lb/>much difficulty to be beat into the capacity of the Vulgar, have <lb/>notwith&longs;tanding forborn to attempt per&longs;wading them unto it, it <lb/>mu&longs;t needs &longs;eem very rea&longs;onable that in other Propo&longs;itions much <lb/>more ab&longs;tru&longs;e they have ob&longs;erved the &longs;ame &longs;tile. </s> <s>Nay <emph type="italics"/>Copernicus<emph.end type="italics"/><lb/>him&longs;elf, knowing what power an antiquated cu&longs;tome and way <lb/>of conceiving things become familiar to us from our infancy <lb/>hath in our Fancy, that he might not increa&longs;e confu&longs;ion and dif­<lb/>ficulty in our apprehen&longs;ions, after he had fir&longs;t demon&longs;trated, <lb/>That the Motions which appear to us to belong to the Sun, or to <lb/>the Firmament, are really in the Earth; in proceeding after­<lb/>wards to reduce rhem into Tables, and to apply them to u&longs;e, he <lb/>calleth them the Motions of the Sun, and of the Heaven that is <lb/>above the Planets; expre&longs;ly terming them the Ri&longs;ing and Set­<lb/>ting of the Sun and Stars; and mutations in the obliquity of <lb/>the Zodiack, and variations in the points of the Equinoxes, the <lb/>Middle Motion, <emph type="italics"/>Anomalia, Pro&longs;thaphære&longs;is<emph.end type="italics"/> of the Sun; and &longs;uch <lb/>other things; which do in reality belong to the Earth: But be­ <pb xlink:href="040/01/473.jpg" pagenum="449"/>cau&longs;e being joyned to it, and con&longs;equently having a &longs;hare in eve­<lb/>ry of its motions, we cannot immediately di&longs;cern them in her, but <lb/>are forced to refer them to the Cele&longs;tial Bodies in which they <lb/>appear; therefore we call them as if they were made there, where <lb/>they &longs;eem to us to be made. </s> <s>Whence it is to be noted how ne­<lb/>ne&longs;&longs;ary it is to accommodate our di&longs;cour&longs;e to our old and accu­<lb/>&longs;tomed manner of under&longs;tanding.</s></p><p type="margin"> <s><margin.target id="marg839"></margin.target>(k) <emph type="italics"/>Qua&longs;i non <lb/>multa in Scriptu­<lb/>ris Sanctis dican­<lb/>tur juxta opinio­<lb/>nem illius tempor is <lb/>quo ge&longs;t a referant, <lb/>& non juxta quod <lb/>rei veritas contine­<lb/>bat.<emph.end type="italics"/> D. Hiero. </s> <s>in c. <lb/></s> <s>28. Jerem.</s></p><p type="margin"> <s><margin.target id="marg840"></margin.target>(l) <emph type="italics"/>Con&longs;uctudi­<lb/>nis Scripturarum <lb/>e&longs;t, ut opinionem <lb/>multarum rerum <lb/>&longs;ic narret Hi&longs;tori­<lb/>cus, quomodo eo <lb/>tempore ab omni­<lb/>bus credebatur.<emph.end type="italics"/> In <lb/>cap. 13. Matth.</s></p><p type="margin"> <s><margin.target id="marg841"></margin.target>* D. Thomas, in <lb/>cap. </s> <s>26. Job. </s> <s>v. </s> <s>7.</s></p><p type="main"> <s>That, in the next place, the common con&longs;ent of Fathers, in re­<lb/>ceiving a Natural Propo&longs;ition of Scripture, all in the &longs;ame &longs;en&longs;e <lb/>ought to Authorize it &longs;o far, as to make it become a matter of <lb/>Faith to believe it to be ^{*} &longs;o, I &longs;hould think that it ought at mo&longs;t <lb/><arrow.to.target n="marg842"></arrow.to.target><lb/>to be under&longs;tood of tho&longs;e Conclu&longs;ions onely, which have beenby <lb/>the &longs;aid Fathers di&longs;cu&longs;&longs;ed, and &longs;ifted with all po&longs;&longs;ible diligence, <lb/>and debated on the one &longs;ide, and on the other, and all things in <lb/>the end concurring to di&longs;prove the one, and prove the other. </s> <s>But <lb/>the Mobility of the Earth, and Stability of the Sun, are not of <lb/>this kinde; For, that the &longs;aid Opinion was in tho&longs;e times total­<lb/>ly buried, and never brought among&longs;t the Que&longs;tions of the Schools, <lb/>and not con&longs;idered, much le&longs;s followed by any one: So that it is to <lb/>be believed that it never &longs;o much as entered into the thought of <lb/>the Fathers to di&longs;pute it, the Places of Scripture, their own Opinion, <lb/>and the a&longs;&longs;ent of men having all concurred in the &longs;ame judgement, <lb/>without the contradiction of any one, &longs;o far as we can finde.</s></p><p type="margin"> <s><margin.target id="marg842"></margin.target>* Namely, ac­<lb/>cording to the Lit­<lb/>teral Sen&longs;e.</s></p><p type="main"> <s>Be&longs;ides, it is not enough to &longs;ay that the Fathers all admit the <lb/>&longs;tability of the Earth, &c. </s> <s>Therefore to believe it is a matter of <lb/>Faith: But its nece&longs;&longs;ary to prove that they have condemned the <lb/>contrary Opinion: For I may affirm and bide by this, That their <lb/>not having occa&longs;ion to make &longs;atisfaction upon the &longs;ame, and to <lb/>di&longs;cu&longs;s it, hath made them to omit and admit it, onely as cur­<lb/>rent, but not as re&longs;olved and proved And I think I have very <lb/>good Rea&longs;on for what I &longs;ay; For either the Fathers did make <lb/>reflection upon this Conclu&longs;ion as controverted, or not: If not, <lb/>then they could determin nothing concerning it no not in their <lb/>private thoughts; and their incogitance doth not oblige us to <lb/>receive tho&longs;e Precepts which they have not, &longs;o much as in their <lb/>intentions enjoyned. </s> <s>But if they did reflect and con&longs;ider there­<lb/>on, they would long &longs;ince have condemned it, if they had judged <lb/>it erroneous; which we do not find that they have done. </s> <s>Nay, after <lb/>that &longs;ome Divines have began to con&longs;ider it, we find that they <lb/>have not deem'd it erroneous; as we read in the Commentaries of <lb/><emph type="italics"/>Didacus a Stunica<emph.end type="italics"/> upon <emph type="italics"/>Job,<emph.end type="italics"/> in <emph type="italics"/>Cap. 9, v. </s> <s>6.<emph.end type="italics"/> on the words, <emph type="italics"/>Qui com­<lb/>movet Terram de loco &longs;uo,<emph.end type="italics"/> &c. </s> <s>Where he at large di&longs;cour&longs;eth upon <lb/>the <emph type="italics"/>Copernican<emph.end type="italics"/> Hypothe&longs;is, and concludeth, <emph type="italics"/>That the Mobility <lb/>of the Earth, is not contrary to Scripture.<emph.end type="italics"/></s></p><p type="main"> <s>Withal, I may ju&longs;tly que&longs;tion the truth of that determination, <lb/>namely, That the Church enjoyneth us to hold &longs;uch like Natural <pb xlink:href="040/01/474.jpg" pagenum="450"/>Conclu&longs;ions as matters of Faith, onely becau&longs;e they bear the <lb/>&longs;tamp of an unanimous Interpretation of all the Fathers: And <lb/>I do &longs;uppo&longs;e that it may po&longs;&longs;ibly be, that tho&longs;e who hold in this <lb/>manner, might po&longs;&longs;ibly have gone about in favour of their own <lb/>Opinion, to have amplified the Decretal of the Councils; which <lb/>I cannot finde in this ca&longs;e to prohibit any other, &longs;ave onely, <emph type="italics"/>Per­<lb/>verting to Sen&longs;es contrary to that of Holy Church, or of the <lb/>concurrent con&longs;ent of Fathers, tho&longs;e places, and tho&longs;e onely that <lb/>do pertain either to Faith or Manners, or concern our edification <lb/>in the Doctrine of Chri&longs;tianity: And thus &longs;peaks the Council of <lb/>Trent. </s> <s>Se&longs;&longs;.<emph.end type="italics"/> 4. But the Mobility or Stability of the Earth, or <lb/><arrow.to.target n="marg843"></arrow.to.target><lb/>of the Sun, are not matters of Faith, nor contrary to Manners, <lb/>nor is there any one, that for the &longs;tabli&longs;hing of this Opinion, <lb/>will pervert places of Scripture in oppo&longs;ition to the Holy Church, <lb/>or to the Fathers: Nay, Tho&longs;e who have writ of this Doctrine, <lb/>did never make u&longs;e of Texts of Scripture; that they might leave <lb/>it &longs;till in the brea&longs;ts of Grave and Prudent Divines to interpret <lb/>the &longs;aid Places, according to their true meaning.</s></p><p type="margin"> <s><margin.target id="marg843"></margin.target><emph type="italics"/>Concil. </s> <s>Trid. </s> <s>Se&longs;&longs;.<emph.end type="italics"/><lb/>4.</s></p><p type="main"> <s>And how far the Decrees of Councills do comply with the Ho­<lb/>ly Fathers in the&longs;e particulars, may be &longs;ufficiently manife&longs;t, in <lb/>that they are &longs;o far from enjoyning to receive &longs;uch like Natural <lb/>Conclu&longs;ions for matters of Faith, or from cen&longs;uring the contrary <lb/>Opinions as erronious; that rather re&longs;pecting the Primitive and <lb/>primary intention of the Holy Church, they do adjudge it un­<lb/>profitable to be bu&longs;ied in examining the truth thereof. </s> <s>Let <lb/>your Highne&longs;s be plea&longs;ed to hear once again what S. <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/><lb/>an&longs;wers to to tho&longs;e Brethren who put the Que&longs;tion, Whether it <lb/><arrow.to.target n="marg844"></arrow.to.target><lb/>be true that Heaven moveth, or &longs;tandeth &longs;till? (*) <emph type="italics"/>To the&longs;e I <lb/>an&longs;wer, That Points of this nature require a curious and pro­<lb/>found examination, that it may truly appear whether they be <lb/>true or fal&longs;e; a work incon&longs;i&longs;tent with my lea&longs;ure to under­<lb/>take or go thorow with, nor is it any way nece&longs;&longs;ary for tho&longs;e, <lb/>whom we de&longs;ire to inform of the things that more nearly <lb/>concern their own &longs;alvation and The Churches Be­<lb/>nefit.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg844"></margin.target>(*) <emph type="italics"/>His re­<lb/>&longs;pondeo, multum <lb/>&longs;ubüliter, & labo­<lb/>rio&longs;is ratiombus, <lb/>i&longs;ta perquirere, ut <lb/>vere percipiatur, <lb/>ntrum ita, an non <lb/>ita &longs;it: quibus in­<lb/>eundis atque tra­<lb/>ctandis, nec mihi <lb/>jam tempus e&longs;t, <lb/>nec illis e&longs;&longs;e debet, <lb/>quos ad &longs;alutem <lb/>&longs;uam, Sanctæ Ec­<lb/>cle&longs;iæ nece&longs;&longs;ariam <lb/>utilitatem cupi <lb/>mus informari.<emph.end type="italics"/></s></p><p type="main"> <s>But yet although in Natural Propo&longs;itions we were to take the <lb/>re&longs;olution of condemning or admitting them from Texts of Scri­<lb/>pture unanimou&longs;ly expounded in the &longs;ame Sen&longs;e by all the Fa­<lb/>thers, yet do I not &longs;ee how this Rule can hold in our Ca&longs;e; for that <lb/>upon the &longs;ame Places we read &longs;everal Expo&longs;itions in the Fathers; <lb/><arrow.to.target n="marg845"></arrow.to.target><lb/><emph type="italics"/>(m) Diony&longs;ius Areopagita<emph.end type="italics"/> &longs;aying, <emph type="italics"/>That the Primum Mobile, and <lb/>not the Sun &longs;tand &longs;till.<emph.end type="italics"/> Saint <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/> is of the &longs;ame Opinion; <lb/><emph type="italics"/>(n) All the Cele&longs;tial Bodies were immoveable.<emph.end type="italics"/> And with them <lb/><arrow.to.target n="marg846"></arrow.to.target><lb/>concurreth <emph type="italics"/>Abulen&longs;is.<emph.end type="italics"/> But which is more, among&longs;t the Jewi&longs;h <lb/>Authors (whom <emph type="italics"/>Jo&longs;ephus<emph.end type="italics"/> applauds) &longs;ome have held, <emph type="italics"/>(o) That<emph.end type="italics"/> <pb xlink:href="040/01/475.jpg" pagenum="451"/><emph type="italics"/>The Sun did not really &longs;tand &longs;till, but &longs;eemed &longs;o to do, during the<emph.end type="italics"/><lb/><arrow.to.target n="marg847"></arrow.to.target><lb/><emph type="italics"/>&longs;hort time in which I&longs;rael gave the overthrow to their Enemies.<emph.end type="italics"/><lb/>So for the Miracle in the time of <emph type="italics"/>Hezekiah, Paulus Burgen&longs;is<emph.end type="italics"/> is of <lb/>opinion that it was not wrought on the Sun, but on the Diall. <lb/></s> <s>But that, in &longs;hort, it is nece&longs;&longs;ary to Glo&longs;&longs;e and Interpret the <lb/>words of the Text in <emph type="italics"/>Jo&longs;hua,<emph.end type="italics"/> when ever the Worlds Sy&longs;teme <lb/><arrow.to.target n="marg848"></arrow.to.target><lb/>is in di&longs;pute, I &longs;hall &longs;hew anon. </s> <s>Now finally, granting to the&longs;e <lb/>Gentlemen more than they demand, to wit, That we are whol­<lb/>ly to acquie&longs;ce in the judgment of Judicious Divines, and that <lb/>in regard that &longs;uch a particular Di&longs;qui&longs;ition is not found to <lb/>have been made by the Ancient Fathers, it may be undertaken <lb/>by the Sages of our Age, who having fir&longs;t heard the Experiments, <lb/>Ob&longs;ervations, Rea&longs;ons, and Demon&longs;trations of Philolophers and <lb/>Aftronomers, on the one &longs;ide, and on the other (&longs;eeing that the <lb/>Controver&longs;ie is about Natural Problems, and Nece&longs;&longs;ary <emph type="italics"/>Dilem­<lb/>ma's,<emph.end type="italics"/> and which cannot po&longs;&longs;ibly be otherwi&longs;e than in one of <lb/>the two manners in controver&longs;ie) they may with competent cer­<lb/>tainty determine what Divine In&longs;pirations &longs;hall dictate to them. <lb/></s> <s>But that without minutely examining and di&longs;cu&longs;&longs;ing all the Rea­<lb/>&longs;ons on both &longs;ides; and without ever comming to any certainty <lb/>of the truth of the Ca&longs;e, &longs;nch a Re&longs;olution &longs;hould be taken, Is <lb/>not to be hoped from tho&longs;e who do not &longs;tick to hazzard the Ma­<lb/>je&longs;ty and Dignity of the Sacred Scripture, in defending the re­<lb/>putation of their vain Fancies; Nor to be feared from tho&longs;e <lb/>who make it their whole bu&longs;ine&longs;&longs;e, to examine with all in­<lb/>ten&longs;ne&longs;s, what the Grounds of this Doctrine are; and that only <lb/>in an Holy Zeal for Truth, the Sacred Scriptures, and for the <lb/>Maje&longs;ty, Dignity, and Authority, in which every Chri&longs;tian <lb/>&longs;hould indeavour to have them maintained. </s> <s>Which Dignity, <lb/>who &longs;eeth not that it is with greater Zeal de&longs;ired and procured <lb/>by tho&longs;e who, ab&longs;olutely &longs;ubmitting them&longs;elves to the Holy <lb/>Church, de&longs;ire, not that this, or that opinion may be prohibi­<lb/>ted, but onely that &longs;uch things may be propo&longs;ed to con&longs;idera­<lb/>tion, as may the more a&longs;certain her in the &longs;afe&longs;t choice, than by <lb/>tho&longs;e who being blinded by their particular Intere&longs;t, or &longs;timula­<lb/>ted by malitious &longs;ugge&longs;tions, preach that &longs;he &longs;hould, without <lb/>more ado, thunder out Cur&longs;es, for that &longs;he had power &longs;o to do: <lb/>Not con&longs;idering that all that may be done is not alwayes conve­<lb/>nient to be done. </s> <s>The Holy Fathers of old were not of this <lb/>opinion, but rather knowing of how great prejudice, and how <lb/>much again&longs;t the primary intent of the Catholick Church, it <lb/>would be to go about from Texts of Scripture to decide Natu­<lb/>ral Conclu&longs;ions, touching which, either Experiments or nece&longs;&longs;ary <lb/>Demon&longs;trations, might in time to come evince the contrary, of <lb/>that which the naked &longs;en&longs;e of the Words &longs;oundeth, they have <pb xlink:href="040/01/476.jpg" pagenum="452"/>not only proceeded with great circum&longs;pection, but have left the <lb/>following Precepts for the in&longs;truction of others. <emph type="italics"/>(p) In points<emph.end type="italics"/><lb/><arrow.to.target n="marg849"></arrow.to.target><lb/><emph type="italics"/>ob&longs;cure and remote from our Sight, if we come to read any thing <lb/>out of Sacred Writ, that, with a<emph.end type="italics"/> Salvo <emph type="italics"/>to the Faith that we have <lb/>imbued, may corre&longs;pond with &longs;everal con&longs;tructions, let us not &longs;o <lb/>farre throw our &longs;elves upon any of them with a precipitous ob­<lb/>&longs;tinacy, as that if, perhaps the Truth being more diligently &longs;earch't <lb/>into, it &longs;hould ju&longs;tly fall to the ground, we might fall together <lb/>with it: and &longs;o &longs;hew that we contend not for the &longs;en&longs;e of Divine <lb/>Scriptures, but our own, in that we would have that which is <lb/>our own to be the &longs;en&longs;e of Scriptures, when as we &longs;hould ra­<lb/>ther de&longs;ire the Scriptures meaning to be ours.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg845"></margin.target><emph type="italics"/>(m) Non Solem, &longs;ed <lb/>Primum Mobile <lb/>immotum con&longs;ti­<lb/>ti&longs;&longs;e<emph.end type="italics"/>: Dioni&longs;. <lb/></s> <s>Areop.</s></p><p type="margin"> <s><margin.target id="marg846"></margin.target><emph type="italics"/>(n) Omnia cor­<lb/>pora Cæle&longs;tia, im­<lb/>mota &longs;ub&longs;titi&longs;&longs;e<emph.end type="italics"/>:</s></p><p type="margin"> <s><margin.target id="marg847"></margin.target><emph type="italics"/>(o) Solem re­<lb/>vera non &longs;ub&longs;titi&longs;­<lb/>&longs;e immorum, &longs;ed <lb/>pro brevi tempore, <lb/>intra quod I&longs;ræeli­<lb/>tæ, ho&longs;tes &longs;uos fu­<lb/>derunt, id ita vi­<lb/>&longs;um e&longs;&longs;e.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg848"></margin.target>I&longs;a. Cap. 38.</s></p><p type="margin"> <s><margin.target id="marg849"></margin.target>(p) <emph type="italics"/>In rebus ob­<lb/>&longs;ouris, atque a no­<lb/>&longs;tris oculis remi­<lb/>ti&longs;&longs;imis, &longs;iqua inde <lb/>&longs;cripta etiam divi­<lb/>næ legerimus, quæ <lb/>po&longs;&longs;int &longs;alva fide, <lb/>qua imbuimur, a­<lb/>liis atque altis pa­<lb/>rere &longs;entextiis, in <lb/>nullam earum nos <lb/>præcipiti affirma­<lb/>tione ita projici­<lb/>amus, ut &longs;i forte <lb/>ailigentiùs di&longs;cu&longs;­<lb/>&longs;a veritas <expan abbr="eã">eam</expan> recte <lb/>labefact averit, corruamus: non pro &longs;ententia Divinarum Scripturarum, &longs;ed pro no&longs;tra ita dimicantes, ut eam <lb/>velimus Scripturarum e&longs;&longs;e, quæ no&longs;tra e&longs;t, cum potius eam quæ Scripturarum e&longs;t, no&longs;tram e&longs;&longs;e velle debeamus,<emph.end type="italics"/><lb/>Divus Augu&longs;tin. </s> <s>in Gen. </s> <s>ad Litteram, lib. 2. c. </s> <s>18. & <expan abbr="&longs;eq.">&longs;eque</expan></s></p><p type="main"> <s>He goeth on, and a little after teacheth us, that no Propo&longs;i­<lb/>tion can be again&longs;t the Faith, unle&longs;&longs;e fir&longs;t it be demon&longs;trated <lb/><arrow.to.target n="marg850"></arrow.to.target><lb/>fal&longs;e; &longs;aying, <emph type="italics"/>(q) Tis not all the while contrary to Faith, until it <lb/>be di&longs;proved by mo&longs;t certain Truth, which if it &longs;hould &longs;o be, the Holy <lb/>Scripture affirm'd it not, but Humane Ignorance &longs;uppo&longs;ed it.<emph.end type="italics"/><lb/>Whereby we &longs;ee that the &longs;en&longs;es which we impo&longs;e on Texts of <lb/>Scripture, would be fal&longs;e, when ever they &longs;hould di&longs;agree with <lb/>Truths demon&longs;trated. </s> <s>And therefore we ought, by help of de­<lb/>mon&longs;trated Truth, to &longs;eek the undoubted &longs;en&longs;e of Scripture: <lb/>and not according to the &longs;ound of the words, that may &longs;eem <lb/>true to our weakne&longs;&longs;e, to go about, as it were, to force Na­<lb/>ture, and to deny Experiments and Nece&longs;&longs;ary Demon&longs;tra­<lb/>tions.</s></p><p type="margin"> <s><margin.target id="marg850"></margin.target>(q) <emph type="italics"/>Tam diu non <lb/>e&longs;t extra fidem, do­<lb/>nec Veritate cer­<lb/>ti&longs;&longs;ima refellatur. <lb/></s> <s>Quod &longs;i fæctum <lb/>fuerit, non hoc ha­<lb/>bebut Divina Scri­<lb/>ptura, &longs;ed hoc &longs;en­<lb/>&longs;er at humana Ig­<lb/>norantia.<emph.end type="italics"/> Ibid.</s></p><p type="main"> <s>Let Your Highne&longs;&longs;e be plea&longs;ed to ob&longs;erve farther, with how <lb/>great circum&longs;pection this Holy Man proceedeth, before he af­<lb/>firmeth any Interpretation of Scripture to be &longs;ure, and in &longs;uch <lb/>wi&longs;e certain, as that it need not fear the encounter of any diffi­<lb/>culty that may procure it di&longs;turbance, for not contenting <lb/>him&longs;elf that &longs;ome &longs;en&longs;e of Scripture agreeth with &longs;ome Demon­<lb/><arrow.to.target n="marg851"></arrow.to.target><lb/>&longs;tration, he &longs;ubjoynes. <emph type="italics"/>(r) But if right Rea&longs;on &longs;hall demon­<lb/>&longs;trate this to be true, yet is it que&longs;tionable whether in the&longs;e words <lb/>of Sacred Scripture the Pen-man would have this to be under­<lb/>&longs;tood, or &longs;omewhat el&longs;e, no le&longs;&longs;e true. </s> <s>And in ca&longs;e the Context <lb/>of his Words &longs;hall prove that he intended not this, yet will not <lb/>that which he would have to be under&longs;tood be therefore fal&longs;e, but <lb/>mo&longs;t true, aad that which is more profitable to be known.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg851"></margin.target>(r) <emph type="italics"/>Si autem <lb/>hoc verum e&longs;&longs;e ve­<lb/>ra ratio demon­<lb/>&longs;traverit, adhuc <lb/>incertum erit, u­<lb/>trum hoc in illis <lb/>verbis Sanctorum <lb/>Librorum, Scrip­<lb/>tor &longs;entiri volue­<lb/>rit, an aliquid a­<lb/>liud non minus ve­<lb/>rum. </s> <s>Quod &longs;i cætera contextio &longs;ermonis non hoc eum volui&longs;&longs;e probaverit, non ideo fal&longs;um erit aliud, quod ip&longs;e <lb/>intelligi voluit, &longs;ed & verum, & quod utilius cogno&longs;catur.<emph.end type="italics"/></s></p><p type="main"> <s>But that which increa&longs;eth our wonder concerning the cir­ <pb xlink:href="040/01/477.jpg" pagenum="453"/>cum&longs;pection, wherewith this Pious Authour proceedeth, is, <lb/><arrow.to.target n="marg852"></arrow.to.target><lb/>that not tru&longs;ting to his ob&longs;erving, that both Demon&longs;trative <lb/>Rea&longs;ons, and the &longs;en&longs;e that the words of Scripture and the re&longs;t <lb/>of the Context both precedent and &longs;ub&longs;equent, do con&longs;pire to <lb/>prove the &longs;ame thing, he addeth the following words.</s></p><p type="margin"> <s><margin.target id="marg852"></margin.target><emph type="italics"/>(&longs;) Si autem con­<lb/>textio Scripturæ, <lb/>hoc volui&longs;&longs;e intel­<lb/>ligi Scriptorem, <lb/>non repugnaverit, <lb/>adhuc re&longs;tabit <lb/>quærere, utrum & <lb/>aliud non potuerit.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>(&longs;) But if the Context do not hold forth any thing that may<emph.end type="italics"/><lb/><arrow.to.target n="marg853"></arrow.to.target><lb/><emph type="italics"/>di&longs;prove this to be the Authors Sen&longs;é, it yet remains to enquire, <lb/>Whether the other may not be intended al&longs;o.<emph.end type="italics"/> And not yet re&longs;olving <lb/>to accept of one Sen&longs;e, or reject another, but thinking that he <lb/>could never u&longs;e &longs;ufficient caution, he proceedeth: <emph type="italics"/>(t) But if <lb/>&longs;o be we finde that the other may be al&longs;o meant, it will be doubted <lb/>which of them he would have to &longs;tand; or which in probability he <lb/>may be thought to aim at, if the true circum&longs;tances on both &longs;ides be <lb/>weighed.<emph.end type="italics"/> And la&longs;tly, intending to render a Rea&longs;on of this his <lb/><arrow.to.target n="marg854"></arrow.to.target><lb/>Rule, by &longs;hewing us to what perils tho&longs;e men expo&longs;e the Scri­<lb/>ptures, and the Church; who, more re&longs;pecting the &longs;upport of <lb/>their own errours, than the Scriptures Dignity, would &longs;tretch its <lb/>Authority beyond the Bounds which it pre&longs;cribeth to it &longs;elf, he <lb/>&longs;ubjoyns the en&longs;uing words, which of them&longs;elves alone might <lb/>&longs;uffice to repre&longs;s and moderate the exce&longs;&longs;ive liberty, which &longs;ome <lb/>think that they may a&longs;&longs;ume to them&longs;elves: <emph type="italics"/>(u) For it many <lb/>times falls out, that a Chri&longs;tian may not &longs;o fully under&longs;tand a <lb/>Point concerning the Earth, lieaven, and the re&longs;t of this Worlds <lb/>Elements; the Motion, Conver&longs;ion, Magnitude, and Di&longs;tances of <lb/>the Stars, the certain defects of the Sun and Moon, the Revoluti­<lb/>ons of Years and Times, the Nature of Animals, Fruits, Stones, <lb/>and other things of like nature, as to defend the &longs;ame by right <lb/>Rea&longs;on, or make it out by Experiments. </s> <s>But its too great an ab­<lb/>&longs;urdity, yea mo&longs;t pernicious, and chiefly to be avoided, to let an <lb/>Infidel finde a Chri&longs;tian &longs;o &longs;tupid, that he &longs;hould argue the&longs;e mat­<lb/>ters; as if they were according to Chri&longs;tian Doctrine; and make <lb/>him (as the Proverb &longs;aith) &longs;carce able to contain his laughter, &longs;ee­<lb/>ing him &longs;o far from the Mark Nor is the matter &longs;o much that one <lb/>in an errour &longs;hould be laught at, but that our Authors &longs;hould be <lb/>thought by them that are without, to be of the &longs;ame Opinion, and to <lb/>the great prejudice of tho&longs;e, who&longs;e &longs;alvation we wait for, &longs;en&longs;urcd <lb/>and rejected as unlearned. </s> <s>For when they &longs;hal confute any one of the <lb/>Chri&longs;tians in that matter, which they them&longs;elvs thorowly under­<lb/>&longs;tand, and &longs;hall thereupon expre&longs;s their light e&longs;teem of our Books; <lb/>how &longs;hall the&longs;e Volumes be believed touching the Re&longs;urrection of <lb/>the Dead, the Hope of eternal Life, and the Kingdom of Heaven; <lb/>when, as to the&longs;e Points which admit of pre&longs;ent Demon&longs;tration, <lb/>or undoubted Rea&longs;ons, they conceive them to be fal&longs;ly written.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/478.jpg" pagenum="454"/><p type="margin"> <s><margin.target id="marg853"></margin.target><emph type="italics"/>(t) Quod &longs;i & <lb/>aliud potui&longs;&longs;e inve­<lb/>nerimus, incertum <lb/>erit; quidnam eo­<lb/>rum ille voluerit: <lb/>aut utrumque vo­<lb/>lui&longs;&longs;e non inconve­<lb/>nienter creditur, &longs;i <lb/>utriu&longs;que &longs;ententiæ <lb/>certa circum&longs;t an­<lb/>tia &longs;ufragatur.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg854"></margin.target><emph type="italics"/>(u) Plerumque <lb/>enim accidit, at a­<lb/>liquid de Terra, de<lb/>Celo, de ceter is hu­<lb/>jus mundi elemen­<lb/>tis, de motu, con­<lb/>ver&longs;ione, vel ctiam <lb/>magnitudine & <lb/>intervallis Syde­<lb/>rum, de certis de­<lb/>fectibus Solis, & <lb/>Lunæ, de eircuiti­<lb/>bus annorum & <lb/>temporum; de Na­<lb/>turis animalium, <lb/>fruticum, lapidum, <lb/>atque buju&longs;modi <lb/>ceter is, etiam non <lb/>Chri&longs;tianus ita no­<lb/>verit, ut cirti&longs;&longs;ima <lb/>ratione vel experi­<lb/>entiâ teneat. </s> <s>Tur­<lb/>pe autem e&longs;t nimis <lb/>& pernicio&longs;um, ae <lb/>maxime caven­<lb/>dum, at Chri&longs;tia­<lb/>num de his rebus <lb/>qua&longs;i &longs;ecundum <lb/>Chri&longs;tianaslitter as <lb/>loquentem, ita de­<lb/>lirare quilibet in­<lb/>fiàelis audiat, ut, <lb/>quemadmodum di­<lb/>citur, toto Cælo er­<lb/>rærecon&longs;piciens, <expan abbr="ri-&longs;ũtenere">ri­<lb/>&longs;untenere</expan> vix po&longs;&longs;it: <lb/>& non tam mole­<lb/>&longs;tum e&longs;t, quod er­<lb/>rans homo deride­<lb/>retur, &longs;ed quod au­<lb/>ctores no&longs;tri, ab tis <lb/>qui foris &longs;unt, ta­<lb/>lia &longs;en&longs;i&longs;&longs;e credun­<lb/>tur, & cum magno exitio eorum, de quorum &longs;alute &longs;atagimus, tanquam indocti reprehenduntur atque re&longs;puuntur. <lb/></s> <s>Cum enim quemquam de numero Chri&longs;tiano um eainre, quam ip &longs;i optime norunt, deprehenderint, & venam &longs;enten­<lb/>tiam &longs;uam de no&longs;tris libris a&longs;&longs;erent; quo pacto illis Libris credituri &longs;unt, de Re&longs;urrectione Mortuorum, & de &longs;pe<lb/>vit æ eternæ, Regnoque Celorum; quando de his rebus quas jam experiri, vel indubitatis rationibus percipere potuerunt<lb/>fallaciter putaverint e&longs;&longs;e con&longs;criptos.<emph.end type="italics"/></s></p><p type="main"> <s>And how much the truly Wi&longs;e and Prudent Fathers are di&longs;­<lb/>plea&longs;ed with the&longs;e men, who in defence of Propo&longs;itions which <lb/>they do not under&longs;tand, do apply, and in a certain &longs;en&longs;e pawn <lb/>Texts of Scripture, and afterwards go on to encrea&longs;e their fir&longs;t <lb/>Errour, by producing other places le&longs;s under&longs;tood than the for­<lb/>mer. </s> <s>The &longs;ame Saint declareth in the expre&longs;&longs;ions following: <lb/><arrow.to.target n="marg855"></arrow.to.target><lb/><emph type="italics"/>(x) What trouble and &longs;orrow weak undertakers bring upon <lb/>their knowing Brethren, is not to be expre&longs;&longs;ed; &longs;ince when they <lb/>begin to be told and convinced of their fal&longs;e and un&longs;ound Opinion, <lb/>by tho&longs;e who have no re&longs;pect for the Authority of our Scriptures, <lb/>in defence of what through a fond Temerity, and mo&longs;t manife&longs;t fal­<lb/>&longs;ity, they have urged; they fall to citing the &longs;aid Sacred Books <lb/>for proof of it, or el&longs;e repeat many words by heart out of them, <lb/>which they conceive to make for their purpo&longs;e; not knowing <lb/>either what they &longs;ay, or whereof they affirm.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg855"></margin.target><emph type="italics"/>(y) Quid enim <lb/>mole&longs;tiæ, tri&longs;tiæque <lb/>ingerant prudenti­<lb/>bus fratribus, te­<lb/>nerarij præ&longs;umpto­<lb/>res, &longs;atis dici non <lb/>pote&longs;t, cum, &longs;i <lb/>quando de fal&longs;a & <lb/>prava opinione &longs;ua <lb/>reprehendi & con­<lb/>vinci cæperint, ab <lb/>iis qui no&longs;trorum <lb/>librorum auctori­<lb/>tate, & aperli&longs;&longs;ima <lb/>falfitate dixerunt, <lb/>eo&longs;dnm libros San­<lb/>ctos, unde id pro­<lb/>bent, proferre co­<lb/>nantur; vel etiam <lb/>memoriter, quæ ad <lb/>te&longs;timonium vale­<lb/>re arbitrantur, <lb/>multa inde verba <lb/>pronunciant, non <lb/>intelligentes, neque <lb/>quæ loquuntur, ne­<lb/>que de quibus af­<lb/>firmant.<emph.end type="italics"/></s></p><p type="main"> <s>In the number of the&longs;e we may, as I conceive, account tho&longs;e, <lb/>who, being either unwilling or unable to under&longs;tand the De­<lb/>mon&longs;trations and Experiments, wherewith the Author and fol­<lb/>lowers of this Opinion do confirm it, run upon all occa&longs;ions to <lb/>the Scriptures, not con&longs;idering that the more they cite them, and <lb/>the more they per&longs;i&longs;t in affirming that they are very clear, and <lb/>do admit no other &longs;en&longs;es, &longs;ave tho&longs;e which they force upon <lb/>them, the greater injury they do to the Dignity of them (if we <lb/>allowed that their judgments were of any great Authority) in <lb/>ca&longs;e that the Truth coming to be manife&longs;tly known to the con­<lb/>trary, &longs;hould occa&longs;ion any confu&longs;ion, at lea&longs;t to tho&longs;e who are <lb/>&longs;eparated from the Holy Church; of whom yet &longs;he is very &longs;olici­<lb/>tous, and like a tender Mother, de&longs;irous to recover them again <lb/>into her Lap. </s> <s>Your Highne&longs;s therefore may &longs;ee how præpo&longs;terou&longs;­<lb/>ly tho&longs;e Per&longs;ons proceed, who in Natural Di&longs;putations do range <lb/>Texts of Scripture in the Front for their Arguments; and &longs;uch <lb/>Texts too many times, as are but &longs;uperficially under&longs;tood by them.</s></p><p type="main"> <s>But if the&longs;e men do verily think, & ab&longs;olutely believe that they <lb/>have the true &longs;ence of Such a particular place of Scripture, it mu&longs;t <lb/>needs follow of con&longs;equence, that they do likewi&longs;e hold for certain, <lb/>that they have found the ab&longs;olute truth of that Natural Conclu&longs;i­<lb/>on, which they intend to di&longs;pute:</s> <s> And that withall, they do know <lb/>that they have a great advantage of their Adver&longs;ary, who&longs;e Lot it <lb/>is to defend the part that is fal&longs;e; in regard that he who maintain­<lb/>eth the Truth, may have many &longs;en&longs;ible experiments, and many ne­<lb/>ce&longs;&longs;ary Demon&longs;trations on his &longs;ide; whereas his Antagoni&longs;t can <lb/>make u&longs;e of no other than deceitful appearances, <emph type="italics"/>Paralogi&longs;ms<emph.end type="italics"/> and <lb/><emph type="italics"/>Sophi&longs;ms.<emph.end type="italics"/> Now if they keeping within natural bounds, & produ­<lb/>cing no other Weapons but tho&longs;e of Philo&longs;ophy, pretend however, <lb/>to have &longs;o much advantage of their Enemy; why do they after­ <pb xlink:href="040/01/479.jpg" pagenum="455"/>wards in coming to engage, pre&longs;ently betake them&longs;elves to a Wea­<lb/>pon inevitable & dreadful to terrifie their Opponent with the &longs;ole <lb/>beholding of it? </s> <s>But if I may &longs;peak the truth, I believe that they are <lb/>the fir&longs;t that are affrighted, and that perceiving them&longs;elves unable <lb/>to bear up again&longs;t the a&longs;&longs;aults of their Adver&longs;ary, go about to find <lb/>out ways how to keep them far enough off, forbidding unto them <lb/>the u&longs;e of the Rea&longs;on which the Divine Bounty had vouch&longs;afed <lb/>them, & abu&longs;ing the mo&longs;t equitable Authority of &longs;acred Scripture, <lb/>which rightly under&longs;tood and applyed, can never, according to <lb/>the common Maxime of Divines, oppo&longs;e the Manife&longs;t Experi­<lb/>ments, or Nece&longs;&longs;ary Demon&longs;trations. </s> <s>But the&longs;e mens running <lb/>to the Scriptures for a Cloak to their inability to comprehend, <lb/>not to &longs;ay re&longs;olve the Rea&longs;ons alledged again&longs;t them, ought (if I <lb/>be not mi&longs;taken) to &longs;tand them in no &longs;tead: the Opinion which <lb/>they oppo&longs;e having never as yet been condemned by Holy <lb/>Church. </s> <s>So that if they would proceed with Candor, they <lb/>&longs;hould either by &longs;ilence confe&longs;s them&longs;elves unable to handle &longs;uch <lb/>like points, or fir&longs;t con&longs;ider that it is not in the power of them or <lb/>others, but onely in that of the Pope, and of Sacred Councils to <lb/><arrow.to.target n="marg856"></arrow.to.target><lb/>cen&longs;ure a Po&longs;ition to be Erroneous: But that it is left to their <lb/>freedome to di&longs;pute concerning its fal&longs;ity. </s> <s>And thereupon, <lb/>knowing that it is impo&longs;&longs;ible that a Propo&longs;ition &longs;hould at the <lb/>&longs;ame time be True and Heretical; they ought, I &longs;ay, to imploy <lb/>them&longs;elves in that work which is mo&longs;t poper to them, namely, <lb/>in demon&longs;trating the fal&longs;ity thereof: whereby they may &longs;ee <lb/>how needle&longs;&longs;e the prohibiting of it is, its fal&longs;hood being once <lb/>di&longs;covered, for that none would follow it: or the Prohibition <lb/>would be &longs;afe, and without all danger of Scandal. </s> <s>Therefore <lb/>fir&longs;t let the&longs;e men apply them&longs;elves to examine the Arguments <lb/>of <emph type="italics"/>Copernicus<emph.end type="italics"/> and others; and leave the condemning of them <lb/>for Erroneous and Heretical to whom it belongeth: But yet let <lb/>them not hope ever to finde &longs;uch ra&longs;h and precipitous Determina­<lb/>tions in the Wary and Holy Fathers, or in the ab&longs;olute Wi&longs;­<lb/>dome of him that cannot erre, as tho&longs;e into which they &longs;uffer <lb/>them&longs;elves to be hurried by &longs;ome particular Affection or Inte­<lb/>re&longs;t of their own. </s> <s>In the&longs;e and &longs;uch other Po&longs;itions, which are <lb/>not directly <emph type="italics"/>de Fide,<emph.end type="italics"/> certainly no man doubts but His Holine&longs;s <lb/>hath alwayes an ab&longs;olute power of Admitting or Condemn­<lb/>ing them, but it is not in the power of any Creature to make <lb/>them to be true or fal&longs;e, otherwi&longs;e than of their own nature, <lb/>and <emph type="italics"/>de facto<emph.end type="italics"/> they are.</s></p><p type="margin"> <s><margin.target id="marg856"></margin.target>If this pa&longs;&longs;age <lb/>&longs;eem har&longs;h, the <lb/>Reader mu&longs;t re­<lb/>member that I do <lb/>but Tran&longs;late.</s></p><p type="main"> <s>Therefore it is in my judgment more di&longs;cretion to a&longs;&longs;ure us <lb/>fir&longs;t of the nece&longs;&longs;ary and immutable Truth of the Fact, (over <lb/>which none hath power) than without that certainty by condem­<lb/>ning one part to deprive ones &longs;elf of that authority of freedome <pb xlink:href="040/01/480.jpg" pagenum="456"/>to elect, making tho&longs;e Determinations to become nece&longs;&longs;ary, <lb/>which at pre&longs;ent are indifferent and arbitrary, and re&longs;t in the <lb/>will of Supreme Authority. </s> <s>And in a word, if it be not po&longs;­<lb/>&longs;ible that a Conclu&longs;ion &longs;hould be declared Heretical, whil&longs;t we <lb/>are not certain, but that it may be true, their pains are in vain <lb/>who pretend to condemn the Mobility of the Earth and Stabili­<lb/>ty of the Sun, unle&longs;&longs;e they have fir&longs;t demon&longs;trated it to be im­<lb/>po&longs;&longs;ible and fal&longs;e.</s></p><p type="main"> <s>It remaineth now, that we con&longs;ider whether it be true, that <lb/>the Place in <emph type="italics"/>Jo&longs;huab<emph.end type="italics"/> may be taken without altering the pure &longs;ig­<lb/>nification of the words: and how it can be that the Sun, obey­<lb/>ing the command of <emph type="italics"/>Jo&longs;huah,<emph.end type="italics"/> which was, <emph type="italics"/>That it &longs;hould &longs;tand <lb/>&longs;till,<emph.end type="italics"/> the day might thereupon be much lengthened. </s> <s>Which bu­<lb/>&longs;ine&longs;&longs;e, if the Cele&longs;tial Motions be taken according to the <emph type="italics"/>Ptolo­<lb/>maick<emph.end type="italics"/> Sy&longs;teme, can never any wayes happen, for that the Sun <lb/>moving thorow the Ecliptick, according to the order of the <lb/>Signes, which is from Ea&longs;t to We&longs;t (which is that which maketh <lb/>Day and Night) it is a thing manife&longs;t, that the Sun cea&longs;ing its <lb/>true and proper Motion, the day would become &longs;horter and not <lb/>longer; and that on the contrary, the way to lengthen it would <lb/>be to ha&longs;ten and velocitate the Suns motion; in&longs;omuch that to <lb/>cau&longs;e the Sun to &longs;tay above the Horizon for &longs;ome time, in one <lb/>and the &longs;ame place, without declining towards the We&longs;t, it would <lb/>be nece&longs;&longs;ary to accelerate its motion in &longs;uch a manner as that it <lb/>might &longs;eem equal to that of the <emph type="italics"/>Primum Mobile,<emph.end type="italics"/> which would be <lb/>an accelerating it about three hundred and &longs;ixty times more than <lb/>ordinary. </s> <s>If therefore <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> had had an intention that his <lb/>words &longs;hould be taken in their pure and proper &longs;ignification, he <lb/>would have bid the Sun to have accelerated its Motion &longs;o, that <lb/>the Rapture of the <emph type="italics"/>Primum Mobile<emph.end type="italics"/> might not carry it to the <lb/>We&longs;t: but becau&longs;e his words were heard by people which hap­<lb/>ly knew no other Cele&longs;tial Motion, &longs;ave this grand and common <lb/>one, from Ea&longs;t to We&longs;t, &longs;tooping to their Capacity, and having <lb/>no intention to teach them the Con&longs;titution of the Spheres, but <lb/>only that they &longs;hould perceive the greatne&longs;s of the Miracle <lb/>wrought, in the lengthening of the Day, he &longs;poke according to <lb/>their apprehen&longs;ion. </s> <s>Po&longs;&longs;ibly this Con&longs;ideration moved <emph type="italics"/>Diony­<lb/>&longs;ius Areopagita<emph.end type="italics"/> to &longs;ay that in this Miracle the <emph type="italics"/>Primum Mobile<emph.end type="italics"/><lb/>&longs;tood &longs;till, and this &longs;topping, all the Cele&longs;tial Spheres did of <lb/>con&longs;equence &longs;tay: of which opinion is S. <emph type="italics"/>Augu&longs;tine<emph.end type="italics"/> him&longs;elf, and <lb/><emph type="italics"/>Abulen&longs;is<emph.end type="italics"/> at large confirmeth it. </s> <s>Yea, that <emph type="italics"/>Jo&longs;hua's<emph.end type="italics"/> intention <lb/>was, that the whole Sy&longs;teme of the Cele&longs;tial Spheres &longs;hould <lb/>&longs;tand &longs;till, is collected from the command he gave at the &longs;ame <lb/>time to the Moon, although that it had nothing to do in the <lb/>lengthening of the day; and under the injunction laid upon the <pb xlink:href="040/01/481.jpg" pagenum="457"/>Moon, we are to under&longs;tand the Orbes of all the other Planets, <lb/>pa&longs;&longs;ed over in &longs;ilence here, as al&longs;o in all other places of the Sacred <lb/>Scriptures; the intention of which, was not to reach us the A&longs;tro­<lb/>nomical Sciences. </s> <s>I &longs;uppo&longs;e therefore, (if I be not deceived) <lb/>that it is very plain, that if we allow the <emph type="italics"/>Ptolemaick<emph.end type="italics"/> Sy&longs;teme, we <lb/>mu&longs;t of nece&longs;&longs;ity interpret the words to &longs;ome &longs;en&longs;e different from <lb/>their &longs;trict &longs;ignification. </s> <s>Which Interpretation (being admo­<lb/>ni&longs;hed by the mo&longs;t u&longs;efull precepts of S. <emph type="italics"/>Augu&longs;tine)<emph.end type="italics"/> I will not <lb/>affirm to be of nece&longs;&longs;ity this above-mentioned, &longs;ince that &longs;ome <lb/>other man may haply think of &longs;ome other more proper, and more <lb/>agreeable Sen&longs;e.</s></p><p type="main"> <s>But now, if this &longs;ame pa&longs;&longs;age may be under&longs;tood in the <emph type="italics"/>Coper­<lb/>nican<emph.end type="italics"/> Sy&longs;teme, to agree better with what we read in <emph type="italics"/>Jo&longs;huah,<emph.end type="italics"/><lb/>with the help of another Ob&longs;ervation by me newly &longs;hewen in <lb/>the Body of the Sun; I will propound it to con&longs;ideration, &longs;peak­<lb/>ing alwaies with tho&longs;e &longs;afe Re&longs;erves; That I am not &longs;o affectio­<lb/>nate to my own inventions, as to prefer them before tho&longs;e of <lb/>other men, and to believe that better and more agreeable to the <lb/>intention of the Sacred Volumes cannot be produced.</s></p><p type="main"> <s>Suppo&longs;ing therefore in the fir&longs;t place, that in the Miracle of <lb/><emph type="italics"/>Jo&longs;huah,<emph.end type="italics"/> the whole Sy&longs;teme of the Cele&longs;tial Revolutions &longs;tood <lb/>&longs;till, according to the judgment of the afore-named Authors: <lb/>And this is the rather to be admitted, to the end, that by the <lb/>&longs;taying of one alone, all the Con&longs;titutions might not be con­<lb/>founded, and a great di&longs;order needle&longs;ly introduced in the whole <lb/>cour&longs;e of Nature: I come in the &longs;econd place to con&longs;ider how the <lb/>Solar Body, although &longs;table in one con&longs;tant place, doth neverthe­<lb/>le&longs;s revolve in it &longs;elf, making an entire Conver&longs;ion in the &longs;pace <lb/>of a Month, or thereabouts; as I conceive I have &longs;olidly demon­<lb/>&longs;trated in my Letters <emph type="italics"/>Delle Machie Solari<emph.end type="italics"/>: Which motion we <lb/>&longs;en&longs;ibly &longs;ee to be in the upper part of its Globe, inclined to­<lb/>wards the South; and thence towards the lower part, to encline <lb/>towards the North, ju&longs;t in the &longs;ame manner as all the other Orbs <lb/>of the Planets do. </s> <s>Thirdly, If we re&longs;pect the Nobility of the <lb/>Sun, and his being the Fountain of Light, by which, (as I nece&longs;­<lb/>&longs;arily demon&longs;trate) not onely the Moon and Earth, but all the <lb/>other Planets (all in the &longs;ame manner dark of them&longs;elves) become <lb/>illuminated; I conceive that it will be no unlogicall Illation to &longs;ay, <lb/>That it, as the Grand Mini&longs;ter of Nature, and in a certain &longs;en&longs;e <lb/>the Soul and Heart of the World, infu&longs;eth into the other Bodies <lb/>which environ it; not onely Light, but Motion al&longs;o; by revol­<lb/>ving ^{*} in it &longs;elf: So that in the &longs;ame manner that the motion of <lb/><arrow.to.target n="marg857"></arrow.to.target><lb/>the Heart of an Animal cea&longs;ing, all the other motions of its <lb/>Members would cea&longs;e; &longs;o, the Conver&longs;ion of the Sun cea&longs;ing, <lb/>the Conver&longs;ions of all the Planets would &longs;tand &longs;till. </s> <s>And though <pb xlink:href="040/01/482.jpg" pagenum="458"/>I could produce the te&longs;timonies of many grave Writers to prove <lb/>the admirable power and influence of the Sun, I will content my <lb/>&longs;elf with one &longs;ole place of Holy <emph type="italics"/>Dioni&longs;ius Areopagita<emph.end type="italics"/> in his Book <lb/><arrow.to.target n="marg858"></arrow.to.target><lb/><emph type="italics"/>de Divinis Nominibus<emph.end type="italics"/>; who thus writes of the Sun: ^{(*)} <emph type="italics"/>His Light <lb/>gathereth and converts all things to him&longs;elf, which are &longs;een, <lb/>moved, illu&longs;trated, wax hot, and (in a word) tho&longs;e things which <lb/>are pre&longs;erved by his &longs;plendor: Wherefore the Sun is called<emph.end type="italics"/> <foreign lang="greek">Hlios,</foreign><lb/><emph type="italics"/>for that he collecteth and gathereth together all things di&longs;per&longs;ed.<emph.end type="italics"/><lb/>And a little after of the Sun again he adds; ^{(*)} <emph type="italics"/>If this Sun which <lb/>wo &longs;ee, as touching the E&longs;&longs;ences and Qualities of tho&longs;e things <lb/>which fall within our Sen&longs;e, being very many and different; yet <lb/>if he who is one, and equally be&longs;towes his Light, doth renew, <lb/>nouri&longs;h, defend, perfect, divide, conjoyn, cheri&longs;h, make fruitfull,<emph.end type="italics"/><lb/><arrow.to.target n="marg859"></arrow.to.target><lb/><emph type="italics"/>encrea&longs;e, change, fix, produce, move, and fa&longs;hion all living crea­<lb/>tures: And every thing in this Vniver&longs;e at his Plea&longs;ure, is par­<lb/>taker of one and the &longs;ame Sun; and the cau&longs;es of many things <lb/>which participate of him, are equally auticipated in him: Certain­<lb/>ly by greater rea&longs;on<emph.end type="italics"/>; &c. </s> <s>The Sun therefore being the Foun­<lb/>tain of Light and, Principle of Motion, God intending, that at <lb/>the Command of <emph type="italics"/>Jo&longs;hua,<emph.end type="italics"/> all the Worlds Sy&longs;teme, &longs;hould con­<lb/>tinue many hours in the &longs;ame &longs;tate, it &longs;ufficeth to make the Sun <lb/>&longs;tand &longs;till, upon who&longs;e &longs;tay (all the other Conver&longs;ions cea&longs;ing) <lb/>the Earth, the Moon, the Sun did abide in the &longs;ame Con&longs;titution <lb/>as before, as likewi&longs;e all the other Planets: Nor in all that time <lb/>did the Day decline towards Night, but it was miraculou&longs;ly pro­<lb/>longed: And in this manner, upon the &longs;tanding &longs;till of the Sun, <lb/>without altering, or in the lea&longs;t di&longs;turbing the other A&longs;pects and <lb/>mutual Po&longs;itions of the Stars, the Day might be lengthned on <lb/>Earth; which exactly agreeth with the Litteral &longs;en&longs;e of the Sacred <lb/>Text.</s></p><p type="margin"> <s><margin.target id="marg857"></margin.target>* <emph type="italics"/>i. </s> <s>i.<emph.end type="italics"/> On its own <lb/>Axis.</s></p><p type="margin"> <s><margin.target id="marg858"></margin.target>(*) <emph type="italics"/>Lux ejus colli­<lb/>git, convertitque ad <lb/>&longs;e omnia, quæ vi­<lb/>dentur, quæ mo­<lb/>ventur, quæ illu­<lb/>&longs;trantur, quæ ca­<lb/>le&longs;cunt, & uno no­<lb/>mine ea, quæ ab e­<lb/>jus &longs;plendore cen­<lb/>tinentur. </s> <s>Itaque <lb/>Sol <foreign lang="greek">Hli<34></foreign> dicitur, <lb/>quod omnia con­<lb/>greger, colligatque <lb/>di&longs;per&longs;a.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg859"></margin.target>(*) <emph type="italics"/>Si enim <lb/>Sol hic quem vi­<lb/>domus, eorum quæ <lb/>&longs;ub &longs;en&longs;um ca­<lb/>dunt, e&longs;&longs;entias & <lb/>qualitates, quæ que <lb/>muliæ &longs;int ac di&longs;­<lb/>&longs;imiles, tamen ip&longs;e <lb/>qui unus e&longs;t, æqua­<lb/>literque lumen <lb/>fundit, renovat, a­<lb/>lit, tuetur, perficit, <lb/>dividit, conjungit, <lb/>fovet, fæcunda red­<lb/>dit, auget, mutat, <lb/>firmat, edit, movet, <lb/><expan abbr="vitaliaq;">vitaliaque</expan> facit om­<lb/>nia: & <expan abbr="unaquæq;">unaquæque</expan> <lb/>res hujus univer­<lb/>&longs;itatis, pro cæptu <lb/>&longs;uo, unius atque e­<lb/>ju&longs;dem Solis e&longs;t <lb/>particeps, cau&longs;æ&longs;­<lb/>que multorum, <lb/>quæ participant, in <lb/>&longs;e æquabiliter an­<lb/>ticipatas habet, <lb/>certe majori ratio­<lb/>ne,<emph.end type="italics"/> &c.</s></p><p type="main"> <s>But that of which, if I be not mi&longs;taken, we are to make no <lb/>&longs;mall account, is, That by help of this <emph type="italics"/>Copernican<emph.end type="italics"/> Hypothe&longs;is, <lb/>we have the Litteral, apert, and Natural Sen&longs;e of another parti­<lb/>cular that we read of in the &longs;ame Miracle; which is, That the <lb/>Sun &longs;tood &longs;till <emph type="italics"/>in Medio Cæli<emph.end type="italics"/>: Upon which pa&longs;&longs;age grave Divines <lb/>rai&longs;e many que&longs;tions, in regard it &longs;eemeth very probable, That <lb/>when <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> de&longs;ired the lengthning of the Day, the Sun was <lb/>near &longs;etting, and not in the Meridian; for if it had been in the <lb/>Meridian, it being then about the Summer <emph type="italics"/>Sol&longs;tice,<emph.end type="italics"/> and con­<lb/>&longs;equently the dayes being at the longe&longs;t, it doth not &longs;eem likely <lb/>that it was nece&longs;&longs;ary to pray for the lengthning of the day, to <lb/>pro&longs;ecute Victory in a Battail, the &longs;pace of &longs;even hours and more, <lb/>which remained to Night, being &longs;ufficient for that purpo&longs;e. <lb/></s> <s>Upon which Grave Divines have been induced to think that the <lb/>Sun was near &longs;etting: And &longs;o the words them&longs;elves &longs;eem to <pb xlink:href="040/01/483.jpg" pagenum="459"/>&longs;ound, &longs;aying, <emph type="italics"/>Ne movearis Sol, ne movearis.<emph.end type="italics"/> For if it had <lb/>been in the Meridian, either it had been needle&longs;s to have asked <lb/>a Miracle, or it would have been &longs;ufficient to have onely praid <lb/>for &longs;ome retardment. </s> <s>Of this opinion is <emph type="italics"/>Cajetan,<emph.end type="italics"/> to which &longs;ub­<lb/>&longs;cribeth <emph type="italics"/>Magaglianes,<emph.end type="italics"/> confirming it by &longs;aying, that <emph type="italics"/>Jo&longs;hua<emph.end type="italics"/> had <lb/>that very day done &longs;o many other things before his commanding <lb/>the Sun, as were not po&longs;&longs;ibly to be di&longs;patch't in half a day. <lb/></s> <s>Whereupon they are forced to read the Words <emph type="italics"/>in Medio Cœli<emph.end type="italics"/><lb/>(to confe&longs;s the truth) with a little har&longs;hne&longs;s, &longs;aying that they <lb/>import no more than this: <emph type="italics"/>That the Sun &longs;tood &longs;till, being in our <lb/>Hemi&longs;phere, that is, above the Horizon.<emph.end type="italics"/> But (if I do not erre) <lb/><arrow.to.target n="marg860"></arrow.to.target><lb/>we &longs;hall avoid that and all other har&longs;h expo&longs;itions, if according <lb/>to the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme we place the Sun in the mid&longs;t, that <lb/>is, in the Centre of the Cœle&longs;tial Orbes, and of the Planetary <lb/>Conver&longs;ions, as it is mo&longs;t requi&longs;ite to do. </s> <s>For &longs;uppo&longs;ing any <lb/>hour of the day (either Noon, or any other, as you &longs;hall plea&longs;e <lb/>neerer to the Evening) the Day was lengthened, and all the <lb/>Cœle&longs;tial Revolutions &longs;tayed by the Suns &longs;tanding &longs;till, <emph type="italics"/>In the <lb/>mid&longs;t,<emph.end type="italics"/> that is, <emph type="italics"/>in the Centre of Heaven,<emph.end type="italics"/> where it re&longs;ides: A <lb/>Sen&longs;e &longs;o much the more accomodate to the Letter (be&longs;ides what <lb/>hath been &longs;aid already) in that, if the Text had de&longs;ired to have <lb/>affirmed the Suns Re&longs;t to have been cau&longs;ed at Noon-day, the <lb/>proper expre&longs;&longs;ion of it had been to &longs;ay, <emph type="italics"/>It &longs;tood &longs;till at Noon-day,<emph.end type="italics"/><lb/>or <emph type="italics"/>in the Meridian Circle,<emph.end type="italics"/> and not <emph type="italics"/>in the mid&longs;t of Heaven<emph.end type="italics"/>: In <lb/>regard that the true and only <emph type="italics"/>Middle<emph.end type="italics"/> of a Spherical Body (as is <lb/>Heaven) is the Centre.</s></p><p type="margin"> <s><margin.target id="marg860"></margin.target><emph type="italics"/>Solem &longs;teti&longs;&longs;e, <lb/>dum adhuc in He­<lb/>mi&longs;pharto no&longs;tro, <lb/>&longs;upra &longs;cilicet Ho­<lb/>rizontem exi&longs;teret.<emph.end type="italics"/><lb/>Cajetan <emph type="italics"/>in loce.<emph.end type="italics"/></s></p><p type="main"> <s>Again, as to other places of Scripture, which &longs;eem contrary to <lb/>this po&longs;ition, I do not doubt but that if it were acknowledged <lb/>for True and Demon&longs;trated tho&longs;e very Divines who &longs;o long as <lb/>they repute it fal&longs;e, hold tho&longs;e places incapable of Expo&longs;itions <lb/>that agree with it would finde &longs;uch Interpretations for them, as <lb/>&longs;hould very well &longs;uit therewith; and e&longs;pecially if to the know­<lb/>ledge of Divine Learning they would but adde &longs;ome knowledge <lb/>of the A&longs;tronomical Sciences: And as at pre&longs;ent, whil&longs;t they <lb/>deem it fal&longs;e they think they meet in Scripture only with &longs;uch <lb/>places as make again&longs;t it, if they &longs;hall but once have entertained <lb/>another conceipt thereof, they would meet peradventure as many <lb/>others that accord with it, and haply would judge, that the Holy <lb/>Church doth very appo&longs;itly teach, That God placed the Sun in <lb/>the Centre of Heaven, and that thereupon by revolving it in it <lb/>&longs;elf, after the manner of a Wheel, He contributed the ordinary <lb/>Cour&longs;es to the Moon and other Erratick Stars, whil&longs;t that &longs;he <lb/>Sings,</s></p><p type="main"> <s><emph type="italics"/>Cœli Deus &longs;ancti&longs;&longs;ime,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Qui lucidum Centrum Poli,<emph.end type="italics"/></s></p> <pb xlink:href="040/01/484.jpg" pagenum="460"/><p type="main"> <s><emph type="italics"/>Candore ping is igneo,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Augens decoro lumine,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Quarto die, qui flammeam<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Solis rotam con&longs;tituens<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Lunœ mini&longs;tras ordinem,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Vago&longs;que cur&longs;us Syderum.<emph.end type="italics"/></s></p><p type="main"> <s>They might &longs;ay, that the Name of <emph type="italics"/>Firmament<emph.end type="italics"/> very well a­<lb/>greeth, <emph type="italics"/>ad literam,<emph.end type="italics"/> to the Starry Sphere, and to all that which <lb/>is above the Planetary Conver&longs;ions; which according to this Hy­<lb/>pothe&longs;is is altogether <emph type="italics"/>firme<emph.end type="italics"/> and immoveable. <emph type="italics"/>Ad litteram<emph.end type="italics"/> (the <lb/>Earth moving circularly) they might under&longs;tand its <emph type="italics"/>Poles,<emph.end type="italics"/><lb/>where it's &longs;aid, <emph type="italics"/>Nec dum Terram fecerat, & flumina, &<emph.end type="italics"/> Cardi­<lb/>nes <emph type="italics"/>Orbis Terrœ,<emph.end type="italics"/> Which <emph type="italics"/>Cardines<emph.end type="italics"/> or ^{*} <emph type="italics"/>liinges<emph.end type="italics"/> &longs;eem to be a&longs;cribed <lb/><arrow.to.target n="marg861"></arrow.to.target><lb/>to the Earth in vain, if it be not to turn upon them.</s></p><p type="margin"> <s><margin.target id="marg861"></margin.target>* Or Poles.</s></p><p type="head"> <s><emph type="italics"/>FINIS.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/485.jpg" pagenum="461"/><p type="head"> <s>AN <lb/>ABSTRACT <lb/>OF THE <lb/>Learned Treati&longs;e <lb/>OF <lb/>JOHANNIS KEPL<emph type="italics"/>E<emph.end type="italics"/>RUS, <lb/>The Emperours <emph type="italics"/>Mathematician<emph.end type="italics"/>: <lb/>ENTITULED <lb/><emph type="italics"/>His Introduction upon<emph.end type="italics"/> MARS:</s></p><p type="main"> <s>It mu&longs;t be confe&longs;&longs;ed, that there are very <lb/>many who are devoted to Holine&longs;&longs;e, <lb/>that di&longs;&longs;ent from the Judgment of <emph type="italics"/>Co­<lb/>pernicus,<emph.end type="italics"/> fearing to give the Lye to the <lb/>Holy Gho&longs;t &longs;peaking in the Scriptures, <lb/>if they &longs;hould &longs;ay, that the Earth mo­<lb/>veth, and the Sun &longs;tands &longs;till. </s> <s>But let <lb/>&longs;uch con&longs;ider, that &longs;ince we judge of ve­<lb/>ry many, and tho&longs;e the mo&longs;t principal <lb/>things by the Sen&longs;e of Seeing, it is impo&longs;&longs;ible that we &longs;hould ali­<lb/>enate our Speech from this Sen&longs;e of our Eyes. </s> <s>Therefore many <lb/>things daily occur, of which we &longs;peak according to the Sen&longs;e of <lb/>Sight, when as we certainly know that the things them&longs;elves are <lb/>otherwi&longs;e. </s> <s>An Example whereof we have in that Ver&longs;e of <lb/><emph type="italics"/>Virgil<emph.end type="italics"/>;</s></p><p type="head"> <s><emph type="italics"/>Provehimur portu, Terrœque urbe&longs;que recedunt.<emph.end type="italics"/></s></p><p type="main"> <s>So when we come forth of the narrow &longs;traight of &longs;ome Val­<lb/>ley, we &longs;ay that a large Field di&longs;covereth it &longs;elf. </s> <s>So Chri&longs;t to <lb/><emph type="italics"/>Peter, Duc in altum<emph.end type="italics"/>; [Lanch forth into the Deep, or on high,] <lb/>as if the Sea were higher than its Shores; For &longs;o it &longs;eemeth to <lb/>the Eye, but the Opticks &longs;hew the cau&longs;e of this fallacy. </s> <s>Yet <lb/>Chri&longs;t u&longs;eth the mo&longs;t received Speech, although it proceed from <lb/>this delu&longs;ion of the Eyes. </s> <s>Thus we conceive of the Ri&longs;ing and <pb xlink:href="040/01/486.jpg" pagenum="462"/>Setting of the Stars, that is to &longs;ay, of their A&longs;cen&longs;ion and De&longs;­<lb/>cen&longs;ion; when at the &longs;ame time that we affirm the Sun ri&longs;eth, o­<lb/>thers &longs;ay, that it goeth down. </s> <s>See my <emph type="italics"/>Optices A&longs;tronomiœ, cap.<emph.end type="italics"/><lb/>10. <emph type="italics"/>fol.<emph.end type="italics"/> 327 So in like manner, the <emph type="italics"/>Ptolomaicks<emph.end type="italics"/> affirm, that the <lb/>Planets <emph type="italics"/>&longs;tand &longs;till,<emph.end type="italics"/> when for &longs;ome dayes together they &longs;eem to be <lb/>fixed, although they believe them at that very time to be moved <lb/>in a direct line, either downwards to, or upwards from the <lb/>Earth. </s> <s>Thus the Writers of all Nations u&longs;e the word <emph type="italics"/>Sol&longs;titi­<lb/>um,<emph.end type="italics"/> and yet they deny that the Sun doth really &longs;tand &longs;till. </s> <s>Like­<lb/>wi&longs;e there will never any man be &longs;o devoted to <emph type="italics"/>Copernicus,<emph.end type="italics"/> but <lb/>he will &longs;ay, the Sun entereth into <emph type="italics"/>Cancer<emph.end type="italics"/> and <emph type="italics"/>Leo,<emph.end type="italics"/> although he <lb/>granteth that the Earth enters <emph type="italics"/>Capricorn<emph.end type="italics"/> or <emph type="italics"/>Aquarius<emph.end type="italics"/>: And &longs;o <lb/>in other ca&longs;es of the like nature. </s> <s>But now the Sacred Scriptures, <lb/>&longs;peaking to men of vulgar matters (in which they were not in­<lb/>tended to in&longs;truct men) after the manner of men, that &longs;o they <lb/>might be under&longs;tood by men, do u&longs;e &longs;uch Expre&longs;&longs;ions as are <lb/>granted by all, thereby to in&longs;inuate other things more My&longs;terious <lb/>and Divine. </s> <s>What wonder is it then, if the Scripture &longs;peaks <lb/>according to mans apprehen&longs;ion, at &longs;uch time when the Truth <lb/>of things doth di&longs;&longs;ent from the Conception that all men, whe­<lb/>ther Learned or Unlearned have of them? </s> <s>Who knows not <lb/>that it is a Poetical allu&longs;ion, <emph type="italics"/>P&longs;al.<emph.end type="italics"/> 19. where, whil&longs;t under the &longs;i­<lb/>militude of the Sun, the Cour&longs;e of the Go&longs;pel, as al&longs;o the Pere­<lb/>grination of our Lord Chri&longs;t in this World, undertaken for our <lb/>&longs;akes, is de&longs;cribed, <emph type="italics"/>The Sun<emph.end type="italics"/> is &longs;aid <emph type="italics"/>to come forth of his Taberna­<lb/>cle<emph.end type="italics"/> of the Horizon, <emph type="italics"/>as a Bridegroom out of his Chamber, re­<lb/>joycing as a Giant to run a Race<emph.end type="italics"/>? </s> <s>Which <emph type="italics"/>Virgil<emph.end type="italics"/> thus imitates;</s></p><p type="head"> <s><emph type="italics"/>Tithono croceum linquens Auror a cubile<emph.end type="italics"/>:</s></p><p type="main"> <s>For the fir&longs;t Poets were among&longs;t the Jews. </s> <s>The P&longs;almi&longs;t knew that <lb/>the Sun went not forth of the Horizon, as out of its Tabernacle, <lb/>& yet it &longs;eemeth to the Eye &longs;o to do: Nor did he believe, that the <lb/>Sun moved, for that it appeared to his &longs;ight &longs;o to do. </s> <s>And yet he <lb/>&longs;aith both, for that both were &longs;o to his &longs;eeming. </s> <s>Neither is it <lb/>to be adjudged fal&longs;e in either Sen&longs;e: for the perception of the <lb/>Eyes hath its verity, fit for the more &longs;ecret purpo&longs;e of the P&longs;al­<lb/>mi&longs;t in &longs;hadowing forth the current pa&longs;&longs;age o&longs; the Go&longs;pel, as <lb/>al&longs;o the Peregrination of the Son of God. <emph type="italics"/>Jo&longs;hua<emph.end type="italics"/> likewi&longs;e <lb/>mentioneth the Vallies on or in, which the Sun and Moon mo­<lb/>ved, for that they appeared to him at <emph type="italics"/>Jordan<emph.end type="italics"/> &longs;o to do: And yet <lb/>both the&longs;e Pen-men may obtain their ends. <emph type="italics"/>David,<emph.end type="italics"/> (and with <lb/>him <emph type="italics"/>Syracides<emph.end type="italics"/>) the magnificence of God being made known, <lb/>which cau&longs;ed the&longs;e things to be in this manner repre&longs;ented to <lb/>&longs;ight, or otherwi&longs;e, the my&longs;tical meaning, by means of the&longs;e <lb/>Vi&longs;ibles being di&longs;cerned: And <emph type="italics"/>Jo&longs;hua,<emph.end type="italics"/> in that the Sun, as to his <pb xlink:href="040/01/487.jpg" pagenum="463"/>Sen&longs;e of Seeing, &longs;taid a whole day in the mid&longs;t of Heaven, where­<lb/>as at the &longs;ame time to others it lay hid under the Earth. </s> <s>But in­<lb/>cogitant per&longs;ons onely look upon the contrariety of the words, <lb/><emph type="italics"/>The Sun &longs;tood &longs;till,<emph.end type="italics"/> that is, <emph type="italics"/>The Earth &longs;tood &longs;till<emph.end type="italics"/>; not con&longs;idering <lb/>that this contradiction is confined within the limits of the Op­<lb/>ticks and A&longs;tronomy: For which cau&longs;e it is not outwardly ex­<lb/>po&longs;ed to the notice and u&longs;e of men: Nor will they under&longs;tand <lb/>that the onely thing <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> prayed for, was that the Mountains <lb/>might not intercept the Sun from him; which reque&longs;t he expre&longs;­<lb/>&longs;ed in words, that &longs;uited with his Ocular Sen&longs;e: Be&longs;ides it had <lb/>been very un&longs;ea&longs;onable at that time to think of A&longs;tronomy, or <lb/>the Errours in Sight; for if any one &longs;hould have told him that <lb/>the Sun could not really move upon the Valley of <emph type="italics"/>Ajalon,<emph.end type="italics"/>, but <lb/>onely in relation to Sen&longs;e, would not <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> have replyed, that <lb/>his de&longs;ire was that the day might be prolonged, &longs;o it were by <lb/>any means what&longs;oever? </s> <s>In like manner would he have an&longs;wered <lb/>if any one had &longs;tarted a que&longs;tion about the Suns Mobility, and <lb/>the Earths Motion. </s> <s>But God ea&longs;ily under&longs;tood by <emph type="italics"/>Jo&longs;huahs<emph.end type="italics"/><lb/>words what he asked for, and by arre&longs;ting the Earths Motion, <lb/>made the Sun in his apprehen&longs;ion &longs;eem to &longs;tand &longs;till. </s> <s>For the <lb/>&longs;umm of <emph type="italics"/>Jo&longs;huahs<emph.end type="italics"/> Prayer amounts to no more but this, that it <lb/>might thus appear to him, let it in the mean time <emph type="italics"/>be what it <lb/>would<emph.end type="italics"/> of it &longs;elf. </s> <s>For that its &longs;o &longs;eeming, was not in vain and <lb/>ridiculous, but accompanied with the de&longs;ired effect. </s> <s>But read <lb/>the tenth <emph type="italics"/>Chap.<emph.end type="italics"/> of my <emph type="italics"/>Book,<emph.end type="italics"/> that treats of <emph type="italics"/>the Optick part of A­<lb/>&longs;tronomy,<emph.end type="italics"/> where thou &longs;halt finde the Rea&longs;ons why the Sun doth <lb/>in this manner &longs;eem to all mens thinking to be moved, and not <lb/>the Earth; as namely, becau&longs;e the Sun appeareth &longs;mall; and the <lb/>Earth bigg. </s> <s>Again, the Motion of the Sun is not di&longs;cerned by <lb/>the eye, by rea&longs;on of his &longs;eeming tardity, but by ratiocina­<lb/>tion onely; in that after &longs;ome time it varieth not its proximity to <lb/>&longs;uch and &longs;uch Mountains. </s> <s>Therefore it is impo&longs;&longs;ible that Rea­<lb/>&longs;on, unle&longs;s it be fir&longs;t in&longs;tructed, &longs;hould frame to it &longs;elf any other <lb/>apprehen&longs;ion, than that the Earth with Heavens Arch placed <lb/>over it, is as it were a great Hou&longs;e, in which, being immoveable, <lb/>the Sun like a Bird flying in the Air, pa&longs;&longs;eth in &longs;o &longs;mall a Species <lb/>out of one Climate into another. </s> <s>Which imagination of all <lb/>Man-kinde being thus, gave the fir&longs;t line in the Sacred Leaves: <lb/>^{*} <emph type="italics"/>In the beginning<emph.end type="italics"/> (&longs;aith <emph type="italics"/>Mo&longs;es) God created the Heaven and the <lb/><arrow.to.target n="marg862"></arrow.to.target><lb/>Earth<emph.end type="italics"/>; for that the&longs;e two are mo&longs;t obvious to the eye. </s> <s>As if <lb/><emph type="italics"/>Mo&longs;es<emph.end type="italics"/> &longs;hould have &longs;aid thus to Man; This whole Mundane Fa­<lb/>brick which thou &longs;ee&longs;t, lucid above, and dark, and of a va&longs;t ex­<lb/>tent beneath, wherein thou ha&longs;t thy being, and with which thou <lb/>art covered, was created by God.</s></p><p type="margin"> <s><margin.target id="marg862"></margin.target>* Gen. <emph type="italics"/>Chv. </s> <s>1. <lb/>v.<emph.end type="italics"/> 1.</s></p><p type="main"> <s>In another place Man is que&longs;tioned; <emph type="italics"/>Whether he can finde out<emph.end type="italics"/> <pb xlink:href="040/01/488.jpg" pagenum="464"/><emph type="italics"/>the height of Heaven above, or depth of the Earth beneath<emph.end type="italics"/>: for <lb/>that each of them appeareth to men of ordinary capacity, to have <lb/>equally an infinite extent. </s> <s>And yet no man that is in his right <lb/>mind will by the&longs;e words circum&longs;cribe and bound the diligence <lb/>of A&longs;tronomers, whether in demon&longs;trating the mo&longs;t contemptible <lb/>Minuity of the Earth, in compari&longs;on of Heaven, or in &longs;earching <lb/>out A&longs;tronomical <emph type="italics"/>Di&longs;tances<emph.end type="italics"/>: Since tho&longs;e words &longs;peak not of the <lb/>Rational, but real Dimention; which to a Humane Body, <lb/>whil&longs;t confin'd to the Earth, and breathing in the open Air, is al­<lb/>together impo&longs;&longs;ible. </s> <s>Read the whole 38. Chapter of <emph type="italics"/>Job,<emph.end type="italics"/> and <lb/>compare it with tho&longs;e Points which are di&longs;puted in A&longs;tronomy, <lb/><arrow.to.target n="marg863"></arrow.to.target><lb/>and Phy&longs;iologie. </s> <s>If any one do alledge from <emph type="italics"/>P&longs;al.<emph.end type="italics"/> 24. That ^{*} <emph type="italics"/>The <lb/>Earth is founded upon the Seas,<emph.end type="italics"/> to the end that he may thence <lb/>infer &longs;ome new Principle in Philo&longs;ophy, ab&longs;urd to hear; as, That <lb/>the Earth doth float upon the Waters; may it not truly be told <lb/>him, That he ought not to meddle with the Holy Spirit, nor to <lb/>bring him with contempt into the School of Phy&longs;iologie. <lb/></s> <s>For the P&longs;almi&longs;t in that place means nothing el&longs;e but <lb/>that which men fore-know, and daily &longs;ee by experience; namely, <lb/>That the Earth (being lifted up after the &longs;eparation of the Wa­<lb/>ters) doth &longs;wim between the Grand Oceans, and float about the <lb/>Sea. </s> <s>Nor is it &longs;trange that the expre&longs;&longs;ion &longs;hould be the &longs;ame <lb/>where the <emph type="italics"/>I&longs;raelites<emph.end type="italics"/> &longs;ing, ^{*} <emph type="italics"/>That they &longs;ate on the River of Baby­<lb/><arrow.to.target n="marg864"></arrow.to.target><lb/>lon<emph.end type="italics"/>; that is, <emph type="italics"/>by<emph.end type="italics"/> the River &longs;ide. </s> <s>or on the Banks of <emph type="italics"/>Euphrates<emph.end type="italics"/> and <lb/><emph type="italics"/>Tygris.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg863"></margin.target>* P&longs;al. </s> <s>24. 2.</s></p><p type="margin"> <s><margin.target id="marg864"></margin.target>P&longs;al. </s> <s>137. 1.</s></p><p type="main"> <s>If any one receive this Reading without &longs;cruple, why not the <lb/>other; that &longs;o in tho&longs;e &longs;ame Texts which are wont to be alledged <lb/>again&longs;t the Motion of the Earth, we may in like manner turn our <lb/>eyes from Natural Philo&longs;ophy, to the &longs;cope and intent of Scri­<lb/>pture. <emph type="italics"/>One Generation pa&longs;&longs;eth away,<emph.end type="italics"/> (&longs;aith <emph type="italics"/>Eccle&longs;ia&longs;tes) and a­<lb/><arrow.to.target n="marg865"></arrow.to.target><lb/>nother Generation cometh: But the Earth abideth for ever.<emph.end type="italics"/> ^{*} As <lb/>if <emph type="italics"/>Solomon<emph.end type="italics"/> did here di&longs;pute with A&longs;tronomers, and not rather put <lb/>men in minde of their Mutability; when as the Earth, Mankindes <lb/>habitation, doth alwaies remain the &longs;ame: The Suns Motion <lb/>doth continually return into what it was at fir&longs;t: The Wind is <lb/>acted in a Circle, and returns in the &longs;ame manner: The Rivers <lb/>flow from their Fountains into the Sea, and return again from <lb/>thence unto their Fountains: To conclude, The Men of this <lb/>Age dying, others are born in their room; the Fable of Life is <lb/>ever the &longs;ame; there is nothing new under the Sun. </s> <s>Here is no <lb/>reference to any Phy&longs;ical Opinion. <foreign lang="greek"><gap/>on<gap/>esi\a</foreign> is Moral of a thing in it <lb/>&longs;elf manife&longs;t, and &longs;een by the eyes of all, but little regarded: Tis <lb/>that therefore which <emph type="italics"/>Solomon<emph.end type="italics"/> doth inculcate. </s> <s>For who knows not <lb/>that the Earth is alwaies the &longs;ame? </s> <s>Who &longs;ees not that the Sun <lb/>dothari&longs;e from the Ea&longs;t; That the Rivers continually run into <pb xlink:href="040/01/489.jpg" pagenum="465"/>the Sea; That the vici&longs;&longs;itudes of the Windes return into their <lb/>primitive State; That &longs;ome men &longs;ucceed others? </s> <s>But who con­<lb/>&longs;idereth that the &longs;elf-&longs;ame <emph type="italics"/>Scene<emph.end type="italics"/> of Life is ever acting, by diffe­<lb/>rent per&longs;ons; and that nothing is <emph type="italics"/>new<emph.end type="italics"/> in humane affairs? </s> <s>There­<lb/>fore <emph type="italics"/>Solomon<emph.end type="italics"/> in&longs;tancing in tho&longs;e things which all men &longs;ee, doth <lb/>put men in minde of that which many thorowly know, but too <lb/>&longs;lightly con&longs;ider.</s></p><p type="margin"> <s><margin.target id="marg865"></margin.target>* Chap. </s> <s>1. v. </s> <s>4, to <lb/>9.</s></p><p type="main"> <s>But the 104. <emph type="italics"/>P&longs;alm<emph.end type="italics"/> is thought by &longs;ome to contain a Di&longs;cour&longs;e <lb/>altogether Phy&longs;ical, in regard it onely concerns Natural Philo&longs;o­<lb/>phy. </s> <s>Now God is there &longs;aid, <emph type="italics"/>To have laid the Foundations of <lb/><arrow.to.target n="marg866"></arrow.to.target><lb/>the Earth, that it &longs;hould not be removed for ever.<emph.end type="italics"/> But here al­<lb/>&longs;o the P&longs;almi&longs;t is far from the Speculation of Phy&longs;ical Cau&longs;es: <lb/>For he doth wholly acquie&longs;ce in the Greatne&longs;&longs;e of God, <lb/>who did all the&longs;e things, and &longs;ings an Hymne to God the <lb/>Maker of them, in which he runneth over the World in order, <lb/>as it appeared to his eyes. </s> <s>And if you well con&longs;ider this <lb/>P&longs;alme, it is a Paraphra&longs;e upon the &longs;ix dayes work of the Crea­<lb/>tion: For as in it the three fir&longs;t dayes were &longs;pent in the Separa­<lb/>tion of Regions; the fir&longs;t of Light from the exteriour Dark­<lb/>ne&longs;s; the &longs;econd, of the Waters from the Waters, by the inter­<lb/>po&longs;ition of the Firm ament; the third, of the Sea from Land; <lb/>when al&longs;o the Earth was cloathed with Herbage and Plants: <lb/>And the three la&longs;t dayes were &longs;pent in the filling the Re­<lb/>gions thus di&longs;tingui&longs;hed; the fourth, of Heaven; the <lb/>fifth, of the Seas and Aire; the fixth, of the Earth: So <lb/>here in this P&longs;alme there are &longs;o many di&longs;tinct parts pro­<lb/>portionable to the Analogy of the &longs;ix dayes Works. </s> <s>For <lb/>in <emph type="italics"/>Ver&longs;e<emph.end type="italics"/> 2. he cloaths and covereth the Creator with Light <lb/>(the fir&longs;t of Creatures, and work of the fir&longs;t day) as with a <lb/>Garment. </s> <s>The &longs;econd part beginneth at <emph type="italics"/>Ver&longs;e<emph.end type="italics"/> 3. and treats of <lb/>the Waters above the Heavens, the extent of Heaven and of Me­<lb/>teors (which the P&longs;almi&longs;t &longs;eemeth to intend by the Waters a­<lb/>bove) as namely of Clouds, Winds, Whirl-winds, Lightnings. <lb/></s> <s>The third part begins at <emph type="italics"/>Ver&longs;e<emph.end type="italics"/> 6. and doth celebrate the Earth <lb/>as the foundation of all tho&longs;e things which he here con&longs;idereth. <lb/></s> <s>For he referreth all things to the Earth, and to tho&longs;e Animals <lb/>which inhabit it, for that in the judgment of Sight the two prin­<lb/>cipal parts of the World are Heaven and Earth. </s> <s>He therefore <lb/>here ob&longs;erveth that the Earth after &longs;o many Ages hath not falte­<lb/>red, tired, or decayed; when as notwith&longs;tanding no man hath <lb/>yet di&longs;covered upon what it is founded. </s> <s>He goeth not about to <lb/>teach men what they do not know, but putteth them in minde <lb/>of what they neglect, to wit, the Greatne&longs;&longs;e and Power of God <lb/>in creating &longs;o huge a Ma&longs;s &longs;o firm and &longs;tedfa&longs;t. </s> <s>If an A&longs;trono­<lb/>mer &longs;hould teach that the Earth is placed among the Planets, he <pb xlink:href="040/01/490.jpg" pagenum="466"/>overthroweth not what the P&longs;almi&longs;t here &longs;aith, nor doth he con­<lb/>tradict Common Experience; for it is true notwith&longs;tanding, <lb/>that the Earth, the Structure of God its Architect, doth not de­<lb/>cay (as our Buildings are wont to do) by age, or con&longs;ume by <lb/>wormes, nor &longs;way and leane to this or that &longs;ide; that the Seats <lb/>and Ne&longs;ts of Living Creatures are not mole&longs;ted; that the <lb/>Mountains and Shores &longs;tand immoveable again&longs;t the violence of <lb/>the Winds and Waves, as they were at the beginning. </s> <s>But the <lb/>P&longs;almi&longs;t addeth a mo&longs;t Elegant Hypothe&longs;is of the Separation of <lb/>the Waters from the Continent or Main-land, and adorns it <lb/>with the production of Fountains, and the benefits that Springs <lb/>and Rocks exhibit to Birds and Bea&longs;ts. </s> <s>Nor doth he omit the <lb/>apparelling the Earths Surface, mentioned by <emph type="italics"/>Mo&longs;es<emph.end type="italics"/> among&longs;t the <lb/>works of the third Day, but more &longs;ublimely de&longs;cribeth it in his <lb/>Ca&longs;e in expre&longs;&longs;ions infu&longs;ed from Divine In&longs;piration; and flouri­<lb/>&longs;heth out the commemoration of the many commodities which <lb/>redound from that Exornation for the Nouri&longs;hment and Com­<lb/><arrow.to.target n="marg867"></arrow.to.target><lb/>fort of Man, and ^{*} Covert of Bea&longs;ts. </s> <s>The fourth part begins <lb/>at <emph type="italics"/>Ver&longs;e<emph.end type="italics"/> 20. celebrating the fourth dayes work, <emph type="italics"/>viz.<emph.end type="italics"/> The Sun <lb/>and Moon, but chiefly the commodiou&longs;ne&longs;&longs;e of tho&longs;e things, <lb/>which in their Sea&longs;ons befall to all Living Creatures and to Man; <lb/>this being the &longs;ubject matter of his Di&longs;cour&longs;e: So that it plain­<lb/>ly appeareth he acted not the part of an A&longs;tronomer. </s> <s>For if he <lb/>had, he would not then have omitted to mention the five Planets, <lb/>than who&longs;e moiton nothing is more admirable, nothing more ex­<lb/>cellent, nothing that can more evidently &longs;et forth the Wi&longs;dome <lb/>of the Creator among&longs;t the Learned. </s> <s>The fifth part begins, <lb/><emph type="italics"/>Ver&longs;e<emph.end type="italics"/> 25. with the fifth Dayes work. </s> <s>And it &longs;tores the Seas with <lb/>Fi&longs;hes, and covers them with Ships. </s> <s>The &longs;ixth part is more ob­<lb/>&longs;curely hinted at, <emph type="italics"/>Ver&longs;e<emph.end type="italics"/> 28. and alludeth to the Land-Creatures <lb/>that were created the &longs;ixth day. </s> <s>And la&longs;tly, he declareth the <lb/>goodne&longs;&longs;e of God in general, who daily createth and pre&longs;erveth <lb/>all things? </s> <s>So that whatever he &longs;aid of the World is in relation <lb/>to Living Creatures; He &longs;peaks of nothing but what is granted <lb/>on all hands; for that it was his intent to extol things known, <lb/>and not to dive into hidden matters, but to invite men to con­<lb/>template the Benefits that redouud unto them from the works of <lb/>each of the&longs;e dayes.</s></p><p type="margin"> <s><margin.target id="marg866"></margin.target>P&longs;al. </s> <s>104. v. </s> <s>5.</s></p><p type="margin"> <s><margin.target id="marg867"></margin.target>* Shelter.</s></p><p type="main"> <s>And I do al&longs;o be&longs;eech my Reader, not forgetting the Divine <lb/>Goodne&longs;&longs;e conferred on Mankind; the con&longs;ideration of which <lb/>the P&longs;almi&longs;t doth chiefly urge, that when he returneth from the <lb/>Temple, and enters into the School of <emph type="italics"/>A&longs;tronomy,<emph.end type="italics"/> he would <lb/>with me prai&longs;e and admire the Wi&longs;dome and Greatne&longs;&longs;e of the <lb/>Creator, which I di&longs;cover to him by a more narrow explication <lb/>of the Worlds Form, the Di&longs;qui&longs;ition of Cau&longs;es, and Detection <pb xlink:href="040/01/491.jpg" pagenum="467"/>of the Errours of Sight: And &longs;o he will not onely extoll the <lb/>Bounty of God in the pre&longs;ervation of Living Creatures of all <lb/>kindes, and e&longs;tabli&longs;hment of the Earth; but even in its Motion <lb/>al&longs;o, which is &longs;o &longs;trange, &longs;o admirable, he will acknowledge the <lb/>Wi&longs;dome of the Creator. </s> <s>But he who is &longs;o &longs;tupid as not to <lb/>comprehend the Science of <emph type="italics"/>A&longs;tronomy,<emph.end type="italics"/> or &longs;o weak and &longs;crupu­<lb/>lous as to think it an offence of Piety to adhere to <emph type="italics"/>Copernicus,<emph.end type="italics"/><lb/>him I advi&longs;e, that leaving the Study of <emph type="italics"/>A&longs;tronomy,<emph.end type="italics"/> and cen&longs;uring <lb/>the opinions of Philo&longs;ophers at plea&longs;ure, he betake him&longs;elf to <lb/>his own concerns, and that de&longs;i&longs;ting from further pur&longs;uit of the&longs;e <lb/>intricate Studies, he keep at home and manure his own Ground; <lb/>and with tho&longs;e Eyes wherewith alone he &longs;eeth, being eleva­<lb/>ted towards this to be admired Heaven, let him pour forth his <lb/>whole heart in thanks and prai&longs;es to God the Creator; and a&longs;­<lb/>&longs;ure him&longs;elf that he &longs;hall therein perform as much Wor&longs;hip to <lb/>God, as the <emph type="italics"/>A&longs;tronomer,<emph.end type="italics"/> on whom God hath be&longs;towed this Gift, <lb/>that though he &longs;eeth more clearly with the Eye of his Under­<lb/>&longs;tanding; yet whatever he hath attained to, he is both able and <lb/>willing to extoll his God above it.</s></p><p type="main"> <s>And thus much concerning the Authority of Sacred Scripture. <lb/></s> <s>Now as touching the opinions of the Saints about the&longs;e Natural <lb/>Points. </s> <s>I an&longs;wer in one word, That in Theology the weight of <lb/>Authority, but in Philo&longs;ophy the weight of Rea&longs;on is to be con­<lb/>&longs;idered. </s> <s>Therefore Sacred was <emph type="italics"/>Lactantius,<emph.end type="italics"/> who denyed the <lb/>Earths rotundity; Sacred was <emph type="italics"/>Augu&longs;tine,<emph.end type="italics"/> who granted the Earth <lb/>to be round, but denyed the <emph type="italics"/>Antipodes<emph.end type="italics"/>; Sacred is the ^{*}Liturgy of <lb/><arrow.to.target n="marg868"></arrow.to.target><lb/>our Moderns, who admit the &longs;mallne&longs;&longs;e of the Earth, but deny <lb/>its Motion: But to me more &longs;acred than all the&longs;e is Truth, who <lb/>with re&longs;pect to the Doctors of the Church, do demon&longs;trate <lb/>from Philo&longs;ophy that the Earth is both round, circumhabited by <lb/><emph type="italics"/>Antipodes,<emph.end type="italics"/> of a mo&longs;t contemptible &longs;malne&longs;&longs;e, and in a word, <lb/>that it is ranked among&longs;t the Planets.</s></p> <pb xlink:href="040/01/492.jpg" pagenum="468"/><p type="margin"> <s><margin.target id="marg868"></margin.target>* Officium</s></p><p type="head"> <s>AN <lb/>ABSTRACT <lb/>OF <lb/>Some pa&longs;&longs;ages in the Commentaries of <lb/>Didacus à Stunica, <lb/>OF <lb/>SALAMANCA <lb/>Upon <emph type="italics"/>JOB:<emph.end type="italics"/></s></p><p type="head"> <s>The Toledo Edition, Printed by <emph type="italics"/>JOHN RODERICK, <lb/>Anno<emph.end type="italics"/> 1584, in <emph type="italics"/>Quarto,<emph.end type="italics"/> Pag. </s> <s>205. & <emph type="italics"/><expan abbr="&longs;eqq.">&longs;eqque</expan><emph.end type="italics"/> on <lb/>the&longs;e Words, Chap. </s> <s>9. Ver&longs;e 6.</s></p><p type="head"> <s><emph type="italics"/>Who &longs;haketh the Earth out of her place, and the Pil­<lb/>lars thereof Tremble.<emph.end type="italics"/></s></p><p type="main"> <s>The Sacred Pen-man here &longs;ets down another ef­<lb/>fect whereby God &longs;heweth his Ahnighty Po­<lb/>wer, joyned with infinite Wi&longs;dom. </s> <s>Which <lb/>place, though it mu&longs;t be confe&longs;&longs;ed very diffi­<lb/>cult to under&longs;tand, might be greatly cleared <lb/>by the Opinion of the <emph type="italics"/>Pythagorians,<emph.end type="italics"/> who <lb/>hold the Earth to be moved of its own Na­<lb/>ture, and that the Motion of the Stars can no other way be a&longs;cer­<lb/>tained, they being &longs;o extreamly different in tardity and velocity. <lb/></s> <s>Of which judgement was <emph type="italics"/>Philolaus,<emph.end type="italics"/> and <emph type="italics"/>Heraclides Ponticus,<emph.end type="italics"/> as <lb/><emph type="italics"/>Plutarch<emph.end type="italics"/> relateth in his Book <emph type="italics"/>De Placitis Philo&longs;ophorum<emph.end type="italics"/>: Who <lb/>were followed by <emph type="italics"/>Numa Pompilius,<emph.end type="italics"/> and, which I more regard, <lb/>The Divine <emph type="italics"/>Plato<emph.end type="italics"/> in his old age; in&longs;omuch that he affirmed that <lb/>it was mo&longs;t ab&longs;urd to think otherwi&longs;e, as the &longs;ame <emph type="italics"/>Plutarch<emph.end type="italics"/> tells <lb/>us in his ^{*} <emph type="italics"/>Numa.<emph.end type="italics"/> And <emph type="italics"/>Hypocrates<emph.end type="italics"/> in his Book <emph type="italics"/>De Flatibus,<emph.end type="italics"/><lb/><arrow.to.target n="marg869"></arrow.to.target><lb/>calleth the Air <foreign lang="greek">thsghso)xh)ma,</foreign> <emph type="italics"/>i. </s> <s>e.<emph.end type="italics"/> The Earths Chariot. </s> <s>But in this <pb xlink:href="040/01/493.jpg" pagenum="469"/>our Age, <emph type="italics"/>Copernicus<emph.end type="italics"/> doth demon&longs;trate the cour&longs;es of the Pla­<lb/>nets to be according to this Opinion. </s> <s>Nor is it to be doubted <lb/>but that the Planets Places may be more exactly and certainly <lb/>a&longs;&longs;igned by his Doctrine, than by <emph type="italics"/>Ptolomies<emph.end type="italics"/> Great Almoge&longs;t of <lb/>Sy&longs;teme, or the Opinions of any others. </s> <s>For its manife&longs;t, that <lb/><emph type="italics"/>Ptolomy<emph.end type="italics"/> could never de&longs;cribe either the Motion of the Equi­<lb/>noxes, or a&longs;&longs;ign the certain and po&longs;itive beginning of the Year:<lb/>the which he ingeniou&longs;ly confe&longs;&longs;eth in <emph type="italics"/>Lih.<emph.end type="italics"/> 3. <emph type="italics"/>De Almage&longs;t. </s> <s>Mag­<lb/>num. </s> <s>Ch.<emph.end type="italics"/> 2. and which he leaveth to be di&longs;covered in after times <lb/>by tho&longs;e A&longs;tronomers, who coming into the World much later <lb/>than he, might be able to invent &longs;ome way to make more accurate <lb/>ob&longs;ervations. </s> <s>And although the ^{*} <emph type="italics"/>Alphon&longs;ines & Thebith Ben Core<emph.end type="italics"/><lb/><arrow.to.target n="marg870"></arrow.to.target><lb/>have attempted to explain them; yet it appeareth that they have <lb/>done as much as nothing. </s> <s>For the Po&longs;itions of the <emph type="italics"/>Alphon&longs;ines<emph.end type="italics"/><lb/>di&longs;agree among&longs;t them&longs;elves, as <emph type="italics"/>Ricius<emph.end type="italics"/> proveth. </s> <s>And although <lb/>the Rea&longs;on of <emph type="italics"/>Thebith<emph.end type="italics"/> be more acute, and that thereby he de­<lb/>termined the certain beginning of the year, (being that which <lb/><emph type="italics"/>Ptolomy<emph.end type="italics"/> &longs;ought for) yet it is now clear, that the Progre&longs;&longs;ions of <lb/>the Equinoxes are much longer than he conceived they could be. <lb/></s> <s>Moreover, the Sun is found to be much nearer to us than it was <lb/><arrow.to.target n="marg871"></arrow.to.target><lb/>held to be in times pa&longs;t, by above fourty thou&longs;and ^{*} <emph type="italics"/>Stadia,<emph.end type="italics"/> or <lb/>furlongs. </s> <s>The Cau&longs;e and Rea&longs;on of who&longs;e Motion, neither <lb/><emph type="italics"/>Ptolomy<emph.end type="italics"/> nor any other A&longs;trologers could ever comprehend: And <lb/>yet the Rea&longs;ons of the&longs;e things are mo&longs;t plainly explained and <lb/>demon&longs;trated by <emph type="italics"/>Copernicus<emph.end type="italics"/> from the Motion of the Earth, with <lb/>which he &longs;heweth that all the other <emph type="italics"/>Phœnomena<emph.end type="italics"/> of the Univer&longs;e <lb/>do more aptly accord. </s> <s>Which opinion of his is not in the lea&longs;t <lb/>contradicted by what <emph type="italics"/>Solomon<emph.end type="italics"/> &longs;aith in ^{*} <emph type="italics"/>Eccle&longs;ia&longs;tes: But the <lb/><arrow.to.target n="marg872"></arrow.to.target><lb/>Earth abideth for ever.<emph.end type="italics"/> For that Text &longs;ignifieth no more but <lb/>this, That although the &longs;ucce&longs;&longs;ion of Ages, and generations of <lb/>Men on Earth, be various; yet the Earth it &longs;elf is &longs;till one and <lb/>the &longs;ame, and continueth without any &longs;en&longs;ible alteration; For <lb/>the words run thus: <emph type="italics"/>One Generation pa&longs;&longs;eth away, and another <lb/>Generation cometh; but the Earth abideth for ever.<emph.end type="italics"/> So that it <lb/>hath no coherence with its Context, (as Philo&longs;ophers &longs;hew) if it <lb/><arrow.to.target n="marg873"></arrow.to.target><lb/>be expounded to &longs;peak of the Earths immobility. </s> <s>And al­<lb/>though in this Chapter <emph type="italics"/>Eccle&longs;ia&longs;tes,<emph.end type="italics"/> and in many others, Holy <lb/>Writ a&longs;cribes Motion to the Sun, which <emph type="italics"/>Copernicus<emph.end type="italics"/> will have to <lb/>&longs;tand fixed in the Centre of the Univer&longs;e; yet it makes nothing <lb/>again&longs;t his Po&longs;ition. </s> <s>For the Motion that belongs to the Earth, <lb/>is by way of &longs;peech a&longs;&longs;igned to the Sun, even by <emph type="italics"/>Copernicus<emph.end type="italics"/> him­<lb/>&longs;elf, and tho&longs;e who are his followers, &longs;o that the Revolution of <lb/>the Earth is often by them phra&longs;ed, The Revolution of the Sun. <lb/></s> <s>To conclude, No place can be produced out of Holy Scripture, <lb/>which &longs;o clearly &longs;peaks the Earths Immobility, as this doth its <pb xlink:href="040/01/494.jpg" pagenum="470"/>Mobility. </s> <s>Therefore this Text, of which we have &longs;poken, is ea­<lb/>&longs;ily reconciled to this Opinion. </s> <s>And to &longs;et forth the Wonder­<lb/>ful power and Wi&longs;dome of God, who can indue and actuate the <lb/>Frame of the Whole Earth (it being of a mon&longs;trous weight by <lb/>Nature) with Motion, this our Divine pen-man addeth; <emph type="italics"/>And <lb/>the pillars thereof tremble:<emph.end type="italics"/> As if he would teach us, from the <lb/>Doctrine laid down, that it is moved from its Foundations.</s></p><p type="margin"> <s><margin.target id="marg869"></margin.target>* <emph type="italics"/>In vita ejus.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg870"></margin.target>* Followers of <lb/>that Learned <lb/>Kings Hypothe­<lb/>&longs;is.</s></p><p type="margin"> <s><margin.target id="marg871"></margin.target>* That is 5000 <lb/>miles; eight of <lb/>the&longs;e making an <lb/><emph type="italics"/>Italian,<emph.end type="italics"/> or <emph type="italics"/>Engli&longs;h<emph.end type="italics"/><lb/>mile of a 1000. <lb/>paces, every pace <lb/>containing 5. <lb/>Feet.</s></p><p type="margin"> <s><margin.target id="marg872"></margin.target>* Chap. </s> <s>1. v. </s> <s>4.</s></p><p type="margin"> <s><margin.target id="marg873"></margin.target>The Motion of <lb/>the Earth, not a­<lb/>gain&longs;t Scripture.</s></p> </chap> <chap> <pb xlink:href="040/01/495.jpg"/><p type="head"> <s>AN <lb/>EPISTLE <lb/>Of the Reverend Father <lb/><emph type="italics"/>PAOLO ANTONIO FOSCARINI,<emph.end type="italics"/><lb/>A CARMELITE; <lb/>Concerning <lb/>The <emph type="italics"/>PYTHAGORIAN<emph.end type="italics"/> and <emph type="italics"/>COPERNICAN<emph.end type="italics"/> Opinion <lb/>OF <lb/>The Mobility of the <emph type="italics"/>EARTH,<emph.end type="italics"/><lb/>AND <lb/>Stability of the <emph type="italics"/>SVN;<emph.end type="italics"/><lb/>AND <lb/>Of the New Sy&longs;teme or Con&longs;titution <lb/>OF THE <lb/>WORLD.</s></p><p type="head"> <s>IN WHICH, <lb/>The Authorities of <emph type="italics"/>SACRED SCRIPTVRE,<emph.end type="italics"/><lb/>and <emph type="italics"/>ASSERTIONS<emph.end type="italics"/> of <emph type="italics"/>DIVINES,<emph.end type="italics"/><lb/>commonly alledged again&longs;t this Opinion, <lb/>are Reconciled.</s></p><p type="head"> <s>WRITTEN <lb/>To the mo&longs;t Reverend FATHER, <lb/>SEBASTIANO FANTONI, <lb/>General of the Order of CARMELITES.</s></p><p type="head"> <s><emph type="italics"/>Engli&longs;hed from the Original,<emph.end type="italics"/><lb/>BY <lb/><emph type="italics"/>THOMAS SALVSBVRIE.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>So quis indiget &longs;apientia, po&longs;tulet <lb/>à Deo.<emph.end type="italics"/> Jacobi 1. ver&longs;u. 5.</s></p><p type="head"> <s><emph type="italics"/>Optavi, & datus e&longs;t mihi &longs;en&longs;us.<emph.end type="italics"/><lb/>Sapientiæ 7. ver&longs;u. </s> <s>7.</s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, MDCLXI.</s></p><pb xlink:href="040/01/496.jpg"/> </chap> <chap> <pb xlink:href="040/01/497.jpg" pagenum="473"/><p type="head"> <s>To the Mo&longs;t <lb/>Reverend Father <lb/>SEBASTIANO FANTONI, <lb/><emph type="italics"/>General of the Order of<emph.end type="italics"/><lb/>CARMELITES.</s></p><p type="main"> <s>In obedience to the command of the No­<lb/>ble <emph type="italics"/>Signore Vincenzo Carraffa,<emph.end type="italics"/> a Neapo­<lb/>litan, and Knight of S. <emph type="italics"/>John of Jeru­<lb/>&longs;alem,<emph.end type="italics"/> (a per&longs;on, to &longs;peak the truth, of <lb/>&longs;o great Merit, that in him Nobility of <lb/>Birth, Affability of Manners, Univer&longs;al <lb/>knowledge of Arts and things, Piety <lb/>and Vertue do all contend for prehemi­<lb/>nence) I re&longs;olved with my &longs;elf to un­<lb/>dertake the Defence of the Writings of the New, or rather Re­<lb/>newed, and from the Du&longs;t of Oblivion (in which it hath long <lb/>lain hid) lately Revived Opinion, <emph type="italics"/>Of the Mobility of the Earth, <lb/>and Stability of the Sun,<emph.end type="italics"/> in times pa&longs;t found out fir&longs;t by <emph type="italics"/>Pytha­<lb/>goras,<emph.end type="italics"/> and at la&longs;t reduced into Practice by <emph type="italics"/>Copernicus<emph.end type="italics"/>; who like­<lb/>wi&longs;e hath deduced the Po&longs;ition of the Sy&longs;teme and Con&longs;titution <lb/>of the World and its parts from that Hypothe&longs;is: on which <lb/>Subject I have formerly writ to You, Mo&longs;t Reverend Sir: But <lb/>in regard I am bound for <emph type="italics"/>Rome<emph.end type="italics"/> to preach there by your Com­<lb/>mand; and &longs;ince this Speculation may &longs;eem more proper for a­<lb/>nother Treati&longs;e, to wit, a Volume of <emph type="italics"/>Co&longs;mography,<emph.end type="italics"/> which I am <lb/>in hand with, and which I am daily bu&longs;ie about, that it may <lb/>come forth in company with my <emph type="italics"/>Compendium of the Liberal Arts,<emph.end type="italics"/><lb/>which I have already fini&longs;hed, rather than now to di&longs;cu&longs;s it by it <lb/>&longs;elf, I thought to forbear, imparting what I have done for the <lb/>pre&longs;ent; Yet I was de&longs;irous to give, in the mean time, a brief ac­<lb/>count of this my Determination, and to &longs;hew You, Mo&longs;t Reve­<lb/>rend Father, (to whom I owe all my indeavours, and my very <lb/>&longs;elf) the Foundations on which this Opinion may be grounded, <lb/>lea&longs;t, whil&longs;t otherwi&longs;e it is favoured with much probability, it be <lb/>found in reality to be extreamly repugnant (as at fir&longs;t &longs;ight it <pb xlink:href="040/01/498.jpg" pagenum="474"/>&longs;eems) not onely to Phy&longs;ical Rea&longs;ons, and Common Principles <lb/>received on all hands (which cannot do &longs;o much harm) but al&longs;o <lb/>(which would be of far wor&longs;e con&longs;equence) to many Authori­<lb/>ties of &longs;acred Scripture: Upon which account many at their <lb/>fir&longs;t looking into it, explode it as the mo&longs;t fond Paradox and <lb/>Mon&longs;trous <emph type="italics"/>Capriccio<emph.end type="italics"/> that ever was heard of. </s> <s>Which thing pro­<lb/>ceeds only from an antiquated and long confirmed Cu&longs;tome, <lb/>which hath &longs;o hardened men in, and habituated them to Vul­<lb/>gar, Plau&longs;ible, and for that cau&longs;e by all men (a&longs;well learned as <lb/>unlearned) Approved Opinions, that they cannot be removed <lb/>one &longs;tep from them: So great is the force of Cu&longs;tome (which <lb/>not unfitly is &longs;tiled a &longs;econd Nature) prevailing over the whole <lb/>World, that touching things men are rather plea&longs;ed with, de­<lb/>lighted in, and de&longs;irous of tho&longs;e, which, though evil and obnox­<lb/>ious, are by u&longs;e made familiar to them, than &longs;uch, wherewith, <lb/>though better, they are not accu&longs;tomed and acquainted. </s> <s>So in <lb/>like manner, and that chiefly, in <emph type="italics"/>Opinions,<emph.end type="italics"/> which when once they <lb/>are rooted in the Mind, men &longs;tart at, and reject all others <lb/>what&longs;oever; not only tho&longs;e that are contrary to, but even all <lb/>that ever &longs;o little di&longs;agree with or vary from theirs, as har&longs;h to <lb/>the Ear, di&longs;coloured to the Eye, unplea&longs;ant to the Smell, nau&longs;e­<lb/>ous to the Ta&longs;t, rough to the Touch. </s> <s>And no wonder: For <lb/>Phy&longs;ical Truths are ordinarily judged and con&longs;idered by men, <lb/>not according to their E&longs;&longs;ence, but according to the pre&longs;cript of <lb/>&longs;ome one who&longs;e de&longs;cription or definition of them gaines him <lb/>Authority among&longs;t the vulgar. </s> <s>Which authority neverthele&longs;s <lb/>(&longs;ince 'tis no more than humane) ought not to be &longs;o e&longs;teemed, as <lb/>that that which doth manife&longs;tly appear to the contrary, whether <lb/>from better Rea&longs;ons lately found out, or from Sen&longs;e it &longs;elf, &longs;hould <lb/>for its &longs;ake be contemned and &longs;lighted; Nor is Po&longs;terity &longs;o to be <lb/>confined, but that it may, and dares, not only proceed farther, <lb/>but al&longs;o bring to light better and truer Experiments than tho&longs;e <lb/>which have been delivered to us by the Ancients. </s> <s>For the <emph type="italics"/>Ge­<lb/>nius's<emph.end type="italics"/> of the Antients, as in Inventions they did not much &longs;ur­<lb/>pa&longs;s the Wits of our times; &longs;o for the perfecting of Inventions <lb/>this Age of ours &longs;eems not only to equal, but far to excell former <lb/>Ages; Knowledge, whether in the Liberal or Mechanical Arts, <lb/>daily growing to a greater height. </s> <s>Which A&longs;&longs;ertion might be <lb/>ea&longs;ily proved, were it not that in &longs;o clear a ca&longs;e, there would be <lb/>more danger of ob&longs;curing, than hopes of illu&longs;trating it with any <lb/>farther light.</s></p><p type="main"> <s>But (that I may not wholly be &longs;ilent in this point) have not the <lb/>&longs;everal Experiments of Moderns, in many things, &longs;topped the <lb/>mouth of Venerable Antiquity, and proved many of their great­<lb/>te&longs;t and weightie&longs;t Opinions, to be vain and fal&longs;e? </s> <s>The Doctrine <pb xlink:href="040/01/499.jpg" pagenum="475"/>of the <emph type="italics"/>Antipodes<emph.end type="italics"/> by many of the Antients of approved Wi&longs;­<lb/>dome and Learning was held a Paradox no le&longs;s ab&longs;urd than this <lb/>Our Opinion of the <emph type="italics"/>Earths Motion<emph.end type="italics"/> may &longs;eem to be; as likewi&longs;e <lb/>that of the <emph type="italics"/>Habitablene&longs;&longs;e of the Torrid Zone<emph.end type="italics"/>: Of the&longs;e Opini­<lb/>ons, the fir&longs;t was accounted unpo&longs;&longs;ible by many, but the latter <lb/>was ab&longs;olutely denyed by the unanimous con&longs;ent of all: But <lb/>later Authors (to the great felicity and perpetual Glory of <lb/>their Age) have, not &longs;o much by Authority, as by accurate <lb/>diligence and indefatigable &longs;tudy to finde out the truth, pro­<lb/>ved them both to be undoubtedly true. </s> <s>Thus I affirm that <lb/>the Antients were deceived, and that in too lightly challenging <lb/>Credid and Authority for their Inventions, they di&longs;covered too <lb/>much folly. </s> <s>Here for brevities &longs;ake I pa&longs;s by many Dreams <lb/>lately detected, both of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and other of the antient Philo­<lb/>&longs;ophers; who in all likelihood if they had dived into the Ob&longs;er­<lb/>vations of Modern Writers, and under&longs;tood their Rea&longs;ons, would, <lb/>by changing their Judgements, have given them the precedency, <lb/>and would have &longs;ub&longs;cribed to their manife&longs;t Truth. </s> <s>Hereby we <lb/>&longs;ee that we are not to have &longs;o high a re&longs;pect for the Antiens, that <lb/>whatever they a&longs;&longs;ert &longs;hould be taken upon tru&longs;t, and that Faith <lb/>&longs;hould be given to their &longs;ayings, as if they were Oracles and <lb/>Truths &longs;ent down from Heaven. </s> <s>But yet (which indeed is <lb/>chiefly to be regarded in the&longs;e matters) if any thing be found out <lb/>that is repugnant to Divine Authority, or to the Sacred Leaves, <lb/>that were dictated by the Holy Gho&longs;t, and by His In&longs;piration <lb/><arrow.to.target n="marg874"></arrow.to.target><lb/>expounded by the Holy Doctors of the Church, in this ca&longs;e not <lb/>onely Humane Rea&longs;on, but even Sen&longs;e it &longs;elf is to &longs;ubmitt: <lb/>which, though by all manner of weighty Conditions and circum­<lb/>&longs;tances it &longs;hould hold forth any thing contrary to Divine Autho­<lb/>rity, (which indeed is &longs;o plain, that there is no way left to evade <lb/>the right un er&longs;tanding of it) yet is it to be rejected; and we <lb/>mu&longs;t conclude our &longs;elves deceived by it, and believe that that is <lb/>not true which Sen&longs;e and Rea&longs;on repre&longs;ents unto us: For, however <lb/>we judge of things, we have, both in this and all other ca&longs;es, a <lb/>more certain knowledge, which proceeds from Divine Faith; as <lb/>S. <emph type="italics"/>Peter<emph.end type="italics"/> hath mo&longs;t excellently expre&longs;t it: Who though with his <lb/>Sen&longs;es he &longs;aw, and perceived the Glory of our Lord in his <lb/>Transfiguration, and heard his words manife&longs;ting his great Pow­<lb/>er, yet neverthele&longs;s all the&longs;e things compared with the Light of <lb/>Faith, he adds: ^{*}<emph type="italics"/>We have al&longs;o a more &longs;ure word of Prophecy,<emph.end type="italics"/> &c. <lb/><arrow.to.target n="marg875"></arrow.to.target><lb/>Wherefore &longs;ince this Opinion of <emph type="italics"/>Pythagoras<emph.end type="italics"/> and <emph type="italics"/>Copernicus<emph.end type="italics"/> hath <lb/>entred upon the Stage of the World in &longs;o &longs;trange a Dre&longs;s, and at <lb/>the fir&longs;t appearance (be&longs;ides the re&longs;t) doth &longs;eem to oppo&longs;e &longs;un­<lb/>dry Authorities of Sacred Scripture, it hath (this being granted) <lb/>been ju&longs;tly rejected of all men as a meer ab&longs;urdity.</s></p> <pb xlink:href="040/01/500.jpg" pagenum="476"/><p type="margin"> <s><margin.target id="marg874"></margin.target><emph type="italics"/>Faith is more <lb/>certain, than ei­<lb/>ther Sen&longs;e or Rea­<lb/>&longs;on.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg875"></margin.target>* 2 Pet. </s> <s>1. 19.</s></p><p type="main"> <s>But yet becau&longs;e the common Sy&longs;teme of the World devi&longs;ed by <lb/><emph type="italics"/>Ptolomy<emph.end type="italics"/> hath hitherto &longs;atisfied none of the Learned, hereupon a <lb/>&longs;u&longs;picion is ri&longs;en up among&longs;t all, even <emph type="italics"/>Ptolemy's<emph.end type="italics"/> followers them­<lb/>&longs;elves, that there mu&longs;t be &longs;ome other Sy&longs;teme, which is more true <lb/>than this of <emph type="italics"/>Ptolemy<emph.end type="italics"/>; For although the <emph type="italics"/>Phœnomena<emph.end type="italics"/> of Cele&longs;tial <lb/>Bodys may &longs;eem to be generally re&longs;olved by this Hypothe&longs;is, yet <lb/>they are found to be involved with many difficulties, and refer­<lb/>red to many devices; as namely of Orbes of &longs;undry Forms and <lb/>Figures, Epicicles, Equations, Differences, Excentricks, andinnu­<lb/>merable &longs;uch like fancies and Chymæra's which &longs;avour of the <lb/><emph type="italics"/>Ens Rationis<emph.end type="italics"/> of Logicians, rather than of any <emph type="italics"/>Realem E&longs;&longs;entiam.<emph.end type="italics"/><lb/>Of which kinde is that of the <emph type="italics"/>Rapid Motion,<emph.end type="italics"/> than which I finde <lb/>not any thing that can be more weakly grounded, and more ea&longs;i­<lb/>ly controverted and di&longs;proved: And &longs;uch is that conceit of the <lb/>^{*} Heaven void of Stars, moving the inferior Heavens or Orbes: <lb/><arrow.to.target n="marg876"></arrow.to.target><lb/>All which are introduced upon occa&longs;ion of the variety of the <lb/>Motions of Cele&longs;tial Bodyes, which &longs;eemed impo&longs;&longs;ible, by any <lb/>other way, to be reduced to any certain and determinate Rule. <lb/></s> <s>So that the A&longs;&longs;ertors of that common Opinion, freely confe&longs;s, <lb/>that in de&longs;cribing the Worlds Sy&longs;teme, they cannot as yet di&longs;co­<lb/>ver, or teach the true Hypothe&longs;is thereof: But that their endea­<lb/>vours are onely to finde out, among&longs;t many things, what is mo&longs;t <lb/>agreeable with truth, and may, upon better and more accomo­<lb/>date Rea&longs;ons, an&longs;wer the Cele&longs;tial <emph type="italics"/>Phœnomena.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg876"></margin.target>* Or <emph type="italics"/>Primum<lb/>Mobile.<emph.end type="italics"/></s></p><p type="main"> <s>Since that, the Tele&longs;cope (an Optick Invention) hath been found <lb/>out, by help of which, many remarkable things in the Heavens, <lb/>mo&longs;t worthy to be known, and till then unthought of, were di&longs;­<lb/>covered by manife&longs;t &longs;en&longs;ation; as for in&longs;tance, That the Moon is <lb/>Mountainous; <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Saturn<emph.end type="italics"/> Tricorporeal; and <emph type="italics"/>Jupiter<emph.end type="italics"/><lb/>Quadricorporeal: Likewi&longs;e that in the <emph type="italics"/>Via Lactea,<emph.end type="italics"/> in the <emph type="italics"/>Ple­<lb/>iades,<emph.end type="italics"/> and in the Stars called <emph type="italics"/>Nobulo&longs;œ<emph.end type="italics"/> there are many Stars, and <lb/>tho&longs;e of the greate&longs;t Magnitude which are by turns adjacent to <lb/>one another; and in the end it hath di&longs;covered to us, new fixed <lb/>Stars, new planets, and new Worlds. </s> <s>And by this &longs;ame In&longs;tru­<lb/>ment it appears very probable, that <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mercury<emph.end type="italics"/> do not <lb/>move properly about the Earth, but rather about the Sun; and <lb/>that the Moon alone moveth about the Earth. </s> <s>What therefore <lb/>can be inferred from hence, but that the Sun doth &longs;tand immo­<lb/>vable in the Centre, and that the Earth, with the other Cele&longs;tial <lb/>Orbes, is circumvolved about it? </s> <s>Wherefore by this and many <lb/>other Rea&longs;ons it appears, That the Opinion of <emph type="italics"/>Pythagor as<emph.end type="italics"/> and <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> doth not di&longs;agree with A&longs;tronomical and Co&longs;mogra­<lb/>phical Principles; yea, that it carryeth with it a great likelihood <lb/>and probability of Truth: Whereas among&longs;t the &longs;o many &longs;eve­<lb/>ral Opinions, that deviate from the common Sy&longs;teme, and devi&longs;e <pb xlink:href="040/01/501.jpg" pagenum="477"/>others, &longs;uch as were tho&longs;e of <emph type="italics"/>Plato, Calippus, Eudoxus<emph.end type="italics"/>; and &longs;ince <lb/><arrow.to.target n="marg877"></arrow.to.target><lb/>them of <emph type="italics"/>Averroe, ^{*} Cardanus, Fraca&longs;torius,<emph.end type="italics"/> and others both Anti­<lb/>ent and Modern, there is not one found that is more facile, more <lb/>regularly ahd determinately, accommodated to the <emph type="italics"/>Phœnomena<emph.end type="italics"/><lb/>and Motions of the Heavens, without <emph type="italics"/>Epicycles, Excentrix, Ho­<lb/>mocentricks<emph.end type="italics"/> Deferents, and the &longs;upputation of the Rapid Motion. <lb/></s> <s>And this Hypothe&longs;is hath been a&longs;&longs;erted for true, not onely by <lb/><emph type="italics"/>Pythagoras,<emph.end type="italics"/> and, after him, by <emph type="italics"/>Copernicus,<emph.end type="italics"/> but by many famous <lb/>men, as namely, <emph type="italics"/>Heraclitus,<emph.end type="italics"/> and <emph type="italics"/>Ecphantus, Pythagoreans,<emph.end type="italics"/> all the <lb/>Di&longs;ciples of that Sect, <emph type="italics"/>Miceta<emph.end type="italics"/> of <emph type="italics"/>Syracu&longs;e, Martianus Capella,<emph.end type="italics"/> and <lb/>many more. </s> <s>Among&longs;t whom, tho&longs;e (as we have &longs;aid) that <lb/>have attempted the finding out of New Sy&longs;temes (for they refu­<lb/>&longs;ed both this of <emph type="italics"/>Pythagoras,<emph.end type="italics"/> and that of <emph type="italics"/>Ptolemy)<emph.end type="italics"/> are numberle&longs;s: <lb/>who yet notwith&longs;tanding allowed this Opinion of <emph type="italics"/>Pythagoras<emph.end type="italics"/> to <lb/>carry with it much probability, and indirectly confirmed it; ina&longs;­<lb/>much as that they rejected the common one as imperfect, defe­<lb/><arrow.to.target n="marg878"></arrow.to.target><lb/>ctive, and attended with many contradictions and difficulties. <lb/></s> <s>Among&longs;t the&longs;e may be numbered Father ^{*} <emph type="italics"/>Clavius,<emph.end type="italics"/> a mo&longs;t learn­<lb/>ed Je&longs;uite; who, although he refutes the Sy&longs;teme of <emph type="italics"/>Pythagoras,<emph.end type="italics"/><lb/>yet acknowledgeth the Levity of the common Sy&longs;teme, and he <lb/>ingeniou&longs;ly confe&longs;&longs;eth, that for the removal of difficulties, in which <lb/>the common Sy&longs;teme will not &longs;erve the turn, A&longs;tronomers are <lb/>forced to enquire after another Sy&longs;teme, to the di&longs;covery of <lb/>which, he doth very earne&longs;tly exhort them.</s></p><p type="margin"> <s><margin.target id="marg877"></margin.target>* Cardan de re­<lb/>rum variet. </s> <s>Lib. 1. <lb/>Cap. 1.</s></p><p type="margin"> <s><margin.target id="marg878"></margin.target>* P. </s> <s>Clavins in <lb/>ultima &longs;uor. </s> <s>Ope­<lb/>rum editione.</s></p><p type="main"> <s>Now can there a better or more commodious Hypothe&longs;is <lb/>be devi&longs;ed, than this of <emph type="italics"/>Copernicus,<emph.end type="italics"/>? </s> <s>For <emph type="italics"/>t<emph.end type="italics"/>his Cau&longs;e many Mo­<lb/>dern Authors are induced to approve of, and follow it: but <lb/>with much hæ&longs;itancy, and fear, in regard that it &longs;eemeth in their <lb/>Opinion &longs;o to contradict the Holy Scriptures, as that it cannot <lb/>po&longs;&longs;ibly be reconciled to them. </s> <s>Which is the Rea&longs;on that this <lb/>Opinion hath been long &longs;uppre&longs;t, and is now entertained by men <lb/>in a mode&longs;t manner, ad as it were with a veiled Face; according <lb/>to that advice of the Poet:</s></p><p type="main"> <s><emph type="italics"/>Judicium populi nunquam contemp&longs;eris unus,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ne nullis place as, dum vis contemnere multos.<emph.end type="italics"/></s></p><p type="main"> <s>Upon con&longs;ideration of which, (out of my very great love to­<lb/>wards the Sciences, and my ardent defire to &longs;ee the encrea&longs;e and <lb/>perfection of them, and the Light of Truth freed from all Er­<lb/>rours and Ob&longs;curities) I began to argue with my &longs;elf touching <lb/>this Point after this manner: This Opinion of the <emph type="italics"/>Pythagoreans<emph.end type="italics"/><lb/>is either true, or fal&longs;e; If fal&longs;e, it ought not to be mentioned, and <lb/>de&longs;erves not to be divulged: If true, it matters not, though it <lb/>contradict all, as well Philo&longs;ophers as A&longs;tronomers: And though <lb/>for its e&longs;tabli&longs;hment and reducement to u&longs;e a new Philo&longs;ophy <pb xlink:href="040/01/502.jpg" pagenum="478"/>and A&longs;tronomy, (&longs;ounded upon new Principles and Hypothe&longs;e) <lb/>&longs;hould be con&longs;tituted: For the Authority of Sacred Scripture <lb/>will not oppo&longs;e it; neither doth one Truth contradict another. <lb/></s> <s>If therefore the Opinion of <emph type="italics"/>Pythagoras<emph.end type="italics"/> be true, without doubt <lb/>God hath di&longs;po&longs;ed and dictated the words of of Holy Writ in <lb/>&longs;uch a manner, that they may admit an apt &longs;en&longs;e and reconcilia­<lb/>tion with that Hypothe&longs;is. </s> <s>Being moved by the&longs;e Rea&longs;ons, and <lb/>the probability of the &longs;aid Opinion, I thought good to try whe­<lb/>ther Texts of Sacred Scripture might be expounded according to <lb/>Theological and Phy&longs;ical Principles, and might be reconciled to <lb/>it, &longs;o that (in regard that hitherto it hath been held probable) it <lb/>may in after times, coming without &longs;cruple to be acknowledged <lb/>for true, advance it &longs;elf, and appear in publick with an uncover­<lb/>ed Face, without any mans prohibition, and may lawfully and <lb/>freely hold a Sacred intelligence with Holy Truth, &longs;o earne&longs;tly <lb/>coveted and commended by good Men. </s> <s>Which de&longs;igne, having hi­<lb/><arrow.to.target n="marg879"></arrow.to.target><lb/>therto been undertaken by none that I know, wil, I am per&longs;waded, <lb/>be very acceptable to the Studious of the&longs;e Learnings, e&longs;pecially to <lb/>the mo&longs;t Learned <emph type="italics"/>Galilœo Galilœi,<emph.end type="italics"/> chief Mathematician to the <lb/>mo&longs;t Serene Grand Duke of <emph type="italics"/>Tu&longs;cany,<emph.end type="italics"/> and <emph type="italics"/>John Kepler,<emph.end type="italics"/> chief <lb/>Mathematician to his Sacred and invincible Maje&longs;ty, the Empe­<lb/>rour, and to all that Illu&longs;trious, and much to be commended Ac­<lb/>cademy of the <emph type="italics"/>Lynceans<emph.end type="italics"/>; whom, if I mi&longs;take not, are all of this <lb/>Opinion. </s> <s>Although I doubt not but they, and many other <lb/>Learned Men might ea&longs;ily have found out the&longs;e or the like Re­<lb/>conciliations of Scriptural expre&longs;&longs;ions; to whom neverthele&longs;s I <lb/>have thought fit (in re&longs;pect of that profe&longs;&longs;ion which I have under­<lb/>taken, upon the faith of my &longs;oul, and the propen&longs;ity that I have <lb/>towards Truth) to offer that of the Poet,</s></p><p type="margin"> <s><margin.target id="marg879"></margin.target><emph type="italics"/>The Author <lb/>fir&longs;t Theologically <lb/>defendeth the <lb/>Earths Mobili­<lb/>ty, approved by <lb/>many of the Mo­<lb/>derns.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Nullius addictus jur are in verba Magi&longs;tri.<emph.end type="italics"/></s></p><p type="main"> <s>And in te&longs;timony of my e&longs;teem to them and all the Learned, <lb/>to communicate the&longs;e my thoughts; confidently a&longs;&longs;uring my &longs;elf <lb/>that they will accept them, with a Candor equal to that where­<lb/>with I have written them.</s></p><p type="main"> <s>Therefore to come to the bu&longs;ine&longs;s: All Authorities of Di­<lb/>vine Writ which &longs;eem to oppo&longs;e this Opinion, are reducible to <lb/>&longs;ix Cla&longs;&longs;es: The fir&longs;t is of tho&longs;e that affirm the Earth to &longs;tand <lb/>&longs;till, and not to move: as <emph type="italics"/>P&longs;al. </s> <s>92. He framed the round World <lb/>&longs;o &longs;ure, that it cannot be moved<emph.end type="italics"/>: Al&longs;o <emph type="italics"/>P&longs;al. </s> <s>104. Who laid the <lb/>Foundations of the Earth, that it &longs;hould not be removed for ever<emph.end type="italics"/>: <lb/>And <emph type="italics"/>Eccle&longs;ia&longs;tes 1. But the Earth abideth for ever<emph.end type="italics"/>: And others <lb/>of the like &longs;en&longs;e.</s></p><p type="main"> <s>The &longs;econd is of tho&longs;e which atte&longs;t the Sun to move, and <pb xlink:href="040/01/503.jpg" pagenum="479"/>Revolve about the Earth; as <emph type="italics"/>P&longs;al. </s> <s>19. (b) In them hath be &longs;et a <lb/><arrow.to.target n="marg880"></arrow.to.target><lb/>Tabernacle for the Sun, which cometh forth as a Bridegroom out <lb/>of his chamber, and rejoyceth as a Gyant to run his Cour&longs;e. </s> <s>It <lb/>cometh forth from the uttermo&longs;t part of the Heaven, and runneth <lb/>about unto the end of it again; and there is nothing hid from the <lb/>heat thereof.<emph.end type="italics"/> And <emph type="italics"/>Eccle&longs;ia&longs;t. </s> <s>1. The Sun ri&longs;eth, and the Sun go­<lb/>eth down, and ha&longs;teth to the place where be aro&longs;e: it goeth towards <lb/>the South, and turneth about unto the North.<emph.end type="italics"/> Whereupon the <lb/>Suns Retrogradation is mentioned as a Miracle, <emph type="italics"/>I&longs;aiah 38. The <lb/>Sun returned ten degrees.<emph.end type="italics"/> And <emph type="italics"/>Eccle&longs;ia&longs;ticus 48. In his time the <lb/>Sun went backward, and lengthened the life of the King.<emph.end type="italics"/> And <lb/>for this rea&longs;on it is related for a Miracle, in the Book of <emph type="italics"/>Jo&longs;buah,<emph.end type="italics"/><lb/>that at the Prayers of that great Captain the Sun &longs;tood &longs;till, its <lb/>motion being forbidden it, by him<emph type="italics"/>: Jo&longs;h.<emph.end type="italics"/>10. <emph type="italics"/>Sun &longs;tand thou <lb/>&longs;till upon Gibeon.<emph.end type="italics"/> Now if the Sun &longs;hould &longs;tand &longs;till, and the <lb/>Earth move about it, its &longs;tation at that time was no Miracle; <lb/>and if <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> had intended, that the light of the day &longs;hould <lb/>have been prolonged by the Suns &longs;plendour, he would not have <lb/>&longs;aid, <emph type="italics"/>Sun &longs;tand thou &longs;till,<emph.end type="italics"/> but rather <emph type="italics"/>Earth &longs;tand thou &longs;till.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg880"></margin.target><emph type="italics"/>(b) Or<emph.end type="italics"/> In Sole <lb/>po&longs;uit tabernacu­<lb/>lum &longs;uum, <emph type="italics"/>accor­<lb/>ding to the Tran­<lb/>&longs;lation our Au­<lb/>thor followeth.<emph.end type="italics"/></s></p><p type="main"> <s>The third Cla&longs;&longs;is is of tho&longs;e Authorities which &longs;ay, that Hea­<lb/>ven is <emph type="italics"/>above,<emph.end type="italics"/> and the Earth <emph type="italics"/>beneath<emph.end type="italics"/>; of which &longs;ort is that place <lb/>of <emph type="italics"/>Joel, chap.<emph.end type="italics"/> 2. cited by S. <emph type="italics"/>Peter,<emph.end type="italics"/> in <emph type="italics"/>Acts. </s> <s>2. I will &longs;hew wonders <lb/>in Heaven above, and &longs;ignes in the Earth beneath,<emph.end type="italics"/> with others of <lb/>the like purport. </s> <s>Hereupon Chri&longs;t at his Incarnation is &longs;aid to <lb/><emph type="italics"/>come down from Heaven<emph.end type="italics"/>; and after his Re&longs;urrection to have <emph type="italics"/>a&longs;­<lb/>cended up into heaven.<emph.end type="italics"/> But if the Earth &longs;hould move about <lb/>the Sun, it would be, as one may &longs;ay, in Heaven, and con&longs;e­<lb/>quently would rather be <emph type="italics"/>above<emph.end type="italics"/> Heaven than <emph type="italics"/>beneath<emph.end type="italics"/> it. </s> <s>And <lb/>this is confirmed; For that the Opinion which placeth the Sun in <lb/>the Centre, doth likewi&longs;e place <emph type="italics"/>Mercury<emph.end type="italics"/> above the Sun, and <lb/><emph type="italics"/>Venus<emph.end type="italics"/> above <emph type="italics"/>Mercury<emph.end type="italics"/>; and the Earth above <emph type="italics"/>Venus,<emph.end type="italics"/> together <lb/>with the Moon, which revolves about the Earth, and therefore <lb/>the Earth, together with the Moon, is placed in the third Heaven. <lb/></s> <s>If therefore in Spherical Bodies, as in the World, <emph type="italics"/>beneath<emph.end type="italics"/> &longs;igni­<lb/><arrow.to.target n="marg881"></arrow.to.target><lb/>fies no more than to be neer to the centre, and <emph type="italics"/>above,<emph.end type="italics"/> than to <lb/>approach the Circumference, it mu&longs;t needs follow, that for ma­<lb/>king good of Theological Po&longs;itions concerning the A&longs;cen&longs;ion <lb/>and De&longs;cen&longs;ion of Chri&longs;t, the Earth is to be placed in the cen­<lb/>tre, and the Sun, with the other Heavens in the Circumference; <lb/>and not according to <emph type="italics"/>Copernicus,<emph.end type="italics"/> who&longs;e Hypothe&longs;is inverts this <lb/>Order: with which one cannot &longs;ee how the true A&longs;cen&longs;ion and <lb/>De&longs;cen&longs;ion can be con&longs;i&longs;tent.</s></p><p type="margin"> <s><margin.target id="marg881"></margin.target><emph type="italics"/>In Spberieall <lb/>Bodies,<emph.end type="italics"/> Deor&longs;um <lb/><emph type="italics"/>is the Centre, and<emph.end type="italics"/><lb/>Sur&longs;um <emph type="italics"/>the Cir­<lb/>cumference.<emph.end type="italics"/></s></p><p type="main"> <s>The fourth Cla&longs;&longs;is is of tho&longs;e Authorities which make Hell to <lb/>be in the Centre of the World, which is the Common Opinion <lb/>of Divines, and confirmed by this Rea&longs;on, That &longs;ince Hell (ta­ <pb xlink:href="040/01/504.jpg" pagenum="480"/>ken in its &longs;trict denomination) ought to be in the lowe&longs;t part of <lb/>the World, and &longs;ince that in a Sphere there is no part lower <lb/>then the Centre, Hell &longs;hall be, as it were, in the Centre of the <lb/>World, which being of a Spherical Figure, it mu&longs;t follow, that <lb/><arrow.to.target n="marg882"></arrow.to.target><lb/>Hell is either in the Sun (fora&longs;much as it is &longs;uppo&longs;ed by this Hy­<lb/>pothe&longs;is to be in the Centre of the World) or el&longs;e &longs;uppo&longs;ing <lb/>that Hell is in the Centre of the Earth, if the Earth &longs;hould move <lb/>about the Sun, it would nece&longs;&longs;arily en&longs;ue, that Hell, together <lb/>with the Earth, is in Heaven, and with it revolveth about the third <lb/>Heaven; than which nothing more ab&longs;urd can be &longs;aid or imagi­<lb/>ned.</s></p><p type="margin"> <s><margin.target id="marg882"></margin.target><emph type="italics"/>Hell is in the <lb/>centre of the <lb/>Earth, not of the <lb/>World.<emph.end type="italics"/></s></p><p type="main"> <s>The fifth Cla&longs;&longs;is, is of tho&longs;e Authorities which alwayes op­<lb/><arrow.to.target n="marg883"></arrow.to.target><lb/>po&longs;e Heaven to the Earth, and &longs;o again the Earth to Heaven; as <lb/>if there were the &longs;ame relation betwixt them, with that of the <lb/>Centre to the Circumference, and of the Circumference to the <lb/>Centre. </s> <s>But if the Earth were in Heaven, it &longs;hould be on one <lb/>&longs;ide thereof, and would not &longs;tand in the Middle, and con&longs;equent­<lb/>ly there would be no &longs;uch relation betwixt them; which never­<lb/>thele&longs;s do, not only in Sacred Writ, but even in Common Speech, <lb/>ever and every where an&longs;wer to each other with a mutual Oppo­<lb/>fition. </s> <s>Whence that of <emph type="italics"/>Gene&longs;. </s> <s>1. In the beginning God created <lb/>the Heaven and the Earth<emph.end type="italics"/>: and <emph type="italics"/>P&longs;al. </s> <s>115. The Heaven, even <lb/>the Heavens are the Lords; but the Earth hath he given to the <lb/>Children of men:<emph.end type="italics"/> and our Saviour in that Prayer which he pre­<lb/>&longs;cribeth to us, <emph type="italics"/>Matth. </s> <s>6. Thy will be done in Earth, as it is in <lb/>Heaven:<emph.end type="italics"/> and S. <emph type="italics"/>Paul, 1 Corinth. </s> <s>15. The fir&longs;t man is of the <lb/>Earth, earthy; the &longs;econd man is of Heaven, heavenly:<emph.end type="italics"/> and <lb/><emph type="italics"/>Colo&longs;&longs;. </s> <s>1. By him were all things created that are in Heaven, and <lb/>that are in Earth<emph.end type="italics"/>: and again, <emph type="italics"/>Having made peace through the <lb/>Blood of his Cro&longs;&longs;e for all things, whether they be things in Earth <lb/>or things in Heaven:<emph.end type="italics"/> and <emph type="italics"/>Chap. </s> <s>3. Set your affections on things <lb/>above, not on things on the Earth<emph.end type="italics"/>; with innumerable other &longs;uch <lb/>like places. </s> <s>Since therefore the&longs;e two Bodies are alwayes mu­<lb/>tually oppo&longs;ed to each other, and Heaven, without all doubt, <lb/>referreth to the Circumference, it mu&longs;t of nece&longs;&longs;ity follow, that <lb/>the Earth is to be adjudged the place of the Centre.</s></p><p type="margin"> <s><margin.target id="marg883"></margin.target><emph type="italics"/>Heaven and <lb/>Earth are always <lb/>mutually oppo&longs;ed <lb/>to each other.<emph.end type="italics"/></s></p><p type="main"> <s>The &longs;ixth and la&longs;t Cla&longs;&longs;is is of tho&longs;e Authorities, which (being <lb/>rather of Fathers and Divines, than of the Sacred Scripture) &longs;ay, <lb/>That the Sun, after the day of Judgment &longs;hall &longs;tand immoveable <lb/><arrow.to.target n="marg884"></arrow.to.target><lb/>in the Ea&longs;t, and the Moon in the We&longs;t. </s> <s>Which Station, if the <lb/><emph type="italics"/>Pythagorick<emph.end type="italics"/> Opinion hold true, ought rather to be a&longs;cribed to <lb/>the Earth, than to the Sun; for if it be true, that the Earth doth <lb/>now move about the Sun, it is nece&longs;&longs;ary that after the day of <lb/>Judgment it &longs;hould &longs;tand immoveable. </s> <s>And truth is, if it mu&longs;t <lb/>&longs;ub&longs;i&longs;t without motion in one con&longs;tant place, there is no rea&longs;on <pb xlink:href="040/01/505.jpg" pagenum="481"/>why it &longs;hould rather &longs;tand in one &longs;ite of that Place than in ano­<lb/>ther, or why it &longs;hould rather turn one part of it than another to <lb/>the Sun, if &longs;o be that every of its parts without di&longs;tinction, which <lb/>is de&longs;titute of the Suns light, cannot choo&longs;e but be di&longs;mal, and <lb/>much wor&longs;e affected than that part which is illuminated. </s> <s>Hence <lb/>al&longs;o would ari&longs;e many other ab&longs;urdities be&longs;ides the&longs;e.</s></p><p type="margin"> <s><margin.target id="marg884"></margin.target><emph type="italics"/>After the day <lb/>of Judgment the <lb/>Earth &longs;hall &longs;tand <lb/>immoveable.<emph.end type="italics"/></s></p><p type="main"> <s>The&longs;e are the Cla&longs;&longs;es, &c. </s> <s>from which great a&longs;&longs;aults are made <lb/>again&longs;t the &longs;tructure of the Pythagorick Sy&longs;teme; yet by that <lb/>time I &longs;hall have fir&longs;t laid down &longs;ix Maximes or Principles, as <lb/>impregnable Bulwarks erected again&longs;t them, it will be ea&longs;ie to <lb/>batter them, and to defend the Hypothe&longs;is of <emph type="italics"/>Pythagoras<emph.end type="italics"/> from <lb/>being attaqued by them. </s> <s>Which before I propound, I do pro­<lb/>fe&longs;s (with that Humility and Mode&longs;ty which becometh a Chri­<lb/>&longs;tian, and a per&longs;on in Religious Orders) that I do with reverence <lb/>&longs;ubmit what I am about to &longs;peak to the Judgment of Holy <lb/>Church. </s> <s>Nor have I undertaken to write the&longs;e things out of <lb/>any inducements of Temerity, or Ambition, but out of Charity <lb/>and a De&longs;ire to be auxiliary to my neighbour in his inqui&longs;ition <lb/>after Truth. </s> <s>And there is nothing in all this Controver&longs;ie <lb/>maintained by me (that expect to be better in&longs;tructed by tho&longs;e <lb/>who profe&longs;s the&longs;e Studies) which I &longs;hall not retract, if any per­<lb/>&longs;ons &longs;hall by &longs;olid Rea&longs;ons & reiterated Experiments, prove &longs;ome <lb/>other Hypothe&longs;is to be more probable; but yet, until &longs;uch time as <lb/>they &longs;hall decide the Point, I &longs;hall labour all I can for its &longs;upport.</s></p><p type="main"> <s>My fir&longs;t and chiefe&longs;t Maxime is this; When any thing is at­<lb/>tributed in Holy Writ, to God, or to a Creature, thats not be­<lb/>&longs;eeming to, or incommen&longs;urate with them, it mu&longs;t of nece&longs;&longs;ity <lb/>be received and expounded one, or more of the four following <lb/>wayes; Fir&longs;t, it may be &longs;aid to agree with them <emph type="italics"/>Metaphorically, <lb/>and Proportionally, or by Similitude.<emph.end type="italics"/> Secondly, <emph type="italics"/>According to <lb/>our manner of Con&longs;idering, Apprehending, Conceiving, Vnder&longs;tand­<lb/>ing, Knowing, &c.<emph.end type="italics"/> Thirdly, <emph type="italics"/>according to the Opinion of the <lb/>Vulgar, and the Common way of Speaking:<emph.end type="italics"/> to which Vulgar <lb/>Speech the Holy Gho&longs;t doth very often with much &longs;tudy acco­<lb/>modate it &longs;elf. </s> <s>Fourthly, <emph type="italics"/>In re&longs;pect of our &longs;elves, and for that <lb/>he makes him&longs;elf like unto us.<emph.end type="italics"/> Of each of the&longs;e wayes there are <lb/>the&longs;e examples: God doth not walk, &longs;ince he is Infinite and Im­<lb/>moveable; He hath no Bodily Members, &longs;ince he is a Pure Act; <lb/>and con&longs;equently is void of all Pa&longs;&longs;ion of Minde; and yet in <lb/>Sacred Scripture, <emph type="italics"/>Gen. </s> <s>3. ver&longs;.<emph.end type="italics"/> 8. it is &longs;aid, <emph type="italics"/>He walked in the cool of <lb/>the day<emph.end type="italics"/>: and <emph type="italics"/>Job 22. ver&longs;.<emph.end type="italics"/> 14. it is &longs;aid, <emph type="italics"/>He walketh in the ^{*} Cir­<lb/><arrow.to.target n="marg885"></arrow.to.target><lb/>cuit of Heaven:<emph.end type="italics"/> and in many other places coming, departing, <lb/>making ha&longs;t is a&longs;cribed to God; and likewi&longs;e Bodily parts, as <lb/>Eyes, Ears, Lips, Face, Voice, Countenance, Hands, Feet, Bow­<lb/>els, Garments, Arms; as al&longs;o many Pa&longs;&longs;ions, &longs;uch as Anger, <pb xlink:href="040/01/506.jpg" pagenum="482"/>Sorrow, Repentance, and the like. </s> <s>What &longs;hall we &longs;ay there­<lb/>fore? </s> <s>Without doubt &longs;uch like Attributes agree with God (to <lb/>u&longs;e the Schoolmens words <emph type="italics"/>Metaphorically, Proportionally, and by <lb/>Similitude<emph.end type="italics"/>: And touching Pa&longs;&longs;ions, it may be &longs;aid, that God <lb/>conde&longs;cendeth to repre&longs;ent him&longs;elf after that manner: as for <lb/>in&longs;tance, <emph type="italics"/>The Lord is angry<emph.end type="italics"/>; i.e. <emph type="italics"/>He revealeth him&longs;elf as one that <lb/>is angry: He grieved<emph.end type="italics"/>; i. </s> <s>e. <emph type="italics"/>He revealeth him&longs;elf, as one that <lb/>is &longs;orrowful: It repented him that he had made man<emph.end type="italics"/>; i.e. <emph type="italics"/>He &longs;ee­<lb/>med as one that repented.<emph.end type="italics"/> And indeed all the&longs;e things are <emph type="italics"/>Com­<lb/>parativè ad nos,<emph.end type="italics"/> and in re&longs;pect of us. </s> <s>So God is &longs;aid to be in <lb/>Heaven, to move in time, to &longs;hew him&longs;elf, to hide him&longs;elf, to <lb/>ob&longs;erve and mark our &longs;teps; to &longs;eek us, to &longs;tand at the door, <lb/>to knock at the door; not that he can be contained in a bodily <lb/>place, nor that he is really moved, nor in time; nor that humane <lb/>manners or cu&longs;tomes can agree with him, &longs;ave only according to <lb/>our manner of Apprehen&longs;ion: This Conception of ours orderly <lb/>di&longs;tingui&longs;heth the&longs;e Attributes in him one from another, when, <lb/>notwith&longs;tanding, they are one and the &longs;ame with him: This Ap­<lb/>prehen&longs;ion of ours divideth al&longs;o his actions into &longs;everal times, <lb/>which, neverthele&longs;&longs;e, for the mo&longs;t part, are produced in one and <lb/>the &longs;ame in&longs;tant: And this, to conclude, alwayes apprehendeth <lb/>tho&longs;e things with &longs;ome defect, which, notwith&longs;tanding are in <lb/>God mo&longs;t perfect. </s> <s>For this rea&longs;on doth the Sacred Scripture <lb/>expre&longs;s it &longs;elf <emph type="italics"/>according to the Vulgar Opinion,<emph.end type="italics"/> whil&longs;t it a&longs;cribes <lb/>to the Earth Ends and Foundations, which yet it hath not; to <lb/>the Sea a Depth not to be fathomed; to Death (which is a Pri­<lb/>vation, and con&longs;equently a Non entity) it appropriates Actions, <lb/>Motion, Pa&longs;&longs;ions, and other &longs;uch like Accidents, of all which it is <lb/>deprived, as al&longs;o Epithites and Adjuncts, which really cannot <lb/>&longs;uit with it: <emph type="italics"/>Is not the bitterne&longs;&longs;e of Death pa&longs;t<emph.end type="italics"/>? </s> <s>1 Sam. </s> <s>15. 32. <lb/><emph type="italics"/>Let death come upon them,<emph.end type="italics"/> P&longs;al 6. <emph type="italics"/>He hath prepared the In&longs;tru­<lb/>ments of Death,<emph.end type="italics"/> P&longs;al. </s> <s>7. 14. <emph type="italics"/>Thou rai&longs;e&longs;t me from the gates of <lb/>Death,<emph.end type="italics"/> P&longs;al. </s> <s>84. <emph type="italics"/>In the mid&longs;t of the &longs;hadow of Death,<emph.end type="italics"/> P&longs;al. </s> <s>23. <lb/><emph type="italics"/>Love is &longs;trong as Death,<emph.end type="italics"/> Cant. </s> <s>8. 9. <emph type="italics"/>The Fir&longs;t-Born of Death,<emph.end type="italics"/> Job <lb/>18. 13. <emph type="italics"/>De&longs;truction and Death &longs;ay, &c.<emph.end type="italics"/> Job 28. 22. And who knows <lb/>not that the whole Hi&longs;tory of the rich Glutton doth con&longs;i&longs;t of <lb/><arrow.to.target n="marg886"></arrow.to.target><lb/>the like phra&longs;es of <emph type="italics"/>Vulgar Speech<emph.end type="italics"/>? </s> <s>So <emph type="italics"/>Eccle&longs;ia&longs;ticus,<emph.end type="italics"/> Chap. </s> <s>27. <lb/>ver&longs;. </s> <s>11. <emph type="italics"/>The godly man abideth in wi&longs;dome, as the Sun; but a <lb/>fool changeth as the Moon<emph.end type="italics"/>; and yet the Moon according to the <lb/>real truth of the matter no wayes changeth, but abides the &longs;ame <lb/>for ever, as <emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> demon&longs;trate, one half thereof remain­<lb/>ing alwayes lucid, and the other alwayes opacous. </s> <s>Nor at any <lb/>time doth this &longs;tate vary in it, unle&longs;&longs;e <emph type="italics"/>in re&longs;pect of us,<emph.end type="italics"/> and <emph type="italics"/>ac­<lb/>cording to the opinion of the Vulgar.<emph.end type="italics"/> Hence it is cleer, that the <lb/>holy Scripture &longs;peaks according to the common form of &longs;peech u­ <pb xlink:href="040/01/507.jpg" pagenum="483"/>&longs;ed among&longs;t the unlearned, and according to the appearance of <lb/>things, and not according to their true Exi&longs;tence. </s> <s>In like man­<lb/>ner <emph type="italics"/>Gene&longs;.<emph.end type="italics"/> 1. in the de&longs;cription of the Creation of all things, <lb/>the Light is &longs;aid to be made fir&longs;t of all, and yet it followeth in <lb/>the Text, <emph type="italics"/>And the Evening and the Morning made the fir&longs;t day<emph.end type="italics"/>: <lb/>and a little after the &longs;everal Acts of the Creation are di&longs;tingui&longs;hed <lb/>and a&longs;&longs;igned to &longs;everal days, and concerning each of them it is <lb/>&longs;aid in the Text, <emph type="italics"/>And the Evening and the Morning made the <lb/>&longs;econd day<emph.end type="italics"/>; and then <emph type="italics"/>the third day, the fourth day, &c.<emph.end type="italics"/> Hence <lb/>many doubts ari&longs;e, all which I &longs;hall propound according to the <lb/>common Sy&longs;teme, that it may appear even from the <emph type="italics"/>H<emph.end type="italics"/>ypothe&longs;is <lb/>of that Sy&longs;teme, that the &longs;acred Scripture &longs;ometimes, for the a­<lb/>voyding of emergent difficulties, is to be under&longs;tood in a vulgar <lb/>&longs;en&longs;e and meaning, and in re&longs;pect of us, and not according to <lb/>the nature of things. </s> <s>Which di&longs;tinction even <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf <lb/><arrow.to.target n="marg887"></arrow.to.target><lb/>&longs;eemeth to have hinted, when he &longs;aith, ^{*} <emph type="italics"/>Some things are more <lb/>intelligible to us; others by nature,<emph.end type="italics"/> or <emph type="italics"/>&longs;ecundum &longs;e.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg885"></margin.target>* Circa Cardi­<lb/>nes Cœli.</s></p><p type="margin"> <s><margin.target id="marg886"></margin.target>Luke 16.</s></p><p type="margin"> <s><margin.target id="marg887"></margin.target>Alia &longs;unt notio­<lb/>ra nobis, alia, no­<lb/>tiora natura, vel <lb/>&longs;ecundum &longs;e, <emph type="italics"/>A­<lb/>r &longs;t. </s> <s>lib. 1. Phy&longs;.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t therefore; If the light were made before heaven, then <lb/>it rolled about without heaven to the making of the di&longs;tinction <lb/>of Day and Night. </s> <s>Now this is contrary to the very doctrine <lb/>of the&longs;e men, who affirm that no Cœle&longs;tial Body can be moved <lb/>unle&longs;&longs;e <emph type="italics"/>per accidens,<emph.end type="italics"/> and by the motion of <emph type="italics"/>H<emph.end type="italics"/>eaven, <emph type="italics"/>and as a knot <lb/>in a board at the motion of the board.<emph.end type="italics"/> Again, if it be &longs;aid, that <lb/>the Light was created at the &longs;ame time with <emph type="italics"/>H<emph.end type="italics"/>eaven, and began <lb/>to be moved with <emph type="italics"/>H<emph.end type="italics"/>eaven, another doubt ari&longs;eth, that likewi&longs;e <lb/>oppo&longs;eth the fore&longs;aid common <emph type="italics"/>Hypothe&longs;is:<emph.end type="italics"/> For it being &longs;aid, <lb/>that Day and Night, Morning and Evening were made, that &longs;ame <lb/>is either in re&longs;pect of the Univer&longs;e, or onely in re&longs;pect of the <lb/>Earth and us. </s> <s>If &longs;o be that the Sun turning round (according to <lb/>the <emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> of the Common Sy&longs;teme) doth not cau&longs;e the <lb/>Night and Day, but only to opacous Bodies which are de&longs;titute <lb/>of all other light, but that of the Sun, whil&longs;t in their half part <lb/>(which is their <emph type="italics"/>Hemi&longs;phœre)<emph.end type="italics"/> and no more, (for that the Suns <lb/>light pa&longs;&longs;eth over but one half of an opacous Body, unle&longs;s a ve­<lb/>ry &longs;mall matter more in tho&longs;e of le&longs;&longs;er bulk) they are illumina­<lb/>ted by the Suns a&longs;pect, the other half remaining dark and tene­<lb/>bro&longs;e, by rea&longs;on of a &longs;hadow proceeding from its own Body. <lb/></s> <s>Therefore the di&longs;tinction of dayes by the light of heaven, ac­<lb/>cording to the de&longs;cription of them in the &longs;acred Scriptures, mu&longs;t <lb/>not be under&longs;tood <emph type="italics"/>ab&longs;olutely,<emph.end type="italics"/> and <emph type="italics"/>&longs;ecundum &longs;e,<emph.end type="italics"/> and <emph type="italics"/>Nature her <lb/>&longs;elf<emph.end type="italics"/>; but in re&longs;pect of the Earth, and of us its inhabitants, and <lb/>con&longs;equently <emph type="italics"/>&longs;ecundum nos.<emph.end type="italics"/> 'Tis not therefore new, nor unu­<lb/>&longs;ual in &longs;acred Scripture to &longs;peak of things <emph type="italics"/>&longs;ecundum nos,<emph.end type="italics"/> and on­<lb/>ly <emph type="italics"/>in re&longs;pect of us,<emph.end type="italics"/> and <emph type="italics"/>&longs;ecundum apparentiam<emph.end type="italics"/>; but not <emph type="italics"/>&longs;ecundum <lb/>&longs;e,<emph.end type="italics"/> and <emph type="italics"/>reinaturam,<emph.end type="italics"/> or <emph type="italics"/>Ab&longs;olutely<emph.end type="italics"/> and <emph type="italics"/>Simply.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/508.jpg" pagenum="484"/><p type="main"> <s>And if any one would under&longs;tand the&longs;e Days of &longs;acred Scri­<lb/>pture, not only <emph type="italics"/>&longs;ecundum nos,<emph.end type="italics"/> but al&longs;o <emph type="italics"/>&longs;ecundum naturam,<emph.end type="italics"/> as <lb/>circulations of Cœle&longs;tial Light returning to the &longs;elf &longs;ame point <lb/>from whence it did at fir&longs;t proceed; &longs;o as that there needs no <lb/>re&longs;pect to be had to Night or to ^{*} Darkne&longs;&longs;e, for which &longs;ole rea­<lb/><arrow.to.target n="marg888"></arrow.to.target><lb/>&longs;on we are fain to imbrace the Interpretation of &longs;acred Scripture <lb/><emph type="italics"/>&longs;ecundum nos<emph.end type="italics"/>; In oppo&longs;ition to this we may thus argue: If the <lb/>&longs;acred Scripture be under&longs;tood to &longs;peak <emph type="italics"/>ab&longs;olutely,<emph.end type="italics"/> of iterated <lb/>and &longs;ucce&longs;&longs;ive circulations of light, and not <emph type="italics"/>re&longs;pectu no&longs;tri,<emph.end type="italics"/> as if <lb/>the&longs;e words <emph type="italics"/>Evening and Morning<emph.end type="italics"/> had never been in&longs;erted, which <lb/>in their natural acceptation denote the Suns habitude to us and to <lb/>the Earth: For that the <emph type="italics"/>Morning<emph.end type="italics"/> is that time when the Sun be­<lb/>gins to wax light, and to ri&longs;e above the <emph type="italics"/>Horizon<emph.end type="italics"/> in the Ea&longs;t, <lb/>and become vi&longs;ible in our <emph type="italics"/>Hemi&longs;phœre,<emph.end type="italics"/> and <emph type="italics"/>Evening<emph.end type="italics"/> is the time <lb/>in which the Sun declines in the We&longs;t, and approacheth with its <lb/>light neerer to the other oppo&longs;ite <emph type="italics"/>Horizon<emph.end type="italics"/> and <emph type="italics"/>Hemi&longs;phœre,<emph.end type="italics"/><lb/>which is contiguous to this of ours. </s> <s>But the word <emph type="italics"/>Day<emph.end type="italics"/> is a Co­<lb/>relative to the word <emph type="italics"/>Night.<emph.end type="italics"/> From hence therefore it evidently <lb/>appeareth, that the&longs;e three words <emph type="italics"/>Evening, Morning,<emph.end type="italics"/> and <emph type="italics"/>Day,<emph.end type="italics"/><lb/>cannot be under&longs;tood of a Circulation of Light <emph type="italics"/>&longs;ecundum &longs;e,<emph.end type="italics"/><lb/>and <emph type="italics"/>ab&longs;olutè,<emph.end type="italics"/> but only <emph type="italics"/>&longs;ecundum nos,<emph.end type="italics"/> and <emph type="italics"/>re&longs;pectu no&longs;tri<emph.end type="italics"/>; and in <lb/>that &longs;en&longs;e indeed the <emph type="italics"/>Morning<emph.end type="italics"/> and <emph type="italics"/>Evening<emph.end type="italics"/> do make the <emph type="italics"/>Night<emph.end type="italics"/><lb/>and <emph type="italics"/>Day,<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg888"></margin.target>* Aut ad Umbram</s></p><p type="main"> <s>In like manner, <emph type="italics"/>Gen.<emph.end type="italics"/> 1. 16. it is &longs;aid, <emph type="italics"/>God made two great Lights; <lb/>the greater Light to rule the Day, and the le&longs;&longs;er Light to rule the <lb/>Night, and the Stars.<emph.end type="italics"/> Where both in the Propo&longs;ition and in the <lb/>&longs;pecification of it, things are &longs;poken which are very di&longs;agreeing <lb/>with Cœle&longs;tial Bodies. </s> <s>Therefore tho&longs;e words are in that place <lb/>to be interpreted according to the fore&longs;aid Rules; namely, ac­<lb/>cording to the third and fourth; &longs;o that they may be &longs;aid to be <lb/>under&longs;tood <emph type="italics"/>according to the &longs;en&longs;e of the vulgar, and the common <lb/>way of &longs;peaking,<emph.end type="italics"/> which is all one, as if we &longs;hould &longs;ay, <emph type="italics"/>&longs;ecundum <lb/>apparentiam,<emph.end type="italics"/> and <emph type="italics"/>&longs;ecundum nos, vel re&longs;pectu no&longs;tri.<emph.end type="italics"/> For fir&longs;t, it <lb/>is &longs;aid in the Propo&longs;ition, <emph type="italics"/>And God made two great Lights<emph.end type="italics"/>; <lb/>meaning by them the Sun and Moon, whereas according to the <lb/>truth of the matter the&longs;e are not the Greater Lights; For al­<lb/>though the Sun may be reckoned among&longs;t the Greater, the Moon <lb/>may not be &longs;o, unle&longs;s <emph type="italics"/>in re&longs;pect of us.<emph.end type="italics"/> Becau&longs;e among&longs;t <lb/>tho&longs;e that are ab&longs;olutely the Greater, and a little le&longs;&longs;er than the <lb/><arrow.to.target n="marg889"></arrow.to.target><lb/>Sun (nay in a manner equal to it) and far bigger than the Moon, <lb/>we may with great rea&longs;on enumerate <emph type="italics"/>Saturn,<emph.end type="italics"/> or &longs;ome of the <lb/>Fixed Stars of the fir&longs;t Magnitude, &longs;uch as <emph type="italics"/>Canopus,<emph.end type="italics"/> (otherwi&longs;e <lb/>called <emph type="italics"/>Arcanar)<emph.end type="italics"/> in the end of a River; or the <emph type="italics"/>Little Dog<emph.end type="italics"/> in <lb/>the mouth of the <emph type="italics"/>Great Dog<emph.end type="italics"/>; or the Foot of <emph type="italics"/>Orion,<emph.end type="italics"/> called <emph type="italics"/>Ri­<lb/>gel<emph.end type="italics"/>; or his <emph type="italics"/>Right &longs;houlder,<emph.end type="italics"/> or any other of that Magnitude. <pb xlink:href="040/01/509.jpg" pagenum="485"/>Therefore the <emph type="italics"/>two great Lights<emph.end type="italics"/> are to be under&longs;tood in re&longs;pect of <lb/>us, and according to vulgar e&longs;timation, and not according to the <lb/>true and reall exi&longs;tence of &longs;uch Bodies. </s> <s>Secondly, in the &longs;peci­<lb/>fication of the Propo&longs;ition it is &longs;aid, <emph type="italics"/>The greater Light to rule the <lb/>Day<emph.end type="italics"/>; hereby denoting the Sun; in which the verbal &longs;en&longs;e of <lb/>Scripture agreeth with the Truth of the Thing; For that the Sun <lb/>is the Greate&longs;t of all Luminaries, and Globes. </s> <s>But that which <lb/>followeth immediately after, <emph type="italics"/>And the le&longs;&longs;er Light to rule the <lb/>Night,<emph.end type="italics"/> meaning the Moon, cannot be taken in the true and real <lb/>&longs;en&longs;e of the words: For the Moon is not the le&longs;&longs;er Light, but <lb/><emph type="italics"/>Mercury<emph.end type="italics"/>; which is not only much le&longs;&longs;er than the Moon, but al&longs;o <lb/>than any other Star. </s> <s>And if, again, it be &longs;aid, That the Holy <lb/>Text doth not &longs;peak of the Stars, but onely of the Luminaries, <lb/>for that pre&longs;ently after they are mentioned apart, <emph type="italics"/>And the Stars<emph.end type="italics"/>; <lb/>and that what we &longs;ay is true touching the compari&longs;on of the Stars <lb/>among&longs;t them&longs;elves, but not in re&longs;pect of the Luminaries, name­<lb/>ly, the Sun and Moon: This reply doth di&longs;cover a man to be <lb/>utterly ignorant in the&longs;e Studies, and &longs;uch who having not the <lb/>lea&longs;t &longs;mattering in them, doth conceive an ab&longs;urd and erroneous <lb/>Opinion of the Cœle&longs;tial Bodies. </s> <s>For the Moon and Sun, con­<lb/>&longs;idered in them&longs;elves, and as they appear to us, if they &longs;hould <lb/>be a far greater di&longs;tance from us, than indeed they are, would be <lb/>no other, nor would appear to us otherwi&longs;e than Stars, as the <lb/>re&longs;t do in the Firmament. </s> <s>But Great Luminaries they neither <lb/><arrow.to.target n="marg890"></arrow.to.target><lb/>are, nor &longs;eem to be, &longs;ave only <emph type="italics"/>in re&longs;pect of us:<emph.end type="italics"/> And &longs;o, on <lb/>the other &longs;ide, the Stars, as to them&longs;elves, are no other than &longs;o <lb/>many Suns and &longs;o many Moons; yet are &longs;o far remote from us, <lb/>that by rea&longs;on of their di&longs;tance they appear thus &longs;mall, and dim <lb/>of light, as we behold them. </s> <s>For the greater and le&longs;&longs;er di&longs;tance <lb/>of heavenly Bodies <emph type="italics"/>(cæteris paribus)<emph.end type="italics"/> doth augment and dimini&longs;h <lb/>their appearance both as to Magnitude and Light. </s> <s>And there­<lb/>fore the words which follow in that place of <emph type="italics"/>Gene&longs;is, And the <lb/>Stars<emph.end type="italics"/> (as di&longs;tingui&longs;hing the Stars from the Sun and Moon) are <lb/>to be taken in no other acceptation than that which we have &longs;po­<lb/>ken of, namely, <emph type="italics"/>according to the &longs;en&longs;e of the Vulgar, and the <lb/>common manner of &longs;peech.<emph.end type="italics"/> For indeed, according to the truth <lb/>of the matter, all Cœle&longs;tial Bodies, being &longs;hining Globes, are of <lb/>a va&longs;t bigne&longs;s, to which if we &longs;hould be &longs;o neer as we are to the <lb/>Moon, they would &longs;eem to us of as great, yea a greater magni­<lb/>tude than the Moon: As likewi&longs;e on the contrary, if we were as <lb/>far di&longs;tant from the Sun and Moon, as we are from them, both <lb/>Moon and Sun would &longs;hew but as &longs;tars to us. </s> <s>And yet the <lb/>&longs;plendor of the Sun would doubtle&longs;s be greater <emph type="italics"/>inten&longs;ivè<emph.end type="italics"/> than <lb/>that of any other &longs;tar. </s> <s>For, although it &longs;hould be granted that <lb/>&longs;ome &longs;tars (as tho&longs;e of the Fixed that twinkle) do &longs;hine of them­ <pb xlink:href="040/01/510.jpg" pagenum="486"/>&longs;elves, aud by their own nature, as the Sun, that derives not its <lb/>light from others (which yet remains undecided and doubtful) <lb/>and borrow not their light from the Sun; Neverthele&longs;s &longs;ince the <lb/>brightne&longs;s of none of the &longs;tars may be compared with the Suns <lb/>&longs;plendour, which was created by God fir&longs;t, and before all other <lb/>Luminaries, in the highe&longs;t kind of Light, it would therefore <lb/>notwith&longs;tanding follow, that none of tho&longs;e &longs;tars, although pla­<lb/>ced in the &longs;ame proximity to us with the Sun, and therefore ap­<lb/>pearing to us of the &longs;ame Magnitude as the Sun, can be&longs;tow up­<lb/>on us &longs;o much Light as we receive from the Sun: As on the <lb/>contrary, the Sun, at the &longs;ame remotene&longs;&longs;e from us as they are, <lb/>would indeed, as to its Magnitude, appear to us as one of tho&longs;e <lb/>&longs;tars, but of a &longs;plendour much more <emph type="italics"/>inten&longs;e<emph.end type="italics"/> than that of theirs. <lb/><arrow.to.target n="marg891"></arrow.to.target><lb/>So that, now, the Earth is nothing el&longs;e but another Moon or &longs;tar, <lb/>and &longs;o would it appear to us, if we &longs;hould behold it from a con­<lb/>venient di&longs;tance <emph type="italics"/>on high.<emph.end type="italics"/> And in it might be ob&longs;erved (in that <lb/>variety of Light and Darkne&longs;s which the Sun produceth in it by <lb/>making Day and Night) the &longs;ame difference of A&longs;pects that are <lb/>&longs;een in the Moon, and &longs;uch as are ob&longs;erved in tricorporate <emph type="italics"/>Ve­<lb/>nus<emph.end type="italics"/>; in like manner al&longs;o 'tis very probable that the &longs;ame might <lb/>be di&longs;cerned in other Planets, which &longs;hine by no light of their <lb/>own, but by one borrowed from the Sun. </s> <s>What ever there­<lb/>fore may touching the&longs;e matters be delivered in the &longs;acred Leaves <lb/>or the common &longs;peech of men, di&longs;&longs;enting from the real truth, it <lb/>ought (as we have &longs;aid before) ab&longs;olutely to be received and un­<lb/>der&longs;tood <emph type="italics"/>&longs;ecundum vulgi &longs;ententiam, & communem loquendi & <lb/>concipiendi &longs;tylum.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg889"></margin.target><emph type="italics"/>Which are really <lb/>the great Lights <lb/>in Heaven.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg890"></margin.target><emph type="italics"/>The Sun, Moon, <lb/>and Stars are one <lb/>& the &longs;ame thing.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg891"></margin.target><emph type="italics"/>The Earth is a­<lb/>nother Moon or <lb/>Star.<emph.end type="italics"/></s></p><p type="main"> <s>And &longs;o, to return to our purpo&longs;e, if, all this con&longs;idered, the <lb/><emph type="italics"/>Pythagorian<emph.end type="italics"/> opinion be true, it will be ea&longs;ie, according to the <lb/>&longs;ame Rule, to reconcile the authority of &longs;acred Scriptures with <lb/>it, however they &longs;eem to oppo&longs;e it, and in particular tho&longs;e of the <lb/>fir&longs;t and &longs;econd Cla&longs;&longs;is, <emph type="italics"/>&longs;cilicet<emph.end type="italics"/> by my fir&longs;t <emph type="italics"/>Maxime:<emph.end type="italics"/> For that in <lb/>tho&longs;e places the holy Records &longs;peak according to our manner of <lb/>under&longs;tanding, and according to that which appeareth in re&longs;pect <lb/>of us; <emph type="italics"/>For thus it is with tho&longs;e Bodies, in compari&longs;on of us, and<emph.end type="italics"/><lb/><arrow.to.target n="marg892"></arrow.to.target><lb/><emph type="italics"/>as they are de&longs;cribed by the vulgar and commune way of humane <lb/>Di&longs;cour&longs;e; So that the Earth appears as if it were &longs;tanding &longs;till <lb/>and immoveable, and the Sun, as if it were circumambient about <lb/>her.<emph.end type="italics"/> And &longs;o the Holy Scripture is u&longs;ed in the Commune and <lb/>Vulgar way of &longs;peaking; becau&longs;e in re&longs;pect of our &longs;ight, the <lb/>Earth &longs;eems rather to &longs;tand fixed in the Centre, and the Sun to <lb/>circumvolve about it, than otherwi&longs;e: as it happens to tho&longs;e that <lb/>are putting off from the Banks of a River to whom the &longs;hose <lb/>&longs;eems to move backwards, and go from them: but they do not <lb/>perceive (which yet is the truth) that they them&longs;elves go forwards. <pb xlink:href="040/01/511.jpg" pagenum="487"/>Which fallacy of our &longs;ight is noted, and the Rea&longs;on thereof a&longs;­<lb/>&longs;igned by the Opticks; upon wich, as being &longs;trange to, and be­<lb/>&longs;ides my purpo&longs;e, I will not &longs;tay) and on this account is <emph type="italics"/>Æneas<emph.end type="italics"/><lb/>brought in by <emph type="italics"/>Virgil,<emph.end type="italics"/> &longs;aying;<lb/><arrow.to.target n="marg893"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg892"></margin.target><emph type="italics"/>Why the Sunne <lb/>&longs;eemeth to us to <lb/>move, & not the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg893"></margin.target><emph type="italics"/>Æneid.<emph.end type="italics"/> 3.</s></p><p type="head"> <s><emph type="italics"/>Provehimur portu, terræque urbe&longs;que recedunt.<emph.end type="italics"/></s></p><p type="main"> <s>But it will not be ami&longs;s to con&longs;ider why the &longs;acred Scripture <lb/>doth &longs;o &longs;tudiou&longs;ly comply with the opinions of the Vulgar, and <lb/>why it doth not rather accurately in&longs;truct men in the truth of the <lb/>matters, and the &longs;ecrets of Nature. </s> <s>The Rea&longs;on is, fir&longs;t, the be­<lb/>nignity of Divine Wi&longs;dome, whereby it &longs;weetly accomodates it <lb/>&longs;elf to all things, in proportion to their Capacity and Nature. <lb/></s> <s>Whence in Natural Sciences, it u&longs;eth natural and nece&longs;&longs;ary cau­<lb/>&longs;es, but in Liberal Arts it worketh liberally, upon Generous <lb/>Per&longs;ons after a &longs;ublime and lofty manner; upon the Common <lb/>People, familiarly and humbly; upon the Skilful, learnedly; <lb/>upon the Simple, vulgarly; and &longs;o on every one, according to <lb/>his condition and quality. </s> <s>Secondly, becau&longs;e it is not its In­<lb/>tention to fill our mindes in this life with vain and various curi­<lb/>o&longs;ities, which might occa&longs;ion our doubt and &longs;u&longs;pen&longs;e. </s> <s>For the <lb/><arrow.to.target n="marg894"></arrow.to.target><lb/>truth is, <emph type="italics"/>(a) He that increa&longs;eth knowledge, increa&longs;eth &longs;orrow.<emph.end type="italics"/><lb/>Moreover it did not only permit, but even decree, thatth e <lb/>World &longs;hould be very much bu&longs;ied in Controver&longs;ies and Di&longs;pu­<lb/>tations, and that it &longs;hould be imployed about the uncertainty of <lb/><arrow.to.target n="marg895"></arrow.to.target><lb/>things; according to that &longs;aying of <emph type="italics"/>Eccle&longs;ia&longs;tes<emph.end type="italics"/> <emph type="italics"/>(b) He hath <lb/>&longs;et the World in their heart; &longs;o that no man can find out the work <lb/>that God maketh from the beginning unto the end.<emph.end type="italics"/> And touching <lb/>tho&longs;e doubts, God will not permit that they &longs;hall be di&longs;covered <lb/><arrow.to.target n="marg896"></arrow.to.target><lb/>to us before the end of the World: <emph type="italics"/>(c) At which time he will <lb/>bring to light the hidden things of darkne&longs;&longs;e:<emph.end type="italics"/> But Gods onely <lb/>&longs;cope in the &longs;acred Scripture is to teach men tho&longs;e things which <lb/>conduce to the attainment of Eternal Life; which having ob­<lb/><arrow.to.target n="marg897"></arrow.to.target><lb/>tained, <emph type="italics"/>(d) We &longs;hall &longs;ee him face to face: (e) and &longs;hall be<emph.end type="italics"/><lb/><arrow.to.target n="marg898"></arrow.to.target><lb/><emph type="italics"/>like him, for we &longs;hall &longs;ee him as he is.<emph.end type="italics"/> Then &longs;hall he clearly <emph type="italics"/>à <lb/>Priori<emph.end type="italics"/> make known unto us all tho&longs;e Curio&longs;ities, and Dogmati­<lb/>cal Que&longs;tions, which in this life, <emph type="italics"/>(f) in which we &longs;ee through a<emph.end type="italics"/><lb/><arrow.to.target n="marg899"></arrow.to.target><lb/><emph type="italics"/>Gla&longs;&longs;e darkly,<emph.end type="italics"/> could be known by us but imperfectly and <emph type="italics"/>à po&longs;te­<lb/>riori,<emph.end type="italics"/> and that not without much pains and &longs;tudy. </s> <s>For this <lb/>cau&longs;e the Wi&longs;dome of God, revealed to us in the &longs;acred Leaves, <lb/>is not &longs;tiled Wi&longs;dome ab&longs;olutely, but <emph type="italics"/>(g) Saving Wi&longs;dome<emph.end type="italics"/>; <lb/><arrow.to.target n="marg900"></arrow.to.target><lb/>Its onely end being to lead us to &longs;alvation. </s> <s>And S. <emph type="italics"/>Paul<emph.end type="italics"/> preach­<lb/>ing to the <emph type="italics"/>Corinthians,<emph.end type="italics"/> &longs;aith; <emph type="italics"/>(h) I determined to know nothing<emph.end type="italics"/><lb/><arrow.to.target n="marg901"></arrow.to.target><lb/><emph type="italics"/>among you, &longs;ave Je&longs;us Chri&longs;t, and him crucified:<emph.end type="italics"/> whereas not­<lb/>with&longs;tanding he was thorowly in&longs;tructed, and profoundly learned <pb xlink:href="040/01/512.jpg" pagenum="488"/>in all humane Sciences; but making no account of the&longs;e things <lb/>he profe&longs;&longs;eth that it was his de&longs;ire to teach them no more but the <lb/>way to Heaven. </s> <s>Hence is that which God &longs;peaketh to us by <lb/><arrow.to.target n="marg902"></arrow.to.target><lb/><emph type="italics"/>I&longs;aiah,<emph.end type="italics"/> <emph type="italics"/>(i) Ego Dominus Deus, docens te utilia<emph.end type="italics"/> [<emph type="italics"/>I am the Lord <lb/>thy God which teacheth thee profitable things:<emph.end type="italics"/>] Where the <emph type="italics"/>Glo&longs;­<lb/>&longs;ary<emph.end type="italics"/> addeth, <emph type="italics"/>non &longs;ubtilia<emph.end type="italics"/> [not &longs;ubtilties.] For God neither taught <lb/>us, Whether the <emph type="italics"/>Materia Prima<emph.end type="italics"/> of Heaven, and the Elements <lb/>be the &longs;ame; nor Whether <emph type="italics"/>Cominual<emph.end type="italics"/> be compo&longs;ed of Indivi&longs;i­<lb/>bles, or whether it be divi&longs;ible <emph type="italics"/>in infinitum<emph.end type="italics"/>; nor, whether the <lb/>Elements are formally <emph type="italics"/>mixt<emph.end type="italics"/>; nor how many the Cœle&longs;tial <lb/>Spheres, and their Orbs are; Whether there be Epicycles or <lb/>Eccentricks; nor the Vertues of Plants and Stones; nor the Na­<lb/>ture of Animals; nor the Motion and Influence of the Planets; <lb/>nor the Order of the Univer&longs;e; nor the Wonders of Minerals, <lb/>and univer&longs;al Nature: but only [<emph type="italics"/>utilia:<emph.end type="italics"/>] things profitable, to <lb/>wit, his Holy Law ordained to the end, that we being put into <lb/>po&longs;&longs;e&longs;&longs;ion of Ble&longs;&longs;edne&longs;s, might at length be made capable of all <lb/>perfect knowledge, and the vi&longs;ion of the whole Order and ad­<lb/>mirable Harmony, as al&longs;o the Sympathy and Antipathy of the <lb/>Univer&longs;e and its parts, <emph type="italics"/>in his Word,<emph.end type="italics"/> wherein all tho&longs;e <lb/>things &longs;hall mo&longs;t clearly and di&longs;tinctly, then, appear to us, which <lb/>mean while, in this life, he hath remitted (as far as its ability <lb/>reacheth) to humane &longs;earch and enquiry: But it was not his <lb/>purpo&longs;e to determine any thing, directly or indirectly, touching <lb/>the truth of them. </s> <s>Becau&longs;e as the knowledge thereof would lit­<lb/>tle or nothing profit Us, but might in &longs;ome ca&longs;es prove prejudi­<lb/>cial; &longs;o the ignorance thereof can doubtle&longs;s be no detriment, <lb/>but may in &longs;ome ca&longs;es be very beneficial to us. </s> <s>And therefore <lb/>by his mo&longs;t admirable Wi&longs;dome it comes to pa&longs;s, that though all <lb/>things in this World are dubious, uncertain, wavering, and per­<lb/>plexed; yet his Holy Faith alone is mo&longs;t certain; and although <lb/>the opinions about Philo&longs;ophical and Doctrinal points be divers, <lb/>there is in the Church but one Truth of Faith and Salvation. <lb/></s> <s>Which Faith, as nece&longs;sary to Salvation, is &longs;o ordered by Divine <lb/>Providence, that it might not only be indubitable, but al&longs;o un­<lb/>&longs;haken, &longs;ure, immutable, and manife&longs;t to all men: the infallible <lb/>Rule of which he hath appointed the Holy Church, that is wa&longs;h­<lb/>ed with his precious Blood, and governed by his Holy Spirit, to <lb/>whom belongs our Sanctification, as being his work. </s> <s>This there­<lb/><arrow.to.target n="marg903"></arrow.to.target><lb/>fore is the Rea&longs;on why God would have Speculative Que&longs;tions, <lb/>which nothing conduce to our Salvation and Edification, and why <lb/>the Holy Gho&longs;t hath very often conde&longs;cended to Vulgar Opini­<lb/>ons and Capacities, and hath di&longs;covered nothing that is &longs;ingular <lb/>or hidden to us, be&longs;ides tho&longs;e things that pertain to Salvation. <lb/></s> <s>So that con&longs;equently it is clear by what hath been &longs;aid, how and <pb xlink:href="040/01/513.jpg" pagenum="489"/>why nothing of certainty can be evinced from the fore&longs;aid Au­<lb/>thorities to the determining of Controver&longs;ies of this Nature; as <lb/>al&longs;o with what Rea&longs;on from this fir&longs;t <emph type="italics"/>Axiome<emph.end type="italics"/> the Objections of <lb/>the fir&longs;t and &longs;econd Cla&longs;&longs;e are ea&longs;ily an&longs;wered, as al&longs;o any other <lb/>Authority of &longs;acred Scripture produced again&longs;t the <emph type="italics"/>Pythagorian<emph.end type="italics"/><lb/>and <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;teme &longs;o long as by other proofs it is true.</s></p><p type="margin"> <s><margin.target id="marg894"></margin.target><emph type="italics"/>(a)<emph.end type="italics"/> Eccle&longs;. <emph type="italics"/>c. </s> <s>1. v. <lb/></s> <s>ult.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg895"></margin.target><emph type="italics"/>(b) Chap. </s> <s>3. v.<emph.end type="italics"/> 11.</s></p><p type="margin"> <s><margin.target id="marg896"></margin.target><emph type="italics"/>(c)<emph.end type="italics"/> 1 Cor. <emph type="italics"/>c. </s> <s>4. v.<emph.end type="italics"/> 5</s></p><p type="margin"> <s><margin.target id="marg897"></margin.target><emph type="italics"/>(d)<emph.end type="italics"/> 1 Cor. <emph type="italics"/>c. </s> <s>13. v.<emph.end type="italics"/><lb/>12.</s></p><p type="margin"> <s><margin.target id="marg898"></margin.target><emph type="italics"/>(e)<emph.end type="italics"/> 1 John <emph type="italics"/>c. </s> <s>3. v.<emph.end type="italics"/><lb/>2.</s></p><p type="margin"> <s><margin.target id="marg899"></margin.target><emph type="italics"/>(f)<emph.end type="italics"/> 1 Cor. <emph type="italics"/>c. </s> <s>13. v.<emph.end type="italics"/><lb/>12.</s></p><p type="margin"> <s><margin.target id="marg900"></margin.target><emph type="italics"/>(g)<emph.end type="italics"/> Eccle&longs;ia&longs;t. </s> <s>15. 3</s></p><p type="margin"> <s><margin.target id="marg901"></margin.target><emph type="italics"/>(h)<emph.end type="italics"/> 1 Cor. <emph type="italics"/>c. </s> <s>2. v.<emph.end type="italics"/> 2</s></p><p type="margin"> <s><margin.target id="marg902"></margin.target><emph type="italics"/>(i)<emph.end type="italics"/> I&longs;a. <emph type="italics"/>c. </s> <s>48. v.<emph.end type="italics"/> 17.</s></p><p type="margin"> <s><margin.target id="marg903"></margin.target>1 The&longs;&longs;. </s> <s>4.</s></p><p type="main"> <s>And the Authorities of the &longs;econd Cla&longs;&longs;e in particular by <lb/>this &longs;ame Maxime, <emph type="italics"/>Of the ordinary manner of apprehending <lb/>things as they appear to us, and after the common way of &longs;peak­<lb/>ing,<emph.end type="italics"/> may be thus reconciled and expounded; namely, Oftentimes <lb/>an Agent is commonly, and not improperly &longs;aid to move, (though <lb/>it have no motion) not becau&longs;e it doth indeed move, but <emph type="italics"/>by ex­<lb/>trin&longs;ick denomination,<emph.end type="italics"/> becau&longs;e receiving its influence and action at <lb/>the motion of the Subject; the Form and Quality infu&longs;ed to <lb/>the Subject by the &longs;aid Agent doth likewi&longs;e move. </s> <s>As for ex­<lb/>ample, a Fire burning in a Chimney is an immoveable Agent, <lb/>before which a man oppre&longs;t with cold &longs;its to warm him&longs;elf who <lb/>being warmed on one &longs;ide, turns the other to the Fire, that he <lb/>may be warmed on that &longs;ide al&longs;o, and &longs;o in like manner he holds <lb/>every part to the Fire &longs;ucce&longs;&longs;ively, till his whole body be warm­<lb/>ed. 'Tis clear, that although the Fire do not move, yet at the <lb/>Motion of the Subject, to wit the Man, who receiveth the heat <lb/>and action of the Fire, the Form and Quality of its Heat doth <lb/>move <emph type="italics"/>&longs;ingulatim, & per partes,<emph.end type="italics"/> round about the mans body, and <lb/>alwayes &longs;eeketh out a new place: and &longs;o, though the Fire do <lb/>not move, yet by rea&longs;on of its effect, it is &longs;aid to go round all <lb/>the parts of the Mans body, and to warm it, not indeed by a <lb/>true and real motion of the Fire it &longs;elf, &longs;ince it is &longs;uppo&longs;ed (and <lb/>that not untruly) not to move, but by the motion to which the <lb/>Body is excited, out of a de&longs;ire of receiving the heat of the Fire <lb/>in each of its parts. </s> <s>The &longs;ame may be applied to the Illumina­<lb/>tion impre&longs;&longs;ed &longs;ucce&longs;&longs;ively on the parts of any Globe, which <lb/>moves Orbicularly at the a&longs;pect of a &longs;hining immoveable <lb/>Light. </s> <s>And in the &longs;ame manner may the Sun be &longs;aid to ri&longs;e and <lb/>&longs;et, and to move above the Earth, although in reality he doth <lb/>not move, nor &longs;uffer any mutation; that is to &longs;ay, Ina&longs;much as <lb/>his Light (which effect is the Form and Quality proceeding from <lb/>him, as the Agent, to the Earth as the Subject) doth &longs;en&longs;ibly <lb/>glide forwards, by rea&longs;on of the Orbicular motion of the Earth; <lb/>and doth alwayes be take it &longs;elf to &longs;ome new place of her &longs;urface; <lb/>upon which ground he is truly &longs;aid <emph type="italics"/>(&longs;ecundum vnlgarem &longs;ermo­<lb/>nem)<emph.end type="italics"/> to move above, and revolve about the Earth: Not that the <lb/>Sun doth move, (for by this Opinion we affirm the Earth to <lb/>move, that it may receive the Sun one while in one, another <lb/>while in another part of it) but that at the motion of the Earth <pb xlink:href="040/01/514.jpg" pagenum="490"/>her &longs;elf a contrary way, the Quality diffu&longs;ed into her, and im­<lb/>pre&longs;&longs;ed upon her by the Sun, namely the Light of the Day is <lb/>moved, which ri&longs;eth in one part of her, and &longs;ets in another con­<lb/>trary to that, according to the nature and condition of her motion; <lb/>And for this rea&longs;on the Sun it &longs;elf by con&longs;equence is &longs;aid to ri&longs;e <lb/>and &longs;et, (which notwith&longs;tanding <emph type="italics"/>ex Hypothe&longs;i<emph.end type="italics"/> &longs;tands immovea­<lb/>ble) and that no otherwi&longs;e then <emph type="italics"/>per donominationem extrin&longs;ecam,<emph.end type="italics"/><lb/>as hath been &longs;aid.</s></p><p type="main"> <s>After this manner the command of <emph type="italics"/>Jo&longs;huah, Sun &longs;tand thou<emph.end type="italics"/><lb/><arrow.to.target n="marg904"></arrow.to.target><lb/><emph type="italics"/>&longs;till,<emph.end type="italics"/> and the Miracle of the Suns ce&longs;&longs;ation of Motion wrought <lb/>by him, may be &longs;o under&longs;tood, as that not the Solar Body pro­<lb/>perly, but the Suns &longs;plendour upon the Earth &longs;tood &longs;till; &longs;o that <lb/>not the Sun it &longs;elf, (being of it &longs;elf before that time immovea­<lb/>ble) but the Earth that receiveth its &longs;plendour, &longs;tayed her Mo­<lb/>tion; which, as &longs;he ince&longs;&longs;antly pur&longs;uing her ordinary Motion to­<lb/><arrow.to.target n="marg905"></arrow.to.target><lb/>wards the Ea&longs;t, ^{*} called up the Light of the Sun in the We&longs;t, &longs;o <lb/>&longs;tanding &longs;till, the Suns light impre&longs;t upon it likewi&longs;e &longs;tood &longs;till. <lb/><arrow.to.target n="marg906"></arrow.to.target><lb/>After the &longs;ame manuer pioportionally is that Text of <emph type="italics"/>I&longs;aiah<emph.end type="italics"/> ex­<lb/>plained, touching the Suns going ten degrees back ward upon the <lb/>Dial of <emph type="italics"/>Ahaz.<emph.end type="italics"/> So (which may &longs;erve for another Example) the <lb/>Hand being moved about the flame of a burning Candle that <lb/>&longs;tands &longs;till, the Light moveth on the Hand, that is to &longs;ay, the <lb/>&longs;aid Hand is illu&longs;trated now in one part, anon in another, when <lb/>as the Candle it &longs;elf all the while removes not out of its place: <lb/>whereupon <emph type="italics"/>per denominationem extrin&longs;ecam,<emph.end type="italics"/> the &longs;aid Light may <lb/>be affirmed to ri&longs;e and &longs;et upon the Hand, namely, by the &longs;ole <lb/>motion of the &longs;aid Hand, the Candle it &longs;elf never moving all the <lb/>while. </s> <s>And let this &longs;uffice for the explanation of my fir&longs;t Prin­<lb/>ciple or <emph type="italics"/>Maxime,<emph.end type="italics"/> which by rea&longs;on of its difficulty and extraordi­<lb/>nary weight required &longs;ome prolixity in the handling of it.</s></p><p type="margin"> <s><margin.target id="marg904"></margin.target>Jo&longs;hua <emph type="italics"/>c. </s> <s>10. <lb/>ver.<emph.end type="italics"/> 12.</s></p><p type="margin"> <s><margin.target id="marg905"></margin.target><emph type="italics"/>* expected.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg906"></margin.target>I&longs;a. <emph type="italics"/>c. </s> <s>38. v.<emph.end type="italics"/> 8.</s></p><p type="main"> <s>My &longs;econd Maxime is this, Things both Spiritual and Cor­<lb/>poreal, Durable and Corruptible, Moveable and Immoveable, <lb/>have received from God a perpetual, unchangeable, and inviola­<lb/>ble Law, con&longs;tituting the E&longs;&longs;ence and Nature of every one of <lb/>them: according to which Law all of them in their own Na­<lb/>ture per&longs;i&longs;ting in a certain Order and Con&longs;tancy, and ob&longs;erving <lb/>the &longs;ame perpetual Cour&longs;e, may de&longs;ervedly be &longs;tiled mo&longs;t Stable <lb/>and Determinate. </s> <s>Thus Fortune (than which there is nothing <lb/>in the World more incon&longs;tant or fickle) is &longs;aid to be con&longs;tant <lb/>and unalterable in her continual volubility, vici&longs;&longs;itude, and in­<lb/>con&longs;tancy, which was the occa&longs;ion of that Ver&longs;e,</s></p><p type="head"> <s><emph type="italics"/>Et &longs;emper con&longs;tans in levitate &longs;ua e&longs;t.<emph.end type="italics"/></s></p><p type="main"> <s>And thus the motion of Heaven (which by the con&longs;tan Law <pb xlink:href="040/01/515.jpg" pagenum="491"/>of Nature ought to be perpetual) may be &longs;aid to be immutable <lb/>and immoveable, and the Heavens them&longs;elves to be immovea­<lb/>bly moved, and Terrene things to be immutably changed, be­<lb/>cau&longs;e tho&longs;e never cea&longs;e moving, nor the&longs;e changing. </s> <s>By this Prin­<lb/>ciple or Maxime all difficulties belonging to the fir&longs;t Cla&longs;&longs;is are <lb/>cleared, by which the Earth is &longs;aid to be &longs;table and immoveable, <lb/>that is, by under&longs;tanding this one thing, That the Earth, as to its <lb/>own Nature, though it include in it &longs;elf a local Motion, and that <lb/>threefold, according to the opinion of <emph type="italics"/>Copernicus (&longs;cilicet<emph.end type="italics"/> Diur­<lb/><arrow.to.target n="marg907"></arrow.to.target><lb/>nal, with which it revolveth about its own Centre; Annual, <lb/>by which it moveth through the twelve Signes of the Zodiack, <lb/>and the motion of Inclination, by which its Axis is alwayes op­<lb/>po&longs;ed to the &longs;ame part of the World) as al&longs;o other Species of <lb/>Mutation, &longs;uch as Generation and Corruption, Accretion and <lb/>Diminution, and Alteration of divers kinds; yet in all the&longs;e &longs;he <lb/>is &longs;table & con&longs;tant, never deviating from that Order which God <lb/>hath appointed her, but moveth continually, con&longs;tantly and im­<lb/>mutably, according to the &longs;ix before named Species of Motion.</s></p><p type="margin"> <s><margin.target id="marg907"></margin.target><emph type="italics"/>Several Motions <lb/>of the Earth ac­<lb/>cording to<emph.end type="italics"/> Coper­<lb/>nicus.</s></p><p type="main"> <s>My third Maxime &longs;hall be this; When a thing is moved ac­<lb/>cording to &longs;ome part of it, and not according to its whole, it <lb/>cannot be &longs;aid to be <emph type="italics"/>&longs;imply & ab&longs;olutely<emph.end type="italics"/> moved, but only <emph type="italics"/>per acci­<lb/>dens,<emph.end type="italics"/> for that &longs;tability taken &longs;imply & ab&longs;olutly do rather accord <lb/>with the &longs;ame. </s> <s>As for example, if a Barrel or other mea&longs;ure of <lb/>Water be taken out of the Sea, and transferred to another place, <lb/>the Sea may not therefore <emph type="italics"/>ab&longs;olutely & &longs;imply<emph.end type="italics"/> be &longs;aid to be remo­<lb/>ved from place to place; but only <emph type="italics"/>per accidens,<emph.end type="italics"/> and <emph type="italics"/>&longs;ecundum <lb/>quid,<emph.end type="italics"/> that is, according to a part of it, but rather (to &longs;peak &longs;im­<lb/>ply) we &longs;hould &longs;ay that the Sea cannot be carried or moved out of <lb/>its proper place,, though as to its parts it be moved, and transfer­<lb/>red to & again. </s> <s>This Maxime is manife&longs;t of it &longs;elf, and by it may <lb/>the Authorities be explained which &longs;eem to make for the immo­<lb/>bility of the Earth in this manner; namely, The Earth <emph type="italics"/>per &longs;e & <lb/>ab&longs;olutè<emph.end type="italics"/> con&longs;idered as to its <emph type="italics"/>Whole,<emph.end type="italics"/> is not mutable, &longs;eeing it is <lb/>neither generated nor corrupted neither increa&longs;ed nor dimini&longs;hed; <lb/>neither is it altered <emph type="italics"/>&longs;ecundum totum,<emph.end type="italics"/> but only <emph type="italics"/>&longs;ecundum partes.<emph.end type="italics"/><lb/><arrow.to.target n="marg908"></arrow.to.target><lb/>Now it plainly appears, that this is the genuine and true Sen&longs;e of <lb/>what is a&longs;cribed to it out of <emph type="italics"/>Eccle&longs;ia&longs;tes, cap. 1. v. </s> <s>4. One Generation <lb/>pa&longs;&longs;eth away, and another Generation cometh, but the Earth abideth <lb/>for ever<emph.end type="italics"/>: as if he &longs;hould &longs;ay; although the Earth, according to its <lb/>parts, doth generate and corrupt, and is liable to the vici&longs;&longs;itudes of <lb/>Generation and corruption, yet in reference to its Whole it never <lb/>generateth nor Corrupteth, but abideth immutable for ever: <lb/>Like as a Ship, which though it be mended one while in the Sail­<lb/>yard, another while in the Stern, and afterwards in other parts <lb/>it yet remains the &longs;ame Ship as it was at fir&longs;t. </s> <s>But tis to be ad­ <pb xlink:href="040/01/516.jpg" pagenum="492"/>vertized, that that Scripture doth not &longs;peak of a Local Motion, <lb/>but of Mutations of another nature; as in the very &longs;ub&longs;tance, <lb/>quantity or quality of the Earth it &longs;elf. </s> <s>But if it be &longs;aid, that <lb/>it is to be under&longs;tood of a Local Motion, then it may be ex­<lb/>plained by the in&longs;uing Maxime, that is to &longs;ay, a re&longs;pect being had <lb/>to the natural Place a&longs;&longs;igned it in the Univer&longs;e, as &longs;hall be &longs;hewed <lb/>by and by.</s></p><p type="margin"> <s><margin.target id="marg908"></margin.target><emph type="italics"/>The Earth Se-<emph.end type="italics"/><lb/>cundum Totum <emph type="italics"/>is <lb/>Immutable, <lb/>though not Immo­<lb/>vable.<emph.end type="italics"/></s></p><p type="main"> <s>The fourth Axiome is this; That every Corporeal thing, mo­<lb/>veable or immoveable from its very fir&longs;t Creation, is alotted its <lb/>proper and natural place; and being drawn or removed from <lb/>thence, its motion is violent, and it hath a natural tendency to <lb/>move back thither again: al&longs;o that nothing can be moved from <lb/>its natural place, <emph type="italics"/>&longs;ecundum Totum<emph.end type="italics"/>; For mo&longs;t great and dread&longs;ul <lb/>mi&longs;chiefs would follow from that perturbation of things in the <lb/>Univer&longs;e. </s> <s>Therefore neither the whole Earth, nor the whole <lb/><arrow.to.target n="marg909"></arrow.to.target><lb/>Water, nor the whole Air can <emph type="italics"/>&longs;ecundum totum<emph.end type="italics"/> be driuen or for­<lb/>ced out of their proper place, &longs;ite, or Sy&longs;teme in the Univer&longs;e, <lb/>in re&longs;pect of the order and di&longs;po&longs;ition of other mundane Bodies. <lb/></s> <s>And thus there is no Star (though Erratick) Orb or Sphere that <lb/>can de&longs;ert its natural place, although it may otherwi&longs;e have &longs;ome <lb/>kind of motion. </s> <s>Therefore all things, how moveable &longs;oever, <lb/>are notwith&longs;tanding &longs;aid to be &longs;table and immoveable in their <lb/>proper place, according to the fore&longs;aid &longs;en&longs;e, <emph type="italics"/>i.e. </s> <s>&longs;ecundum to­<lb/>tum<emph.end type="italics"/>; For nothing hinders, but that <emph type="italics"/>&longs;ecundum partes<emph.end type="italics"/> they may <lb/>&longs;ome waymove; which motion &longs;hall not be natural, but violent. <lb/></s> <s>Therefore the Earth, although it &longs;hould be moveable, yet it <lb/>might be &longs;aid to be immoveable, according to the precedent <lb/>Maxime, for that its neither moved in a right Motion nor out of <lb/>the Cour&longs;e a&longs;&longs;igned it in its Creation for the &longs;tanding Rule of its <lb/>motion; but keep within its own &longs;ite, being placed in that <lb/>which is called the Grand Orb, above <emph type="italics"/>Venus,<emph.end type="italics"/> and beneath <emph type="italics"/>Mars,<emph.end type="italics"/><lb/><arrow.to.target n="marg910"></arrow.to.target><lb/>and being in the middle betwixt the&longs;e (which according to the <lb/>common opinion is the Suns place) it equally and continually <lb/>moveth about the Sun, and the two other intermediate Planets, <lb/>namely <emph type="italics"/>Venus<emph.end type="italics"/> and <emph type="italics"/>Mercury,<emph.end type="italics"/> and hath the Moon (which is another <lb/>Earth, but Ætherial, as <emph type="italics"/>Macrobius<emph.end type="italics"/> after &longs;ome of the ancient Phi­<lb/><arrow.to.target n="marg911"></arrow.to.target><lb/>lo&longs;ophers, will have it) about it &longs;elf. </s> <s>From whence, ina&longs;much as <lb/>&longs;he per&longs;i&longs;teth uniformly in her Cour&longs;e, and never at any time <lb/>departeth from it, &longs;he may be &longs;aid to be &longs;table and immoveable: <lb/>and in the &longs;ame &longs;en&longs;e Heaven likewi&longs;e, with all the Elements, <lb/>may be &longs;aid to be immoveable.</s></p><p type="margin"> <s><margin.target id="marg909"></margin.target><emph type="italics"/>The Earth can­<lb/>not<emph.end type="italics"/> Secundum To­<lb/>tum, <emph type="italics"/>remove out of <lb/>its Natural Place.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg910"></margin.target><emph type="italics"/>The Natural <lb/>Place of the Earth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg911"></margin.target><emph type="italics"/>The Moon is an <lb/>Ætherial Body.<emph.end type="italics"/></s></p><p type="main"> <s>The fifth Maxime followeth, being little different from the <lb/>former. </s> <s>Among&longs;t the things created by God, &longs;ome are of &longs;uch a <lb/>nature, that their parts may be <emph type="italics"/>ab invicem,<emph.end type="italics"/> or by turns, &longs;e­<lb/>parated from them&longs;elves, and di&longs;-joyned from their Whole; <pb xlink:href="040/01/517.jpg" pagenum="493"/>others may not, at lea&longs;t, taken <emph type="italics"/>collectively<emph.end type="italics"/>: now tho&longs;e are pe­<lb/>ri&longs;hable, but the&longs;e perpetual. </s> <s>The Earth therefore &longs;ince it <lb/>is reckoned among&longs;t tho&longs;e things that are permanent, as hath <lb/><arrow.to.target n="marg912"></arrow.to.target><lb/>been &longs;aid already, hath its parts, not di&longs;&longs;ipable, nor <emph type="italics"/>ab invicem,<emph.end type="italics"/><lb/>&longs;eparable from its Centre (whereby its true and proper place is <lb/>a&longs;&longs;igned it) and from its whole, taken collectively: becau&longs;e ac­<lb/>cording to its whole it is always pre&longs;erved, compact, united, and <lb/>cohærent in it &longs;elf, nor can its parts be &longs;eperated from the Cen­<lb/>tre, or from one another, unle&longs;s it may &longs;o fall out <emph type="italics"/>per accidens,<emph.end type="italics"/><lb/>and violently in &longs;ome of its parts; which afterwards, the ob&longs;tacle <lb/>being removed, return to their Natural Station &longs;pontaneou&longs;ly, <lb/>and without any impul&longs;e. </s> <s>In this Sen&longs;e therefore the Earth is <lb/>&longs;aid to be Immoveable, and Immutable: yea even the Sea, Aire, <lb/>Heaven, and any other thing (although otherwi&longs;e moveable) &longs;o <lb/>long as its parts are not di&longs;&longs;ipable and &longs;eperable, may be &longs;aid to <lb/>be Immoveable, at lea&longs;t taken <emph type="italics"/>collectively.<emph.end type="italics"/> This Principle <lb/>or Maxim differeth from the precedent only in that this referrs <lb/>to the parts in order to <emph type="italics"/>Place,<emph.end type="italics"/> and this, in order to the Whole.</s></p><p type="margin"> <s><margin.target id="marg912"></margin.target><emph type="italics"/>The Earths Cen­<lb/>tre keepeth it in <lb/>its Natural Place.<emph.end type="italics"/></s></p><p type="main"> <s>From this Speculation another Secret is di&longs;covered. </s> <s>For hence <lb/><arrow.to.target n="marg913"></arrow.to.target><lb/>it is manife&longs;t wherein the proper and genuine formality of the <lb/>Gravity aad Levity of Bodyes con&longs;i&longs;teth; a point which is not &longs;o <lb/>clearly held forth, nor &longs;o undeniably explained by the Peripate­<lb/>tick Phylo&longs;ophy. <emph type="italics"/>Gravity<emph.end type="italics"/> therefore is nothing el&longs;e according to <lb/>the Principles of this new Opinion, than a certain power and ap­<lb/>petite of the Parts to rejoyn with their Whole, and there to re&longs;t <lb/>as in their proper place. </s> <s>Which Faculty or Di&longs;po&longs;ition is by <lb/>Divine Providence be&longs;towed not only on the Earth, and Ter­<lb/>rene Bodies, but, as is believed, on Cœle&longs;tial Bodies al&longs;o, name­<lb/><arrow.to.target n="marg914"></arrow.to.target><lb/>ly the Sun, Moon, and Starrs; all who&longs;e parts are by this Impul­<lb/>&longs;ion connected, and con&longs;erved together, cleaving clo&longs;ely to each <lb/>other, and on all &longs;ides pre&longs;&longs;ing towards their Centre, until they <lb/>come to re&longs;t there. </s> <s>From which Concour&longs;e and Compre&longs;&longs;ion a <lb/>Sphærical and Orbicular Figure of the Cæle&longs;tial Orbes is produ­<lb/>ced, wherein by this occult Quality naturally incident to <lb/>each of them they of them&longs;elves &longs;ub&longs;i&longs;t, and are alwayes pre&longs;er­<lb/>ved. </s> <s>But <emph type="italics"/>Levity<emph.end type="italics"/> is the Extru&longs;ion and Exclu&longs;ion of a more te­<lb/>nuo&longs;e and thin Body from the Commerce of one more Solid and <lb/><arrow.to.target n="marg915"></arrow.to.target><lb/>den&longs;e, that is Heterogeneal to it, by vertue of Heat. </s> <s>Where­<lb/>upon, as the Motion of Grave Bodies is <emph type="italics"/>Compre&longs;&longs;ive,<emph.end type="italics"/> &longs;o the Mo­<lb/>tion of Light Bodies is <emph type="italics"/>Exten&longs;ive:<emph.end type="italics"/> For its the propperty of Heat <lb/>to dilate and rarify tho&longs;e things to which it doth apply, conjoine <lb/>and communicate it &longs;elf. </s> <s>And for this rea&longs;on we find Levity <lb/>and Gravity not only in re&longs;pect of this our Tere&longs;trial Globe, and <lb/>the Bodies adjacent to it, but al&longs;o in re&longs;pect of tho&longs;e Bodies <lb/>which are &longs;aid to be in the Heavens, in which tho&longs;e parts which <pb xlink:href="040/01/518.jpg" pagenum="494"/>by rea&longs;on of their proclivity make towards their Centre are <lb/>Grave, and tho&longs;e that incline to the Circumference Light. </s> <s>And <lb/>&longs;o in the Sun, Moon, and Starrs, there are parts as well Grave as <lb/><arrow.to.target n="marg916"></arrow.to.target><lb/>Light. </s> <s>And con&longs;equently Heaven it &longs;elf that &longs;o Noble Body, <lb/>and of a fifth E&longs;&longs;ence, &longs;hall not be con&longs;tituted of a Matter diffe­<lb/>rent from that of the Elements, being free from all Mutation in <lb/>it's Sub&longs;tance, Quantity, and Quality: Nor &longs;o admirable and <lb/><arrow.to.target n="marg917"></arrow.to.target><lb/>excellent as <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> would make us to believe; nor yet a &longs;olid <lb/>Body, and impermeable; and much le&longs;&longs;e (as the generality of <lb/>men verily believe) of an impenetrable and mo&longs;t obdurate Den­<lb/>&longs;ity: but in it (as this Opinion will have it) Comets may be ge­<lb/>nerated; and the Sun it &longs;elf, as tis probable, exhaling or attract­<lb/>ing &longs;undry vapours to the &longs;urface of its Body, may perhaps pro­<lb/>duce tho&longs;e Spots which were ob&longs;erved to be &longs;o various, and irre­<lb/><arrow.to.target n="marg918"></arrow.to.target><lb/>gular in its <emph type="italics"/>Di&longs;cus<emph.end type="italics"/>: of which <emph type="italics"/>Galilæus<emph.end type="italics"/> in a perticular ^{*} Treati&longs;e <lb/>hath mo&longs;t excellently and mo&longs;t accurately &longs;poken; in&longs;omuch, <lb/>that though it were not be&longs;ides my pre&longs;ent purpo&longs;e, yet it is con­<lb/>venient that I forbear to &longs;peak any thing touching tho&longs;e matters, <lb/>lea&longs;t I &longs;hould &longs;eem to do that which he hath done before me: But <lb/>now if there be found in the Sacred Scriptures any Authority <lb/>contrary to the&longs;e things, it may be &longs;alved by the fore&longs;aid Argu­<lb/>ments Analogically applyed. </s> <s>And further more it may be &longs;aid, <lb/>that that Solidity is to be &longs;o under&longs;tood, <emph type="italics"/>as that it admits of no <lb/>vacuum, cleft, or penetration from whence the lea&longs;t vacuity might <lb/>proceed<emph.end type="italics"/> For the truth is, as that cannot be admitted in bodily <lb/>Creatures, &longs;o it is likewi&longs;e repugnant to Heaven it &longs;elf, being <lb/>indeed a Body of its own Nature the mo&longs;t Rare of all o­<lb/><arrow.to.target n="marg919"></arrow.to.target><lb/>thers, and tenuo&longs;e beyond all Humane Conception, and happly <lb/>hath the &longs;ame proportion to the Aire, as the Aire to the <lb/>Water.</s></p><p type="margin"> <s><margin.target id="marg913"></margin.target><emph type="italics"/>Gravity and Le­<lb/>vity of Bodies, <lb/>what it is.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg914"></margin.target><emph type="italics"/>All Cœle&longs;tial Bo­<lb/>dies have Gravity <lb/>and Levety.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg915"></margin.target><emph type="italics"/>Compre&longs;&longs;ive Ma­<lb/>tion, proper to <lb/>Gravity; the Ex­<lb/>ten&longs;ive, to Levity.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg916"></margin.target><emph type="italics"/>Heaven is not <lb/>compo&longs;ed of a fift <lb/>E&longs;&longs;ence differing <lb/>from the matter of <lb/>inferior Bodies.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg917"></margin.target><emph type="italics"/>Nor yet a Solid <lb/>or den&longs;e Body but <lb/>Rare.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg918"></margin.target>* Delle Macchie <lb/>&longs;olarj.</s></p><p type="margin"> <s><margin.target id="marg919"></margin.target>* <emph type="italics"/>Vnius Corporis <lb/>fimplicis, unus e&longs;t <lb/>motus &longs;implex, et <lb/>huic duæ &longs;pecies, <lb/>Rectus & Circu­<lb/>laris: Rectus du­<lb/>plex à medio, & <lb/>ad medium; pri­<lb/>mus levium, ut A­<lb/>eris & Ignis: &longs;e­<lb/>cundus gravium, <lb/>ut Aquæ & Ter­<lb/>ræ: Circularis, <lb/>quie&longs;t circa medi­<lb/>um competit Cœlo, <lb/>quod neque e&longs;t <lb/>grave, neque leve.<emph.end type="italics"/><lb/>Ari&longs;t. <emph type="italics"/>de Cœlo.<emph.end type="italics"/><lb/>Lib. 1.</s></p><p type="main"> <s>It is clear al&longs;o from the&longs;e Principles how fal&longs;e the&longs;e words of <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> are, that: <emph type="italics"/>Of one &longs;imple Body, there is one &longs;imple Motion<emph.end type="italics"/>; <lb/><emph type="italics"/>and this is of two kindes, Right and Circular: the Right is two­<lb/>fold, from the medium, and to the medium; the fir&longs;t of Light Bo­<lb/>dyes, as the Aire and Fire: the &longs;econd of Grave Bodyes, as the <lb/>Water and Earth: the Circular, which is about the medium, be­<lb/>longeth to Heaven, which is neither Grave nor Light<emph.end type="italics"/>: For all this <lb/>Philo&longs;ophy is now for&longs;aken, and of it &longs;elf grown into di&longs;-e&longs;teem; <lb/>for though it be received for an unque&longs;tionable truth in this new <lb/>Opinion, that to a &longs;imple body appertains one only &longs;imple Moti­<lb/><arrow.to.target n="marg920"></arrow.to.target><lb/>on, yet it granteth no Motion but what is Circular, by which alone <lb/>a&longs;imple body is con&longs;erved in its naturall Place, and &longs;ub&longs;i&longs;ts in its <lb/>Unity, and is properly &longs;aid to move <emph type="italics"/>in loco<emph.end type="italics"/> [<emph type="italics"/>in a place<emph.end type="italics"/>:] whereby <lb/><arrow.to.target n="marg921"></arrow.to.target><lb/>it comes to pa&longs;s that a Body for this rea&longs;on doth continue to move <lb/>in it &longs;elf, [<emph type="italics"/>or about its own axis<emph.end type="italics"/>;] and although it have a Motion, <pb xlink:href="040/01/519.jpg" pagenum="495"/>yet it abideth &longs;till in the &longs;ame place, as if it were perpetually im­<lb/>moveable. </s> <s>But right Motion, which is properly <emph type="italics"/>ad locum, [to a <lb/>place]<emph.end type="italics"/> can be a&longs;cribed only to tho&longs;e things which are out of their <lb/>naturall place, being far from union with one another, and from <lb/>unity with their whole, yea that are &longs;eperated and divided from <lb/>it: Which being that it is contrary to the Nature and forme of <lb/>the Univer&longs;e, it nece&longs;&longs;arily followeth, that right Motion doth in <lb/><arrow.to.target n="marg922"></arrow.to.target><lb/>&longs;hort &longs;ute with tho&longs;e things which are de&longs;titute of that perfection, <lb/>that according to their proper Nature belongeth to them, and <lb/>which by this &longs;ame right Motion they labour to obtaine, untill <lb/>they are redintigrated with their Whole, and with one another, <lb/>and re&longs;tored to their Naturall place; in which at the length, <lb/>having obtained their perfection, they &longs;ettle and remaine immove­<lb/>able. </s> <s>Therefore in right Motions there can be no Uniformity, <lb/><arrow.to.target n="marg923"></arrow.to.target><lb/>nor &longs;implicity; for that they vary by rea&longs;on of the uncertaine <lb/>Levity or Gravity of their re&longs;pective Bodyes: for which cau&longs;e <lb/>they do not per&longs;evere in the &longs;ame Velocity or Tardity to the end <lb/>which they had in the beginning. </s> <s>Hence we &longs;ee that tho&longs;e things <lb/>who&longs;e weight maketh them tend downwards, do de&longs;cend at fir&longs;t <lb/>with a &longs;low Motion; but afterwards, as they approach neerer <lb/>and neerer to the Centre, they precipitate more and more &longs;wiftly. <lb/></s> <s>And on the other&longs;ide, tho&longs;e things which by rea&longs;on of their light­<lb/>ne&longs;s are carryed upwards (as this our Terre&longs;triall fire, which is no­<lb/>thing el&longs;e but a &longs;moak that burneth, and is inkindled into a flame) <lb/>are no &longs;ooner a&longs;cended on high, but, in almo&longs;t the &longs;elf-&longs;ame mo­<lb/>ment, they fly and vani&longs;h out of fight; by rea&longs;on of the rare­<lb/>faction and exten&longs;ion, that they as &longs;oon as they acquire, are freed <lb/>from tho&longs;e bonds which violently and again&longs;t their own Nature <lb/><arrow.to.target n="marg924"></arrow.to.target><lb/>kept them under, and deteined them here below. </s> <s>For which <lb/>rea&longs;on, it is very apparent, that no Right Motion can be called <lb/>Simple, not only in regard that (as hath been &longs;aid) it is not <lb/>^{*} even and uniforme, but al&longs;o becau&longs;e it is mixt with the Circu­<lb/><arrow.to.target n="marg925"></arrow.to.target><lb/>lar, which lurketh in the Right by an occult con&longs;ent, <emph type="italics"/>&longs;cilicet<emph.end type="italics"/> by <lb/>rea&longs;on of the Natural affection of the Parts to conforme unto <lb/>their Whole. </s> <s>For when the Whole moveth Circularly, it is re­<lb/>qui&longs;ite likewi&longs;e that the Parts, to the end that they may be uni­<lb/>ted to their Whole, (howbeit <emph type="italics"/>per accidens<emph.end type="italics"/> they are &longs;ometimes <lb/>moved with a Right Motion) do move (though not &longs;o appa­<lb/>rently) with a Circular Motion, as doth their Whole. </s> <s>And thus <lb/>at length we have evinced that Circular Motion only is Simple, <lb/><arrow.to.target n="marg926"></arrow.to.target><lb/>Uniform and ^{*} Æquable, and of the &longs;ame tenor [<emph type="italics"/>or rate<emph.end type="italics"/>] for that <lb/><arrow.to.target n="marg927"></arrow.to.target><lb/>it is never de&longs;titute of its interne Cau&longs;e: whereas on the contra­<lb/>ry, Right Motion, (which pertains to things both Heavy and <lb/>Light) hath a Cau&longs;e that is imperfect and deficient, yea that ari­<lb/>&longs;eth from Defect it &longs;elf, and that tendeth to, and &longs;eeketh after <pb xlink:href="040/01/520.jpg" pagenum="496"/>nothing el&longs;e but the end and termination of it &longs;elf: in regard <lb/>that Grave and Light Bodies, when once they have attained their <lb/>proper and Natural Place, do de&longs;i&longs;t from that Motion to which <lb/>they were incited by Levity and Gravity. </s> <s>Therefore: &longs;ince Cir­<lb/><arrow.to.target n="marg928"></arrow.to.target><lb/>cular Motion is proper <emph type="italics"/>to the Whole,<emph.end type="italics"/> and Right Motion <emph type="italics"/>to the <lb/>Parts,<emph.end type="italics"/> the&longs;e differences are not rightly referred to Motion, &longs;o as <lb/>to call one Motion Right, another Circular, as if they were not <lb/>con&longs;i&longs;tent with one another: For they may be both together, and <lb/><arrow.to.target n="marg929"></arrow.to.target><lb/>that Naturally, in the &longs;ame Body; no le&longs;&longs;e than it is equally <lb/>Natural for a Man to participate of Sen&longs;e and Rea&longs;on, &longs;eeing <lb/>that the&longs;e differences are not directly oppo&longs;ite to one another. <lb/></s> <s>Hereupon Re&longs;t and Immobility only are oppo&longs;ed to Motion; <lb/>and not one Species of Motion to another. </s> <s>And for the other <lb/>differences <emph type="italics"/>à medio, ad medium,<emph.end type="italics"/> and <emph type="italics"/>circa medium,<emph.end type="italics"/> they are di­<lb/>&longs;tingui&longs;hed not <emph type="italics"/>really,<emph.end type="italics"/> but only <emph type="italics"/>formally,<emph.end type="italics"/> as the Point, Line and <lb/>Superficies, none of which can be without the other two, or <lb/>without a Body. </s> <s>Hence it appears, that in as much as this Phy­<lb/>lo&longs;ophy differs from that of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> &longs;o in like manner doth this <lb/>New Co&longs;mographical Sy&longs;tem vary from the Common one, that <lb/>hath been hitherto received. </s> <s>But this by the way, upon occa&longs;ion <lb/>of explaining the Fifth Maxim: For as to the truth or fal&longs;hood <lb/>of the&longs;e foregoing Po&longs;itions (although I conceive them very pro­<lb/>bable) I am re&longs;olved to determine nothing at pre&longs;ent, neither <lb/>&longs;hall I make any farther enquiry into them.</s></p><p type="margin"> <s><margin.target id="marg920"></margin.target>* <emph type="italics"/>Vide Coperni­<lb/>cum de Revolutio­<lb/>nibus Cœle&longs;t.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg921"></margin.target><emph type="italics"/>Simple Motion <lb/>peculiar to only <lb/>Simple Bodies.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg922"></margin.target><emph type="italics"/>Right Motion <lb/>belongeth to Im­<lb/>perfect Bodies, and <lb/>that are out of <lb/>their natural Pla­<lb/>ces.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg923"></margin.target><emph type="italics"/>Right Motion <lb/>cannot be Simple.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg924"></margin.target><emph type="italics"/>Right Motion is <lb/>ever mixt with <lb/>the Circular.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg925"></margin.target>* <emph type="italics"/>æquabilis.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg926"></margin.target>* <emph type="italics"/>Even.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg927"></margin.target><emph type="italics"/>Circular Mo­<lb/>tion is truly Sim­<lb/>ple and Perpetual.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg928"></margin.target><emph type="italics"/>Circular Mo­<lb/>tion belongeth to <lb/>the Whole Body, <lb/>and the Right to <lb/>its parts.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg929"></margin.target><emph type="italics"/>Circular and <lb/>Right Motion co­<lb/>incedent, and may <lb/>con&longs;i&longs;t together in <lb/>the &longs;ame Body.<emph.end type="italics"/></s></p><p type="main"> <s>The Sixth and La&longs;t Maxim is this. </s> <s>Every thing is Simply deno­<lb/>minated &longs;uch as it is in compari&longs;on of all things, or of many <lb/>things which make the greater number of that kinde, but not in <lb/>re&longs;pect of a few which make but the le&longs;&longs;er part of them. </s> <s>As, <lb/>for in&longs;tance, a Ve&longs;&longs;el &longs;hall not be called ab&longs;olutely Great be­<lb/>cau&longs;e it is &longs;o whil&longs;t it is compared with two or three others: but <lb/>it &longs;hall be &longs;aid to be great ab&longs;olutely, and will be &longs;o, if it ex­<lb/>ceed in magnitude all indivials, or the greater part of them. </s> <s>Nor <lb/>again &longs;hall a Man be &longs;aid to be ab&longs;olutely Big, becau&longs;e he is big­<lb/>ger than a Pigmey; nor yet ab&longs;olutely Little, becau&longs;e le&longs;&longs;e than <lb/>a Gyant: but he &longs;hall be termed ab&longs;olutely Big or Little in com­<lb/>pari&longs;on of the ordinary Stature of the greater part of Men. </s> <s>Thus <lb/>the Earth cannot ab&longs;olutely be &longs;aid to be High or Low for that it <lb/>is found to be &longs;o in re&longs;pect of &longs;ome &longs;mall part of the Univer&longs;e; nor <lb/>again &longs;hall it be ab&longs;olutely affirmed to be High, being compared <lb/>to the Centre of the World, or &longs;ome few parts of the Univer&longs;e, <lb/>more near to the &longs;aid Centre, as is the <emph type="italics"/>Sun, Mercury<emph.end type="italics"/> or <emph type="italics"/>Venus<emph.end type="italics"/>: <lb/><arrow.to.target n="marg930"></arrow.to.target><lb/>but it &longs;hall receive its ab&longs;olute denomination according as it &longs;hall <lb/>be found to be in compari&longs;on of the greater number of the <lb/>Spheres and Bodies of the Univer&longs;e. </s> <s>The Earth therefore, in <lb/>compari&longs;on of the whole Circuit of the Eighth Sphære which in­ <pb xlink:href="040/01/521.jpg" pagenum="497"/>cludeth all Corporeal Creatures, and in compari&longs;on of <emph type="italics"/>Jupiter, <lb/>Mars,<emph.end type="italics"/> and <emph type="italics"/>Saturn<emph.end type="italics"/> together with the <emph type="italics"/>Moon,<emph.end type="italics"/> and much more in <lb/>compari&longs;on of other Bodies, (if any &longs;uch there be) above the <lb/>Eighth Sphere and e&longs;pecially the Empyrial Heaven, may be truly <lb/>&longs;aid to be in the lowe&longs;t place of the World, and almo&longs;t in the <lb/>Centre of it; nor can it he &longs;aid to be above any of them, except <lb/>the <emph type="italics"/>Sun, Mercury<emph.end type="italics"/> and <emph type="italics"/>Venus<emph.end type="italics"/>: So that one may apply unto it the <lb/>name of an Infime and Low, but not a Supreme or Middle Body. <lb/></s> <s>And &longs;o to come down from Heaven, e&longs;pecially the Empyrian, to it <lb/>(as it is accepted in the De&longs;cent of Chri&longs;t from Heaven to his Holy <lb/>Incarnation) and from it to go up to Heaven (as in Chri&longs;ts return <lb/><arrow.to.target n="marg931"></arrow.to.target><lb/>to Heaven in his Glorious A&longs;cention) is truly and properly to <lb/><emph type="italics"/>De&longs;cend<emph.end type="italics"/> from the Circumference to the Centre, and to <emph type="italics"/>a&longs;cend<emph.end type="italics"/><lb/>from the parts which are neare&longs;t to the Centre of the World <lb/>to its utmo&longs;t Circumference. </s> <s>This Maxim therefore may ea&longs;ily <lb/>and according to truth explain Theologicall Propo&longs;itions: and <lb/>this is &longs;o much the more confirmed, in that (as I have ob&longs;erved) <lb/>almo&longs;t all Texts of Sacred Scripture which oppo&longs;e the Earth to <lb/>Heaven, are mo&longs;t conveniently and aptly under&longs;tood of the Em­<lb/>pyrial Heaven (being the Highe&longs;t of all the Heavens, and Spiritual <lb/>in re&longs;pect of its end) but not of the inferiour or intermediate Hea­<lb/>vens, which are a Corporeal, and were framed for the benefit of <lb/>Corporeal Creatures: and thus when in the Plural Number <lb/>Heavens are mentioned, then all the Heavens promi&longs;cuou&longs;ly and <lb/>without di&longs;tinction are to be under&longs;tood, as well the Empyrian <lb/>it &longs;elf as the Inferiour Heavens. </s> <s>And this Expo&longs;ition indeed any <lb/>man (that doth but take notice of it) may find to be mo&longs;t true. <lb/></s> <s>And &longs;o for this Rea&longs;on the Third Heaveu into which St. <emph type="italics"/>Paul<emph.end type="italics"/><lb/><arrow.to.target n="marg932"></arrow.to.target><lb/>was wrapt up, by this Maxim may be taken for the Empyrean: <lb/>if for the the Fir&longs;t Heaven we under&longs;tand that immen&longs;e Space of <lb/>Erratick and Moveable Bodies illuminated by the Sun, in which <lb/>are comprehended the Planets, as al&longs;o the Earth moveable, and <lb/>the Sun immoveable, Who like a King upon his Augu&longs;t Tribu­<lb/>nal, &longs;its with venerable Maje&longs;ty immoveable and con&longs;tant in <lb/>Centre of all the Sphæres, and, with his Divine Beames, doth <lb/>bountifully exhilerate all Cœle&longs;tial Bodies that &longs;tand in need of <lb/>his vital Light, for which they cravingly wander about him; and <lb/>doth liberally and on every &longs;ide comfort and illu&longs;trate the Thea­<lb/>tre of the whole World, and all its parts, even the very lea&longs;t, like <lb/>an immortal and perpetual Lamp of high and un&longs;peakable va­<lb/>lue. </s> <s>The Second Heaven &longs;hall be the Starry Heaven, common­<lb/>ly called the Eighth Sphære, or the Firmament, wherein are all <lb/>the Fixed Starrs, which according to this Opinion of <emph type="italics"/>Pythagoras,<emph.end type="italics"/><lb/>is (like as the Sun and Centre) void of all Motion, the Centre <lb/>and utmo&longs;t Circumference mutually agreeing with each other in <pb xlink:href="040/01/522.jpg" pagenum="498"/>Immobility. </s> <s>And the Third &longs;hall be the Empyrean Heaven, that <lb/>is the Seat of the Ble&longs;&longs;ed. </s> <s>And in this manner we may come to <lb/>explain and under&longs;tand that admirable Secret, and profound My­<lb/><arrow.to.target n="marg933"></arrow.to.target><lb/>&longs;tery ænigmatically revealed by <emph type="italics"/>Plato<emph.end type="italics"/> to <emph type="italics"/>Diony&longs;ius<emph.end type="italics"/> of <emph type="italics"/>Syracu&longs;e<emph.end type="italics"/>: <lb/><arrow.to.target n="marg934"></arrow.to.target><lb/><emph type="italics"/>(a) All things are about the King of all things, Second things <lb/>about the &longs;econd, and Third things about the Third<emph.end type="italics"/>: For that <lb/>God being the Centre of Spiritual things, the Sun, of Cor­<lb/>poreal, Chri&longs;t, of tho&longs;e that are Mixt, or made up of both, things <lb/>do doubtle&longs;&longs;e depend of that of the&longs;e three Centres that is mo&longs;t <lb/>corre&longs;pondent and proportionable to them, and the Centre is <lb/>ever adjudged to be the nobler and worthier place: and therefore <lb/>in Animals the Heart, in Vegitables the Pith or Kernell wherein <lb/>the Seed lyeth that con&longs;erveth their perpetuity, and virtually in­<lb/>cludes the whole Plant, are in the Mid&longs;t, and in the Centre: and <lb/>thus much &longs;hall &longs;uffice to have hinted at, &longs;ince there may another <lb/>occa&longs;ion offer it &longs;elf for a larger Explication of the&longs;e things. </s> <s>By <lb/>this Maxim the Authorities and Arguments of the Third Fourth <lb/>and Fifth Cla&longs;&longs;es are re&longs;olved.</s></p><p type="margin"> <s><margin.target id="marg930"></margin.target><emph type="italics"/>The Earth in <lb/>what &longs;en&longs;e it may <lb/>ab&longs;olutely be &longs;aid <lb/>to be in the lowe&longs;t <lb/>part of the World.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg931"></margin.target><emph type="italics"/>Chri&longs;t in his <lb/>Incarnation tru­<lb/>ly de&longs;cended from <lb/>Heaven, and in <lb/>his A&longs;cen&longs;ion tru­<lb/>ly a&longs;cended into <lb/>Heaven.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg932"></margin.target>2 Cor. </s> <s>c. </s> <s>12. v. <lb/></s> <s>3. <emph type="italics"/>Whether in the <lb/>body or out of the <lb/>body, I cannot tell, <lb/>The Sun is King, <lb/>Heart and Lamp <lb/>of the World him­<lb/>&longs;elf being<emph.end type="italics"/> <foreign lang="greek">autarkhs</foreign><lb/><emph type="italics"/>ab&longs;olutely indepen­<lb/>dent.<emph.end type="italics"/>)</s></p><p type="margin"> <s><margin.target id="marg933"></margin.target><emph type="italics"/>The Ænignsa of <lb/>Plato.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg934"></margin.target><emph type="italics"/>(a) Circa omni­<lb/>um Regem &longs;unt <lb/>omnia. </s> <s>& Secun­<lb/>da circa Secun­<lb/>dum, et Tertia <lb/>circa Tertium: <lb/>Vide<emph.end type="italics"/> Theodo. </s> <s>de <lb/>Græc. </s> <s>affect. </s> <s>curat. <lb/></s> <s>lib. 2. Steuch. </s> <s>lib. <lb/></s> <s>de Parennj. </s> <s>Phi­<lb/>lo&longs;o.</s></p><p type="main"> <s>It may be added withall, that even the <emph type="italics"/>Sun, Mercury<emph.end type="italics"/> and <emph type="italics"/>Ve­<lb/>nus<emph.end type="italics"/> (that is to &longs;ay in re&longs;pect of the Earth) are to be thought <lb/><emph type="italics"/>aboue,<emph.end type="italics"/> and not <emph type="italics"/>beneath<emph.end type="italics"/> the Earth it &longs;elf, although in re&longs;pect of <lb/>the Univer&longs;e, yea and al&longs;o ab&longs;olutely, they are <emph type="italics"/>below.<emph.end type="italics"/> The rea­<lb/>&longs;on is, becau&longs;e in re&longs;pect of the Earth they alwayes appear above <lb/>its Surface: and although they do not environe it, yet by the <lb/>Motion of the &longs;aid Earth they behold one while one part, another <lb/>while another part of its Circumference. </s> <s>Since therefore tho&longs;e <lb/>things which in a Sphærical Body are nearer to the Circumfe­<lb/>rence and more remote from the Cenrre are &longs;aid to be <emph type="italics"/>above,<emph.end type="italics"/> but <lb/>tho&longs;e that are next adjoyning to the Centre are &longs;aid to be <emph type="italics"/>below<emph.end type="italics"/>; <lb/>it clearly followeth that whil&longs;t the <emph type="italics"/>Sun, Mercury<emph.end type="italics"/> and <emph type="italics"/>Venus<emph.end type="italics"/> are <lb/>not only turned towards the Surface and Circumference of the <lb/>&longs;aid Earth, but are at a very great di&longs;tance without it, &longs;ucce&longs;&longs;ively <lb/>turned about it, and every way have a view of it, and are very <lb/>far remote from its Centre, they may, in re&longs;pect of the &longs;aid Earth, <lb/>be &longs;aid to be <emph type="italics"/>above<emph.end type="italics"/> it; as al&longs;o on the other &longs;ide, the Earth in <lb/>re&longs;pect of them may be &longs;aid to be <emph type="italics"/>beneath<emph.end type="italics"/>: howbeit on the con­<lb/>trary, in re&longs;pect of the Univer&longs;e, the Earth in reality is much <lb/>higher than they. </s> <s>And thus is &longs;alved the Authority of <emph type="italics"/>Eccle&longs;i-<emph.end type="italics"/><lb/><arrow.to.target n="marg935"></arrow.to.target><lb/><emph type="italics"/>a&longs;tes<emph.end type="italics"/> in many places, expre&longs;&longs;ing tho&longs;e things that are, or are done <lb/>on the Eeath in the&longs;e words, <emph type="italics"/>Which are done, or which are under<emph.end type="italics"/><lb/><arrow.to.target n="marg936"></arrow.to.target><lb/><emph type="italics"/>the Sun,<emph.end type="italics"/> And in the &longs;ame manner tho&longs;e words are reduced to their <lb/>true Sen&longs;e wherein it is &longs;aid, That we are <emph type="italics"/>under the Sun,<emph.end type="italics"/> and <emph type="italics"/>un­<lb/>der the Moon,<emph.end type="italics"/> whereupon Terrene things are expre&longs;&longs;ed by the <lb/>name of <emph type="italics"/>Sublunary.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg935"></margin.target>Eccle&longs;. </s> <s>c. </s> <s>1. 2. 3. <lb/><emph type="italics"/>and almo&longs;t tho­<lb/>out.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg936"></margin.target>* <emph type="italics"/>Quod fiunt, vel <lb/>&longs;unt &longs;ub &longs;ole.<emph.end type="italics"/></s></p><p type="main"> <s>The Sixth Cla&longs;&longs;is threatneth a difficulty which is common as <pb xlink:href="040/01/523.jpg" pagenum="499"/>well to this of <emph type="italics"/>Copernicus,<emph.end type="italics"/> as to the Vulgar Opinion; &longs;o that they <lb/>are both alike concerned in the &longs;olution of it: But &longs;o far as it <lb/>oppo&longs;eth that of <emph type="italics"/>Copernicus,<emph.end type="italics"/> its an&longs;wer is ea&longs;y from the Fir&longs;t <lb/>Maxim.</s></p><p type="main"> <s>But that which is added in the Fourth Cla&longs;&longs;e, That it follow­<lb/>eth from this Opinion, that Hell (for that it is included by the <lb/>Earth, as is commonly held) doth move circularly about the <lb/>Sun, and in Heaven, and that &longs;o Hell it &longs;elf will be found to be <lb/>in Heaven; di&longs;covers, in my judgment, nothing but Ignorance <lb/>and Calumny, that in&longs;inuate the belief of their Arguments ra­<lb/>ther by a corrupt &longs;en&longs;e of the Words, than by &longs;olid Rea&longs;ons <lb/>taken from the bo&longs;ome of the Nature of things. </s> <s>For in this <lb/>place Heaven is no wi&longs;e to be taken for Paradice, nor according <lb/>to the Sen&longs;e of Common Opinion, but (as hath been &longs;aid above) <lb/><arrow.to.target n="marg937"></arrow.to.target><lb/>according to the <emph type="italics"/>Copernican<emph.end type="italics"/> Hypothe&longs;is, for the &longs;ubtile&longs;t and <lb/>Pure&longs;t Aire, far more tenuous and rare than this of ours; where­<lb/>upon the Solid Bodies of the Stars, Moon, and Earth, in their <lb/>Circular and Ordinary Motions, do pa&longs;&longs;e thorow it, (the Sphære <lb/>of Fire being by this Opinion taken away.) And as according <lb/>to the Common Opinion it was no ab&longs;urdity to &longs;ay, That Hell <lb/>being demerged in the Centre of the Earth and of the World it <lb/>&longs;elf, hath Heaven and Paradice above and below it, yea and on <lb/>all &longs;ides of it, and that it is in the middle of all the Cœle&longs;tial <lb/>Bodies (as if it were po&longs;ited in a more unworthy place) &longs;o, nei­<lb/>ther in this will it be deemed an Error, if from the other Sy&longs;tem, <lb/>which differeth not much from the Vulgar one, tho&longs;e or the like <lb/>things follow as do in that. </s> <s>For both in that of <emph type="italics"/>Copernicus,<emph.end type="italics"/> and <lb/>the Vulgar Hypothe&longs;is, Hell is &longs;uppo&longs;ed to be placed among&longs;t the <lb/>very dreggs of the Elements, and in the Centre of the Earth it <lb/>&longs;elf, for the confinement and puni&longs;hment of the damned. </s> <s>There­<lb/>fore we ought not for want of Rea&longs;ons to trifle away time in <lb/>vain and impertinent &longs;trife about words, &longs;ince their true Sen&longs;e <lb/>is clouded then with no ob&longs;curity, and in regard that it is very <lb/>clear to any man indued with a refined Intellect, and that hath <lb/>but an indifferent judgment in the Liberal Arts, and e&longs;pecially <lb/>in the Mathematicks, that the &longs;ame, or not very different Gon­<lb/>&longs;equences do flow from both the&longs;e Opinions.</s></p><p type="margin"> <s><margin.target id="marg937"></margin.target><emph type="italics"/>Heaven accord­<lb/>ing to Copernicus <lb/>is the &longs;ame with <lb/>the mo&longs;t tenuous <lb/>Æther; but dif­<lb/>ferent from Para­<lb/>dice, which &longs;ar­<lb/>pa&longs;&longs;eth all the <lb/>Heavens.<emph.end type="italics"/></s></p><p type="main"> <s>By the&longs;e Maxims and their Interpretations it appears, that <lb/>the <emph type="italics"/>Pythagorick<emph.end type="italics"/> and <emph type="italics"/>Copernican<emph.end type="italics"/> Opinion is &longs;o probable, that its <lb/>po&longs;&longs;ible it may exceed even the <emph type="italics"/>Ptolemaick<emph.end type="italics"/> in probability; and <lb/>&longs;ince there may be deduced from it a mo&longs;t ordinate Sy&longs;teme, and <lb/>a mroe admirable and my&longs;terious Hypothe&longs;is of the World <lb/>than from that of <emph type="italics"/>Ptolomy:<emph.end type="italics"/> the Authorities of Sacred Scripture <lb/>and Theological Tenents in the mean while not oppo&longs;ing it, be­<lb/>ing opportunely and appo&longs;itely (as I have &longs;hown how they may <pb xlink:href="040/01/524.jpg" pagenum="500"/>be) reconciled with it: And &longs;ince that by it not only the Phœ­<lb/>nomena of all the Cœle&longs;tial Bodies are mo&longs;t readily &longs;alved, but <lb/>al&longs;o many Natural Rea&longs;ons are di&longs;covered, which could not o­<lb/>therwi&longs;e, (but with extream difficulty) have been found out: <lb/>And &longs;ince it, la&longs;t of all, doth open a more ea&longs;y way into A&longs;tro­<lb/>nomy and Phylo&longs;ophy, and rejecteth all tho&longs;e &longs;uperfluous and <lb/>imaginary inventions produced by A&longs;tronomers to the end only, <lb/>that they might be able by them to render a rea&longs;on of the &longs;o ma­<lb/>ny and &longs;o various Motions of the Cœle&longs;tial Orbs.</s></p><p type="main"> <s>And who knows, but that in that admirable compo&longs;ure of the <lb/>Candle&longs;tick which was to be placed in the Tabernacle of God, he <lb/>might out of his extraordinary love to us have been plea&longs;ed to <lb/>&longs;haddow forth unto us the Sy&longs;teme of the Univer&longs;e, and more <lb/><arrow.to.target n="marg938"></arrow.to.target><lb/>e&longs;pecially of the Planets? <emph type="italics"/>(a) Thou &longs;halt make a Candle&longs;tick of<emph.end type="italics"/><lb/><arrow.to.target n="marg939"></arrow.to.target><lb/><emph type="italics"/>pure Gold,<emph.end type="italics"/> (&longs;aith the Text;) <emph type="italics"/>of beaten work &longs;hall it be made: <lb/>his Shaft, and his Branches, his Bowls, his Knops, and his <lb/>Flowers (b) &longs;hall be of the &longs;ame.<emph.end type="italics"/> Here are five things de&longs;cribed, the <lb/>Shaft of the Candle&longs;tick in the midle, the Branches on the &longs;ides, <lb/>the Bowls, the Knops and the Flowers. </s> <s>And &longs;ince there can be no <lb/>more Shafts but one, the Branches are immediatly de&longs;cribed in <lb/>the&longs;e <emph type="italics"/>(c)<emph.end type="italics"/> words: <emph type="italics"/>Six Branches &longs;hall come out of the &longs;ides of it: <lb/>three Branches out of the one &longs;ide, and three Branches out of the <lb/>other &longs;ide:<emph.end type="italics"/> Happly the&longs;e fix Branches may point out to us &longs;ix <lb/><emph type="italics"/>(d)<emph.end type="italics"/> Heavens, which are moved about the Sun in this order; <emph type="italics"/>Saturn,<emph.end type="italics"/><lb/>the &longs;lowe&longs;t and mo&longs;t remote of all, fini&longs;heth his cour&longs;e about the <lb/><arrow.to.target n="marg940"></arrow.to.target><lb/>Sun thorrow all the twelve Signes of the Zodiack in thirty Years: <lb/><arrow.to.target n="marg941"></arrow.to.target><lb/><emph type="italics"/>Jupiter,<emph.end type="italics"/> being nearer than he, in twelve Years: <emph type="italics"/>Mars,<emph.end type="italics"/> being yet <lb/><arrow.to.target n="marg942"></arrow.to.target><lb/>nearer than him, in two Years: The <emph type="italics"/>Earth,<emph.end type="italics"/> which is &longs;till nearer <lb/>than he, doth perform the &longs;ame Revolution, together with <lb/>the Orbe of the <emph type="italics"/>Moon,<emph.end type="italics"/> in the &longs;pace of a Year, that is in Twelve <lb/>Months: <emph type="italics"/>Venus,<emph.end type="italics"/> which is yet nearer than all the&longs;e, in <emph type="italics"/>(e)<emph.end type="italics"/> 9 Months: <lb/>And la&longs;t of all <emph type="italics"/>Mercury,<emph.end type="italics"/> who&longs;e vicinity to the Sun is the greate&longs;t <lb/>of all, accompli&longs;heth its whole conver&longs;ion about the Sun in eighty <lb/>Dayes. </s> <s>After the de&longs;cription of the &longs;ix Branches, the &longs;acred <lb/>Text proceeds to the de&longs;cription of the Bowls, the Knops, and <lb/>the Flowers, &longs;aying, <emph type="italics"/>(f) Three Bowls made like unto Almonds, <lb/>with a Knop and a Flower in one Branch; and three Bowls made <lb/>like Almonds in the other Branch, with a Knop and a Flower: this <lb/>&longs;hall be the work of the &longs;ix Branches that come out of the Shaft. <lb/></s> <s>And in the Candle&longs;tick &longs;hall be four Bowls made like unto Al­<lb/>monds, with their Knops and their Flowers: there &longs;hall be a knop <lb/>under two branches of the &longs;ame, and a Knop under two Branches <lb/>of the &longs;ame, and a Knop under two Branches of the &longs;ame; which <lb/>together are &longs;ix Branches, proceeding from one Shaft.<emph.end type="italics"/> The truth <lb/><arrow.to.target n="marg943"></arrow.to.target><lb/>is, the &longs;hallowne&longs;&longs;e of my under&longs;tanding cannot fathome the <pb xlink:href="040/01/525.jpg" pagenum="501"/>depth of all the My&longs;teries that are couched in this mo&longs;t wi&longs;e <lb/>di&longs;po&longs;ure of things: neverthele&longs;&longs;e being amazed, and tran&longs;ported <lb/>with admiration, I will &longs;ay; Who knows but that tho&longs;e three <lb/>Bowls like unto Almonds to be repre&longs;ented on each of the <lb/>Branches of the Candle&longs;tick may &longs;ignifie tho&longs;e Globes which are <lb/>apter (as is this our Earth) for the receiving than emitting of Influ­<lb/>ences? </s> <s>Perhaps al&longs;o they denote tho&longs;e Globes of late di&longs;covered <lb/>by the help of the Optick Tele&longs;cope, which participate with <lb/><emph type="italics"/>Saturn, Jupiter, Venus,<emph.end type="italics"/> and po&longs;&longs;ibly al&longs;o with the other Planets? <lb/></s> <s>Who knows likewi&longs;e, but that there may be &longs;ome occult propor­<lb/>tion between the&longs;e Globes and tho&longs;e My&longs;terious Knops and <lb/>Lilies in&longs;inuated unto us in the &longs;acred Scriptures? </s> <s>But this <lb/>&longs;hall here &longs;uffice to bound humane Pre&longs;umption, and to teach us <lb/>to ex&longs;pect with an Harpocratick &longs;ilence from Time, the Indice of <lb/>Truth, a di&longs;covery of the&longs;e My&longs;teries: <emph type="italics"/>(g) Solomon<emph.end type="italics"/> made ten <lb/><arrow.to.target n="marg944"></arrow.to.target><lb/>Candle&longs;ticks by the &longs;ame Patern of <emph type="italics"/>Mo&longs;es,<emph.end type="italics"/> which he placed, five <lb/>on one hand and five on another, in the Temple erected by him <lb/>in honour of the mo&longs;t High God; which very thing doth al&longs;o, <lb/>without all que&longs;tion, contain mo&longs;t ab&longs;tru&longs;e &longs;igni&longs;ications. </s> <s>More­<lb/>over, that Apple of the Knowledg of Good and Evil prohibited <lb/>our fir&longs;t Parents by God is not without a My&longs;tery; which &longs;ome <lb/>&longs;ay was an Indian Figg. </s> <s>In which the&longs;e things are to be ob&longs;erv­<lb/>ed: Fir&longs;t, That it is replete with many Kernels, every one of <lb/>which hath a particular Centre. </s> <s>Secondly, Though of it &longs;elf it <lb/>be hard and &longs;olid, yet about its Circumference it is of a more rare <lb/>and tenuou&longs;e &longs;ub&longs;tance; herein re&longs;embling the Earth, which <lb/>though in its Centre, and tho&longs;e parts which are neare&longs;t to it, it <lb/>be &longs;tony, Metallick, and compact, yet the nearer one approacheth <lb/>to the Circumference, its parts are &longs;een to be the more rare and <lb/>tenuou&longs;e: and withall it hath another body, more rare than its <lb/>own, namely the Water, above which there is yet another, more <lb/>&longs;ubtil than all the re&longs;t of inferiour Bodyes, that is to &longs;ay, <lb/>the Aire,</s></p><p type="margin"> <s><margin.target id="marg938"></margin.target>(a) Exod. </s> <s>25. 31.</s></p><p type="margin"> <s><margin.target id="marg939"></margin.target>(b) <emph type="italics"/>My Authour <lb/>following the vul­<lb/>gar Tran&longs;lation, <lb/>which hath an E­<lb/>ligance in &longs;ome <lb/>things beyond ours, <lb/>cites the words <lb/>thus,<emph.end type="italics"/> Facies Can­<lb/>delabrum ducti­<lb/>le de auro mun­<lb/>di&longs;&longs;imo, Ha&longs;tile <lb/>ejus, & Calamos, <lb/>& Sphærulas, ac <lb/>Lilia, ex ip&longs;o pro­<lb/>cedentia.</s></p><p type="margin"> <s><margin.target id="marg940"></margin.target>(c) <emph type="italics"/>ver&longs;e<emph.end type="italics"/> 12.</s></p><p type="margin"> <s><margin.target id="marg941"></margin.target>(d) <emph type="italics"/>or Spheres.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg942"></margin.target>(e) <emph type="italics"/>Though our <lb/>Authour &longs;peaketh <lb/>here po&longs;itively of <lb/>nine Months,<emph.end type="italics"/> &c. <lb/><emph type="italics"/>Fathers are not a­<lb/>greed about the pe­<lb/>riod of this planet, <lb/>nor that of<emph.end type="italics"/> Mercu­<lb/>ry, <emph type="italics"/>as you may &longs;ee <lb/>at large in<emph.end type="italics"/> Riccio­<lb/>lus, Almage&longs;t. </s> <s>nov. <lb/><emph type="italics"/>Tom. </s> <s>1. part 1. l. <lb/></s> <s>7. &longs;ect. </s> <s>3. cha. </s> <s>11. <lb/>num. </s> <s>11. page 627. <lb/>where he maketh<emph.end type="italics"/><lb/>Venus <emph type="italics"/>to con&longs;um­<lb/>mate her Revolu­<lb/>tion in neer 225 <lb/>dayes, or 7 1/2 Mon. <lb/></s> <s>and<emph.end type="italics"/> Mecury <emph type="italics"/>in a­<lb/>bout 88 dayes, or 3 <lb/>Months: in which <lb/>he followeth<emph.end type="italics"/> Kepl. <lb/><emph type="italics"/>in Epitome A&longs;tro­<lb/>nom. </s> <s>p.<emph.end type="italics"/> 760.</s></p><p type="margin"> <s><margin.target id="marg943"></margin.target>(f) <emph type="italics"/>ver&longs;.<emph.end type="italics"/> 33, 34.</s></p><p type="margin"> <s><margin.target id="marg944"></margin.target>(g) 1 Kings <emph type="italics"/>c.<emph.end type="italics"/> 7. <lb/><emph type="italics"/>v.<emph.end type="italics"/> 49. 2 Chron. <emph type="italics"/>c.<emph.end type="italics"/><lb/>4. <emph type="italics"/>ver&longs;.<emph.end type="italics"/> 7.</s></p><p type="main"> <s>The &longs;ame Repre&longs;entation with that of the Indian Figg is held <lb/>forth to us by the <emph type="italics"/>Malum Punicum,<emph.end type="italics"/> or Pomegranate, with its <lb/>innumerable poly centrick Stones or Kernels, all which in the parts <lb/>more remote from their Centre, and nearer approaching towards <lb/>the Circumference, are of a &longs;ub&longs;tance &longs;o &longs;ubtil and rare, that being <lb/>but lightly compre&longs;&longs;ed, they in a manner wholly convert into a <lb/>mo&longs;t tenuo&longs;e Liquor or juice: Of which fruit it plea&longs;ed Divine <lb/>Wi&longs;dom to make mention, and ordained that its Figure &longs;hould be <lb/>imbroidered and wrought with a needle in the <emph type="italics"/>&longs;acerdotal<emph.end type="italics"/> Garment <lb/>of <emph type="italics"/>Aaron: (h) Beneath<emph.end type="italics"/> (&longs;aith God) <emph type="italics"/>upon the hem of it thou<emph.end type="italics"/><lb/><arrow.to.target n="marg945"></arrow.to.target><lb/><emph type="italics"/>&longs;halt make Pomegranates of blew, and of purple, and of &longs;carlet, <lb/>round about the border thereof; and Bells of gold between them<emph.end type="italics"/> <pb xlink:href="040/01/526.jpg" pagenum="502"/><emph type="italics"/>round about: a golden bell and a pomegranate, a golden bell and a <lb/>pomegranate, upon the hem of the Robe round about.<emph.end type="italics"/> And that this <lb/>was a My&longs;tical Repre&longs;entation of the Worlds Effigies, is averred <lb/><arrow.to.target n="marg946"></arrow.to.target><lb/>by <emph type="italics"/>Solomon,<emph.end type="italics"/> &longs;aying; <emph type="italics"/>(i) For in the long (k) Garment that be <lb/>had on was the (l) whole World; and in the foure rows of the &longs;tones<emph.end type="italics"/><lb/><arrow.to.target n="marg947"></arrow.to.target><lb/><emph type="italics"/>was the Glory of the Fathers graven, and thy Maje&longs;ty in the Di-<emph.end type="italics"/><lb/><arrow.to.target n="marg948"></arrow.to.target><lb/><emph type="italics"/>adem of his Head.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg945"></margin.target>(h) Exod. </s> <s>28. 33, <lb/>34, & 39. v. </s> <s>24, <lb/>25, 26.</s></p><p type="margin"> <s><margin.target id="marg946"></margin.target><emph type="italics"/>(i)<emph.end type="italics"/> Sap. </s> <s>c. </s> <s>18. v. <lb/></s> <s>24.</s></p><p type="margin"> <s><margin.target id="marg947"></margin.target><emph type="italics"/>(k)<emph.end type="italics"/> Exod. </s> <s>c. </s> <s>28. <lb/>v. </s> <s>6, 9. 17, 36.</s></p><p type="margin"> <s><margin.target id="marg948"></margin.target><emph type="italics"/>(l)<emph.end type="italics"/> Or, <emph type="italics"/>totus Or­<lb/>bis Terrarum,<emph.end type="italics"/> as <lb/>the vulgar Tran&longs;­<lb/>lation hath it.</s></p><p type="main"> <s>The &longs;ame likewi&longs;e is &longs;ignified to us by the Grape, and in like <lb/>manner by all other Fruits; but e&longs;pecially the Figg, Grape, and <lb/>Pomegranate: whence the&longs;e three are almo&longs;t alwayes placed to­<lb/>gether in the Sacred Scriptures. </s> <s>So <emph type="italics"/>Numb.<emph.end type="italics"/> 20. the People of I&longs;ra­<lb/>el complain again&longs;t <emph type="italics"/>Mo&longs;es<emph.end type="italics"/> and <emph type="italics"/>Aaron: (m) Wherefore have you<emph.end type="italics"/><lb/><arrow.to.target n="marg949"></arrow.to.target><lb/><emph type="italics"/>made us to come up out of Egypt, to bring us into this evil place, <lb/>where there can grow no Seed, neither is there either Figgs, or <lb/>Vines, or Pomegranates<emph.end type="italics"/>? </s> <s>Intimating that the&longs;e kinds of Fruits <lb/>were preferred by them for their excellency before all others. <lb/></s> <s>And in <emph type="italics"/>Joel (n) The Vine is dryed up, and the Figg-tree langui&longs;h-<emph.end type="italics"/><lb/><arrow.to.target n="marg950"></arrow.to.target><lb/><emph type="italics"/>eth, the Pomegranate-trce, the Palm-tree al&longs;o, and the Apple-tree, <lb/>even all the Trees of the field are withered; becau&longs;e joy is wither­<lb/>ed away from the Sons of Men.<emph.end type="italics"/> Likewi&longs;e in <emph type="italics"/>Haggai: (o) Is the<emph.end type="italics"/><lb/><arrow.to.target n="marg951"></arrow.to.target><lb/><emph type="italics"/>&longs;eed yet in the Bud? </s> <s>and hath as yet the Vine and the Fig-tree, <lb/>and the Pomegranate, and the Olive-tree brought forth<emph.end type="italics"/>? </s> <s>In like <lb/>manner in <emph type="italics"/>Deuteronomie<emph.end type="italics"/> the Land of Promi&longs;e is commended to <lb/>be <emph type="italics"/>(p) A Land of Wheat, and Barly, and Vines in which grow,<emph.end type="italics"/><lb/><arrow.to.target n="marg952"></arrow.to.target><lb/><emph type="italics"/>Figg-trees, and Pomegranates, and Olive-trees,<emph.end type="italics"/> &c. </s> <s>And in the <lb/>Structure of the Temple undertaken by <emph type="italics"/>Solomon<emph.end type="italics"/> upon Divine In­<lb/><arrow.to.target n="marg953"></arrow.to.target><lb/>&longs;piration the <emph type="italics"/>(q)<emph.end type="italics"/> Chapiters of the Pillars were adorned with &longs;eve­<lb/>ral rowes of Pomegranates: which particular is mentioned, not <lb/>in one but many places of Holy Writ. </s> <s>Yea and &longs;ometimes acci­<lb/>dentally and occa&longs;ionally the Holy hath Gho&longs;t ænigmatically re­<lb/>pre&longs;ented this mo&longs;t admirable and Mo&longs;t Wi&longs;e Sructure of the <lb/>World, the Order of the Heavens, and the di&longs;po&longs;ure of Crea­<lb/>tures Spiritual and Corporeal by Emblems, Parables, and Figures, <lb/>lea&longs;t they &longs;hould be as it were dazled and blinded, by the reful­<lb/>gent &longs;plendor of &longs;o excellent an Object. </s> <s>Hence we &longs;ee, that in <lb/>the&longs;e Doctrinal & Dubious Points we may di&longs;cour&longs;e in &longs;uch man­<lb/>ner by help of the Holy Scripture as is meet for the under&longs;tanding <lb/>of the Prophets; which &longs;eeing they are very ob&longs;cure, they &longs;hall be <lb/>fully under&longs;tood, and may be aptly applyed only then when they <lb/>&longs;hall be fulfilled, and not before: So al&longs;o when once the true <lb/>Sy&longs;teme of the Univer&longs;e is found out, then, and not till then, the <lb/>meaning of the&longs;e Figures, and Ænigma's &longs;hall be made known <lb/>unto us: Thus before the coming of the Son of God had di&longs;co­<lb/>vered unto us the My&longs;tery of the Holy Trinity, none were able <lb/>to comprehend or imagine what was concealed under tho&longs;e <pb xlink:href="040/01/527.jpg" pagenum="503"/>words; <emph type="italics"/>(r) In Principio creavit Elohim Cœlum & Terram:<emph.end type="italics"/> for <lb/><arrow.to.target n="marg954"></arrow.to.target><lb/>that they did not &longs;ee how the Noun Plural <emph type="italics"/>Elohim<emph.end type="italics"/> (which is as much <lb/>as to &longs;ay <emph type="italics"/>Dij,<emph.end type="italics"/> [Gods] &longs;hould be joyned with the Verb Singular, <lb/><emph type="italics"/>Creavit<emph.end type="italics"/>: But the My&longs;tery of the Unity of E&longs;&longs;ence and Trinity <lb/>of Per&longs;ons in God being revealed, it was pre&longs;ently known, that <lb/>the Singular Number, <emph type="italics"/>Creavit,<emph.end type="italics"/> had reference to the Unity of E&longs;­<lb/>&longs;ence, (in regard that the Works of the Trinity <emph type="italics"/>ad extra<emph.end type="italics"/> are in­<lb/>divi&longs;ible) and the Plural, <emph type="italics"/>Elohim,<emph.end type="italics"/> to the Per&longs;ons. </s> <s>Who, I pray, <lb/>in elder times could have found out this My&longs;tery? </s> <s>And thus the <lb/>Name of God is thrice repeated in <emph type="italics"/>P&longs;al. </s> <s>67. (s) God, even our<emph.end type="italics"/><lb/><arrow.to.target n="marg955"></arrow.to.target><lb/><emph type="italics"/>God &longs;hall ble&longs;&longs;e us, God &longs;hall ble&longs;&longs;e us, &c.<emph.end type="italics"/> Which at fir&longs;t might <lb/>&longs;eem a Pleona&longs;me, and &longs;uperfluous repetition; but afterwards it <lb/>was evident that <emph type="italics"/>David<emph.end type="italics"/> did there &longs;et out the Benedictions of &longs;e­<lb/>veral Per&longs;ons implyed, to wit, the Father, Son, and Holy Gho&longs;t. <lb/></s> <s>Innumerable Examples of the like kind may be found in the Sa­<lb/>cred Leaves. </s> <s>Therefore, to conclude, I will &longs;ay with ^{*}<emph type="italics"/>David,<emph.end type="italics"/><lb/><arrow.to.target n="marg956"></arrow.to.target><lb/><emph type="italics"/>P&longs;al.<emph.end type="italics"/> 92. <emph type="italics"/>Oh Lord how glorious are thy Works! thy thoughts <lb/>are very deep: an unwi&longs;eman knoweth not, and a fool doth not <lb/>under&longs;tand the&longs;e things.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg949"></margin.target><emph type="italics"/>(m)<emph.end type="italics"/> Numb. c. >20. <lb/>v. 5.</s></p><p type="margin"> <s><margin.target id="marg950"></margin.target><emph type="italics"/>(n)<emph.end type="italics"/> Joel c. </s> <s>1. v. </s> <s>12.</s></p><p type="margin"> <s><margin.target id="marg951"></margin.target><emph type="italics"/>(o)<emph.end type="italics"/> Hagg. c. 2. <lb/>v. 19.</s></p><p type="margin"> <s><margin.target id="marg952"></margin.target><emph type="italics"/>(p)<emph.end type="italics"/> Deut. c. 8. v. 8.</s></p><p type="margin"> <s><margin.target id="marg953"></margin.target><emph type="italics"/>(q)<emph.end type="italics"/> 1 Kings c 7. <lb/>v. 20. & 2 Kings <lb/>c. 25. v. 17. & <lb/>2 Chro. c. 3. v. 15, <lb/>16. & c. 4. v. 12. <lb/>13. & Jerem. c. <lb/>52. v. 21, 22.</s></p><p type="margin"> <s><margin.target id="marg954"></margin.target><emph type="italics"/>(r)<emph.end type="italics"/> Gen. c. 1. v. 1</s></p><p type="margin"> <s><margin.target id="marg955"></margin.target><emph type="italics"/>(s) P<emph.end type="italics"/>&longs;al. 67. v. 6 <lb/>7.</s></p><p type="margin"> <s><margin.target id="marg956"></margin.target>* P&longs;al. 92 v. 536.</s></p><p type="main"> <s>The&longs;e are the particulars that I have thought fit to offer, as <lb/>a Divine, concerning the not-improbable Opinion of the Mobili­<lb/>ty of the Earth and Stability of the Sun: which I hope will be <lb/>acceptable to you, Reverend Sir, out of the love and diligence <lb/>wherewith you per&longs;ue Virtue and Learning. </s> <s>But (to the end <lb/>that you may al&longs;o receive an account of my other Studies) I <lb/>hope very &longs;hortly to publi&longs;h in Print my Second Tome ^{*}<emph type="italics"/>Of the In-<emph.end type="italics"/><lb/><arrow.to.target n="marg957"></arrow.to.target><lb/><emph type="italics"/>&longs;titutions of all Learnings,<emph.end type="italics"/> which &longs;hall containe all the Liberall <lb/>Arts, as I have already &longs;ignified in that <emph type="italics"/>Syntax,<emph.end type="italics"/> and <emph type="italics"/>Spicimen<emph.end type="italics"/> by <lb/>me heretofore put forth, and publi&longs;hed under your Name. </s> <s>The <lb/>other five following Tomes by me promi&longs;ed (which &longs;hall treat of <lb/>Phylo&longs;ophy and Theology) are not altogether &longs;o forward, ne­<lb/>verthele&longs;s they will be &longs;peedily fini&longs;hed. </s> <s>In the mean time there <lb/>will come forth my Book <emph type="italics"/>Concerning ^{*} Oracles,<emph.end type="italics"/> now fini&longs;hed, to­<lb/><arrow.to.target n="marg958"></arrow.to.target><lb/>gether with a Treati&longs;e ^{*} <emph type="italics"/>Of Artificial Divination.<emph.end type="italics"/> And for a <lb/><arrow.to.target n="marg959"></arrow.to.target><lb/>pledge thereof, I &longs;end you at this time annexed to this Epi&longs;tle a <lb/>Tract ^{*} <emph type="italics"/>Concerning Natural Co&longs;mological Divination,<emph.end type="italics"/> or of Natu­<lb/><arrow.to.target n="marg960"></arrow.to.target><lb/>ral Progno&longs;ticks, and Pre&longs;ages of the Changes o&longs; Weather, and <lb/>other things which fall within the compa&longs;&longs;e of Natue. </s> <s>God grant <lb/>you all Happine&longs;&longs;e.</s></p><p type="margin"> <s><margin.target id="marg957"></margin.target>* <emph type="italics"/>In&longs;titutionum<lb/>omnium Doctri­<lb/>narum.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg958"></margin.target>* <emph type="italics"/>De Oraculis.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg959"></margin.target>* <emph type="italics"/>De Divinatio­<lb/>ne artificio&longs;a.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg960"></margin.target>* <emph type="italics"/>De Divinatio­<lb/>ne Naturali Co&longs;­<lb/>mologica.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>Mo&longs;t Reverend Sir<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>NAPLES,<emph.end type="italics"/> from the Covent <lb/>of the <emph type="italics"/>Carmelites,<emph.end type="italics"/> Jan. <lb/></s> <s>6. 1615.</s></p><p type="main"> <s><emph type="italics"/>Your Mo&longs;t Humble Servant<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>PAOLO ANTONIO FOSCARINI.<emph.end type="italics"/></s></p><p type="head"> <s>FINIS.</s></p><pb xlink:href="040/01/528.jpg"/><p type="head"> <s><emph type="italics"/>Imprimatur,<emph.end type="italics"/> P. ANT. GHIBERT, <emph type="italics"/>Vic. Gen.</s><emph.end type="italics"/><lb/><s>JOANNES LONGUS <emph type="italics"/>Can. & Cur. Archiep. <lb/>Neap.<emph.end type="italics"/> THEOL. <emph type="italics"/>Vidit.<emph.end type="italics"/></s></p> </chap> <pb xlink:href="040/01/529.jpg"/><chap><p type="head"> <s>A <lb/>TABLE <lb/>Of the mo&longs;t Ob&longs;ervable <lb/>PERSONS and MATTERS <lb/>Mentioned in the FIRST PART Of <lb/>The Fir&longs;t Tome.<lb/><arrow.to.target n="table72"></arrow.to.target></s></p><table><table.target id="table72"></table.target><row><cell>A</cell><cell></cell></row><row><cell>ABSTACT.</cell><cell></cell></row><row><cell>Things are exactly the &longs;ame in <emph type="italics"/>Abstract,<emph.end type="italics"/> as in Concrete.</cell><cell>185</cell></row><row><cell>AIRE.</cell><cell></cell></row><row><cell>The part of the <emph type="italics"/>Aire<emph.end type="italics"/> inferiour to the Higher Mountains doth follow the Motion of the Earth.</cell><cell>124</cell></row><row><cell> The motion of the <emph type="italics"/>Aire<emph.end type="italics"/> apt to carry with it light things, but not heavy.</cell><cell>124</cell></row><row><cell> The <emph type="italics"/>Aire<emph.end type="italics"/> alwayes touching us with the &longs;ame part of it, cannot make us feel it.</cell><cell>228</cell></row><row><cell> It is more rea&longs;onable that the <emph type="italics"/>Aire<emph.end type="italics"/> be commoved by the rugged &longs;urface of the Earth, than by the Cele&longs;tial Motion.</cell><cell>400</cell></row><row><cell> It is demon&longs;trated, inverting the Argument, that the perpetual Motion of the <emph type="italics"/>Aire<emph.end type="italics"/> from Ea&longs;t to We&longs;t, commeth from the Motion of Heaven.</cell><cell>403</cell></row><row><cell>ANIMALS.</cell><cell></cell></row><row><cell><emph type="italics"/>Animals, Vide,<emph.end type="italics"/> The Motion of <emph type="italics"/>Animals.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The cau&longs;e of the Wearine&longs;&longs;e that attends the Motion of <emph type="italics"/>Animals.<emph.end type="italics"/></cell><cell>244</cell></row><row><cell>APOLLONIUS.</cell><cell></cell></row><row><cell><emph type="italics"/>Apollonius<emph.end type="italics"/> and Copernicus demon&longs;trate the Re­trogradations of Venus and Mercury.</cell><cell>311</cell></row><row><cell><emph type="italics"/>Arguing, Arguments, & Argumentations<emph.end type="italics"/></cell><cell></cell></row><row><cell>Somein <emph type="italics"/>Arguing<emph.end type="italics"/> fix in their minds the Conclu­&longs;ion believed by them, and then adapt their Rea&longs;ons to that.</cell><cell>250</cell></row><row><cell>One &longs;ingle Experiment or &longs;ound Demon&longs;trati­on, overthroweth all <emph type="italics"/>Arguments<emph.end type="italics"/> meerly pro­bable.</cell><cell>105</cell></row><row><cell>A plea&longs;ant Example &longs;hewing the invalidity of &longs;ome Phi&longs;ical <emph type="italics"/>Argumentations.<emph.end type="italics"/></cell><cell>363</cell></row><row><cell>ARISTARCHUS.</cell><cell></cell></row><row><cell>Rea&longs;on and Di&longs;cour&longs;e in <emph type="italics"/>Ari&longs;tarchus<emph.end type="italics"/> and Coper­nicus prevailed over manife&longs;t Sen&longs;e.</cell><cell>301</cell></row><row><cell>ARISTOTLE.</cell><cell></cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> maketh the World perfect, becau&longs;eit hath the Threefold Dimen&longs;ion.</cell><cell>2</cell></row><row><cell><emph type="italics"/>Ari&longs;t.<emph.end type="italics"/> his Demon&longs;trations to prove the Worlds Dimen&longs;ions to be three, and no more.</cell><cell>2</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> his Definition of Nature either imper­fect or un&longs;ea&longs;onable.</cell><cell>7</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> accomodates the Rules of Architecture to the Frame of the World, and not the Frame to the Rules.</cell><cell>8</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> cannot equivocate, being the Inventer o&longs; Logick.</cell><cell>23</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> his Paralogi&longs;me in proving the Earth to be in the centre of the World.</cell><cell>24</cell></row><row><cell><emph type="italics"/>Ari&longs;t.<emph.end type="italics"/> Paralogi&longs;me another way di&longs;covered.</cell><cell>24</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> his Di&longs;cour&longs;e to prove the Incorrupti­bility of Heaven.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> proveth that Circular Motion hath no Contrary.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> defective in a&longs;&longs;igning the Cau&longs;es, why the Elements are Generable and Corrup­tible.</cell><cell>31</cell></row><row><cell><emph type="italics"/>Ari&longs;iotle<emph.end type="italics"/> would change his opinion, did he &longs;ee the Novelties of our Age.</cell><cell>37</cell></row><pb xlink:href="040/01/530.jpg"/><row><cell><emph type="italics"/>Ari&longs;t,<emph.end type="italics"/> preferres Sen&longs;e before Ratiocination.</cell><cell>42</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> affirmeth the Heavens alterable, rather then otherwi&longs;e, by his Doctrine.</cell><cell>42</cell></row><row><cell>Requifites to fit a man to Philo&longs;ophate well in the way of <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell>Some of <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> Sectators impaire his Repu­tation, in going about to enhan&longs;e it.</cell><cell>93</cell></row><row><cell>The &longs;ervile Spirit of &longs;ome of <emph type="italics"/>Ari&longs;t.<emph.end type="italics"/> followers.</cell><cell>95</cell></row><row><cell>Too clo&longs;e an adherence to <emph type="italics"/>Aristotle<emph.end type="italics"/> is blame­able.</cell><cell>95</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and <emph type="italics"/>Ptolomy<emph.end type="italics"/> argue again&longs;t the Diurnal Motion a&longs;cribed to the Earth.</cell><cell>97</cell></row><row><cell>A Propo&longs;ition that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> filched from the Ancients, and &longs;omewhat altered.</cell><cell>99</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> his Arguments for the Earths Quie­&longs;cence and Immobility.</cell><cell>107</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> were he alive, would either refute his Adver&longs;aries Arguments, or el&longs;e would alter his Opinion.</cell><cell>113</cell></row><row><cell><emph type="italics"/>Aristotles<emph.end type="italics"/> fir&longs;t Argument again&longs;t the Earths Mo­tion, is defective in two things.</cell><cell>121</cell></row><row><cell>The Paralogi&longs;me of <emph type="italics"/>Aristotle<emph.end type="italics"/> and Ptolomy in &longs;uppo&longs;ing that for known, which is in que­&longs;tion.</cell><cell>121</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> admitteth that the Fire moveth direct­ly upwards by Nature, and round about, by Participation.</cell><cell>122</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> and Ptolomy &longs;eem to confute the Earths Mobility again&longs;t tho&longs;e who think that it, ha­ving along time &longs;tood &longs;till, began to move in the time of Pythagoras.</cell><cell>168</cell></row><row><cell><emph type="italics"/>Aristotle<emph.end type="italics"/> his errour in affirming falling Grave Bodies to move according to the proportion of their gravities.</cell><cell>199</cell></row><row><cell><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> his Demon&longs;trations to prove the Earth is finite, are all nullified, by denying it to be moveable.</cell><cell>294</cell></row><row><cell><emph type="italics"/>Aristotle<emph.end type="italics"/> maketh that Point to be the Centre of the Univer&longs;e, about which all the Cele&longs;tial Spheres do revolve</cell><cell>294</cell></row><row><cell>A que&longs;tion is put, if <emph type="italics"/>Ari&longs;t.<emph.end type="italics"/> were forced to receive one of two Propo&longs;itions, that make again&longs;t his Doctrine, which he would admit.</cell><cell>294</cell></row><row><cell><emph type="italics"/>Aristotle<emph.end type="italics"/> his Argument again&longs;t the Ancients, who held that the Earth was a Planet.</cell><cell>344</cell></row><row><cell><emph type="italics"/>Aristotle<emph.end type="italics"/> taxeth Plato of being over­&longs;tudious of Geometry.</cell><cell>361</cell></row><row><cell><emph type="italics"/>Aristotle<emph.end type="italics"/> holdeth tho&longs;e Effects to be miraculous, of which the Cau&longs;es are unknown.</cell><cell>384</cell></row><row><cell>ASTRONOMERS.</cell><cell></cell></row><row><cell><emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> confuted by Anti­Tycho.</cell><cell>38</cell></row><row><cell>The principal Scope of <emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> is to give a rea&longs;on of Appearances and Phænomena.</cell><cell>308</cell></row><row><cell><emph type="italics"/>Actronomers<emph.end type="italics"/> all agree that the greater Magni­tudes of the Orbes is the cau&longs;e of the tardity in their Conver&longs;ions.</cell><cell>331</cell></row><row><cell><emph type="italics"/>A&longs;tronomers<emph.end type="italics"/> perhaps have not known what Appearances ought to follow, upon the An­nual Motion of the Earth.</cell><cell>338</cell></row><row><cell><emph type="italics"/>Actronomers<emph.end type="italics"/> having omitted to in&longs;tance what al­terations tho&longs;e are, that may be derived from the Annual Motion of the Earth, do thereby te&longs;tifie that they never rightly un­der&longs;tood the &longs;ame.</cell><cell>343</cell></row><row><cell>ASTRONOMICAL.</cell><cell></cell></row><row><cell><emph type="italics"/>A&longs;tronomical<emph.end type="italics"/> Ob&longs;ervations wre&longs;ted by Anti­Ty­cho to his own purpo&longs;e.</cell><cell>39</cell></row><row><cell><emph type="italics"/>Actronomical<emph.end type="italics"/> In&longs;truments are very &longs;ubject to errour.</cell><cell>262</cell></row><row><cell>ASTRONOMY.</cell><cell></cell></row><row><cell><emph type="italics"/>A&longs;tronomy<emph.end type="italics"/> re&longs;tored by Copernicus upon the Suppo&longs;itions of Ptolomy</cell><cell>308</cell></row><row><cell>Many things may remain as yet unob&longs;erved in <emph type="italics"/>A&longs;tronomy<emph.end type="italics"/></cell><cell>415</cell></row><row><cell>AUCUPATORIAN.</cell><cell></cell></row><row><cell>An <emph type="italics"/>Aucupatorian<emph.end type="italics"/> Problem for &longs;hooting of Birds flying.</cell><cell>157</cell></row><row><cell>AXIOME, or <emph type="italics"/>Axiomes.<emph.end type="italics"/></cell><cell></cell></row><row><cell>In the <emph type="italics"/>Axiome, Fru&longs;tra fit per plura, &c.<emph.end type="italics"/> the addi­tion of <emph type="italics"/>æquœ bene<emph.end type="italics"/> is &longs;uperfluous.</cell><cell>106</cell></row><row><cell>Three <emph type="italics"/>Axiomes<emph.end type="italics"/> that are &longs;uppo&longs;ed manife&longs;t.</cell><cell>230</cell></row><row><cell>Certain <emph type="italics"/>Axiomes<emph.end type="italics"/> commonly admitted by all Philo&longs;ophers.</cell><cell>361</cell></row><row><cell>B</cell><cell></cell></row><row><cell>BODY and <emph type="italics"/>Bodies.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Contraries that corrupt, re&longs;ide not in the &longs;ame <emph type="italics"/>Body<emph.end type="italics"/> that corrupteth.</cell><cell>30</cell></row><row><cell>GRAVE BODY; If the Cele&longs;tial Globe were perforated, a <emph type="italics"/>Grave Body<emph.end type="italics"/> de&longs;cending by that Bore, would pa&longs;&longs;e and a&longs;cend as far beyond the Centre, as it did de&longs;cend.</cell><cell>203</cell></row><row><cell>The motion of <emph type="italics"/>Grave Bodies,<emph.end type="italics"/> Vide <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The Accelleration of <emph type="italics"/>Grave Bodies<emph.end type="italics"/> that de&longs;cend naturally, increa&longs;eth from moment to moment.</cell><cell>205</cell></row><row><cell>We know no more who moveth <emph type="italics"/>Grave Bodies<emph.end type="italics"/>downwards, than who moveth the Stars round; nor know we any thing of the&longs;e <pb xlink:href="040/01/531.jpg"/>Cour&longs;es, more than the Names impo&longs;ed on them by our &longs;elves.</cell><cell>210</cell></row><row><cell>The great Ma&longs;&longs;e of <emph type="italics"/>Grave Bodies<emph.end type="italics"/> being tran&longs;­ferred out of their Place, the &longs;eperated parts would follow that Ma&longs;&longs;e.</cell><cell>221</cell></row><row><cell>PENSILE BODY; Every <emph type="italics"/>Pen&longs;ile Body<emph.end type="italics"/> carried round in the Circumference of a Circle, ac­quireth of it &longs;elf a Motion in it &longs;elf contrary to the &longs;ame.</cell><cell>362</cell></row><row><cell>CBLESTIAL BODIES neither heavy nor light according to <emph type="italics"/>Ari&longs;toile.<emph.end type="italics"/></cell><cell>23</cell></row><row><cell><emph type="italics"/>Cele&longs;tial Bodies<emph.end type="italics"/> are Generable and Corruptible becau&longs;e they are Ingenerable aud Incorrup­tible.</cell><cell>29</cell></row><row><cell>Among&longs;t <emph type="italics"/>Cele&longs;t. Bodies<emph.end type="italics"/> there is no contrariety.</cell><cell>29</cell></row><row><cell><emph type="italics"/>Cele&longs;tial Bodies<emph.end type="italics"/> touch, but are not touched by the Elements.</cell><cell>30</cell></row><row><cell>Rarity and Den&longs;ity in <emph type="italics"/>Celectial Bodies,<emph.end type="italics"/> different from Rarity and Den&longs;ity in the Elements.</cell><cell>30</cell></row><row><cell><emph type="italics"/>Cele&longs;tial Bodies<emph.end type="italics"/> de&longs;igned to &longs;erve the Earth, need no more but Motion and Light.</cell><cell>45</cell></row><row><cell><emph type="italics"/>Cele&longs;tial Bodies<emph.end type="italics"/> wantan interchangeable Opera­tion on each other.</cell><cell>46</cell></row><row><cell><emph type="italics"/>Cele&longs;tial Bodies<emph.end type="italics"/> alterable in their externe parts.</cell><cell>46</cell></row><row><cell>Perfect Sphericity why a&longs;cribed to <emph type="italics"/>Cele&longs;tial Bo­dies<emph.end type="italics"/> by Peripateticks.</cell><cell>69</cell></row><row><cell>All <emph type="italics"/>Celectial Bodies<emph.end type="italics"/> have Gravity and Levity.</cell><cell>493</cell></row><row><cell>ELEMENTARY BODIES; Their propen&longs;i­on to follow the Earth, hath a limited Sphere of Activity.</cell><cell>213</cell></row><row><cell>LIGHT BODIES ea&longs;ier to be moved than heavy, but le&longs;&longs;e apt to con&longs;erve the Motion.</cell><cell>400</cell></row><row><cell>LUMINOUS BODIES; <emph type="italics"/>Bodies<emph.end type="italics"/> naturally <emph type="italics"/>Lu­minous<emph.end type="italics"/> are different from tho&longs;e that are by na­ture Ob&longs;cure.</cell><cell>34</cell></row><row><cell>The rea&longs;on why <emph type="italics"/>Luminous Bodies<emph.end type="italics"/> appear &longs;o much the more enlarged, by how much they are le&longs;&longs;er.</cell><cell>304</cell></row><row><cell>Manife&longs;t Experience &longs;hews that the more <emph type="italics"/>Lumi­nous Bodies<emph.end type="italics"/> do much more irradiate than the le&longs;&longs;e Lucid.</cell><cell>306</cell></row><row><cell>SIMPLE BODYES have but one Simple Motion that agreeth with them.</cell><cell>494</cell></row><row><cell>SPHERICAL BODIES; In <emph type="italics"/>Spherical Bodies Deor&longs;um<emph.end type="italics"/> is the Centre, and <emph type="italics"/>Sur&longs;um<emph.end type="italics"/> the Cir­ference.</cell><cell>479</cell></row><row><cell>BONES.</cell><cell></cell></row><row><cell>The ends of the <emph type="italics"/>Bones<emph.end type="italics"/> are rotund, and why.</cell><cell>232</cell></row><row><cell>BUONARRUOTTI.</cell><cell></cell></row><row><cell><emph type="italics"/>Buonarruotti<emph.end type="italics"/> a Statuary of admirable ingenuity.</cell><cell>86</cell></row><row><cell>C</cell><cell></cell></row><row><cell>CANON.</cell><cell></cell></row><row><cell>A &longs;hameful Errour in the Argument taken from the <emph type="italics"/>Canon<emph.end type="italics"/>­Bullets falling from the Moons Concave.</cell><cell>197</cell></row><row><cell>An exact Computation of the fall of the <emph type="italics"/>Canon<emph.end type="italics"/>­Bullet from the Moons Concave, to the Centre of the Earth.</cell><cell>198</cell></row><row><cell>CELESTIAL</cell><cell></cell></row><row><cell><emph type="italics"/>Cele&longs;tial<emph.end type="italics"/> Sub&longs;tances that be Unalterable, and Elementary that be Alterable, nece&longs;&longs;ary in the opinion of <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell>CENTRE.</cell><cell></cell></row><row><cell>The Sun more probably in the <emph type="italics"/>Centre<emph.end type="italics"/> of the U­niver&longs;e, than the Earth.</cell><cell>22</cell></row><row><cell>Natural inclination of all the Globes of the World to go to their <emph type="italics"/>Centre.<emph.end type="italics"/></cell><cell>22</cell></row><row><cell>Grave Bodies may more rationally be affirmed to tend towards the <emph type="italics"/>Centre<emph.end type="italics"/> of the Earth, than of the Univer&longs;e.</cell><cell>25</cell></row><row><cell>CHYMISTS.</cell><cell></cell></row><row><cell><emph type="italics"/>Chymi&longs;ts<emph.end type="italics"/> interpret the Fables of Poets to be Se­crets for making of Gold.</cell><cell>93</cell></row><row><cell>CIRCLE, and <emph type="italics"/>Circular.<emph.end type="italics"/></cell><cell></cell></row><row><cell>It is not impo&longs;&longs;ible with the Circumference of a &longs;mall <emph type="italics"/>Circle<emph.end type="italics"/> few times revolved, to mea&longs;ure and de&longs;cribe a line bigger than any great <emph type="italics"/>Cir­cle<emph.end type="italics"/> what&longs;oever.</cell><cell>222</cell></row><row><cell>The <emph type="italics"/>Circular Line<emph.end type="italics"/> perfect, according to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/>and the Right imperfect, and why.</cell><cell>9</cell></row><row><cell>CLARAMONTIUS.</cell><cell></cell></row><row><cell>The Paralogi&longs;me of <emph type="italics"/>Claramontius.<emph.end type="italics"/></cell><cell>241</cell></row><row><cell>The Argument of <emph type="italics"/>Claramontius<emph.end type="italics"/> recoileth upon him&longs;elf.</cell><cell>245</cell></row><row><cell>The Method ob&longs;erved by <emph type="italics"/>Claramontius<emph.end type="italics"/> in confu­ting A&longs;tronomers, and by Salviatus in re­futing him.</cell><cell>253</cell></row><row><cell>CLOUDS.</cell><cell></cell></row><row><cell><emph type="italics"/>Clouds<emph.end type="italics"/> no le&longs;&longs;e apt than the Moon to be illumi­nated by the Sun.</cell><cell>73</cell></row><pb xlink:href="040/01/532.jpg"/><row><cell>CONCLUSION and <emph type="italics"/>Conclu&longs;ions.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The certainty of the <emph type="italics"/>Conclu&longs;ion<emph.end type="italics"/> helpeth by a re&longs;o­lutive Method to finde the Demon&longs;tration.</cell><cell>37</cell></row><row><cell>The Book of <emph type="italics"/>Conclu&longs;io s,<emph.end type="italics"/> frequently mentioned, was writ by Chri&longs;topher Scheiner a Je&longs;uit.</cell><cell>195, & 323.</cell></row><row><cell>CONTRARIES.</cell><cell></cell></row><row><cell><emph type="italics"/>Contraries<emph.end type="italics"/> that corrupt, re&longs;ide not in the &longs;ame Body that corrupteth.</cell><cell>30</cell></row><row><cell>COPERNICAN.</cell><cell></cell></row><row><cell>An&longs;wers to the three fir&longs;t Objections again&longs;t the <emph type="italics"/>Copernican Sy&longs;tem.<emph.end type="italics"/></cell><cell>303</cell></row><row><cell>The <emph type="italics"/>Copernican Sy&longs;tem<emph.end type="italics"/> difficul to be under&longs;tood, but ea&longs;ie to be effected.</cell><cell>354</cell></row><row><cell>A plain Scheme repre&longs;enting the <emph type="italics"/>Copernican Sy­cteme<emph.end type="italics"/> and its con&longs;equences.</cell><cell>354</cell></row><row><cell>The pro&longs;cribing of the <emph type="italics"/>Copernican<emph.end type="italics"/> Doctrine, af­ter &longs;o long a Tolleration, and now that it is more than ever followed, &longs;tudied and con­firmed, would be an affront to Truth.</cell><cell>444</cell></row><row><cell>The <emph type="italics"/>Copern.<emph.end type="italics"/> Sy&longs;tem admirably agreeth with the Miracle of <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> in the Literal Sen&longs;e.</cell><cell>456</cell></row><row><cell>If Divines would admit of the <emph type="italics"/>Copernican<emph.end type="italics"/> Sy­&longs;tem, they might &longs;oon find out Expo&longs;itions for all Scriptures that &longs;eem to make again&longs;t it.</cell><cell>459</cell></row><row><cell>The <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;tem rejected by many, out of a devout re&longs;pect to Scripture Authorities.</cell><cell>461</cell></row><row><cell>The <emph type="italics"/>Copernican<emph.end type="italics"/> Sy&longs;tem more plainly a&longs;&longs;erted in Scripture than the <emph type="italics"/>Ptolomaick.<emph.end type="italics"/></cell><cell>469</cell></row><row><cell>COPERNICANS.</cell><cell></cell></row><row><cell><emph type="italics"/>Copernicans<emph.end type="italics"/> are not moved through ignorance of the Arguments on the Adver&longs;e part.</cell><cell>110</cell></row><row><cell><emph type="italics"/>Copernicans<emph.end type="italics"/> were all fir&longs;t again&longs;t that Opinion, but the Peripateticks were never on the other &longs;ide.</cell><cell>110</cell></row><row><cell><emph type="italics"/>Copernicans<emph.end type="italics"/> too freely admit certain Propo&longs;iti­ons for true, which are doubtful.</cell><cell>159</cell></row><row><cell>He that will be a <emph type="italics"/>Copernican<emph.end type="italics"/> mu&longs;t deny his Sen­&longs;es.</cell><cell>228</cell></row><row><cell>A Great Mathematician made a <emph type="italics"/>Copernican,<emph.end type="italics"/> by looking into that Doctrine, with a purpo&longs;e to confute it.</cell><cell>443</cell></row><row><cell>COPERNICUS.</cell><cell></cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> e&longs;teemeth the Earth a Globe, like to a Planet.</cell><cell>1</cell></row><row><cell>Objections of two Moderne Authours [Schei­ner and Claramontius] again&longs;t <emph type="italics"/>Copernicus.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> his Opinion overthrows the <emph type="italics"/>Criterium<emph.end type="italics"/>of Phylo&longs;ophers.</cell><cell>223</cell></row><row><cell>A gro&longs;le Errour in the Oppo&longs;er of <emph type="italics"/>Copernicus,<emph.end type="italics"/>and wherein it appears.</cell><cell>234, 235, & 236</cell></row><row><cell>A &longs;ubtle and withal &longs;imple Argument again&longs;t <emph type="italics"/>Copernicus.<emph.end type="italics"/></cell><cell>234</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> his Opponent had but little &longs;tudied him, as appears by another gro&longs;&longs;e Errour.</cell><cell>235</cell></row><row><cell>Its que&longs;tioned whither he under&longs;tood the third Motion a&longs;&longs;igned to the Earth by <emph type="italics"/>Copern.<emph.end type="italics"/></cell><cell>236</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> erroneou&longs;ly a&longs;&longs;ignes the &longs;ame Opera­tions to different Natures.</cell><cell>238</cell></row><row><cell>A declaration of the improbability of <emph type="italics"/>Copernicus<emph.end type="italics"/>his Opinion.</cell><cell>301</cell></row><row><cell>Rea&longs;on and Di&longs;cour&longs;e in <emph type="italics"/>Copernicus<emph.end type="italics"/> and Ari&longs;tar­chus prevailed over Sen&longs;e.</cell><cell>301</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> &longs;peaketh nothing of the &longs;mall Variati­on of Bigne&longs;&longs;e in Venus and Mars.</cell><cell>302</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> per&longs;waded by Rea&longs;ons contrary to Sen&longs;ible Experiments.</cell><cell>306</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> re&longs;tored A&longs;tronomy upon the Suppo­&longs;itions of Ptolomy.</cell><cell>308</cell></row><row><cell>What moved <emph type="italics"/>Copernicus<emph.end type="italics"/> to e&longs;tabli&longs;h his Sy­&longs;teme.</cell><cell>308</cell></row><row><cell>Its a great argument in favour of <emph type="italics"/>Copernicus,<emph.end type="italics"/> that he obviates the Stations and Retrogradati­ons of the Motions of the Planets.</cell><cell>309</cell></row><row><cell>In&longs;tances Ironically propounded by Scheiner again&longs;t <emph type="italics"/>Copernicus.<emph.end type="italics"/></cell><cell>323</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> under&longs;tood not &longs;ome things for want of In&longs;truments.</cell><cell>338</cell></row><row><cell>The grand difficulty in <emph type="italics"/>Copernicus<emph.end type="italics"/> his Doctrine, is that which concerns the Phænomena of the Sun and fixed Stars.</cell><cell>343</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> the Re&longs;torer of the Pythagorean Hy­pothe&longs;is, and the Occa&longs;ion of it.</cell><cell>429</cell></row><row><cell><emph type="italics"/>Copernicus<emph.end type="italics"/> founded not his Doctrine on Rea&longs;ons depending on Scripture, wherein he might have mi&longs;taken their Sen&longs;e, but upon Natu­ral Conclu&longs;ions and A&longs;tronomical and Ge­ometrical Demon&longs;trations.</cell><cell>431</cell></row><row><cell>CORRUPTIBLE, and <emph type="italics"/>Corruptibility.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The perfection of Figure operates in <emph type="italics"/>Corruptible Bodies,<emph.end type="italics"/> but not in Eternal.</cell><cell>69</cell></row><row><cell>The Di&longs;paragers of <emph type="italics"/>Corruptibility<emph.end type="italics"/> ought to be turned into Statua's.</cell><cell>37</cell></row><row><cell><emph type="italics"/>Corruptibility<emph.end type="italics"/> admits of more and le&longs;&longs;e, &longs;o doth not Incorruptibility.</cell><cell>69</cell></row><row><cell>COUNCILS.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Councils<emph.end type="italics"/> refu&longs;e to impo&longs;e Natural Conclu­&longs;ions as matters of Faith.</cell><cell>450</cell></row><pb xlink:href="040/01/533.jpg"/><row><cell>D</cell><cell></cell></row><row><cell>DIAMONDS.</cell><cell></cell></row><row><cell><emph type="italics"/>Diamonds<emph.end type="italics"/> ground to divers &longs;ides, and why.</cell><cell>63</cell></row><row><cell>DIDACUS.</cell><cell></cell></row><row><cell><emph type="italics"/> Didacus à Stunica<emph.end type="italics"/> reconcileth Texts of Scripture with the Copernican Hypothe&longs;is.</cell><cell>468</cell></row><row><cell>DEFINITIONS.</cell><cell></cell></row><row><cell><emph type="italics"/>Definitions<emph.end type="italics"/> contain virtually all the Pa&longs;&longs;ions of the things defined.</cell><cell>87</cell></row><row><cell>E</cell><cell></cell></row><row><cell>EARTH.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> Spherical by the Con&longs;piration of its parts to go to its Centre.</cell><cell>21</cell></row><row><cell>Itis ea&longs;ier to prove the <emph type="italics"/>Earth<emph.end type="italics"/> to move, than that Corruptibility is made by Contraries.</cell><cell>27</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> very Noble, by rea&longs;on of the Mu­tations made therein.</cell><cell>45</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> unprofitable and full of Idlene&longs;&longs;e, its Alterations being taken away.</cell><cell>45</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> more Noble than Gold and Jewels.</cell><cell>45</cell></row><row><cell>The Cele&longs;tial Bodies de&longs;igned to &longs;erve the <emph type="italics"/>Earth,<emph.end type="italics"/>need no more but Motion and Light.</cell><cell>45</cell></row><row><cell> The Generations and Mutations that are in the <emph type="italics"/>Earth,<emph.end type="italics"/> are all for the Good of Man.</cell><cell>47</cell></row><row><cell>From the <emph type="italics"/>Earth<emph.end type="italics"/> we &longs;ee more than half the Lu­nar Globe.</cell><cell>51</cell></row><row><cell>Seven Re&longs;emblances between the <emph type="italics"/>Earth<emph.end type="italics"/> and Moon.</cell><cell>48 to 53</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> unable to reflect the Suns Rays.</cell><cell>54</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> may reciprocally operate on Cele&longs;ti­al Bodies with its Light.</cell><cell>80</cell></row><row><cell>Affinity between the <emph type="italics"/>Earth<emph.end type="italics"/> and Moon, by rea­&longs;on of their Vicinity.</cell><cell>81</cell></row><row><cell>The Motions of the <emph type="italics"/>Earth<emph.end type="italics"/> imperceptible to its Inhabitants.</cell><cell>97</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> can have no other Motions than tho&longs;e which to us appear commune to all the re&longs;t of the Univer&longs;e, the <emph type="italics"/>Earth<emph.end type="italics"/> excepted.</cell><cell>97</cell></row><row><cell>The Diurnal Motion &longs;eemeth commune to all the Univer&longs;e, the <emph type="italics"/>Earth<emph.end type="italics"/> onely excepted.</cell><cell>97</cell></row><row><cell>Ari&longs;totle and Ptolomy argue again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/>Diurnal Motion.</cell><cell>97</cell></row><row><cell>The Diurnal Motion of the <emph type="italics"/>Earth.<emph.end type="italics"/> Vide <emph type="italics"/>Diur­nal Motion.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Seven Arguments to prove the Diurnal Moti­on to belong to the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>99 to 103</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> a pendent Body, and equilibrated in a fluid Medium, &longs;eems unable to re&longs;i&longs;t the Rapture of the Diurnal Motion.</cell><cell>103</cell></row><row><cell>Two kinds of Arguments again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/>Motion.</cell><cell>108</cell></row><row><cell>Arguments of Ari&longs;totle, Ptolomy, Tycho, and other per&longs;ons, again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/> Motion.</cell><cell>107 & 108</cell></row><row><cell>The fir&longs;t Argument again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/> Motion taken from Grave Bodies falling from on high to the Ground.</cell><cell>108</cell></row><row><cell>Which Argument is con&longs;irmed by the Experi­ment of a Body let fall from the Round­top of a Ships Ma&longs;t.</cell><cell>108</cell></row><row><cell>The &longs;econd Argument taken from a Project &longs;hot very high.</cell><cell>108</cell></row><row><cell>The third Argument taken from the Shot of a Canon towards the Ea&longs;t, and towards the We&longs;t.</cell><cell>108</cell></row><row><cell>This Argument is con&longs;irmed by two Shots to­wards the North and South, and two others towards the Ea&longs;t and We&longs;t.</cell><cell>109</cell></row><row><cell>The fourth Argument taken from the Clouds and from Birds.</cell><cell>113</cell></row><row><cell>A fifth Argument taken from the Aire which we feel beat upon us when we run an Hor&longs;e at full &longs;peed.</cell><cell>114</cell></row><row><cell>A &longs;ixth Argument taken from the whirling of Circular Bodies, which hath a faculty to extrude and di&longs;&longs;ipate.</cell><cell>114</cell></row><row><cell>The An&longs;wer to Ari&longs;totles fir&longs;t Argument.</cell><cell>115</cell></row><row><cell>The An&longs;wer to the &longs;econd Argument.</cell><cell>117</cell></row><row><cell>The An&longs;wer to the third Argument.</cell><cell>120 to 150</cell></row><row><cell>An In&longs;tance of the Diurnal Motion of the <emph type="italics"/>Earth,<emph.end type="italics"/>taken from the Shot of a Piece of Ordinance perpendicularly, and the An&longs;wers to the &longs;ame, &longs;hewing the Equivoke.</cell><cell>153, 154</cell></row><row><cell>The An&longs;wer to the Argument of the Shots of Canons made towards the North and South.</cell><cell>158</cell></row><row><cell>The An&longs;wer to the Argument taken from the Shots at point blank towards the Ea&longs;t and We&longs;t.</cell><cell>159</cell></row><row><cell>The An&longs;wer to the Argument of the flying of Birds contrary to the Motion of the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>165</cell></row><row><cell>An Experiment by which alone is &longs;hewn the Nullity of all the Arguments produced a­gain&longs;t the Motion of the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>165</cell></row><row><cell>The Stupidity of &longs;ome that think the <emph type="italics"/>Earth<emph.end type="italics"/> be­gan to move, when Pythagoras began to af­firme that it did &longs;o.</cell><cell>167</cell></row><row><cell>A Geometrical Demon&longs;tration to prove the Impo&longs;&longs;ibility of Extru&longs;ion, by means of the <emph type="italics"/>Earths<emph.end type="italics"/> Vertigo, in An&longs;wer to the &longs;ixth <pb xlink:href="040/01/534.jpg"/>Argument.</cell><cell>176</cell></row><row><cell>Granting the Diurnal Vertigo of the <emph type="italics"/>Earth,<emph.end type="italics"/> and that by &longs;ome &longs;udden Stop or Ob&longs;tacle it were Arre&longs;ted, Hou&longs;es, Mountains them&longs;elves, and perhaps the whole Globe, would be &longs;haken in pieces.</cell><cell>190</cell></row><row><cell>Other Arguments of two Modern Authours [Scheiner and. Claramontius] again&longs;t the Copernican Hypothe&longs;is of the <emph type="italics"/>Earths<emph.end type="italics"/> Mo­tion.</cell><cell>195</cell></row><row><cell>The fir&longs;t Objection of the Modern Authour [Scheiner] in his Book of Conclu&longs;ions.</cell><cell>195</cell></row><row><cell>The Argument of [Claramontius] again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/> Motion, taken from things falling per­pendicularly, another way an&longs;wered.</cell><cell>223</cell></row><row><cell>The <emph type="italics"/>Earths<emph.end type="italics"/> Motion collected from the Stars.</cell><cell>229</cell></row><row><cell>Argumeuts again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/> Motion, taken <emph type="italics"/>ex rerum natura.<emph.end type="italics"/></cell><cell>230</cell></row><row><cell>A Simple Body as the <emph type="italics"/>Earth,<emph.end type="italics"/> cannot move with three &longs;everal Motions.</cell><cell>231</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> cannot move with any of the Moti­ons a&longs;&longs;igned it by Copernicus.</cell><cell>231</cell></row><row><cell>An&longs;wers to the Arguments again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/>Motion, token <emph type="italics"/>ex rerum natnra.<emph.end type="italics"/></cell><cell>231</cell></row><row><cell>Four Axiomes again&longs;t the Motion of the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>230 to 232</cell></row><row><cell>One onely Principle might cau&longs;e a Plurality of Motions in the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>233</cell></row><row><cell>The &longs;ame Argument again&longs;t the Plurality of Motions in the <emph type="italics"/>Earth,<emph.end type="italics"/> an&longs;wered by Exam­ples of the like Motions in other Cele&longs;tial Bodies.</cell><cell>236</cell></row><row><cell>A fourth Argument [of Claramontius] again&longs;t the Copernican Hypothe&longs;is of the <emph type="italics"/>Earths<emph.end type="italics"/>Mobility.</cell><cell>239</cell></row><row><cell>From the <emph type="italics"/>Earths<emph.end type="italics"/> ob&longs;curity, and the &longs;plendor of the fixed Stars, it is argued that it is move­able, and they immoveable.</cell><cell>239</cell></row><row><cell>A fifth Argument [of Claramontius] again&longs;t the Copernican Hypothe&longs;is of the <emph type="italics"/>Earths<emph.end type="italics"/>Mobility.</cell><cell>240</cell></row><row><cell>Another difference between the <emph type="italics"/>Earth<emph.end type="italics"/> and Ce­le&longs;tial Bodies, taken from Purity and im­purity.</cell><cell>240</cell></row><row><cell>It &longs;eems a Soleci&longs;me, to affirme that the <emph type="italics"/>Earth<emph.end type="italics"/>is not in Heaven.</cell><cell>241</cell></row><row><cell>Granting to the <emph type="italics"/>Earth<emph.end type="italics"/> the Annual, it mu&longs;t of nece&longs;&longs;ity al&longs;o have the Diurnal Motion a&longs;&longs;i­gned to it.</cell><cell>300</cell></row><row><cell>Di&longs;cour&longs;es more than childi&longs;h, that &longs;erve to keep Fools in the Opinion of the <emph type="italics"/>Earths<emph.end type="italics"/> Sta­bility.</cell><cell>301</cell></row><row><cell>The Difficulties removed that ari&longs;e from the <emph type="italics"/>Earths<emph.end type="italics"/> moving about the Sun, not &longs;olitari­ly, but in con&longs;ort with the Moon.</cell><cell>307</cell></row><row><cell>The Axis of the <emph type="italics"/>Earth<emph.end type="italics"/> continueth alwayes pa­rallel to it &longs;elf, and de&longs;cribeth a Cylindrai­cal Superficies, inclining to the Orb.</cell><cell>344</cell></row><row><cell>The Orb of the <emph type="italics"/>Earth<emph.end type="italics"/> never incllneth, but is immutably the &longs;ame.</cell><cell>345</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> approacheth or recedeth from the fixed Stars of the Ecliptick the quantity of the Grand Orb.</cell><cell>349</cell></row><row><cell>If in the fixed Stars one &longs;hould di&longs;cover any Mu­tation, the Motion of the <emph type="italics"/>Earth<emph.end type="italics"/> would be undeniable.</cell><cell>351</cell></row><row><cell>Nece&longs;&longs;ary Propo&longs;itions for the better concei­ving of the Con&longs;equences of the <emph type="italics"/>Earths<emph.end type="italics"/> Mo­tion.</cell><cell>354</cell></row><row><cell>An admirable Accident depending on the not­inclining of the <emph type="italics"/>Earths<emph.end type="italics"/> Axis.</cell><cell>358</cell></row><row><cell>Four &longs;everal Motions a&longs;&longs;igned to the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>362</cell></row><row><cell>The third Motion a&longs;cribed to the <emph type="italics"/>Earth,<emph.end type="italics"/> is ra­ther a re&longs;ting immoveable.</cell><cell>363</cell></row><row><cell>An admirable interne vertue [or faculty] of the <emph type="italics"/>Earths<emph.end type="italics"/> Globe, to behold alwayes the &longs;ame part of Heaven.</cell><cell>363</cell></row><row><cell>Nature, as iu &longs;port, maketh the Ebbing and Flowing of the Sea to prove the <emph type="italics"/>Earths<emph.end type="italics"/> Mo­bility.</cell><cell>379</cell></row><row><cell>All Terrene Effects indifferently confirm the Motion or Re&longs;t of the <emph type="italics"/>Earth,<emph.end type="italics"/> except the Eb­bing and Flowing of the Sea.</cell><cell>380</cell></row><row><cell>The Cavities of the <emph type="italics"/>Earth<emph.end type="italics"/> cannot approach or recede from the Centre of the &longs;ame.</cell><cell>387</cell></row><row><cell>The Hypothe&longs;is of the <emph type="italics"/>Earths<emph.end type="italics"/> Mobility taken in favour of the Ebbing and Flowing op­po&longs;ed.</cell><cell>399</cell></row><row><cell>The An&longs;wers to tho&longs;e Objections made again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/> Motion.</cell><cell>399</cell></row><row><cell>The Revolution of the <emph type="italics"/>Earth<emph.end type="italics"/> confirmed by a new Argument taken from the Aire.</cell><cell>400</cell></row><row><cell>The vaporous parts of the <emph type="italics"/>Earth<emph.end type="italics"/> partake of its Motions.</cell><cell>400</cell></row><row><cell>Another ob&longs;ervation taken from the Ayr, in confirmation of the motion of the <emph type="italics"/>Earth.<emph.end type="italics"/></cell><cell>402</cell></row><row><cell>A Rea&longs;on of the continual Motion of the Air and Water may be given by making the <emph type="italics"/>Earth<emph.end type="italics"/> moveable, rather then by making it immoveable.</cell><cell>405</cell></row><row><cell>The <emph type="italics"/>Earths<emph.end type="italics"/> Mobility held by &longs;undry great Phi­lo&longs;ophers among&longs;t the Antients.</cell><cell>437 & 468</cell></row><row><cell>The Fathers agree not in expounding the Texts of Scripture that are alledged again&longs;t the <emph type="italics"/>Earths<emph.end type="italics"/> Mobility.</cell><cell>450</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> Mobility defended by many a­mong&longs;t the Modern Writers.</cell><cell>478</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> &longs;hall &longs;tand &longs;till after the Day of Judgement.</cell><cell>480</cell></row><row><cell>The <emph type="italics"/>Earth<emph.end type="italics"/> is another Moon or Star.</cell><cell>486</cell></row><row><cell>The <emph type="italics"/>Earths<emph.end type="italics"/> &longs;everal Motions, according to Co­<pb xlink:href="040/01/535.jpg"/>pernicus.</cell><cell>491</cell></row><row><cell>The <emph type="italics"/>Earth &longs;ecundum totum<emph.end type="italics"/> is Immutable, though not Immoveable.</cell><cell>491</cell></row><row><cell>The <emph type="italics"/>Earths<emph.end type="italics"/> Natural Place.</cell><cell>492</cell></row><row><cell>The <emph type="italics"/>Earths<emph.end type="italics"/> Centre keepeth her in her Natural Place.</cell><cell>493</cell></row><row><cell>The <emph type="italics"/>Earth,<emph.end type="italics"/> in what Sen&longs;e it may <emph type="italics"/>ab&longs;olutely<emph.end type="italics"/> be &longs;aid to be in the lowe&longs;t part of the World.</cell><cell>496</cell></row><row><cell>EBBING and <emph type="italics"/>Ebbings.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The fir&longs;t general Conclu&longs;ion of the impo&longs;&longs;ibi­lity of <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing the Immobility of the Terre&longs;trial Globe being granted.</cell><cell>380</cell></row><row><cell>The Periods of <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings, Diurnal, Monethly, and Annual.</cell><cell>381</cell></row><row><cell>Varieties that happen in the Diurnal Period of the <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings.</cell><cell>382</cell></row><row><cell>The Cau&longs;es of <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings alledged by a Modern Phylo&longs;opher.</cell><cell>382</cell></row><row><cell>The Cau&longs;e of the <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing a&longs;eribed to the Moon by a certain Prelate.</cell><cell>383</cell></row><row><cell>The Cau&longs;e of the <emph type="italics"/>Ebbing, &c.<emph.end type="italics"/> referred by Hye­ronimus Borrius and other Peripateticks, to the temperate heat of the Moon.</cell><cell>383</cell></row><row><cell>An&longs;wersto the Vanities alledged as Cau&longs;es of the <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing.</cell><cell>383</cell></row><row><cell>Its proved impo&longs;&longs;ible that there &longs;hould natu­rally be any <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing, the Earth being immoveable.</cell><cell>386</cell></row><row><cell>The mo&longs;t potent and primary Cau&longs;e of the <emph type="italics"/>Eb­bing<emph.end type="italics"/> and Flowing.</cell><cell>390</cell></row><row><cell>Sundry accidents that happen in the <emph type="italics"/>Ebbings<emph.end type="italics"/>and Flowings.</cell><cell>391</cell></row><row><cell>Rea&longs;ons renewed of the particular Accidents ob&longs;erved in the <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings.</cell><cell>393</cell></row><row><cell>Second Cau&longs;es why in &longs;everal Seas and Lakes there are no <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings.</cell><cell>394</cell></row><row><cell>The Rea&longs;on why the <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings for the mo&longs;t part, are every Six Hours.</cell><cell>395</cell></row><row><cell>The Cau&longs;e why &longs;ome Seas though very long, &longs;uffer no <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing.</cell><cell>395</cell></row><row><cell><emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings, why greate&longs;t in the Ex­tremities of Gulphs, and lea&longs;t in the middle parts.</cell><cell>396</cell></row><row><cell>A Di&longs;cu&longs;&longs;ion of &longs;ome more Ab&longs;truce Accidents ob&longs;erved in the <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing.</cell><cell>396</cell></row><row><cell>The <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing may depend on the Di­urnal Motion of Heaven.</cell><cell>404</cell></row><row><cell>The <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flowing cannot depend on the Motion of Heaven.</cell><cell>405</cell></row><row><cell>The Cau&longs;es of the Periods of the <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings Monethly and Annual, at large a&longs;&longs;igned</cell><cell>407</cell></row><row><cell>The Monethly and Annual alterations of the <emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings, can depend on no­thing, &longs;ave on the alteration of the Additions and Subtractions of the Diurnal Period from the Annual.</cell><cell>408</cell></row><row><cell>Three wayes of altering the proportion of the Additions of the Diurnal Revolutions, to the Annual Motion of the <emph type="italics"/>Ebbing<emph.end type="italics"/> and Flow­ing.</cell><cell>409</cell></row><row><cell><emph type="italics"/>Ebbings<emph.end type="italics"/> and Flowings are petty things, in compari&longs;on of the va&longs;tne&longs;&longs;e of the Seas, and the Velocity of the Motion of the Terre&longs;trial Globe.</cell><cell>417</cell></row><row><cell>EFFECT and <emph type="italics"/>Effects.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Of anew <emph type="italics"/>Effect<emph.end type="italics"/> its nece&longs;&longs;ary that the Cau&longs;e be likewi&longs;e new.</cell><cell>370</cell></row><row><cell>The Knowledge of the <emph type="italics"/>Effects<emph.end type="italics"/> contribute to the inve&longs;tigation of the Cau&longs;es.</cell><cell>380</cell></row><row><cell>True and Natural <emph type="italics"/>Effects<emph.end type="italics"/> follow without diffi­culty.</cell><cell>387</cell></row><row><cell>Alterations in the <emph type="italics"/>Effects<emph.end type="italics"/> argue alteration in the Cau&longs;e.</cell><cell>407</cell></row><row><cell>ELEMENTS, <emph type="italics"/>and their Motions,<emph.end type="italics"/> Vide MOTION.</cell><cell></cell></row><row><cell>ENCYCLOPEDIA.</cell><cell></cell></row><row><cell>Subtilties fufficiently in&longs;ipid, ironically &longs;poken, and taken from a certain <emph type="italics"/>Encyclopedia.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell>EXPERIMENTS.</cell><cell></cell></row><row><cell>Sen&longs;ible <emph type="italics"/>Experiments<emph.end type="italics"/> are to be preferred before Humane Argumentations.</cell><cell>21, 33, 42.</cell></row><row><cell>It is good to be very cautious in admitting <emph type="italics"/>Ex­periments<emph.end type="italics"/> for true, to tho&longs;e that never tryed them.</cell><cell>162</cell></row><row><cell><emph type="italics"/>Experiments<emph.end type="italics"/> and Arguments again&longs;t the Earths Motion, &longs;eem &longs;o far concluding, as they lye under Equivokes</cell><cell>162</cell></row><row><cell>The Authority of Sen&longs;ible <emph type="italics"/>Experiments<emph.end type="italics"/> and ne­ce&longs;&longs;ary Demon&longs;trations in deciding of Phy­&longs;ical Controver&longs;ies.</cell><cell>436</cell></row><row><cell>EYE.</cell><cell></cell></row><row><cell>The Circle of the Pupil of the <emph type="italics"/>Eye<emph.end type="italics"/> contracteth and enlargeth.</cell><cell>329</cell></row><row><cell>How to finde the di&longs;tance of the Rays Con­cour&longs;e from the Pupil of the <emph type="italics"/>Eye.<emph.end type="italics"/></cell><cell>329</cell></row><row><cell>F</cell><cell></cell></row><row><cell>FAITH.</cell><cell></cell></row><row><cell><emph type="italics"/>Faith<emph.end type="italics"/> more infallible than either Sen&longs;e of <pb xlink:href="040/01/536.jpg"/>Rea&longs;on.</cell><cell>475</cell></row><row><cell>FIRE.</cell><cell></cell></row><row><cell><emph type="italics"/>Fire<emph.end type="italics"/> moveth directly upwards by Nature, and round about by Participation, according to Ari&longs;totle.</cell><cell>122</cell></row><row><cell>It is improbable that the Element of <emph type="italics"/>Fire<emph.end type="italics"/> &longs;hould be carried round by the Concave of the Moon.</cell><cell>405</cell></row><row><cell>FIGURE and <emph type="italics"/>Figures.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Figure<emph.end type="italics"/> is not the Cau&longs;e of Incorruptibility, but of Longer Duration.</cell><cell>66</cell></row><row><cell>The perfection of <emph type="italics"/>Figure<emph.end type="italics"/> appeareth in Corrup­tible Bodies, but not in the Eternal.</cell><cell>69</cell></row><row><cell>If the Spherical <emph type="italics"/>Figure<emph.end type="italics"/> conferred Eternity, all things would be Eternal.</cell><cell>69</cell></row><row><cell>It is more difficult to finde <emph type="italics"/>Figures<emph.end type="italics"/> that touch in a part of their Surface, then in one &longs;ole point.</cell><cell>185</cell></row><row><cell>The Circular <emph type="italics"/>Figure<emph.end type="italics"/> placed among&longs;t the <emph type="italics"/>Postu­lata<emph.end type="italics"/> of Mathematicians.</cell><cell>186</cell></row><row><cell>Irregular <emph type="italics"/>Figure<emph.end type="italics"/> and Formes difficult to be in­troduced.</cell><cell>187</cell></row><row><cell>Superficial figures increa&longs;e in proportion dou­ble to their Lines.</cell><cell>304</cell></row><row><cell>FLFXURES.</cell><cell></cell></row><row><cell>The nece&longs;&longs;ity and u&longs;e of <emph type="italics"/>Flexures<emph.end type="italics"/> in Animals, for varying of their Motions.</cell><cell>232</cell></row><row><cell>FOSCARINI.</cell><cell></cell></row><row><cell><emph type="italics"/>Fo&longs;carini<emph.end type="italics"/> his Reconciling of Scripture Texts with the Copernican <emph type="italics"/>Hypothe&longs;is.<emph.end type="italics"/></cell><cell>473</cell></row><row><cell>G</cell><cell></cell></row><row><cell>GENERABILITY.</cell><cell></cell></row><row><cell><emph type="italics"/>Generability<emph.end type="italics"/> and Corruptibility are onely a­mong&longs;t Contraries, according to Ari&longs;t.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Generability<emph.end type="italics"/> and Alterability are greater perfecti­ons in Mundane Bodies, then the Contrary Qualities.</cell><cell>44</cell></row><row><cell>GEOMETRICAL, and <emph type="italics"/>Geometry.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Geometrical<emph.end type="italics"/> Demon&longs;trations of the Triple Di­men&longs;ion.</cell><cell>4</cell></row><row><cell><emph type="italics"/>Geometrical<emph.end type="italics"/> Exactne&longs;&longs;e needle&longs;&longs;e in Phy&longs;ical Proofs.</cell><cell>6</cell></row><row><cell>Ari&longs;totle taxeth Plato for being too &longs;tudious of <emph type="italics"/>Geometry.<emph.end type="italics"/></cell><cell>334</cell></row><row><cell>Peripatetick Phylo&longs;ophers condemne the Stu­dy of <emph type="italics"/>Geometry,<emph.end type="italics"/> and why.</cell><cell>461</cell></row><row><cell>GILBERT.</cell><cell></cell></row><row><cell>The Magnetick Phylo&longs;ophy of <emph type="italics"/>Will. Gilbert.<emph.end type="italics"/></cell><cell>364</cell></row><row><cell>The Method of <emph type="italics"/>Gilbert<emph.end type="italics"/> in his Philo&longs;ophy.</cell><cell>367</cell></row><row><cell>GLOBE.</cell><cell></cell></row><row><cell>Our <emph type="italics"/>Globe<emph.end type="italics"/> would have been called Stone, in&longs;tead of Earth, if that name had been given it in the beginning.</cell><cell>367</cell></row><row><cell>GOD.</cell><cell></cell></row><row><cell><emph type="italics"/>God<emph.end type="italics"/> and Nature do employ them&longs;elves in caring for Men, as if they minded nothing el&longs;e.</cell><cell>333</cell></row><row><cell>An Example of <emph type="italics"/>Gods<emph.end type="italics"/> care of Man­kind, taken from the Sun.</cell><cell>333</cell></row><row><cell><emph type="italics"/>God<emph.end type="italics"/> hath given all things an inviolable Law to ob&longs;erve.</cell><cell>4..</cell></row><row><cell>GREAT.</cell><cell></cell></row><row><cell><emph type="italics"/>Great<emph.end type="italics"/> and Small, Immen&longs;e, &c. are Relative Terms.</cell><cell>334</cell></row><row><cell>GRAVITY.</cell><cell></cell></row><row><cell><emph type="italics"/>Grave<emph.end type="italics"/>; Vide <emph type="italics"/>Body.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Gravity<emph.end type="italics"/> and Levity, Rarity and Den&longs;ity, are contrary qualities.</cell><cell>30</cell></row><row><cell>Things Grave had being before the Common Centre of <emph type="italics"/>Gravity.<emph.end type="italics"/></cell><cell>221</cell></row><row><cell><emph type="italics"/>Gravity<emph.end type="italics"/> and Levity of Bodies defined.</cell><cell>493</cell></row><row><cell>GUN and <emph type="italics"/>Gunnery.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The Rea&longs;on why a <emph type="italics"/>Gun<emph.end type="italics"/> &longs;hould &longs;eem to carry farther towards the We&longs;t than towards the Ea&longs;t.</cell><cell>148</cell></row><row><cell>The Revolution of the Earth &longs;uppo&longs;ed, the Ball in the <emph type="italics"/>Gun<emph.end type="italics"/> erected perpendicularly, doth not move by a perpendicular, but an incli­ned Line.</cell><cell>155</cell></row><row><cell>It is ingenuou&longs;ly demon&longs;trated, that, the Earths Motion &longs;uppo&longs;ed, the Shot of Great <emph type="italics"/>Guns<emph.end type="italics"/>ought to vary no more than in its Re&longs;t.</cell><cell>161</cell></row><row><cell>The Experiment of a Running Chariot to find out the difference of Ranges in <emph type="italics"/>Gunnery.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell>A Computation in <emph type="italics"/>Gunnery,<emph.end type="italics"/> how much the Ranges of Great Shot ought to vary from the Mark, the Earths Motion being Granted.</cell><cell>160</cell></row><pb xlink:href="040/01/537.jpg"/><row><cell>H</cell><cell></cell></row><row><cell>HEAVEN.</cell><cell></cell></row><row><cell><emph type="italics"/>Heaven<emph.end type="italics"/> an Habitation for the Immortal Gods.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Heavens<emph.end type="italics"/> Immutability evident to Sen&longs;e.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Heaven<emph.end type="italics"/> Immutable, becau&longs;e there never was any Mutation &longs;een in it.</cell><cell>34</cell></row><row><cell>One cannot (&longs;aith <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>) &longs;peak confident­ly of <emph type="italics"/>Heaven,<emph.end type="italics"/> by rea&longs;on of its great di­&longs;tance.</cell><cell>42</cell></row><row><cell>The &longs;ub&longs;tance of the <emph type="italics"/>Heavens<emph.end type="italics"/> impenetrable, ac­cording to <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></cell><cell>54</cell></row><row><cell>The Sub&longs;tance of <emph type="italics"/>Heaven<emph.end type="italics"/> Intangible.</cell><cell>55</cell></row><row><cell> Many things may be in <emph type="italics"/>Heaven,<emph.end type="italics"/> that are Invi&longs;i­ble to us.</cell><cell>334</cell></row><row><cell>There are more Documents in the Open Book of <emph type="italics"/>Heaven,<emph.end type="italics"/> than Vulgar Wits are able to Penetrate.</cell><cell>444</cell></row><row><cell><emph type="italics"/>Heaven<emph.end type="italics"/> and Earth ever mutually oppo&longs;ed to each other.</cell><cell>480</cell></row><row><cell>Which are really the Greater Lights in <emph type="italics"/>Heaven,<emph.end type="italics"/>and which the le&longs;&longs;er.</cell><cell>484</cell></row><row><cell><emph type="italics"/>Heaven<emph.end type="italics"/> is not compo&longs;ed of a fifth E&longs;&longs;ence, differ­ing from the Matter of inferiour Bodies.</cell><cell>494</cell></row><row><cell><emph type="italics"/>Heaven<emph.end type="italics"/> is no Solid or Den&longs;e Body, but Rare.</cell><cell>494</cell></row><row><cell>Chri&longs;t at his Incarnatiou truly de&longs;cended from <emph type="italics"/>Heaven,<emph.end type="italics"/> and at his A&longs;cen&longs;ion truly a&longs;cended into <emph type="italics"/>Heaven.<emph.end type="italics"/></cell><cell>496</cell></row><row><cell>Of the Fir&longs;t, Second and Third <emph type="italics"/>Heaven.<emph.end type="italics"/></cell><cell>497</cell></row><row><cell><emph type="italics"/>Heaven<emph.end type="italics"/> in the Sen&longs;e of Copernicus, is the &longs;ame with the mo&longs;t tenuous Æther, but different from Paradice, which excells all the <emph type="italics"/>Hea­vens.<emph.end type="italics"/></cell><cell>499</cell></row><row><cell>HELL.</cell><cell></cell></row><row><cell><emph type="italics"/>Hell<emph.end type="italics"/> is in the Centre of the Earth, not of the World.</cell><cell>480</cell></row><row><cell>HELIX.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Helix<emph.end type="italics"/> about the Cylinder may be &longs;aid to be a Simple Line.</cell><cell>7</cell></row><row><cell>HYPOTHESIS.</cell><cell></cell></row><row><cell>The true <emph type="italics"/>Hypothe&longs;is<emph.end type="italics"/> may di&longs;patch its Revoluti­ons in a &longs;horter time in le&longs;&longs;er Circles, than in greater, the which is proved by two Examples.</cell><cell>410</cell></row><row><cell>I</cell><cell></cell></row><row><cell>JEST.</cell><cell></cell></row><row><cell>A <emph type="italics"/>Je&longs;t<emph.end type="italics"/> put upon one that offered to &longs;ell a cer­tain Secret of holding Corre&longs;pondence at a Thou&longs;and Miles di&longs;tance.</cell><cell>79</cell></row><row><cell>A <emph type="italics"/>Jest<emph.end type="italics"/> of a certain Statuary.</cell><cell>94</cell></row><row><cell>IMPOSSIBILITY and <emph type="italics"/>Impo&longs;&longs;ibilities.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Nature attempts not <emph type="italics"/>Impo&longs;&longs;ibilities.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell>To &longs;eek what would follow upon an <emph type="italics"/>Impo&longs;&longs;ibi­lity<emph.end type="italics"/> is Folly.</cell><cell>22</cell></row><row><cell>INCORRUPTIBILITY.</cell><cell></cell></row><row><cell><emph type="italics"/>Incorruptibility<emph.end type="italics"/> e&longs;teemed by the Vulgar, out of their fear of Death.</cell><cell>45</cell></row><row><cell>INFINITY.</cell><cell></cell></row><row><cell>Of <emph type="italics"/>Infinity<emph.end type="italics"/> the Parts are not one greater than another, although they are comparatively unequal.</cell><cell>105</cell></row><row><cell>INSTRUMENT and <emph type="italics"/>In&longs;truments.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>In&longs;truments<emph.end type="italics"/> A&longs;tronomical very &longs;ubject to Er­rour.</cell><cell>262</cell></row><row><cell>Copernicus under&longs;tood not &longs;ome things for want of <emph type="italics"/>Instruments.<emph.end type="italics"/></cell><cell>338</cell></row><row><cell>A proof of the &longs;mall credit that is to be given to A&longs;tronomical <emph type="italics"/>Instruments<emph.end type="italics"/> in Minute Ob­&longs;ervations.</cell><cell>351</cell></row><row><cell>Ptolomy did not confide in an <emph type="italics"/>Instruments<emph.end type="italics"/> made by Archimedes.</cell><cell>352</cell></row><row><cell><emph type="italics"/>In&longs;truments<emph.end type="italics"/> of Tycho made with great Ex­pence.</cell><cell>352</cell></row><row><cell>What <emph type="italics"/>In&longs;truments<emph.end type="italics"/> are mo&longs;t apt for exact Ob&longs;er­vations.</cell><cell>352</cell></row><row><cell>INVENTORS.</cell><cell></cell></row><row><cell>The Fir&longs;t <emph type="italics"/>Inventors<emph.end type="italics"/> and Ob&longs;ervers of things ought to be admired.</cell><cell>370</cell></row><row><cell>JOSHUAH.</cell><cell></cell></row><row><cell>The Miracle of <emph type="italics"/>Jo&longs;huah<emph.end type="italics"/> in commanding the Sun to &longs;tand &longs;till, contradicts the Ptolomaick Sy&longs;tem.</cell><cell>456</cell></row><row><cell><emph type="italics"/>Jo&longs;huahs<emph.end type="italics"/> Miracle admirably agreeth with the Pythagorick Sy&longs;teme.</cell><cell>457</cell></row><pb xlink:href="040/01/538.jpg"/><row><cell>IRON.</cell><cell></cell></row><row><cell>Its proved that <emph type="italics"/>Iron<emph.end type="italics"/> con&longs;i&longs;ts of parts more &longs;ubtil, pure and compact than the Magner.</cell><cell>370</cell></row><row><cell>JUPITER.</cell><cell></cell></row><row><cell><emph type="italics"/>Jupiter<emph.end type="italics"/> and Saturn do encompa&longs;&longs;e the Earth, and the Sun.</cell><cell>258</cell></row><row><cell><emph type="italics"/>Jupiter<emph.end type="italics"/> augments le&longs;&longs;e by Irradiation, than the Dog­Star.</cell><cell>305</cell></row><row><cell>K</cell><cell></cell></row><row><cell>KEPLER.</cell><cell></cell></row><row><cell>The Argument of <emph type="italics"/>Kepler<emph.end type="italics"/> in favour of Coper­nicus.</cell><cell>242</cell></row><row><cell>An Explanation of the true Sen&longs;e of <emph type="italics"/>Kepler,<emph.end type="italics"/> and his Defence.</cell><cell>243</cell></row><row><cell>The feigned An&longs;wer of <emph type="italics"/>Kepler<emph.end type="italics"/> couched in an Artificial Irony.</cell><cell>244</cell></row><row><cell><emph type="italics"/>Kepler<emph.end type="italics"/> is, with re&longs;pect, blamed.</cell><cell>422</cell></row><row><cell><emph type="italics"/>Keplers<emph.end type="italics"/> reconciling of Scripture Texts whith the Copernican Hypothe&longs;is.</cell><cell>461</cell></row><row><cell>KNOW, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The having a perfect <emph type="italics"/>Knowledge<emph.end type="italics"/> of nothing, maketh &longs;ome beleeve they under&longs;tand all things.</cell><cell>84</cell></row><row><cell>Gods manner of <emph type="italics"/>Knowing<emph.end type="italics"/> different from that of Man.</cell><cell>87</cell></row><row><cell>The great Felicity for which they are to be en­vied, who per&longs;wade them&longs;elves that they <emph type="italics"/>Know<emph.end type="italics"/> every thing.</cell><cell>164</cell></row><row><cell>Our <emph type="italics"/>Knowledge<emph.end type="italics"/> is a kind of Remini&longs;cence, ac­cording to Plato.</cell><cell>169</cell></row><row><cell>L</cell><cell></cell></row><row><cell>LIGHT.</cell><cell></cell></row><row><cell><emph type="italics"/>Light<emph.end type="italics"/> reflected from the Earth into the Moon.</cell><cell>52</cell></row><row><cell>The Reflex <emph type="italics"/>Light<emph.end type="italics"/> of uneven Bodies is more uni­ver&longs;al than that of the &longs;mooth, and why.</cell><cell>62</cell></row><row><cell>The more rough Superficies make greater Re­flection of <emph type="italics"/>Light<emph.end type="italics"/> than the le&longs;&longs;e rough</cell><cell>65</cell></row><row><cell>Perpendicular Rays of <emph type="italics"/>Light<emph.end type="italics"/> illuminate more than the Oblique, and why.</cell><cell>65</cell></row><row><cell>The more Oblique Rays of <emph type="italics"/>Light<emph.end type="italics"/> illuminate le&longs;&longs;e, and why,</cell><cell>65</cell></row><row><cell><emph type="italics"/>Light<emph.end type="italics"/> or Luminous Bodies appear the brighter in an Ob&longs;cure Ambient.</cell><cell>74</cell></row><row><cell>LINE.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Right Line<emph.end type="italics"/> and Circumference of an infi­nite Circle are the &longs;ame thing.</cell><cell>342</cell></row><row><cell>LAWYERS.</cell><cell></cell></row><row><cell>Contentious <emph type="italics"/>Lawyers<emph.end type="italics"/> that are retained in an ill Cau&longs;e, keep clo&longs;e to &longs;ome expre&longs;&longs;ion fallen from the adver&longs;e party at unawares.</cell><cell>324</cell></row><row><cell>LOOKING­GLASSES.</cell><cell></cell></row><row><cell>Flat <emph type="italics"/>Looking­Gla&longs;&longs;es<emph.end type="italics"/> ca&longs;t forth their Reflection to­wards but one place, but the Spherical eve­ry way.</cell><cell>39</cell></row><row><cell>LYNCEAN.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Lyncean<emph.end type="italics"/> Academick the fir&longs;t Di&longs;coverer of the Solar &longs;pots, and all the other Cele&longs;tial Novelties.</cell><cell>312</cell></row><row><cell>The Hi&longs;tory of his proceedings for a long time, about the Ob&longs;ervation of the Solar Spots.</cell><cell>312</cell></row><row><cell>M</cell><cell></cell></row><row><cell>MAGNET.</cell><cell></cell></row><row><cell>Many properties in the <emph type="italics"/>Magnet.<emph.end type="italics"/></cell><cell>367</cell></row><row><cell>The <emph type="italics"/>Magnet<emph.end type="italics"/> armed takes up more Iron, than when unarmed.</cell><cell>369</cell></row><row><cell>The true cau&longs;e of the Multiplication of Vertue in the <emph type="italics"/>Magnet,<emph.end type="italics"/> by means of the Arming.</cell><cell>370</cell></row><row><cell>A &longs;en&longs;ible proof of the Impurity of the <emph type="italics"/>Mag­net.<emph.end type="italics"/></cell><cell>371</cell></row><row><cell>The &longs;everal Natural Motions of the <emph type="italics"/>Mag­net.<emph.end type="italics"/></cell><cell>374</cell></row><row><cell>Philo&longs;ophers are forced to confe&longs;&longs;e that the <emph type="italics"/>Magnet<emph.end type="italics"/> is compounded of Cele&longs;tial Sub&longs;tan­ces, and of Elementary.</cell><cell>375</cell></row><row><cell>The Error of tho&longs;e who call the <emph type="italics"/>Magnet<emph.end type="italics"/> a mixt Body, and the Terre&longs;trial Globe, a &longs;imple Body.</cell><cell>375</cell></row><row><cell>An improbable Effect admired by Gilbertus in the <emph type="italics"/>Magnet.<emph.end type="italics"/></cell><cell>376</cell></row><row><cell>MAGNETICK <emph type="italics"/>Philo&longs;ophy.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The <emph type="italics"/>Magnetick Philo&longs;ophy<emph.end type="italics"/> of William Gilbert.</cell><cell>364</cell></row><row><cell>MAGNITUDE.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Magnitude<emph.end type="italics"/> of the Orbs and the Velocity of the Motions of Planets an&longs;wer proporti­<pb xlink:href="040/01/539.jpg"/>onably, as if de&longs;cended from the &longs;ame place.</cell><cell>19</cell></row><row><cell>Immen&longs;e <emph type="italics"/>Magnitudes<emph.end type="italics"/> and Numbers are incom­prehen&longs;ible by our Under&longs;tandings.</cell><cell>332</cell></row><row><cell>MARS.</cell><cell></cell></row><row><cell><emph type="italics"/>Mars<emph.end type="italics"/> nece&longs;&longs;arily includeth within its Orb the Earth, and al&longs;o the Sun.</cell><cell>298</cell></row><row><cell><emph type="italics"/>Mars<emph.end type="italics"/> at its Oppo&longs;ition to the Sun, &longs;eems &longs;ixty times bigger than towards the Conjuncti­on.</cell><cell>298</cell></row><row><cell><emph type="italics"/>Mars<emph.end type="italics"/> makes an hot a&longs;&longs;ault upon the Coperni­can Sy&longs;teme.</cell><cell>302</cell></row><row><cell>MARSILIUS.</cell><cell></cell></row><row><cell><emph type="italics"/>Signor Cæ&longs;ar Mar&longs;ilius<emph.end type="italics"/> ob&longs;erveth the Meridian to be moveable.</cell><cell>422</cell></row><row><cell>MEDICEAN.</cell><cell></cell></row><row><cell>The time of the <emph type="italics"/>Medicean<emph.end type="italics"/> Planets conver&longs;i­ons.</cell><cell>101</cell></row><row><cell>The <emph type="italics"/>Medicean<emph.end type="italics"/> Planets are as it were four Moons about <emph type="italics"/>Jupiter.<emph.end type="italics"/></cell><cell>307</cell></row><row><cell>MEDITERRAN.</cell><cell></cell></row><row><cell><emph type="italics"/>Mediterranean<emph.end type="italics"/> Sea made by the Seperation of Abila and Calpen.</cell><cell>35</cell></row><row><cell>The Voyages in the <emph type="italics"/>Mediterran<emph.end type="italics"/> from Ea&longs;t to We&longs;t are made in &longs;horter times than from We&longs;t to Ea&longs;t.</cell><cell>403</cell></row><row><cell>MERCURY.</cell><cell></cell></row><row><cell>The Revolution of <emph type="italics"/>Mercury<emph.end type="italics"/> concluded to be about the Sun, within the Orb of Venus.</cell><cell>298</cell></row><row><cell><emph type="italics"/>Mercury<emph.end type="italics"/> admitteth not of clear Ob&longs;ervati­ons.</cell><cell>307</cell></row><row><cell>MOON.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> hath no Generation of things, like as we have, nor is it inhabited by Men.</cell><cell>47</cell></row><row><cell>In the <emph type="italics"/>Moon<emph.end type="italics"/> may be a Generation of things dif­ferent from ours.</cell><cell>47</cell></row><row><cell>There may be Sub&longs;tances in the <emph type="italics"/>Moon,<emph.end type="italics"/> very different from ours.</cell><cell>48</cell></row><row><cell>The fir&longs;t re&longs;emblance between the <emph type="italics"/>Moon<emph.end type="italics"/> and Earth, which is that of Figure, is proved, by their manner of being illuminated by the Sun.</cell><cell>48</cell></row><row><cell>The &longs;econd re&longs;emblance is the <emph type="italics"/>Moons<emph.end type="italics"/> being Opacous, as the Earth.</cell><cell>48</cell></row><row><cell>The third re&longs;emblance is the <emph type="italics"/>Moons<emph.end type="italics"/> being Den&longs;e and Mountainous as the Earth.</cell><cell>49</cell></row><row><cell>The fourth re&longs;emblance is the <emph type="italics"/>Moons<emph.end type="italics"/> being di­&longs;tingui&longs;hed into two different parts for Cla­rity and Ob&longs;curity, as the Terre&longs;trial Globe into Sea and Land.</cell><cell>49</cell></row><row><cell>The fifth re&longs;emblance is Mutation of Figures in the Earth, like tho&longs;e of the <emph type="italics"/>Moon,<emph.end type="italics"/> and made with the &longs;ame Periods.</cell><cell>49</cell></row><row><cell>All the Earth &longs;eeth halfe onely of the <emph type="italics"/>Moon,<emph.end type="italics"/>and halfe onely of the <emph type="italics"/>Moon<emph.end type="italics"/> &longs;eeth all the Earth</cell><cell>51</cell></row><row><cell>Two Spots in the <emph type="italics"/>Moon,<emph.end type="italics"/> by which it is percei­ved that She hath re&longs;pect to the Centre of the Earth in her Motion.</cell><cell>52</cell></row><row><cell>Light reflected from the Earth into the <emph type="italics"/>Moon.<emph.end type="italics"/></cell><cell>52</cell></row><row><cell>The &longs;ixth re&longs;emblance is that the Earth and <emph type="italics"/>Moon<emph.end type="italics"/> interchangeably illuminate.</cell><cell>53</cell></row><row><cell>The &longs;eventh re&longs;emblance is that the Earth and <emph type="italics"/>Moon<emph.end type="italics"/> interchangeably Ecclip&longs;e.</cell><cell>53</cell></row><row><cell>The Secondary Clarity of the <emph type="italics"/>Moon<emph.end type="italics"/> e&longs;teemed to be its Native Light.</cell><cell>54</cell></row><row><cell>The Surface of the <emph type="italics"/>Moon<emph.end type="italics"/> more &longs;leek then any Looking­Gla&longs;&longs;e.</cell><cell>55</cell></row><row><cell>The eminencies and Cavities in the <emph type="italics"/>Moon,<emph.end type="italics"/> are illu­&longs;ions of its Opacous and Per&longs;picuous parts.</cell><cell>55</cell></row><row><cell>The <emph type="italics"/>Moons<emph.end type="italics"/> Surface is &longs;harp, as is largely pro­ved.</cell><cell>57</cell></row><row><cell>The <emph type="italics"/>Moon,<emph.end type="italics"/> if it it were &longs;leek like a Spherical Looking­Gla&longs;&longs;e, would be invi&longs;ible.</cell><cell>60 & 62</cell></row><row><cell>The apparent Unevenne&longs;&longs;es of the <emph type="italics"/>Moons<emph.end type="italics"/> Sur­face aptly repre&longs;ented by Mother of Pearl.</cell><cell>70</cell></row><row><cell>The apparent Unevenne&longs;&longs;es of the <emph type="italics"/>Moon<emph.end type="italics"/> cannot be imitated by way of more and le&longs;&longs;e Opa­city, and Per&longs;picuity</cell><cell>71</cell></row><row><cell>The various A&longs;pects of the <emph type="italics"/>Moon<emph.end type="italics"/> imitable by any Opacous matter.</cell><cell>71</cell></row><row><cell>Sundry Phænomena from whence the <emph type="italics"/>Moons<emph.end type="italics"/>Montuo&longs;ity is argued.</cell><cell>71</cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> appears brighter by night, than by day.</cell><cell>72</cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> beheld in the day time, is like to a little Cloud.</cell><cell>72</cell></row><row><cell>Clouds are no le&longs;&longs;e apt than the <emph type="italics"/>Moon<emph.end type="italics"/> to be il­luminated by the Sun.</cell><cell>73</cell></row><row><cell>A Wall illuminated by the Sun, compared to the <emph type="italics"/>Moon,<emph.end type="italics"/> &longs;hines no le&longs;&longs;e than it.</cell><cell>73</cell></row><row><cell>The third reflection of a Wall illuminates more than the fir&longs;t of the <emph type="italics"/>Moon.<emph.end type="italics"/></cell><cell>74</cell></row><row><cell>The Light of the <emph type="italics"/>Moon<emph.end type="italics"/> weaker than that of the Twy­light.</cell><cell>74</cell></row><row><cell>The &longs;econdary Light of the <emph type="italics"/>Moon<emph.end type="italics"/> cau&longs;ed by the Sun, according to &longs;ome.</cell><cell>76</cell></row><pb xlink:href="040/01/540.jpg"/><row><cell>The &longs;econdary Light of the <emph type="italics"/>Moon<emph.end type="italics"/> appears in form of a Ring, <emph type="italics"/>i. e.<emph.end type="italics"/> bright in the extreme Circumference, and not in the mid&longs;t, and why.</cell><cell>77</cell></row><row><cell>The &longs;econdary Light of the <emph type="italics"/>Moon,<emph.end type="italics"/> how it is to be ob&longs;erved.</cell><cell>78</cell></row><row><cell>The <emph type="italics"/>Moons<emph.end type="italics"/> Di&longs;cus in a Solar Eclip&longs;e can be &longs;een onely by Privation.</cell><cell>78</cell></row><row><cell>Solidity of the <emph type="italics"/>Moons<emph.end type="italics"/> Globe argued from its being Mountainous.</cell><cell>81</cell></row><row><cell>The &longs;econdary Light of the <emph type="italics"/>Moon<emph.end type="italics"/> clearer before the Conjunction than after.</cell><cell>82</cell></row><row><cell>The ob&longs;curer parts of the <emph type="italics"/>Moon<emph.end type="italics"/> are Plains, and the more bright Mountains.</cell><cell>83</cell></row><row><cell>Long Ledges of Mountains about the Spots of the <emph type="italics"/>Moon.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell>There are not generated in the <emph type="italics"/>Moon<emph.end type="italics"/> things like to ours, but if there be any Producti­ons, they are very different.</cell><cell>83</cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> not compo&longs;ed of Water and Earth.</cell><cell>83</cell></row><row><cell>Tho&longs;e A&longs;pects of the Sun nece&longs;&longs;ary for our Productions, are not &longs;o in the <emph type="italics"/>Moon.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell>Natural Dayes in the <emph type="italics"/>Moon<emph.end type="italics"/> are of a Moneth long.</cell><cell>84</cell></row><row><cell>To the <emph type="italics"/>Moon<emph.end type="italics"/> the Sun declineth with a difference of ten Degrees, and to the Earth of Forty &longs;even Degrees.</cell><cell>84</cell></row><row><cell>There are no Rains in the <emph type="italics"/>Moon.<emph.end type="italics"/></cell><cell>84</cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> cannot &longs;eperate from the Earth.</cell><cell>295</cell></row><row><cell>The <emph type="italics"/>Moons<emph.end type="italics"/> Orbe environeth the Earth, but not the Sun.</cell><cell>299</cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> much di&longs;turbeth the Order of the other Planets.</cell><cell>362</cell></row><row><cell>The <emph type="italics"/>Moons<emph.end type="italics"/> Motion principally &longs;ought in the Account of Eclip&longs;es.</cell><cell>416</cell></row><row><cell>The <emph type="italics"/>Moon<emph.end type="italics"/> is an Æthereal Earth.</cell><cell>492</cell></row><row><cell>MOTION and <emph type="italics"/>Motions.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Motion<emph.end type="italics"/> of Projects. Vide <emph type="italics"/>Projects.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The Conditions and Attributes which differ the Cele&longs;tial and Elementary Bodies depend on the <emph type="italics"/>Motions<emph.end type="italics"/> a&longs;&longs;igned them by Ari&longs;totle.</cell><cell>25</cell></row><row><cell>Peripateticks improperly a&longs;&longs;ign tho&longs;e <emph type="italics"/>Motions<emph.end type="italics"/> to the Elements for Natural with which they never were moved, and tho&longs;e for Preternatu­ral with which they alwayes move.</cell><cell>33</cell></row><row><cell><emph type="italics"/>Motion,<emph.end type="italics"/> as to the things that move thereby, is as if it never were, and &longs;o farre operates, as it relates to things deprived of <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>98</cell></row><row><cell><emph type="italics"/>Motion<emph.end type="italics"/> cannot be made without its moveable Subject.</cell><cell>104</cell></row><row><cell><emph type="italics"/>Motion<emph.end type="italics"/> and Re&longs;t principal Accidents in Na­ture.</cell><cell>112</cell></row><row><cell>Two things nece&longs;&longs;ary for the perpetuating of a <emph type="italics"/>Motion<emph.end type="italics"/>; an unlimited Space, and an incor­ruptible Moveable.</cell><cell>117</cell></row><row><cell>Di&longs;parity in the <emph type="italics"/>Motions<emph.end type="italics"/> of a Stone falling from the Round Top of a Ship, and from the Top of a Tower.</cell><cell>123</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of grave Pendula might be perpe­tuated, impediments being removed.</cell><cell>203</cell></row><row><cell>Whence the <emph type="italics"/>Motion<emph.end type="italics"/> of a Cadent Body is col­lected.</cell><cell>224</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of the Eye argueth the <emph type="italics"/>Motion<emph.end type="italics"/> of the Body looked on.</cell><cell>224</cell></row><row><cell>Different <emph type="italics"/>Motions<emph.end type="italics"/> depending on the Fluctuati­on of the Ship.</cell><cell>226</cell></row><row><cell>Our <emph type="italics"/>Motion<emph.end type="italics"/> may be either interne, or externe, and yet we never perceive or feelit.</cell><cell>229</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of a Boat in&longs;en&longs;ible to tho&longs;e that are within it, as to the Sen&longs;e of Feeling.</cell><cell>229</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of a Boat &longs;en&longs;ible to Sight joyned with Rea&longs;on.</cell><cell>229</cell></row><row><cell>A &longs;imple Body, as the Earth, cannot move with three &longs;everal <emph type="italics"/>Motions.<emph.end type="italics"/></cell><cell>231</cell></row><row><cell><emph type="italics"/>Motion<emph.end type="italics"/> and Re&longs;t are more different than Right <emph type="italics"/>Motion<emph.end type="italics"/> and Circular.</cell><cell>237</cell></row><row><cell>One may more rationally a&longs;cribe to the Earth two intern Principles to the Right and Cir­cular <emph type="italics"/>Motion,<emph.end type="italics"/> than two to <emph type="italics"/>Motion<emph.end type="italics"/> and Re&longs;t.</cell><cell>237</cell></row><row><cell>The diver&longs;ity of <emph type="italics"/>Motions<emph.end type="italics"/> helpeth us to know the Diver&longs;ity of Natures.</cell><cell>237</cell></row><row><cell>Bodies of the &longs;ame kind, have <emph type="italics"/>Motions<emph.end type="italics"/> that agree in kinde.</cell><cell>239</cell></row><row><cell>The greatne&longs;&longs;e and &longs;mallne&longs;&longs;e of the Body make a difference in <emph type="italics"/>Motion<emph.end type="italics"/> and not in Re&longs;t.</cell><cell>243</cell></row><row><cell>Every pen&longs;ile and librated Body carried round in the Circumference of a Circle acquireth of it &longs;elf a <emph type="italics"/>Motion<emph.end type="italics"/> in it &longs;elf equal to the &longs;ame.</cell><cell>362</cell></row><row><cell>Two &longs;orts of <emph type="italics"/>Motion<emph.end type="italics"/> in the containing Ve&longs;&longs;el may make the containing Water to ri&longs;e and fall.</cell><cell>387</cell></row><row><cell>An Accident in the Earths <emph type="italics"/>Motion<emph.end type="italics"/> impo&longs;&longs;ible to be imitated.</cell><cell>392</cell></row><row><cell>ABSOLUTE MOTION: Things &longs;aid to move according to certain of their parts, and not according to their whole, may not be &longs;aid to move with an Ab&longs;olute <emph type="italics"/>Motion,<emph.end type="italics"/> but <emph type="italics"/>per accidens.<emph.end type="italics"/></cell><cell>491</cell></row><row><cell>ANIMAL MOTION: The Diver&longs;ity of the <emph type="italics"/>Motions<emph.end type="italics"/> of Animals, depend on their Flex­ures.</cell><cell>232</cell></row><row><cell>The Flexures in Animals are not made for vary­ing of their <emph type="italics"/>Motions.<emph.end type="italics"/></cell><cell>232</cell></row><row><cell>The <emph type="italics"/>Motions<emph.end type="italics"/> of Animals are of one&longs;ort.</cell><cell>232</cell></row><row><cell>The <emph type="italics"/>Motions<emph.end type="italics"/> of Animals are all Circular.</cell><cell>233</cell></row><row><cell>Secondary <emph type="italics"/>Motion<emph.end type="italics"/> of Animals dependent on the fir&longs;t.</cell><cell>233</cell></row><pb xlink:href="040/01/541.jpg"/><row><cell>Animals would not grow weary of their <emph type="italics"/>Mo­tion,<emph.end type="italics"/> proceeding as that which is a&longs;&longs;igned to the Terre&longs;trial Globe.</cell><cell>244</cell></row><row><cell>The Cau&longs;e of the wearine&longs;&longs;e that attends the <emph type="italics"/>Motion<emph.end type="italics"/> of Animals.</cell><cell>244</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of an Animal is rather to be called Violent than Natural.</cell><cell>244</cell></row><row><cell>ANNUAL MOTION: The Annual <emph type="italics"/>Motion<emph.end type="italics"/>of the Earth mu&longs;t cau&longs;e a con&longs;tant and &longs;trong Winde.</cell><cell>228</cell></row><row><cell>The Errour o&longs; the Antagoni&longs;t of Copernicus is manife&longs;t, in that he declareth that the Annual and Diurnal Motion belonging to the Earth, are both one way, and not contrary.</cell><cell>235</cell></row><row><cell>The Annual <emph type="italics"/>Motion<emph.end type="italics"/> of the Earth mixing with the <emph type="italics"/>Motions<emph.end type="italics"/> of the other Planets, produce extravagant Appearances.</cell><cell>296</cell></row><row><cell>Re&longs;t, Annual <emph type="italics"/>Motion,<emph.end type="italics"/> and the Diurnal, ought to be di&longs;tributed betwixt the Sun, Earth, and Firmament.</cell><cell>300</cell></row><row><cell>Granting to the Earth the Annual, it mu&longs;t of hece&longs;&longs;ity have the Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> a&longs;&longs;igned to it.</cell><cell>300</cell></row><row><cell>The &longs;ole Annual <emph type="italics"/>Motion<emph.end type="italics"/> of the Earth, cau&longs;eth great inequality in the <emph type="italics"/>Motions<emph.end type="italics"/> of the Pla­nets.</cell><cell>310</cell></row><row><cell>A Demon&longs;tration of the inequalities of the three &longs;uperiour Planets dependent on the Annual <emph type="italics"/>Motion<emph.end type="italics"/> of the Earth.</cell><cell>310</cell></row><row><cell>The Annual <emph type="italics"/>Motion<emph.end type="italics"/> of the Earth mo&longs;t apt to render a rea&longs;on of the Exorbitance of the five Planets.</cell><cell>312</cell></row><row><cell>Argument of Tycho again&longs;t the Annual <emph type="italics"/>Moti­on,<emph.end type="italics"/> from the invariable Elevation of the Pole.</cell><cell>338</cell></row><row><cell>Upon the Annual <emph type="italics"/>Motion<emph.end type="italics"/> o&longs; the Earth, alterati­on may en&longs;ue in &longs;ome Fixed Stars, not in the Pole.</cell><cell>341</cell></row><row><cell>The Parallogi&longs;me of tho&longs;e who believe that in the Annual <emph type="italics"/>Motion<emph.end type="italics"/> great alterations are to be made about the Elevation of the Fixed Stars, is confuted.</cell><cell>341</cell></row><row><cell>Enquiry is made what mutations, and in what Stars, are to be di&longs;covered by means of the Earths Annual <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>342</cell></row><row><cell>A&longs;tronomers having omitted to in&longs;tance what alterations tho&longs;e are that may be derived from the Annual <emph type="italics"/>Motion<emph.end type="italics"/> of the Earth, do thereby te&longs;tifie that they never rightly un­der&longs;tood the &longs;ame.</cell><cell>343</cell></row><row><cell>The Anuual <emph type="italics"/>Motion<emph.end type="italics"/> made by the Centre of the Earth under the Ecliptick, and the Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> made by the Earth about its own Centre.</cell><cell>344</cell></row><row><cell>Objections again&longs;t the Earths Annual <emph type="italics"/>Motion<emph.end type="italics"/>taken from the Fixed Stars placed in the E­cliptick.</cell><cell>345</cell></row><row><cell>An Indice or Ob&longs;ervation in the Fixed Stars like to that which is &longs;een in the Planets, is an Ar­gument of the Earths Annual <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>347</cell></row><row><cell>The Suns Annual <emph type="italics"/>Motion<emph.end type="italics"/> how it cometh to pa&longs;&longs;e, according to Copernicus.</cell><cell>355</cell></row><row><cell>The Annual and Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> are con&longs;i&longs;tent in the Earth.</cell><cell>362</cell></row><row><cell>Three wayes of altering the proportion of the Additions of the Diurnal Revolution to the Annual <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>409</cell></row><row><cell>The Earths Annual <emph type="italics"/>Motion<emph.end type="italics"/> thorow the Ecliptick unequal, by rea&longs;on of the Moons <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>413</cell></row><row><cell>The Cau&longs;es of the inequality of the Additions and Sub&longs;tractions of the Diurnal Conver&longs;i­on from the Annual <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>418</cell></row><row><cell>CIRCULAR MOTION: Circular and Right <emph type="italics"/>Motion<emph.end type="italics"/> are &longs;imple, as proceeding in &longs;imple Lines.</cell><cell>6</cell></row><row><cell>The Circular <emph type="italics"/>Motion<emph.end type="italics"/> is never acquired Natural­ly, unle&longs;&longs;e Right <emph type="italics"/>Motion<emph.end type="italics"/> precede it.</cell><cell>18</cell></row><row><cell>Circular <emph type="italics"/>Motion<emph.end type="italics"/> perpetually uniforme.</cell><cell>18</cell></row><row><cell>In the Circular <emph type="italics"/>Motion<emph.end type="italics"/> every point in the Cir­cumference is the beginning and end.</cell><cell>20</cell></row><row><cell>Circular <emph type="italics"/>Motion<emph.end type="italics"/> onely is Uniforme.</cell><cell>20</cell></row><row><cell>Circular <emph type="italics"/>Motion<emph.end type="italics"/> may be continued pcrpetu­ally.</cell><cell>20</cell></row><row><cell>Circular <emph type="italics"/>Motion<emph.end type="italics"/> onely and Re&longs;t are apt to con­&longs;erve Order.</cell><cell>20</cell></row><row><cell>To the Circular <emph type="italics"/>Motion<emph.end type="italics"/> no other <emph type="italics"/>Motion<emph.end type="italics"/> is con­trary.</cell><cell>26</cell></row><row><cell>Circular <emph type="italics"/>Motions<emph.end type="italics"/> are not contrary, according to Ari&longs;totle.</cell><cell>100</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of the Parts of the Earth returning to their Whole, may be Circular.</cell><cell>237</cell></row><row><cell>The Velocity in the Circular <emph type="italics"/>Motion<emph.end type="italics"/> encrea&longs;eth according to the encrea&longs;e of the Diameter of the Circle.</cell><cell>242</cell></row><row><cell>Circular <emph type="italics"/>Motion<emph.end type="italics"/> is truly &longs;imple and perpetu­al.</cell><cell>495</cell></row><row><cell>Circular Motion belongeth to the Whole Bo­dy, and the Right to its Parts.</cell><cell>496</cell></row><row><cell>Circular and Right <emph type="italics"/>Motion<emph.end type="italics"/> are coincident, and may con&longs;i&longs;t together in the &longs;ame Body.</cell><cell>496</cell></row><row><cell>COMMON MOTION: A notable In&longs;tance of Sagredus, to &longs;hew the non­operating of Common <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>151</cell></row><row><cell>An Experiment that &longs;heweth how the Com­mon <emph type="italics"/>Motion<emph.end type="italics"/> is imperceptible.</cell><cell>224</cell></row><row><cell>The concurrence of the Elements in a Com­mon <emph type="italics"/>Motion<emph.end type="italics"/> imports no more than their con­currence in a Common Re&longs;t.</cell><cell>239</cell></row><row><cell>Common <emph type="italics"/>Motion<emph.end type="italics"/> is as if it never were.</cell><cell>223, 340</cell></row><row><cell>COMPRESSIVE MOTION: Compre&longs;&longs;ive <emph type="italics"/>Motion<emph.end type="italics"/> is proper to Gravity, Exten&longs;ive to Levity.</cell><cell>493</cell></row><pb xlink:href="040/01/542.jpg"/><row><cell>CONTRARY MOTIONS: An Experi­ment which plainly &longs;hews that two Con­trary <emph type="italics"/>Motions<emph.end type="italics"/> may agree in the &longs;ame Move­able.</cell><cell>363</cell></row><row><cell>The parts of a Circle regularly moved about its own Centre, move in diver&longs;e times with Contrary <emph type="italics"/>Motions.<emph.end type="italics"/></cell><cell>389</cell></row><row><cell>DESCENDING MOTION: The Inclination of Grave Bodies to the <emph type="italics"/>Motion<emph.end type="italics"/> of De&longs;cent, is e­qual to their re&longs;i&longs;tance to the <emph type="italics"/>Motion<emph.end type="italics"/> of A&longs;cent.</cell><cell>191</cell></row><row><cell>The Spaces pa&longs;t in the De&longs;cending <emph type="italics"/>Motion<emph.end type="italics"/> of the &longs;alling Grave Body, are as the Squares|of their times.</cell><cell>198</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of De&longs;cent belongs not to the Ter­re&longs;trial Globe, but to its parts.</cell><cell>362</cell></row><row><cell>DIVRNAL MOTION: The Diurnal <emph type="italics"/>Motion<emph.end type="italics"/>&longs;eemeth Commune to all the Univer&longs;e, the Earth onely excepted.</cell><cell>97</cell></row><row><cell>Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> why it &longs;hould more probably belong to the Earth than to the Re&longs;t of the Univer&longs;e.</cell><cell>98</cell></row><row><cell>The fir&longs;t Di&longs;cour&longs;e to prove that the Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> belongs to the Earth.</cell><cell>99</cell></row><row><cell>The Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> cau&longs;eth no Mutation among Cele&longs;tial Bodies, but all changes have relati­on to the Earth.</cell><cell>100</cell></row><row><cell>A &longs;econd Confirmation that|the Diurnal <emph type="italics"/>Moti­on<emph.end type="italics"/> belongs to the Earth.</cell><cell>100</cell></row><row><cell>A third Confirmation that the Diurnal <emph type="italics"/>Motion<emph.end type="italics"/>belongs to the Earth.</cell><cell>101</cell></row><row><cell>A fourth, fi&longs;th, and &longs;ixth Confirmation that the Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> belongs to the Eatth.</cell><cell>102</cell></row><row><cell>A&longs;eventh Confirmation that the Diurnal <emph type="italics"/>Mo­tion<emph.end type="italics"/> belongs to the Earth.</cell><cell>103</cell></row><row><cell>If the Diurnal <emph type="italics"/>Motion<emph.end type="italics"/> &longs;hould alter, the Annual Period would cea&longs;e.</cell><cell>409</cell></row><row><cell>LOCAL MOTION: Local <emph type="italics"/>Motion<emph.end type="italics"/> of three kinds, Right, Circular, and Mixt.</cell><cell>6</cell></row><row><cell>An entire and new Science of our Academick [Galileo] concerning Local <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell>MIXT MOTION: Of Mixt <emph type="italics"/>Motion<emph.end type="italics"/> we &longs;ee not the part that is Circular, becau&longs;e we pertake thereof.</cell><cell>218</cell></row><row><cell>Ari&longs;totle granteth a Mixt <emph type="italics"/>Motion<emph.end type="italics"/> to Mixt Bodies.</cell><cell>375</cell></row><row><cell>The <emph type="italics"/>Motion<emph.end type="italics"/> of Mixt Bodies ought to be &longs;uch as may re&longs;ult from the Compo&longs;ition of the <emph type="italics"/>Mo­tions<emph.end type="italics"/> of the &longs;imple Bodies compounding.</cell><cell>375</cell></row><row><cell>NATVRAL MOTION: Accelleration of the Natural <emph type="italics"/>Motion<emph.end type="italics"/> of Graves is made according to the Odd Numbers beginning at Uni­ty.</cell><cell>198</cell></row><row><cell>Natural <emph type="italics"/>Motion<emph.end type="italics"/> changeth into that which is Preter­Natural and Violent.</cell><cell>212</cell></row><row><cell>PROGRESSIVE MOTION: The Progre&longs;&longs;ive <emph type="italics"/>Motion<emph.end type="italics"/> may make the Water in a Ve&longs;&longs;el to run to and fro.</cell><cell>387</cell></row><row><cell>RIGHT MOTION: Sometimes Simple, and &longs;ometimes Mixt, according to Ari&longs;totle.</cell><cell>8</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> impo&longs;&longs;ible in the World exactly Ordinate.</cell><cell>10</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> Naturally Infinite.</cell><cell>10</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> Naturally Impo&longs;&longs;ible.</cell><cell>10</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> might po&longs;&longs;ibly have been in the Fir&longs;t Chaos.</cell><cell>11</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> is u&longs;eful to reduce into Order things out of Order.</cell><cell>11</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> cannot naturally be Perpetual.</cell><cell>20</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> a&longs;&longs;igned to Natural Bodies, to re­duce them to perfect Order, when removed from their Places.</cell><cell>20</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> of Grave Bodies manife&longs;t to Sen&longs;e.</cell><cell>22</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> with more rea&longs;on a&longs;cribed to the Parts, than to the whole Elements.</cell><cell>33</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> cannot be Eternal, and con&longs;e­quently cannot be Natural to the Earth.</cell><cell>117</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> &longs;eemeth to be wholly excluded in Nature.</cell><cell>147</cell></row><row><cell>With two Right <emph type="italics"/>Motions<emph.end type="italics"/> one cannot compo&longs;e Circular <emph type="italics"/>Motions.<emph.end type="italics"/></cell><cell>375</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> belongeth to imperfect Bodies, and that are out of their Natural Places.</cell><cell>495</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> is not Simple.</cell><cell>495</cell></row><row><cell>Right <emph type="italics"/>Motion<emph.end type="italics"/> is ever mixt with the Circular.</cell><cell>495</cell></row><row><cell>SIMPLE MOTION peculiar onely to Simple Bodies.</cell><cell>494</cell></row><row><cell>TERRESTRIAL MOTION collected from the Stars.</cell><cell>229</cell></row><row><cell>The Parts of the Terre&longs;trial Globe accelerate and retard in their <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell>388</cell></row><row><cell>One &longs;ingle Terre&longs;trial <emph type="italics"/>Motion<emph.end type="italics"/> &longs;ufficeth not to produce the Ebbing and Flowing.</cell><cell>421</cell></row><row><cell>UNEVEN MOTION may make the Water in a Ve&longs;&longs;el to Run to and fro.</cell><cell>387</cell></row><row><cell>The Mixture of the two <emph type="italics"/>Motions<emph.end type="italics"/> Annual and Diurnal, cau&longs;eth the unevenne&longs;&longs;e in the <emph type="italics"/>Motion<emph.end type="italics"/> of the parts of the Terre&longs;trial Globe.</cell><cell>390</cell></row><row><cell>MOVE.</cell><cell></cell></row><row><cell>Its que&longs;tionable whether de&longs;cending Bodies <emph type="italics"/>Move<emph.end type="italics"/> in a Right Line.</cell><cell>21</cell></row><row><cell>Ari&longs;totles Argument to prove that Grave Bodies <emph type="italics"/>Move<emph.end type="italics"/> with an inclination to arrive at the Centre.</cell><cell>22</cell></row><row><cell>Grave Bodies <emph type="italics"/>Move<emph.end type="italics"/> towards the Centre of the Centre of the Earth <emph type="italics"/>per Accidens.<emph.end type="italics"/></cell><cell>22</cell></row><row><cell>Things for&longs;aking the place which was natural ro them by Creation, are &longs;aid to <emph type="italics"/>Move<emph.end type="italics"/> violently, <pb xlink:href="040/01/543.jpg"/>and naturally tend to return back to the &longs;ame.</cell><cell>492</cell></row><row><cell>MOVEABLE, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell>A <emph type="italics"/>Moveable<emph.end type="italics"/> being in the &longs;tate of Re&longs;t &longs;hall not move unle&longs;&longs;e it have an inclination to &longs;ome particular Place.</cell><cell>11</cell></row><row><cell>The <emph type="italics"/>Moveable<emph.end type="italics"/> accellerates its Motion in going towards the Place whither it hath an inclina­tion.</cell><cell>11</cell></row><row><cell>The <emph type="italics"/>Moveable<emph.end type="italics"/> departing from Re&longs;t goeth thorow all the Degrees of Tardity.</cell><cell>11</cell></row><row><cell>The <emph type="italics"/>Moveable<emph.end type="italics"/> doth not accelerate &longs;ave only as it approacheth near to its terme of Re&longs;t.</cell><cell>12</cell></row><row><cell>To introduce in a <emph type="italics"/>Moveable<emph.end type="italics"/> a certain Degree of Velocity, Nature made it to move in a Right Line.</cell><cell>12</cell></row><row><cell>The <emph type="italics"/>Moveable<emph.end type="italics"/> departing from Re&longs;t pa&longs;&longs;eth through all the Degrees of Velocity without &longs;taying in any.</cell><cell>13</cell></row><row><cell>The Grave <emph type="italics"/>Moveable<emph.end type="italics"/> de&longs;cending, acquireth Impetus &longs;ufficient to re­carry it to the like height.</cell><cell>13</cell></row><row><cell>The Impetus of <emph type="italics"/>Moveables<emph.end type="italics"/> equally approaching to the Centre are equal.</cell><cell>14</cell></row><row><cell>Upon an Horizontal Plane the <emph type="italics"/>Moveable<emph.end type="italics"/> lyeth &longs;till.</cell><cell>14</cell></row><row><cell>A &longs;ingle <emph type="italics"/>Moveable<emph.end type="italics"/> hath but one only Natural Motion, and all the re&longs;t are by participa­tion.</cell><cell>103</cell></row><row><cell>A Line de&longs;cribed by a <emph type="italics"/>Moveable<emph.end type="italics"/> in its Natural De&longs;cent, the Motion of the Earth about its own Centre being pre&longs;uppo&longs;ed, would pro­bably be the Circumference of a Circle.</cell><cell>145</cell></row><row><cell>A <emph type="italics"/>Moveable<emph.end type="italics"/> falling from the top of a Tower moveth in the Circumference of a Circle.</cell><cell>146</cell></row><row><cell>A <emph type="italics"/>Moveable<emph.end type="italics"/> falling from a Tower moveth neither more nor le&longs;&longs;e, then if it had &longs;taid alwayes there.</cell><cell>146</cell></row><row><cell>A <emph type="italics"/>Moveable<emph.end type="italics"/> falling from a Tower moveth with an Uniforme not an Accelerate Motion.</cell><cell>146</cell></row><row><cell>The Cadent <emph type="italics"/>Moveable,<emph.end type="italics"/> if it fall with a Degree of Velocity acquired in a like time with an Uniform Motion, it &longs;hall pa&longs;&longs;e a &longs;pace double to that pa&longs;&longs;ed with the Accelerate Mo­tion.</cell><cell>202</cell></row><row><cell>Admirable Problems of <emph type="italics"/>Moveables<emph.end type="italics"/> de&longs;cending by the Quadrant of a Circle, and tho&longs;e de&longs;cending by all the Chords of the whole Circle.</cell><cell>412</cell></row><row><cell>MUNDANE.</cell><cell></cell></row><row><cell><emph type="italics"/>Mundane<emph.end type="italics"/> Bodies were moved in the beginning in a Right Line, and afterwards circularly, according to <emph type="italics"/>Plato.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell>N</cell><cell></cell></row><row><cell>NATURAL.</cell><cell></cell></row><row><cell>That which is Violent cannot be Eternall, and that which is Eternal cannot be <emph type="italics"/>Natural.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell>NATURE, and <emph type="italics"/>Natures.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Nature<emph.end type="italics"/> attempts not things impo&longs;&longs;ible to be effected.</cell><cell>10</cell></row><row><cell><emph type="italics"/>Nature<emph.end type="italics"/> never doth that by many things which may be done by a few.</cell><cell>99</cell></row><row><cell><emph type="italics"/>Nature<emph.end type="italics"/> fir&longs;t made things as &longs;he plea&longs;ed, and afterwards capacitated Mans under&longs;tanding for conceiving of them.</cell><cell>238</cell></row><row><cell>From Common Accidents one cannot know different <emph type="italics"/>Natures.<emph.end type="italics"/></cell><cell>238</cell></row><row><cell><emph type="italics"/>Natures<emph.end type="italics"/> Order is to make the le&longs;&longs;er Orbes to Cir­culate in &longs;horter times, and the bigger in longer.</cell><cell>243</cell></row><row><cell>That which to us is hard to be under&longs;tood, is with <emph type="italics"/>Nature<emph.end type="italics"/> ca&longs;ie to be effected.</cell><cell>403</cell></row><row><cell><emph type="italics"/>Nature<emph.end type="italics"/> keeping within the bounds a&longs;&longs;igned her, little careth that her Methods of opperating fall within the reach of Humane Capacity.</cell><cell>433</cell></row><row><cell><emph type="italics"/>Natures<emph.end type="italics"/> Actions no le&longs;s admirably di&longs;cover God to us than Scripture Dictions.</cell><cell>434</cell></row><row><cell>NERVES.</cell><cell></cell></row><row><cell>The Original of the <emph type="italics"/>Nerves<emph.end type="italics"/> according to Ari&longs;to­tle, and according to Phy&longs;itians.</cell><cell>91</cell></row><row><cell>The ridieulous An&longs;wer of a Phylo&longs;opher deter­mining the Original of the <emph type="italics"/>Nerves.<emph.end type="italics"/></cell><cell>91</cell></row><row><cell>O</cell><cell></cell></row><row><cell>OBJECTS.</cell><cell></cell></row><row><cell><emph type="italics"/>Objects,<emph.end type="italics"/> the more Vigorous they are in Light, the more they do &longs;eem to encrea&longs;e.</cell><cell>305</cell></row><row><cell>That Remote <emph type="italics"/>Objects<emph.end type="italics"/> appear &longs;o &longs;mall is the Defect of the Eye, as is demon&longs;trated.</cell><cell>337</cell></row><row><cell>In <emph type="italics"/>Objects<emph.end type="italics"/> far Remote and Luminous, a &longs;mall acce&longs;&longs;ion or rece&longs;&longs;ion is imperceptible.</cell><cell>350</cell></row><row><cell>OPINIONS.</cell><cell></cell></row><row><cell>It's all one, whether <emph type="italics"/>Opinions<emph.end type="italics"/> are new to Men, or Men new to <emph type="italics"/>Opinions.<emph.end type="italics"/></cell><cell>77</cell></row><row><cell>ORBE, and <emph type="italics"/>Orbes.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The greater <emph type="italics"/>Orbes<emph.end type="italics"/> make their Conver&longs;ions in <pb xlink:href="040/01/544.jpg"/>greater times.</cell><cell>101 <emph type="italics"/>&<emph.end type="italics"/> 331</cell></row><row><cell>It's more rational, that the <emph type="italics"/>Orbe<emph.end type="italics"/> containing and the Parts contained do move all about one Centre, than about divers.</cell><cell>295</cell></row><row><cell>P</cell><cell></cell></row><row><cell>PASSIONS.</cell><cell></cell></row><row><cell>Infinite <emph type="italics"/>Pa&longs;&longs;ions<emph.end type="italics"/> are perhaps but one onely.</cell><cell>87</cell></row><row><cell>PENDULUM, and <emph type="italics"/>Pendula.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Pendula<emph.end type="italics"/> might have a perpetual Motion, impedi­ments being removed.</cell><cell>203</cell></row><row><cell>The <emph type="italics"/>Pendulum<emph.end type="italics"/> hanging at a longer thread maketh its Vibrations more &longs;eldome than the <emph type="italics"/>Pendu­lum<emph.end type="italics"/> hanging at a &longs;horter.</cell><cell>206</cell></row><row><cell>The Vibrations of the &longs;ame <emph type="italics"/>Pendulum<emph.end type="italics"/> are made with the &longs;ame frequency, whether they be &longs;mall or great.</cell><cell>206</cell></row><row><cell>The cau&longs;e which impedeth the <emph type="italics"/>Pendulum,<emph.end type="italics"/> and reduceth it to re&longs;t.</cell><cell>206</cell></row><row><cell>The thread or Chain to which the <emph type="italics"/>Pendulum<emph.end type="italics"/> is fa&longs;tened maketh an Arch, and doth not &longs;tretch it &longs;elf &longs;traight out in its Vibrations.</cell><cell>207</cell></row><row><cell>Two particular notable Accidents in the <emph type="italics"/>Pendula<emph.end type="italics"/>and their Vibrations.</cell><cell>411</cell></row><row><cell>PERIPATETICK, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Peripatetick<emph.end type="italics"/> Phylo&longs;ophy unchangeable.</cell><cell>42</cell></row><row><cell>A brave re&longs;olution of a certain <emph type="italics"/>Peripatetick<emph.end type="italics"/>Philo&longs;opher to prove the Right Line to be the &longs;horte&longs;t of all Lines.</cell><cell>182</cell></row><row><cell>The Paralogi&longs;me of the &longs;aid <emph type="italics"/>Peripatetick<emph.end type="italics"/> who proveth <emph type="italics"/>Ignotum per ignotius.<emph.end type="italics"/></cell><cell>183</cell></row><row><cell>The Di&longs;cour&longs;es of <emph type="italics"/>Peripateticks<emph.end type="italics"/> full of Errors and Contradictions.</cell><cell>376</cell></row><row><cell>The <emph type="italics"/>Peripateticks<emph.end type="italics"/> per&longs;ecuted Galileo out of envy to his happy Di&longs;coveries in Phylo&longs;ophy.</cell><cell>427</cell></row><row><cell>The <emph type="italics"/>Peripateticks<emph.end type="italics"/> in defect of Rea&longs;ons repair to Scripture for Arguments again&longs;t their Adver&longs;aries.</cell><cell>429</cell></row><row><cell>PHYLOSOPHERS.</cell><cell></cell></row><row><cell>It is not ju&longs;t, that tho&longs;e who never. Phylo&longs;ophate, &longs;hould u&longs;urp the title of <emph type="italics"/>Phylo&longs;ophers.<emph.end type="italics"/></cell><cell>96</cell></row><row><cell>PHYLOSOPHY.</cell><cell></cell></row><row><cell>The Di&longs;putes and Contradictions of <emph type="italics"/>Phylo&longs;ophers<emph.end type="italics"/>may conduce to the benefit of <emph type="italics"/>Phylo&longs;ophy.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell>A cunning way to gather <emph type="italics"/>Phylo&longs;ophy<emph.end type="italics"/> out of any Book what&longs;oever.</cell><cell>92</cell></row><row><cell>PLANETS.</cell><cell></cell></row><row><cell>The approximation and rece&longs;&longs;ion of the three &longs;uperiour <emph type="italics"/>Planets<emph.end type="italics"/> importeth double the Suns di&longs;tance.</cell><cell>299</cell></row><row><cell>The difference of the <emph type="italics"/>Tlanets<emph.end type="italics"/> apparent Magni­tude le&longs;&longs;e in Saturn than in Jupiter, and le&longs;&longs;e in Jupiter than in Mars, and why.</cell><cell>299</cell></row><row><cell>The Station, Direction, and Retrogradation of the <emph type="italics"/>Planets<emph.end type="italics"/> is known in relation to the fixed Stars.</cell><cell>347</cell></row><row><cell>The particular Structures of the Orbes of the <emph type="italics"/>Planets<emph.end type="italics"/> not yet well re&longs;olved.</cell><cell>416</cell></row><row><cell>The <emph type="italics"/>Planets<emph.end type="italics"/> places may more certainly be a&longs;&longs;igred by this Doctrine, than by that of Ptolomies great Almage&longs;t.</cell><cell>469</cell></row><row><cell>PLATO.</cell><cell></cell></row><row><cell><emph type="italics"/>Plato<emph.end type="italics"/> held, that Humane under&longs;tanding pertook of Divinity, becau&longs;e it under&longs;tood Num­bers.</cell><cell>3</cell></row><row><cell><emph type="italics"/>Plato<emph.end type="italics"/> his Ænigma, and the Interpretation of it.</cell><cell>498</cell></row><row><cell>POLE.</cell><cell></cell></row><row><cell>The invariable Elevation of the <emph type="italics"/>Pole<emph.end type="italics"/> urged as an Argument again&longs;t the Annual Motion.</cell><cell>338</cell></row><row><cell>An Example to prove that the Altitude of the <emph type="italics"/>Pole<emph.end type="italics"/> ought not to vary by means of the Earths Annual Motion.</cell><cell>340</cell></row><row><cell>POWER.</cell><cell></cell></row><row><cell>Of an infinite <emph type="italics"/>Power<emph.end type="italics"/> one would think a greater part &longs;hould rather be imployed than a le&longs;&longs;er.</cell><cell>105</cell></row><row><cell>PRINCIPLES.</cell><cell></cell></row><row><cell>By denying <emph type="italics"/>Principles<emph.end type="italics"/> in Sciences, any Paradox may be maintained.</cell><cell>28</cell></row><row><cell>Contrary <emph type="italics"/>Principles<emph.end type="italics"/> cannot naturally re&longs;ide in the &longs;ame Subject.</cell><cell>211</cell></row><row><cell>PROJECT, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The <emph type="italics"/>Project,<emph.end type="italics"/> according to Ari&longs;totle, is not mo­ved by virtue impre&longs;&longs;ed, but by the Me­dium.</cell><cell>130</cell></row><row><cell>Operation of the Medium in continuing the Motion of the <emph type="italics"/>Project.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell>Many Experiments and Rea&longs;ons again&longs;t the Motions of <emph type="italics"/>Projects<emph.end type="italics"/> a&longs;&longs;igned by Ari&longs;totle.</cell><cell>132</cell></row><row><cell>The Medium doth impede and not conferre the <pb xlink:href="040/01/545.jpg"/>Motion of <emph type="italics"/>Projests.<emph.end type="italics"/></cell><cell>134</cell></row><row><cell>An admirable accident in the Motion of <emph type="italics"/>Pro­jects.<emph.end type="italics"/></cell><cell>135</cell></row><row><cell>Sundry curious Problems touching the Motion of <emph type="italics"/>Projects.<emph.end type="italics"/></cell><cell>137</cell></row><row><cell><emph type="italics"/>Projects<emph.end type="italics"/> continue their <emph type="italics"/>Motion<emph.end type="italics"/> by a Right Line that follows the direction of the Motion made together with the <emph type="italics"/>Projicient,<emph.end type="italics"/> whil&longs;t they were conjoyned therewith.</cell><cell>154</cell></row><row><cell>The Motion impre&longs;&longs;ed by the <emph type="italics"/>Projicient<emph.end type="italics"/> is onely in a Right Line.</cell><cell>170</cell></row><row><cell>The <emph type="italics"/>Project<emph.end type="italics"/> moveth by the Tangent of the Cir­cle of the Motion preceeding in the in&longs;tant of Seperation.</cell><cell>172</cell></row><row><cell>A Grave <emph type="italics"/>Project<emph.end type="italics"/> a&longs;&longs;oon as it is &longs;eperated from the <emph type="italics"/>Projicient,<emph.end type="italics"/> beginneth to decline.</cell><cell>173</cell></row><row><cell>The Cau&longs;e of the <emph type="italics"/>Projection<emph.end type="italics"/> encrea&longs;eth not ac­cording to the Proportion of Velocity en­crea&longs;ed by making the Wheel bigger.</cell><cell>189</cell></row><row><cell>The Virtue which carrieth Grave <emph type="italics"/>Projects<emph.end type="italics"/> up­wards, is no le&longs;&longs;e Natural to them than the Gravity which moveth them down­wards.</cell><cell>211</cell></row><row><cell>PTOLOMY, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Inconveniences that are in the Sy&longs;tem of <emph type="italics"/>Pto­lomy.<emph.end type="italics"/></cell><cell>309</cell></row><row><cell><emph type="italics"/>Ptolomies<emph.end type="italics"/> Sy&longs;tem full of defects.</cell><cell>476</cell></row><row><cell>The Learned both of elder and later times di&longs;­&longs;atisfied with the <emph type="italics"/>Ptolomaick<emph.end type="italics"/> Sy&longs;tem.</cell><cell>477</cell></row><row><cell>PYTHAGORAS, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Pythagorick<emph.end type="italics"/> Mi&longs;tery of Numbers fabulous.</cell><cell>3</cell></row><row><cell><emph type="italics"/>Pythagoras<emph.end type="italics"/> offered an Hecatombe for a Geo­metrical Demon&longs;tration which he found.</cell><cell>38</cell></row><row><cell><emph type="italics"/>Pythagoras<emph.end type="italics"/> and many other Ancients enumera­ted, that held the Earths Mobility.</cell><cell>437 <emph type="italics"/>&<emph.end type="italics"/> 468</cell></row><row><cell>R</cell><cell></cell></row><row><cell>RAYS.</cell><cell></cell></row><row><cell>Shining Objects &longs;eem fringed and environed with adventitious <emph type="italics"/>Rays.<emph.end type="italics"/></cell><cell>304</cell></row><row><cell>RIST.</cell><cell></cell></row><row><cell><emph type="italics"/>Re&longs;t.<emph.end type="italics"/> Vide <emph type="italics"/>Motion.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Re&longs;t<emph.end type="italics"/> the Infinite degree of Tardity.</cell><cell>11</cell></row><row><cell>RBTROGRADATIONS.</cell><cell></cell></row><row><cell><emph type="italics"/>Retrogradations<emph.end type="italics"/> more frequent in Saturn, le&longs;&longs;e fre quent in Jupiter, and yet le&longs;&longs;e in Mars, and why.</cell><cell>311</cell></row><row><cell>The <emph type="italics"/>Retrogradations<emph.end type="italics"/> of Venus and Mercury demon&longs;trated by Apollonius and Coper­nicus.</cell><cell>311</cell></row><row><cell>S</cell><cell></cell></row><row><cell>SATURN.</cell><cell></cell></row><row><cell><emph type="italics"/>Saturn<emph.end type="italics"/> for its &longs;lowne&longs;&longs;e, and Mercury for its late appearing, were among&longs;t tho&longs;e that were la&longs;t ob&longs;erved.</cell><cell>416</cell></row><row><cell>SCARCITY.</cell><cell></cell></row><row><cell><emph type="italics"/>Scarcity<emph.end type="italics"/> and Plenty enhan&longs;e and deba&longs;e the price of all things.</cell><cell>43</cell></row><row><cell>SCHEINER.</cell><cell></cell></row><row><cell>Chri&longs;topher <emph type="italics"/>Scheiner<emph.end type="italics"/> the Jefuit his Book of Con­clu&longs;ions confuted.</cell><cell>78 <emph type="italics"/>& 195, & <expan abbr="&longs;eq.">&longs;eque</expan> &<emph.end type="italics"/> 323</cell></row><row><cell>A Canon Bullet would &longs;pend more than &longs;ix dayes in falling from the Concave of the Moon to the Center of the Earth, according to <emph type="italics"/>Scheiner.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell>Chri&longs;topher <emph type="italics"/>Scheiner<emph.end type="italics"/> his Book entituled <emph type="italics"/>Apelles po&longs;t Tabulam<emph.end type="italics"/> cen&longs;ured, and di&longs;proved.</cell><cell>313</cell></row><row><cell>The Objections of <emph type="italics"/>Scheiner<emph.end type="italics"/> by way of Interro­gation.</cell><cell>336</cell></row><row><cell>An&longs;wers to the Interrogations of <emph type="italics"/>Schtiner.<emph.end type="italics"/></cell><cell>336</cell></row><row><cell>Que&longs;tions put to <emph type="italics"/>Scheiner,<emph.end type="italics"/> by which the weak­ne&longs;le of his is made appear.</cell><cell>336</cell></row><row><cell>SCIENCES.</cell><cell></cell></row><row><cell>In Natural <emph type="italics"/>Sciences<emph.end type="italics"/> the Art of Oratory is of no u&longs;e.</cell><cell>40</cell></row><row><cell>In Natural <emph type="italics"/>Sciences<emph.end type="italics"/> it is not nece&longs;&longs;ary to &longs;eek Mathematical evidence.</cell><cell>206</cell></row><row><cell>SCRIPTURE, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The Caution we are to u&longs;e in determining the Sen&longs;e of <emph type="italics"/>Scripture<emph.end type="italics"/> in difficult points of Phy­lo&longs;ophy.</cell><cell>427</cell></row><row><cell><emph type="italics"/>Scripture<emph.end type="italics"/> &longs;tudiou&longs;ly conde&longs;cendeth to the ap­prehen&longs;ion of the Vulgar.</cell><cell>432</cell></row><row><cell>In dicu&longs;&longs;ing of Natural Que&longs;tions, we ought not to begin at <emph type="italics"/>Scripture,<emph.end type="italics"/> but at Sen&longs;ible Experiments and Nece&longs;&longs;ary Demon&longs;tra­tions.</cell><cell>433</cell></row><row><cell>The intent of <emph type="italics"/>Scripture<emph.end type="italics"/> is by its Authority to recommend tho&longs;e Truths to our beliefe, which being un­intelligible, could no other wayes be rendered credible.</cell><cell>434</cell></row><pb xlink:href="040/01/546.jpg"/><row><cell><emph type="italics"/>Scripture<emph.end type="italics"/> Authority to be preferred, even in Na­tural Controver&longs;ies to &longs;uch Sciences as are not confined to a Demon&longs;trative Me­thod.</cell><cell>434</cell></row><row><cell>The Pen­men of <emph type="italics"/>Scripture,<emph.end type="italics"/> though read in A­&longs;tronomy, intentionally forbear to teach us anything of the Nature of the Stars.</cell><cell>435</cell></row><row><cell>The Spirit had no intent at the Writing of the <emph type="italics"/>Scripture,<emph.end type="italics"/> to teach us whether the Earth mo­veth or &longs;tandeth &longs;till, as nothing concerning our Salvation.</cell><cell>436</cell></row><row><cell>Inconveniencies that ari&longs;e from licentious u­&longs;urping of <emph type="italics"/>Scripture,<emph.end type="italics"/> to &longs;tuffe out Books that treat of Nat. Arguments.</cell><cell>438</cell></row><row><cell>The Literal Sen&longs;e of <emph type="italics"/>Scripture<emph.end type="italics"/> joyned with the univer&longs;al con&longs;ent of the Fathers, is to be re­ceived without farther di&longs;pute</cell><cell>444</cell></row><row><cell>A Text of <emph type="italics"/>Scripture<emph.end type="italics"/> ought no le&longs;&longs;e diligently to be reconciled with a Demon&longs;trated Pro­po&longs;ition in Philo&longs;ophy, than with another Text of <emph type="italics"/>Scripture<emph.end type="italics"/> &longs;ounding to a contrary Sen&longs;e.</cell><cell>446</cell></row><row><cell>Demon&longs;trated Truth ought to a&longs;&longs;i&longs;t the Com­mentator in finding the true Sen&longs;e of <emph type="italics"/>Scrip­ture.<emph.end type="italics"/></cell><cell>446</cell></row><row><cell>It was nece&longs;&longs;ary by way of conde&longs;cen&longs;ion to Vulgar Capacities, that the <emph type="italics"/>Scripture<emph.end type="italics"/> &longs;hould &longs;peak of the Re&longs;t and Motion of the Sun and Earth in the &longs;ame manner that it doth.</cell><cell>447</cell></row><row><cell>Not onely the Incapacity of the Vulgar, but the Current Opinion of tho&longs;e times, made the Sacred Writers of the <emph type="italics"/>Scripture<emph.end type="italics"/> to ac­commodate them&longs;elves to Popular E&longs;teem more than Truth.</cell><cell>447</cell></row><row><cell>The <emph type="italics"/>Scripture<emph.end type="italics"/> had much more rea&longs;on to affirm the Sun Moveable, and the Earth Immove­able, than otherwi&longs;e.</cell><cell>448</cell></row><row><cell>Circum&longs;pection of the Fathers about impo&longs;ing po&longs;itive Sen&longs;es on Doubtful Texts of <emph type="italics"/>Scrip­ture.<emph.end type="italics"/></cell><cell>451</cell></row><row><cell>Tis Cowardice makes the Anti­Copernican fly to Scripture Authorities, thinking thereby to affright their Adver&longs;aries.</cell><cell>455</cell></row><row><cell><emph type="italics"/>Scripture<emph.end type="italics"/> &longs;peaks in Vulgar and Common Points after the manner of Men.</cell><cell>462</cell></row><row><cell>The intent of <emph type="italics"/>Scripture<emph.end type="italics"/> is to be ob&longs;erved in Pla­ces that &longs;eem to affirme the Earths Stabi­lity.</cell><cell>464</cell></row><row><cell><emph type="italics"/>Scripture<emph.end type="italics"/> Authorities that &longs;eem to affirm the Mo­tion of the Sun and Stability of the Earth, divided into &longs;ix Cla&longs;&longs;es.</cell><cell>478</cell></row><row><cell>Six Maximes to be ob&longs;erved in Expounding Dark Texts of <emph type="italics"/>Scripture.<emph.end type="italics"/></cell><cell>481</cell></row><row><cell><emph type="italics"/>Scripture<emph.end type="italics"/> Texts &longs;peaking of things inconveni­ent to be under&longs;tood in their Literal Sen&longs;e, are to be interpreted one of the four wayes named.</cell><cell>81</cell></row><row><cell>Why the Sacred <emph type="italics"/>Scripture<emph.end type="italics"/> accommodates it &longs;elf to the Sen&longs;e of the Vulgar.</cell><cell>487</cell></row><row><cell>SEA.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Seas<emph.end type="italics"/> Surface would &longs;hew at a di&longs;tance more ob&longs;cure than the Land.</cell><cell>49</cell></row><row><cell>The <emph type="italics"/>Seas<emph.end type="italics"/> Reflection of Light much weaker than that of the Earth.</cell><cell>81</cell></row><row><cell>The I&longs;les are tokens of the unevenne&longs;&longs;e of the Bottoms of <emph type="italics"/>Seas.<emph.end type="italics"/></cell><cell>383</cell></row><row><cell>SELEUCUS.</cell><cell></cell></row><row><cell>Opinion of <emph type="italics"/>Seleucus<emph.end type="italics"/> the Mathematician cen­&longs;ured.</cell><cell>422</cell></row><row><cell>SENSE.</cell><cell></cell></row><row><cell>He who denieth <emph type="italics"/>Sen&longs;e,<emph.end type="italics"/> de&longs;erves to be deprived of it.</cell><cell>21</cell></row><row><cell><emph type="italics"/>Sen&longs;e<emph.end type="italics"/> &longs;heweth that things Grave move <emph type="italics"/>ad Me­dium,<emph.end type="italics"/> and the Light to the Concave.</cell><cell>21</cell></row><row><cell>It is not probable that God who gave us our <emph type="italics"/>Sen&longs;es,<emph.end type="italics"/> would have us lay them a&longs;ide, and look for other Proofs for &longs;uch Natural Points as <emph type="italics"/>Sen&longs;e<emph.end type="italics"/> &longs;ets before our Eyes.</cell><cell>434</cell></row><row><cell><emph type="italics"/>Sen&longs;e<emph.end type="italics"/> and Rea&longs;on le&longs;&longs;e certain than Faith.</cell><cell>475</cell></row><row><cell>SILVER.</cell><cell></cell></row><row><cell><emph type="italics"/>Silver<emph.end type="italics"/> burni&longs;hed appears much more ob&longs;cure than the unburni&longs;hed, and why.</cell><cell>64</cell></row><row><cell>SIMPLICIUS.</cell><cell></cell></row><row><cell><emph type="italics"/>Simplicius<emph.end type="italics"/> his Declamation.</cell><cell>43</cell></row><row><cell>SOCRATES.</cell><cell></cell></row><row><cell>The An&longs;wer of the Oracle true in judging <emph type="italics"/>So­crates<emph.end type="italics"/> the Wi&longs;e&longs;t of his time.</cell><cell>85</cell></row><row><cell>SORITES.</cell><cell></cell></row><row><cell>The Forked Sylogi&longs;me called <foreign lang="greek">Sopeites</foreign></cell><cell>29</cell></row><row><cell>SPEAKING.</cell><cell></cell></row><row><cell>We cannot ab&longs;tract our manner of <emph type="italics"/>Speaking<emph.end type="italics"/>from our Sen&longs;e of Seeing.</cell><cell>461</cell></row><row><cell>SPHERE.</cell><cell></cell></row><row><cell>The Motion of 24 hours a&longs;cribed to the Highe&longs;t <pb xlink:href="040/01/547.jpg"/><emph type="italics"/>Sphere,<emph.end type="italics"/> di&longs;orders the Period of the Inferi­our.</cell><cell>102</cell></row><row><cell>The <emph type="italics"/>Sphere<emph.end type="italics"/> although Material, toucheth the Material Plane but in one point onely.</cell><cell>182</cell></row><row><cell>The Definition of the <emph type="italics"/>Sphere.<emph.end type="italics"/></cell><cell>182</cell></row><row><cell>A Demon&longs;tration that the <emph type="italics"/>Sphere<emph.end type="italics"/> toucheth the Plane but in one point.</cell><cell>183</cell></row><row><cell>Why the <emph type="italics"/>Sphere<emph.end type="italics"/> in ab&longs;tract toucheth the Plane onely in one point, and not the Material in Concrete.</cell><cell>184</cell></row><row><cell>Contact in a Single Point is not peculiar to the perfect <emph type="italics"/>Sphere<emph.end type="italics"/> onely, but belongeth to all Curved Figures.</cell><cell>185</cell></row><row><cell>In a Moveable <emph type="italics"/>Sphere<emph.end type="italics"/> it &longs;eemeth more rea&longs;ona­ble that its Centre be &longs;table, than any of its parts.</cell><cell>300</cell></row><row><cell>SPHERE of <emph type="italics"/>Activity.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The <emph type="italics"/>Sphere of Activity<emph.end type="italics"/> greater in Cele&longs;tial Bo­dies than in Elimentary.</cell><cell>59</cell></row><row><cell>STARRY SPHERE.</cell><cell></cell></row><row><cell>Wearine&longs;&longs;e more to be feared in the <emph type="italics"/>Starry Sphere<emph.end type="italics"/>than in the Terre&longs;trial Globe.</cell><cell>245</cell></row><row><cell>By the proportion of Jupiter and of Mars, the <emph type="italics"/>Starry Sphere<emph.end type="italics"/> is found to be yet more re­mote.</cell><cell>331</cell></row><row><cell>Vanity of tho&longs;e mens di&longs;cour&longs;e, who argue the <emph type="italics"/>Starry Sphere<emph.end type="italics"/> to be too va&longs;t in the Coper­nican Hypothe&longs;is.</cell><cell>335</cell></row><row><cell>The whole <emph type="italics"/>Starry Sphere<emph.end type="italics"/> beheld from a great di­&longs;tance, might appear as &longs;mall as one &longs;ingle Star.</cell><cell>335</cell></row><row><cell>SPHERICAL.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Spherical<emph.end type="italics"/> Figure is ea&longs;ier to be made than any other.</cell><cell>186</cell></row><row><cell><emph type="italics"/>Spherical<emph.end type="italics"/> Figures of &longs;undry Magnitudes, may be made with one &longs;ole In&longs;trument.</cell><cell>187</cell></row><row><cell>SPIRIT.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Spirit<emph.end type="italics"/> had no intent to teach us whether the Earth moveth or &longs;tandeth &longs;till, as no­thing concerning our Salvation.</cell><cell>436</cell></row><row><cell>SOLAR SPOTS.</cell><cell></cell></row><row><cell><emph type="italics"/>Spots<emph.end type="italics"/> generate and di&longs;&longs;olve in the face of the Sun.</cell><cell>38</cell></row><row><cell>Sundry Opinions touching the <emph type="italics"/>Solar Spots.<emph.end type="italics"/></cell><cell>39</cell></row><row><cell>An Argument that nece&longs;&longs;arily proveth the <emph type="italics"/>So­lar Spots<emph.end type="italics"/> to generate and di&longs;&longs;olve.</cell><cell>40</cell></row><row><cell>A conclu&longs;ive Demon&longs;tration to prove that the <emph type="italics"/>Spots<emph.end type="italics"/> are contiguous to the Body of the Sun.</cell><cell>41</cell></row><row><cell>The Motion of the <emph type="italics"/>Spots<emph.end type="italics"/> towards the Circum­cumference of the Sun appears &longs;low.</cell><cell>41</cell></row><row><cell>The Figure of the <emph type="italics"/>Spots<emph.end type="italics"/> towards the Circumfe­rence of the Suns Di&longs;cus, appear narrow, and why.</cell><cell>41</cell></row><row><cell>The <emph type="italics"/>Solar Spots<emph.end type="italics"/> are not Spherical, but flat, like thin plates.</cell><cell>41</cell></row><row><cell>The Hi&longs;tory of the proceedings of the Acade­mian for a long time about the Ob&longs;ervation of the <emph type="italics"/>Solas Spots.<emph.end type="italics"/></cell><cell>312</cell></row><row><cell>A conceit that &longs;uddenly came into the mind of our Academian concerning the great con&longs;e­quence that followeth upon the Motion of the <emph type="italics"/>Solar Spots.<emph.end type="italics"/></cell><cell>314</cell></row><row><cell>Extravagant Mutations to be ob&longs;erved in the Motions of the <emph type="italics"/>Solar Spots<emph.end type="italics"/> fore&longs;een by the Academick, in ca&longs;e the Earth had the Annu­al Motion.</cell><cell>314</cell></row><row><cell>The fir&longs;t Accident to be ob&longs;erved in the Moti­on of the <emph type="italics"/>Solar Spots,<emph.end type="italics"/> and con&longs;equently all the re&longs;t, explained.</cell><cell>315</cell></row><row><cell>The events being ob&longs;erved were an&longs;werable to the Predictions touching the&longs;e <emph type="italics"/>Spots.<emph.end type="italics"/></cell><cell>318</cell></row><row><cell>Though the Annual Motion a&longs;&longs;igned to the Earth, an&longs;wereth to the Phænomena of the <emph type="italics"/>Solar Spots,<emph.end type="italics"/> yet doth it not follow by conver­&longs;ion, that from the Phænomena of the <emph type="italics"/>Spots<emph.end type="italics"/>one may inferre the Annual Motion to be­long to the Earth.</cell><cell>319</cell></row><row><cell>The Pure Peripatetick Philo&longs;ophers will laugh at the <emph type="italics"/>Spots<emph.end type="italics"/> and their Phænomena, as the Illu&longs;ions of the Chri&longs;tals in the Tele­&longs;cope.</cell><cell>319</cell></row><row><cell>The <emph type="italics"/>Solar Spots<emph.end type="italics"/> of Galileo.</cell><cell>494</cell></row><row><cell>STAR and <emph type="italics"/>Stars.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The <emph type="italics"/>Stars<emph.end type="italics"/> infinitely &longs;urpa&longs;&longs;e the re&longs;t of Heaven in Den&longs;ity.</cell><cell>30</cell></row><row><cell>It is no le&longs;&longs;e impo&longs;&longs;ible for a <emph type="italics"/>Star<emph.end type="italics"/> to corrupt, than the whole Terre&longs;trial Globe.</cell><cell>37</cell></row><row><cell>New <emph type="italics"/>Stars<emph.end type="italics"/> di&longs;covered in Heaven.</cell><cell>38</cell></row><row><cell>The &longs;mall Body of a <emph type="italics"/>Star<emph.end type="italics"/> fringed about with Rays, appeareth very much bigger than plain, naked, and in its native Clarity.</cell><cell>61</cell></row><row><cell>An ea&longs;ie Experiment that &longs;heweth the encrea&longs;e in the <emph type="italics"/>Stars,<emph.end type="italics"/> by means of the Adventitious Rays.</cell><cell>305</cell></row><row><cell>A <emph type="italics"/>Star<emph.end type="italics"/> of the Sixth Magnitude &longs;uppo&longs;ed by Ty­cho and Scheiner an hundred and &longs;ix Millions of times bigger than needs.</cell><cell>326</cell></row><row><cell>A common errour of all A&longs;tronomers touching the Magnitude of the <emph type="italics"/>Stars.<emph.end type="italics"/></cell><cell>326</cell></row><pb xlink:href="040/01/548.jpg"/><row><cell> <gap/>2 Full PAGES MISSING<pb xlink:href="040/01/549.jpg"/><pb xlink:href="040/01/550.jpg"/><gap/><pb xlink:href="040/01/551.jpg"/> a fal&longs;e one, none.</cell><cell>112. 245</cell></row><row><cell>TRUTH, and <emph type="italics"/>Truths.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Untruths cannot be Demon&longs;trated as <emph type="italics"/>Truths<emph.end type="italics"/>are.</cell><cell>112</cell></row><row><cell>The <emph type="italics"/>Truth<emph.end type="italics"/> &longs;ometimes gains &longs;trength by Con­tradiction.</cell><cell>181</cell></row><row><cell><emph type="italics"/>Truth<emph.end type="italics"/> hath not &longs;o little light as not to be di&longs;co­vered among&longs;t the Umbrages of Fal­&longs;hoods.</cell><cell>384</cell></row><row><cell>TYCHO.</cell><cell></cell></row><row><cell>The Argument of <emph type="italics"/>Tycho<emph.end type="italics"/> grounded upon a fal&longs;e Hypothe&longs;is.</cell><cell>324</cell></row><row><cell><emph type="italics"/>Tycho<emph.end type="italics"/> and his Followers never attempted to &longs;ee whether there were any Phænomena in the Firmament for or again&longs;t the Annual Mo­tion.</cell><cell>337</cell></row><row><cell><emph type="italics"/>Tycho<emph.end type="italics"/> and others argue again&longs;t the Annual Mo­tion, from the invariable Elevation of the Pole.</cell><cell>338</cell></row><row><cell>V</cell><cell></cell></row><row><cell>VELOCITY.</cell><cell></cell></row><row><cell>Vniform <emph type="italics"/>Velocity<emph.end type="italics"/> &longs;utable with Circular Mo­tion.</cell><cell>12</cell></row><row><cell>Nature doth not immediately conferre a de­terminate degree of <emph type="italics"/>Velocity,<emph.end type="italics"/> although She could.</cell><cell>12</cell></row><row><cell>The <emph type="italics"/>Velocity<emph.end type="italics"/> by the inclining plane equal to the <emph type="italics"/>Velocity<emph.end type="italics"/> by the Perpendicular, and the Mo­tion by the Perpendicular &longs;wifter than by the inclining plane.</cell><cell>14</cell></row><row><cell><emph type="italics"/>Velocities<emph.end type="italics"/> are &longs;aid to be equal, when the Spa­ces pa&longs;&longs;ed are proportionate to their times.</cell><cell>15</cell></row><row><cell>The greater <emph type="italics"/>Velocity<emph.end type="italics"/> exactly compen&longs;ates the greater Gravity.</cell><cell>192</cell></row><row><cell>VENUS.</cell><cell></cell></row><row><cell>The Mutation of Figure in <emph type="italics"/>Venus<emph.end type="italics"/> argueth its Motion to be about the Sun.</cell><cell>295</cell></row><row><cell><emph type="italics"/>Veuus<emph.end type="italics"/> very great towards the Ve&longs;pertine Con­junction, and very &longs;mall towards the Ma­cutine.</cell><cell>297</cell></row><row><cell><emph type="italics"/>Venus<emph.end type="italics"/> nece&longs;&longs;arily proved to move about the Sun.</cell><cell>298</cell></row><row><cell>The Phænomena of <emph type="italics"/>Venus<emph.end type="italics"/> appear contrary to the Sy&longs;tem of Copernicus.</cell><cell>302</cell></row><row><cell>Another Difficulty rai&longs;ed by <emph type="italics"/>Venus<emph.end type="italics"/> again&longs;t Co­pernicus.</cell><cell>302</cell></row><row><cell><emph type="italics"/>Venus<emph.end type="italics"/> according to Copernicus either lucid in it &longs;elf, or a tran&longs;parent &longs;ub&longs;tance.</cell><cell>302</cell></row><row><cell>The Rea&longs;on why <emph type="italics"/>Venus<emph.end type="italics"/> and Mars do not ap­pear to vary Magnitude &longs;o much as is re­qui&longs;ite.</cell><cell>303</cell></row><row><cell>A &longs;econd Rea&longs;on of the &longs;mall apparent encreale of <emph type="italics"/>Venus.<emph.end type="italics"/></cell><cell>306</cell></row><row><cell><emph type="italics"/>Venus<emph.end type="italics"/> renders the Errour of A&longs;tronomers in de­termining the Magnitude of Stars inex­cu&longs;eable.</cell><cell>327</cell></row><row><cell>VESSEL.</cell><cell></cell></row><row><cell>Of the Motion of Water in a <emph type="italics"/>Ve&longs;&longs;el.<emph.end type="italics"/> Vide <emph type="italics"/>Water.<emph.end type="italics"/></cell><cell></cell></row><row><cell>UNDERSTAND, <emph type="italics"/>&c.<emph.end type="italics"/></cell><cell></cell></row><row><cell>Man <emph type="italics"/>Under&longs;tandeth<emph.end type="italics"/> very much <emph type="italics"/>inten&longs;ive,<emph.end type="italics"/> but little <emph type="italics"/>exten&longs;ive.<emph.end type="italics"/></cell><cell>86</cell></row><row><cell>Humane <emph type="italics"/>Uuder&longs;tanding<emph.end type="italics"/> operates by Ratioci­nation.</cell><cell>87</cell></row><row><cell>UNIVERSE.</cell><cell></cell></row><row><cell>The Con&longs;titution of the <emph type="italics"/>Uuiver&longs;e<emph.end type="italics"/> is one of the Noble&longs;t Problems a Man can &longs;tudy.</cell><cell>187</cell></row><row><cell>The Centre of the <emph type="italics"/>Univer&longs;e<emph.end type="italics"/> according to Ari­&longs;totle is that Polnt about which the Cele­&longs;tial Spheres do revolve.</cell><cell>294</cell></row><row><cell>Which ought to be accounted the Sphere of the <emph type="italics"/>Univer&longs;e.<emph.end type="italics"/></cell><cell>299</cell></row><row><cell>It is a great ra&longs;hne&longs;&longs;e to cen&longs;ure that to be &longs;u­perfluous in the <emph type="italics"/>Univer&longs;e<emph.end type="italics"/> which we do not perceive to be made for us.</cell><cell>334</cell></row><row><cell>VURSTITIUS.</cell><cell></cell></row><row><cell>Chri&longs;tianus <emph type="italics"/>Vur&longs;titius<emph.end type="italics"/> read certain Lectures touching the Opinion of Copernicus, and what happened thereupon.</cell><cell>110</cell></row><row><cell>W</cell><cell></cell></row><row><cell>WATER.</cell><cell></cell></row><row><cell>He that had not heard of the Element of <emph type="italics"/>Water,<emph.end type="italics"/>could never fancie to him&longs;elf Ships and Fi­&longs;hes.</cell><cell>47</cell></row><row><cell>An Experiment to prove the Reflection of <emph type="italics"/>Wa­ter<emph.end type="italics"/> lefs bright than that of the Land.</cell><cell>81</cell></row><row><cell>The Motion of the <emph type="italics"/>Water<emph.end type="italics"/> in Ebbing and Flow­ing, not interrupted by Re&longs;t.</cell><cell>251</cell></row><row><cell>The vain Argumentation of &longs;ome, to prove the Element of <emph type="italics"/>Water<emph.end type="italics"/> to be of a Spherical Superficies.</cell><cell>377</cell></row><pb xlink:href="040/01/552.jpg"/><row><cell>The Progre&longs;&longs;ive and uneven Motion makes the <emph type="italics"/>Water<emph.end type="italics"/> in a Ve&longs;&longs;el to run to and fro.</cell><cell>387</cell></row><row><cell>The Several Motions in the conteining Ve&longs;&longs;el, may make the conteined <emph type="italics"/>Water<emph.end type="italics"/> to ri&longs;e and fall.</cell><cell>387</cell></row><row><cell>The <emph type="italics"/>Water<emph.end type="italics"/> rai&longs;ed in one end of the Ve&longs;&longs;el re­turneth it &longs;elf to <emph type="italics"/>Æquilibrium.<emph.end type="italics"/></cell><cell>391</cell></row><row><cell>In the &longs;horter Ve&longs;&longs;els the Undulations of <emph type="italics"/>Wa­ters<emph.end type="italics"/> are more frequent.</cell><cell>391</cell></row><row><cell>The greater profundity maketh the Undulati­ons of <emph type="italics"/>Water<emph.end type="italics"/> the more frequent.</cell><cell>391</cell></row><row><cell>Why in narrow places the Cour&longs;e of the <emph type="italics"/>Wa­ters<emph.end type="italics"/> is &longs;wifter than in larger.</cell><cell>396</cell></row><row><cell>The cau&longs;e why in &longs;ome narrow Chanels, we &longs;ee the Sea­<emph type="italics"/>Waters<emph.end type="italics"/> run alwayes one way.</cell><cell>398</cell></row><row><cell>The <emph type="italics"/>Water<emph.end type="italics"/> more apt to con&longs;erve an Impetus conceived than the Air.</cell><cell>400</cell></row><row><cell>The Motion of the <emph type="italics"/>Water<emph.end type="italics"/> dependeth on the Motion of Heaven.</cell><cell>404</cell></row><row><cell>WEIGHTS.</cell><cell></cell></row><row><cell>Its que&longs;tionable whether De&longs;cending <emph type="italics"/>Weights<emph.end type="italics"/>move in a Right Line.</cell><cell>21</cell></row><row><cell>WEST.</cell><cell></cell></row><row><cell>The Cour&longs;e to the <emph type="italics"/>West<emph.end type="italics"/> India's ea&longs;ie, the re­turn difficult.</cell><cell>402</cell></row><row><cell>WINDE.</cell><cell></cell></row><row><cell>Con&longs;tant Gales of <emph type="italics"/>Winde<emph.end type="italics"/> within the Tropicks blow towards the We&longs;t.</cell><cell>402</cell></row><row><cell><emph type="italics"/>Windes<emph.end type="italics"/> from the Land, make rough the Seas.</cell><cell>402</cell></row><row><cell>WISDOME <emph type="italics"/>Divine.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Divine Wi&longs;dome<emph.end type="italics"/> infinitely infinite.</cell><cell>85</cell></row><row><cell>The Di&longs;cour&longs;es which Humane Rea&longs;on makes in time, the <emph type="italics"/>Divine Wi&longs;dom<emph.end type="italics"/> re&longs;olveth in a Moment, that is hath them alwayes pre­&longs;ent.</cell><cell>87</cell></row><row><cell>WIT.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Wit<emph.end type="italics"/> of Man admirably acute.</cell><cell>87</cell></row><row><cell>The Pu&longs;ilanimity of Popular <emph type="italics"/>Wits.<emph.end type="italics"/></cell><cell>364</cell></row><row><cell>Poctick <emph type="italics"/>Wits<emph.end type="italics"/> of two kinds.</cell><cell>384</cell></row><row><cell>WORLD.</cell><cell></cell></row><row><cell><emph type="italics"/>World.<emph.end type="italics"/> Vide <emph type="italics"/>Univer&longs;e.<emph.end type="italics"/></cell><cell></cell></row><row><cell>The <emph type="italics"/>Worlds<emph.end type="italics"/> parts are according to Ari&longs;totle two, Cele&longs;tial and Elementary, contrary to each other.</cell><cell>6</cell></row><row><cell>The <emph type="italics"/>World<emph.end type="italics"/> &longs;uppo&longs;ed by the Anthour [Galileo] to be perfectly Ordinate.</cell><cell>10</cell></row><row><cell>The Sen&longs;ible <emph type="italics"/>World.<emph.end type="italics"/></cell><cell>96</cell></row><row><cell>It hath not been hitherto proved by any whe­ther the <emph type="italics"/>World<emph.end type="italics"/> be finite or infinite.</cell><cell>293</cell></row><row><cell>If the Centre of the <emph type="italics"/>World<emph.end type="italics"/> be the &longs;ame with that about which the Planets move, the Sun and not the Earth is placed in it.</cell><cell>295</cell></row><row><cell>WRITING.</cell><cell></cell></row><row><cell>Some <emph type="italics"/>Write<emph.end type="italics"/> what they under&longs;tand not, and therefore under&longs;tand not what they <emph type="italics"/>Write.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell>The Invention of <emph type="italics"/>Writing<emph.end type="italics"/> Stupendious above all others.</cell><cell>88</cell></row><row><cell>Y</cell><cell></cell></row><row><cell>YEAR.</cell><cell></cell></row><row><cell>The <emph type="italics"/>Years<emph.end type="italics"/> beginning and ending, which Ptolomy and his Followers could never po&longs;itively a&longs;­&longs;ign, is exactly determined by the Coper­nican Hypothe&longs;is.</cell><cell>469</cell></row></table><p type="head"> <s><emph type="italics"/>THE END OF THE TABLE.<emph.end type="italics"/></s></p></chap><pb xlink:href="040/01/553.jpg"/><pb xlink:href="040/01/554.jpg"/><chap><p type="head"> <s>The ERRATA of the <emph type="italics"/>fir&longs;t<emph.end type="italics"/> PART of the <emph type="italics"/>fir&longs;t<emph.end type="italics"/> TOME.</s></p><p type="main"> <s>line 31. <emph type="italics"/>for<emph.end type="italics"/> where leave, <emph type="italics"/>read<emph.end type="italics"/> why omit. </s> <s>p 3, l 32, only for. </s> <s>p 5, l 8, Dimen&longs;ions of a Superficies, </s> <s><emph type="italics"/>ibid.<emph.end type="italics"/> l 15, <emph type="italics"/>for<emph.end type="italics"/> line <emph type="italics"/>r.<emph.end type="italics"/> thread, </s> <s>l <emph type="italics"/>ult.<emph.end type="italics"/><lb/> <emph type="italics"/>for<emph.end type="italics"/> on all &longs;ides, <emph type="italics"/>r.<emph.end type="italics"/> every way. </s> <s>p 6, l 41, by nece&longs;&longs;ary. </s> <s>p 9, l 15, <emph type="italics"/>for<emph.end type="italics"/> Medium, <emph type="italics"/>r.<emph.end type="italics"/> Way. </s> <s>l 40. <emph type="italics"/>for<emph.end type="italics"/> &longs;ome <emph type="italics"/>r.<emph.end type="italics"/> &longs;ave, <emph type="italics"/></s> <s>marg<emph.end type="italics"/> and the. </s> <s>p 10, l 1. farther be <lb/>l 28. intigrall, </s> <s>l 44, prefixed. </s> <s>p 11, 19, oppo&longs;itely might have. </s> <s>l 10, con&longs;tituted Bodie. </s> <s>l 11, &longs;o are. </s> <s>l 15, would only en&longs;ue. </s> <s>p 12, l 28, <lb/>doth, </s> <s>p 14, l 25. inclined plane. </s> <s>l 16. p 34, <emph type="italics"/>for<emph.end type="italics"/> by <emph type="italics"/>r.<emph.end type="italics"/> through. </s> <s>p 17, l 20, beyond T, p 19, l 3, <emph type="italics"/>dele<emph.end type="italics"/> of. </s> <s>l 6, <emph type="italics"/>for<emph.end type="italics"/> of a&longs;&longs;igning, <emph type="italics"/>r.<emph.end type="italics"/> that he <lb/>a&longs;&longs;igned. </s> <s>l 9, <emph type="italics"/>for<emph.end type="italics"/> and with the &c. <emph type="italics"/>r.<emph.end type="italics"/> and given them the intended inclinations of moving thence towards the Centre. </s> <s>l 15, <emph type="italics"/>for<emph.end type="italics"/> Orbes, <lb/><emph type="italics"/>r.<emph.end type="italics"/> Globes, l 38, <emph type="italics"/>for<emph.end type="italics"/> truly <emph type="italics"/>r.<emph.end type="italics"/> exactly. </s> <s>p 21, l 36, <emph type="italics"/>for<emph.end type="italics"/> another, <emph type="italics"/>r.<emph.end type="italics"/> one. </s> <s>p 22, l 19, that <emph type="italics"/>contra,<emph.end type="italics"/></s> <s> l 20. <emph type="italics"/>for<emph.end type="italics"/> than contend with you, <emph type="italics"/>r.<emph.end type="italics"/> than as being. <lb/>convinced by the &longs;trength of your Rea&longs;ons. </s> <s>p 23, 18. <emph type="italics"/>for<emph.end type="italics"/> to di&longs;cover, <emph type="italics"/>r.<emph.end type="italics"/> to be &longs;howne, </s> <s>l 17, &longs;uppo&longs;ing. </s> <s>l 22, <emph type="italics"/>for<emph.end type="italics"/> follow, <emph type="italics"/>r.<emph.end type="italics"/> hit upon. </s> <s>l 52, as <lb/>you well under&longs;tand. </s> <s>p 24, l 17, <emph type="italics"/>for<emph.end type="italics"/> thither <emph type="italics"/>r.<emph.end type="italics"/> there. </s> <s>l 33, <emph type="italics"/>r.<emph.end type="italics"/> Earth a&longs;cend and de&longs;cend. </s> <s>p 25, l 7, <emph type="italics"/>for<emph.end type="italics"/> quality <emph type="italics"/>r.<emph.end type="italics"/> power. </s> <s>l <emph type="italics"/>ult.<emph.end type="italics"/> part. </s> <s>p 26, <lb/>l 9. contraries; But of contraries the motions are contrary, </s> <s>l 32, <emph type="italics"/>for<emph.end type="italics"/> be&longs;ides <emph type="italics"/>r.<emph.end type="italics"/> in ca&longs;e. </s> <s>p 27, l 2, <emph type="italics"/>for<emph.end type="italics"/> repeat, <emph type="italics"/>r.<emph.end type="italics"/> go over. </s> <s>l 3. <emph type="italics"/>for<emph.end type="italics"/> rea&longs;&longs;ume, <emph type="italics"/>r.<emph.end type="italics"/><lb/>repeat. </s> <s> p 29, l <emph type="italics"/>ult. for<emph.end type="italics"/> &longs;ay <emph type="italics"/>r.<emph.end type="italics"/> mean. </s> <s>l 18, re&longs;ide. </s> <s>l 39, <emph type="italics"/>for<emph.end type="italics"/> may. <emph type="italics"/>r.<emph.end type="italics"/> can. </s> <s>p 32, l 1, <emph type="italics"/>for<emph.end type="italics"/> others, <emph type="italics"/>r.<emph.end type="italics"/> one. </s> <s>l 15, <emph type="italics"/>for<emph.end type="italics"/> the be&longs;t we can whether, <emph type="italics"/>r.<emph.end type="italics"/> whats to <lb/>be done with it in ca&longs;e that. </s> <s>l 37, <emph type="italics"/>for<emph.end type="italics"/> they m<emph type="italics"/>u<emph.end type="italics"/>&longs;t grant us, <emph type="italics"/>r.<emph.end type="italics"/> let it be granted, p 32, l 5, what. </s> <s>l 12, unalterable. </s> <s>p 37, l 28, <emph type="italics"/>for<emph.end type="italics"/> confront <emph type="italics"/>r.<emph.end type="italics"/><lb/> preferre. </s> <s>l 37, <emph type="italics"/>for<emph.end type="italics"/> bethink, <emph type="italics"/>r.<emph.end type="italics"/> think, p 41. l 39, <emph type="italics"/>for<emph.end type="italics"/> ob&longs;erve them to be hid, <emph type="italics"/>r.<emph.end type="italics"/> observe that he hath concealed from you tho&longs;e that are <lb/>di&longs;&longs;olved. </s> <s>p 42, l 17. which experience and &longs;en&longs;e. </s> <s>l 17, unalterable. </s> <s>p 43, l 15, <emph type="italics"/>for<emph.end type="italics"/> more <emph type="italics"/>r.<emph.end type="italics"/> le&longs;&longs;e. </s> <s>p 44. l 4, Globes? </s> <s>p 46, l 18, <emph type="italics"/>r.<emph.end type="italics"/> liquifie, <lb/><emph type="italics"/>for<emph.end type="italics"/> them <emph type="italics"/>r.<emph.end type="italics"/> it, p 49. l 11, <emph type="italics"/>for<emph.end type="italics"/> thing <emph type="italics"/>r.<emph.end type="italics"/> thinke. </s> <s>p 50, l 19. <emph type="italics"/>and<emph.end type="italics"/> p 51, l 3, Superficies p 53, l 14, Truths. </s> <s>p 54, l 38, be &longs;olid. </s> <s>p 55, l 15, <lb/>ult. </s> <s>l 36, of the. </s> <s>l 40, <emph type="italics"/>omit<emph.end type="italics"/> &longs;o. </s> <s>p 57, l 44, maketh, p 59, l 1, <emph type="italics"/>for<emph.end type="italics"/> that <emph type="italics"/>r.<emph.end type="italics"/> the. </s> <s>p 61, l 5, tho&longs;e. </s> <s>p 62, l 6, di&longs;per&longs;e. </s> <s>p 64, l 13, evene. </s> <s>l 26, <lb/>change. </s> <s>l 37, <emph type="italics"/>for<emph.end type="italics"/> of, <emph type="italics"/>r.<emph.end type="italics"/> in. </s> <s>l 42, acquie&longs;&longs;e. </s> <s>p 65. l 20, happeneth. </s> <s>p 67, l 13, Solutions, l 15, vi&longs;ive. </s> <s>p 69, l 18, wood?. l 31, wayes,. p 70, l 7, <lb/>conclu&longs;ion is very good for, l 10, &longs;hould we, l 11, would alter. </s> <s>l 12, <emph type="italics"/>for<emph.end type="italics"/> or, <emph type="italics"/>r.<emph.end type="italics"/> and, l 22, Propo&longs;itions, l 29, Protubrances, l 41, <emph type="italics"/>for<emph.end type="italics"/> their, <emph type="italics"/>r.<emph.end type="italics"/> its. </s> <s><lb/>p. 71, l 5, by one <emph type="italics"/>dele<emph.end type="italics"/>;. </s> <s>l 12, of the Moon, l 37, <emph type="italics"/>for<emph.end type="italics"/> in youes, &c. <emph type="italics"/>r.<emph.end type="italics"/> with your Opacity and Per&longs;picuity. </s> <s>p 72, l 20, what time do. <lb/><emph type="italics"/>for<emph.end type="italics"/> p 74. <emph type="italics"/>r.<emph.end type="italics"/> 73. l 26, yea and more. </s> <s>p 76, l 18, <emph type="italics"/>Vitellio.<emph.end type="italics"/> p 81, l 6, <emph type="italics"/>dele<emph.end type="italics"/> more. </s> <s>p 81, l 25, of a fluid matter, l 29, <emph type="italics"/>for<emph.end type="italics"/> &longs;entence <emph type="italics"/>r.<emph.end type="italics"/> Centre. <emph type="italics"/>for<emph.end type="italics"/> on <lb/><emph type="italics"/>r.<emph.end type="italics"/> one.</s> <s> p 85, l 39, <emph type="italics"/>for<emph.end type="italics"/> make rai&longs;ins, <emph type="italics"/>r.<emph.end type="italics"/> make the kernels, p 86, l 29 <emph type="italics"/>inten&longs;ivè,<emph.end type="italics"/> p 87, l 17, the which, neither,. p. </s> <s>88. l. </s> <s>8. <emph type="italics"/>Raffaelio,<emph.end type="italics"/> or <emph type="italics"/>a Tiziano<emph.end type="italics"/>?<lb/></s> <s>p 90. l 20. <emph type="italics"/>for<emph.end type="italics"/> rece&longs;&longs;e <emph type="italics"/>r.<emph.end type="italics"/> remote. </s> <s>p 91. l 11, curio&longs;ity. </s> <s>p 94. l 41. reputation. </s> <s>p 101, l 18, altercations. </s> <s>p 107, l 29, &longs;tar. </s> <s>p 104, l 32, <lb/>naturally. </s> <s>p 107, l 26, <emph type="italics"/>accidens.<emph.end type="italics"/> p 111, l 24, &longs;elfe, l 18, third teime, p. </s> <s>113, l 21, Guns. </s> <s>p 111, l 3, tran&longs;ported, l. </s> <s>7, we pa&longs;&longs;e. </s> <s>p 116, l 15, <lb/>otherwi&longs;e <emph type="italics"/>r.<emph.end type="italics"/> any wayes. </s> <s>p 118, <emph type="italics"/>Marg.<emph.end type="italics"/> rendred, p 128, 35, a&longs;cending?. p 130, l 42, as being the. </s> <s>p 131, l 19, occa&longs;ion, l 30, &longs;eparated. <lb/></s> <s>3, l 11, <emph type="italics"/>pendula.<emph.end type="italics"/> p 134, ll 20, arows? </s> <s>p 135, l 12, time to prove it,. p 137, l 2, <emph type="italics"/>and<emph.end type="italics"/> 6, <emph type="italics"/>for<emph.end type="italics"/> ball, <emph type="italics"/>r.<emph.end type="italics"/> bowl. </s> <s>p 142, l 17, <emph type="italics"/>dele<emph.end type="italics"/> very. </s> <s>p 143, l 3, <lb/>l, l 4, liberty. </s> <s>p 144, l 8, find out. </s> <s>p 145, l 21, <emph type="italics"/>dele<emph.end type="italics"/>;. </s> <s>p 147, l 9, <emph type="italics"/>dele<emph.end type="italics"/> that. </s> <s>p 148, l 7, which &longs;o far exceeds their flight, l 33, is the. </s> <s>l <emph type="italics"/>ult.<emph.end type="italics"/><lb/>moment of. </s> <s>p 149, l 44, <emph type="italics"/>Tycho.<emph.end type="italics"/> p 153, l 21, <emph type="italics"/>for<emph.end type="italics"/> that is <emph type="italics"/>r.<emph.end type="italics"/> or. </s> <s>p 154. 3. <emph type="italics"/>dele<emph.end type="italics"/> of. </s> <s>p 157, l 7, <emph type="italics"/>for<emph.end type="italics"/> to the, <emph type="italics"/>r.<emph.end type="italics"/> by the. </s> <s>p 161, l 15, fifteen &longs;econds: <lb/></s> <s> <emph type="italics"/>Marg<emph.end type="italics"/> in its re&longs;t. </s> <s>p 162, l 13, <emph type="italics"/>for<emph.end type="italics"/> motion <emph type="italics"/>r.<emph.end type="italics"/> Immobility. </s> <s>p. </s> <s>163, l 30, like. </s> <s>p 164, l 22, &longs;eeing. </s> <s>l 31, <emph type="italics"/>for<emph.end type="italics"/> as great as, <emph type="italics"/>r<emph.end type="italics"/> no greater than. </s> <s>166, <lb/>l 24, poope, l 40, Aufractions. </s> <s>p 175, l 26, &longs;peak. </s> <s>p 177, l 13, contra&longs;t. </s> <s>p 184, l 15, <emph type="italics"/>for<emph.end type="italics"/> becau&longs;e it cannot, <emph type="italics"/>r.<emph.end type="italics"/> why may it not?. p 185, l 6, 7, is <lb/><emph type="italics"/>Marg<emph.end type="italics"/> Sphere. </s> <s>p 188. l 19 freind. </s> <s>p 190, l 28. <emph type="italics"/>for<emph.end type="italics"/> give leave, <emph type="italics"/>r.<emph.end type="italics"/> permit. </s> <s>p 191, l 17, <emph type="italics"/>for<emph.end type="italics"/> on, <emph type="italics"/>r.<emph.end type="italics"/> one. </s> <s>l 31. &longs;ee you. </s> <s>p 193, l 21, <emph type="italics"/>Vertigo?<emph.end type="italics"/> <lb/>p 197, l 1, &longs;ubject. </s> <s>p 200, l 36, <emph type="italics"/>dele<emph.end type="italics"/> that, p 201, l 21, pace, l 35, will profe&longs;&longs;e, with. </s> <s>p 203, l 6, <emph type="italics"/>dele<emph.end type="italics"/> &longs;o, l 31, dimini&longs;heth, l 33, degrees. </s> <s>p <lb/>104, l 14, <emph type="italics"/>dele<emph.end type="italics"/> and. </s> <s>p 206, l 19, and 44. <emph type="italics"/>Pendula,<emph.end type="italics"/> </s> <s>p 212, l 14, <emph type="italics"/>dele<emph.end type="italics"/> it. </s> <s>p 216, l <emph type="italics"/>ult. propieres.<emph.end type="italics"/></s> <s> p 219, 10, <emph type="italics"/>for<emph.end type="italics"/> to the&longs;e that, <emph type="italics"/>r.<emph.end type="italics"/> &longs;eeing that to the&longs;e. <lb/></s> <s>p 220, l 12, what. </s> <s>p 221, l 2, than an. </s> <s>l 222, 6, us take. </s> <s>p 224, 37, <emph type="italics"/>for<emph.end type="italics"/> that to <emph type="italics"/>r.<emph.end type="italics"/> that for. </s> <s>225, 25, invented it, </s> <s>227, 9, that the </s> <s>229, l 6, <emph type="italics"/>dele<emph.end type="italics"/><lb/>either. </s> <s>l 18, <emph type="italics"/>dele<emph.end type="italics"/> and wee, </s> <s>l 45, <emph type="italics"/>for<emph.end type="italics"/> From, <emph type="italics"/>r.<emph.end type="italics"/> By. </s> <s>p 230, l 14, in the. </s> <s>p. 232. l 41. augre, </s> <s>p 233, l 22, inarticulate. </s> <s>p 234, l 20, <emph type="italics"/>for<emph.end type="italics"/> were of, <emph type="italics"/>r.<emph.end type="italics"/><lb/>were with. </s> <s>p 233, l 6, the error, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 14, revolve. </s> <s>p 240, l 40, virtue; among&longs;t. </s> <s>l 41, <emph type="italics"/>for Mars, &c. r. Mars.<emph.end type="italics"/> </s> <s>l 44, more &longs;uiting. </s> <s>p 224, l 44, <lb/> <emph type="italics"/>r.<emph.end type="italics"/>contrary. </s> <s>p 245, l 10, interfere. </s> <s>p 250, l 44, <emph type="italics"/>dele<emph.end type="italics"/> being. </s> <s>p 252, l 26, mainteined. </s> <s>p 254, l 7, it was, </s> <s>l 43, uphold. </s> <s>p 258, l 8, &longs;elfe. </s> <s>p 259, l 9, <lb/>being </s> <s>p 260, l 35, calculations. </s> <s>p 61, l 16, interfering. </s> <s>l 15. if not. </s> <s>p 264, l 11, &longs;ame that you do, </s> <s><emph type="italics"/>line<emph.end type="italics"/> 18, rather than. </s> <s>p 266, <emph type="italics"/>l<emph.end type="italics"/> 8, I make. </s> <s>p 267, <lb/><emph type="italics"/>l<emph.end type="italics"/> 24 <emph type="italics"/>Bu&longs;chins.<emph.end type="italics"/></s> <s> p 266, <emph type="italics"/>l 16, r. 40 min. </s> <s>pr.<emph.end type="italics"/> p 272, <emph type="italics"/>l 20, r.<emph.end type="italics"/> B G, is 42657. </s> <s>p 272. <emph type="italics"/>l<emph.end type="italics"/> 29, of the ^{*} 67^{d} 36. </s> <s>p 274, <emph type="italics"/>l<emph.end type="italics"/> 32, every. </s> <s>p 275. <emph type="italics"/>l<emph.end type="italics"/> 25, halfe &longs;o<lb/></s> <s>p 277, <emph type="italics"/>l<emph.end type="italics"/> 18, and 37, <emph type="italics"/>r.<emph.end type="italics"/> B.D. Chord. </s> <s>p 281, <emph type="italics"/>l<emph.end type="italics"/> 30. <emph type="italics"/>r.<emph.end type="italics"/> 540. ­­­­­540 00. </s> <s>p. 285, <emph type="italics"/>l.<emph.end type="italics"/> 8. <emph type="italics"/>r.<emph.end type="italics"/> been the, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 38, &longs;ay of: </s> <s><emph type="italics"/>l<emph.end type="italics"/> 39, <emph type="italics"/>circà.<emph.end type="italics"/> </s> <s>p 286, <emph type="italics"/>l<emph.end type="italics"/> 24, than: BP, PB. <lb/>being bigger than P D. </s> <s>p 287, <emph type="italics"/>l<emph.end type="italics"/> 4, &longs;ee, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 33, 582 ­­­­100000. </s> <s>p 288, <emph type="italics"/>l<emph.end type="italics"/> 21, <emph type="italics"/>r.<emph.end type="italics"/> 276, <expan abbr="q.">que</expan></s> <s>p 289 <emph type="italics"/>l<emph.end type="italics"/> 32, &longs;pake. </s> <s>p, 290, <emph type="italics"/>for<emph.end type="italics"/> p. 274. <emph type="italics"/>r.<emph.end type="italics"/> 290. </s> <s><emph type="italics"/>l<emph.end type="italics"/> 12. they kept. <lb/></s> <s>p 291, <emph type="italics"/>l<emph.end type="italics"/> 8, uncertain, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 37, Braces, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 42, breadth. </s> <s>p 292, <emph type="italics"/>l<emph.end type="italics"/> 6. <emph type="italics"/>dele<emph.end type="italics"/> the other ar. </s> <s>p 244. <emph type="italics"/>l<emph.end type="italics"/> 23, Peripateticks ­­­­­, </s> <s>p 295. <emph type="italics"/>l<emph.end type="italics"/> 1. figure, and morning­<lb/></s> <s>p 297, l 11, oppo&longs;ition, </s> <s><emph type="italics"/>marg r. ve&longs;pertine conjunction.<emph.end type="italics"/> </s> <s>p 298. <emph type="italics"/>l<emph.end type="italics"/> 23, argument and. </s> <s>p 301, <emph type="italics"/>l<emph.end type="italics"/> 1, your, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 30, are yet p. </s> <s>304, <emph type="italics"/>l<emph.end type="italics"/> 9, and allured, </s> <s><emph type="italics"/>marg<lb/> enlarged &longs;oe.<emph.end type="italics"/> p 305, l 27, we leave. </s> <s>p 306, <emph type="italics"/>l<emph.end type="italics"/> 25, it ought. </s> <s>p 307, <emph type="italics"/>for<emph.end type="italics"/> 330, <emph type="italics"/>r.<emph.end type="italics"/> 307. <emph type="italics"/>l<emph.end type="italics"/> 10, digre&longs;&longs;ions, </s> <s><emph type="italics"/>l 16, di&longs;cus. </s> <s>l<emph.end type="italics"/> 32, years, together, with, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 34, <lb/>Jovial, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 41, alwayes all <emph type="italics"/>lucid.<emph.end type="italics"/> </s> <s>p 308, <emph type="italics"/>for<emph.end type="italics"/> 394, <emph type="italics"/>r.<emph.end type="italics"/> 308. </s> <s>p 309, <emph type="italics"/>for<emph.end type="italics"/> 395, <emph type="italics"/>r.<emph.end type="italics"/> 309. </s> <s><emph type="italics"/>l<emph.end type="italics"/> in it. </s> <s><emph type="italics"/>l<emph.end type="italics"/> 34, &longs;ole and &longs;ingle </s> <s>p 310, <emph type="italics"/>l<emph.end type="italics"/> 11, CD. DE. EF. </s> <s>p 312. <emph type="italics"/>l<emph.end type="italics"/> 19, <lb/>shaking off,</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 19, matters that. </s> <s>p 314, <emph type="italics"/>l 8, &<emph.end type="italics"/> 10, Ecliptick. </s> <s>in 316, <emph type="italics"/>l<emph.end type="italics"/> 5, nor, </s> <s><emph type="italics"/>l<emph.end type="italics"/> FG: whereupon </s> <s>p 319, l 7, circuition, <lb/></s> <s><emph type="italics"/>l<emph.end type="italics"/> 31, that he hath. </s> <s>p 220, <emph type="italics"/>l<emph.end type="italics"/> 31, extreme Terminator. </s> <s>p 124. <emph type="italics"/>l<emph.end type="italics"/> 30, Solar Globe,</s> <s> p 322. <emph type="italics"/>l<emph.end type="italics"/> 40. tho&longs;e Phy&longs;ical and. </s> <s>p 324, l 20, &longs;aith that, <emph type="italics"/>l<emph.end type="italics"/> 29 <lb/><emph type="italics"/>Copernicus<emph.end type="italics"/> &longs;aith. </s> <s>p 329, <emph type="italics"/>l<emph.end type="italics"/> 39, this &longs;econd. </s> <s><emph type="italics"/>marg.<emph.end type="italics"/> to be the &longs;ame. </s> <s>p. 332, <emph type="italics"/>l<emph.end type="italics"/> 24, below it. </s> <s>p 333, <emph type="italics"/>l<emph.end type="italics"/> 17, &longs;tar, that. </s> <s>p 335, <emph type="italics"/>l<emph.end type="italics"/> 24, &longs;tar now, <emph type="italics"/>marg. </s> <s>called <lb/>small in.<emph.end type="italics"/> </s> <s>p 338, <emph type="italics"/>l<emph.end type="italics"/> 41, Into this </s> <s><emph type="italics"/>l<emph.end type="italics"/> 24, now, no not for an.</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 28, follow thereupon,</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 31, point equidi&longs;tant. </s> <s>p 341, <emph type="italics"/>l<emph.end type="italics"/> 10, out <lb/>till</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 18, yet the force (which. </s> <s>p 342, <emph type="italics"/>l<emph.end type="italics"/> 25, Orbe; &longs;o, </s> <s>p 343, <emph type="italics"/>l<emph.end type="italics"/> 21, be &longs;een, <emph type="italics"/>l<emph.end type="italics"/> 33, Latitudes and, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 38, ours, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 91, greater varieth. </s> <s>p 344, <emph type="italics"/>l<emph.end type="italics"/> 39, and, <lb/>that. </s> <s>p 345. <emph type="italics"/>l<emph.end type="italics"/> 23. <emph type="italics"/>Cancer<emph.end type="italics"/> and <emph type="italics"/>Capricorn,<emph.end type="italics"/> </s> <s>p 347, <emph type="italics"/>l<emph.end type="italics"/> 1, feinedly, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 30, Stars are. </s> <s>p 349, <emph type="italics"/>l<emph.end type="italics"/> 35, [in Fig. </s> <s>9.]. p 350, <emph type="italics"/>l<emph.end type="italics"/> 42, knew. </s> <s>p 355. <emph type="italics"/>l<emph.end type="italics"/> 12, We&longs;t to <lb/>&longs;t. </s> <s>p 356, <emph type="italics"/>l<emph.end type="italics"/> 15, G N. </s> <s>p 360, <emph type="italics"/>l<emph.end type="italics"/> 38, circle l K. </s> <s>p 382, <emph type="italics"/>l<emph.end type="italics"/> 30, the propen&longs;ion. </s> <s><emph type="italics"/>marg.<emph.end type="italics"/> librated body. </s> <s>p 363, <emph type="italics"/>l<emph.end type="italics"/> 3, Experiment, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 7, ba&longs;on &longs;hall. </s> <s>p 364, <emph type="italics"/>l<emph.end type="italics"/> 2 of <emph type="italics"/>William, </s> <s>l<emph.end type="italics"/> 17, them as, <emph type="italics"/>l<emph.end type="italics"/> 38, that, think. </s> <s>p 366, <emph type="italics"/>l<emph.end type="italics"/> 14, <emph type="italics"/>and<emph.end type="italics"/> 39, &longs;tived. </s> <s>p 367, <emph type="italics"/>l.<emph.end type="italics"/> that this, </s> <s>p 370, <emph type="italics"/>l<emph.end type="italics"/> 3, do that for natural, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 12, appli­<lb/>cation of a per&longs;on to. </s> <s>p 372, <emph type="italics"/>l ult.<emph.end type="italics"/> tho&longs;e. </s> <s>p 373, <emph type="italics"/>l<emph.end type="italics"/> 17, than if, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 39, Launes, Woods, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 43, whither, </s> <s>p 374, <emph type="italics"/>l<emph.end type="italics"/> 16, <emph type="italics"/>dele<emph.end type="italics"/> &longs;elfe. </s> <s>p 375, l 28. &longs;treight <lb/>motion is peculiar, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 39, and an. </s> <s>p 376, <emph type="italics"/>l<emph.end type="italics"/> 5, (For, <emph type="italics"/>l<emph.end type="italics"/> 6, together, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 12, granted ought, </s> <s>p 380, <emph type="italics"/>l<emph.end type="italics"/> 1, <emph type="italics"/>dele<emph.end type="italics"/> hath. </s> <s><emph type="italics"/>l<emph.end type="italics"/> 5, a mutual, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 6, <emph type="italics"/>Indices<emph.end type="italics"/>, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 45, admit. <lb/></s> <s>p 381, <emph type="italics"/>l<emph.end type="italics"/> 36, which with, </s> <s><emph type="italics"/>ibid. dele<emph.end type="italics"/> with. </s> <s>p 382, <emph type="italics"/>l<emph.end type="italics"/> 3, place), </s> <s><emph type="italics"/>l<emph.end type="italics"/> 13, extremities. </s> <s>p 384, <emph type="italics"/>l<emph.end type="italics"/> 3. write of, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 29, SALU. </s> <s>p 385, <emph type="italics"/>l<emph.end type="italics"/> 18, more, in </s> <s><emph type="italics"/>l<emph.end type="italics"/> 13, again&longs;t <lb/>the</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 24, &longs;wagg, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 37, reply, </s> <s>p 386, l 16, as if it. </s> <s>p. 387, <emph type="italics"/>l<emph.end type="italics"/> 33, Water, conteined. </s> <s>p 389, <emph type="italics"/>l<emph.end type="italics"/> 43, at the. </s> <s>p 290 <emph type="italics"/>l<emph.end type="italics"/> 22, that the diurnall litle. </s> <s>p 391, <lb/>11, grow even, it, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 13, <emph type="italics"/>Æquilibrium,<emph.end type="italics"/> but. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 392, <emph type="italics"/>l<emph.end type="italics"/> 35, unitedly, equally. </s> <s>p 394, <emph type="italics"/>l<emph.end type="italics"/> 16, velocity, when. </s> <s>p 396, l 11, <emph type="italics"/>Sardigna<emph.end type="italics"/> </s> <s>p 397, <emph type="italics"/>l<emph.end type="italics"/> 38, returns. <lb/></s> <s>p399, <emph type="italics"/>l<emph.end type="italics"/> 30, is free. </s> <s>p 401, <emph type="italics"/>l<emph.end type="italics"/> 10, pound you, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 13, and argument. </s> <s>p 402, <emph type="italics"/>l<emph.end type="italics"/> 25, alledged that,</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 37, interruptions for. </s> <s>p 405, <emph type="italics"/>l<emph.end type="italics"/> 19, contact, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 37, <lb/>at in a Sea only which, <emph type="italics"/>l penult.<emph.end type="italics"/> ordinate. </s> <s>p 205, <emph type="italics"/>l<emph.end type="italics"/> 38, concern. </s> <s>p 407, <emph type="italics"/>l<emph.end type="italics"/> 3, for &longs;peculation and the, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 8, light, with, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 23, at tho&longs;e, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 28, <lb/>showwings, con&longs;i&longs;teth, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 42, from the, </s> <s><emph type="italics"/>l penult,<emph.end type="italics"/> &longs;ub&longs;tractions that, </s> <s><emph type="italics"/>l ult.<emph.end type="italics"/> maketh to or from. </s> <s>p 48, <emph type="italics"/>l<emph.end type="italics"/> 4, proportion in,</s> <s> <emph type="italics"/>l<emph.end type="italics"/> 14, le&longs;&longs;er, &longs;o as that, </s> <s>p <lb/>409, l 12, &longs;wift, </s> <s>p 411, <emph type="italics"/>l<emph.end type="italics"/> 24 circles </s> <s><emph type="italics"/>marg, pendula,<emph.end type="italics"/> </s> <s>p 412, <emph type="italics"/>l<emph.end type="italics"/> 27, &longs;ubtend,</s> <s> p 413, <emph type="italics"/>l<emph.end type="italics"/> 14, projected, l 24, con&longs;ume, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 93, is, contracted, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 34, of in the <lb/></s> <s>p 441, <emph type="italics"/>l<emph.end type="italics"/> 3, differs, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 5, Moon about, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 21, Orb, by. </s> <s>p 415, <emph type="italics"/>l<emph.end type="italics"/> 4, do either with. </s> <s>p 416, <emph type="italics"/>l<emph.end type="italics"/> 8, ran, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 11, Excentricks, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 13, apparitions, how, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 33, <lb/>cliptick divided, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 44, on account. </s> <s>p 417, <emph type="italics"/>l<emph.end type="italics"/> 43, on which. </s> <s>p 418, <emph type="italics"/>l<emph.end type="italics"/> 4, inequalities. </s> <s>p 419, <emph type="italics"/>l<emph.end type="italics"/> 12, <emph type="italics"/>dele<emph.end type="italics"/> therefore. </s> <s>p 430, <emph type="italics"/>l<emph.end type="italics"/> 33, Anomalies, <lb/><emph type="italics"/>l<emph.end type="italics"/> 45, tracts. </s> <s>p 421,, <emph type="italics"/>l<emph.end type="italics"/> 4, We&longs;tern. </s> <s>p 423, <emph type="italics"/>l<emph.end type="italics"/> 41, <emph type="italics"/>dele<emph.end type="italics"/> in. </s> <s>p 425, <emph type="italics"/>l<emph.end type="italics"/> 16, GALILEO GALILEI</s> <s> p 428, <emph type="italics"/>l<emph.end type="italics"/> 32, the&longs;e. </s> <s>p 430, <emph type="italics"/>l<emph.end type="italics"/> 27, from its. </s> <s>p 431, <emph type="italics"/>marg. <lb/>parum, </s> <s>ibid. marg. de iis.<emph.end type="italics"/> </s> <s>p 432, <emph type="italics"/>l<emph.end type="italics"/> 39, corporeal. </s> <s>p 433, <emph type="italics"/>l<emph.end type="italics"/> 26, <emph type="italics"/>dele<emph.end type="italics"/> in, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 37, appearance and. </s> <s>p 435, <emph type="italics"/>marg. Cœli e&longs;&longs;e, </s> <s>l<emph.end type="italics"/> 27, Spirit of God who <lb/>pake by them. </s> <s>p 430, <emph type="italics"/>l<emph.end type="italics"/> 34, tatling </s> <s>p 440, <emph type="italics"/>l<emph.end type="italics"/> 40, propo&longs;e.</s> <s> <emph type="italics"/>p<emph.end type="italics"/> 443, <emph type="italics"/>l<emph.end type="italics"/> 2, interfere. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 445, <emph type="italics"/>l<emph.end type="italics"/> 34, <emph type="italics"/>dele<emph.end type="italics"/> with. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 448, <emph type="italics"/>l<emph.end type="italics"/> 14, but. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 449, <emph type="italics"/>l<emph.end type="italics"/> 27, make reflection. <lb/></s> <s><emph type="italics"/>p<emph.end type="italics"/> 450, <emph type="italics"/>marg. & Sanctœ, </s> <s>l<emph.end type="italics"/> 42, <emph type="italics"/>&longs;tood &longs;till,. </s> <s>p<emph.end type="italics"/> 451, <emph type="italics"/>l<emph.end type="italics"/> 37, her cur&longs;es. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 453, <emph type="italics"/>marg. l<emph.end type="italics"/> 13, <emph type="italics"/>evoluerit. </s> <s>p<emph.end type="italics"/> 454, <emph type="italics"/>l<emph.end type="italics"/> 29, Lap. Your. </s> <s><emph type="italics"/>marg. l<emph.end type="italics"/> 6, <emph type="italics"/>prœ&longs;umptores, <lb/>&longs;atis, </s> <s>l<emph.end type="italics"/> 14, <emph type="italics"/>auctoritate non tenentur, ad de&longs;cendendum id, quod levi&longs;&longs;ima temeritate, &. </s> <s>p<emph.end type="italics"/> 451, <emph type="italics"/>l<emph.end type="italics"/> 27, or at lea&longs;t the. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 456, l 47, in </s> <s><emph type="italics"/>marg In <lb/>Epist ad Polycarpum. </s> <s>p<emph.end type="italics"/> 463, <emph type="italics"/>l<emph.end type="italics"/> 17, Stabil try. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 454, <emph type="italics"/>l ult.<emph.end type="italics"/> ri&longs;e, </s> <s><emph type="italics"/>p<emph.end type="italics"/> 468, l 25, motion. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 467, <emph type="italics"/>l<emph.end type="italics"/> 26, Sacred, is the Inqui&longs;ition. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 469, <lb/><emph type="italics"/>l<emph.end type="italics"/> 4, Almage&longs;t. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 471, <emph type="italics"/>l<emph.end type="italics"/> 28, <emph type="italics"/>Si quis. </s> <s>p<emph.end type="italics"/> 475, <emph type="italics"/>l<emph.end type="italics"/> 12, <emph type="italics"/>Credit. </s> <s>l<emph.end type="italics"/> 19, Antlents. </s> <s>p 476, <emph type="italics"/>l<emph.end type="italics"/> 9, Deferents, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 33, and in a word. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 477, <emph type="italics"/>l<emph.end type="italics"/> 10, <emph type="italics"/>Nicetas. </s> <s>p<emph.end type="italics"/> 478, <emph type="italics"/>l<emph.end type="italics"/> 1, <lb/>Hypothe&longs;es), </s> <s><emph type="italics"/>l<emph.end type="italics"/> 5, <emph type="italics"/>dece<emph.end type="italics"/> of, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 19, <emph type="italics"/>Galileo Galilei, </s> <s>l<emph.end type="italics"/> 21, Invin&longs;ible, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 23, who. </s> <s>p 481, <emph type="italics"/>l<emph.end type="italics"/> 26, or thats incommen&longs;urate, </s> <s><emph type="italics"/>l<emph.end type="italics"/> 33, vulgar mode of, </s> <s><emph type="italics"/>p<emph.end type="italics"/> 482<lb/><emph type="italics"/>l<emph.end type="italics"/> 7, grieveth. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 485, <emph type="italics"/>l<emph.end type="italics"/> 18, &longs;uch that having, </s> <s><emph type="italics"/>p<emph.end type="italics"/> 487, <emph type="italics"/>l<emph.end type="italics"/> 3, &longs;tay: and. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 488, <emph type="italics"/>l<emph.end type="italics"/> 41, Edification, le&longs;t undecided in Holy Scripture. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 491, <emph type="italics"/>l<emph.end type="italics"/> 15, <lb/>Alterations. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 492, <emph type="italics"/>l<emph.end type="italics"/> 30, keeps, </s> <s><emph type="italics"/>marg Æthereal Earth. </s> <s>p<emph.end type="italics"/> 493, <emph type="italics"/>l<emph.end type="italics"/> 17, that that. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 495, <emph type="italics"/>l<emph.end type="italics"/> 27, frees them. </s> <s><emph type="italics"/>p<emph.end type="italics"/> 500, <emph type="italics"/>marg<emph.end type="italics"/> Authors are not agreed, <lb/> </s> <s><emph type="italics"/>p<emph.end type="italics"/> 582, <emph type="italics"/>l<emph.end type="italics"/> 30, Holy Gho&longs;t hath.</s></p> </chap> <chap> <pb xlink:href="040/01/555.jpg"/><pb xlink:href="040/01/556.jpg"/><p type="head"> <s>MATHEMATICAL <lb/>COLLECTIONS <lb/>AND <lb/>TRANSLATIONS: <lb/>THE SECOND <lb/>TOME.</s></p><p type="head"> <s>THE SECOND PART, <lb/>Containing,</s></p><p type="main"> <s>D. BENEDICTUS CASTELLUS, <emph type="italics"/>his DISCOURSE <lb/>of the MENSURATION of RUN­<lb/>NING WATERS.<emph.end type="italics"/></s></p> </chap> <chap> <p type="main"> <s><emph type="italics"/>His Geometrical DEMONSTRATIONS of <lb/>the Mea&longs;ure of RUNNING WATERS.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>I. </s> <s>His LETTERS and CONSIDERATIONS <lb/>touching the Draining of FENNS, Diver&longs;ions of <lb/>RIVERS, &c.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>V.<emph.end type="italics"/> D. CORSINUS, <emph type="italics"/>His RELATION of the &longs;tate of the <lb/>Inundations, &c. </s> <s>in the Territories of BOLOGNA, <lb/>and FERRARA.<emph.end type="italics"/></s></p><p type="head"> <s>By <emph type="italics"/>THOMAS SALUSBURY, <expan abbr="E&longs;q.">E&longs;que</expan><emph.end type="italics"/></s></p><p type="head"> <s>LONDON, <lb/>Printed by WILLIAM LEYBOURNE, MDCLXI.</s></p> <pb xlink:href="040/01/557.jpg"/><pb xlink:href="040/01/558.jpg"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>RUNNING WATERS.</s></p><p type="head"> <s>An Excellent Piece <lb/><emph type="italics"/>Written in ITALIAN<emph.end type="italics"/><lb/>BY</s></p><p type="head"> <s>DON BENEDETTO CASTELLI, <lb/>Abbot of St. <emph type="italics"/>BENEDETTO ALOYSIO,<emph.end type="italics"/><lb/>and Profe&longs;&longs;our of the Mathematicks to <lb/>Pope <emph type="italics"/>URBAN VIII.<emph.end type="italics"/> in <emph type="italics"/>ROME.<emph.end type="italics"/></s></p><p type="head"> <s>Engli&longs;hed from the Third and be&longs;t Edition, with <lb/>the addition of a Second Book not before extant:</s></p><p type="head"> <s>By <emph type="italics"/>THOMAS SALUSBURY.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, 1661.</s></p><pb xlink:href="040/01/559.jpg"/><pb xlink:href="040/01/560.jpg"/><p type="head"> <s>THE <lb/>AUTHOURS EPISTLE <lb/>TO <lb/>Pope VRBAN VIII.</s></p><p type="main"> <s>I lay at the Feet of your Ho­<lb/>line&longs;&longs;e the&longs;e my Con&longs;ide­<lb/>rations concerning the <lb/>MENSURATION OF <lb/>RUNNING WATERS: <lb/>Wherein if I &longs;hall have &longs;ucceeded, being a <lb/>matter &longs;o difficult and unhandled by Wri­<lb/>ters both Ancient Modern, the di&longs;covery of <lb/>any thing of truth hath been the Effect of <lb/>Your Holine&longs;&longs;es Command; and if through <lb/>inability I have mi&longs;&longs;ed the Mark, the &longs;ame <pb xlink:href="040/01/561.jpg"/>Command will &longs;erve me for an Excu&longs;e with <lb/>Men of better Judgment, and more e&longs;peci­<lb/>ally with Your Holine&longs;&longs;e, to whom I humbly <lb/>pro&longs;trate my &longs;elf, and ki&longs;&longs;e Your Sacred <lb/>Feet.</s></p><p type="main"> <s><emph type="italics"/>From ROME.<emph.end type="italics"/></s></p><p type="main"> <s>Your Holine&longs;&longs;es</s></p><p type="main"> <s><emph type="italics"/>Mo&longs;t humble Servant<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>BENEDETTO.<emph.end type="italics"/></s></p><p type="main"> <s>A Monk of <emph type="italics"/>Ca&longs;&longs;ino.<emph.end type="italics"/></s></p><pb xlink:href="040/01/562.jpg"/><p type="head"> <s>AN <lb/>ACCOUNT <lb/>OF THE <lb/>Authour and Work.</s></p><p type="main"> <s>DON BENEDETTO CASTELLI, <lb/><emph type="italics"/>the famous Authour of the&longs;e en&longs;uing <lb/>Di&longs;cour&longs;es of the<emph.end type="italics"/> Men&longs;uration of <lb/>Running Waters, <emph type="italics"/>is de&longs;cended from <lb/>the Wor&longs;hipful FAMILY of the<emph.end type="italics"/><lb/>GASTELLII, <emph type="italics"/>and took his <lb/>fir&longs;t breath near to the lake THR A­<lb/>SIMENVS, (where<emph.end type="italics"/> Hanibal <emph type="italics"/>gave <lb/>a fatal overthrow to the<emph.end type="italics"/> Roman <lb/><emph type="italics"/>Legions) in that &longs;weet and fertile part <lb/>of happy<emph.end type="italics"/> ITALY, <emph type="italics"/>called the<emph.end type="italics"/> Territory <lb/><emph type="italics"/>of<emph.end type="italics"/> PERUGIA, <emph type="italics"/>a branch of the Dukedome of<emph.end type="italics"/> TUSCANY, <emph type="italics"/>which <lb/>at pre&longs;ent &longs;ubmitteth to the Juri&longs;diction of the Church, as being a <lb/>part of<emph.end type="italics"/> St. </s> <s>PETER'S Patrimony. <emph type="italics"/>His Parents, who were more <lb/>zealous of the good of his Soul than ob&longs;ervant of the Propen&longs;ion of <lb/>his Genius, dedicated him (according to the Devotion of that Coun­<lb/>try) to the Service of the Church; and entered him into the Flou­<lb/>ri&longs;hing Order of Black-Friers, called from the place Moncks <lb/>of<emph.end type="italics"/> Monte Ca&longs;ino, <emph type="italics"/>and from the Founder<emph.end type="italics"/> Benedictines. <emph type="italics"/>Na­<lb/>ture, that She might con&longs;ummate the Profu&longs;ion of her Fa­<lb/>vours upon him, &longs;ent him into the World in an Age that was &longs;o <lb/>ennobled and illuminated with Eminent Scholars in all Kinds of <lb/>Literature, that hardly any Century &longs;ince the Creation can boa&longs;t <lb/>the like.<emph.end type="italics"/></s></p><pb xlink:href="040/01/563.jpg"/><p type="main"> <s>§. <emph type="italics"/>In particular, the<emph.end type="italics"/> SCIENCES MATHEMATI­<lb/>CAL <emph type="italics"/>had then got that Fame and E&longs;teem in the Learned World, <lb/>that all men of Spirit or Quality became either Students in, or <lb/>Patrons of tho&longs;e Sublime Knowledges. </s> <s>On this occa&longs;ion the Curi­<lb/>o&longs;ity of our<emph.end type="italics"/> AUTHOUR <emph type="italics"/>being awakened, his Active Wit <lb/>could not endure to be any longer confined to the Slavi&longs;h Tuition <lb/>of Hermetical Pedagogues; but in concurrence with the Genius <lb/>of the Age, he al&longs;o betook him&longs;elf to tho&longs;e mo&longs;t Generous and <lb/>Liberal Studies. </s> <s>His helps in this his de&longs;ign were &longs;o many, and <lb/>&longs;o extraordinary, that had his Inclination been weaker, or his <lb/>Apprehen&longs;ion le&longs;&longs;er, he could hardly have failed attaining more <lb/>than a Common Eminency in the&longs;e Sciences. </s> <s>For be&longs;ides the De­<lb/>luge of Learned and V&longs;eful Books, which the Pre&longs;&longs;e at that <lb/>time &longs;ent forth from all parts of<emph.end type="italics"/> EUROPE, <emph type="italics"/>he had the good <lb/>Fortune to fall into the Acquaintance, and under the In&longs;truction <lb/>of the mo&longs;t Demon&longs;trative and mo&longs;t Familiar Man in the World, <lb/>the Famous<emph.end type="italics"/> GALILEO<emph type="italics"/>: who&longs;e &longs;ucce&longs;&longs;e being no le&longs;&longs;e upon <lb/>this his<emph.end type="italics"/> Pupil <emph type="italics"/>than upon the re&longs;t of tho&longs;e Illu&longs;trious and Ingeni­<lb/>ous Per&longs;ons that re&longs;orted from all parts to &longs;it under his Admi­<lb/>rable Lectures, he in a &longs;hort time attained to that Name in the <lb/>Mathematicks, that he was invited to<emph.end type="italics"/> ROME, <emph type="italics"/>Complemen­<lb/>ted, and Preferred by his then Holine&longs;&longs;e the Eighth<emph.end type="italics"/> URBAN, <lb/><emph type="italics"/>upon his very fir&longs;t Acce&longs;&longs;ion to the<emph.end type="italics"/> Papacy, <emph type="italics"/>which was in the <lb/>Year<emph.end type="italics"/> 1623.</s></p><p type="main"> <s>§. <emph type="italics"/>This Pope being moved with a Paternal Providence for the <lb/>Concerns of his Subjects in that part of<emph.end type="italics"/> ITALY <emph type="italics"/>about<emph.end type="italics"/> BO­<lb/>LOGNA, FERRARA, <emph type="italics"/>and<emph.end type="italics"/> COMMACHIO, <emph type="italics"/>ly­<lb/>ing between the Rivers of<emph.end type="italics"/> PO <emph type="italics"/>and<emph.end type="italics"/> RENO, <emph type="italics"/>which is part of<emph.end type="italics"/><lb/>Lo Stato della Chie&longs;a, <emph type="italics"/>or the Church Patrimony, appoints this <lb/>our<emph.end type="italics"/> CASTELLI <emph type="italics"/>in the Year 1625, to accompany the Right <lb/>Honourable<emph.end type="italics"/> Mon&longs;ignore GORSINI <emph type="italics"/>(a mo&longs;t ob&longs;ervant and <lb/>intelligent per&longs;on in the&longs;e affaires, and at that time Superinten­<lb/>dent of the General Draines, and Pre&longs;ident of<emph.end type="italics"/> ROMAGNA) <lb/><emph type="italics"/>in the Grand Vi&longs;itation which he was then ordered to make con­<lb/>cerning the di&longs;orders occa&longs;ioned by the Waters of tho&longs;e parts.<emph.end type="italics"/></s></p><p type="main"> <s>§. </s> <s>CASTELLI, <emph type="italics"/>having now an Opportunity to employ, <lb/>yea more, to improve &longs;uch Notions as he had imbued from the <lb/>Lectures of his Excellent<emph.end type="italics"/> MASTER, <emph type="italics"/>falls to his work with <lb/>all indu&longs;try: and in the time that his Occa&longs;ions detained him in<emph.end type="italics"/><lb/>ROMAGNA <emph type="italics"/>he perfected the Fir&longs;t Book of this his Di&longs;­<lb/>cour&longs;e concerning the<emph.end type="italics"/> Men&longs;uration of Running Waters. <emph type="italics"/>He con­<lb/>fe&longs;&longs;eth that he had &longs;ome years before applyed him&longs;elf to this part <lb/>of Practical Geometry, and from &longs;everal Ob&longs;ervations collected <lb/>part of that Doctrine which at this time he put into Method, and <lb/>which had procured him the Repute of &longs;o much Skill that he began<emph.end type="italics"/><pb xlink:href="040/01/564.jpg"/><emph type="italics"/>to be Courted by &longs;undry Princes, and great Prelates. </s> <s>In particu­<lb/>lar about the beginning of the Year 1623. and before his Invita­<lb/>tion to<emph.end type="italics"/> ROME <emph type="italics"/>he was employed by Prince<emph.end type="italics"/> Ferdinando I, <emph type="italics"/>Grand <lb/>Duke of<emph.end type="italics"/> TUSCANY, <emph type="italics"/>to remedy the Di&longs;orders which at that <lb/>time happened in the Valley of<emph.end type="italics"/> PISA <emph type="italics"/>in the Meadows that lye <lb/>upon the Banks of<emph.end type="italics"/> Serchio <emph type="italics"/>and<emph.end type="italics"/> Fiume Morto: <emph type="italics"/>and in the pre­<lb/>&longs;ence of the Grand Duke, Grand Dutche&longs;&longs;e Mother, the Commi&longs;­<lb/>&longs;ioners of Sewers, and &longs;undry other Per&longs;ons in a few hours he <lb/>made &longs;o great a progre&longs;&longs;e in that affair, as gave his Mo&longs;t Serene <lb/>Highne&longs;&longs;e high &longs;atisfaction, and gained him&longs;elf much Honour.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>No &longs;ooner had he in his fore-mentioned Voiage to<emph.end type="italics"/> RO­<lb/>MAGNA <emph type="italics"/>(which was but few Moneths after, in the &longs;ame <lb/>Year) committed his Conceptions to paper, but he communicated <lb/>them to certain of his Friends. </s> <s>In which number we finde<emph.end type="italics"/> Signo­<lb/>re Ciampoli <emph type="italics"/>Secretary of the Popes Private Affaires; whom in <lb/>the beginning of the Fir&longs;t Book he gratefully acknowledgeth to <lb/>have been contributary, in his Pur&longs;e, towards defraying the <lb/>charge of Experiments, and in his Per&longs;on, towards the debating <lb/>and compleating of Arguments upon this Subject. </s> <s>Some few years <lb/>after the Importunity of Friends, and the Zeal he had for the <lb/>Publique Good prevailed with him to pre&longs;ent the World with his <lb/>Fir&longs;t Di&longs;cour&longs;e, accompanied with a Treati&longs;e of the Geometrical <lb/>Demon&longs;trations of his whole Doctrine. </s> <s>What Reception it found <lb/>with the Judicious mu&longs;t needs be imagined by any one that hath <lb/>ob&longs;erved how<emph.end type="italics"/> Novelty <emph type="italics"/>and<emph.end type="italics"/> Facility <emph type="italics"/>in conjunction with<emph.end type="italics"/> Verity <lb/><emph type="italics"/>make a Charm of irre&longs;i&longs;table Operation.<emph.end type="italics"/></s></p><p type="main"> <s>§. </s> <s>New <emph type="italics"/>it was, for that no man before him had ever attemp­<lb/>ted to Demon&longs;trate all the three Dimen&longs;ions, to wit, the Length, <lb/>Breadth and Profundity, of this Fluid and Current Ele­<lb/>ment. </s> <s>And he detecteth &longs;uch gro&longs;&longs;e Errours in tho&longs;e few that <lb/>had untertook to write upon the Subject (of which he in&longs;tan­<lb/>ceth in<emph.end type="italics"/> Frontinus <emph type="italics"/>and<emph.end type="italics"/> Fontana, <emph type="italics"/>as tho&longs;e that include the rest) <lb/>and delivereth &longs;uch &longs;ingular and unheard-of Paradoxes (for &longs;o <lb/>they &longs;ound in Vulgar Eares) as cannot but procure un&longs;peakable <lb/>delight to his Reader.<emph.end type="italics"/></s></p><p type="main"> <s>§. </s> <s>Eafie <emph type="italics"/>it is likewi&longs;e and<emph.end type="italics"/> True; <emph type="italics"/>and that upon &longs;o Familiar <lb/>Experiments and Manife&longs;t Demon&longs;trations, that I have oft que­<lb/>&longs;tioned with my &longs;elf which merited the greater wonder, he, for <lb/>di&longs;covering, or all men that handled the Argument before him <lb/>for not di&longs;covering a Doctrine of &longs;uch &longs;trange Facility and Infal­<lb/>libility. </s> <s>But yet as if our Authour de&longs;igned to oblige the whole <lb/>World to him by &longs;o excellent a<emph.end type="italics"/> Pre&longs;ent, <emph type="italics"/>he &longs;elects a Subject that <lb/>he knew would be carre&longs;&longs;ed by all per&longs;ons of Nobler Souls, upon <lb/>the accounts afore-named, and by all Mankind in General, as <lb/>gratifying them in their much adored Idol<emph.end type="italics"/> Utility. <emph type="italics"/>And to ren-<emph.end type="italics"/><pb xlink:href="040/01/565.jpg"/><emph type="italics"/>der his Art the more profitable, he reduceth the lofty, and ea&longs;ie-to­<lb/>be-mi&longs;taken Speculations of the Theory, into certain and facile <lb/>Directions for Practice; teaching us how to prevent and repaire <lb/>the Breaches of Seas, and Inundations of Rivers; to draine <lb/>and recover Fenns and Marches; to divert, conveigh and di­<lb/>&longs;tribute Waters for the Flowing and Stercoration of Grounds, <lb/>&longs;trengthening of Fortifications, &longs;erving of Aquaducts, pre&longs;er­<lb/>ving of Health (by clean&longs;ing Streets, and &longs;cowring Sewers) and <lb/>maintaining of Commer&longs;e (by defending Bridges, cleering Ri­<lb/>vers, and opening Ports and Channels) with innumerable other <lb/>Benefits of the like nature. </s> <s>And, that I may omit no circum&longs;tance <lb/>that may recommend my Authour, the Fortune of this his Trea­<lb/>ti&longs;e hath been &longs;uch, that as if he intended a<emph.end type="italics"/> Plus ultra <emph type="italics"/>by it, <lb/>or as if all men de&longs;paired to out-do it, or la&longs;tly, as if<emph.end type="italics"/> CA­<lb/>STELLI <emph type="italics"/>hath been &longs;o great a<emph.end type="italics"/> Ma&longs;ter <emph type="italics"/>that none have pre&longs;u­<lb/>med to take Pencil in hand for the fini&longs;hing of what he<emph.end type="italics"/> Pour­<lb/>foild, <emph type="italics"/>this &longs;mall Tract like the Arabian Phœnix (of which it is <lb/>&longs;aid<emph.end type="italics"/> Unica &longs;emper Avis) <emph type="italics"/>did for &longs;everal years together continue <lb/>&longs;ingle in the World, till that to verifie it to be truly<emph.end type="italics"/> Phœnician, <lb/><emph type="italics"/>it renewed its Age by undergoing a &longs;econd Impre&longs;&longs;ion. </s> <s>And as if <lb/>this did not make out the Immortal vertue of it, it hath had<emph.end type="italics"/><lb/>Anno 1660 <emph type="italics"/>a third Circulation, and ri&longs;en in this la&longs;t Edition as <lb/>it were from the Vrne of its Authour; and that &longs;o improved by <lb/>the Addition of a &longs;econd part, that it promi&longs;eth to perpetuate <lb/>his Merits to all Po&longs;terity. </s> <s>To be brief, the meer Fame of this <lb/>Work re&longs;ounded the Honourable Name of<emph.end type="italics"/> CASTELLI <emph type="italics"/>in­<lb/>to all the Corners of<emph.end type="italics"/> Italy, <emph type="italics"/>I may &longs;ay of<emph.end type="italics"/> Europe; <emph type="italics"/>in&longs;omuch, <lb/>that, in hopes to reap great benefit by his Art, the re&longs;pective <lb/>Grandees of the adjacent Countries courted his Judgment and <lb/>Advice about their Draining of Fenns, Diver&longs;ion of Rivers, <lb/>Evacuation of Ports, Preventing of Inundations, &c. </s> <s>So that <lb/>every Summer he made one or more of the&longs;e Journies or Vi&longs;itati­<lb/>ons. </s> <s>Particularly, the Senate of<emph.end type="italics"/> Venice <emph type="italics"/>con&longs;ulted him about their <lb/>Lake; to whom he delivered his Opinion in<emph.end type="italics"/> May 1641. <emph type="italics"/>and up­<lb/>on farther thoughts he pre&longs;ented them with another Paper of Con­<lb/>&longs;iderations the<emph.end type="italics"/> 20 December <emph type="italics"/>following. </s> <s>Prince<emph.end type="italics"/> LEOPOLDO <lb/><emph type="italics"/>of<emph.end type="italics"/> TUSCANY <emph type="italics"/>likewi&longs;e reque&longs;ted his Advice in the begin­<lb/>ning of the en&longs;uing year 1642, which occa&longs;ioned his Letter to <lb/>Father<emph.end type="italics"/> France&longs;co di San Giu&longs;eppe, <emph type="italics"/>bearing date<emph.end type="italics"/> February 1, <lb/><emph type="italics"/>To which<emph.end type="italics"/> Signore Bartolotti <emph type="italics"/>oppo&longs;ing, he writes a &longs;econd Let­<lb/>ter, directed to one of the Commi&longs;&longs;ioners of Sewers, vindicating <lb/>his former, and refuting<emph.end type="italics"/> Bartolotti, <emph type="italics"/>both which I here give <lb/>you.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>The Preferments which his Merits recommended him unto, <lb/>were fir&longs;t to be Abbot of<emph.end type="italics"/> Ca&longs;&longs;ino, <emph type="italics"/>from which he was removed<emph.end type="italics"/><pb xlink:href="040/01/566.jpg"/>Anno 1640, <emph type="italics"/>or thereabouts, unto the Abbey of<emph.end type="italics"/> Santo Benedet­<lb/>to Aloy&longs;io; <emph type="italics"/>and much about the &longs;ame time preferred to the Dig­<lb/>nity of Chief Mathematician to his grand Patron Pope<emph.end type="italics"/> URBAN <lb/>VIII. <emph type="italics"/>and Publique Profe&longs;&longs;our of Mathematicks in the Vni­<lb/>ver&longs;ity of<emph.end type="italics"/> ROME.</s></p><p type="main"> <s>§. <emph type="italics"/>Here a Stop was put to the Carier of his Fortunes, and be­<lb/>ing fuller of Honour than of Years, was by Death, the Importu­<lb/>nate Intrerupter of Generous De&longs;igns, prevented in doing that <lb/>farther Good which the World had good rea&longs;on to promi&longs;e it &longs;elf <lb/>from &longs;o Profound and Indu&longs;trious a Per&longs;onage, leaving many <lb/>Friends and Di&longs;ciples of all Degrees and Qualities to lament <lb/>his lo&longs;&longs;e, and honour his Memory.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>His &longs;ingular Virtues and Abilities had gained him the <lb/>Friend&longs;hip of very many; as to in&longs;tance in &longs;ome, he had con­<lb/>racted &longs;trict Amity with<emph.end type="italics"/> Mon&longs;ignore Maffei Barberino <emph type="italics"/>a Floren­<lb/>tine, Præfect of the Publique Wayes, and afterwards Pope with <lb/>the Name of<emph.end type="italics"/> URBAN VIII. <emph type="italics"/>as was &longs;aid before; with the <lb/>above-named<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini <emph type="italics"/>Superintendant of the General <lb/>Draines: with<emph.end type="italics"/> Mon&longs;ignore Piccolomini <emph type="italics"/>Arch-Bi&longs;hop of<emph.end type="italics"/> Siena<emph type="italics"/>: <lb/>with Cardinal<emph.end type="italics"/> Serra: <emph type="italics"/>with Cardinal<emph.end type="italics"/> Caponi, <emph type="italics"/>who hath &longs;tudied <lb/>much and writ well upon this Subject; and with Cardinal<emph.end type="italics"/> Gae­<lb/>tano <emph type="italics"/>who frequently con&longs;ulted with him in his de&longs;ign of Drain­<lb/>ing the Fenns of<emph.end type="italics"/> ROMAGNA. <emph type="italics"/>Moreover Prince<emph.end type="italics"/> LEO­<lb/>POLDO, <emph type="italics"/>and his Brother the Grand Duke had very great <lb/>kindne&longs;&longs;e for him; which &longs;peaks no &longs;mall attractions in him, <lb/>con&longs;idering him as a favourite of the Family of<emph.end type="italics"/> Barberini, <emph type="italics"/>be­<lb/>tween whom and the Hou&longs;e of<emph.end type="italics"/> Medeci <emph type="italics"/>there is an inveterate <lb/>Fewd. </s> <s>Among&longs;t per&longs;ons of a lower Quality he acknowledgeth<emph.end type="italics"/><lb/>Signore Ciampoli <emph type="italics"/>the Popes Secretary,<emph.end type="italics"/> Sig. </s> <s>Ferrante Ce&longs;arini, <lb/>Sig. </s> <s>Giovanni Ba&longs;adonna <emph type="italics"/>Senator of<emph.end type="italics"/> Venice; <emph type="italics"/>and I find menti­<lb/>oned<emph.end type="italics"/> Sig. </s> <s>Lana, Sig. </s> <s>Albano, Padre Serafino, Pad. </s> <s>France&longs;co <lb/>de San. </s> <s>Giu&longs;eppe, <emph type="italics"/>and many others.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>The Works in which he will &longs;urvive to all &longs;ucceeding Ages <lb/>are fir&longs;t His &longs;olid and &longs;ober Confutation of the Arguments of<emph.end type="italics"/><lb/>Signore Lodovico dell Columbo, <emph type="italics"/>and<emph.end type="italics"/> Signore Vincentio di <lb/>Gratia <emph type="italics"/>again&longs;t the Tract of<emph.end type="italics"/> Galileo Delle co&longs;e che &longs;tanno &longs;opra <lb/>Aqua, <emph type="italics"/>wherein he vindicates bis &longs;aid<emph.end type="italics"/> Ma&longs;ter <emph type="italics"/>with a Gratitude <lb/>that Tutors very rarely reap from the pains they take in Culti­<lb/>vating their Pupils. </s> <s>This Apology was fir&longs;t Printed<emph.end type="italics"/> Anno 1615. <lb/><emph type="italics"/>and was a &longs;econd time publi&longs;hed, as al&longs;o tho&longs;e of his Antago­<lb/>ni&longs;ts, among&longs;t the Works of<emph.end type="italics"/> GALILEO, <emph type="italics"/>&longs;et forth by the <lb/>Learned<emph.end type="italics"/> Viviani 1656. <emph type="italics"/>He hath likewi&longs;e writ &longs;everal other <lb/>curious Pieces, as I am informed by the mo&longs;t Courteous<emph.end type="italics"/> Carolo <lb/>Manole&longs;&longs;i <emph type="italics"/>of<emph.end type="italics"/> Bologna; <emph type="italics"/>among&longs;t others an excellent Treati&longs;e <lb/>concerning<emph.end type="italics"/> Colours, <emph type="italics"/>which he putteth me in hopes to &longs;ee printed<emph.end type="italics"/><pb xlink:href="040/01/567.jpg"/><emph type="italics"/>very &longs;peedily. </s> <s>And la&longs;t of all the&longs;e Di&longs;cour&longs;es and Reflections <lb/>upon the<emph.end type="italics"/> Men&longs;uration of Running Waters, <emph type="italics"/>with the addition of <lb/>a Second Book, three Epi&longs;tles, and four Con&longs;iderations upon <lb/>the &longs;ame Argument, which conduce much to Illu&longs;trate his Do­<lb/>ctrine and Facilitate the Practice of it; and which with a Rela­<lb/>tion of<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini, <emph type="italics"/>make the &longs;econd part of my Fir&longs;t <lb/>Tome.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>I might here &longs;ally forth into the Citation of &longs;undry Au­<lb/>thours of Good Account, that have tran&longs;mitted his Character <lb/>to Po&longs;terity, but &longs;hall confine my &longs;elf to onely two; the one is <lb/>of his<emph.end type="italics"/> Ma&longs;ter, <emph type="italics"/>the other of his<emph.end type="italics"/> Scholar; <emph type="italics"/>than whom there can­<lb/>not be two more competent Judges of his Accompli&longs;hments. </s> <s>To <lb/>begin with his<emph.end type="italics"/> Ma&longs;ter, <emph type="italics"/>the Quick-&longs;ighted, and truly Lyncean<emph.end type="italics"/><lb/>GALILEO, <emph type="italics"/>who &longs;peaking of his Abilities in A&longs;tronomy &longs;aith<emph.end type="italics"/><lb/><arrow.to.target n="marg961"></arrow.to.target><lb/><emph type="italics"/>(a)<emph.end type="italics"/> Che la felicità del &longs;uo ingegno non la fà bi&longs;ogno&longs;a dell' o­<lb/>pera &longs;uo. <emph type="italics"/>And again, &longs;ubmitting a certain Demon&longs;tration, <lb/>which he intended to divulge, to the Judgment of this our Abbot, he<emph.end type="italics"/><lb/><arrow.to.target n="marg962"></arrow.to.target><lb/><emph type="italics"/>writes to him in this manner: (b)<emph.end type="italics"/> Que&longs;to lo comunico a V. S. <lb/>per lettera prima che ad alcun altro, con attenderne principal­<lb/>mente il parer &longs;uo, e doppo quello de' no&longs;tri Amici di&longs;co&longs;ti, <lb/>conpen&longs;iero d' inviarne poi altre Copie ad altri Amici d' Italia, <lb/>e di Francia, quando io ne venga da lei con&longs;igliato: e qui pre­<lb/>gandola a farci parte d' alcuna delle &longs;ue peregrine &longs;peculationi; <lb/>con &longs;inceri&longs;&longs;imo affetto, &c. <emph type="italics"/>And the mo&longs;t acute Mathematician<emph.end type="italics"/><lb/>Signore Evangeli&longs;ta Terricelli, <emph type="italics"/>late Profe&longs;&longs;our to the Grand <lb/>Duke in immediate Succe&longs;&longs;ion after<emph.end type="italics"/> GALILEO, <emph type="italics"/>maketh this<emph.end type="italics"/><lb/><arrow.to.target n="marg963"></arrow.to.target><lb/><emph type="italics"/>Honourable and Grateful Mention of him, and his Book: (c)<emph.end type="italics"/> O­<lb/>mitto magnum illum nutantis Maris motum; Prætereo etiam <lb/>omnem Fluminum, Aquarumque Currentium tum men&longs;urum, <lb/>tum u&longs;um, quarum omnis doctrina reperta primum fuit ab <lb/>Abbate BENEDICTO CASTELLIO Preceptore <lb/>meo. </s> <s>Scrip&longs;it ille Scientiam &longs;uam, & illam non &longs;olum demon&longs;tra­<lb/>tione, verum etiam opere confirmavit, maxima cum Princi­<lb/>pum & populorum utilitatate, majore cum admiratione Phylo­<lb/>&longs;ophorum. </s> <s>Extat illius Liber, vere aureus.</s></p><p type="margin"> <s><margin.target id="marg961"></margin.target><emph type="italics"/>(a)<emph.end type="italics"/>Nella continu­<lb/>atione dell Nun­<lb/>tio &longs;iderio.</s></p><p type="margin"> <s><margin.target id="marg962"></margin.target><emph type="italics"/>(b)<emph.end type="italics"/> Lettera al P. <lb/></s> <s>Abbate D. B. </s> <s>Ca­<lb/>&longs;telli D'Arcetro; <lb/>li. </s> <s>3. Decemb. <lb/></s> <s>1639.</s></p><p type="margin"> <s><margin.target id="marg963"></margin.target><emph type="italics"/>(c)<emph.end type="italics"/> De Motu A­<lb/>quarum. </s> <s>Lib. 2. <lb/>Prop. </s> <s>37. p. </s> <s>191.</s></p><p type="main"> <s>§. <emph type="italics"/>I have onely two particulars more to offer the Engli&longs;h Rea­<lb/>der: The one concerns the Book, and it is this, That after the <lb/>general Aprobation it hath had in<emph.end type="italics"/> Italy, <emph type="italics"/>I cannot but think it <lb/>de&longs;erveth the &longs;ame Civil Entertainment with us, in regard that <lb/>it cometh with no le&longs;&longs;e<emph.end type="italics"/> Novelty, Facility, Verity, and Utility <emph type="italics"/>to <lb/>us than to tho&longs;e whom the Authour favoured with the Original. <lb/></s> <s>Our Rivers and Sewers through Publique Di&longs;tractions and Pri­<lb/>vate Incroachments are in great di&longs;order, as tho&longs;e Channels for <lb/>iu&longs;tance which formerly were Navigable unto the very Walls of<emph.end type="italics"/><pb xlink:href="040/01/568.jpg"/>York <emph type="italics"/>and<emph.end type="italics"/> Salisbury, <emph type="italics"/>&c: Our Ports are choaked and ob&longs;tructed <lb/>by Shelfes and Setlements: Our Fenns do in a great part lie wa&longs;te <lb/>and unimproved: Now all the&longs;e may be (and, as I find by the <lb/>Confe&longs;&longs;ion of &longs;ome who&longs;e Practi&longs;es upon the Copy of the Fir&longs;t <lb/>Book onely of our Authour hath got them both Money and Repu­<lb/>tation, in part have been) remedied by the Ways and Means he <lb/>here &longs;ets down. </s> <s>The truth is the Argument hath been pa&longs;t over <lb/>with an Vniver&longs;al Silence; &longs;o that to this day I have not &longs;een <lb/>any thing that hath been written Demon&longs;tratively and with Ma­<lb/>thematical Certainty concerning the &longs;ame, &longs;ave onely what this <lb/>Learned Prelate hath delivered of his Own Invention in the&longs;e <lb/>Treati&longs;es: who yet hath &longs;o fully and plainly handled the Whole <lb/>Doctrine, that I may affirm his Work to be every way ab&longs;olute. </s> <s>It <lb/>mu&longs;t be confe&longs;t the Demon&longs;tration of the Second Propo&longs;ition of the <lb/>Second Book did not well plea&longs;e the Authour, and had he lived <lb/>he would have &longs;upplyed that defect, but being prevented by <lb/>Death, the Reader mu&longs;t content him&longs;elf with the Mechanical <lb/>Proof that he giveth you of the truth of &longs;o Excellent a Con­<lb/>clu&longs;ion.<emph.end type="italics"/></s></p><p type="main"> <s>§. <emph type="italics"/>The other particular that I am to offer is, that out of my de­<lb/>&longs;ire to contribute what lyeth in me to the compleating of this Piece <lb/>for Engli&longs;h Practice, I have exeeded my promi&longs;e not onely in gi­<lb/>ving you the Second and following Books which were not extant at <lb/>the time of tendring my Overtures, but al&longs;o in that I have added <lb/>a Map or Plat of all the Rivers, Lakes, Fenns, &c. </s> <s>mentioned <lb/>thorow out the Work. </s> <s>And if I have not kept touch in point of <lb/>Time, let it be con&longs;idered that I am the Tran&longs;lator and not the <lb/>Printer. </s> <s>To conclude, according to your acceptance of the&longs;e my <lb/>endeavours, you may expect &longs;ome other Tracts of no le&longs;&longs;e Profit <lb/>and Delight.<emph.end type="italics"/> Farewell.</s></p><p type="head"> <s><emph type="italics"/>T. S.<emph.end type="italics"/></s></p><pb xlink:href="040/01/569.jpg"/><p type="head"> <s>ERRATA of the <emph type="italics"/>&longs;econd<emph.end type="italics"/> PART of the <emph type="italics"/>fir&longs;t<emph.end type="italics"/> TOME.</s></p><p type="main"> <s>In PREFACE, I cad <emph type="italics"/>Ferdinando II.<emph.end type="italics"/> ibid. <emph type="italics"/>l' Aqua.<emph.end type="italics"/></s></p><p type="main"> <s>PAGE 2. LINE 26, <emph type="italics"/>for<emph.end type="italics"/> mu&longs;t <emph type="italics"/>read<emph.end type="italics"/> much. </s> <s>P. 3. l. </s> <s>22, <emph type="italics"/>r.<emph.end type="italics"/> and let. </s> <s>l. </s> <s>25. <emph type="italics"/>r.<emph.end type="italics"/> water, from l. </s> <s>41. <lb/><emph type="italics"/>r.<emph.end type="italics"/> Tappe, (<emph type="italics"/>as every where el&longs;e).<emph.end type="italics"/> Page 4. l. </s> <s>18. <emph type="italics"/>r<emph.end type="italics"/> cords. </s> <s>Page 6. l. </s> <s>9. <emph type="italics"/>r.<emph.end type="italics"/> acquire, or. <lb/></s> <s>Page 9. l. </s> <s>1. <emph type="italics"/>r.<emph.end type="italics"/> irreperable. </s> <s>P. 10. l. </s> <s>13. <emph type="italics"/>r.<emph.end type="italics"/> di&longs;&longs;imboguement. <emph type="italics"/>For<emph.end type="italics"/> Page 17. <emph type="italics"/>r.<emph.end type="italics"/> P. 15. <lb/>P. 15. l. </s> <s>27, <emph type="italics"/>r.<emph.end type="italics"/> in. </s> <s>l. </s> <s>36, <emph type="italics"/>r.<emph.end type="italics"/> is as. </s> <s>l. </s> <s>38, <emph type="italics"/>r. </s> <s>Panaro.<emph.end type="italics"/> P. 17. l. </s> <s>12, <emph type="italics"/>Giulio.<emph.end type="italics"/> l. </s> <s>17. <emph type="italics"/>r.<emph.end type="italics"/> Mea&longs;urers. </s> <s>l. <lb/></s> <s>25, <emph type="italics"/>r.<emph.end type="italics"/> mea&longs;ured it,. <emph type="italics"/>r.<emph.end type="italics"/> nece&longs;&longs;arily. </s> <s>P. 23. l. </s> <s>19. <emph type="italics"/>r.<emph.end type="italics"/> for help. <emph type="italics"/>for<emph.end type="italics"/> Page 31. <emph type="italics"/>r.<emph.end type="italics"/> P. 32. P. 24. <lb/>l. </s> <s>14, <emph type="italics"/>r.<emph.end type="italics"/> to. </s> <s>l. </s> <s>17, <emph type="italics"/>r.<emph.end type="italics"/> namly, of the. </s> <s>l. </s> <s>23, <emph type="italics"/>r.<emph.end type="italics"/> ea&longs;ie. </s> <s>P. 25. l. </s> <s>38. <emph type="italics"/>r.<emph.end type="italics"/> Cock. </s> <s>p. </s> <s>29. l. </s> <s>7. <emph type="italics"/>r.<emph.end type="italics"/> la&longs;ted,. <lb/>p. </s> <s>31. l. </s> <s>32. <emph type="italics"/>r.<emph.end type="italics"/> Soe. </s> <s>p. </s> <s>41. l. </s> <s>20. <emph type="italics"/>r.<emph.end type="italics"/> to the line. </s> <s>p. </s> <s>48. l. </s> <s>19. <emph type="italics"/>r.<emph.end type="italics"/> us the ^{*}. id. <emph type="italics"/>Figure fal&longs;e<emph.end type="italics"/> p. </s> <s>52. <lb/>l. </s> <s>30, and 31. <emph type="italics"/>for<emph.end type="italics"/> Theorem <emph type="italics"/>r.<emph.end type="italics"/> Propo&longs;ition. </s> <s>p. </s> <s>53. l. </s> <s>29. <emph type="italics"/>r.<emph.end type="italics"/> again. </s> <s>p. </s> <s>57. l. </s> <s>19, <emph type="italics"/>r.<emph.end type="italics"/> &longs;ame if. <lb/></s> <s>l. </s> <s>44. <emph type="italics"/>r.<emph.end type="italics"/> bodily. </s> <s>p. </s> <s>58. l. </s> <s>9, <emph type="italics"/>r.<emph.end type="italics"/> gathering. </s> <s>l. </s> <s>40. <emph type="italics"/>omit<emph.end type="italics"/>;. </s> <s>p. </s> <s>60. l. </s> <s>2. <emph type="italics"/>omit,<emph.end type="italics"/> if. </s> <s>p. </s> <s>65. l. </s> <s>1. <emph type="italics"/>r.<emph.end type="italics"/> tide <lb/><emph type="italics"/>dele<emph.end type="italics"/>;. </s> <s>p. </s> <s>66. l. </s> <s>35. <emph type="italics"/>r.<emph.end type="italics"/> Stoppage of. </s> <s>p. </s> <s>68. l. </s> <s>12, <emph type="italics"/>for<emph.end type="italics"/> Lords the <emph type="italics"/>r.<emph.end type="italics"/> Lords. </s> <s>l. <emph type="italics"/>ult. </s> <s>for<emph.end type="italics"/> they <lb/><emph type="italics"/>r.<emph.end type="italics"/> it. </s> <s>p. </s> <s>69. l. </s> <s>14. <emph type="italics"/>r.<emph.end type="italics"/> to one. <emph type="italics"/>id.<emph.end type="italics"/> carried <emph type="italics"/>dele<emph.end type="italics"/> to. </s> <s>p. </s> <s>71. l. </s> <s>20, <emph type="italics"/>r.<emph.end type="italics"/> and that. </s> <s>l. </s> <s>25, <emph type="italics"/>r.<emph.end type="italics"/> Braces; it. </s> <s>l. <lb/></s> <s>29. <emph type="italics"/>r.<emph.end type="italics"/> Braces. </s> <s>l. </s> <s>44, <emph type="italics"/>r.<emph.end type="italics"/> the <emph type="italics"/>Brent.<emph.end type="italics"/> p. </s> <s>72. l. </s> <s>23. <emph type="italics"/>r. </s> <s>Serene Highne&longs;&longs;e.<emph.end type="italics"/> p. </s> <s>73. l. </s> <s>24, <emph type="italics"/>r.<emph.end type="italics"/> deliberation:. <lb/>l. </s> <s>26, <emph type="italics"/>for<emph.end type="italics"/> &longs;umme <emph type="italics"/>r.<emph.end type="italics"/> Moddel. </s> <s>l. </s> <s>40. <emph type="italics"/>r.<emph.end type="italics"/> Months. </s> <s>p. </s> <s>79. l. </s> <s>18. <emph type="italics"/>r.<emph.end type="italics"/> that into. </s> <s>p. </s> <s>82. l. </s> <s>22. <emph type="italics"/>dele<emph.end type="italics"/>;. </s> <s>p. <lb/></s> <s>85. l. </s> <s>9, 10. <emph type="italics"/>dele<emph.end type="italics"/> a free drame. </s> <s>p. </s> <s>88. l. </s> <s>5. <emph type="italics"/>r.<emph.end type="italics"/> Palmes. </s> <s>p. </s> <s>89. l. </s> <s>8. <emph type="italics"/>r.<emph.end type="italics"/> Princes. </s> <s>p. </s> <s>92. l. </s> <s>3. <emph type="italics"/>r.<emph.end type="italics"/> Di&longs;­<lb/>cour&longs;es. </s> <s>p. </s> <s>93. l. </s> <s>31. <emph type="italics"/>r.<emph.end type="italics"/> Tautologie. </s> <s>p. </s> <s>94. l. </s> <s>9. <emph type="italics"/>r.<emph.end type="italics"/> miracle;. </s> <s>p. </s> <s>97. l. </s> <s>13. <emph type="italics"/>r,<emph.end type="italics"/> weighty. </s> <s>p. </s> <s>101. <lb/>l. </s> <s>21. <emph type="italics"/>r.<emph.end type="italics"/> Marrara. </s> <s>p. </s> <s>107. l. </s> <s>28, <emph type="italics"/>r.<emph.end type="italics"/> Patrimony. </s> <s>l. </s> <s>40, <emph type="italics"/>r.<emph.end type="italics"/> above. </s> <s>p. </s> <s>111. l. </s> <s>16. <emph type="italics"/>r.<emph.end type="italics"/> &longs;aid. <emph type="italics"/>For<emph.end type="italics"/> p. </s> <s>432. <lb/><emph type="italics"/>r.<emph.end type="italics"/> p. </s> <s>114. p. </s> <s>114. l. </s> <s>35. <emph type="italics"/>r.<emph.end type="italics"/> of 200, l. </s> <s>41. <emph type="italics"/>r.<emph.end type="italics"/> clo&longs;ed. </s> <s>p. </s> <s>115. l. </s> <s>29. <emph type="italics"/>r.<emph.end type="italics"/> con&longs;tant;.</s></p><pb xlink:href="040/01/570.jpg" pagenum="1"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s><emph type="italics"/>LIB.<emph.end type="italics"/> I.</s></p><p type="main"> <s>What, and of how great moment the confi­<lb/>deration of <emph type="italics"/>Motion<emph.end type="italics"/> is in natural things, <lb/>is &longs;o manife&longs;t, that the Prince of <emph type="italics"/>Peri­<lb/>pateticks<emph.end type="italics"/> pronounced that in his Schools <lb/>now much u&longs;ed Sentence: <emph type="italics"/>Ignorato mo­<lb/>tu, ignoratur natura.<emph.end type="italics"/> Thence it is that <lb/>true Philo&longs;ophers have &longs;o travailed in the <lb/>contemplation of the Cele&longs;tial motions, <lb/>and in the &longs;peculation of the motions of <lb/>Animals, that they have arrived to a wonderful height and &longs;ub­<lb/>limity of under&longs;tanding. </s> <s>Under the &longs;ame Science of <emph type="italics"/>Motion<emph.end type="italics"/><lb/>is comprehended all that which is written by Mechanitians con­<lb/>cerning Engines moving of them&longs;elves, <emph type="italics"/>Machins<emph.end type="italics"/> moving by the <lb/>force of Air, and tho&longs;e which &longs;erve to move weights and im­<lb/>men&longs;e magnitudes with &longs;mall force. </s> <s>There appertaineth to the <lb/>Science of <emph type="italics"/>Motion<emph.end type="italics"/> all that which hath been written of the <lb/>alteration not onely of Bodies, but of our Minds al&longs;o; and <lb/>in &longs;um, this ample matter of <emph type="italics"/>Motion<emph.end type="italics"/> is &longs;o extended and di­<lb/>lated, that there are few things which fall under mans no­<lb/>tice, which are not conjoyned with <emph type="italics"/>Motion,<emph.end type="italics"/> or at lea&longs;t de­<lb/>pending thereupon, or to the knowledge thereof directed; <lb/>and of almo&longs;t every of them, there hath been written and <lb/>compo&longs;ed by &longs;ublime wits, learned Treati&longs;es and In&longs;tructions. <pb xlink:href="040/01/571.jpg" pagenum="2"/>And becau&longs;e that in the years pa&longs;t I had occa&longs;ion by Order of <lb/>our Lord Pope <emph type="italics"/>Vrban<emph.end type="italics"/> 8. to apply my thoughts to the motion of <lb/>the Waters of Rivers, (a matter difficult, mo&longs;t important, and <lb/>little handled by others) having concerning the &longs;ame ob&longs;erved <lb/>&longs;ome particulars not well ob&longs;erved, or con&longs;idered till now, but of <lb/>great moment both in publick and private affairs; I have thought <lb/>good to publi&longs;h them, to the end that ingenious &longs;pirits might <lb/>have occa&longs;ion to di&longs;cu&longs;&longs;e more exactly then hitherto hath been <lb/>done, &longs;o nece&longs;&longs;ary and profitable a matter, and to &longs;upply al&longs;o my <lb/>defects in this &longs;hort and difficult Tractate. </s> <s>Difficult I &longs;ay, for <lb/>the truth is, the&longs;e knowledges, though of things next our &longs;en&longs;es, <lb/>are &longs;ometimes more ab&longs;truce and hidden, then the knowledge of <lb/>things more remote; and much better, and with greater exqui&longs;it­<lb/>ne&longs;s are known the motions of the Planets, and Periods of the <lb/>Stars, than tho&longs;e of Rivers and Seas: As that &longs;ingular light of <lb/>Philo&longs;ophie of our times, and my Ma&longs;ter <emph type="italics"/>Signore Galileo Galilei<emph.end type="italics"/><lb/>wi&longs;ely ob&longs;erveth in his Book concerning the Solar &longs;pots. </s> <s>And <lb/>to proceed with a due order in Sciences, I will take &longs;ome &longs;uppo­<lb/>&longs;itions and cognitions &longs;ufficiently clear; from which I will after­<lb/>wards proceed to the deducing of the principal conclu&longs;ions. </s> <s>But <lb/>to the end that what I have written at the end of this di&longs;cour&longs;e in <lb/>a demon&longs;trative and Geometrical method, may al&longs;o be under­<lb/>&longs;tood of tho&longs;e which never have applyed their thoughts to the <lb/>&longs;tudy of Geometry; I have endeavoured to explain my conceit <lb/>by an example, and with the con&longs;ideration of the natural things <lb/>them&longs;elves, mu&longs;t after the &longs;ame order in which I began to doubt <lb/>in this matter; and have placed this particular Treati&longs;e here in <lb/>the beginning, adverting neverthele&longs;s, that he who de&longs;ires more <lb/>full and ab&longs;olute &longs;olidity of Rea&longs;ons, may overpa&longs;s this prefatory <lb/>di&longs;cour&longs;e, and onely con&longs;ider what is treated of in the demon&longs;tra­<lb/>tions placed towards the end, and return afterwards to the con&longs;i­<lb/>deration of the things collected in the <emph type="italics"/>Corollaries<emph.end type="italics"/> and Appendices; <lb/>which demon&longs;trations notwith&longs;tanding, may be pretermitted by <lb/>him that hath not &longs;een at lea&longs;t the fir&longs;t &longs;ix Books of the Elements <lb/>of Euclid; &longs;o that he diligently ob&longs;erveth that which fol­<lb/>loweth.</s></p><p type="main"> <s>I &longs;ay therefore, that having in times pa&longs;t, on divers occa&longs;i­<lb/>ons heard &longs;peak of the mea&longs;ures of the waters of Rivers, and <lb/>Fountains, &longs;aying, &longs;uch a River is two or three thou&longs;and feet of <lb/>water; &longs;uch a &longs;pring-water is twenty, thirty, or forty inches, <emph type="italics"/>&c.<emph.end type="italics"/><lb/>Although in &longs;uch manner I have found all to treat thereof in <lb/>word and writing, without variety, and as we are wont to &longs;ay, <lb/><emph type="italics"/>con&longs;tanti &longs;ermone,<emph.end type="italics"/> yea even Arti&longs;ts and Ingeneers, as if it were <lb/>a thing that admitted not of any doubt, yet how&longs;oever I re­<lb/>mained &longs;till infolded in &longs;uch an ob&longs;curity, that I well knew I un­<pb xlink:href="040/01/572.jpg" pagenum="3"/>der&longs;tood nothing at all, of that which others pretended full and <lb/>clearly to under&longs;tand. </s> <s>And my doubt aro&longs;e from my frequent <lb/>ob&longs;ervation of many Trenches and Channels, which carry <lb/>water to turn Mills, in which Trenches, and Channels, the <lb/>water being mea&longs;ured, was found pretty deep; but if afterwards <lb/>the &longs;ame water was mea&longs;ured in the fall it made to turn the <lb/>Wheel of the Mill, it was much le&longs;&longs;e, not amounting often to the <lb/>tenth part, nor &longs;ometimes to the twentieth, in&longs;omuch, that the <lb/>&longs;ame running water came to be one while more, another while le&longs;s <lb/>in mea&longs;ure, in divers parts of its Channel; and for that rea&longs;on this <lb/>vulgar manner of mea&longs;uring running Waters, as indeterminate and <lb/>uncertain, was by me ju&longs;tly &longs;u&longs;pected, the mea&longs;ure being to be de­<lb/>terminate, and the &longs;ame. </s> <s>And here I freely confe&longs;&longs;e that I had fin­<lb/>gular help to re&longs;olve this difficulty from the excellent & accurate <lb/>way of di&longs;cour&longs;ing, as in allother matters, &longs;o al&longs;o in this, of the <lb/>Right Honourable and Truly Noble Signior <emph type="italics"/>Ciampoli,<emph.end type="italics"/> Secretary <lb/>of the Popes &longs;ecret affairs. </s> <s>Who moreover, not &longs;paring &longs;or the co&longs;ts <lb/>of the &longs;ame, generou&longs;ly gave me occa&longs;ion a few years pa&longs;t to try by <lb/>exact experiments that which pa&longs;t concerning this particular. </s> <s>And <lb/>to explain all more clearly with an example; we &longs;uppo&longs;e a Ve&longs;&longs;el <lb/>filled with Water, as for in&longs;tance a Butt, which is kept full, though <lb/>&longs;till water runneth out, and the Water run out by two Taps equal <lb/>of bigne&longs;&longs;e, one put in the bottom of the Ve&longs;&longs;el, and the other in <lb/>the upper part; it is manife&longs;t that in the time wherein from the <lb/>upper part &longs;hall i&longs;&longs;ue a determinate mea&longs;ure of water &longs;rom <lb/>the inferiour part there &longs;hall i&longs;&longs;ue four, five, and many more of <lb/>the &longs;ame mea&longs;ures, according to the difference of the height of <lb/>the Taps, and the di&longs;tance of the upper Tap from the Superfici­<lb/>es and level of the water of the Ve&longs;&longs;el: and all this will alwayes <lb/>follow, though, as hath been &longs;aid, the Taps be equal, and the <lb/>water in di&longs;charging keep the &longs;aid Taps alwayes full. </s> <s>Where fir&longs;t <lb/>we note, that, although the mea&longs;ure of the Taps be equal, never­<lb/>thele&longs;&longs;e there i&longs;&longs;ueth from them in equal times unequal quantities <lb/>of water, And if we &longs;hould more attentively con&longs;ider this bu&longs;i­<lb/>ne&longs;&longs;e, we &longs;hould find, that the water by the lower Tap, run­<lb/>neth and pa&longs;&longs;eth with much greater velocity, then it doth by the <lb/>upper, whatever is the rea&longs;on. </s> <s>If therefore we would have <lb/>&longs;uch a quantity of Water di&longs;charge from the upper tap, as <lb/>would di&longs;charge from the neather in the &longs;ame time, it is plain, that <lb/>either the upper Taps mu&longs;t be multiplyed in &longs;uch &longs;ort, that &longs;o <lb/>many more Taps in number be placed above than below, as the <lb/>neather tap &longs;hall be more &longs;wift than the upper, or the upper Tap <lb/>made &longs;o much bigger than the nether, by how much that be­<lb/>neath &longs;hall be more &longs;wift than that above; and &longs;o then in equal <lb/>times, the &longs;ame quantity of Water &longs;hall di&longs;charge from the upper, <lb/>as doth from the neather part.</s></p><pb xlink:href="040/01/573.jpg" pagenum="4"/><p type="main"> <s>I will declare my &longs;elf by another example. </s> <s>If we &longs;hould ima­<lb/>gine, that two cords or lines of equal thickne&longs;s, be drawn through <lb/>two holes of equal bore; but &longs;o that the fir&longs;t pa&longs;s with quadruple <lb/>velocity to the &longs;econd: It is manife&longs;t, that if in a determinate <lb/>time, we &longs;hall by the fir&longs;t bore have drawn four Ells of the line, <lb/>in the &longs;ame time, by the &longs;econd hole we &longs;hall have drawn but one <lb/>Ell of cord onely; and if by the fir&longs;t there pa&longs;&longs;e twelve Ells, then <lb/>through the &longs;econd there &longs;hall pa&longs;&longs;e onely three Ells; and in <lb/>&longs;hort the quantity of cord &longs;hall have the &longs;ame proportion to the <lb/>cord, that the volocity hath to the velocity. </s> <s>And therefore we <lb/>de&longs;iring to compen&longs;ate the tardity of the &longs;econd cord, and main­<lb/>taining the &longs;ame tardity to draw through the &longs;econd hole as much <lb/>cord as through the fir&longs;t, it will be nece&longs;&longs;ary to draw through the <lb/>&longs;econd bore four ends of cord; &longs;o that the thickne&longs;s of all the <lb/>cords by the &longs;econd hole, have the &longs;ame proportion to the thick­<lb/>ne&longs;s of the cord which pa&longs;&longs;eth onely by the fir&longs;t, as the velocity <lb/>of the cord by the fir&longs;t hole hath reciprocally to the velocity of <lb/>the codrs by the &longs;econd hole. </s> <s>And thus its clear, that when <lb/>there is drawn through two holes equal quantity of cords in <lb/>equal time, but with unequal velocity, it will be nece&longs;&longs;ary, that <lb/>the thickne&longs;s of all the four cords &longs;hall have the &longs;ame reciprocal <lb/>proportion to the thickne&longs;s of the &longs;wifter cord, that the velo­<lb/>city of the &longs;wifter cord hath to the velocity of the &longs;lower. </s> <s>The <lb/>which is verified likewi&longs;e in the fluid Element of Water.</s></p><p type="main"> <s>And to the end that this principal fundamental be well under­<lb/>&longs;tood, I will al&longs;o note a certain ob&longs;ervation made my me in the <lb/>Art of Wyer-drawing, or &longs;pinning Gold, Silver, Bra&longs;s, and Iron, <lb/>and it is this; That &longs;uch Artificers de&longs;iring more and more to <lb/>di&longs;gro&longs;&longs;e and &longs;ubtillize the &longs;aid Metals, having would about a <lb/><emph type="italics"/>R<emph.end type="italics"/>ocket or Barrel, the thread of the Metal, they place the Roc­<lb/>ket in a frame upon a &longs;tedfa&longs;t Axis, in &longs;uch &longs;ort that the Rocket <lb/>may turn about in it &longs;elf; then making one end of the thread to <lb/>pa&longs;&longs;e by force through a Plate of Steel pierced with divers holes, <lb/>greater and le&longs;&longs;er, as need requireth, fa&longs;tning the &longs;ame end of the <lb/>thread to another Rocket, they wind up the thread, which pa&longs;­<lb/>&longs;ing through a bore le&longs;s than the thickne&longs;&longs;e of the thread, is of <lb/>force con&longs;trained to di&longs;gro&longs;&longs;e and &longs;ubtillize. </s> <s>Now that which is <lb/>inten&longs;ly to be ob&longs;erved in this bu&longs;ine&longs;s, is this, That the parts of <lb/>the thread before the hole, are of &longs;uch a thickne&longs;&longs;e, but the parts <lb/>of the &longs;ame thread after it is pa&longs;&longs;ed the hole, are of a le&longs;&longs;er thick­<lb/>ne&longs;&longs;e: and yet neverthele&longs;&longs;e the ma&longs;&longs;e and weight of the thread <lb/>which is drawn forth, is ever equal to the ma&longs;&longs;e and weight of the <lb/>thread which is winded up. </s> <s>But if we &longs;hould well con&longs;ider the mat­<lb/>ter, we &longs;hould finde, that the thicker the thread before the hole is, <lb/>than the thread pa&longs;&longs;ed the hole, the greater reciprocally is the <pb xlink:href="040/01/574.jpg" pagenum="5"/>velocity of the parts of the thread pa&longs;&longs;ed the hole, than the volo­<lb/>city of the parts before the hole: In&longs;omuch that if <emph type="italics"/>verbi gratia<emph.end type="italics"/><lb/>the thickne&longs;&longs;e of the thread before the hole, were double to the <lb/>thickne&longs;&longs;e after the hole, in &longs;uch ca&longs;e the velocity of the parts of <lb/>the thread pa&longs;&longs;ed the hole, &longs;hould be double to the velocity of the <lb/>parts of the thread before the hole; and thus the thickne&longs;&longs;e <lb/>compen&longs;ates the velocity, and the velocity compen&longs;ates the thick­<lb/>ne&longs;&longs;e. </s> <s>So that the &longs;ame occurreth in the &longs;olid Metals of Gold, <lb/>Silver, Bra&longs;s, Iron, &c. </s> <s>that eveneth al&longs;o in the fluid Element of <lb/>Water, and other liquids, namely, That the velocity beareth the <lb/>&longs;ame proportion to the velocity, that the thickne&longs;&longs;e of the Me­<lb/>tal, or Water, hath to the thickne&longs;&longs;e.</s></p><p type="main"> <s>And therefore granting this di&longs;cour&longs;e, we may &longs;ay, that as of­<lb/>ten as two Taps with different velocity di&longs;charge equal quanti­<lb/>ties of Water in equal times, it will be nece&longs;&longs;ary that the Tap <lb/>le&longs;&longs;e &longs;wift be &longs;o much greater, and larger, than the Tap more <lb/>&longs;wift, by how much the &longs;wifter &longs;uperates in velocity the &longs;lower; <lb/>and to pronounce the Propo&longs;ition in more proper terms, we &longs;ay; <lb/>That if two Taps of unequal velocity, di&longs;charge in equal times <lb/>equal quantities of Water, the greatne&longs;&longs;e of the fir&longs;t &longs;hall be to <lb/>the greatne&longs;&longs;e of the &longs;econd, in reciprocal proportion, as the ve­<lb/>locity of the &longs;econd to the velocity of the fir&longs;t. </s> <s>As for example, <lb/>if the fir&longs;t Tap &longs;hall be ten times &longs;wifter than the &longs;econd Tap, it <lb/>will be nece&longs;&longs;ary, that the &longs;econd be ten times bigger and larger <lb/>than the fir&longs;t; and in &longs;uch ca&longs;e the Taps &longs;hall di&longs;charge equall <lb/>quantities of water in equal times; and this is the principal and <lb/>mo&longs;t important point, which ought to be kept alwayes in minde, <lb/>for that on it well under&longs;tood depend many things profitable, <lb/>and worthy of our knowledge.</s></p><p type="main"> <s>Now applying all that hath been &longs;aid neerer to our purpo&longs;e, I <lb/>con&longs;ider, that it being mo&longs;t true, that in divers parts of the &longs;ame <lb/>River or Current of running water, there doth always pa&longs;&longs;e equal <lb/>quantity of Water in equal time (which thing is al&longs;o demon­<lb/>&longs;trated in out fir&longs;t Propo&longs;ition) and it being al&longs;o true, that in di­<lb/>vers parts the &longs;ame River may have various and different veloci­<lb/>ty; it follows of nece&longs;&longs;ary con&longs;equence, that where the River <lb/>hath le&longs;&longs;e velocity, it &longs;hall be of greater mea&longs;ure, and in tho&longs;e <lb/>parts, in which it hath greater velocity, it &longs;hall be of le&longs;&longs;e mea­<lb/>&longs;ure; and in &longs;um, the velocity of &longs;everal parts of the &longs;aid River, <lb/>&longs;hall have eternally reciprocall and like proportion with <lb/>their mea&longs;ures. </s> <s>This principle and fundamental well e&longs;tabli&longs;h­<lb/>ed, that the &longs;ame Current of Water changeth mea&longs;ure, accor­<lb/>ding to its varying of velocity; that is, le&longs;&longs;ening the mea&longs;ure, <lb/>when the velocity encrea&longs;eth, and encrea&longs;ing the mea&longs;ure, when <lb/>the velocity decrea&longs;eth; I pa&longs;&longs;e to the con&longs;ideration of many <pb xlink:href="040/01/575.jpg" pagenum="6"/>particular accidents in this admirable matter, and all depending <lb/>on this &longs;ole Propo&longs;ition, the &longs;en&longs;e of which I have oft repeated, <lb/>that it might be well under&longs;tood.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> I.</s></p><p type="main"> <s>And fir&longs;t, we hence conclude, that the &longs;ame Streams of a <lb/>Torrent, namely, tho&longs;e &longs;treams which carry equal quantity of <lb/>Water in equal times, make not the &longs;ame depths or mea&longs;ures in <lb/>the River, in which they enter, unle&longs;&longs;e when in the entrance in­<lb/>to the River they acquire; or to &longs;ay better, keep the &longs;ame velo­<lb/>city; becau&longs;e if the velocicities acquired in the River &longs;hall be <lb/>different, al&longs;o the mea&longs;ures &longs;hall be diver&longs;e; and con&longs;equently <lb/>the depths, as is demon&longs;trated.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> II.</s></p><p type="main"> <s>And becau&longs;e &longs;ucce&longs;&longs;ively, as the River is more and more full, <lb/>it is con&longs;tituted ordinarily in greater & greater velocity: hence <lb/>it is that the &longs;ame &longs;treams of the Torrent, that enter into the Ri­<lb/>ver, make le&longs;&longs;e and le&longs;&longs;e depths, as the River grows more and <lb/>more full; &longs;ince that al&longs;o the Waters of the Torrent being en­<lb/>tered into the River, go acquiring greater and greater velocities, <lb/>and therefore dimini&longs;h in mea&longs;ure and height.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> III.</s></p><p type="main"> <s>We ob&longs;erve al&longs;o, that while the main River is &longs;hallow, if there <lb/>fall but a gentle rain, it &longs;uddenly much increa&longs;eth and ri&longs;eth; <lb/>but when the River is already &longs;welled, though there fall again a­<lb/>nother new violent &longs;hower, yet it increa&longs;eth not at the &longs;ame rate <lb/>as before, proportionably to the rain which fell: which thing <lb/>we may affirm particularly to depend on this, that in the fir&longs;t <lb/>ca&longs;e, while the River is low, it is found al&longs;o very &longs;low, and there­<lb/>fore the little water which entereth into it, pa&longs;&longs;eth and runs with <lb/>little velocity, and con&longs;equently occupieth a great mea&longs;ure: <lb/>But when the River is once augmented, by new water being al&longs;o <lb/>made more &longs;wift, it cau&longs;eth the great Flood of water which fal­<lb/>leth, to bear a le&longs;&longs;e mea&longs;ure, and not to make &longs;uch a depth.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> IV.</s></p><p type="main"> <s>From the things demon&longs;trated is manife&longs;t al&longs;o, that whil&longs;t a <lb/>Torrent entereth into a River, at the time of Ebbe, then the <lb/>Torrent moveth with &longs;uch a certain velocity, what ever it be, <pb xlink:href="040/01/576.jpg" pagenum="7"/>pa&longs;&longs;ing by its extreame&longs;t parts, wherewith it communicateth with <lb/>the River; in which parts, the Torrent being mea&longs;ured, &longs;hall <lb/>have &longs;uch a certain mea&longs;ure: but the River &longs;welling and ri&longs;ing, <lb/>al&longs;o tho&longs;e parts of the Torrent augment in greatne&longs;&longs;e and mea­<lb/>&longs;ure, though the Torrent, in that in&longs;tant, di&longs;-imbogue no more <lb/>water than it did before: &longs;o that the River being &longs;welled, we <lb/>are to con&longs;ider two mouths of the &longs;ame Torrent, one le&longs;&longs;e be­<lb/>fore the ri&longs;ing, the other greater after the ri&longs;ing, which mouths <lb/>di&longs;charge equal quantities of water in equal times; therefore the <lb/>velocity by the le&longs;&longs;er mouth &longs;hall be greater than the velocity by <lb/>the greater mouth; and thus the Torrent &longs;hall be retarded from <lb/>its ordinary cour&longs;e.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> V.</s></p><p type="main"> <s>From which operation of Nature proceedeth another effect <lb/>worthy of con&longs;ideration; and it is, that the cour&longs;e of the water <lb/>retarding, as hath been &longs;aid in tho&longs;e ultimate parts of the Tor­<lb/>rent, if it &longs;hall happen that the Torrent grow torbid and mud­<lb/>dy, and its &longs;treame be retarded in &longs;uch a degree, that it is not <lb/>able to carry away tho&longs;e minute grains of Earth, which com­<lb/>po&longs;e the muddine&longs;&longs;e; in this ca&longs;e the Torrent &longs;hall clear away <lb/>the mud, and carry away the Sand at the bottome of its own <lb/>Chanel, in the extream parts of its mouth, which rai&longs;ed and <lb/>voided Sand, &longs;hall again afterwards be carried away, when the <lb/>River abating, the Torrent &longs;hall return to move with its primitive <lb/>velocity.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> VI.</s></p><p type="main"> <s>Whil&longs;t it is demon&longs;trated, that the &longs;ame water hath different <lb/>mea&longs;ures in its Chanel or cour&longs;e, according as it varieth in <lb/>velocity; &longs;o that the mea&longs;ure of the water is alwayes greater, where <lb/>the velocity is le&longs;&longs;er; and on the contrary, the mea&longs;ure le&longs;&longs;er, <lb/>where the velocity is greater: from hence we may mo&longs;t ele­<lb/>gantly render the rea&longs;on of the u&longs;ual Proverb, <emph type="italics"/>Take heed of the <lb/>&longs;till waters:<emph.end type="italics"/> For that if we con&longs;ider the &longs;elf &longs;ame water of a <lb/>River in tho&longs;e parts, wherein it is le&longs;s &longs;wift, and thence called <emph type="italics"/>&longs;till<emph.end type="italics"/><lb/>or <emph type="italics"/>&longs;mooth<emph.end type="italics"/> water, it &longs;hall be, of nece&longs;&longs;ity, of greater mea&longs;ure <lb/>than in tho&longs;e parts, in which it is more &longs;wift, and therefore ordi­<lb/>narily &longs;hall be al&longs;o more deep and dangerous for pa&longs;&longs;engers; <lb/>whence it is well &longs;aid, <emph type="italics"/>Take heed of the &longs;till Waters<emph.end type="italics"/>; and this <lb/>&longs;aying hath been &longs;ince applied to things moral.</s></p><pb xlink:href="040/01/577.jpg" pagenum="8"/><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> VII.</s></p><p type="main"> <s>Likewi&longs;e, from the things demon&longs;trated may be concluded, <lb/>that the windes, which &longs;top a <emph type="italics"/>R<emph.end type="italics"/>iver, and blowing again&longs;t the <lb/>Current, retard its cour&longs;e and ordinary velocity &longs;hall nece&longs;&longs;arily <lb/>amplifie the mea&longs;ure of the &longs;ame River, and con&longs;equently &longs;hall <lb/>be, in great part, cau&longs;es; or we may &longs;ay, potent con-cau&longs;es of <lb/>making the extraordinary inundations which Rivers u&longs;e to make. <lb/></s> <s>And its mo&longs;t certain, that as often as a &longs;trong and continual wind <lb/>&longs;hall blow again&longs;t the Current of a River, and &longs;hall reduce the <lb/>water of the River to &longs;uch tardity of motion, that in the time <lb/>wherein before it run five miles, it now moveth but one, &longs;uch a <lb/>River will increa&longs;e to five times the mea&longs;ure, though there &longs;hould <lb/>not be added any other quantity of water; which thing indeed <lb/>hath in it &longs;omething of &longs;trange, but it is mo&longs;t certain, for that <lb/>look what proportion the waters velocity before the winde, hath <lb/>to the velocity after the winde, and &longs;uch reciprocally is the mea­<lb/>&longs;ure of the &longs;ame water after the winde, to the mea&longs;ure before <lb/>the winde; and becau&longs;e it hath been &longs;uppo&longs;ed in our ca&longs;e that the <lb/>velocity is dimini&longs;hed to a fifth part, therefore the mea&longs;ure &longs;hall <lb/>be increa&longs;ed five times more than that, which it was before.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> VIII.</s></p><p type="main"> <s>We have al&longs;o probable the cau&longs;e of the inundations of <emph type="italics"/>Tyber,<emph.end type="italics"/><lb/>which befel at <emph type="italics"/>Rome,<emph.end type="italics"/> in the time of <emph type="italics"/>Alexander<emph.end type="italics"/> the Sixth, & of <lb/><emph type="italics"/>Clement<emph.end type="italics"/> the Seventh; which innundations came in a &longs;erene time, <lb/>and without great thaws of the Snows; which therefore much <lb/>puzzled the wits of tho&longs;e times. </s> <s>But we may with much pro­<lb/>bability affirm, That the River ro&longs;e to &longs;uch a height and excre&longs;­<lb/>cence, by the retardation of the Waters dependant on the <lb/>boi&longs;trous and con&longs;tant Winds, that blew in tho&longs;e times, as is no­<lb/>red in the memorials.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/> IX.</s></p><p type="main"> <s>It being mo&longs;t manife&longs;t, that by the great abundance of Water <lb/>the Torrents may increa&longs;e, and of them&longs;elves alone exorbitantly <lb/>&longs;well the River; and having demon&longs;trated that al&longs;o without new <lb/>Water, but onely by the notable retardment the River ri&longs;eth and <lb/>increa&longs;eth in mea&longs;ure, in proportion as the velocity decrea&longs;eth: <lb/>hence it is apparent, that each of the&longs;e cau&longs;es being able of it &longs;elf, <lb/>and &longs;eparate from the other to &longs;well the River; when it &longs;hall <lb/>happen that both the&longs;e two cau&longs;es con&longs;pire the augmentation of <pb xlink:href="040/01/578.jpg" pagenum="9"/>the River, in &longs;uch a ca&longs;e there mu&longs;t follow very great and irre­<lb/>pable innundations.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> X.</s></p><p type="main"> <s>From what hath been demon&longs;trated, we may with facility re­<lb/>&longs;olve the doubt which hath troubled, and &longs;till po&longs;eth the mo&longs;t <lb/>diligent, but incautelous ob&longs;ervers of Rivers, who mea&longs;uring <lb/>the Streams and Torrents which fall into another River; as tho&longs;e <lb/>for in&longs;tance, which enter into the <emph type="italics"/>Po,<emph.end type="italics"/> or tho&longs;e which fall into <emph type="italics"/>Ti­<lb/>ber<emph.end type="italics"/>; and having &longs;ummed the total of the&longs;e mea&longs;ures, and con­<lb/>ferring the mea&longs;ures of the Rivers and Brooks, which fall into <lb/><emph type="italics"/>Tiber,<emph.end type="italics"/> with the mea&longs;ure of <emph type="italics"/>Tiber,<emph.end type="italics"/> and the mea&longs;ures of tho&longs;e which <lb/>di&longs;imbogue into <emph type="italics"/>Po,<emph.end type="italics"/> with the mea&longs;ure of <emph type="italics"/>Po,<emph.end type="italics"/> they find them not <lb/>equal, as, it &longs;eems to them, they ought to be, and this is becau&longs;e <lb/>they have not well noted the mo&longs;t important point of the varia­<lb/>tion of velocity, and how that it is the mo&longs;t potent cau&longs;e of won­<lb/>derfully altering the mea&longs;ures of running Waters; but we mo&longs;t <lb/>facilly re&longs;olving the doubt, may &longs;ay that the&longs;e Waters dimini&longs;h <lb/>the mea&longs;ure, being once entered the principal Channel, becau&longs;e <lb/>they increa&longs;e in velocity.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XI.</s></p><p type="main"> <s>Through the ignorance of the force of the velocity of the Wa­<lb/>ter, in altering its mea&longs;ure, & augmenting it when the velocity <lb/>dimini&longs;heth; and dimini&longs;hing it when the velocity augmenteth: <lb/>The Architect <emph type="italics"/>Giovanni Fontana,<emph.end type="italics"/> endeavoured to mea&longs;ure, and <lb/>and to cau&longs;e to be mea&longs;ured by his Nephew, all the Brooks and <lb/>Rivers which di&longs;charged their Waters into <emph type="italics"/>Tiber,<emph.end type="italics"/> at the time of <lb/>the Innundation; which happened at <emph type="italics"/>Rome<emph.end type="italics"/> in the year 1598, <lb/>and publi&longs;hed a &longs;mall Treati&longs;e thereof, wherein he &longs;ummeth up <lb/>the mea&longs;ures of the extraordinary Water which fell into <emph type="italics"/>Tiber,<emph.end type="italics"/><lb/>and made account that it was about five hundred Ells more than <lb/>ordinary; and in the end of that Treati&longs;e concludeth, that to re­<lb/>move the Innundation wholly from <emph type="italics"/>Rome,<emph.end type="italics"/> it would be nece&longs;&longs;ary <lb/>to make two other Channels, equal to that at pre&longs;ent, and that <lb/>le&longs;&longs;e would not &longs;uffice; and finding afterwards that the whole <lb/>Stream pa&longs;&longs;ed under the Bridge <emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> (the Arch where­<lb/>of is of a far le&longs;s mea&longs;ure then five hundred Ells) concludeth, <lb/>that under the &longs;aid Bridge pa&longs;t a hundred fifty one Ells of Water <lb/>compre&longs;&longs;ed, (I have &longs;et down the preci&longs;e term of compre&longs;t Wa­<lb/>ter, written by <emph type="italics"/>Fontana<emph.end type="italics"/>) wherein I finde many errors.</s></p><p type="main"> <s>The fir&longs;t of which is to think that the mea&longs;ures of the&longs;e Wa­<lb/>ters compre&longs;&longs;ed in the Channels of tho&longs;e Brooks and Rivers, <pb xlink:href="040/01/579.jpg" pagenum="10"/>&longs;hould maintain them&longs;elves the &longs;ame in <emph type="italics"/>Tiber,<emph.end type="italics"/> which by his leave, <lb/>is mo&longs;t fal&longs;e, when ever tho&longs;e waters reduced into <emph type="italics"/>Tiber,<emph.end type="italics"/> retain <lb/>not the &longs;ame velocity which they had in the place in which <emph type="italics"/>Fon­<lb/>tana<emph.end type="italics"/> and his Nephew mea&longs;ured them: And all this is manife&longs;t <lb/>from the things which we have above explained; for, if the Wa­<lb/>ters reduced into <emph type="italics"/>Tiber<emph.end type="italics"/> increa&longs;e in velocity, they decrea&longs;e in mea­<lb/>&longs;ure; and if they decrea&longs;e in velocity, they increa&longs;e in mea­<lb/>&longs;ure.</s></p><p type="main"> <s>Secondly, I con&longs;ider that the mea&longs;ures of tho&longs;e Brooks and <lb/>Rivers, which enter into <emph type="italics"/>Tiber<emph.end type="italics"/> at the time of Innundation, are <lb/>not between them&longs;elves really the &longs;ame, when their velocities are <lb/>not equal, though they have the &longs;ame names of Ells and Feet; <lb/>for that its po&longs;&longs;ible that a di&longs;inboguement of ten Ells requadrated <lb/>(to &longs;peak in the phra&longs;e of <emph type="italics"/>Fontana<emph.end type="italics"/>) of one of tho&longs;e Brooks, <lb/>might di&longs;charge into <emph type="italics"/>Tiber<emph.end type="italics"/> at the time of Innundation, four, ten, <lb/>and twenty times le&longs;s Water, than another mouth equal to the <lb/>fir&longs;t in greatne&longs;s, as would occur when the fir&longs;t mouth were four, <lb/>ten, or twenty times le&longs;s &longs;wift than the &longs;econd. </s> <s>Whereupon, <lb/>whil&longs;t <emph type="italics"/>Fontana<emph.end type="italics"/> &longs;ummes up the Ells and Feet of the mea&longs;ures of <lb/>tho&longs;e Brooks and Rivers into a total aggregate, he commits the <lb/>&longs;ame error with him, which would add into one &longs;umme diver&longs;e <lb/>moneys of diver&longs;e values, and diver&longs;e places, but that had the <lb/>&longs;ame name; as if one &longs;hould &longs;ay ten Crowns of <emph type="italics"/>Roman<emph.end type="italics"/> money, <lb/>four Crowns of Gold, thirteen Crowns of <emph type="italics"/>Florence,<emph.end type="italics"/> five Growns <lb/>of <emph type="italics"/>Venice,<emph.end type="italics"/> and eight Crowns of <emph type="italics"/>Mantua,<emph.end type="italics"/> &longs;hould make the &longs;ame <lb/>&longs;umme with forty Crowns of Gold, or forty Crowns of <emph type="italics"/>Mantua.<emph.end type="italics"/></s></p><p type="main"> <s>Thirdly, It might happen that &longs;ome River or Current in the <lb/>parts nearer <emph type="italics"/>Rome,<emph.end type="italics"/> in the time of its flowing, did not &longs;end forth <lb/>more Water than ordinary; and however, its a thing very clear, <lb/>that whil&longs;t the &longs;tream came from the &longs;uperior parts, that &longs;ame <lb/>Brook or River would be augmented in mea&longs;ure, as hath been <lb/>noted in the fourth <emph type="italics"/>Corollary<emph.end type="italics"/>; in &longs;uch &longs;ort, that <emph type="italics"/>Fontana<emph.end type="italics"/> might <lb/>have inculcated, and noted that &longs;ame River or Current as con­<lb/>curring to the Innundation, although it were therein altogether <lb/>unconcerned.</s></p><p type="main"> <s>Moreover, in the fourth place we mu&longs;t note, That it might <lb/>&longs;o fall out, that &longs;uch a River not onely was unintere&longs;&longs;ed in the <lb/>Innundation, though augmented in mea&longs;ure, but it might I &longs;ay <lb/>happen, that it was in&longs;trumental to the a&longs;&longs;waging the Innunda­<lb/>tion, by augmenting in the mea&longs;ure of its own Channel; which <lb/>matter is &longs;ufficiently evident; for if it be &longs;uppo&longs;ed that the Ri­<lb/>ver in the time of flood, had not had of it &longs;elf, and from its pro­<lb/>per &longs;prings more Water than ordinary, its a thing certain, that <lb/>the Water of <emph type="italics"/>Tiber<emph.end type="italics"/> ri&longs;ing and increa&longs;ing; al&longs;o that River, to le­<lb/>vel it &longs;elf with the Water of <emph type="italics"/>Tiber,<emph.end type="italics"/> would have retained &longs;ome of <pb xlink:href="040/01/580.jpg" pagenum="11"/>its Waters in its own Chanel, without di&longs;charging them into <emph type="italics"/>Ty­<lb/>ber,<emph.end type="italics"/> or el&longs;e would have ingorged and &longs;wallowed (if I may &longs;o &longs;ay) <lb/>&longs;ome of the water of <emph type="italics"/>Tyber<emph.end type="italics"/>; and in this ca&longs;e, at the time of In­<lb/>undation, le&longs;&longs;e abundance of water would have come to <emph type="italics"/>Rome,<emph.end type="italics"/><lb/>and yet neverthele&longs;&longs;e the mea&longs;ure of that River would have been <lb/>increa&longs;ed.</s></p><p type="main"> <s>Fifthly, <emph type="italics"/>Fontana<emph.end type="italics"/> deceiveth him&longs;elf, when he concludeth, that <lb/>to remove the Inundation from <emph type="italics"/>Rome,<emph.end type="italics"/> it would be nece&longs;&longs;ary to <lb/>make two other Chanels of Rivers, that were as large as that, <lb/>which is the pre&longs;ent one, and that le&longs;s would not &longs;uffice, which, <lb/>I &longs;ay, is a fallacy: and to convince him ea&longs;ily of his errour, it <lb/>&longs;ufficeth to &longs;ay, that all the Streams being pa&longs;&longs;ed under the Bridge <lb/><emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> as he him&longs;elf atte&longs;ts, a Channel would &longs;uffice on­<lb/>ly of the capacity of the &longs;aid Bridge, provided that the water <lb/>there might run with the &longs;ame velocity, as it did under the Bridge <lb/>at the time of Inundation; and on the contrary, twenty Cur­<lb/>rents of capacity equal to the pre&longs;ent one, would not &longs;uffice, if <lb/>the water &longs;hould run with twenty times le&longs;s velocity, than it made <lb/>at the time of the Inundation.</s></p><p type="main"> <s>Sixthly, to me it &longs;eemeth a great weakne&longs;&longs;e to &longs;ay, that there <lb/>&longs;hould pa&longs;&longs;e under the Bridge <emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> an hundred fifty one <lb/>ells of water compre&longs;&longs;ed; for that I do not under&longs;tand that wa­<lb/>ter is like Cotton or Wool, which matters may be pre&longs;t and trod, <lb/>as it happeneth al&longs;o to the air, which receiveth compre&longs;&longs;ion in <lb/>&longs;uch &longs;ort, that after that in &longs;ome certain place a quantity of air <lb/>&longs;hall be reduced to its natural con&longs;titution; and having taken up <lb/>all the &longs;aid place, yet neverthele&longs;&longs;e compre&longs;&longs;ing the fir&longs;t Air <lb/>with force and violence, it is reduced into far le&longs;s room, and will <lb/>admit four or &longs;ix times as much air, as before, as is experimen­<lb/>tally ^{*} &longs;een in the Wind-Gun, invented in our dayes by <emph type="italics"/>M. Vin,<emph.end type="italics"/><lb/><arrow.to.target n="marg964"></arrow.to.target><lb/><emph type="italics"/>cenzo Vincenti<emph.end type="italics"/> of <emph type="italics"/>Vrbin,<emph.end type="italics"/> which property of the Air of admit­<lb/>ting conden&longs;ation, is al&longs;o &longs;een in the portable Fountains of the <lb/>&longs;ame <emph type="italics"/>M. Vincenzo:<emph.end type="italics"/> which Fountains &longs;pirt the Water on high, <lb/>by force of the Air compre&longs;&longs;ed, which whil&longs;t it &longs;eeks to reduce <lb/>its &longs;elf to its natural con&longs;titution, in the dilation cau&longs;eth that vi­<lb/>olence. </s> <s>But the water can never, for any thing I know, crowd, <lb/>or pre&longs;s &longs;o, as that if before the compre&longs;&longs;ion it held or po&longs;&longs;e&longs;t a <lb/>place, being in its natural con&longs;titution, I believe not, I &longs;ay, that it <lb/>is po&longs;&longs;ible, by pre&longs;&longs;ing and crowding to make it po&longs;&longs;e&longs;s le&longs;s room, <lb/>for if it were po&longs;&longs;ible to compre&longs;s the Water, and make it to oc­<lb/>cupy a le&longs;s place, it would thence follow, that two Ve&longs;&longs;els of e­<lb/>qual mea&longs;ure, but of unequal height, &longs;hould be of unequal capa­<lb/>city, and that &longs;hould hold more water which was higher; al&longs;o a <lb/>Cylinder, or other Ve&longs;&longs;el more high than broad, would containe <lb/>more water erected, than being laid along; for that being erect­<pb xlink:href="040/01/581.jpg" pagenum="12"/>ed, the water put therein would be more pre&longs;&longs;ed and crowded.</s></p><p type="margin"> <s><margin.target id="marg964"></margin.target>* And as is at <lb/>large demon&longs;trated <lb/>by that mo&longs;t excel­<lb/>lent and lonour­<lb/>able per&longs;onage Mr. <lb/><emph type="italics"/>Botle<emph.end type="italics"/> in the indu­<lb/>&longs;trious experiment <lb/>of his Pneumatical <lb/>Engine.</s></p><p type="main"> <s>And therefore, in our ca&longs;e, according to our principles we will <lb/>&longs;ay, that the water of that Stream pa&longs;seth all under the &longs;aid <lb/>Bridge <emph type="italics"/>Quattro-Capi,<emph.end type="italics"/> for that being there mo&longs;t &longs;wift, it ought of <lb/>con&longs;equence to be le&longs;s in mea&longs;ure.</s></p><p type="main"> <s>And here one may &longs;ee, into how many errours a man may run <lb/>through ignorance of a true and real Principle, which once known <lb/>and well under&longs;tood, takes away all mi&longs;ts of doubting, and ea­<lb/>&longs;ily re&longs;olveth all difficulties.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/> XII.</s></p><p type="main"> <s>Through the &longs;ame inadvertency of not regarding the variation <lb/>of velocity in the &longs;ame Current, therea re committed by Ingi­<lb/>neers and Learned men, errours of very great moment (and I <lb/>could thereof produce examples, but for good rea&longs;ons I pa&longs;s <lb/>them over in &longs;ilence) when they think, and propo&longs;e, by deriving <lb/>new Channels from great Rivers, to dimini&longs;h the mea&longs;ure of the <lb/>water in the River, and to dimini&longs;h it proportionally, according <lb/>to the mea&longs;ure of the Water which they make to pa&longs;s through <lb/>the Channel, as making <emph type="italics"/>v.g<emph.end type="italics"/> a Channel fifty foot broad, in which <lb/>the derived water is to run wa&longs;te, ten foot deep, they think they <lb/>have dimini&longs;hed the mea&longs;ure of the Water in the River five hun­<lb/>dred feet, which thing doth not indeed &longs;o fall out; and the rea­<lb/>&longs;on is plain; for that the Chanel being derived, the re&longs;t of the <lb/>main River, dimini&longs;heth in velocity, and therefore retains a grea­<lb/>ter mea&longs;ure than it had at fir&longs;t before the derivation of the Cha­<lb/>nel; and moreover, if the Chanel being derived, it &longs;hall not <lb/>con&longs;erve the &longs;ame velocity which it had at fir&longs;t in the main Ri­<lb/>ver, but &longs;hall dimini&longs;h it, it will be nece&longs;&longs;ary, that it hath a grea­<lb/>ter mea&longs;ure than it had before in the River; and therefore <lb/>to accompt aright, there &longs;hall not be &longs;o much water derived into <lb/>the Channel, as &longs;hall dimini&longs;h the River, according to the quanti­<lb/>ty of the water in the Channel, as is pretended.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XIII.</s></p><p type="main"> <s>This &longs;ame con&longs;ideration giveth me occa&longs;ion to di&longs;cover a mo&longs;t <lb/>ordinary errour, ob&longs;erved by me in the bu&longs;ine&longs;&longs;e of the wa­<lb/>ter of <emph type="italics"/>Ferara,<emph.end type="italics"/> when I was in tho&longs;e parts, in &longs;ervice of the mo&longs;t <lb/>Reverend and Illu&longs;trious Monfignor <emph type="italics"/>Cor&longs;ini<emph.end type="italics"/>; the &longs;ublime wit of <lb/>whom hath been a very great help to me in the&longs;e contemplations; <lb/>its very true, I have been much perplexed, whether I &longs;hould <lb/>commit this particular to paper, or pa&longs;&longs;e it over in &longs;ilence, for <lb/>that I have ever doubted, that the opinion &longs;o common and <pb xlink:href="040/01/582.jpg" pagenum="13"/>moreover confirmed with a mo&longs;t manife&longs;t experiment, may not <lb/>onely make this my conjecture to be e&longs;teemed far from true, <lb/>but al&longs;o to di&longs;credit with the World the re&longs;t of this my Treati&longs;e: <lb/>Neverthele&longs;&longs;e I have at la&longs;t re&longs;olved not to be wanting to my <lb/>&longs;elf, and to truth in a matter of it &longs;elf, and for other con&longs;e­<lb/>quences mo&longs;t important; nor doth it &longs;eem to me requi&longs;ite in <lb/>difficult matters, &longs;uch as the&longs;e we have in hand, to refigne our <lb/>&longs;elves to the common opinion, &longs;ince it would be very &longs;trange if <lb/>the multitude in &longs;uch matters &longs;hould hit on the truth, nor ought <lb/>that to be held difficult, in which even the vulgar do know the <lb/>truth and right; be&longs;ides that I hope morever to prove all in &longs;uch <lb/>&longs;ort, that per&longs;ons of &longs;olid judgment, &longs;hall re&longs;t fully per&longs;waded, <lb/>&longs;o that they but keep in mind the principal ground and foundation <lb/>of all this Treati&longs;e; and though that which I will propo&longs;e, be a par­<lb/>ticular, as I have &longs;aid, pertaining onely to the intere&longs;ts of <emph type="italics"/>Ferara<emph.end type="italics"/>; <lb/>yet neverthele&longs;&longs;e from this particular Doctrine well under&longs;tood, <lb/>good judgement may be made of other the like ca&longs;es in general.</s></p><p type="main"> <s>I &longs;ay then, for greater per&longs;pecuity, and better under&longs;tanding <lb/>of the whole, That about thirteen miles above <emph type="italics"/>Ferara,<emph.end type="italics"/> near to <lb/><emph type="italics"/>Stellata,<emph.end type="italics"/> the main of P<emph type="italics"/>o,<emph.end type="italics"/> branching it &longs;elf into two parts, with one <lb/>of its Arms it cometh clo&longs;e to <emph type="italics"/>Ferara,<emph.end type="italics"/> retaining the name of the <lb/>P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/>; and here again it divideth it &longs;elf into two other <lb/>branches, and that which continueth on the right hand, is called <lb/>the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> and of <emph type="italics"/>Primaro<emph.end type="italics"/>; and that on the left the P<emph type="italics"/>o<emph.end type="italics"/><lb/>of <emph type="italics"/>Volana.<emph.end type="italics"/> But for that the bed of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being here­<lb/>tofore augmented and rai&longs;ed, it followeth that it re&longs;teth wholly <lb/>deprived of the Water of the great P<emph type="italics"/>o,<emph.end type="italics"/> except in the time of its <lb/>greater &longs;welling; for in that ca&longs;e, this P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being re­<lb/>&longs;trained with a Bank near to <emph type="italics"/>Bondeno,<emph.end type="italics"/> would come al&longs;o in the <lb/>overflowings of the main P<emph type="italics"/>o,<emph.end type="italics"/> to be free from its Waters: But the <lb/>Lords of <emph type="italics"/>Ferara<emph.end type="italics"/> are wont at &longs;uch time as the P<emph type="italics"/>o<emph.end type="italics"/> threateneth to <lb/>break out, to cut the bank; by which cutting, there di&longs;­<lb/>gorgeth &longs;uch a Torrent of Water, that it is ob&longs;erved, that the <lb/>main P<emph type="italics"/>o<emph.end type="italics"/> in the &longs;pace of &longs;ome few hours abateth near a foot, and <lb/>all per&longs;ons that I have &longs;poken with hitherto, moved by this ex­<lb/>periment, think that it is of great profit and benefit to keep ready <lb/>this Vent, and to make u&longs;e of it in the time of its fullne&longs;&longs;e. </s> <s>And <lb/>indeed, the thing con&longs;idered &longs;imply, and at the fir&longs;t appearance, <lb/>it &longs;eemeth that none can think otherwi&longs;e; the rather, for that <lb/>many examining the matter narrowly, mea&longs;ure that body of <lb/>Water which runneth by the Channel, or Bed of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Fera­<lb/>ra,<emph.end type="italics"/> and make account, that the body of the Water of the great <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> is dimini&longs;hed the quantity of the body of the Water which <lb/>runneth by the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara.<emph.end type="italics"/> But if we well remember what <lb/>hath been &longs;aid in the beginning of the Treati&longs;e, and how much <pb xlink:href="040/01/583.jpg" pagenum="14"/>the variety of the velocities of the &longs;aid Water importeth, and the <lb/>knowledge of them is nece&longs;&longs;ary to conclude the true quantity of <lb/>the running Water, we &longs;hall finde it manife&longs;t, that the benefit of <lb/>this Vent is far le&longs;&longs;e than it is generally thought: And mereover, <lb/>we &longs;hall finde, if I deceive not my &longs;elf, that there follow from <lb/>thence &longs;o many mi&longs;chiefs, that I could greatly incline to believe, <lb/>that it were more to the purpo&longs;e wholly to &longs;top it up, than to <lb/>maintain it open: yet I am not &longs;o wedded to my opinion, but <lb/>that I am ready to change my judgement upon &longs;trength of better <lb/>rea&longs;ons; e&longs;pecially of one that &longs;hall have fir&longs;t well under&longs;tood <lb/>the beginning of this my di&longs;cour&longs;e, which I frequently inculcate, <lb/>becau&longs;e its ab&longs;olutely impo&longs;&longs;ible without this adverti&longs;ement to <lb/>treat of the&longs;e matters, and not commit very great errours.</s></p><p type="main"> <s>I propo&longs;e therefore to con&longs;ideration, that although it be true, <lb/>that whil&longs;t the water of the main P<emph type="italics"/>o<emph.end type="italics"/> is at its greate&longs;t height, the <lb/>Bank and Dam then cut of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara,<emph.end type="italics"/> and the &longs;uperior <lb/>waters having a very great fall into the Channel of <emph type="italics"/>Ferara,<emph.end type="italics"/> they <lb/>precipitate into the &longs;ame with great violence and velocity, and <lb/>with the &longs;ame in the beginning, or little le&longs;&longs;e, they run towards <lb/>the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Volana,<emph.end type="italics"/> and of <emph type="italics"/>Argenta<emph.end type="italics"/> on the &longs;ea coa&longs;ts; yet after the <lb/>&longs;pace of &longs;ome few hours, the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being full, and the &longs;u­<lb/>perior Waters not finding &longs;o great a diclivity there, as they had <lb/>at the beginning of the cutting, they fall not into the &longs;ame with <lb/>the former velocity, but with far le&longs;&longs;e, and thereby a great deal <lb/>le&longs;&longs;e Water begins to i&longs;&longs;ue from the great P<emph type="italics"/>o<emph.end type="italics"/>; and if we dili­<lb/>gently compare the velocity at the fir&longs;t cutting, with the velocity <lb/>of the Water after the cutting made, and when the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/><lb/>&longs;hall be full of Water, we &longs;hall finde perhaps that to be fifteen or <lb/>twenty times greater than this, and con&longs;equently the Water <lb/>which i&longs;&longs;ues from the great P<emph type="italics"/>o,<emph.end type="italics"/> that fir&longs;t impetuo&longs;ity being pa&longs;t, <lb/>&longs;hall be onely the fifteenth or twentieth part of that which i&longs;&longs;ued <lb/>at the beginning; and therefore the Waters of the main P<emph type="italics"/>o<emph.end type="italics"/> will <lb/>return in a &longs;mall time almo&longs;t to the fir&longs;t height. </s> <s>And here I will <lb/>pray tho&longs;e who re&longs;t not wholly &longs;atisfied with what hath been &longs;aid, <lb/>that for the love of truth, and the common good, they would <lb/>plea&longs;e to make diligent ob&longs;ervation whether in the time of great <lb/>Floods, the &longs;aid Bank or Dam at <emph type="italics"/>Bondeno<emph.end type="italics"/> is cut, and that in few <lb/>hours the main P<emph type="italics"/>o<emph.end type="italics"/> dimini&longs;heth, as hath been &longs;aid about a foot in <lb/>its height; that they would ob&longs;erve I &longs;ay, whether, a day or two <lb/>being pa&longs;t, the Waters of the main P<emph type="italics"/>o<emph.end type="italics"/> return almo&longs;t to their fir&longs;t <lb/>height; for if this &longs;hould follow, it would be very clear, that the <lb/>benefit which re&longs;ulteth from this diver&longs;ion or Vent, is not &longs;o great <lb/>as is univer&longs;ally pre&longs;umed; I &longs;ay, it is not &longs;o great as is <lb/>pre&longs;umed; becau&longs;e, though it be granted for true, that <lb/>the Waters of the main P<emph type="italics"/>o,<emph.end type="italics"/> abate at the beginning of <pb xlink:href="040/01/584.jpg" pagenum="17"/>the Vent, yet this benefit happens to be but temporary and for a <lb/>few hours: If the ri&longs;ing of P<emph type="italics"/>o,<emph.end type="italics"/> and the dangers of breaking forth <lb/>were of &longs;hort duration, as it ordinarily befalleth in the overflow­<lb/>ings of Torrents, in &longs;uch a ca&longs;e the profit of the Vent would be <lb/>of &longs;ome e&longs;teem: But becau&longs;e the &longs;wellings of P<emph type="italics"/>o<emph.end type="italics"/> continue for <lb/>thirty, or &longs;ometimes for forty dayes, therefore the gain which <lb/>re&longs;ults from the Vent proveth to be incon&longs;iderable. </s> <s>It remain­<lb/>eth now to con&longs;ider the notable harms which follow the &longs;aid <lb/>Sluice or Vent, that &longs;o reflection being made, and the profit and <lb/>the detriment compared, one may rightly judge, and choo&longs;e that <lb/>which &longs;hall be mo&longs;t convenient. </s> <s>The fir&longs;t prejudice therefore <lb/>which ari&longs;eth from this Vent or Sluice, is; That the Channels of <lb/><emph type="italics"/>Ferara, Primaro,<emph.end type="italics"/> and <emph type="italics"/>Volana<emph.end type="italics"/> filling with Water, all tho&longs;e parts <lb/>from <emph type="italics"/>Bondeno<emph.end type="italics"/> to the Sea &longs;ide are allarmed and endangered <lb/>thereby. </s> <s>Secondly, The Waters of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro<emph.end type="italics"/> having <lb/>free ingre&longs;&longs;e into the upper Valleys, they fill them to the great <lb/>damage of the Fields adjacent, and ob&longs;truct the cour&longs;e of the <lb/>ordinary Trenches in the &longs;ame Valleys; in&longs;omuch that all the <lb/>care, co&longs;t, and labour about the draining, and freeing the upper <lb/>Valleys from Water, would al&longs;o become vain and ineffectual. <lb/></s> <s>Thirdly, I con&longs;ider that the&longs;e Waters of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> being <lb/>pa&longs;&longs;ed downwards towards the Sea, at the time that the main P<emph type="italics"/>o<emph.end type="italics"/><lb/>was in its greater excre&longs;cences and heights, it is manife&longs;t by expe­<lb/>rience, that when the great P<emph type="italics"/>o<emph.end type="italics"/> dimini&longs;heth, then the&longs;e Waters <lb/>pa&longs;&longs;ed by the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferara<emph.end type="italics"/> begin to retard in their cour&longs;e, and <lb/>finally come to turn the current upwards towards <emph type="italics"/>Stellata,<emph.end type="italics"/> re&longs;ting <lb/>fir&longs;t iu the intermediate time, almo&longs;t fixed and &longs;tanding, and <lb/>therefore depo&longs;ing the muddine&longs;&longs;e, they fill up the Channel of <lb/>the River or Current of <emph type="italics"/>Ferara.<emph.end type="italics"/> Fourthly and la&longs;tly, There <lb/>followeth from this &longs;ame diver&longs;ion another notable damage, and <lb/>it is like to that which followeth the breaches made by Rivers; <lb/>near to which breaches in the lower parts, namely below the <lb/>breach, there is begot in the Channel of the River, a certain ridge <lb/>or &longs;helf, that is, the bottom of the River is rai&longs;ed, as if &longs;ufficiently <lb/>manife&longs;t by experience; and thus ju&longs;t in the &longs;ame manner cutting <lb/>the Bank at <emph type="italics"/>Bondeno,<emph.end type="italics"/> there is at it were a breach made, from which <lb/>followeth the ri&longs;ing in the lower parts of the main P<emph type="italics"/>o,<emph.end type="italics"/> being pa&longs;t <lb/>the mouth of <emph type="italics"/>Pamaro<emph.end type="italics"/>; which thing, how pernitious it is, let any one <lb/>judge that under&longs;tandeth the&longs;e matters. </s> <s>And therefore both for <lb/>the &longs;mall benefit, and &longs;o many harms that en&longs;ue from maintain­<lb/>ing this diver&longs;ion, I &longs;hould think it were more &longs;ound advice to <lb/>keep that Bank alwaies whole at <emph type="italics"/>Bondeno,<emph.end type="italics"/> or in any other conve­<lb/>nient place, and not to permit that the Water of the Grand P<emph type="italics"/>o<emph.end type="italics"/><lb/>&longs;hould ever come near to <emph type="italics"/>Ferara.<emph.end type="italics"/></s></p><pb xlink:href="040/01/585.jpg" pagenum="16"/><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XIV.<lb/><arrow.to.target n="marg965"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg965"></margin.target>* <emph type="italics"/>Arte&longs;ia.<emph.end type="italics"/></s></p><p type="main"> <s>In the Grand Rivers, which fall into the Sea, as here in <emph type="italics"/>Italy <lb/>Po, Adige,<emph.end type="italics"/>^{*} and <emph type="italics"/>Arno,<emph.end type="italics"/> which are armed with Banks again&longs;t their <lb/>excre&longs;cencies, its ob&longs;erved that far from the Sea, they need <lb/>Banks of a notable height; which height goeth afterwards by <lb/>degrees dimini&longs;hing, the more it approacheth to the Sea-coa&longs;ts: <lb/>in &longs;uch &longs;ort, that the P<emph type="italics"/>o,<emph.end type="italics"/> di&longs;tant from the Sea about fifty or &longs;ixty <lb/>miles at <emph type="italics"/>Ferara,<emph.end type="italics"/> &longs;hall have Banks that be above twenty feet <lb/>higher than the ordinary Water marks; but ten or twelve miles <lb/>from the Sea, the Banks are not twelve feet higher than the &longs;aid <lb/>ordinary Water-marks, though the breadth of the River be the <lb/>&longs;ame, &longs;o that the excre&longs;cence of the &longs;ame Innundation happens <lb/>to be far greater in mea&longs;ure remote from the Sea, then near; and <lb/>yet it &longs;hould &longs;eem, that the &longs;ame quantity of Water pa&longs;&longs;ing by <lb/>every piace, the River &longs;hould need to have the &longs;ame altitude of <lb/>Banks in all places: But we by our Principles and fundamentals <lb/>may be able to render the rea&longs;on of that effect, and &longs;ay; That <lb/>that exce&longs;&longs;e of quantity of Water, above the ordinary Water, <lb/>goeth alwaies acquiring greater velocity; the nearer it approach­<lb/>eth the Sea, and therefore decrea&longs;eth in mea&longs;ure, and con&longs;equenly <lb/>in height. </s> <s>And this perhaps might have been the cau&longs;e in great <lb/>part, why the <emph type="italics"/>Tyber<emph.end type="italics"/> in the Innundation <emph type="italics"/>Anno<emph.end type="italics"/> 1578. i&longs;&longs;ued not <lb/>forth of its Channel below <emph type="italics"/>Rome<emph.end type="italics"/> towards the Sea.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XV.</s></p><p type="main"> <s>From the &longs;ame Doctrine may be rendred a mo&longs;t manife&longs;t rea­<lb/>&longs;on why the falling Waters go le&longs;&longs;ening in their de&longs;cent, &longs;o <lb/>that the &longs;ame falling Water, mea&longs;ured at the beginning of <lb/>its fall, is greater, and bigger, and afterwards by degrees le&longs;&longs;eneth <lb/>in mea&longs;ure the more it is remote from the beginning of the fall. <lb/></s> <s>Which dependeth on no other, than on the acqui&longs;ition, which <lb/>it &longs;ucce&longs;&longs;ively makes of greater velocity; it being a mo&longs;t fami­<lb/>liar conclu&longs;ion among Philo&longs;ophers, that grave bodies falling, <lb/>the more they remove from the beginning of their motion, the <lb/>more they acquire of &longs;wiftne&longs;&longs;e; and therefore the Water, as a <lb/>grave body, falling, gradually velocitates, and therefore de­<lb/>crea&longs;eth in mea&longs;ure, and le&longs;&longs;eneth.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/> XVI.</s></p><p type="main"> <s>And on the contrary, the &longs;pirtings of a Fountain of Water, <lb/>which &longs;pring on high, work a contrary effect; namely <pb xlink:href="040/01/586.jpg" pagenum="17"/>in the beginning they are &longs;mall, and afterwards become greater <lb/>and bigge; and the rea&longs;on is mo&longs;t manife&longs;t, becau&longs;e in the be­<lb/>ginning they are very &longs;wift, and afterwards gradually relent <lb/>their impetuo&longs;ity, and motion, &longs;o that in the beginning of the <lb/>excur&longs;ion that they make, they ought to be &longs;mall, and after­<lb/>wards to grow bigger, as in the effect is &longs;een.</s></p><p type="head"> <s>APPENDIX. I.</s></p><p type="main"> <s>Into the errour of not con&longs;idering how much the different <lb/>velocities of the &longs;ame running water in &longs;everal places of <lb/>its current, are able to change the mea&longs;ure of the &longs;ame <lb/>water, and to make it greater, or le&longs;&longs;e, I think, if I be not <lb/>deceived, that <emph type="italics"/>Ginlio Frontino<emph.end type="italics"/> a noble antient Writer, may <lb/>have faln in the Second Book which he writ, of the Aqueducts <lb/>of the City of <emph type="italics"/>Rome<emph.end type="italics"/>: Whil&longs;t finding the mea&longs;ure of the Water <lb/>^{*}<emph type="italics"/>Commentaries<emph.end type="italics"/> le&longs;&longs;e than it was <emph type="italics"/>in erogatione 1263. Quinaries,<emph.end type="italics"/> he </s></p><p type="main"> <s><arrow.to.target n="marg966"></arrow.to.target><lb/>thought that &longs;o much difference might proceed from the negligence <lb/>of the Mea&longs;ures; and when afterwards with his own indu&longs;try he <lb/>mea&longs;ured the &longs;ame water at the beginnings of the Aqueducts, <lb/>finding it neer 10000. <emph type="italics"/>Quinaries<emph.end type="italics"/> bigger than it was <emph type="italics"/>in Commenta­<lb/>riis<emph.end type="italics"/> he judged, that the overplus was imbeziled by Mini&longs;ters and <lb/>Partakers; which in part might be &longs;o, for it is but too true, that <lb/>the publique is almo&longs;t alwayes defrauded; yet neverthele&longs;&longs;e, I <lb/>verily believe withal, that be&longs;ides the frauds of the&longs;e Officers, <lb/>the velocities of the water in the place wherein <emph type="italics"/>Frontino<emph.end type="italics"/> mea&longs;u­<lb/>red, it might be different from tho&longs;e velocities, which are <lb/>found in other places before mea&longs;ured by others; and there­<lb/>fore the mea&longs;ures of the waters might, yea ought nec&longs;&longs;arily to <lb/>be diffcrent, it having been by us demon&longs;trated, that the mea­<lb/>&longs;ures of the &longs;ame running water have reciprocal proportion to <lb/>their velocities. </s> <s>Which <emph type="italics"/>Frontino<emph.end type="italics"/> not well con&longs;idering, and find­<lb/>ing the water <emph type="italics"/>in Commentariis 12755. Quinaries in erogati­<lb/>one<emph.end type="italics"/> 14018, and in his own mea&longs;ure <emph type="italics"/>ad capita ductuum,<emph.end type="italics"/> at the <lb/>head of the fountain 22755. <emph type="italics"/>Quinaries,<emph.end type="italics"/> or thereabouts, he <lb/>thought, that in all the&longs;e places there pa&longs;t different quantities of <lb/>water; namely, greater at the fountain head then that which was <lb/><emph type="italics"/>in Erogatione,<emph.end type="italics"/> and this he judged greater than that which was <lb/><emph type="italics"/>in Commentariis.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg966"></margin.target>+ <emph type="italics"/>Commentarius<emph.end type="italics"/><lb/>beareth many &longs;en­<lb/>&longs;es, but in this <lb/>place &longs;ignifieth a <lb/>certain Regi&longs;ter of <lb/>the quantities of <lb/>the Waters in the <lb/>&longs;everal publique A­<lb/>qu ducts of <emph type="italics"/>Rome<emph.end type="italics"/>; <lb/>which word I find <lb/>frequently u&longs;ed in <lb/>the Law-books of <lb/>antient Civilians: <lb/>Andby errogation <lb/>we are to under­<lb/>&longs;tand the di&longs;tribu­<lb/>tion or delivering <lb/>out of tho&longs;e &longs;tores <lb/>of Water.</s></p><p type="head"> <s>APPENDIX II.</s></p><p type="main"> <s>Alike mi&longs;take chanced lately in the Aqueduct of <emph type="italics"/>Acqua­<lb/>Paola,<emph.end type="italics"/> which Water &longs;hould be 2000 Inches, and &longs;o many <lb/>effectively ought to be allowed; and it hath been given in <pb xlink:href="040/01/587.jpg" pagenum="18"/>&longs;o to be by the Signors of <emph type="italics"/>Bracciano<emph.end type="italics"/> to the <emph type="italics"/>Apo&longs;tolick-Chamber<emph.end type="italics"/>; <lb/>and there was a mea&longs;ure thereof made at the beginning of the <lb/>Aqueduct; which mea&longs;ure proved afterwards much le&longs;&longs;e and <lb/>&longs;hort, con&longs;idered and taken in <emph type="italics"/>Rome,<emph.end type="italics"/> and thence followed di&longs;­<lb/>contents and great di&longs;orders, and all becau&longs;e this property of <lb/>Running-Waters, of increa&longs;ing in mea&longs;ure, where the velocity <lb/>decrea&longs;ed; and of dimini&longs;hing in mea&longs;ure, where the velocity <lb/>augmented, was not lookt into.</s></p><p type="head"> <s>APPENDIX III.</s></p><p type="main"> <s>Alike errour, in my judgement, hath beeen committed by <lb/>all tho&longs;e learned men, which to prevent the diver&longs;ion of <lb/>the <emph type="italics"/>Reno<emph.end type="italics"/> of <emph type="italics"/>Bologna<emph.end type="italics"/> into P<emph type="italics"/>o<emph.end type="italics"/> by the Channels, through <lb/>which it at pre&longs;ent runneth, judged, that the <emph type="italics"/>Reno<emph.end type="italics"/> being in its <lb/>greater excre&longs;cence about 2000 feet, and the P<emph type="italics"/>o<emph.end type="italics"/> being near <lb/>1000 feet broad, they judged, I &longs;ay, that letting the <emph type="italics"/>Reno<emph.end type="italics"/> into <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> it would have rai&longs;ed the Water of P<emph type="italics"/>o<emph.end type="italics"/> two feet; from which <lb/>ri&longs;e, they concluded afterwards mo&longs;t exorbitant di&longs;orders, either <lb/>of extraordinary Inundations, or el&longs;e of immen&longs;e and intolera­<lb/>ble expences to the people in rai&longs;ing the Banks of P<emph type="italics"/>o<emph.end type="italics"/> and <emph type="italics"/>Reno,<emph.end type="italics"/><lb/>and with &longs;uch like weakne&longs;&longs;es, often vainly di&longs;turbed the minds <lb/>of the per&longs;ons concerned: But now from the things demon&longs;tra­<lb/>ted, it is manife&longs;t, That the mea&longs;ure of the <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno,<emph.end type="italics"/> would <lb/>be different from the mea&longs;ure of <emph type="italics"/>Reno<emph.end type="italics"/> in P<emph type="italics"/>o<emph.end type="italics"/>; in ca&longs;e that the <lb/>velocity of the <emph type="italics"/>Reno<emph.end type="italics"/> in P<emph type="italics"/>o,<emph.end type="italics"/> &longs;hould differ from the velocity <lb/>of <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno,<emph.end type="italics"/> as is more exactly determined in the fourth Pro­<lb/>po&longs;ition.</s></p><p type="head"> <s>APPENDIX IV.</s></p><p type="main"> <s>No le&longs;s likewi&longs;e are tho&longs;e Ingeneers and Arti&longs;ts deceived, <lb/>that have affirmed, That letting the <emph type="italics"/>Reno<emph.end type="italics"/> into P<emph type="italics"/>o,<emph.end type="italics"/> there <lb/>would be no ri&longs;e at all in the Water of P<emph type="italics"/>o<emph.end type="italics"/>: For the truth <lb/>is, That letting <emph type="italics"/>Reno<emph.end type="italics"/> into P<emph type="italics"/>o,<emph.end type="italics"/> there would alwaies be a ri&longs;ing; but <lb/>&longs;ometimes greater, &longs;ometimes le&longs;&longs;e, as the P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall have a &longs;wifter <lb/>or &longs;lower Current; &longs;o that if the P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall be con&longs;tituted in a great <lb/>velocity, the ri&longs;e will be very &longs;mall; and if the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall be <lb/>&longs;low in its cour&longs;e, then the ri&longs;e will be notable.</s></p><p type="head"> <s>APPENDIX V.</s></p><p type="main"> <s>And here it will not be be&longs;ides the purpo&longs;e to adverti&longs;e, That <lb/>the mea&longs;ures, partments, and di&longs;tributions of the Waters <lb/>of Fountains, cannot be made exactly, unle&longs;s there be con­<pb xlink:href="040/01/588.jpg" pagenum="19"/>fidered, be&longs;ides the mea&longs;ure, the velocity al&longs;o of the Water; <lb/>which particular not being thorowly ob&longs;erved, is the cau&longs;e of <lb/>continual mi&longs;cariages in &longs;uch like affairs.</s></p><p type="head"> <s>APPENDIX VI.</s></p><p type="main"> <s>Like con&longs;ideration ought to be had with the greater diligence, <lb/>for that an errour therein is more prejudicial; I &longs;ay, ought to <lb/>be had by tho&longs;e which part and divide Waters; for the <lb/>watering of fields, as is done in the Territories of <emph type="italics"/>Bre&longs;cia, Ber­<lb/>gama, Crema, Pavia, Lodigiano, Cremona,<emph.end type="italics"/> and other places: <lb/>For if they have not regard to the mo&longs;t important point of the <lb/>variation of the velocity of the Water, but onely to the bare <lb/>Vulgar mea&longs;ure, there will alwaies very great di&longs;orders and pre­<lb/>judices en&longs;ue to the per&longs;ons concerned.</s></p><p type="head"> <s>APPENDIX VII.</s></p><p type="main"> <s>It &longs;eemeth that one may ob&longs;erve, that whil&longs;t the Water run­<lb/>neth along a Channel, Current, or Conduit, its velocity is <lb/>retarded, withheld, and impeded by its touching the Bank or <lb/>&longs;ide of the &longs;aid Channel or Current; which, as immoveable, not <lb/>following the motion of the Water, interrupteth its velocity: <lb/>From which particular, being true, as I believe it to be mo&longs;t <lb/>true, and from our con&longs;iderations, we have an occa&longs;ion of di&longs;­<lb/>covering a very nice mi&longs;take, into which tho&longs;e commonly fall <lb/>who divide the Waters of Fountains. </s> <s>Which divi&longs;ion is wont <lb/>to be, by what I have &longs;een here in <emph type="italics"/>Rome,<emph.end type="italics"/> performed two wayes; <lb/>The fir&longs;t of which is with the mea&longs;ures of like figures, as Cir­<lb/>cles, or Squares, having cut through a Plate of metal &longs;everal <lb/>Circles or Squares, one of half an inch, another of one inch, <lb/>another of two, of three, of four, <emph type="italics"/>&c.<emph.end type="italics"/> with which they after­<lb/>wards adju&longs;t the Cocks to di&longs;pence the Waters. </s> <s>The other <lb/>manner of dividing the Waters of Fountains, is with rectangle <lb/>paralellograms, of the &longs;ame height, but of different Ba&longs;es, in &longs;uch <lb/>&longs;ort likewi&longs;e, that one paralellogram be of half an inch, another <lb/>of one, two, three, <emph type="italics"/>&c.<emph.end type="italics"/> In which manner of mea&longs;uring and <lb/>dividing the Water, it &longs;hould &longs;eem that the Cocks being placed <lb/>in one and the &longs;ame plain, equidi&longs;tant from the level, or &longs;uperior <lb/>&longs;uperficies of the water of the Well; and the &longs;aid mea&longs;ures be­<lb/>ing mo&longs;t exactly made, the Water ought con&longs;equently al&longs;o to <lb/>be equally divided, and parted according to the proportion of <lb/>the mea&longs;ures. </s> <s>But if we well con&longs;ider every particular, we &longs;hall <lb/>finde, that the Cocks, as they &longs;ucce&longs;&longs;ively are greater, di&longs;charge <lb/>alwaies more Water than the ju&longs;t quantity, in compari&longs;on of <pb xlink:href="040/01/589.jpg" pagenum="20"/>the le&longs;&longs;er; that is, to &longs;peak more properly, The Water which <lb/>pa&longs;&longs;eth through the greater Cock, hath alwaies a greater pro­<lb/>portion to that which pa&longs;&longs;eth through the le&longs;&longs;er, than the greater <lb/>Cock hath to the le&longs;&longs;er. </s> <s>All which I will declare by an exam­<lb/>ple.</s></p><p type="main"> <s>Let there be &longs;uppo&longs;ed for more plainne&longs;s two Squares; (the <lb/>&longs;ame may be under&longs;tood of Circles, and other like Figures) The <lb/>fir&longs;t Square is, as we will &longs;uppo&longs;e, quadruple to the other, and <lb/>the&longs;e Squares are the mouths of two Cocks.; one of four inches, <lb/>the other of one: Now its manife&longs;t by what hath been &longs;aid, that <lb/>the Water which pa&longs;&longs;eth by the le&longs;s Cock, findeth its velocity <lb/>impeded in the circumference of the Cock; which impediment <lb/><figure id="id.040.01.589.1.jpg" xlink:href="040/01/589/1.jpg"/><lb/>is mea&longs;ured by the &longs;aid circumfe­<lb/>rence. </s> <s>Now it is to be con&longs;ider­<lb/>ed, that if we would have the Wa­<lb/>ter which pa&longs;&longs;eth through the <lb/>greater Cock, to be onely qua­<lb/>druple to that which pa&longs;&longs;eth <lb/>through the le&longs;&longs;e, in equal &longs;paces of time, it would be nece&longs;&longs;ary, <lb/>that not onely the capacity and the mea&longs;ure of the greater Cock <lb/>be quadruple to the le&longs;&longs;er Cock, but that al&longs;o the impediment be <lb/>quadrupled. </s> <s>Now in our ca&longs;e it is true, That the belly and <lb/>mouth of the Cock is quadrupled, and yet the impediment is not <lb/>quadrupled, but is onely doubled; &longs;eeing that the circumference <lb/>of the greater Square, is onely double to the circumference of <lb/>the le&longs;ier Square; for the greater circumference containeth eight <lb/>of tho&longs;e parts, of which the le&longs;&longs;er containeth but four, as is ma­<lb/>nife&longs;t by the de&longs;cribed Figure; and for that cau&longs;e there &longs;hall <lb/>pa&longs;s by the greater Cock, above four times as much Water, as <lb/>&longs;hall pa&longs;s by the le&longs;&longs;er Cock.</s></p><p type="main"> <s>The like errour occurreth al&longs;o in the other manner of mea&longs;u­<lb/>ring the Water of a Fountain, as may ea&longs;ily be collected from <lb/>what hath been &longs;aid and ob&longs;erved above.</s></p><p type="head"> <s>APPENDIX VIII.</s></p><p type="main"> <s>The &longs;ame contemplation di&longs;covereth the errour of tho&longs;e <lb/>Architects, who being to erect a Bridge of &longs;undry Arches <lb/>over a River, con&longs;ider the ordinary breadth of the River; <lb/>which being <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> fourty fathom, and the Bridge being to con&longs;i&longs;t <lb/>of four Arches, it &longs;ufficeth them, that the breadth of all the four <lb/>Arches taken together, be fourty fathom; not con&longs;idering that <lb/>in the ordinary Channel of the River, the Water hath onely <lb/>two impediments which retard its velocity; namely, the touching <lb/>and gliding along the two &longs;ides or &longs;hores of the River: but <pb xlink:href="040/01/590.jpg" pagenum="21"/>the &longs;ame water in pa&longs;&longs;ing under the Bridge, in our ca&longs;e meeteth <lb/>with eight of the &longs;ame impediments, bearing, and thru&longs;ting upon <lb/>two &longs;ides of each Arch (to omit the impediment of the bottom, <lb/>for that it is the &longs;ame in the River, and under the Bridge) from <lb/>which inadvertency &longs;ometimes follow very great di&longs;orders, as <lb/>quotidian practice &longs;hews us.</s></p><p type="head"> <s>APPENDIX IX.</s></p><p type="main"> <s>It is al&longs;o worthy to con&longs;ider the great and admirable benefit <lb/>that tho&longs;e fields receive, which are wont to drink up the Rain­<lb/>water with difficulty, through the height of the water in the <lb/>principal Ditches; in which ca&longs;e the careful Husbandman cutteth <lb/>away the reeds and ru&longs;hes in the Ditches, through which the <lb/>waters pa&longs;s; whereupon may be pre&longs;ently &longs;een, &longs;o &longs;oon as the <lb/>reeds and ru&longs;hes are cut, a notable Ebb in the level of the water <lb/>in the Ditches; in&longs;omuch that &longs;ometimes it is ob&longs;erved, that the <lb/>water is abated after the &longs;aid cutting a third and more, of what it <lb/>was before the cutting. </s> <s>The which effect &longs;eemingly might de­<lb/>pend on this, That, before tho&longs;e weeds took up room in the <lb/>Ditch, and for that cau&longs;e the water kept a higher level, and the <lb/>&longs;aid Plants being afterwards cut and removed, the water came to <lb/>abate, po&longs;&longs;e&longs;&longs;ing the place that before was occupied by the <lb/>weeds: Which opinion, though probable, and at fir&longs;t &longs;ight &longs;a­<lb/>tisfactory, is neverthele&longs;s in&longs;ufficient to give the total rea&longs;on of <lb/>that notable abatement which hath been &longs;poken of: But it is ne­<lb/>ce&longs;&longs;ary to have recour&longs;e to our confideration of the velocity in <lb/>the cour&longs;e of the water, the chiefe&longs;t and true cau&longs;e of the vari­<lb/>ation of the mea&longs;ure of the &longs;ame Running-Water; for, that <lb/>multitudes of reeds, weeds, and plants di&longs;per&longs;ed through the cur­<lb/>rent of the Ditch, do chance notably to retard the cour&longs;e of the <lb/>water, and therefore the mea&longs;ure of the water increa&longs;eth; and <lb/>tho&longs;e impediments removed, the &longs;ame water gaineth velocity, <lb/>and therefore decrea&longs;eth in mea&longs;ure, and con&longs;equently in <lb/>height.</s></p><p type="main"> <s>And perhaps this point well under&longs;tood, may be of great <lb/>profit to the fields adjacent to the <emph type="italics"/>Pontine<emph.end type="italics"/> Fens, and I doubt not <lb/>but if the River <emph type="italics"/>Ninfa,<emph.end type="italics"/> and the other principal Brooks of tho&longs;e <lb/>Territories were kept well clean&longs;ed from weeds, their waters <lb/>would be at a lower level, and con&longs;equently the drains of the <lb/>fields would run into them more readily; it being alwayes to be <lb/>held for undoubted, that the mea&longs;ure of the water before the <lb/>clean&longs;ing, hath the &longs;ame proportion to the mea&longs;ure after clean­<lb/>&longs;ing, that the velocity after the clean&longs;ing hath to the velocity <lb/>before the clean&longs;ing: An dbecau&longs;e tho&longs;e weeds being clean&longs;ed <pb xlink:href="040/01/591.jpg" pagenum="22"/>away, the cour&longs;e ef the water notably increa&longs;eth, it is therefore <lb/>nece&longs;&longs;ary that the &longs;aid water abate in mea&longs;ure, and become <lb/>lower.</s></p><p type="head"> <s>APPENDIX. X.</s></p><p type="main"> <s>We having above ob&longs;erved &longs;ome errors that are commit­<lb/>ted in di&longs;tributing the waters of Fountains, and tho&longs;e <lb/>that &longs;erve to water fields; it &longs;eemeth now fit, by way of <lb/>a clo&longs;e to this di&longs;cour&longs;e, to adverti&longs;e by what means the&longs;e divi­<lb/>&longs;ions may be made ju&longs;tly and without error. </s> <s>I therefore think <lb/>that one might two &longs;everal wayes exqui&longs;itly divide the water of <lb/>Fountains; The fir&longs;t would be by diligently examining, Fir&longs;t, <lb/>how much water the whole Fountain di&longs;chargeth in a determi­<lb/>nate time, as for in&longs;tance: How many Barrels, or Tuns it carri­<lb/>eth in a &longs;et time; and in ca&longs;e you are afterwards to di&longs;tribute <lb/>the water, di&longs;tribute it at the rate of &longs;omany Barrels or Tuns, in <lb/>that &longs;ame time; and in this ca&longs;e the participants would have <lb/>their punctual &longs;hares: Nor could it ever happen to &longs;end out more <lb/>water, than is reckoned to be in the principal Fountain; as befel <lb/><emph type="italics"/>Giulio Frontino,<emph.end type="italics"/> and as al&longs;o it frequently happeneth in the Mo­<lb/>dern Aqueducts, to the publick and private detriment.</s></p><p type="main"> <s>The other way of dividing the &longs;ame waters of a Fountain, is <lb/>al&longs;o &longs;ufficiently exact and ea&longs;ie, and may be, by having one one­<lb/>ly &longs;ize for the Cock or Pipe, as &longs;uppo&longs;e of an inch, or of half an <lb/>inch; and when the ca&longs;e requireth to di&longs;pence two, three, and <lb/>more inches, take &longs;o many Cocks of the &longs;aid mea&longs;ure as do eva­<lb/>cuate the water, which is to be emitted; and if we are to make <lb/>u&longs;e onely of one greater Cock, we being to place one to di&longs;­<lb/>charge for example four inches; and having the former &longs;ole mea­<lb/>&longs;ure of an inch, we mu&longs;t make a Cock that is bigger, its true, than <lb/>the Cock of one inch; but not &longs;imply in a quadruple propor­<lb/>tion, for that it would di&longs;charge more than ju&longs;t &longs;o much water, <lb/>as hath been &longs;aid above; but we ought to examine diligently <lb/>how much water the little Cock emitteth in an hour; and then <lb/>enlarge, and contract the greater Cock, &longs;o, that it may di&longs;­<lb/>charge four times as much water as the le&longs;&longs;er in the &longs;ame time; <lb/>and by this means we &longs;hall avoid the di&longs;order hinted in the <lb/>&longs;eventh Appendix. </s> <s>It would be nece&longs;&longs;ary neverthele&longs;s, to ac­<lb/>commodate the Cocks of the Ci&longs;tern &longs;o, that the level of the <lb/>water in the Ci&longs;tern may alwayes re&longs;t at one determinate mark <lb/>above the Cock, otherwi&longs;e the Cocks will emit &longs;ometimes <lb/>greater, and &longs;ometimes le&longs;&longs;e abundance of water: And becau&longs;e <lb/>it may be that the &longs;ame water of the Fountain may be &longs;ometimes <lb/>more abundant, &longs;ometimes le&longs;s; in &longs;uch ca&longs;e it will be nece&longs;&longs;ary <pb xlink:href="040/01/592.jpg" pagenum="23"/>to adju&longs;t the Ci&longs;tern &longs;o, that the exce&longs;s above the ordinary wa­<lb/>ter, di&longs;charge into the publick Fountains, that &longs;o the particular <lb/>participants may have alwayes the &longs;ame abundance of <lb/>water.</s></p><p type="head"> <s>APPENDIX XI.</s></p><p type="main"> <s>Much more difficult is the divi&longs;ion of the waters which <lb/>&longs;erve to water the fields, it not being po&longs;&longs;ible to ob&longs;erve <lb/>&longs;o commodiou&longs;ly, what quantity of water the whole <lb/>Ditch &longs;ends forth in one determinate time, as may be done in <lb/>Fountains: Yet neverthele&longs;s, if the &longs;econd propo&longs;ition by us a <lb/>little below demon&longs;trated, be well under&longs;tood, there may be <lb/>thence taken a very &longs;afe and ju&longs;t way to di&longs;tribute &longs;uch waters. <lb/></s> <s>The Propo&longs;ition therefore by us demon&longs;trated is this: If there <lb/>be two Sections, (namely two mouths of Rivers) the quantity of <lb/>the water which pa&longs;&longs;eth by the fir&longs;t, hath a proportion to that <lb/>which pa&longs;&longs;eth by the &longs;econd, compounded of the proportions of <lb/>the fir&longs;t Section to the &longs;econd, and of the velocity through <lb/>the fir&longs;t, to the velocity through the &longs;econd: As I will declare <lb/>for example by help of practice, that I may be under&longs;tood by <lb/>all, in a matter &longs;o important. </s> <s>Let the two mouths of the <lb/>Rivers be A, and B, and let <lb/><figure id="id.040.01.592.1.jpg" xlink:href="040/01/592/1.jpg"/><lb/>the mouth A be in mea&longs;ure <lb/>and content thirty two feet, <lb/>and the mouth B, eight feet. <lb/></s> <s>Here you mu&longs;t take notice, <lb/>that it is not alwayes true, that <lb/>the Water which pa&longs;&longs;eth by A, <lb/>hath the &longs;ame proportion to that which pa&longs;&longs;eth by B, that the <lb/>mouth A hath to the mouth B; but onely when the velocityes <lb/>by each of tho&longs;e pa&longs;&longs;ages are equal: But if the velocityes &longs;hall <lb/>be unequal, it may be that the &longs;aid mouths may emit equal <lb/>quantity of Water in equal times, though their mea&longs;ure be un­<lb/>equal; and it may be al&longs;o, that the bigger doth di&longs;charge a great­<lb/>er quantity of Water: And la&longs;tly, it may be, that the le&longs;s mouth <lb/>di&longs;chargeth more Water than the greater; and all this is mani­<lb/>fe&longs;t by the things noted in the beginning of this di&longs;cour&longs;e, and <lb/>by the &longs;aid &longs;econd Propo&longs;ition. </s> <s>Now to examine the propor­<lb/>tion of the Water that pa&longs;&longs;eth by one Ditch, to that which pa&longs;­<lb/>&longs;eth by another, that this being known, the &longs;ame Waters and <lb/>mouths of Ditches may be then adju&longs;ted; we are to keep ac­<lb/>count not onely of the greatne&longs;s of the mouths or pa&longs;&longs;ages of the <lb/>Water, but of the velocity al&longs;o; which we will do, by fir&longs;t find­<lb/>ing two numbers that have the &longs;ame proportion between them­<pb xlink:href="040/01/593.jpg" pagenum="24"/>&longs;elves, as have the mouths, which are the numbers 32 and 8 <lb/>in our example: Then this <lb/><figure id="id.040.01.593.1.jpg" xlink:href="040/01/593/1.jpg"/><lb/>being done, let the velocity <lb/>of the Water by the pa&longs;&longs;a­<lb/>ges A and B, be examined <lb/>(which may be done keeping <lb/>account what &longs;pace a piece <lb/>of Wood, or other body that <lb/>&longs;wimmeth, is carried by the &longs;tream in one determinate time; as <lb/>for in&longs;tance in 50 pul&longs;es) and then work by the golden Rule, as <lb/>the velocity by A, is to the velocity by B, &longs;o is the number 8, to <lb/>another number, which is 4. It is clear by what is demon&longs;tra­<lb/>ted in the &longs;aid &longs;econd Propo&longs;ition, that the quantity of water, <lb/>which pa&longs;&longs;eth by the mouth A, &longs;hall have the &longs;ame proportion of <lb/>that which pa&longs;&longs;eth by the mouth B, that 8 hath to 1. Such pro­<lb/>portion being compo&longs;ed of the proportions of 32 to 8, and of 8 to <lb/>4; namely, tothe greatne&longs;s of the mouth A, to the greatne&longs;s of the <lb/>mouth B, and of the velocity in A, to the velocity in B. </s> <s>This being <lb/>done, we mu&longs;t then contract the mouth which di&longs;chargeth more <lb/>then its ju&longs;t quantity of water, or enlarge the other which di&longs;char­<lb/>geth le&longs;s, as &longs;hal be mo&longs;t commodious in practice, which to him that <lb/>hath under&longs;tood this little that hath been delivered, will be very <lb/>afie.</s></p><p type="head"> <s>APPENDIX XII.</s></p><p type="main"> <s>The&longs;e opperations about Water, as I have hitherto on &longs;un­<lb/>dry occa&longs;ions ob&longs;erved, are involved in &longs;o many difficul­<lb/>ties, and &longs;uch a multiplicity of mo&longs;t extravagant accidents, <lb/>that it is no marvel if continually many, and very important er­<lb/>rours be therein committed by many, and even by Ingeneers <lb/>them&longs;elves, and Learned-men; and becau&longs;e many times they <lb/>concern not onely the publique, but private intere&longs;ts: Hence it <lb/>is, that it not onely belongeth to Arti&longs;ts to treat thereof, but very <lb/>oft even the vulgar them&longs;elves pretend to give their judgement <lb/>therein: And I have been troubled many times with a nece&longs;&longs;ity <lb/>of treating, not onely with tho&longs;e, which either by practice, or <lb/>particular &longs;tudy, under&longs;tood &longs;omewhat in the&longs;e matters; but al&longs;o <lb/>with people wholly void of tho&longs;e notions, which are nece&longs;&longs;ary for <lb/>one that would on good grounds di&longs;cour&longs;e about this particular; <lb/>and thus many times have met with more difficulty in the thick <lb/>skulls of men, than in precipitous Torrents, and va&longs;t Fennes. <lb/></s> <s>And in particular, I had occafion &longs;ome years pa&longs;t to go &longs;ee the <lb/>Gave or Emi&longs;&longs;ary of the Lake of <emph type="italics"/>Perugia,<emph.end type="italics"/> made many years agon <lb/>by <emph type="italics"/>Braccio Fortobraccio,<emph.end type="italics"/> but for that it was with great ruines by <lb/>Time decayed, and rendred unu&longs;eful, it was repaired with in­<pb xlink:href="040/01/594.jpg" pagenum="25"/>du&longs;try truly heroicall and admirable, by Mon&longs;ignor <emph type="italics"/>Maffei Bar­<lb/>herino,<emph.end type="italics"/> then Prefect for the Wayes, and now Pope. </s> <s>And being <lb/>nece&longs;&longs;itated, that I might be able to walk in the Cave, and for <lb/>other cau&longs;es, I let down the Sluices of the &longs;aid Cave, at the mouth <lb/>of the Lake: No &longs;ooner were they &longs;topt, but a great many of the <lb/>people of the Towns and Villages coa&longs;ting upon the <emph type="italics"/>L<emph.end type="italics"/>ake <lb/>flocking thither, began to make grievous complaints, that if tho&longs;e <lb/>Sluices were kept &longs;hut, not onely the Lake would want its due <lb/>Vent, but al&longs;o the parts adjacent to the Lake would be over <lb/>flown to their very great detriment. </s> <s>And becau&longs;e at fir&longs;t appea­<lb/>rance their motion &longs;eemed very rea&longs;onable, I found my &longs;elf hard <lb/>put to it, &longs;eeing no way to per&longs;wade &longs;uch a multitude, that the <lb/>prejudice which they pretended I &longs;hould do them by keeping <lb/>the Sluices &longs;hut for two dayes, was ab&longs;olutely in&longs;en&longs;ible; and that <lb/>by keeping them open, the Lake did not ebb in the &longs;ame time &longs;o <lb/>much as the thickne&longs;s of a &longs;heet of Paper: And therefore I was <lb/>nece&longs;&longs;itated to make u&longs;e of the authority I had, and &longs;o followed <lb/>my bu&longs;ine&longs;s as cau&longs;e required, without any regard to that Rab­<lb/>ble tumultuou&longs;ly a&longs;&longs;embled. </s> <s>Now when I am not working with <lb/>Mattock or Spade, but with the Pen and Di&longs;cour&longs;e, I intend to <lb/>demon&longs;trate clearly to tho&longs;e that are capable of rea&longs;on, and that <lb/>have well under&longs;tood the ground of this my Treati&longs;e, that the <lb/>fear was altogether vain which tho&longs;e people conceited. </s> <s>And <lb/>therefore I &longs;ay, that the Emi&longs;&longs;ary or Sluice of the Lake of <emph type="italics"/>Peru­<lb/>gia,<emph.end type="italics"/> &longs;tanding in the &longs;ame mannner as at pre&longs;ent, and the water <lb/>pa&longs;&longs;ing thorow it with the &longs;ame velocity as now; to examine <lb/>how much the Lake may abate in two days &longs;pace, we ought to <lb/>con&longs;ider, what proportion the &longs;uperficies of the whole Lake hath <lb/>to the mea&longs;ure of the Section of the Emi&longs;&longs;ary, and afterwards to <lb/>infer, that the velocity of the water by the Emi&longs;&longs;ary or Sluice, <lb/>&longs;hall have the &longs;ame proportion to the abatement of the Lake, <lb/>and to prove thorowly and clearly this di&longs;cour&longs;e, I intend to <lb/>demon&longs;trate the following Propo&longs;ition.</s></p><p type="main"> <s>Suppo&longs;e a Ve&longs;&longs;el of any bigne&longs;&longs;e, and that it hath an Emi&longs;&longs;ary <lb/>or Cock, by which it di&longs;chargeth its water. </s> <s>And look what pro­<lb/>portion the &longs;uper&longs;icies of the <lb/>ve&longs;&longs;el hath to the mea&longs;ure of <lb/><figure id="id.040.01.594.1.jpg" xlink:href="040/01/594/1.jpg"/><lb/>the &longs;ection of the cock, &longs;uch pro­<lb/>portion &longs;hall the velocity of the <lb/>Water in the Cock have to the <lb/>abatement of the Lake Let the <lb/>Ve&longs;&longs;el be A B C D, H I L B, through which the Water runneth, <lb/>the &longs;uperficies of the Water in the Ve&longs;&longs;el A D, and the &longs;ection <lb/>of the Cock H L: and let the Water in the Ve&longs;&longs;el <lb/>be &longs;uppo&longs;ed to have falne in one determinate time from A to F. <pb xlink:href="040/01/595.jpg" pagenum="26"/>I &longs;ay that the proportion of the &longs;uperficies of the Ve&longs;&longs;el A D is <lb/>in proportion to the mea&longs;ure of the &longs;ection of the Emi&longs;&longs;ary <lb/>H L, as the velocity of the Emi&longs;&longs;ary or Cock to the line A F; <lb/>which is manife&longs;t, for that the Water in the Ve&longs;sel moving by <lb/>the line A F; as far as F, and the whole ma&longs;s of Water A G <lb/>di&longs;charging it &longs;elf, and in the &longs;ame time the &longs;ame quantity of <lb/>Water being di&longs;charged by the &longs;ection of the Emi&longs;&longs;ary H L; it <lb/>is nece&longs;&longs;ary by what I have demon&longs;trated in the third Propo&longs;ition, <lb/>and al&longs;o explained in the beginning of this Treati&longs;e, that the ve­<lb/>locity by the Emi&longs;&longs;ary or Cock be in proportion to the velocity <lb/>of the abatement, as the &longs;uperficies of the Ve&longs;&longs;el to the mea­<lb/>&longs;ure of the &longs;ection of the Emi&longs;&longs;ary, which was to be demon­<lb/>&longs;trated.</s></p><p type="main"> <s>That which hath been demon&longs;trated in the Ve&longs;&longs;el, falls out ex­<lb/>actly al&longs;o in our Lake of <emph type="italics"/>Perugia,<emph.end type="italics"/> and its Emi&longs;sary; and becau&longs;e <lb/>the immen&longs;ity of the &longs;uperficies of the Lake is in proportion to <lb/>the &longs;uperficies of the Emi&longs;sary or Sluice, as many millions to <lb/>one, as may be ea&longs;ily calculated; it is manife&longs;t, that &longs;uch abate­<lb/>ment &longs;hall be imperceptible, and almo&longs;t nothing, in two dayes <lb/>&longs;pace, nay in four or &longs;ix: and all this will be true, when we <lb/>&longs;uppo&longs;e that for that time there entreth no other Water into the <lb/>Lake from Ditches or Rivolets, which falling into the Lake would <lb/>render &longs;uch abatement yet le&longs;s.</s></p><p type="main"> <s>Now we &longs;ee, that it's nece&longs;sary to examine &longs;uch abatements <lb/>and ri&longs;ings, with excellent rea&longs;ons, or at lea&longs;t, with accurate ex­<lb/>periments, before we re&longs;olve and conclude any thing; and how <lb/>farre the vulgar are di&longs;tant from a right judgment in &longs;uch <lb/>matters.</s></p><p type="head"> <s>APPENDIX XIII.</s></p><p type="main"> <s>For greater confirmation of all this which I have &longs;aid, I <lb/>will in&longs;tance in another like ca&longs;e, which al&longs;o I met with here­<lb/>tofore, wherein, for that the bu&longs;ine&longs;s was not rightly un­<lb/>der&longs;tood, many di&longs;orders, va&longs;t expences, and con&longs;iderable mi&longs;­<lb/>chiefs have followed. </s> <s>There was heretofore an Emi&longs;sary or <lb/>Sluice made to drain the Waters, which from Rains, Springs, and <lb/>Rivolets fall into a Lake; to the end, the &longs;hores adjoyning on <lb/>the Lake, &longs;hould be free from the overflowing of the Waters; <lb/>but becau&longs;e perhaps the enterprize was not well managed and <lb/>carried on, it fell out, that the Fields adjacent to the &longs;aid Chanel <lb/>could not drain, but continued under water; to which di&longs;orders <lb/>a pre&longs;ent remedy hath been u&longs;ed, namely, in a time convenient <lb/>to &longs;top up the Sluice, by meanes of certain Floodgates kept on <lb/>purpo&longs;e for that end; and thus abating the Level of the Water <pb xlink:href="040/01/596.jpg" pagenum="27"/>in the Emi&longs;&longs;ary, in the &longs;pace of three or four dayes, the Fields <lb/>have been haply drained. </s> <s>But on the other part, the proprietors <lb/>bordering on the Lake oppo&longs;ed this, grievou&longs;ly complaining, that <lb/>whil&longs;t the Floodgates are &longs;hut, and the cour&longs;e of the Water of <lb/>the Sluice hindered, the Lake overflowes the Lands adjacent, by <lb/>meanes of the Rivers that fell into it, to their very great damage; <lb/>and &longs;o continuing their &longs;uits, they got more of vexation than &longs;a­<lb/>tisfaction. </s> <s>Now, being asked my opinion herein, I judged it <lb/>requi&longs;ite (&longs;ince the point in controver&longs;ie was about the ri&longs;ing <lb/>and falling of the Lake) that the &longs;aid abatement, when the <lb/>Floodgates are open, and increa&longs;e when they are &longs;hut &longs;hould be <lb/>exactly mea&longs;ured, and told them, that it might be ea&longs;ily done at <lb/>a time when no extraordinary Waters fell into the Lake, neither <lb/>of Rain, or otherwi&longs;e; and the Lake was undi&longs;turbed by winds <lb/>that might drive the Water to any &longs;ide, by planting neer to an <lb/>I&longs;let, which is about the middle of the Lake, a thick po&longs;t, on <lb/>which &longs;hould be made the marks of the Lakes ri&longs;ing and falling <lb/>for two or three dayes. </s> <s>I would not, at that time, pawn, or re­<lb/>&longs;olutely declare, my judgment, in regard I might be, by divers <lb/>accidents mi&longs;led. </s> <s>But this I told them, that (by what I have <lb/>demon&longs;trated, and particularly that which I have &longs;aid above <lb/>touching the Lake of <emph type="italics"/>Perugia<emph.end type="italics"/>) I inclined greatly to think, <lb/>that the&longs;e ri&longs;ings and fallings would prove imperceptible, and <lb/>incon&longs;iderable; and therefore, that in ca&longs;e experience &longs;hould <lb/>make good my rea&longs;on, it would be to no purpo&longs;e for them to <lb/>continue di&longs;puting and wrangling, which cau&longs;eth, (according <lb/>to the Proverb) <emph type="italics"/>A great deal of cry,<emph.end type="italics"/> but produceth not much <lb/><emph type="italics"/>Wool.<emph.end type="italics"/></s></p><p type="main"> <s>La&longs;tly, it importing very much to know what a Rain conti­<lb/>nued for many dayes can do in rai&longs;ing the&longs;e Lakes, I will here in­<lb/>&longs;ert the Copy of a Letter, which I writ formerly to <emph type="italics"/>Signior Ga­<lb/>lilæo Galilæi,<emph.end type="italics"/> chief Philo&longs;opher to the Grand Duke of <emph type="italics"/>Tu&longs;cany,<emph.end type="italics"/><lb/>wherein I have delivered one of my conceits in this bu&longs;ine&longs;&longs;e, and <lb/>it may be, by this Letter, I may, more &longs;trongly, confirm what I <lb/>have &longs;aid above.</s></p><pb xlink:href="040/01/597.jpg" pagenum="28"/><p type="main"> <s><emph type="italics"/>The Copy of a Letter to<emph.end type="italics"/> Signore GALILÆO <lb/>GALILÆI, <emph type="italics"/>Chief Philo&longs;opher to the mo&longs;t Serene <lb/>Great Duke of TVSCANY.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Worthy and mo&longs;t Excellent<emph.end type="italics"/> SIR,</s></p><p type="main"> <s>In &longs;atisfaction of my promi&longs;e, in my former Letters of <lb/>repre&longs;enting unto you &longs;ome of my Con&longs;iderations <lb/>made upon the Lake <emph type="italics"/>Thra&longs;imeno,<emph.end type="italics"/> I &longs;ay, That in times <lb/>pa&longs;t, being in <emph type="italics"/>Perugia,<emph.end type="italics"/> where we held our General <lb/>Convention, having under&longs;tood that the Lake <emph type="italics"/>Thra&longs;imeno,<emph.end type="italics"/> by <lb/>the great drought of many Moneths was much abated, It came <lb/>into my head, to go privately and &longs;ee this novelty, both for my <lb/>particular &longs;atisfaction, as al&longs;o that might I be able to relate the <lb/>whole to my Patrons, upon the certitude of my own &longs;ight of the <lb/>place. </s> <s>And &longs;o being come to the Emi&longs;&longs;ary of the Lake, I found <lb/>that the Level of the Lakes &longs;urface was ebbed about five Ro­<lb/>man Palmes of its wonted watermark, in&longs;omuch that it was lower <lb/>than the tran&longs;ome of the mouth of the Emi&longs;&longs;ary, by the length <lb/>of ----------------------------this de&longs;cribed line, and there­<lb/>fore no Water i&longs;&longs;ued out of the Lake, to the great prejudice of <lb/>all the places and villages circumjacent, in regard that the Wa­<lb/>ter which u&longs;ed to run from the &longs;aid Lake turned 22 Mills, which <lb/>not going, nece&longs;&longs;itated the inhabitants of tho&longs;e parts to go a <lb/>dayes journey and more, to grinde upon the <emph type="italics"/>Tiber.<emph.end type="italics"/> Being retur­<lb/>ned to <emph type="italics"/>Perugia,<emph.end type="italics"/> there followed a Rain, not very great, but con­<lb/>&longs;tant, and even, which la&longs;ted for the &longs;pace of eight hours, or <lb/>thereabouts; and it came into my thoughts to examine, being <lb/>in <emph type="italics"/>Perugia,<emph.end type="italics"/> how much the Lake was increa&longs;ed and railed by this <lb/>Rain, &longs;uppo&longs;ing (as it was probable enough) that the Rain had <lb/>been univer&longs;al over all the Lake; and like to that which fell in <lb/><emph type="italics"/>Perugia,<emph.end type="italics"/> and to this purpo&longs;e I took a Gla&longs;&longs;e formed like a Cy­<lb/>linder, about a palme high, and half a palme broad; and having <lb/>put in water &longs;nfficient to cover the bottome of the Gla&longs;&longs;e, I no­<lb/>ted diligently the mark of the height of the Water in the Gla&longs;&longs;e, <lb/>and afterwards expo&longs;ed it to the open weather, to receive the <lb/>Raine-water, which fell into it; and I let it &longs;tand for the <lb/>&longs;pace of an hour; and having ob&longs;erved that in that time the Wa­<lb/>ter was ri&longs;en in the Ve&longs;&longs;el the height of the following line---, <lb/>I con&longs;idered that if I had expo&longs;ed to the &longs;ame rain &longs;uch other ve&longs;­<lb/>&longs;els equal to that, the Water would have ri&longs;en in them all accor­<lb/>ding to that mea&longs;ure: And thereupon concluded, that al&longs;o in all <pb xlink:href="040/01/598.jpg" pagenum="29"/>the whole extent of the Lake, it was nece&longs;&longs;ary the Water &longs;hould <lb/>be rai&longs;ed in the &longs;pace of an hour the &longs;ame mea&longs;ure. </s> <s>Yet here I <lb/>con&longs;idered two difficulties that might di&longs;tutb and altar &longs;uch an <lb/>effect, or at lea&longs;t render it inob&longs;erveable, which afterwards well <lb/>weighed, and re&longs;olved, left me (as I will tell you anon) in the <lb/>conclu&longs;ion the more confirmed; that the Lake ought to be in­<lb/>crea&longs;ed in the &longs;pace of eight hours, that the rain la&longs;ted eight <lb/>times that mea&longs;ure. </s> <s>And whil&longs;t I again expo&longs;ed the Gla&longs;s to re­<lb/>peat the experiment, there came unto me an Ingeneer to talk <lb/>with me touching certain affairs of our Mona&longs;tary of <emph type="italics"/>Perugia,<emph.end type="italics"/> and <lb/>di&longs;cour&longs;ing with him, I &longs;hewed him the Gla&longs;s out at my Cham­<lb/>ber-window, expo&longs;ed in a Court-yard; and communicated to <lb/>him my fancy, relacing unto him all that I had done. </s> <s>But I <lb/>&longs;oon perceived that this brave fellow conceited me to be but of <lb/>a dull brain, for he &longs;milling &longs;aid unto me; Sir, you deceive <lb/>your &longs;elf: I am of opinion that the Lake will not be increa&longs;­<lb/>ed by this rain, &longs;o much as the thickne&longs;&longs;e of a ^{*} <emph type="italics"/>Julio.<emph.end type="italics"/><lb/><arrow.to.target n="marg967"></arrow.to.target><lb/>Hearing him pronounce this his opinion with freene&longs;s and <lb/>confidence, I urged him to give me &longs;ome rea&longs;on for what he <lb/>&longs;aid, a&longs;&longs;uring him, that I would change my judgement, when I <lb/>&longs;aw the &longs;trength of his Arguments: To which he an&longs;wered, that <lb/>he had been very conver&longs;ant about the Lake, and was every day <lb/>upon it, and was well a&longs;&longs;ured that it was not at all increa&longs;ed. </s> <s>And <lb/>importuning him further, that he would give me &longs;ome rea&longs;on <lb/>for his &longs;o thinking, he propo&longs;ed to my con&longs;ideration the great <lb/>drought pa&longs;&longs;ed, and that that &longs;ame rain was nothing for the <lb/>great parching: To which I an&longs;wered, I believe Sir that the &longs;ur­<lb/>face of the Lake, on which the rain had fallen was moi&longs;tned; and <lb/>therefore &longs;aw not how its drought, which was nothing at all, <lb/>could have drunk up any part of the rain. </s> <s>For all this he per­<lb/>&longs;i&longs;ting in his conceit, without yielding in the lea&longs;t to my allega­<lb/>tion; he granted in the end (I believe in civility to me) that <lb/>my rea&longs;on was plau&longs;ible and good, but that in practi&longs;e it could <lb/>not hold. </s> <s>At la&longs;t to clear up all, I made one be called, and <lb/>&longs;ent him to the mouth of the Emi&longs;&longs;ary of the Lake, with order <lb/>to bring me an exact account, how he found the water of the <lb/>Lake, in re&longs;pect of the Tran&longs;ome of the Sluice. </s> <s>Now here, <lb/>Signore <emph type="italics"/>Galilo,<emph.end type="italics"/> I would not have you think that I had brought <lb/>the matter in hand to concern me in my honour; but believe me <lb/>(and there are witne&longs;&longs;es of the &longs;ame &longs;till living) that my me&longs;&longs;en­<lb/>ger returning in the evening to <emph type="italics"/>Perugia,<emph.end type="italics"/> he brought me word, <lb/>that the water of the Lake began to run through the Cave; and <lb/>that it was ri&longs;en almo&longs;t a fingers breadth above the Tran&longs;ome: <lb/>In&longs;omuch, that adding this mea&longs;ure, to that of the lowne&longs;s of <lb/>the &longs;urface of the Lake, beneath the Tran&longs;ome before the rain, <pb xlink:href="040/01/599.jpg" pagenum="30"/>it was manife&longs;t that the ri&longs;ing of the Lake cau&longs;ed by the rain, was <lb/>to a hair tho&longs;e four fingers breadth that I had judged it to be. <lb/></s> <s>Two dayes after I had another bout with the Ingeneer, and re­<lb/>lated to him the whole bu&longs;ine&longs;s, to which he knew not what to <lb/>an&longs;wer.</s></p><p type="margin"> <s><margin.target id="marg967"></margin.target>* A Coyn of Pope <lb/><emph type="italics"/>Julius<emph.end type="italics"/> worth &longs;ix <lb/>pence.</s></p><p type="main"> <s>Now the two difficulties which I thought of, able to impede <lb/>my conclu&longs;ion, were the&longs;e following: Fir&longs;t, I con&longs;idered that <lb/>it might be, that the Wind blowing from the &longs;ide where the <lb/>Sluice &longs;tood, to the Lake-ward; the mole and ma&longs;s of the Wa­<lb/>ter of the Lake might be driven to the contrary &longs;hore; on which <lb/>the Water ri&longs;ing, it might be fallen at the mouth of the Emi&longs;&longs;a­<lb/>ry, and &longs;o the ob&longs;ervation might be much ob&longs;cured. </s> <s>But this <lb/>difficulty wholly vani&longs;hed by rea&longs;on of the Aires great tranqui­<lb/>lity; which it kept at that time, for no Wind was &longs;tirring on any <lb/>&longs;ide, neither whil&longs;t it rained, nor afterwards.</s></p><p type="main"> <s>The &longs;econd difficulty which put the ri&longs;ing in doubt, was, That <lb/>having ob&longs;erved in <emph type="italics"/>Florence,<emph.end type="italics"/> and el&longs;ewhere, tho&longs;e Ponds into <lb/>which the rain-water, falling from the hou&longs;e, is conveyed <lb/>through the Common-&longs;hores: And that they are not thereby <lb/>ever filled, but that they &longs;wallow all that abundance of water, <lb/>that runs into them by tho&longs;e conveyances which &longs;erve them with <lb/>water; in&longs;omuch that tho&longs;e conveyances which in time of <lb/>drought maintain the Pond, when there comes new abundance <lb/>of water into the Pond, they drink it up, and &longs;wallow it: A like <lb/>effect might al&longs;o fall out in the Lake, in which there being many <lb/>veins (as it is very likely) that maintain and feed the Lake; the&longs;e <lb/>veins might imbibe the new addition of the Rain-water, and &longs;o <lb/>by that means annuall the ri&longs;ing; or el&longs;e dimini&longs;h it in &longs;uch &longs;ort, as <lb/>to render it inob&longs;ervable. </s> <s>But this difficulty was ea&longs;ily re&longs;olved <lb/>by con&longs;idering my Treati&longs;e of the mea&longs;ure of Running-Waters; <lb/>fora&longs;much as having demon&longs;trated, that the abatement of a Lake <lb/>beareth the reciprocal proportion to the velocity of the Emi&longs;&longs;a­<lb/>ry, which the mea&longs;ure of the Section of the Emi&longs;&longs;ary of the Lake, <lb/>hath to the mea&longs;ure of the &longs;urface of the Lake: making the <lb/>calculation and account, though in gro&longs;s; by &longs;uppo&longs;ing that its <lb/>veins were &longs;ufficiently large, and that the velocity in them were <lb/>notable in drinking up the water of the Lake; yet I found never­<lb/>thele&longs;s, that many weeks and moneths would be &longs;pent in drink­<lb/>ing up the new-come abundance of water by the rain, &longs;o that <lb/>I re&longs;ted &longs;ure, that the ri&longs;ing would en&longs;ue, as in effect it did.</s></p><p type="main"> <s>And becau&longs;e many of accurate judgement, have again cau&longs;ed <lb/>me to que&longs;tion this ri&longs;ing, &longs;etting before me, that the Earth be­<lb/>ing parched by the great drought, that had &longs;o long continued, it <lb/>might be, that that Bank of Earth which environed the brink of <lb/>the Lake, being dry, and imbibing great abundance of Water <pb xlink:href="040/01/600.jpg" pagenum="31"/>from the increa&longs;ing Lake, would not &longs;uffer it to increa&longs;e in <lb/>height: I &longs;ay therefore, that if we would rightly con&longs;ider this <lb/>doubt here propo&longs;ed, we &longs;hould, in the very con&longs;ideration of it, <lb/>&longs;ee it re&longs;olved; for, it being &longs;uppo&longs;ed that that li&longs;t or border of <lb/>Banks which was to be occupied by the increa&longs;e of the Lake, be <lb/>a Brace in breadth quite round the Lake, and that by rea&longs;on of <lb/>its dryne&longs;s it &longs;ucks in water, and that by that means this propor­<lb/>tion of water co-operates not in rai&longs;ing of the Lake: It is ab&longs;o­<lb/>lutely nece&longs;&longs;ary on the other hand, that we con&longs;ider, That the <lb/>Circuit of the water of the Lake being thirty miles, as its com­<lb/>monly held, that is to &longs;ay, Ninety thou&longs;and Braces of <emph type="italics"/>Florence<emph.end type="italics"/><lb/>in compa&longs;s; and therefore admitting for true, that each Brace of <lb/>this Bank drink two quarts of water, and that for the &longs;pieading <lb/>it require three quarts more, we &longs;hall finde, that the whole agre­<lb/>gate of this portion of water, which is not imployed in the rai&longs;ing <lb/>of the Lake, will be four hundred and fifty thou&longs;and Quarts of <lb/>water; and &longs;uppo&longs;ing that the Lake be &longs;ixty &longs;quare miles, three <lb/>thou&longs;and Braces long, we &longs;hall finde, that to di&longs;pence the water <lb/>po&longs;&longs;e&longs;t by the Bank about the Lake, above the total &longs;urface of <lb/>the Lake, it ought to be &longs;pread &longs;o thin, that one &longs;ole quart of <lb/>water may over-&longs;pread ten thou&longs;and &longs;quare Braces of &longs;urface: <lb/>&longs;uch a thinne&longs;s, as mu&longs;t much exceed that of a leaf of beaten <lb/>Gold, and al&longs;o le&longs;s than that skin of water which covers the Bub­<lb/>bles of it: and &longs;uch would that be, which tho&longs;e men would have <lb/>&longs;ub&longs;tracted from the ri&longs;ing of the Lake: But again, in the &longs;pace <lb/>of a quarter of an hour at the beginning of the rain, all that <lb/>Bank is &longs;oaked by the &longs;aid rain, &longs;o that we need not for the <lb/>moi&longs;tning of it, imploy a drop of that water which falleth into <lb/>the Lake. </s> <s>Be&longs;ides we have not brought to account that abun­<lb/>dance of water which runs in time of rain into the Lake, from <lb/>the &longs;teepne&longs;s of the adjacent Hills and Mountains; which would <lb/>be enough to &longs;upply all our occa&longs;ions: So that, neither ought <lb/>we for this rea&longs;on to que&longs;tion our pretended ri&longs;ing. </s> <s>And this <lb/>is what hath fallen in my way touching the con&longs;ideration of the <lb/><emph type="italics"/>Thra&longs;imenian<emph.end type="italics"/> Lake.</s></p><p type="main"> <s>After which, perhaps &longs;omewhat ra&longs;hly, wandring beyond my <lb/>bounds, I proceeded to another contemplation, which I will re­<lb/>late to you, hoping that you will receive it, as collected with <lb/>the&longs;e cautions requi&longs;ite in &longs;uch like affairs; wherein we ought <lb/>not too po&longs;itively to affirm any thing of our own heads for cer­<lb/>tain, but ought to &longs;ubmit all to the &longs;ound and &longs;ecure delibera­<lb/>tion of the Holy Mother-Church, as I do this of mine, and all <lb/>others; mo&longs;t ready to change my judgement, and conform my <lb/>&longs;elf alwaies to the deliberations of my Superiors. </s> <s>Continu­<pb xlink:href="040/01/601.jpg" pagenum="32"/>ing therefore my above-&longs;aid conceit about the ri&longs;ing of the wa­<lb/>ter in the gla&longs;s tried before, it came into my minde, that the <lb/>forementioned rain having been very gentle, it might well be, <lb/>that if there &longs;hould have faln a Rain fifty, an hundred, or a thou­<lb/>&longs;and times greater than this, and much more inten&longs;e (which <lb/>would in&longs;ue as oft as tho&longs;e falling drops were four, &longs;ive or ten <lb/>times bigger than tho&longs;e of the above-mentioned rain, keeping <lb/>the &longs;ame number) in &longs;uch a ca&longs;e its manife&longs;t, that in the &longs;pace <lb/>of an hour the Water would ri&longs;e in our Gla&longs;s, two, three, and <lb/>perhaps more Yards or Braces; and con&longs;equently, if &longs;uch a <lb/>Raine &longs;hould fall upon a Lake, that the &longs;aid Lake would <lb/>ri&longs;e, according to the &longs;ame rate: And likewi&longs;e, if &longs;uch a <lb/>Rain were univer&longs;all, over the whole Terre&longs;triall Globe, it <lb/>would nece&longs;&longs;arily, in the &longs;pace of an hour, make a ri­<lb/>&longs;ing of two, or three braces round about the &longs;aid Globe, <lb/>And becau&longs;e we have from Sacred Records, that in the <lb/>time of the Deluge, it rained fourty dayes and fourty nights; <lb/>namely, for the &longs;pace of 960 houres; its clear, that if the &longs;aid <lb/>Rain had been ten times bigger than ours at <emph type="italics"/>Perugia,<emph.end type="italics"/> the ri&longs;ing <lb/>of the Waters above the Terre&longs;trial Globe would reach and pa&longs;s <lb/>a mile higher than the tops of the Hills and Mountains that are <lb/>upon the &longs;uperficies of the Earth; and they al&longs;o would concur <lb/>to increa&longs;e the ri&longs;e. </s> <s>And therefore I conclude, that the ri&longs;e of <lb/>the Waters of the Deluge have a rational congruity with natural <lb/>Di&longs;cour&longs;es, of which I know very well that the eternal truths of <lb/>the Divine leaves have no need; but however I think &longs;o clear an <lb/>agreement is worthy of our con&longs;ideration, which gives us occa­<lb/>&longs;ion to adore and admire the greatne&longs;&longs;e of God in his mighty <lb/>Works, in that we are &longs;ometimes able, in &longs;ome &longs;ort, to mea&longs;ure <lb/>them by the &longs;hort Standard of our Rea&longs;on.</s></p><p type="main"> <s>Many Le&longs;&longs;ons al&longs;o may be deduced from the &longs;ame Doctrine, <lb/>which I pa&longs;&longs;e by, for that every man of him&longs;elf may ea&longs;ily know <lb/>them, having once &longs;tabli&longs;hed this Maxime; That it is not po&longs;&longs;i­<lb/>ble to pronounce any thing, of a certainty, touching the quantity <lb/>of Running Waters, by con&longs;idering only the &longs;ingle vulgar mea­<lb/>&longs;ure of the Water wichout the velocity; and &longs;o on the contrary, <lb/>he that computes only the velocity, without the mea&longs;ure, &longs;hall <lb/>commit very great errours; for treating of the mea&longs;ure of Run­<lb/>ning Waters, it is nece&longs;&longs;ary, the water being a body, in handling <lb/>its quantity, to con&longs;ider in it all the three dimen&longs;ions of breadth, <lb/>depth, and length: the two fir&longs;t dimen&longs;ions are ob&longs;erved by all <lb/>in the common manner, and ordinary way of mea&longs;uring Running <lb/>Waters; but the third dimen&longs;ion of length is omitted; and hap­<lb/>ly &longs;uch an over&longs;ight is committed, by rea&longs;on the length of Run­<pb xlink:href="040/01/602.jpg" pagenum="33"/>ning Water is reputed in &longs;ome &longs;en&longs;e infinite, in that it never cea­<lb/>&longs;eth to move away, and as infinite is judged incomprehen&longs;ible; <lb/>and &longs;uch as that there is no exact knowledge to be had thereof; <lb/>& &longs;o there comes to be no account made thereof; but if we &longs;hould <lb/>make &longs;trict reflection upon our con&longs;ideration of the velocity of <lb/>Water, we &longs;hould find, that keeping account of the &longs;ame, there <lb/>is a reckoning al&longs;o made of the length; fora&longs;much as whil&longs;t we <lb/>&longs;ay, the Water of &longs;uch a Spring runs with the velocity of pa&longs;&longs;ing <lb/>a thou&longs;and or two thou&longs;and paces an hour: this in &longs;ub&longs;tance is <lb/>no other than if we had &longs;aid, &longs;uch a Fountain di&longs;chargeth in an <lb/>hour a Water of a thou&longs;and or two thou&longs;and paces long. </s> <s>So <lb/>that, albeit the total length of Running water be incomprehen­<lb/>&longs;ible, as being infinite, yet neverthele&longs;&longs;e its rendered intelligible <lb/>by parts in its velocity. </s> <s>And &longs;o much &longs;ufficeth to have hinted <lb/>about this matter, hoping to impart on &longs;ome other occa&longs;ion other <lb/>more accurate Ob&longs;ervations in this affair.</s></p><p type="head"> <s><emph type="italics"/>LAVS DEO.<emph.end type="italics"/></s></p><figure id="id.040.01.602.1.jpg" xlink:href="040/01/602/1.jpg"/><pb xlink:href="040/01/603.jpg"/><p type="head"> <s>GEOMETRICAL <lb/>DEMONSTRATIONS <lb/>OF THE <lb/>MEASURE <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s>BY <lb/>D. BENEDETTO CASTELLI, <lb/>Abbot of CASSINA, and Mathematician to <lb/>P. <emph type="italics"/>VRBAN. VIII.<emph.end type="italics"/></s></p><p type="head"> <s>DEDICATED <lb/><emph type="italics"/>To the mo&longs;t Illu&longs;trious, and mo&longs;t Excellent Prince<emph.end type="italics"/></s></p><p type="head"> <s>DON THADDEO BARBERINI, <lb/>PRINCE OF <lb/>PALESTRINA, <lb/>AND <lb/>GENERAL of the HOLY CHURCH.</s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed <emph type="italics"/>Anno Domini,<emph.end type="italics"/> MDCLXI.</s></p><pb xlink:href="040/01/604.jpg" pagenum="37"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>Let it be &longs;uppo&longs;ed, that the banks of the Rivers of which <lb/>we &longs;peak be erected perpendicular to the plane of the up­<lb/>per &longs;uperficies of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>We &longs;uppo&longs;e that the plane of the bottome of the River, of <lb/>which we &longs;peak is at right angles with the banks.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>It is to be &longs;uppo&longs;ed, that we &longs;peak of Rivers, when they are at <lb/>ebbe, in that &longs;tate of &longs;hallowne&longs;&longs;e, or at flowing in that &longs;tate <lb/>of deepne&longs;&longs;e, and not in their tran&longs;ition from the ebbe to the <lb/>flowing, or fr m the flowing to the ebbe.</s></p><p type="head"> <s><emph type="italics"/>Declaration of Termes.<emph.end type="italics"/></s></p><p type="head"> <s>FIRST.</s></p><p type="main"> <s>If a River &longs;hall be cut by a Plane at right angles to the &longs;urface <lb/>of the water of the River, and to the banks of the River, <lb/>that &longs;ame dividing Plane we call the Section of the River; and <lb/>this Section, by the Suppo&longs;itions above, &longs;hall be a right angled <lb/>Parallelogram.</s></p><p type="head"> <s>SECOND.</s></p><p type="main"> <s>We call tho&longs;e Sections equally Swift, by which the water runs <lb/>with equal velocity; and more &longs;wift and le&longs;s &longs;wift that <lb/>Section of another, by which the water runs with greater or le&longs;&longs;e <lb/>velocity.</s></p><pb xlink:href="040/01/605.jpg" pagenum="38"/><p type="head"> <s>AXIOME I.</s></p><p type="main"> <s>Sections equal, and equally &longs;wift, di&longs;charge equal quantities <lb/>of Water in equal times.</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s>Sections equally &longs;wift, and that di&longs;charge equal quantity of <lb/>Water, in equal time, &longs;hall be equal.</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s>Sections equal, and that di&longs;charge equal quantities of Water <lb/>in equal times, &longs;hall be equally &longs;wift.</s></p><p type="head"> <s>AXIOME IV.</s></p><p type="main"> <s>When Sections are unequal, but equally &longs;wift, the quanti­<lb/>ty of the Water that pa&longs;&longs;eth through the fir&longs;t Section, <lb/>&longs;hall have the &longs;ame proportion to the quantity that pa&longs;­<lb/>&longs;eth through the Second, that the fir&longs;t Section hath to the &longs;econd <lb/>Section. </s> <s>Which is manife&longs;t, becau&longs;e the velocity being the <lb/>&longs;ame, the difference of the Water that pa&longs;&longs;eth &longs;hall be according <lb/>to the difference of the Sections.</s></p><p type="head"> <s>AXIOME V.</s></p><p type="main"> <s>If the Sections &longs;hall be equal, and of unequal velocity, the <lb/>quantity of the Water that pa&longs;&longs;eth through the fir&longs;t, &longs;hall <lb/>have the &longs;ame proportion to that which pa&longs;&longs;eth through the <lb/>&longs;econd, that the velocity of the fir&longs;t Section, &longs;hall have to the <lb/>velocity of the &longs;econd Section. </s> <s>Which al&longs;o is manife&longs;t, becau&longs;e <lb/>the Sections being equal, the difference of the Water which <lb/>pa&longs;&longs;eth, dependeth on the velocity.</s></p><p type="head"> <s><emph type="italics"/>PETITION.<emph.end type="italics"/></s></p><p type="main"> <s>A Section of a River being given, we may &longs;uppo&longs;e another <lb/>equal to the given, of different breadth, heigth, and ve­<lb/>locity.</s></p><pb xlink:href="040/01/606.jpg" pagenum="37"/><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s><emph type="italics"/>The Sections of the &longs;ame River di&longs;charge equal quan­<lb/>tities of Water in equal times, although the Secti­<lb/>ons them&longs;elves he unequal.<emph.end type="italics"/></s></p><p type="main"> <s>Let the two Sections be A and B, in the River C, running <lb/>from A, towards B; I &longs;ay, that they di&longs;charge equal quan­<lb/>tity of Water in equal times; for if greater quantity of Wa­<lb/>ter &longs;hould pa&longs;s through A, than pa&longs;&longs;eth through B, it would <lb/><figure id="id.040.01.606.1.jpg" xlink:href="040/01/606/1.jpg"/><lb/>follow that the Water in the intermediate &longs;pace of the River C, <lb/>would increa&longs;e continually, which is manife&longs;tly fal&longs;e, but if <lb/>more Water &longs;hould i&longs;&longs;ue through the Section B, than entreth at <lb/>the Section A, the Water in the intermediate &longs;pace C, would <lb/>grow continually le&longs;s, and alwaies ebb, which is likewi&longs;e fal&longs;e; <lb/>therefore the quantity of Water that pa&longs;&longs;eth through the Secti­<lb/>on B, is equal to the quantity of Water which pa&longs;&longs;eth through <lb/>the Section A, and therefore the Sections of the &longs;ame River di&longs;­<lb/>charge, <emph type="italics"/>&c.<emph.end type="italics"/> Which w s to be demon&longs;trated.</s></p><p type="head"> <s>PROPOSITION II.</s></p><p type="main"> <s><emph type="italics"/>In two Sections of Rivers, the quantity of the Water <lb/>which pa&longs;&longs;eth by one Section, is to that which pa&longs;­<lb/>&longs;eth by the &longs;econd, in a Proportion compounded of <lb/>the proportions of the fir&longs;t Section to the &longs;econd, and <lb/>of the velocitie through the first, to the velocitie <lb/>of the &longs;econd.<emph.end type="italics"/></s></p><p type="main"> <s>I Et A, and B be two Sections of a River; I &longs;ay, that the <lb/>quantity of Water which pa&longs;&longs;eth through A, is to that which <lb/>pa&longs;&longs;eth through B, in a proportion compounded of the pro­<lb/>portions of the fir&longs;t Section A, to the Section B; and of the velo­<lb/>city through A, to the velocity through B: Let a Section be <pb xlink:href="040/01/607.jpg" pagenum="40"/>&longs;uppo&longs;ed equal to the Section A, in magnitude; but of velocity <lb/>equal to the Section B, and let it be G, and as the Section A is <lb/><figure id="id.040.01.607.1.jpg" xlink:href="040/01/607/1.jpg"/><lb/>to the Section B, &longs;o let the line F be to the line D; and as the <lb/>velocity A, is to the velocity by B, &longs;o let the line D be to the <lb/>line R: Therefore the Water which pa&longs;&longs;eth thorow A, &longs;hall be <lb/>to that which pa&longs;&longs;eth through G (in regard the Sections A and <lb/>G are of equal bigne&longs;s, but of unequal velocity) as the velocity <lb/>through A, to the velocity through G; But as the velocity <lb/>through A, is to the velocity through G, &longs;o is the velocity through <lb/>A, to the velocity through B; namely, as the line D, to the <lb/>line R: therefore the quantity of the Water which pa&longs;&longs;e the <lb/>through A, &longs;hall be to the quantity which pa&longs;&longs;eth through G, as <lb/>the line D is to the line R; but the quantity which pa&longs;&longs;eth <lb/>through G, is to that which pa&longs;&longs;eth through B, (in regard the <lb/>Sections G, and B, are equally &longs;wift) as the Section G to the Se­<lb/>ction B; that is, as the Section A, to the Section B; that is, as <lb/>the line F, to the line D: Therefore by the equal and perturbed <lb/>proportionality, the quantity of the Water which pa&longs;&longs;eth through <lb/>A, hath the &longs;ame proportion to that which pa&longs;&longs;eth through B, <lb/>that the line F hath to the line R; but F to R, hath a proportion <lb/>compounded of the proportions of F to D, and of D to R; that <lb/>is, of the Section A to the Section B; and of the velocity through <lb/>A, to the velocity through B. </s> <s>Therefore al&longs;o the quantity of <lb/>Water which pa&longs;&longs;eth through the Section A, &longs;hall have a propor­<lb/>tion to that which pa&longs;&longs;eth through the Section B, compounded of <lb/>the proportions of the Section A, to the Section B; and of <lb/>the velocity through A, to the velocity through B: And <lb/>therefore in two Sections of Rivers, the quantity of Water which <lb/>pa&longs;&longs;eth by the fir&longs;t, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be demon&longs;trated.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/></s></p><p type="main"> <s>The &longs;ame followeth, though the quantity of the Water which <lb/>pa&longs;&longs;eth through the Section A, be equal to the quantity of <lb/>Water which pa&longs;&longs;eth through the Section B, as is manife&longs;t by the <lb/>&longs;ame demon&longs;tration.</s></p><pb xlink:href="040/01/608.jpg" pagenum="41"/><p type="head"> <s>PROPOSITION III.</s></p><p type="main"> <s><emph type="italics"/>In two Sections unequal, through which pa&longs;s equal <lb/>quantities of Water in equal times, the Sections <lb/>have to one another, reciprocal proportion to their <lb/>velocitie.<emph.end type="italics"/></s></p><p type="main"> <s>Let the two unequal Sections, by which pa&longs;s equal quantities <lb/>of Water in equal times be A, the greater; and B, the le&longs;&longs;er: <lb/>I &longs;ay, that the Section A, &longs;hall have the &longs;ame Proportion <lb/>to the Section B, that reciprocally the velocity through B, hath to <lb/>the velocity through A; for &longs;uppo&longs;ing that as the Water that <lb/>pa&longs;&longs;eth through A, is to that which pa&longs;&longs;eth through B, &longs;o is the <lb/><figure id="id.040.01.608.1.jpg" xlink:href="040/01/608/1.jpg"/><lb/>line E to the line F: therefore the quantity of water which pa&longs;­<lb/>&longs;eth through A, being equal to that which pa&longs;&longs;eth through B, <lb/>the line E &longs;hall al&longs;o be equal to the line F: Suppo&longs;ing moreover, <lb/>That as the Section A, is to the Section B, &longs;o is the line F, to the <lb/>line G; and becau&longs;e the quantity of water which pa&longs;&longs;eth <lb/>through the Section A, is to that which pa&longs;&longs;eth through the <lb/>Section B, in a proportion compo&longs;ed of the proportions of the <lb/>Section A, to the Section B, and of the velocity through A, to the <lb/>velocity through B; therefore the line E, &longs;hall be the line to F, in <lb/>a proportion compounded of the &longs;ame proportions; namely, of <lb/>the proportion of the Section A, to the Section B, and of the ve­<lb/>locity through A, to the velocity through B; but the line E, hath <lb/>to the line G, the proportion of the Section A, to the Section B, <lb/>therefore the proportion remaining of the line G, to the line F, <lb/>&longs;hall be the proportion of the velocity through A, to the velocity <lb/>through B; therefore al&longs;o the line G, &longs;hall be to the line E, as <lb/>the velocity by A, to the velocity by B: And conver&longs;ly, the ve­<lb/>locity through B, &longs;hall be to the velocity through A, as the line <lb/>E, to the line G; that is to &longs;ay, as the Section A, to the Section B, <lb/>and therefore in two Sections, &c. </s> <s>which was to be demon&longs;trated.</s></p><pb xlink:href="040/01/609.jpg" pagenum="42"/><p type="head"> <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/></s></p><p type="main"> <s>Hence it is manife&longs;t, that Sections of the &longs;ame River (which <lb/>are no other than the vulgar mea&longs;ures of the River) have <lb/>betwixt them&longs;elves reciprocal proportions to their veloci­<lb/>ties; for in the fir&longs;t Propo&longs;ition we have demon&longs;trated that the <lb/>Sections of the &longs;ame River, di&longs;charge equal quantities of Water <lb/>in equal times; therefore, by what hath now been demon&longs;trated <lb/>the Sections of the &longs;ame River &longs;hall have reciprocal proportion <lb/>to their velocities; And therefore the &longs;ame running water chan­<lb/>geth mea&longs;ure, when it changeth velocity; namely, increa&longs;eth the <lb/>mea&longs;ure, when it decrea&longs;eth the velocity, and decrea&longs;eth the <lb/>mea&longs;ure, when it increa&longs;eth the velocity.</s></p><p type="main"> <s>On which principally depends all that which hath been &longs;aid <lb/>above in the <emph type="italics"/>Di&longs;cour&longs;e,<emph.end type="italics"/> and ob&longs;erved in the <emph type="italics"/>Corollaries<emph.end type="italics"/> and <emph type="italics"/>Ap­<lb/>pendixes<emph.end type="italics"/>; and therefore is worthy to be well under&longs;tood and <lb/>heeded.</s></p><p type="head"> <s>PROPOSITION IV.</s></p><p type="main"> <s><emph type="italics"/>If a River fall into another River, the height of the <lb/>fir&longs;t in its own Chanel &longs;hall be to the height that it <lb/>&longs;hall make in the &longs;econd Chanel, in a proportion <lb/>compounded of the proportions of the breadth of <lb/>the Chanel of the &longs;econd, to the breadth of the <lb/>Chanel of the fir&longs;t, and of the velocitie acquired in <lb/>the Chanel of the &longs;econd, to that which it had in <lb/>its proper and first Chanel.<emph.end type="italics"/></s></p><p type="main"> <s>Let the River A B, who&longs;e height is A C, and breadth C B, <lb/>that is, who&longs;e Section is A C B; let it enter, I &longs;ay, into a­<lb/>nother River as broad as the line E F, and let it therein make <lb/>the ri&longs;e or height D E, that is to &longs;ay, let it have its Section in <lb/>the River whereinto it falls D E F; I &longs;ay, that the height A C <lb/>hath to the height D E the proportion compounded of the pro­<lb/>portions of the breadth E F, to the breadth C B, and of the ve­<lb/>locity through D F, to the velocity through A B. </s> <s>Let us &longs;up­<lb/>po&longs;e the Section G, equal in velocity to the Section A B, and in <lb/>breadth equal to E F, which carrieth a quantity of Water e­<lb/>qual to that which the Section A B carrieth, in equal times, <lb/>and con&longs;equently, equal to that which D F carrieth. </s> <s>Moreover, <lb/>as the breadth E F is to the breadth C B, &longs;o let the line H be to <pb xlink:href="040/01/610.jpg" pagenum="43"/>the line I; and as the velocity of D F is to the velocity of A B, <lb/>&longs;o let the line I be to the line L; becau&longs;e therefore the two <lb/>Sections A B and G are equally &longs;wift, and di&longs;charge equal quan­<lb/>tity of Water in equal times, they &longs;hall be equal Sections; and <lb/><figure id="id.040.01.610.1.jpg" xlink:href="040/01/610/1.jpg"/><lb/>therefore the height of A <emph type="italics"/>B<emph.end type="italics"/> to the height of G, &longs;hall be as the <lb/>breadth of G, to the breadth of A <emph type="italics"/>B,<emph.end type="italics"/> that is, as E F to C <emph type="italics"/>B,<emph.end type="italics"/><lb/>that is, as the line H to the line I: but becau&longs;e the Water which <lb/>pa&longs;&longs;eth through G, is equal to that which pa&longs;&longs;eth through D E F, <lb/>therefore the Section G, to the Section D E F, &longs;hall have the re­<lb/>ciprocal proportion of the velocity through D E F, to the velo­<lb/>city through G; but al&longs;o the height of G, is to the height D E, <lb/>as the Section G, to the Section D E F: Therefore the height of <lb/>G, is to the height D E, as the velocity through D E F, is to the <lb/>velocity through G; that is, as the velocity through D E F, is to <lb/>the velocity through A <emph type="italics"/>B<emph.end type="italics"/>; That is, finally, as the line I, to the <lb/>line L; Therefore, by equal proportion, the height of <emph type="italics"/>A B,<emph.end type="italics"/> that <lb/>is, A C, &longs;hall be to the height D E; as H to L, that is, com­<lb/>pounded of the proportions of the breadth E F, to the breadth <lb/>C <emph type="italics"/>B,<emph.end type="italics"/> and of the velocity through D F, to the velocity through <lb/>A <emph type="italics"/>B<emph.end type="italics"/>: So that if a River fall into another River, &c. </s> <s>which was <lb/>to be demon&longs;trated.</s></p><pb xlink:href="040/01/611.jpg" pagenum="44"/><p type="head"> <s>PROPOSITION V.</s></p><p type="main"> <s><emph type="italics"/>If a River di&longs;charge a certain quantitie of Water <lb/>in a certain time; and after that there come into it <lb/>a Flood, the quantity of Water which is di&longs;char­<lb/>ged in as much time at the Flood, is to that which <lb/>was di&longs;charged before, whil&longs;t the River was low, <lb/>in a proportion compounded of the proportions of <lb/>the velocity of the Flood, to the velocity of the first <lb/>Water, and of the height of the Flood, to the <lb/>height of the first Water.<emph.end type="italics"/></s></p><p type="main"> <s>Suppo&longs;e a River, which whil&longs;t it is low, runs by the Section <lb/>AF; and after a Flood cometh into the &longs;ame, and runneth <lb/>through the Section D F, I &longs;ay, that the quantity of the Wa­<lb/>ter which is di&longs;charged through D F, is to that which is di&longs;charged <lb/><figure id="id.040.01.611.1.jpg" xlink:href="040/01/611/1.jpg"/><lb/>through A F, in a proportion compounded of the proportions of <lb/>the velocity through D F, to the velocity through A F, and of <lb/>the height D <emph type="italics"/>B,<emph.end type="italics"/> to the height A <emph type="italics"/>B<emph.end type="italics"/>; As the velocity through DF <lb/>is to the velocity through A F, &longs;o let the line R, to the line S; <lb/>and as the height D <emph type="italics"/>B<emph.end type="italics"/> is to the height A <emph type="italics"/>B,<emph.end type="italics"/> &longs;o let the line S, to <lb/>the line T; and let us &longs;uppo&longs;e a Section L M N, equal to D F <lb/>in height and breadth; that is L M equal to D <emph type="italics"/>B,<emph.end type="italics"/> and M N equal <lb/>to <emph type="italics"/>B F<emph.end type="italics"/>; but let it be in velocity equal to the Section A F, there­<lb/>fore the quantity of Water which runneth through D F, &longs;hall be <lb/>to that which runneth through LN, as the velocity through DF, <lb/>is to the velocity through L N, that is, to the velocity through <lb/><emph type="italics"/>A F<emph.end type="italics"/>; and the line R being to the line S, as the velocity through <lb/>D <emph type="italics"/>F,<emph.end type="italics"/> to the velocity through <emph type="italics"/>A F<emph.end type="italics"/>; therefore the quantity which <lb/>runneth through D <emph type="italics"/>F,<emph.end type="italics"/> to that which runneth through L N, &longs;hall <lb/>have the proportion of R to S; but the quantity which runneth <lb/>through L N, to that which runneth through <emph type="italics"/>A F,<emph.end type="italics"/> (the Sections <pb xlink:href="040/01/612.jpg" pagenum="45"/>being equally &longs;wift) &longs;hall be in proportion as the Section <emph type="italics"/>L<emph.end type="italics"/> N, to <lb/>the Section A F; that is, as D B, to A B; that is as the line S, to <lb/>the line T: Therefore by equal proportion, the quantity of the <lb/>water which runneth through D F, &longs;hall be in proportion to that <lb/>which runneth through A F, as R is to T; that is, compounded of <lb/>the proportions of the height D B, to the height A B, and of the <lb/>velocity through <emph type="italics"/>D F,<emph.end type="italics"/> to the velocity through <emph type="italics"/>A F<emph.end type="italics"/>; and therefore <lb/>if a River di&longs;charge a certain quantity, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be de­<lb/>mon&longs;trated.</s></p><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>The &longs;ame might have been demon&longs;trated by the &longs;econd <lb/>Propo&longs;ition above demon&longs;trated, as is manife&longs;t.</s></p><p type="head"> <s>PROPOSITION VI.</s></p><p type="main"> <s><emph type="italics"/>If two equal &longs;treams of the &longs;ame Torrent, fall into a <lb/>River at divers times, the heights made in the Ri­<lb/>ver by the Torrent, &longs;hall have between them­<lb/>&longs;elves the reciprocal proportion of the velocities <lb/>acquired in the River.<emph.end type="italics"/></s></p><p type="main"> <s>Let A and B, be two equal &longs;treams of the &longs;ame Torrent, <lb/>which falling into a River at divers times, make the heights <lb/>C D, and F G; that is the &longs;tream A, maketh the height <lb/>C D, and the &longs;tream B, maketh the height F G; that is, Let <lb/>their Sections in the River, into which they are fallen, be C E, <lb/>and FH; I &longs;ay, that the height C D, &longs;hall be to the height F G, <lb/>in reciprocal proportion, as the velocity through F H, to the ve­<lb/>locity through C E; for the quantity of water which pa&longs;&longs;eth <lb/>through A, being equal to the quantity which pa&longs;&longs;eth through B, <lb/>in equal times; al&longs;o the quantity which pa&longs;&longs;eth through C E, &longs;hall <lb/><figure id="id.040.01.612.1.jpg" xlink:href="040/01/612/1.jpg"/><lb/>be equal to that which pa&longs;&longs;eth through F H: And therefore the <lb/>proportion that the Section C E, hath to the Section F H; &longs;hall <lb/>be the &longs;ame that the velocity through F H, hath to the velocity <lb/>through C E; But the Section C E, is to the Section F H, as <lb/>C D, to F G, by rea&longs;on they are of the &longs;ame breadth: Therefore <lb/>C D, &longs;hall be to F G, in reciprocal proportion, as the velocity <lb/>through F H, is to the velocity through C E, and therefore if two <lb/>equal &longs;treams of the &longs;ame Torrent, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be de­<lb/>mon&longs;trated.</s></p><pb xlink:href="040/01/613.jpg" pagenum="47"/><p type="head"> <s>OF THE <lb/>MENSURATION <lb/>OF <lb/>Running Waters.</s></p><p type="head"> <s><emph type="italics"/>Lib.<emph.end type="italics"/> II.</s></p><p type="main"> <s>Having, in the clo&longs;e of my Treati&longs;e of the <lb/>Men&longs;uration of Running Waters promi&longs;ed <lb/>to declare upon another occa&longs;ion other par­<lb/>ticulars more ob&longs;cure, and of very great <lb/>concern upon the &longs;ame argumement: I now <lb/>do perform my promi&longs;e on the occa&longs;ion <lb/>that I had the pa&longs;t year 1641. to propound <lb/>my thoughts touching the &longs;tate of the Lake <lb/>of <emph type="italics"/>Venice,<emph.end type="italics"/> a bu&longs;ine&longs;s certainly mo&longs;t important, as being the <lb/>concernment of that mo&longs;t noble and mo&longs;t admirable City; and <lb/>indeed of all <emph type="italics"/>Italy,<emph.end type="italics"/> yea of all <emph type="italics"/>Europe, A&longs;ia, & Africa<emph.end type="italics"/>; & one may <lb/>truly &longs;ay of all the whole World. </s> <s>And being to proceed according <lb/>to the method nece&longs;&longs;ary in Sciences, I wil propo&longs;e, in the fir&longs;t place <lb/>certain Definitions of tho&longs;e Terms whereof we are to make u&longs;e <lb/>in our Di&longs;cour&longs;e: and then, laying down certain Principles we <lb/>will demon&longs;trate &longs;ome Problemes and Theoremes nece&longs;&longs;ary for <lb/>the under&longs;tanding of tho&longs;e things which we are to deliver; and <lb/>moreover, recounting &longs;undry ca&longs;es that have happened, we will <lb/>prove by practice, of what utility this contemplation of the <lb/>Mea&longs;ure of Running Waters is in the more important affairs both <lb/>Publique and Private.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s>Two Rivers are &longs;aid to move with equal velocity, when in e­<lb/>qual times they pa&longs;&longs;e &longs;paces of equal length.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s>Rivers are &longs;aid to move with like velocity, when their propor­<lb/>tional parts do move alike, that is, the upper parts alike to <lb/>the upper, and the lower to the lower; &longs;o that if the upper <lb/>part of one River &longs;hall be more &longs;wift than the upper part of ano­<lb/>ther; then al&longs;o the lower part of the former &longs;hall be more &longs;wift <lb/>than the part corre&longs;pondent to it in the &longs;econd, proportionally.</s></p><pb xlink:href="040/01/614.jpg" pagenum="48"/><p type="head"> <s>DEFINITON III.</s></p><p type="main"> <s>To mea&longs;ure a River, or running Water, is in our &longs;en&longs;e to finde <lb/>out how many determinate mea&longs;ures, or weights of Water <lb/>in a given time pa&longs;&longs;eth through the River, or Channel of the <lb/>Water that is to be mea&longs;ured.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s>If a Machine be made either of Brick, or of Stone, or of <lb/>Wood, &longs;o compo&longs;ed that two &longs;ides of the &longs;aid Machine be <lb/>placed at right angles upon the ends of a third &longs;ide, that is <lb/>&longs;uppo&longs;ed to be placed in the bottom of a River, parallel to the <lb/>Horizon, in &longs;uch a manner, that all the water which runneth <lb/>through the &longs;aid River, pa&longs;&longs;eth thorow the &longs;aid Machine: And <lb/>if all the water coming to be diverted <lb/><figure id="id.040.01.614.1.jpg" xlink:href="040/01/614/1.jpg"/><lb/>that runneth through the &longs;aid River, the <lb/>upper &longs;uperficies of that third &longs;ide placed <lb/>in the bottom do remain uncovered <lb/>and dry, and that the dead water be not <lb/>above it; This &longs;ame Machine &longs;hall be <lb/><arrow.to.target n="marg968"></arrow.to.target><lb/>called by us ^{*} REGULATOR: And that third &longs;ide of the <lb/>Machine which &longs;tandeth Horizontally is called the bottom of <lb/>the Regulator; and the other two &longs;ides, are called the banks of <lb/>the Regulator; as is &longs;een in this fir&longs;t Figure: A B C D, &longs;hall be <lb/>the Regulator; B C the bottom; and the other two &longs;ides A B, <lb/>and C D are its banks.</s></p><p type="margin"> <s><margin.target id="marg968"></margin.target>* Or Sluice.</s></p><p type="head"> <s>DEFINITION V.</s></p><p type="main"> <s>By the quick height, we mean the Perpendicular from the upper <lb/>&longs;uperficies of the River, unto the upper &longs;uperficies of the bot­<lb/>tom of the Regulator; as in the foregoing Figure the line. </s> <s>G H.</s></p><p type="head"> <s>DEFINITION VI.</s></p><p type="main"> <s>If the water of a <emph type="italics"/>R<emph.end type="italics"/>iver be &longs;uppo&longs;ed to be marked by three <lb/>&longs;ides of a Regulator, that Rightangled Parallelogram compre­<lb/>hended between the banks of the Regulator, and the bottom, <lb/>and the &longs;uperficies of the Water is called a Section of the <lb/>River.</s></p><pb xlink:href="040/01/615.jpg" pagenum="49"/><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>Here it is to be noted, that the River it &longs;elf may have &longs;undry <lb/>and divers heights, in &longs;everal parts of its Chanel, by rea&longs;on of <lb/>the various velocities of the water, and its mea&longs;ures; as hath <lb/>been demon&longs;trated in the fir&longs;t book.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>It is &longs;uppo&longs;ed, that the Rivers equal in breadth, and quick <lb/>height, that have the &longs;ame inclination of bed or bottom, ought <lb/>al&longs;o to have equal velocities, the accidental impediments being <lb/>removed that are di&longs;per&longs;ed throughout the cour&longs;e of the water, <lb/>and ab&longs;tracting al&longs;o from the external windes, which may velo­<lb/>citate, and retard the cour&longs;e of the water of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>Let us &longs;uppo&longs;e al&longs;o, that if there be two Rivers that are in <lb/>their beds of equal length, and of the &longs;ame inclination, but of <lb/>quick heights unequal, they ought to move with like velocity, <lb/>according to the &longs;en&longs;e explained in the &longs;econd definition.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>Becau&longs;e it will often be requi&longs;ite to mea&longs;ure the time exactly <lb/>in the following Problems, we take that to be an excellent <lb/>way to mea&longs;ure the time, which was &longs;hewed me many years &longs;ince <lb/>by <emph type="italics"/>Signore Galilæo Galilæi,<emph.end type="italics"/> which is as followeth.</s></p><p type="main"> <s>A &longs;tring is to be taken three Roman feet long, to the end of <lb/>which a Bullet of Lead is to be hanged, of about two or three <lb/>ounces; and holding it by the other end, the Plummet is to be <lb/>removed from its perpendicularity a Palm, more or le&longs;s, and then <lb/>let go, which will make many &longs;wings to and again, pa&longs;&longs;ing and <lb/>repa&longs;&longs;ing the Perpendicular, before that it &longs;tay in the &longs;ame: Now <lb/>it being required to mea&longs;ure the time that is &longs;pent in any what­<lb/>&longs;oever operation, tho&longs;e vibrations are to be numbred, that are <lb/>made whil&longs;t the work la&longs;teth; and they &longs;hall be &longs;o many &longs;econd <lb/>minutes of an hour, if &longs;o be, that the &longs;tring be three Roman feet <lb/>long, but in &longs;horter &longs;trings, the vibrations are more frequent, and <lb/>in longer, le&longs;s frequent; and all this &longs;till followeth, whether the <lb/>Plummet be little or much removed from its Perpendicularity, or <lb/>whether the weight of the Lead be greater or le&longs;&longs;er.</s></p><p type="main"> <s>The&longs;e things being pre-&longs;uppo&longs;ed, we will lay down &longs;ome fa­<pb xlink:href="040/01/616.jpg" pagenum="50"/>miliar Problems, from which we &longs;hall pa&longs;s to the Notions and <lb/>que&longs;tions more &longs;ubtil and curious; which will al&longs;o prove profi­<lb/>table, and not to be &longs;leighted in this bu&longs;ine&longs;s of Waters.</s></p><p type="head"> <s>PROPOSITION I. PROBLEME I.</s></p><p type="main"> <s><emph type="italics"/>Achanel of Running-Water being given, the breadth <lb/>of which pa&longs;sing through a Regulator, is three <lb/>Palms; and the height one Palm, little more or <lb/>le&longs;s, to mea&longs;ure what water pa&longs;&longs;eth through the <lb/>Regulator in a time given.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t, we are to dam up the Chanel; &longs;o that there pa&longs;s not any <lb/>water below the Dam; then we mu&longs;t place in the &longs;ide of the <lb/>Chanel, in the parts above the Regulator three, or four, or five <lb/>Bent-pipes, or Syphons, according to the quantity of the water <lb/>that runneth along the Chanel; in &longs;uch &longs;ort, as that they may <lb/>drink up, or draw out of the Chanel all the water that the Cha­<lb/>nel beareth (and then &longs;hall we know that the Syphons drink up <lb/>all the water, when we &longs;ee that the water at the Dam doth nei­<lb/>ther ri&longs;e higher, nor abate, but alwaies keepeth in the &longs;ame Le­<lb/>vel.) The&longs;e things being prepared, taking the In&longs;trument to <lb/>mea&longs;ure the time, we will examine the quantity of the water that <lb/>i&longs;&longs;ueth by one of tho&longs;e Syphons in the &longs;pace of twenty vibrations, <lb/>and the like will we do one by one with the other Syphons; and <lb/>then collecting the whole &longs;umme, we will &longs;ay, that &longs;o much is <lb/>the water that pa&longs;&longs;eth and runneth thorow the Regulator or <lb/>Chanel (the Dam being taken away) in the &longs;pace of twenty &longs;e­<lb/>cond minutes of an hour; and calculating, we may ea&longs;ily reduce <lb/>it to hours, dayes, months, and years: And it hath fallen to my <lb/>turn to mea&longs;ure this way the waters of Mills and Fountains, and I <lb/>have been well a&longs;&longs;ured of its exactne&longs;s, by often repeating the <lb/>&longs;ame work.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>And this method mu&longs;t be made u&longs;e of in mea&longs;uring the waters, <lb/>that we are to bring into Conducts, and carry into Cities <lb/>and Ca&longs;tles, for Fountains; and that we may be able afterwards <lb/>to divide and &longs;hare them to particular per&longs;ons ju&longs;tly; which will <lb/>prevent infinite &longs;uits and controver&longs;ies that every day happen in <lb/>the&longs;e matters..</s></p><pb xlink:href="040/01/617.jpg" pagenum="51"/><p type="head"> <s>PROPOSITION II. THEOREM I.</s></p><p type="main"> <s><emph type="italics"/>If a River moving with &longs;uch a certain velocitie <lb/>through its Regulator, &longs;hall have a given quick <lb/>height, and afterwards by new water &longs;hall increa&longs;e <lb/>to be double, it &longs;hall al&longs;o increa&longs;e double in ve­<lb/>locitie.<emph.end type="italics"/></s></p><p type="main"> <s>Let the quick height of a River in the Regulator A B C D, <lb/>be the perpendicular F B, and afterwards, by new water that <lb/>is added to the River, let the water be &longs;uppo&longs;ed to be rai&longs;­<lb/>ed to G, &longs;o that G B may be double to E B. </s> <s>I &longs;ay, that all the <lb/>water G C &longs;hall be double in velocity to <lb/><figure id="id.040.01.617.1.jpg" xlink:href="040/01/617/1.jpg"/><lb/>that of E C: For the water G F, having <lb/>for its bed the bottom E F, equally in­<lb/>clined as the bed B C, and its quick <lb/>height G E being equal to the quick <lb/>height E C, and having the &longs;ame breadth <lb/>B C, it &longs;hall have of it &longs;elf a velocity e­<lb/>qual to the velocity of the fir&longs;t water <lb/>F C: but becau&longs;e, be&longs;ides its own moti­<lb/>on, which is imparted to it by the motion of the water E C, it <lb/>hath al&longs;o over and above its own motion, the motion of E C. </s> <s>And <lb/>becau&longs;e the two waters G C, and E C, are alike in velocity, by <lb/>the third Suppo&longs;ition; therefore the whole water G C &longs;hall be <lb/>double in velocity to the water E C; which was that which we <lb/>were to demon&longs;trate.</s></p><p type="main"> <s><emph type="italics"/>This demon&longs;tration is not here in&longs;erted, as perfect, the Authour ha­<lb/>ving by &longs;everal letters to his friends confe&longs;&longs;ed him&longs;elf un&longs;atisfi­<lb/>ed therewith; and that he intended not to publi&longs;h the<emph.end type="italics"/> Theorem <lb/><emph type="italics"/>without a more &longs;olid demon&longs;tration, which he was in hope to light <lb/>upon. </s> <s>But being overtaken by Death, he could not give the <lb/>fini&longs;hing touch either to this, or to the rest of the &longs;econd Book. </s> <s>In <lb/>con&longs;ideration of which, it &longs;eemed good to the Publi&longs;her of the <lb/>&longs;ame, rather to omit it, than to do any thing contrary to the mind of <lb/>the Authour. </s> <s>And this he hints, by way of adverti&longs;ement, to <lb/>tho&longs;e that have Manu&longs;cript Copies of this Book, with the &longs;aid de­<lb/>mon&longs;tration. </s> <s>For this time let the Reader content him&longs;elf with <lb/>the knowledge of &longs;o ingenious and profitable a Conclu&longs;ion; of the <lb/>truth of which he may, with &longs;mall expence and much plea&longs;ure, be <lb/>a&longs;&longs;ured by means of the experiment to be made in the &longs;ame man­<lb/>ner, with that which is laid down in the &longs;econd Corollary of<emph.end type="italics"/><pb xlink:href="040/01/618.jpg" pagenum="52"/><emph type="italics"/>the fourth<emph.end type="italics"/> Theorem <emph type="italics"/>of this, with its Table, and the u&longs;e there­<lb/>of annexed.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>COROLLARIE<emph.end type="italics"/></s></p><p type="main"> <s>Hence it followeth, that when a River increa&longs;eth in quick <lb/>height by the addition of new water, it al&longs;o increa&longs;eth in ve­<lb/>locity; &longs;o that the velocity hath the &longs;ame proportion to the velo­<lb/>city that the quick height hath to the quick height; as may be <lb/>demon&longs;trated in the &longs;ame manner.</s></p><p type="head"> <s>PROPOS. III. PROBLEME II.</s></p><p type="main"> <s><emph type="italics"/>Achanel of Water being given who&longs;e breadth exceeds not <lb/>twenty Palms, or thereabouts, and who&longs;e quick beight <lb/>is le&longs;s than five Palms, to mea&longs;ure the quantity of the <lb/>Water that runneth thorow the Chanel in a time <lb/>given.<emph.end type="italics"/></s></p><p type="main"> <s>Place in the Chanel a Regulator, and ob&longs;erve the quick <lb/>height in the &longs;aid Regulator; then let the water be turned <lb/>away from the Chanel by a Chanellet of three or four Palms <lb/>in breadth, or thereabouts: And that being done, mea&longs;ure the <lb/>quantity of the water which pa&longs;&longs;eth thorow the &longs;aid Chanellet, <lb/>as hath been taught in the &longs;econd Propo&longs;ition; and at the &longs;ame <lb/>time ob&longs;erve exactly how much the quick height &longs;hall be abated <lb/>in the greater Chanel, by means of the diver&longs;ion of the Chancl­<lb/>let; and all the&longs;e particulars being performed, multiply the quick <lb/>height of the greater Chanel into it &longs;elf, and likewi&longs;e multiply <lb/>into it &longs;elf the le&longs;&longs;er height of the &longs;aid bigger Chanel, and the <lb/>le&longs;&longs;er &longs;quare being taken, from the greater, the remainder &longs;hall <lb/>have the &longs;ame proportion to the whole greater &longs;quare, as the wa­<lb/>ter of the Chanellet diverted, hath to the water of the bigger <lb/>Chanel: And becau&longs;e the water of the Chanellet is known by <lb/>the Method laid down in the fir&longs;t Theorem, and the terms of the <lb/>Theorem being al&longs;o known, the quantity of the water which run­<lb/>neth thorow the bigger Chanel, &longs;hall be al&longs;o known by the Gol­<lb/>den <emph type="italics"/>R<emph.end type="italics"/>ule, which was that that was de&longs;ired to be known. </s> <s>We <lb/>will explain the whole bu&longs;ine&longs;s by an example.</s></p><p type="main"> <s>Let a Chanel be, for example, 15 Palms broad, its quick height <lb/>before its diver&longs;ion by the Chanellet &longs;hall be &longs;uppo&longs;ed to be 24 <lb/>inches; but after the diver&longs;ion, let the quick height of the Chanel <lb/>be onely 22 inches. </s> <s>Therefore the greater height to the le&longs;&longs;er, <lb/>is as the number 11. to 12. But the &longs;quare of 11. is 121, and the <lb/>&longs;quare of 12. is 144, the difference between the &longs;aid le&longs;&longs;er <pb xlink:href="040/01/619.jpg" pagenum="53"/>&longs;quare and the greater is 23. Therefore the diverted water, is <lb/>to the whole water, as 23. to 144: which is well near as 1 to <lb/>6 6/23: and that is the proportion that the quantity of the water <lb/>which runneth through the Chanellet &longs;hall have, to all the water <lb/>that runneth thorow the great Chanel. </s> <s>Now if we &longs;hould finde <lb/>by the Rule mentioned above in the fir&longs;t Propo&longs;ition, that the <lb/>quantity of the water that runneth through the Chanellet, is <lb/><emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> an hundred Barrels, in the &longs;pace of 15 &longs;econd minutes of <lb/>an hour, it is manife&longs;t, that the water which runneth through the <lb/>great Chanel in the &longs;aid time of 35 min. </s> <s>&longs;ec. </s> <s>&longs;hall be about 600 <lb/>Barrels.</s></p><p type="head"> <s><emph type="italics"/>The &longs;ame operation performed another way.<emph.end type="italics"/></s></p><p type="main"> <s>And becau&longs;e very often in applying the Theory to Practice <lb/>it happeneth, that all the nece&longs;&longs;ary particulars in the The­<lb/>ory cannot &longs;o ea&longs;ily be put in execution; therefore we will <lb/>here add another way of performing the &longs;ame Problem, if it &longs;hould <lb/>chance to happen that the Chanellet could not commodiou&longs;ly be <lb/>diverted from the great Chanel, but that it were ea&longs;ier for the <lb/>water of another &longs;maller Chanel to be brought into the greater <lb/>Chanel; which water of the &longs;maller Chanel might be ea&longs;ily mea­<lb/>&longs;ured, as hath been &longs;hewen in the fir&longs;t Probleme; or in ca&longs;e that <lb/>there did fall into a greater Chanel, a le&longs;&longs;er Chanel that might <lb/>be diverted and mea&longs;ured. </s> <s>Therefore I &longs;ay in the fir&longs;t ca&longs;e, If <lb/>we would mea&longs;ure the quantity of the water that runneth in a <lb/>certain time thorow the greater Chanel, into which another le&longs;&longs;er <lb/>Chanel that is mea&longs;urable may be brought, we mu&longs;t fir&longs;t exactly <lb/>mea&longs;ure the Chanellet, and then ob&longs;erve the quick height of the <lb/>greater Chanel, before the introduction of the le&longs;&longs;er; and having <lb/>brought in the &longs;aid Chanellet, we mu&longs;t agnin find the propor­<lb/>tion that the water of the Chanellet hath to all the water of the <lb/>great Ghanel; for the&longs;e terms of the proportion being known, as <lb/>al&longs;o the quantity of the water of the Chanellet, we &longs;hall al&longs;o <lb/>come to know the quantity of the water that runneth thorow <lb/>the great Chanel. </s> <s>It is likewi&longs;e manife&longs;t, that we &longs;hall obtain <lb/>our intent, if the ca&longs;e were that there entered into the great <lb/>Chanel, another le&longs;&longs;er Chanel that was mea&longs;urable, and that <lb/>might be diverted.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>It would be nece&longs;&longs;ary to make u&longs;e of this Doctrine in the di­<lb/>&longs;tribution of the waters that are imploy'd to overflow the fields, <lb/>as is u&longs;ed in the <emph type="italics"/>Bre&longs;ciau, Cremone&longs;e, Bergama&longs;e, Lodigian, Mila-<emph.end type="italics"/><pb xlink:href="040/01/620.jpg" pagenum="54"/><emph type="italics"/>ne&longs;e<emph.end type="italics"/> territories, and many other places, where very great &longs;uits <lb/>and differences ari&longs;e, which not being to be determined with in­<lb/>telligible rea&longs;ons, come oftentimes to be decided, by force of <lb/>armes; and in&longs;tead of flowing their Grounds with Waters, they <lb/>cruelly flow them with the &longs;hedding of humane blood, impiou&longs;ly <lb/>inverting the cour&longs;e of Peace and Ju&longs;tice, &longs;owing &longs;uch di&longs;orders <lb/>and feuds, as that they are &longs;ometimes accompanied with the ru­<lb/>ine of whole Cities, or el&longs;e unprofitably charge them with vain, <lb/>and &longs;ometimes prejudicial expences.</s></p><p type="head"> <s>PROPOS. IV. THEOR. II.</s></p><p type="main"> <s><emph type="italics"/>If a River increa&longs;e in quick height, the quantitie of <lb/>Water which the River di&longs;chargeth after the in­<lb/>crea&longs;e, hath the Proportion compounded of the <lb/>Proportions of the Quick height to the Quick <lb/>height, and of the velocity to the velocity.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a River, which whil&longs;t it is low, runneth thorow <lb/>the Regulator D F, with the Quick height A B, and after­<lb/>wards let a Flood come; and then let it run with the height <lb/>D B, I &longs;ay, that the quantity of the Water that is di&longs;charged <lb/>through D F, to that which di&longs;chargeth through A F, hath the <lb/>proportion compounded of the proportions of the velocity <lb/>through D F to the velocity through A F, and of the height <lb/>D B to the height A B. </s> <s>As the velocity through D F is to the <lb/>velocity through A F, &longs;o let the line R be to the line S; and as <lb/>the height D B is to the height A B; &longs;o let the line S be to the <lb/><figure id="id.040.01.620.1.jpg" xlink:href="040/01/620/1.jpg"/><lb/>line T. </s> <s>And let a Section be &longs;uppo&longs;ed L M N equal to the <lb/>Section D F in height and length, but let it be in velocity equal <lb/>to the Section AF. </s> <s>Therefore the quantity of the Water that run­<lb/>neth through D F to that which runneth through L N, &longs;hall be <pb xlink:href="040/01/621.jpg" pagenum="55"/>as the velocity through D F, to the velocity of L N, that is, to <lb/>the velocity through L N, that is, to the velocity through <emph type="italics"/>A F.<emph.end type="italics"/><lb/>therefore the quantity of Water which runneth through D <emph type="italics"/>F,<emph.end type="italics"/><lb/>to that which pa&longs;&longs;eth through L N, &longs;hall have the proportion <lb/>that R hath to S; but the quantity of the Water that runneth <lb/>through L N, to that which runneth through <emph type="italics"/>A F<emph.end type="italics"/>; (the Sections <lb/>being equally &longs;wift) &longs;hall have the proportion that the Section <lb/>L N hath to the Section A F, that is, that the height <emph type="italics"/>B<emph.end type="italics"/> D hath to <lb/>the height <emph type="italics"/>B<emph.end type="italics"/> A, that is, that S hath to T. Therefore, by equal <lb/>proportion, the quantity of the Water which runneth by D F, <lb/>to that which runneth by A F, &longs;hall have the proportion of R to <lb/>T, that is, &longs;hall be compounded of the proportions of the height <lb/>D <emph type="italics"/>B,<emph.end type="italics"/> to the height A <emph type="italics"/>B<emph.end type="italics"/>; and of the velocity through D F, to <lb/>the velocity through A F. </s> <s>And therefore if a River increa&longs;e in <lb/>quick height, the quantity of the Water that runneth after the <lb/>increa&longs;e, to that which runneth before the increa&longs;e, hath the <lb/>proportion compounded, &c. </s> <s>Which was to be demon&longs;trated.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE I.<emph.end type="italics"/></s></p><p type="main"> <s>Hence it followeth, that we having &longs;hewn, that the quantity of <lb/>the Water which runneth, whil&longs;t the River is high, to that <lb/>which ran, whil&longs;t it was low, hath the proportion compounded <lb/>of the velocity to the velocity, and of the height to the height. <lb/></s> <s>And it having been demon&longs;trated, that the velocity to the velo­<lb/>city is as the height to the height; it followeth, I &longs;ay, that the <lb/>quantity of the Water that runneth, whil&longs;t the River is high, to <lb/>that which runneth, whil&longs;t it is low, hath duplicate proportion of <lb/>the height to the height, that is, the proportion that the &longs;quares <lb/>of the heights have.</s></p><p type="head"> <s><emph type="italics"/>COROLLARIE II.<emph.end type="italics"/></s></p><p type="main"> <s>Vpon which things dependeth the rea&longs;on of that which I have <lb/>&longs;aid, in my &longs;econd Con&longs;ideration, that if by the diver&longs;ion of <lb/>5/9 of the Water that entereth by the Rivers into the Moor or <lb/>Fen, the Water be abated &longs;uch a mea&longs;ure, that &longs;ame &longs;hall be <lb/>only one third of its whole height; but moreover diverting the 4/9, it <lb/>&longs;hall abate two other thirds, a mo&longs;t principal point; and &longs;uch, <lb/>that its not having been well under&longs;tood, hath cau&longs;ed very great <lb/>di&longs;orders, and there would now, more than ever, follow extream <lb/>dammage, if one &longs;hould put in execution the diver&longs;ion of the <emph type="italics"/>Sile<emph.end type="italics"/><lb/>and other Rivers; and it is manife&longs;t, that in the &longs;ame manner, <lb/>wherewith it hath been demon&longs;trated, that the quantity of the <lb/>Water increa&longs;ing quadruple, the height would increa&longs;e onely <pb xlink:href="040/01/622.jpg" pagenum="56"/>double, and the quantity increa&longs;ing nonuple, the height increa­<lb/>&longs;eth triple; &longs;o that, by adding to units all the odde numbers, ac­<lb/>cording to their Series, the heights increa&longs;e according to the na­<lb/>tural progre&longs;&longs;ion of all the numbers, from units. </s> <s>As for exam­<lb/>ple, there pa&longs;&longs;ing thorow a Regulator &longs;uch a certain quantity of <lb/>Water in one time; adding three of tho&longs;e mea&longs;ures, the quick <lb/>height is two of tho&longs;e parts, which at fir&longs;t was one; and con­<lb/>tinuing to adde five of tho&longs;e &longs;aid mea&longs;ures, the height is three of <lb/>tho&longs;e parts which at fir&longs;t were one; and thus adding &longs;even, and <lb/>then nine, and then 11. and then 13, &c. </s> <s>the heights &longs;hall be 4. <lb/>then 5, then 6. then 7, &c. </s> <s>And for the greater facility of the <lb/>Work, we have de&longs;cribed the following Table, of which we will <lb/>declare the u&longs;e: The Table is divided into three Series or Pro­<lb/>gre&longs;&longs;ions of Numbers: the fir&longs;t Series containeth all the Num­<lb/>bers in the Natural Progre&longs;&longs;ion, beginning at a Unit, and is called <lb/>the Series of the Heights; the &longs;econd containeth all the odde <lb/>numbers, beginning at an unit, and is called the Series of the <lb/>Additions: the third containeth all the &longs;quare numbers, begin­<lb/>ning at an unit, and is called the Series of Quantity.<lb/><arrow.to.target n="table73"></arrow.to.target></s></p><table><table.target id="table73"></table.target><row><cell>Heights.</cell><cell>1</cell><cell>2</cell><cell>3</cell><cell>4</cell><cell>5</cell><cell>6</cell><cell>7</cell><cell>8</cell><cell>9</cell><cell>10</cell><cell>11</cell></row><row><cell>Additions.</cell><cell>1</cell><cell>3</cell><cell>5</cell><cell>7</cell><cell>9</cell><cell>11</cell><cell>13</cell><cell>15</cell><cell>17</cell><cell>19</cell><cell>21</cell></row><row><cell>Quantities.</cell><cell>1</cell><cell>4</cell><cell>9</cell><cell>16</cell><cell>25</cell><cell>36</cell><cell>49</cell><cell>64</cell><cell>81</cell><cell>100</cell><cell>121</cell></row></table><p type="head"> <s><emph type="italics"/>The u&longs;e of the afore-mentioned Table.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t, if we &longs;uppo&longs;e the whole quick height of a River of Run­<lb/>ning Water to be divided into any number of equal parts, at <lb/>plea&longs;ure, and would abate the &longs;ame one fift, by means of a divi­<lb/>&longs;ron; let there be found in the Table in the Series of heights the <lb/>number 5. the denominator of the part which the River is to a­<lb/>bate, and take the number that is immediately under it in the <lb/>row of Additions, which is 9. which let be &longs;ub&longs;tracted from the <lb/>number 25. placed underneath the &longs;ame in the row of Quanti­<lb/>ties, the remainder 16. &longs;ignifieth that of the 25. parts of Water <lb/>that ran in the River, whil&longs;t it was 5 mea&longs;ures high, there do <lb/>onely run 16. parts; &longs;o that to make it abate 1/5 it is nece&longs;&longs;ary to <lb/>take 9/25 from the Water that the whole River did carry; &longs;o that <lb/>with &longs;ub&longs;tracting &longs;omewhat more than one third of the Water of <lb/>the River, it is abated but only one fift.</s></p><p type="main"> <s>2. And thus, in the &longs;econd place, if on the contrary, one would <lb/>know how much water is to be added to the &longs;aid River to make <lb/>it increa&longs;e one fift more in height, &longs;o as that it may run in the <pb xlink:href="040/01/623.jpg" pagenum="57"/>Regulator 6. of tho&longs;e parts high; of which it ran before but 5. let <lb/>6 be found in the row of heights, and let the number 11. &longs;tand­<lb/>ing under the &longs;ame be taken and added to the number 25. <lb/>that is placed under the number 9. in the Additions, and 5. in <lb/>the heights, and you &longs;hall have 36; which is the quantity of the <lb/>water that runneth with the height of the River, when it is high <lb/>6 of tho&longs;e parts, whereof it was before but 5.</s></p><p type="main"> <s>3. But if it &longs;hould be de&longs;ired, to know how much water it is <lb/>requi&longs;ite to add to make the River ri&longs;e &longs;o, as that it may run in <lb/>height 8. of tho&longs;e parts of which before it ran but 5; one <lb/>ought to take the &longs;um of the number of the Series of Additions <lb/>&longs;tanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39. <lb/>and this &longs;hall be the &longs;umme that mu&longs;t be added to 25: So that <lb/>to make the River to run 8. of tho&longs;e parts in height, of which it <lb/>before did run 5, it will be nece&longs;&longs;ary to add 39. of tho&longs;e parts, <lb/>of which the River before was 25.</s></p><p type="main"> <s>4. Likewi&longs;e the &longs;ame Table giveth the quantity of water <lb/>that runneth from time to time through a River, that increa&longs;eth <lb/>by the addition of new water to the &longs;ame in one of its heights, the <lb/>quantity of its water be known. </s> <s>As for example: If we knew that <lb/>the River in one minute of an hour di&longs;chargeth 2500. of tho&longs;e mea­<lb/>&longs;ures of water, and runneth in height 5. parts in the Regulator, and <lb/>afterwards &longs;hould &longs;ee that it runneth 8 Palms high, finding in the <lb/>row of quantity the number placed under 8. which is 64. we would <lb/>&longs;ay that the River heightned, carrieth of water 64. of tho&longs;e parts <lb/>whereof it carried before but 25; and becau&longs;e before it carried <lb/>2500. mea&longs;ures, by the Golden Rule we will &longs;ay, that the River <lb/>carrieth 6400. of tho&longs;e mea&longs;ures, of which before it carried 2500.</s></p><p type="main"> <s>In this progre&longs;s of Nature, is one thing really curious, and that <lb/>at fir&longs;t &longs;ight &longs;eemeth to be &longs;omewhat Paradoxal, that we pro­<lb/>ceeding ordinately in the diver&longs;ions and additions, with additi­<lb/>ons and diver&longs;ions &longs;o unequal, the abatings do notwith&longs;tanding <lb/>alwaies prove equal, and &longs;o do the ri&longs;ings: And who would ever <lb/>think that a River in height, <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> 10. Palms, running and carry­<lb/>ing an hundred mea&longs;ures in a minute of an hour, is to abate but <lb/>one Palm, onely by the diver&longs;ion of 19. of tho&longs;e mea&longs;ures; and <lb/>then again, that the bui&longs;ine&longs;s cometh to that pa&longs;s, that it abateth <lb/>likewi&longs;e a Palm by the diver&longs;ion of three onely of tho&longs;e mea&longs;ures, <lb/>nay, by the diver&longs;ion of but one mea&longs;ure? </s> <s>and yet it is mo&longs;t <lb/>certain: And this truth meets with &longs;o manife&longs;t proofs in experi­<lb/>ence, that it is very admirable! And for the full &longs;atisfaction of <lb/>tho&longs;e, who not being able to comprehend &longs;ubtil demon&longs;trati­<lb/>ons, desire to be clearly inform'd by the matters of fact, and to <lb/>&longs;ee with their bobily eyes, and touch with their hands, what their <lb/>under&longs;tanding and rea&longs;on cannot reach unto: I will hear add <lb/>another very ea&longs;ie way to reduce all to an experiment, the <pb xlink:href="040/01/624.jpg" pagenum="58"/>which may be made in little, in great, or in very great; of <lb/>which I make u&longs;e frequently, to the admiration of &longs;uch as &longs;ee it.</s></p><p type="main"> <s>I prepared an hundred Siphons, or, if you will, bowed Pipes, <lb/>all equal; and placed them at the brim of a Ve&longs;&longs;el, wherein the <lb/>water is kept at one and the &longs;ame level (whether all the Syphons <lb/>work, or but a certain number of them) the mouths by which <lb/>the water i&longs;&longs;ueth being all placed in the &longs;ame level, parallel to <lb/>the Horizon; but lower in level than the water in the Ve&longs;&longs;el; and <lb/>gathered all the water falling from the Syphons into another <lb/>Ve&longs;&longs;el &longs;tanding lower than the former, I made it to run away <lb/>thorow a Chanel, in &longs;uch manner inclined, that wanting water <lb/>from the Syphons, the &longs;aid Chanel remained quite dry.</s></p><p type="main"> <s>And this done, I mea&longs;ured the quick height of the Chanel <lb/>with care, and afterwards divided it exactly into 10 equal parts, <lb/>and cau&longs;ing 19. of tho&longs;e Syphons to be taken away, &longs;o that the <lb/>Chanel did not run water, &longs;ave onely with 81 of tho&longs;e Syphons, <lb/>I again ob&longs;erved the quick height of the water in the &longs;ame &longs;ite <lb/>ob&longs;erved before, and found that its height was dimini&longs;hed pre­<lb/>ci&longs;ely the tenth part of all its fir&longs;t height; and thus continuing to <lb/>take away 17. other Syphons, the height was likewi&longs;e dimini&longs;h­<lb/>ed 1/1. of all its fir&longs;t quick height; and trying to take away 15. <lb/>Syphons, then 13, then 11, then 9, then 7, then 5, and then 3. <lb/>alwaies in the&longs;e diver&longs;ions, made in order as hath been &longs;aid, there <lb/>en&longs;ued &longs;till an abatement of 1/1. of the whole height.</s></p><p type="main"> <s>And here was one thing worthy of ob&longs;ervation, that the water <lb/>encrea&longs;ing in [<emph type="italics"/>or through<emph.end type="italics"/>] the Chanel, its quick height was diffe­<lb/>rent in different &longs;ites of the Chanel, that is &longs;till le&longs;&longs;er, the more <lb/>one approached to the Out-let; notwith&longs;tanding which the abate­<lb/>ment followed in all places proportionably, that is in all its &longs;ites <lb/>the fir&longs;t part of the height of that &longs;ite dimini&longs;hed: And more­<lb/>over the water i&longs;&longs;ued from the Chanel, and dilated into a broader <lb/>cour&longs;e, from which likewi&longs;e having divers Out-lets and Mouths; <lb/>yet neverthele&longs;s in that breadth al&longs;o the quick heights &longs;ucce&longs;&longs;ive­<lb/>ly varied and altered in the &longs;ame proportions. </s> <s>Nor did I here <lb/>de&longs;i&longs;t my ob&longs;ervation, but the water being dimini&longs;hed, that i&longs;&longs;u­<lb/>ed from the Syphons, and there being but one of them left that <lb/>di&longs;charged water; I ob&longs;erved the quick height that it made in the <lb/>above-&longs;aid &longs;ites, (the which was likewi&longs;e 1/1. of all the fir&longs;t height) <lb/>there being added to the water of that Syphon, the water of <lb/>three other Syphons; &longs;o that all the water was of 4 Syphons, <lb/>and con&longs;equently quadruple to the fir&longs;t Syphon; but the quick <lb/>height was onely double, and adding five Siphons, the quick <lb/>height became triple, and with adding &longs;even Syphons, the height <lb/>increa&longs;ed quadruple; and &longs;o by adding of 9. it increa&longs;ed quin­<lb/>tuple, and by adding of 11. it increa&longs;ed &longs;extuple, and by ad­<pb xlink:href="040/01/625.jpg" pagenum="59"/>ding of 13. it increa&longs;ed &longs;eptuple, and by adding of 15. octuple, <lb/>and by adding of 17. nonuple, and la&longs;tly by adding 19. Syphons; <lb/>&longs;o that all the water was centuple to the water of one Syphon, <lb/>yet neverthele&longs;s the quick height of all this water was onely de­<lb/>cuple to the fir&longs;t height conjoyned by the water that i&longs;&longs;ued from <lb/>one onely Syphon.</s></p><p type="main"> <s>For the more clear under&longs;tanding of all which, I have made <lb/>the following Figure; in which we have the mouth A, that <lb/>maintaineth the water of the Ve&longs;&longs;el B C in the &longs;ame level; though <lb/>it continually run; to the brim of the Ve&longs;&longs;el are put 25. Sy­<lb/>phons (and there may be many more) divided into 5 Cla&longs;&longs;es, <lb/>D E F G H, and the fir&longs;t D, are of one onely Syphon; the &longs;econd <lb/>E, of three Syphons; the third F, of five; the fourth G, of 7; the <lb/>fifth H, of 9; and one may &longs;uppo&longs;e the &longs;ixth of 11, the &longs;eventh <lb/>of 13 Syphons, and &longs;o of the other Cla&longs;&longs;es, all containing in con­<lb/>&longs;equent odd numbers &longs;ucce&longs;&longs;ively (we are content to repre&longs;ent in <lb/>the Figure no more but the five forenamed Cla&longs;&longs;es to avoid con­<lb/>fu&longs;ion) the gathered water D E F G H, which runneth thorow <lb/>the Chanel I K L, and falleth into the out-let M N O P; and &longs;o <lb/>much &longs;ufficeth for the explanation of this experiment.</s></p><figure id="id.040.01.625.1.jpg" xlink:href="040/01/625/1.jpg"/><pb xlink:href="040/01/626.jpg" pagenum="60"/><p type="head"> <s>PROPOS. V. PROB. III.</s></p><p type="main"> <s><emph type="italics"/>Any River of any bigne&longs;s, if being given to examine the <lb/>quantity of the Water that runneth thorow the River <lb/>in a time a&longs;&longs;igned.<emph.end type="italics"/></s></p><p type="main"> <s>By what we have &longs;aid already in the two preceding Pro­<lb/>blems, we may al&longs;o re&longs;olve this that we have now before <lb/>us; and it is done, by diverting in the fir&longs;t place from the <lb/>great River a good big mea&longs;urable Chanel, as is taught in the <lb/>&longs;econd Probleme, and ob&longs;erving the abatement of the River, <lb/>cau&longs;ed by the diver&longs;ion of the Chanel; and finding the proporti­<lb/>on that the Water of the Chanel hath to that of the River, then <lb/>let the Water of the Chanel be mea&longs;ured by the &longs;econd Pro­<lb/>bleme, and work as above, and you &longs;hall have your de&longs;ire.</s></p><p type="head"> <s>CONSIDERATION. I.</s></p><p type="main"> <s>And although it &longs;eemeth as if it might prove difficult, and <lb/>almo&longs;t impo&longs;&longs;ible to make u&longs;e of the Regulator number, if <lb/>one be about to mea&longs;ure the water of &longs;ome great River, <lb/>and con&longs;equently would be impo&longs;&longs;ible, or at lea&longs;t very difficult <lb/>to reduce the Theory of the fir&longs;t Probleme into practice: Yet ne­<lb/>verthele&longs;s, I could &longs;ay that &longs;uch great conceits of mea&longs;uring the <lb/>water of a great River, are not to come into the minds of any <lb/>but great Per&longs;onages, and potent Princes; of whom it is expected <lb/>for their extraordinary concerns, that they will make the&longs;e kinde <lb/>of enquiries; as if here in <emph type="italics"/>Italy<emph.end type="italics"/> it &longs;hould be of the Rivers <emph type="italics"/>Tyber, <lb/>Velino, Chiana, Arno, Serchio, Adice,<emph.end type="italics"/> in which it &longs;eemeth real­<lb/>ly difficult to apply the <emph type="italics"/>R<emph.end type="italics"/>egulator, to finde exactly the quick <lb/>height of the <emph type="italics"/>R<emph.end type="italics"/>iver: But becau&longs;e in &longs;uch like ca&longs;es &longs;ometimes <lb/>it would turn to account to be at &longs;ome charge, to come to the <lb/>exact and true knowledge of the quantity of water which that <lb/><emph type="italics"/>R<emph.end type="italics"/>iver carrieth, by knowledge whereof, other greater di&longs;­<lb/>bur&longs;ments might afterwards be avoided, that would oft times be <lb/>made in vain; and prevent the di&longs;gu&longs;ts, which &longs;ometimes happen <lb/>among&longs;t Princes: Upon this ground I think it will be well to <lb/>&longs;hew al&longs;o the way how to make u&longs;e of the <emph type="italics"/>R<emph.end type="italics"/>egulator in the&longs;e <lb/>great <emph type="italics"/>R<emph.end type="italics"/>ivers; in which if we will but open our eyes, we &longs;hall meet <lb/>with good ones, and tho&longs;e made without great co&longs;t or labour, <lb/>which will &longs;erve our turn.</s></p><p type="main"> <s>For upon &longs;uch like <emph type="italics"/>R<emph.end type="italics"/>ivers there are Wears, or Lockes made, <pb xlink:href="040/01/627.jpg" pagenum="61"/>to cau&longs;e the Waters to ri&longs;e, and to turn them for the &longs;ervice of <lb/>Mills, or the like. </s> <s>Now in the&longs;e Ca&longs;es it is &longs;ufficient, that one <lb/>erect upon the two extreames of the Weare two Pila&longs;ters either <lb/>of Wood or Brick, which with the bottome of the Weare do <lb/>compo&longs;e our Regulator, wherewith we may make our de&longs;ired <lb/>operation, yea the Chanel it &longs;elf diverted &longs;hall &longs;erve, without <lb/>making any other diver&longs;ion or union. </s> <s>And in brief, if the bu­<lb/>fine&longs;&longs;es be but managed by a judicious per&longs;on, there may wayes <lb/>and helps be made u&longs;e of, according to occa&longs;ion, of which it <lb/>would be too tedious to &longs;peak, and therefore this little that hath <lb/>been hinted &longs;hall &longs;u&longs;&longs;ice.</s></p><p type="head"> <s>CONSIDERATION II.</s></p><p type="main"> <s>From what hath been declared, if it &longs;hall be well under­<lb/>&longs;tood, may be deduced many benefits and conveniences, <lb/>not onely in dividing of Running Waters for infinite u&longs;es <lb/>that they are put to in turning of Corne-Mills, Paper-Mills, <lb/>Gins, Powder-Mills, Rice-Mills, Iron Mills, Oil-Mills, Saw­<lb/>ing-Mills, Mirtle-Mills, Felling-Mills, Fulling-Mills, Silk-Mills, <lb/>and &longs;uch other Machines; but al&longs;o in ordering Navigable Cha­<lb/>nels, diverting Rivers and Chanels of Waters, or terminating <lb/>and limiting the &longs;izes of Pipes for Fountains: In all which af­<lb/>fairs there are great errours committed, to the lo&longs;&longs;e of much <lb/>expence, the Chanels and Pipes that are made, &longs;ometimes not <lb/>being &longs;ufficient to carry the de&longs;igned Waters, and &longs;ometimes they <lb/>are made bigger than is nece&longs;&longs;ary; which di&longs;orders &longs;hall be <lb/>avoided, if the Engineer be advi&longs;ed of the things above&longs;aid: and <lb/>in ca&longs;e that to the&longs;e Notions there be added the knowledge of <lb/>Philo&longs;ophy and Mathematicks, agreeable to the &longs;ublime Di&longs;co­<lb/>veries of <emph type="italics"/>Signore Galilæo,<emph.end type="italics"/> and the further improvement thereof <lb/>by <emph type="italics"/>Signore Evangeli&longs;ta Torricelli,<emph.end type="italics"/> Mathematician to the Grand <lb/><emph type="italics"/>Duke of Tu&longs;cany,<emph.end type="italics"/> who hath &longs;ubtilly and admirably handled this <lb/>whole bu&longs;ine&longs;&longs;e of Motion, one &longs;hall then come to the know­<lb/>ledge of particular notions of great curio&longs;ity in the Theoricks, <lb/>and of extraordinary benefit in the Practicks that daily occur in <lb/>the&longs;e bu&longs;ine&longs;&longs;es.</s></p><p type="main"> <s>And to &longs;hew, in effect, of what utility the&longs;e Notions are, I <lb/>have thought fit to in&longs;ert, in this place, the Con&longs;iderations by <lb/>me made upon the Lake of <emph type="italics"/>Venice,<emph.end type="italics"/> and to repre&longs;ent, <lb/>at large, by the experience of the la&longs;t year 1641. the mo&longs;t Se­<lb/>rene <emph type="italics"/>Erizzo,<emph.end type="italics"/> then Duke of the &longs;aid Republique. </s> <s>Being <lb/>therefore at <emph type="italics"/>Venice,<emph.end type="italics"/> in the year afore&longs;aid, I was reque&longs;ted by the <lb/>mo&longs;t Illu&longs;trious and mo&longs;t Excellent <emph type="italics"/>Signore Giovanni Ba&longs;a-<emph.end type="italics"/><pb xlink:href="040/01/628.jpg" pagenum="62"/><emph type="italics"/>donna,<emph.end type="italics"/> a Senatour of great worth and merit, that I would inge­<lb/>nuou&longs;ly deliver my opinion touching the &longs;tate of the Lake <lb/>of <emph type="italics"/>Venice<emph.end type="italics"/>; and after I had di&longs;cour&longs;ed with his Honour &longs;eve­<lb/>ral times, in the end I had order to &longs;et down the whole <lb/>bu&longs;ine&longs;&longs;e in writing, who having afterwards read it privately, <lb/>the &longs;aid <emph type="italics"/>Signore<emph.end type="italics"/> imparted the &longs;ame, with like privacy, to the <lb/>mo&longs;t Serene PRINCE, and I received order to repre&longs;ent the <lb/>&longs;ame to the full <emph type="italics"/>Colledge,<emph.end type="italics"/> as accordingly I did in the Moneth <lb/>of <emph type="italics"/>May,<emph.end type="italics"/> the &longs;ame year, and it was as followeth.</s></p><figure id="id.040.01.628.1.jpg" xlink:href="040/01/628/1.jpg"/><pb xlink:href="040/01/629.jpg" pagenum="63"/><p type="head"> <s>CONSIDER ATIONS <lb/>Concerning the <lb/>LAKE <lb/>OF <lb/>VENICE. <lb/>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, <lb/>Abbot of S. <emph type="italics"/>Benedetto Aloy&longs;io,<emph.end type="italics"/> Mathematician to <lb/>Pope <emph type="italics"/>VR BAN VIII.<emph.end type="italics"/> and Profe&longs;&longs;or in <lb/>ROME.</s></p><p type="head"> <s><emph type="italics"/>CONSIDERATION I.<emph.end type="italics"/></s></p><p type="main"> <s>Though the principal cau&longs;e be but one <lb/>onely, that in my judgment threatneth <lb/>irreparable ruine to the Lake of <lb/><emph type="italics"/>Venice,<emph.end type="italics"/> in the pre&longs;ent &longs;tate in which it <lb/>now &longs;tands; Yet neverthele&longs;&longs;e, I think <lb/>that two Heads may be con&longs;idered. <lb/></s> <s>And this Con&longs;ideration may peradven­<lb/>ture &longs;erve us for to facilitate and explain <lb/>the opportune remedies, though not to <lb/>render the &longs;tate of things ab&longs;olutely unchangeable and eternal: <lb/>an enterprize impo&longs;&longs;ible, and e&longs;pecially in that which having had <lb/>&longs;ome beginning, ought likewi&longs;e nece&longs;&longs;arily to have its end; or <lb/>at lea&longs;t to prevent the danger for many hundreds of years; and <lb/>po&longs;&longs;ibly it may, in the mean time, by the mutation it &longs;elf be <lb/>brought into a better condition.</s></p><p type="main"> <s>I &longs;ay therefore, that the pre&longs;ent di&longs;order may be con&longs;idered <lb/>under two Heads; One is the very notable di&longs;covery of Land <lb/>that is ob&longs;erved at the time of low Water, the which, be&longs;ides <lb/>the ob&longs;tructing of Navigation in the Lake and al&longs;o in the <lb/>Chanels, doth likewi&longs;e threaten another mi&longs;chief and di&longs;order <pb xlink:href="040/01/630.jpg" pagenum="64"/>worthy of very particular con&longs;ideration, which is, That the Sun <lb/>drying up that mudde, e&longs;pecially in the times of hot Summers, <lb/>doth rai&longs;e thence the putrified and pernicious vapours, fogs, and <lb/>exhalations that infect the Air, and may render the City unha­<lb/>bitable.</s></p><p type="main"> <s>The &longs;econd Head is the great Stoppage that daily is grow­<lb/>ing in the Ports, e&longs;pecially of <emph type="italics"/>Venice,<emph.end type="italics"/> at <emph type="italics"/>Malamoco<emph.end type="italics"/>; concerning <lb/>which matters I will hint certain general points, and then <lb/>will proceed to the more particular and important affairs.</s></p><p type="main"> <s>And fir&longs;t, I &longs;ay, that I hold it altogether impo&longs;&longs;ible to effect <lb/>any thing, though never &longs;o profitable, which doth not bring with <lb/>it &longs;ome mi&longs;chief; and therefore the good and the hurt ought to <lb/>be very well weighed, and then the le&longs;&longs;e harmful part to be im­<lb/>braced.</s></p><p type="main"> <s>Secondly, I propo&longs;e to con&longs;ideration, that the &longs;o notable di&longs;­<lb/>covery of Earth & Mud, hath not been long ob&longs;erved, as I under­<lb/>&longs;tand, from old per&longs;ons that can remember pa&longs;&longs;ages for fifty <lb/>years pa&longs;t; which thing being true, as to me it &longs;eemeth mo&longs;t <lb/>true, it &longs;hould appear that it could not but be good to reduce <lb/>matters to that pa&longs;&longs;e that they were at formerly, (laying a&longs;ide <lb/>all affection or pa&longs;&longs;ion that &longs;elf-flattering minds have entertained <lb/>for their own conceits) or at lea&longs;t it &longs;hall be nece&longs;&longs;ary &longs;peedily to <lb/>con&longs;ult the whole.</s></p><p type="main"> <s>Thirdly, I hold that it is nece&longs;&longs;ary to weigh, whether from the <lb/>fore&longs;aid di&longs;covery of Land, it followeth, that onely the Earth ri­<lb/>&longs;eth, as it is commonly thought by all, without di&longs;pute; or whe­<lb/>ther the Waters are abated and faln away; or el&longs;e whether it <lb/>proceedeth from both the one and other cau&longs;e. </s> <s>And here it would <lb/>be &longs;ea&longs;onable to enquire, what &longs;hare the &longs;aid cau&longs;es may have, <lb/>each con&longs;idered apart in the fore&longs;aid effect. </s> <s>For, in the fir&longs;t <lb/>ca&longs;e, if the Earth have been rai&longs;ed, it would be nece&longs;&longs;ary to <lb/>con&longs;ider of taking it down, and removing it: But if the Wa­<lb/>ters have failed or abated, I believe that it would be extreamly ne­<lb/>ce&longs;&longs;ary to re&longs;tore and rai&longs;e them: And if both the&longs;e rea&longs;ons have <lb/>con&longs;pired in this effect, it will be nece&longs;&longs;ary to remedy them each <lb/>apart. </s> <s>And I do, for my part, think, that the &longs;o notable appea­<lb/>rance of Shelves at the time of low Water, proceeds principally <lb/>from the decrea&longs;e and abatement of the Waters, which may <lb/>confidently be affirmed to need no other proof, in regard that the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> hath been actually diverted which did formerly di&longs;charge <lb/>its Water into the Lake.</s></p><p type="main"> <s>As to the other point of the great Stoppage of Ports, I hold, <lb/>that all proceedeth from the violence of the Sea, which being <lb/>&longs;ometimes di&longs;turbed by windes, e&longs;pecially at the time of the wa­<lb/>ters flowing, doth continually rai&longs;e from its bottome immen&longs;e <pb xlink:href="040/01/631.jpg" pagenum="65"/>heaps of &longs;and, carrying them by the tide; and force of the waves <lb/>into the Lake; it not having on its part any &longs;ttength of current <lb/>that may rai&longs;e and carry them away, they &longs;ink to the bottom, and <lb/>&longs;o they choke up the Ports. </s> <s>And that this effect happeneth in <lb/>this manner, we have mo&longs;t frequent experiences thereof along the <lb/>Sea-coa&longs;ts: And I have ob&longs;erved in <emph type="italics"/>Tu&longs;cany<emph.end type="italics"/> on the <emph type="italics"/>Roman­<lb/>&longs;hores,<emph.end type="italics"/> and in the Kingdom of of <emph type="italics"/>Naples,<emph.end type="italics"/> that when a river fal­<lb/>leth into the Sea, there is alwaies &longs;een in the Sea it &longs;elf, at the place <lb/>of the rivets out-let, the re&longs;emblance, as it were, of an half-Moon, <lb/>or a great &longs;helf of &longs;ettled &longs;and under water, much higher then the <lb/>re&longs;t of the &longs;hore, and it is called in <emph type="italics"/>Tu&longs;cany, il Cavallo<emph.end type="italics"/>; and here <lb/>in <emph type="italics"/>Venice, lo Scanto<emph.end type="italics"/>: the which cometh to be cut by the current <lb/>of the river, one while on the right &longs;ide, another while on the <lb/>left, and &longs;ometimes in the mid&longs;t, according as the Wind fits. </s> <s>And <lb/>a like effect I have ob&longs;erved in certain little Rillets of water, <lb/>along the Lake of <emph type="italics"/>Bol&longs;ena<emph.end type="italics"/>; with no other difference, &longs;ave that of <lb/>&longs;mall and great.</s></p><p type="main"> <s>Now who&longs;o well con&longs;idereth this effect, plainly &longs;eeth that it <lb/>proceeds from no other, than from the contrariety of the &longs;tream <lb/>of the River, to the <emph type="italics"/>impetus<emph.end type="italics"/> of the Sea waves; &longs;eeing that <lb/>great abundance of &longs;and which the Sea continually throws upon <lb/>the &longs;hore, cometh to be driven into the Sea by the &longs;tream of the <lb/>river; and in that place where tho&longs;e two impediments meet <lb/>with equal force, the &longs;and &longs;etleth under water, and thereupon is <lb/>made that &longs;ame Shelf or <emph type="italics"/>Cavallo<emph.end type="italics"/>; the which if the river carry <lb/>water, and that any con&longs;iderable &longs;tore, it &longs;hall be thereby cut <lb/>and broken; one while in one place, and another while in ano­<lb/>ther; as hath been &longs;aid, according as the Wind blows: And <lb/>through that Chanel it is that Ve&longs;&longs;els fall down into the Sea, and <lb/>again make to the river, as into a Port. </s> <s>But if the Water of <lb/>the river &longs;hall not be continual or &longs;hall be weak, in that ca&longs;e the <lb/>force of the Sea-Wind &longs;hall drive &longs;uch a quantity of &longs;and into <lb/>the mouth of the Port, and of the river, as &longs;hall wholly choak it <lb/>up. </s> <s>And hereupon there are &longs;een along the Sea-&longs;ide, very many <lb/>Lakes and Meers, which at certain times of the year abound with <lb/>waters, and the Lakes bear down that enclo&longs;ure, and run into <lb/>the Sea.</s></p><p type="main"> <s>Now it is nece&longs;&longs;ary to make the like reflections on our Ports <lb/>of <emph type="italics"/>Venice, Malamocco, Bondolo,<emph.end type="italics"/> and <emph type="italics"/>Chiozza<emph.end type="italics"/>; which in a certain <lb/>&longs;en&longs;e are no other than Creeks, mouths, and openings of the &longs;hore <lb/>that parts the Lake from the main Sea; and therefore I hold that <lb/>if the Waters in the Lake were plentiful, they would have <lb/>&longs;trength to &longs;cowr the mouths of the Ports thorowly, & with great <lb/>force; but the Water in the Lake failing, the Sea will with­<lb/>out any oppo&longs;al, bring &longs;uch a drift of &longs;and into the Ports; that if <pb xlink:href="040/01/632.jpg" pagenum="66"/>it doth not wholly choke them up, it &longs;hall render them at lea&longs;t <lb/>unprofitable, and impo&longs;&longs;ible for Barks and great Ve&longs;&longs;els.</s></p><p type="main"> <s>Many other con&longs;iderations might be propounded concerning <lb/>the&longs;e two heads of the &longs;toppage of the Ports, and of the appea­<lb/>rance of the Ouze and Mud in the Lakes, but &longs;o much &longs;hall &longs;uf­<lb/>fice us to have hinted, to make way for di&longs;cour&longs;ing of the opera­<lb/>tions about the oportune remedies.</s></p><p type="main"> <s>Yet before that I propound my opinion, I &longs;ay, That I know <lb/>very well that my propo&longs;al, at fir&longs;t &longs;ight, will &longs;eem ab&longs;urd and in­<lb/>convenient; and therefore, as &longs;uch, will perhaps be rejected by <lb/>the mo&longs;t: and &longs;o much the rather, for that it will prove directly <lb/>contrary to what hath hitherto been, and as I hear, is intended to <lb/>be done. </s> <s>And I am not &longs;o wedded to my opinions, but that I <lb/>do con&longs;ider what others may judge thereof: But be it as it will, <lb/>I am obliged to &longs;peak my thoughts freely, and that being done, <lb/>I will leawe it to wi&longs;er men than my &longs;elf; when they &longs;hall have <lb/>well con&longs;idered my rea&longs;ons, to judge and deliberate of the <emph type="italics"/>quid <lb/>agendum:<emph.end type="italics"/> And if the &longs;entence &longs;hall go again&longs;t me, I appeal to the <lb/>mo&longs;t equitable and inexorable Tribunal of Nature, who not <lb/>caring in the lea&longs;t to plea&longs;e either one party or another, will be <lb/>alwaies a punctual and inviolable executrix of her eternal De­<lb/>crees, again&longs;t which neither humane deliberations, nor our vain <lb/>de&longs;ires; &longs;hall ever have power to rebell. </s> <s>I added by word of <lb/>mouth that which followeth.</s></p><p type="main"> <s>Though your Highne&longs;s intere&longs;t your &longs;elf in this Noble Col­<lb/>ledge, and cau&longs;e it to be confirmed in the ^{*} Senate by univer&longs;al <lb/><arrow.to.target n="marg969"></arrow.to.target><lb/>Vote, that the Winds do not blow, that the Sea doth not fluctuate, <lb/>that the Rivers do not run; yet &longs;hall the Winds be alwaies deaf, <lb/>the Sea &longs;hall be con&longs;tant in its incon&longs;tancy, and the Rivers mo&longs;t <lb/>ob&longs;tinate: And the&longs;e &longs;hall be my Judges, and to their determi­<lb/>nation I refer my &longs;elf.</s></p><p type="margin"> <s><margin.target id="marg969"></margin.target>* In <emph type="italics"/>Pregadi,<emph.end type="italics"/> a <lb/>particular Coun­<lb/>cil, the Senators of <lb/>which have great <lb/>Authority.</s></p><p type="main"> <s>By what hath been &longs;aid, in my opinion, that is made very clear <lb/>and manife&longs;t, which in the beginning of this di&longs;cour&longs;e I glanced <lb/>at; namely, That the whole di&longs;order, although it be divided into <lb/>two heads, into the di&longs;covery of the Mud, and of the &longs;toppage <lb/>Ports, yet neverthele&longs;s, by the application of one onely remedy, <lb/>and that in my e&longs;teem very ea&longs;ie, the whole &longs;hall be removed: <lb/>And this it is; That there be re&longs;tored into the Lake as much <lb/>Water as can be po&longs;&longs;ible, and in particular from the upper parts <lb/>of <emph type="italics"/>Venice,<emph.end type="italics"/> taking care that the Water be as free from Mud as is <lb/>po&longs;&longs;ible. </s> <s>And that this is the true and real remedy of the prece­<lb/>dent di&longs;orders, is manife&longs;t: For in the pa&longs;&longs;age that this Water <lb/>&longs;hall make thorow the Lakes, it &longs;hall of it &longs;elf by degrees clear <lb/>the Chanels in &longs;undry parts of them, according to the currents <lb/>that it &longs;hall &longs;ucce&longs;&longs;ively acquire, and in this manner being di&longs;­<pb xlink:href="040/01/633.jpg" pagenum="67"/>per&longs;ed thorow the Lake, it &longs;hall maintain the waters in the &longs;ame, <lb/>and in the Chanels much higher, as I &longs;hall prove hereafter; a <lb/>thing that will make Navigation commodious; and that, which <lb/>moreover is of great moment in our bu&longs;ine&longs;&longs;e; tho&longs;e Shelves <lb/>of Mud which now di&longs;cover them&longs;elves at the time of Low­<lb/>Waters &longs;hall be alwayes covered, &longs;o that the putrefaction of <lb/>the Air &longs;hall al&longs;o be remedied.</s></p><p type="main"> <s>And la&longs;tly, this abundance of Water being alwayes to di&longs;­<lb/>charge it &longs;elf into the Sea by the Ports, I do not doubt, but that <lb/>their bottomes will be &longs;coured. </s> <s>And that the&longs;e effects mu&longs;t fol­<lb/>low, Nature her &longs;elf &longs;eemeth to per&longs;wade, there remaining onely <lb/>one great doubt, whether that abundance of Water that &longs;hall be <lb/>brought into the Lake may be really &longs;ufficient to make the Wa­<lb/>ters ri&longs;e &longs;o much as to keep the Shelves covered, and to facilitate <lb/>Navigation, which ought to be at lea&longs;t half a ^{*} Brace, or there­<lb/><arrow.to.target n="marg970"></arrow.to.target><lb/>abouts. </s> <s>And indeed it &longs;eemeth at fir&longs;t &longs;ight to be impo&longs;&longs;ible, <lb/>that the &longs;ole Water of the ^{*} <emph type="italics"/>Brent<emph.end type="italics"/> let into the Lake, and di&longs;­<lb/><arrow.to.target n="marg971"></arrow.to.target><lb/>per&longs;ed over the &longs;ame, can occa&longs;ion &longs;o notable an height of water; <lb/>and the more to confirm the difficulties, one might &longs;ay, reducing <lb/>the rea&longs;on to calculation, that in ca&longs;e the <emph type="italics"/>Brent<emph.end type="italics"/> were 40. Bra­<lb/>ces broad, and two and an half high, and the breadth of the <lb/>Lake were 20000. Braces, it would &longs;eem nece&longs;&longs;ary that the <lb/>height of the water of the <emph type="italics"/>Brent<emph.end type="italics"/> dilated and di&longs;tended thorow <lb/>the Lake would be but onely 1/200 of a Brace in height, which is <lb/>imperceptible, and would be of no avail to our purpo&longs;e; nay <lb/>more, it being very certain that the <emph type="italics"/>Brent<emph.end type="italics"/> runneth very muddy <lb/>and foul, this would occa&longs;ion very great mi&longs;chief, filling and <lb/>contracting the Lake, and for that rea&longs;on this remedy ought, as <lb/>pernicious, to be totally excluded and condemned.</s></p><p type="margin"> <s><margin.target id="marg970"></margin.target>* A <emph type="italics"/>Venice<emph.end type="italics"/> Brace <lb/>is 11/16 of our yard.</s></p><p type="margin"> <s><margin.target id="marg971"></margin.target>* A River of <lb/>that name.</s></p><p type="main"> <s>I here confe&longs;&longs;e that I am &longs;urprized at the forme of the Argu­<lb/>ment, as if I were in a certain manner convinced, that I dare not <lb/>adventure to &longs;ay more, or open my mouth in this matter; but <lb/>the &longs;trength it &longs;elf of the Argument, as being founded upon <lb/>the means of Geometrical and Arithmetical Calculation, hath <lb/>opened me the way to di&longs;cover a very crafty fraud that is couch­<lb/>ed in the &longs;ame Argument, which fraud I will make out to any <lb/>one that hath but any in&longs;ight in <emph type="italics"/>Geometry<emph.end type="italics"/> and <emph type="italics"/>Arithmetick.<emph.end type="italics"/><lb/>And as it is impo&longs;&longs;ible, that &longs;uch an argument &longs;hould be produced <lb/>by any but &longs;uch as have ta&longs;ted of the&longs;e, in &longs;uch affairs, mo&longs;t pro­<lb/>fitable, and mo&longs;t nece&longs;&longs;ary Sciences; &longs;o do not I pretend to make <lb/>my &longs;elf under&longs;tood, &longs;ave onely by &longs;uch, to whom I will evince <lb/>&longs;o clearly, as that more it cannot be de&longs;ired, the errour and fraud <lb/>wherein tho&longs;e Ancients and Moderns have been, and alwayes <lb/>are intangled, that have in any way yet handled this matter of <lb/>con&longs;idering the Mea&longs;ure and Quantity of the Waters that move. <pb xlink:href="040/01/634.jpg" pagenum="68"/>And &longs;o great is the e&longs;teem that I have for that which I am now <lb/>about to &longs;ay touching this particular, that I am content that all <lb/>the re&longs;t of my Di&longs;cour&longs;e be rejected; provided, that that be per­<lb/>fectly under&longs;tood, which I am hereafter to propo&longs;e, I holding <lb/>and knowing it to be a main Principle, upon which all that is <lb/>founded that can be &longs;aid either well or hand&longs;omely on this parti­<lb/>cular. </s> <s>The other Di&longs;cour&longs;es may have an appearance of being <lb/>probable, but this hits the mark as full as can be de&longs;ired, arriving <lb/>at the highe&longs;t degree of certainty.</s></p><p type="main"> <s>I have, &longs;eventeen years &longs;ince, as I repre&longs;ented to the mo&longs;t Se­<lb/>rene Prince, and to the Right Honourable the Pre&longs;ident of the <lb/>Lords the Commi&longs;&longs;ioners of the ^{*}Sewers, written a Treati&longs;e of the <lb/><arrow.to.target n="marg972"></arrow.to.target><lb/>Mea&longs;ure of the waters that move, in which I Geometrically de­<lb/>mon&longs;trate and declare this bu&longs;ine&longs;&longs;e, and they who &longs;hall have <lb/>well under&longs;tood the ground of my Di&longs;cour&longs;e, will re&longs;t fully &longs;a­<lb/>tisfied with that which I am now about to propo&longs;e: But that all <lb/>may become rhe more ea&longs;ie, I will more briefly explicate and <lb/>declare &longs;o much thereof as I have demon&longs;trated in the Di&longs;cour&longs;e, <lb/>which will &longs;uffice for our purpo&longs;e: And if that &longs;hould not be <lb/>enough, we have alwayes the experiment of a very ea&longs;ie and <lb/>cheap way to clear up the whole bu&longs;ine&longs;&longs;e. </s> <s>And moreover I <lb/>will take the boldne&longs;&longs;e to affirm, that in ca&longs;e there &longs;hould not for <lb/>the pre&longs;ent any deliberation be made concerning this affair, ac­<lb/>cording to my opinion; yet neverthele&longs;&longs;e it will be, at &longs;ome <lb/>time or other; or if it be not, things will grow wor&longs;e and <lb/>wor&longs;e.</s></p><p type="margin"> <s><margin.target id="marg972"></margin.target>* <emph type="italics"/>I. </s> <s>Savii dell' <lb/>Acque,<emph.end type="italics"/> a particu­<lb/>lar Council that <lb/>take care of the <lb/>Lakes and other <lb/>Aquatick affairs.</s></p><p type="main"> <s>For more clear under&longs;tanding, therefore, it ought to be known, <lb/>that it being required, as it is generally u&longs;ed, to mea&longs;ure the wa­<lb/>ters of a River, its breadth and its depth is taken, and the&longs;e two <lb/>dimen&longs;ions being multiplied together, the product is affirmed to <lb/>be the quantity of that River: As for example, if a River &longs;hall <lb/>be 100. feet broad, and 20. feet high, it will be &longs;aid, that that <lb/>River is 2000 feet of Water, and &longs;o if a Ditch &longs;hall be 15. feet <lb/>broad, and 5. feet high, this &longs;ame Ditch will be affirmed to be <lb/>75. feet of Water: And this manner of mea&longs;uring Running <lb/>Water hath been u&longs;ed by the Ancients, and by Moderns, with <lb/>no other difference, &longs;ave onely that &longs;ome have made u&longs;e of the <lb/>Foot, others of the Palme, others of the Brace, and others of <lb/>other mea&longs;ures.</s></p><p type="main"> <s>Now becau&longs;e that in ob&longs;erving the&longs;e Waters that move, I fre­<lb/>quently found, that the &longs;ame Water of the &longs;ame River was in <lb/>&longs;ome &longs;ites of its Chanel pretty big, and in others much le&longs;&longs;e, <lb/>not arriving in &longs;ome places to the twentieth, nor to the hundreth <lb/>part of that which it is &longs;een to be in other places; therefore this <lb/>vulgar way of mea&longs;uring the Waters that move, for that they did <pb xlink:href="040/01/635.jpg" pagenum="69"/>not give me a certain and &longs;table mea&longs;ure and quantity of Water, <lb/>began de&longs;ervedly to be &longs;u&longs;pected by me, as difficult and defective, <lb/>being alwayes various, and the mea&longs;ure, on the contrary, being <lb/>to be alwayes determinate, and the &longs;ame; it is therefore written, <lb/>that <emph type="italics"/>Pondus & Pondus, Men&longs;ura & Men&longs;ura, utrumque abomi­<lb/>nabile e&longs;t apud Deum,<emph.end type="italics"/> Exod. </s> <s>I con&longs;idered that in the Terri­<lb/>tory of <emph type="italics"/>Bre&longs;cia,<emph.end type="italics"/> my native Countrey, and in other places, where <lb/>Waters are divided to overflow the Grounds, by the like way of <lb/>mea&longs;uring them, there were committed grievous and mo&longs;t impor­<lb/>tant errours, to the great prejudice of the Publique and of Pri­<lb/>vate per&longs;ons, neither they that &longs;ell, nor they that buy under­<lb/>&longs;tanding the true quantity of that which is &longs;old and bought: In <lb/>regard that the &longs;ame &longs;quare mea&longs;ure, as is accu&longs;tomed in tho&longs;e <lb/>parts, a&longs;&longs;igned one particular per&longs;on, carried to &longs;ometimes above <lb/>twice or thrice as much water, as did the &longs;ame &longs;quare mea&longs;ure a&longs;­<lb/>&longs;igned to another. </s> <s>Which thing proveth to be the &longs;ame incon­<lb/>venience, as if the mea&longs;ure wherewith Wine and Oil is bought <lb/>and &longs;old, &longs;hould hold twice or thrice as much Wine or Oil at one <lb/>time as at another. </s> <s>Now this Con&longs;ideration invited my minde <lb/>and curio&longs;ity to the finding out of the true mea&longs;ure of Running <lb/>Waters. </s> <s>And in the end, by occa&longs;ion of a mo&longs;t important bu­<lb/>&longs;ine&longs;&longs;e that I was imployed in &longs;ome years &longs;ince, with great in­<lb/>ten&longs;ene&longs;&longs;e of minde, and with the &longs;ure direction of <emph type="italics"/>Geometry,<emph.end type="italics"/> I <lb/>have di&longs;covered the mi&longs;take, which was, that we being upon the <lb/>bu&longs;ine&longs;&longs;e of taking the mea&longs;ure of the Waters that move, do make <lb/>u&longs;e of two dimen&longs;ions onely, namely, breadth and depth, keep­<lb/>ing no account of the length. </s> <s>And yet the Water being, though <lb/>running, a Body, it is nece&longs;&longs;ary in forming a conceit of its quan­<lb/>tity, in relation to another, to keep account of all the three Di­<lb/>men&longs;ions, that is of length, breadth, and depth.</s></p><p type="main"> <s>Here an objection hath been put to me, in behalf of the ordi­<lb/>nary way of mea&longs;uring Running Waters, in oppo&longs;ition to what <lb/>I have above con&longs;idered and propo&longs;ed: and I was told, Its true, <lb/>that in mea&longs;uring a Body that &longs;tands &longs;till, one ought to take all <lb/>the three Dimen&longs;ions; but in mea&longs;uring a Body that continually <lb/>moveth, as the Water, the ca&longs;e is not the &longs;ame: For the length <lb/>is not to be had, the length of the water that moveth being infi­<lb/>nite, as never fini&longs;hing its running; and con&longs;equently is incom­<lb/>prehen&longs;ible by humane under&longs;tanding, and therefore with rea&longs;on, <lb/>nay upon nece&longs;&longs;ity it cometh to be omitted.</s></p><p type="main"> <s>In an&longs;wer to this, I &longs;ay, that in the above&longs;aid Di&longs;cour&longs;e, two <lb/>things are to be con&longs;idered di&longs;tinctly; Fir&longs;t, whether it be po&longs;&longs;ible <lb/>to frame any conceit of the quantity of the Body of the Water <lb/>with two Dimen&longs;ions onely. </s> <s>And &longs;econdly, whether this length <lb/>be to be found. </s> <s>As to the fir&longs;t, I am very certain that no man, let <pb xlink:href="040/01/636.jpg" pagenum="70"/>him be never &longs;o great a Wit, can never promi&longs;e to frame a con­<lb/>ceit of the quantity of the Body of Water, without the third <lb/>Dimen&longs;ion of length: and hereupon I return to affirm, that the <lb/>vulgar Rule of mea&longs;uring Running water is vain and erroneous. <lb/></s> <s>This point being agreed on, I come to the &longs;econd, which is, Whe­<lb/>ther the third Dimen&longs;ion of length may be mea&longs;ured. </s> <s>And I &longs;ay, <lb/>that if one would know the whole length of the water of a <lb/>Fountain or River, thereby to come to know the quantity of all <lb/>the Water, it would prove an impo&longs;&longs;ible enterprize, nay the <lb/>knowing of it would not be u&longs;eful. </s> <s>But if one would know how <lb/>much water a Fountain, or a River carrieth in a determinate time <lb/>of an hour, of a day, or of a moneth, &c. </s> <s>I &longs;ay, that it is a very <lb/>po&longs;&longs;ible and profitable enquiry, by rea&longs;on of the innumerable <lb/>benefits that may be derived thence, it much importing to know <lb/>how much Water a Chanel carrieth in a time given; and I have <lb/>demon&longs;trated the &longs;ame above in the beginning of this Book; and <lb/>of this we &longs;tand in need in the bu&longs;ine&longs;&longs;e of the Lake, that &longs;o we <lb/>may be able to determine how much &longs;hall be the height of the <lb/><emph type="italics"/>Brent,<emph.end type="italics"/> when it is &longs;pread all over the Lake: For the three dimen­<lb/>&longs;ions of a Body being given, the Body is known; and the quan­<lb/>tity of a Body being given, if you have but two dimen&longs;ions, the <lb/>third &longs;hall be known. </s> <s>And thus diving farther and farther into <lb/>this Con&longs;ideration, I found that the Velocity of the cour&longs;e of the <lb/>water may be an hundred times greater or le&longs;&longs;er in one part of <lb/>its Chanel than in another. </s> <s>And therefore although there &longs;hould <lb/>be two mouths of Waters equal in bigne&longs;&longs;e; yet neverthele&longs;s it <lb/>might come to pa&longs;&longs;e, that one might di&longs;charge an hundred or a <lb/>thou&longs;and times more water than another: and this would be, if <lb/>the water in one of the mouths &longs;hould run with an hundred or a <lb/>thou&longs;and times greater velocity, than the other; for that it <lb/>would be the &longs;ame as to &longs;ay, that the &longs;wifter was an hundred or <lb/>a thou&longs;and times longer, than the &longs;lower: and in this manner I <lb/>di&longs;covered that to keep account of the velocity, was the keeping <lb/>account of the Length.</s></p><p type="main"> <s>And therefore it is manife&longs;t, that when two Mouths di&longs;charge <lb/>the &longs;ame quantity of Wa r in an equal velocity, it is nece&longs;&longs;ary <lb/>that the le&longs;s &longs;wift Mouth be &longs;o much bigger than the more &longs;wift; <lb/>as the more &longs;wift exceedeth in velocity the le&longs;s &longs;wift; as for <lb/>example.</s></p><p type="main"> <s>In ca&longs;e two Rivers &longs;hould carry equal quantity of water in <lb/>equal times, but that one of them &longs;hould be four times more <lb/>&longs;wift than the other, the more &longs;low &longs;hould of nece&longs;&longs;ity be four <lb/>times more large. </s> <s>And becau&longs;e the &longs;ame River in any part <lb/>thereof alwaies di&longs;chargeth the &longs;ame quantity of Water in equal <lb/>times (as is demon&longs;trated in the fir&longs;t Propo&longs;ition of the fir&longs;t <pb xlink:href="040/01/637.jpg" pagenum="71"/><arrow.to.target n="marg973"></arrow.to.target><lb/>Book^{*} of the mea&longs;ure of Running Watets;) but yet doth not <lb/>run thorowout with the &longs;ame velocity: Hence it is, that the vul­<lb/>gar mea&longs;ures of the &longs;aid River, in divers parts of its Chanel, are <lb/>alwaies divers; in&longs;omuch, that if a River pa&longs;&longs;ing through its cha­<lb/>nel had &longs;uch velocity, that it ran 100 Braces in the 1/60 of an hour­<lb/>and afterwards the &longs;aid River &longs;hould be reduced to &longs;o much tardi, <lb/>ty of motion, as that in the &longs;ame time it &longs;hould not run more than <lb/>one Brace, it would be nece&longs;&longs;ary that that &longs;ame River &longs;hould be­<lb/>come 100. times bigger in that place where it was retarded; I <lb/>mean, 100. times bigger than it was in the place where it was <lb/>&longs;wifter. </s> <s>And let it be kept well in mind, that this point rightly <lb/>under&longs;tood, will clear the under&longs;tanding to di&longs;cover very many <lb/>accidents worthy to be known. </s> <s>But for this time let it &longs;uffice, <lb/>that we have onely declared that which makes for our purpo&longs;e, <lb/>referring apprehen&longs;ive and &longs;tudious Wits to the peru&longs;al of my <lb/>aforenamed Treati&longs;e; for therein he &longs;hall finde profit and delight <lb/>both together.</s></p><p type="margin"> <s><margin.target id="marg973"></margin.target>* He here intends <lb/>the Demon&longs;trati­<lb/>ons following, at <lb/>the end of the fir&longs;t <lb/>Book</s></p><p type="main"> <s>Now applying all to our principal intent, I &longs;ay, That by what <lb/>hath been declared it is manife&longs;t, that if the <emph type="italics"/>Brent<emph.end type="italics"/> were 40. Bra­<lb/>ces broad, and 2 1/2 high, in &longs;ome one part of its Chanel, that after­<lb/>wards the &longs;ame Water of the <emph type="italics"/>Brent<emph.end type="italics"/> falling into the Lake, andpa&longs;­<lb/>&longs;ing thorow the &longs;ame to the Sea, it &longs;hould lo&longs;e &longs;o much of its ve­<lb/>locity, that it &longs;hould run but one Brace, in the time wherein <lb/>whil&longs;t it was in its Chanel at the place afore&longs;aid, it ran 100. Bra­<lb/>ces. </s> <s>It would be ab&longs;olutely nece&longs;&longs;ary, that increa&longs;ing in mea­<lb/>&longs;ure, it &longs;hould become an hundred times ^{*} thicker; and therefore <lb/><arrow.to.target n="marg974"></arrow.to.target><lb/>if we &longs;hould &longs;uppo&longs;e that the Lake were 20000. Braces, the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> that already hath been &longs;uppo&longs;ed in its Chanel 100. Braces, <lb/>being brought into the Lake, &longs;hould be 100. times 100. Brates; <lb/>that is, &longs;hall be 10000. Braces in thickne&longs;s, and con&longs;equently &longs;hall <lb/>be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a <lb/>Brace, as was concluded in the Argument.</s></p><p type="margin"> <s><margin.target id="marg974"></margin.target>* Deeper.</s></p><p type="main"> <s>Now one may &longs;ee into what a gro&longs;s errour of 99. in 100. one <lb/>may fall through the not well under&longs;tanding the true quantity <lb/>of Running Water, which being well under&longs;tood, doth open a <lb/>direct way to our judging aright in this mo&longs;t con&longs;iderable affair.</s></p><p type="main"> <s>And therefore admitting that wich hath been demon&longs;trated, <lb/>I fay, that I would (if it did concern me) greatly encline to con­<lb/>&longs;ult upon the returning of the <emph type="italics"/>Brent<emph.end type="italics"/> again into the Lake: For it <lb/>being mo&longs;t evident, that the <emph type="italics"/>Brent<emph.end type="italics"/> in the Chanel of its mouth, is <lb/>much &longs;wifter than the <emph type="italics"/>Brent<emph.end type="italics"/> being brought into the Lake, it will <lb/>certainly follow thereupon, that the thickne&longs;s of the Water of <lb/><emph type="italics"/>Brent<emph.end type="italics"/> in the Lake, &longs;hall be &longs;o much greater than that of <emph type="italics"/>Brent<emph.end type="italics"/> in <lb/><emph type="italics"/>Brent,<emph.end type="italics"/> by how much the <emph type="italics"/>Bront<emph.end type="italics"/> in <emph type="italics"/>Brent<emph.end type="italics"/> is &longs;wifter than thh <emph type="italics"/>Brent<emph.end type="italics"/><lb/>in the Lake.</s></p><pb xlink:href="040/01/638.jpg" pagenum="72"/><p type="main"> <s>1. From which operation doth follow in the fir&longs;t place, that <lb/>the Lake being filled and increa&longs;ed by tbe&longs;e Waters, &longs;hall be <lb/>more Navigable, and pa&longs;&longs;ible, than at pre&longs;ent we &longs;ee it to be.</s></p><p type="main"> <s>2. By the current of the&longs;e Waters, the Chanels will be &longs;cour­<lb/>ed, and will be kept clean from time to time.</s></p><p type="main"> <s>3. There will not appear at the times of low-waters &longs;o many <lb/>Shelves, and &longs;uch heaps of Mud, as do now appear.</s></p><p type="main"> <s>4. The Ayr will become more whole&longs;om, for that it &longs;hall not <lb/>be &longs;o infected by putrid vapours exhaled by the Sun, &longs;o long as <lb/>the Miery Ouze &longs;hall be covered by the Waters.</s></p><p type="main"> <s>5. La&longs;tly, in the current of the&longs;e advantagious Waters,, which <lb/>mu&longs;t i&longs;&longs;ue out of the Lake into the Sea, be&longs;ides tho&longs;e of the Tyde, <lb/>the Ports will be kept &longs;coured, and clear: And this is as much as <lb/>I &longs;hall offer for the pre&longs;ent, touching this weighty bui&longs;ine&longs;s; al­<lb/>waies &longs;ubmitting my &longs;elf to &longs;ounder judgements.</s></p><p type="main"> <s>Of the above-&longs;aid Writing I pre&longs;ented a Copy at <emph type="italics"/>Venice,<emph.end type="italics"/> at a <lb/>full Colledge, in which I read it all, and it was hearkned to with <lb/>very great attention; and at la&longs;t I pre&longs;ented it to the Duke, and <lb/>left &longs;ome Copies thereof with &longs;undry Senators, and went my way, <lb/>promi&longs;ing with all inten&longs;ene&longs;s to apply my pains with reiterated <lb/>&longs;tudies in the publick &longs;ervice; and if any other things &longs;hould come <lb/>into my minde, I promi&longs;ed to declare them &longs;incerely, and &longs;o took <lb/>leave of <emph type="italics"/>His &longs;erenity,<emph.end type="italics"/> and that Noble Council. </s> <s>When I was <lb/>returned to <emph type="italics"/>Rome,<emph.end type="italics"/> this bu&longs;ine&longs;s night and day continually run­<lb/>ning in my mind, I hapned to think of another admirable and <lb/>mo&longs;t important conceit, which with effectual rea&longs;ons, confirmed <lb/>by exact operations, I with the Divine a&longs;&longs;i&longs;tance, made clear and <lb/>manife&longs;t; and though the thing at fir&longs;t &longs;ight &longs;eemed to me a mo&longs;t <lb/>extravagant Paradox, yet notwith&longs;tanding, having &longs;atisfied my <lb/>&longs;elf of the whole bu&longs;ine&longs;s, I &longs;ent it in writing to the mo&longs;t Illu&longs;tri­<lb/>ous and mo&longs;t Noble <emph type="italics"/>Signore Gio. </s> <s>Ba&longs;adonna<emph.end type="italics"/>; who after he had <lb/>well con&longs;idered my Paper, carried it to the Council; and after <lb/>that tho&longs;e Lords had for many months maturely con&longs;idered <lb/>thereon, they in the end re&longs;olved to &longs;u&longs;pend the execution of the <lb/>diver&longs;ion which they had before con&longs;ulted to make of the River <lb/><emph type="italics"/>Sile,<emph.end type="italics"/> and of four other Rivers, which al&longs;o fall into the Lake; a <lb/>thing by me blamed in this &longs;econd Paper, as mo&longs;t prejudicial, <lb/>and harmful. </s> <s>The writing &longs;pake as followeth.</s></p><pb xlink:href="040/01/639.jpg" pagenum="73"/><p type="head"> <s>CONSIDERATIONS <lb/>Concerning the <lb/>LAKE <lb/>OF <lb/>VENICE.</s></p><p type="head"> <s><emph type="italics"/>CONSIDERATION II.<emph.end type="italics"/></s></p><p type="main"> <s>If the di&longs;cour&longs;ing well about the truth of <lb/>things, Mo&longs;t Serene Prince, were as the <lb/>carrying of Burdens, in which we &longs;ee <lb/>that an hundred Hor&longs;es carry a greater <lb/>weight than one Hor&longs;e onely; it would <lb/>&longs;eem that one might make more account <lb/>of the opinion of many men, than of <lb/>one alone; But becau&longs;e that di&longs;cour&longs;ing <lb/>more re&longs;embleth running, than carrying <lb/>Burdens, in which we &longs;ee that one Barb alone runneth fa&longs;ter <lb/>than an hundred heavy-heel'd Jades; therefore I have ever more <lb/>e&longs;teemed one Conclu&longs;ion well managed, and well con&longs;idered by <lb/>one under&longs;tanding man, although alone, than the common and <lb/>Vulgar opinions; e&longs;pecially, when they concern ab&longs;truce and <lb/>arduous points: Nay in &longs;uch ca&longs;es the opinions moulded and <lb/>framed by the mo&longs;t ignorant and &longs;tupid Vulgar, have been ever <lb/>&longs;u&longs;pected by me as fal&longs;e, for that it would be a great wonder if <lb/>in difficult matters a common capacity &longs;hould hit upon that <lb/>which is hand&longs;om, good, and true. </s> <s>Hence I have, and do hold <lb/>in very great veneration the &longs;umme of the Government of the <lb/>mo&longs;t Serene, and eternal Republick of <emph type="italics"/>Venice<emph.end type="italics"/>; which although, <lb/>as being in nature a Common-wealth, it ought to be governed by <lb/>the greater part; yet neverthele&longs;s, in arduous affairs, it is alwaies <lb/>directed by the Grave Judgement of few, and not judged blindly <pb xlink:href="040/01/640.jpg" pagenum="74"/>by the <emph type="italics"/>Plebeian<emph.end type="italics"/> Rout. </s> <s>Tis true, that he that propoundeth Pro­<lb/>po&longs;itions far above the reach of common capacity, runneth a <lb/>great hazard of being very often condemned without further Pro­<lb/>ce&longs;s, or knowledge of the Cau&longs;e; but yet for all that, the truth <lb/>is not to be de&longs;erted in mo&longs;t weighty affairs, but ought rather to <lb/>be explained in due place and time with all po&longs;&longs;ible per&longs;picuity; <lb/>that &longs;o being well under&longs;tood, and con&longs;idered, it may come after­<lb/>wards for the Common good to be embraced.</s></p><p type="main"> <s>This which I &longs;peak in general, hath often been my fortune in <lb/>very many particulars, not onely when I have kept within the <lb/>bounds of meer &longs;peculation, but al&longs;o when I have chanced to de­<lb/>&longs;cend to Practice, and to Operations: and your Highne&longs;s know­<lb/>eth very well what befel me the la&longs;t Summer 1641. when in obe­<lb/>dience to your Soveraign Command, I did in full Colledge repre­<lb/>&longs;ent my thoughts touching the &longs;tate of the Lake of <emph type="italics"/>Venice<emph.end type="italics"/>; for <lb/>there not being &longs;uch wanting, who without &longs;o much as vouch­<lb/>&longs;afing to under&longs;tand me, but having onely had an inkling, and <lb/>bad apprehen&longs;ion of my opinion, fell furiou&longs;ly upon me, and by <lb/>violent means both with the Pen and Pre&longs;s, full of Gall, did abu&longs;e <lb/>me in reward of the readine&longs;s that I had expre&longs;t to obey and <lb/>&longs;erve them: But I was above mea&longs;ure encouraged and plea&longs;ed, to <lb/>&longs;ee that tho&longs;e few who vouch&longs;afed to hear me, were all either <lb/>thorowly per&longs;waded that my opinion was well grounded, or at <lb/>lea&longs;t &longs;u&longs;pended their prudent verdict to more mature deliberati­<lb/>on. </s> <s>And though at the fir&longs;t bout I chanced to propo&longs;e a thing <lb/>that was totally contrary to the mo&longs;t received and antiquated <lb/>opinion, and to the re&longs;olutions and con&longs;ultations taken above an <lb/>hundred years ago: Moved by the&longs;e things, and to &longs;atisfie al&longs;o <lb/>to the promi&longs;e that I had made of tendering unto them what <lb/>&longs;hould farther offer it &longs;elf unto me touching the &longs;ame bu&longs;ine&longs;s; I <lb/>have re&longs;olved to pre&longs;ent to the Throne of your Highne&longs;s, another <lb/>Con&longs;ideration of no le&longs;s importance, which perhaps at fir&longs;t &longs;ight <lb/>will appear a &longs;tranger Paradox; but yet brought to the Te&longs;t and <lb/>Touch-&longs;tone of experience, it &longs;hall prove mo&longs;t clear and evident. <lb/></s> <s>If it &longs;hall be accounted of, &longs;o that it &longs;ucceedeth to the benefit of <lb/>your Highne&longs;s, I &longs;hall have obtained my defire and intent: And <lb/>if not, I &longs;hall have &longs;atisfied my &longs;elf, and &longs;hall not have been <lb/>wanting to the Obligation of your mo&longs;t faithful Servant, and na­<lb/>tive &longs;ubject.</s></p><p type="main"> <s>That which I propounded in the Mouths pa&longs;s, touching the <lb/>mo&longs;t important bu&longs;ine&longs;s of the Lake, though it did onely expre&longs;­<lb/>ly concern the point of the diver&longs;ion of the Mouth of the Lake, <lb/>already made and put in execution; yet it may be under&longs;tood <lb/>and applyed al&longs;o to the diver&longs;ion under debate, to be made of <lb/>the other five Rivers, and of the <emph type="italics"/>Sile<emph.end type="italics"/> in particular.</s></p><pb xlink:href="040/01/641.jpg" pagenum="75"/><p type="main"> <s>Now touching this, I had the fortune to offer an admirable <lb/>accident that we meet with when we come to the effect, which <lb/>I verily believe will be an utter ruine to the Lake of <emph type="italics"/>Ve­<lb/>nice.<emph.end type="italics"/></s></p><p type="main"> <s>I &longs;ay therefore, that by diverting the&longs;e five Rivers that re­<lb/>main, although their water that they di&longs;charge for the pre&longs;ent in­<lb/>to the Lake is not all taken together 4/5 parts of what the <emph type="italics"/>Brent<emph.end type="italics"/><lb/>alone did carry, yet neverthele&longs;&longs;e the abatement of the water of <lb/>the Lake which &longs;hall en&longs;ue upon this la&longs;t diver&longs;ion of four parts, <lb/>which was the whole water, &longs;hall prove double to that which hath <lb/>happened by the diver&longs;ion of <emph type="italics"/>Brent<emph.end type="italics"/> onely, although that the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> alone carried five parts of that water, of which the Rivers <lb/>that are to be diverted carry four: A wonder really great, and <lb/>altogether unlikely; for the reducing all this Propo&longs;ition to be <lb/>under&longs;tood, is as if we &longs;hould &longs;ay, that there being given us <lb/>three Rivers, of which the fir&longs;t di&longs;chargeth five parts, the &longs;econd <lb/>three, and the third one, and that from the diver&longs;ion of the <lb/>fir&longs;t, there did follow &longs;uch a certain abatement or fall; from <lb/>the taking away of the &longs;econd there ought to follow al&longs;o &longs;o <lb/>much more abatement; And la&longs;tly, from the withdrawing of <lb/>the third the water ought to fall &longs;o much more, which is wholly <lb/>impo&longs;&longs;ible: And yet it is mo&longs;t certain, and be&longs;ides the demon­<lb/>&longs;tration that per&longs;wades me to it, which I &longs;hall explain in due <lb/>time, I can &longs;et before your eyes &longs;uch an experiment as is not to <lb/>be denied by any one, although ob&longs;tinate: and I will make it <lb/>plainly &longs;een and felt, that by taking away only four parts of the <lb/>five, which &longs;hall have been taken away, the abatement proveth <lb/>double to the abatement en&longs;uing upon the diverting fir&longs;t of the <lb/>five onely; which thing being true, as mo&longs;t certainly it is, it <lb/>will give us to under&longs;tand how pernicious this diver&longs;ion of five <lb/>Rivers is like to prove, if it &longs;hall be put in execution.</s></p><p type="main"> <s>By this little that I have hinted, and the much that I could <lb/>&longs;ay, let your Highne&longs;&longs;e gather with what circum&longs;pection this bu­<lb/>&longs;ine&longs;&longs;e ought to be managed, and with how great skill he ought <lb/>to be furni&longs;hed who would behave him&longs;elf well in the&longs;e difficult <lb/>affairs.</s></p><p type="main"> <s>I have not at this time explained the demon&longs;tration, nor have <lb/>I &longs;o much as propounded the way to make the Experiment, that <lb/>I am able to make in confirmation of what I have &longs;aid, that &longs;o <lb/>by &longs;ome one or others mi&longs;-apprehending the Demon&longs;tration, <lb/>and maiming the Experiment, the truth may not happen to &longs;hine <lb/>with le&longs;&longs;e clarity than it doth, when all mi&longs;ts of difficulty are re­<lb/>moved: and if &longs;o be, no account &longs;hould be made of the Rea&longs;ons <lb/>by me alledged, and that men &longs;hould &longs;hut their eyes again&longs;t the <lb/>Experiments that without co&longs;t or charge may be made, I do de­<pb xlink:href="040/01/642.jpg" pagenum="76"/>clare and prote&longs;t that there &longs;hall follow very great dammages <lb/>to the Fields of the main Land, and extraordinary &longs;ummes <lb/>&longs;hall be expended to no purpo&longs;e. </s> <s>The Lake undoubtedly will <lb/>become almo&longs;t dry, and will prove impa&longs;&longs;ible for Navigation, <lb/>with a manife&longs;t danger of corrupting the Air: And in the la&longs;t <lb/>place there will unavoidably en&longs;ue the choaking and &longs;toppage of <lb/>the Ports of <emph type="italics"/>Venice.<emph.end type="italics"/></s></p><p type="main"> <s>Upon the 20th. </s> <s>of <emph type="italics"/>December,<emph.end type="italics"/> 1641. I imparted this my &longs;econd <lb/>Con&longs;ideration to the mo&longs;t Excellent <emph type="italics"/>Signore Ba&longs;adonna,<emph.end type="italics"/> pre&longs;en­<lb/>ting him with a Copy thereof among&longs;t other Writings, which I <lb/>have thought good to in&longs;ert, although they &longs;eem not to belong <lb/>directly to our bu&longs;ine&longs;&longs;e of the Lake.</s></p><p type="head"> <s>The way to examine the MUD and SAND <lb/>that entereth and remaineth in the <lb/>LAKE of <emph type="italics"/>VENICE.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>To the mo&longs;t Excellent<emph.end type="italics"/></s></p><p type="head"> <s>SIGNORE GIO. BASADONNA.</s></p><p type="main"> <s>Two very con&longs;iderable Objections have been made a­<lb/>gain&longs;t my opinion concerning the Lake of <emph type="italics"/>Venice:<emph.end type="italics"/> One <lb/>was that, of which I have &longs;poken at large in my fir&longs;t <lb/>Con&longs;ideration, namely, that the <emph type="italics"/>Brents<emph.end type="italics"/> having been taken out of <lb/>the Lake, cannot have been the occa&longs;ion of the notable fall of <lb/>the Waters in the Lake, as I pretend, and con&longs;equently, that <lb/>the turning <emph type="italics"/>Brent<emph.end type="italics"/> into the Lake would be no con&longs;iderable reme­<lb/>dy, in regard that the water of <emph type="italics"/>Brent,<emph.end type="italics"/> and the great expan&longs;ion <lb/>of the Lake over which the water of <emph type="italics"/>Brent<emph.end type="italics"/> is to diffu&longs;e and <lb/>&longs;pread being con&longs;idered, it is found that the ri&longs;e proveth in­<lb/>&longs;en&longs;ible.</s></p><p type="main"> <s>The &longs;econd Objection was, that the <emph type="italics"/>Brent<emph.end type="italics"/> is very muddy, and <lb/>therefore if it &longs;hould fall muddy into the Lake, the Sand would <lb/>&longs;ink and fill up the &longs;ame.</s></p><p type="main"> <s>Touching the fir&longs;t Query, enough hath been &longs;aid in my fir&longs;t <lb/>Con&longs;ideration, where I have plainly di&longs;covered the deceipt of the <lb/>Argument, and &longs;hewn its fallacy; It remaineth now to examine <pb xlink:href="040/01/643.jpg" pagenum="77"/>the &longs;econd: to which in the fir&longs;t place I &longs;ay, that one of the fir&longs;t <lb/>things that I propo&longs;ed in this affair was, that I held it impo&longs;&longs;ible <lb/>to do any act, though never &longs;o beneficial, that was not al&longs;o ac­<lb/>companied by &longs;ome inconvenience and mi&longs;chief; and therefore <lb/>we are to con&longs;ider well the profit, and the lo&longs;&longs;e and prejudice; <lb/>and they both being weighed, we &longs;hall be able to choo&longs;e the le&longs;­<lb/>&longs;er evil: Secondly, I admit it to be mo&longs;t true, that <emph type="italics"/>Brent<emph.end type="italics"/> is at &longs;ome <lb/>times muddy, but it is al&longs;o true, that for the greater part of the <lb/>year it is not muddy. </s> <s>Thirdly, I do not &longs;ee nor under&longs;tand <lb/>what &longs;trength this objection hath, being taken &longs;o at large, and in <lb/>general; and methinks that it is not enough to &longs;ay, that the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> runneth muddy, and to a&longs;&longs;ert that it depo&longs;eth its Muddi­<lb/>ne&longs;&longs;e in the Lake, but we ought moreover to proceed to particu­<lb/>lars, and &longs;hew how much this Mud is, and in what time this <lb/>choaking up of the Ports may be effected. </s> <s>For the Rea&longs;ons are <lb/>but too apparent and particular, that conclude the ruine of the <lb/>Lake, and that in a very &longs;hort time, (for mention is made of <lb/>dayes) the Waters diver&longs;ion being made, and moreover we <lb/>have the circum&longs;tance of an Experiment, the &longs;tate of things be­<lb/>ing ob&longs;erved to have grown wor&longs;e &longs;ince the &longs;aid diver&longs;ion. </s> <s>And <lb/>I have demon&longs;trated, that in ca&longs;e the Diver&longs;ion of the <emph type="italics"/>Sile<emph.end type="italics"/> and <lb/>the other Rivers &longs;hould be put in execution, the Lake would in a <lb/>few dayes become almo&longs;t dry; and the Ports would be lo&longs;t, with <lb/>other mi&longs;chievous con&longs;equences. </s> <s>But on the other &longs;ide, al­<lb/>though that we did grant the choaking of them, we may very <lb/>probably &longs;ay, that it will not happen, &longs;ave onely in the &longs;ucce&longs;&longs;ion <lb/>of many and many Centuries of years. </s> <s>Nor can I think it pru­<lb/>dent coun&longs;el to take a re&longs;olution and imbrace a De&longs;igne now, to <lb/>obtain a benefit very uncertain, and more than that, which only <lb/>&longs;hall concern tho&longs;e who are to come very many Ages after us, <lb/>and thereby bring a certain inconvenience upon our &longs;elves, and <lb/>upon our children that are now alive and pre&longs;ent.</s></p><p type="main"> <s>Let it be alledged therefore, (although I hold it fal&longs;e) that by <lb/>the diver&longs;ions of the Rivers the Lake may be kept in good con­<lb/>dition for &longs;everal years to come.</s></p><p type="main"> <s>But I &longs;ay confidently, and hope to demon&longs;trate it; That the <lb/>Diver&longs;ions will bring the Lake, even in our dayes, to be almo&longs;t <lb/>dry, and at lea&longs;t will leave &longs;o little water in it, that it &longs;hall cea&longs;e <lb/>to be Navigable, and the Ports &longs;hall mo&longs;t infallibly be choaked <lb/>up. </s> <s>I will therefore &longs;ay upon experience, in an&longs;wer to this Ob­<lb/>jection, that it is very nece&longs;&longs;ary fir&longs;t well to di&longs;cour&longs;e, and ratio­<lb/>nally to particularize and a&longs;certain the be&longs;t that may be this <lb/>point of the quantity of this &longs;inking Mud or Sand.</s></p><p type="main"> <s>Now I fear I &longs;hall make my &longs;elf ridiculous to tho&longs;e, who mea­<lb/>&longs;uring the things of Nature with the &longs;hallowne&longs;&longs;e of their brains <pb xlink:href="040/01/644.jpg" pagenum="78"/>do think that it is ab&longs;olutely impo&longs;&longs;ible to make this enquiry, and <lb/>will &longs;ay unto me, <emph type="italics"/>Quis men&longs;us e&longs;t pugillo aquas, & terram palmo <lb/>ponderavit<emph.end type="italics"/>? </s> <s>Yet neverthele&longs;s I will propound a way whereby, <lb/>at lea&longs;t in gro&longs;s, one may find out the &longs;ame.</s></p><p type="main"> <s>Take a Ve&longs;&longs;el of Cylindrical Figure, holding two barrels of <lb/>water, or thereabouts; and then fill it with the water of <emph type="italics"/>Brent,<emph.end type="italics"/><lb/>at its Mouth or Fall into the Lake; but in the Lake at the time <lb/>that the <emph type="italics"/>Brent<emph.end type="italics"/> runneth muddy, and after it hath begun to run <lb/>muddy for eight or ten hours, to give the mud time to go as far <lb/>as S. <emph type="italics"/>Nicolo,<emph.end type="italics"/> to i&longs;&longs;ue into the Sea; and at the &longs;ame time take <lb/>another Ve&longs;&longs;el, like, and equal to the fir&longs;t, and fill it with the wa­<lb/>ter of the Lake towards S. <emph type="italics"/>Nicolo,<emph.end type="italics"/> (but take notice that this ope­<lb/>ration ought to be made at the time when the waters go out, <lb/>and when the Sea is calm) and then, when the waters &longs;hall have <lb/>&longs;etled in the afore&longs;aid Ve&longs;&longs;els, take out the clear water, and con­<lb/>&longs;ider the quantity of Sand that remains behind, and let it be &longs;et <lb/>down, or kept in mind: And I am ea&longs;ily induced to think, that <lb/>that &longs;hall be a greater quantity of Sand which &longs;hall be left in the <lb/>fir&longs;t Ve&longs;&longs;el, than that left in the &longs;econd Ve&longs;&longs;el. </s> <s>Afterwards <lb/>when the <emph type="italics"/>Brent<emph.end type="italics"/> &longs;hall come to be clear, let both the operations be <lb/>repeated, and ob&longs;erve the quantity of Sand in the afore&longs;aid Ve&longs;­<lb/>&longs;els; for if the Sand in the fir&longs;t Ve&longs;&longs;el &longs;hould be mo&longs;t, it would <lb/>be a &longs;ign, that in the revolution of a year the <emph type="italics"/>Brent<emph.end type="italics"/> would depo&longs;e <lb/>Sand in the Lake: And in this manner one may calculate to a <lb/>&longs;mall matter what proportion the Sand that entreth into the Lake, <lb/>hath to that which remains: And by that proportion one may <lb/>judge how expedient it &longs;hall be for publick benefit. </s> <s>And if at <lb/>&longs;everal times of the year you carefully repeat the &longs;ame operati­<lb/>ons, or rather ob&longs;ervations, you would come to a more exact <lb/>knowledge in this bu&longs;ine&longs;s: And it would be good to make the <lb/>&longs;aid operations at tho&longs;e times, when the Lake is di&longs;turbed by <lb/>&longs;trong high Winds, and made muddy by its own Mud, rai&longs;ed by <lb/>the commotion of the Waters.</s></p><p type="main"> <s>This notion would give us great light, if the &longs;ame ob&longs;ervations <lb/>&longs;hould be made towards the Mouth of <emph type="italics"/>Lio,<emph.end type="italics"/> at &longs;uch time as the <lb/>waters flow and ebb, in calm &longs;ea&longs;ons; for &longs;o one &longs;hould come to <lb/>know whether the waters of the Lake are more thick at the going <lb/>out, than at the entrance. </s> <s>I have propounded the foregoing <lb/>way of mea&longs;uring Sands and Mud, to &longs;hew that we are not &longs;o <lb/>generally, and incon&longs;iderately to pronounce any &longs;entence, but <lb/>proceed to &longs;tricter inquiries, and then deliberate what &longs;hall be <lb/>mo&longs;t expedient to be done. </s> <s>Others may propo&longs;e more exqui­<lb/>&longs;ite examinations, but this &longs;hall &longs;erve me for the pre&longs;ent.</s></p><p type="main"> <s>I will add onely, that if any one had greater curio&longs;ity (it would <lb/>be profitable to have it) in inve&longs;tigating more exactly the quan­<pb xlink:href="040/01/645.jpg" pagenum="79"/>tity of the Water that entereth into the Lake, by the means that <lb/>I have &longs;hewen in the beginning of this Book: When he &longs;hall <lb/>have found the proportion of the quantity of water to the quan­<lb/>tity of Sand or Mud, he &longs;hall come to know how much Sand the <lb/><emph type="italics"/>Brent<emph.end type="italics"/> &longs;hall leave in the Lake in the &longs;pace of a year. </s> <s>But to <lb/>perform the&longs;e things, there are required per&longs;ons of di&longs;cretion, and <lb/>fidelity, and that are imployed by publick Order; for there <lb/>would thence re&longs;ult eminent benefit and profit.</s></p><p type="main"> <s><emph type="italics"/>Here are wanting<emph.end type="italics"/> LETTERS <emph type="italics"/>from &longs;everal per&longs;ons.<emph.end type="italics"/></s></p><p type="head"> <s>To the Reverend Father, <emph type="italics"/>France&longs;co di<emph.end type="italics"/></s></p><p type="head"> <s>S. GIUSEPPE.</s></p><p type="main"> <s>In execution of the command that you laid upon me in your <lb/>former Letters, by order from the mo&longs;t Serene, my Lord, <lb/><emph type="italics"/>Prince Leopold<emph.end type="italics"/>; that I &longs;hould &longs;peak my judgment concern­<lb/>ing the di&longs;imboguement of the River called <emph type="italics"/>Fiume morto,<emph.end type="italics"/> whe­<lb/>ther it ought to be let into the Sea, or into <emph type="italics"/>Serchio<emph.end type="italics"/>; I &longs;ay, that <lb/>I chanced 18. years &longs;ince to be pre&longs;ent, when the &longs;aid Mouth was <lb/>opened into the Sea, and that of <emph type="italics"/>Serchio<emph.end type="italics"/> &longs;topt; which work was <lb/>done to remedy the great Innundation that was made in all that <lb/>Country, and Plain of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> that lyeth between the River <emph type="italics"/>Arno,<emph.end type="italics"/><lb/>and the Mountains of <emph type="italics"/>S. Giuliano,<emph.end type="italics"/> and the River <emph type="italics"/>Serchio<emph.end type="italics"/>; which <lb/>Plain continued long under water, in&longs;omuch that not onely in the <lb/>Winter, but al&longs;o for a great part of the Summer, tho&longs;e fields <lb/>were overflowed; and when that the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> was <lb/>effectually opened into the Sea, the place was pre&longs;ently freed from <lb/>the waters. </s> <s>and drained, to the great &longs;atisfaction of the Owners <lb/>of tho&longs;e Grounds. </s> <s>And here I judge it worth your notice, that <lb/>for the generality of tho&longs;e that po&longs;&longs;e&longs;s e&longs;tates in tho&longs;e parts, they <lb/>de&longs;ired that the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> might &longs;tand open to the <lb/>Sea, and tho&longs;e who would have it open into <emph type="italics"/>Serchio,<emph.end type="italics"/> are per&longs;ons <lb/>that have no other concernment there, &longs;ave the hopes of gaining <lb/>by having the di&longs;po&longs;e of Commi&longs;&longs;ions, and the like, &c,</s></p><p type="main"> <s>But for the more plain under&longs;tanding of that which is to be <lb/>&longs;aid, it mu&longs;t be known, That the re&longs;olution of opening the &longs;aid <lb/>Mouth into <emph type="italics"/>Serchio,<emph.end type="italics"/> was taken in the time of the Great Duke <lb/><emph type="italics"/>Ferdinando<emph.end type="italics"/> the fir&longs;t, upon the &longs;ame motives that are at this time <lb/>again propo&longs;ed, as your Letters tell me, Since that, it manife&longs;t­<lb/>ly appearing, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> had, and hath its Mouth open to <lb/>the Sea, the Plain hathbeen kept dry; and it being al&longs;o true, that <pb xlink:href="040/01/646.jpg" pagenum="80"/>the fury of the South, and South-We&longs;t-Winds carryed &longs;uch <lb/>abundance of &longs;and into the Mouth, or Out-let of <emph type="italics"/>Fiume morto,<emph.end type="italics"/><lb/>that it wholly &longs;topt it up: e&longs;pecially when the waters on <emph type="italics"/>Pi&longs;a<emph.end type="italics"/><lb/>&longs;ide were low and &longs;hallow, And they think, that turning the <lb/>Lake of <emph type="italics"/>Fiume morto<emph.end type="italics"/> into <emph type="italics"/>Serchio,<emph.end type="italics"/> and the <emph type="italics"/>Serchio<emph.end type="italics"/> maintaining <lb/>continually its own Mouth with the force of its waters open to the <lb/>Sea, and con&longs;equently al&longs;o <emph type="italics"/>Fiume morto,<emph.end type="italics"/> they would have had the <lb/>Out-let clear and open; and in this manner they think, that the <lb/>Plain of <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> would have been freed from the waters. </s> <s>The bu­<lb/>&longs;ine&longs;s pa&longs;&longs;eth for current, at fir&longs;t &longs;ight; but experience proveth <lb/>the contrary, and Rea&longs;on confirmeth the &longs;ame: For the height <lb/>of the water of tho&longs;e Plains, was regulated by the height of the <lb/>waters in the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/>; that is, The waters at the <lb/>Mouth being high, the waters al&longs;o do ri&longs;e in the fields; and when <lb/>the waters at the Mouth are low, the waters of the fields do like­<lb/>wi&longs;e abate: Nor is it enough to &longs;ay, That the Out-let or Vent <lb/>of <emph type="italics"/>Fiume morto<emph.end type="italics"/> is continual, but it mu&longs;t be very low: Now if <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> did determine in <emph type="italics"/>Serchio,<emph.end type="italics"/> it is manife&longs;t that it <lb/>would determine high; for <emph type="italics"/>Serchio<emph.end type="italics"/> terminating in the Sea, when <lb/>ever it more and more aboundeth with water, and ri&longs;eth, it is ne­<lb/>ce&longs;lary that al&longs;o <emph type="italics"/>Fiume morto<emph.end type="italics"/> hath its level higher, and con&longs;e­<lb/>quently &longs;hall keep the waters in the Plains higher. </s> <s>Nay, it hath <lb/>happened &longs;ometimes (and I &longs;peak it upon my own &longs;ight) that <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> hath rever&longs;ed its cour&longs;e upwards towards <emph type="italics"/>Pi&longs;a<emph.end type="italics"/>; <lb/>which ca&longs;e will ever happen, when&longs;oever the <emph type="italics"/>Pi&longs;an<emph.end type="italics"/> waters chance <lb/>to be lower than the level of tho&longs;e of <emph type="italics"/>Serchio<emph.end type="italics"/>; for in that ca&longs;e <lb/>the waters of <emph type="italics"/>Serchio<emph.end type="italics"/> return back upon the Plains thorow <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> in &longs;uch &longs;ort, that the Muddine&longs;&longs;es, and the <emph type="italics"/>Serchio<emph.end type="italics"/> have <lb/>been ob&longs;erved to be carried by this return as farr as the Walls of <lb/><emph type="italics"/>Pi&longs;a<emph.end type="italics"/>; and then before &longs;uch time as &longs;o great waters can be a&longs;­<lb/>&longs;waged, which come in with great fury, and go out by little and <lb/>little, there do pa&longs;s very many days, and moneths, nay &longs;ome­<lb/>times one being never able to find the waters of <emph type="italics"/>Serchio,<emph.end type="italics"/><lb/>when at the &longs;hallowe&longs;t, &longs;o low as the Sea in level; (which is the <lb/>lowe&longs;t place of the waters) it thence doth follow, that the wa­<lb/>ters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hould never at any time of the year, &longs;o long <lb/>as they determine in <emph type="italics"/>Serchio,<emph.end type="italics"/> be &longs;o low, as they come to be when <lb/>the &longs;ame <emph type="italics"/>Fiume morto<emph.end type="italics"/> determineth in the Sea. </s> <s>Tis true indeed, <lb/>that the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> opened into the Sea, is &longs;ubject to <lb/>the inconvenience of being &longs;topt up by the force of Winds: But <lb/>in this ca&longs;e, it is nece&longs;&longs;ary to take &longs;ome pains in opening it; which <lb/>may ea&longs;ily be done, by cutting that Sand a little which &longs;tayeth <lb/>in the Mouth, after that the Wind is laid; and it is enough if you <lb/>make a Trench little more than two Palms in breadth; for the <lb/>water once beginning to run into it, it will in a few hours carry <pb xlink:href="040/01/647.jpg" pagenum="81"/>that Sand away with it, and there will en&longs;ue a deep and broad <lb/>Trench that will drain away all the water of the Plains in very lit­<lb/>tle time. </s> <s>And I have found by practice, that there having been <lb/>a great quantity of Sand driven back, by the fury of the South­<lb/>We&longs;t-Wind, into the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> I having cau&longs;ed the <lb/>little gutter to be made in the Morning, &longs;omewhat before Noon, <lb/>a Mouth hath been opened of 40. Braces wide, and notably deep, <lb/>in&longs;omuch that the water, which before had incommoded all the <lb/>Champian ran away in le&longs;s than three dayes, and left the Coun­<lb/>try free and dry, to the admiration of all men. </s> <s>There was pre­<lb/>&longs;ent upon the place, at this bu&longs;ine&longs;s, on the &longs;ame day that I <lb/>opened the Mouth, the mo&longs;t Serene great Duke, the mo&longs;t Serene <lb/>Arch-Dutche&longs;s Mother, all the Commi&longs;&longs;ioners of Sewers, with <lb/>many other Per&longs;ons and Pea&longs;ants of tho&longs;e parts; and they all &longs;aw <lb/>very well, that it was never po&longs;&longs;ible that a little Bark of eight <lb/>Oars, which was come from <emph type="italics"/>Legorn<emph.end type="italics"/> to wait upon the great <lb/>Duke, &longs;hould ever be able to ma&longs;ter the Current, and to make <lb/>up into <emph type="italics"/>Fiume morto<emph.end type="italics"/>; and his Highne&longs;s, who came with an intent <lb/>to cau&longs;e the &longs;aid Mouth towards the Sea to be &longs;topt; and that <lb/>into <emph type="italics"/>Serchio<emph.end type="italics"/> to be opened, changed his judgement, giving order <lb/>that it &longs;hould be left open towards the Sea, as it was done. </s> <s>And <lb/>if at this day it &longs;hall return into <emph type="italics"/>Serchio,<emph.end type="italics"/> I am very certain that it <lb/>will be nece&longs;&longs;ary to open it again into the Sea. </s> <s>And there was <lb/>al&longs;o charge and order given to a per&longs;on appointed for the pur­<lb/>po&longs;e, that he &longs;hould take care to open the &longs;aid Mouth, as hath <lb/>been &longs;aid upon occa&longs;ion. </s> <s>And thus things have &longs;ucceeded very <lb/>well unto this very time. </s> <s>But from the middle of <emph type="italics"/>October,<emph.end type="italics"/> until <lb/>this fir&longs;t of <emph type="italics"/>February,<emph.end type="italics"/> there having continued high South, and <lb/>South-We&longs;t-Winds, with frequent and abundant Rains; it is no <lb/>wonder that &longs;ome innundation hath happened; but yet I will <lb/>affirm, that greater mi&longs;chiefs would have followed, if the Mouth <lb/>had been opened into <emph type="italics"/>Serchio.<emph.end type="italics"/> This which I have hitherto &longs;aid, <lb/>is very clear and intelligible to all &longs;uch as have but competent in­<lb/>&longs;ight, and indifferent skill in the&longs;e affairs. </s> <s>But that which I am <lb/>now about to propo&longs;e farther, will, I am very certain, be under­<lb/>&longs;tood by your &longs;elf, but it will &longs;eem &longs;trange and unlikely to many <lb/>others. </s> <s>The point is, that I &longs;ay, That by rai&longs;ing the level of <lb/><emph type="italics"/>Fiume morto,<emph.end type="italics"/> one half Brace, onely at its Mouth, (it will peni­<lb/>penitrate into <emph type="italics"/>Serchio<emph.end type="italics"/> farther than it would into the Sea) it &longs;hall <lb/>cau&longs;e the waters to ri&longs;e three, or perhaps more Braces upon the <lb/>fields towards <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and &longs;till more by degrees as they &longs;hall recede <lb/>farther from the Sea-&longs;ide; and thus there will follow very great <lb/>Innundations, and con&longs;iderable mi&longs;chiefs. </s> <s>And to know that <lb/>this is true, you are to take notice of an accident, which I give <lb/>warning of in my di&longs;cour&longs;e of the Mea&longs;ure of Running Waters: <pb xlink:href="040/01/648.jpg" pagenum="82"/>where al&longs;o I give the rea&longs;on thereof, ^{*} <emph type="italics"/>Coroll.<emph.end type="italics"/> 14. The ac­<lb/>cident is this, That there coming a Land-Flood, for example, <lb/>into <emph type="italics"/>Arno,<emph.end type="italics"/> which maketh it to ri&longs;e above its ordinary Mouth <lb/>wthin <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> or a little above or below the City &longs;ix or &longs;even Bra­<lb/>ces; this &longs;ame height becometh alwaies le&longs;&longs;er and le&longs;&longs;er, the more <lb/>we approach towards the Sea-&longs;ide; in&longs;omuch, that near to the <lb/>Sea the &longs;aid River &longs;hall be rai&longs;ed hardly half a Brace: Whence <lb/>it followeth of nece&longs;&longs;ary con&longs;equence, that &longs;hould I again be at <lb/>the Sea-&longs;ide, and knowing nothing of what hapneth, &longs;hould &longs;ee <lb/>the River <emph type="italics"/>Arno<emph.end type="italics"/> rai&longs;ed by the acce&longs;&longs;ion of a Land-flood, one third <lb/>of a Brace; I could certainly infer, that the &longs;ame River was rai&longs;ed <lb/>in <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> tho&longs;e &longs;ame &longs;ix or &longs;even Braces. </s> <s>And that which I &longs;ay of <lb/><emph type="italics"/>Arno,<emph.end type="italics"/> is true of all Rivers that fall into the Sea. </s> <s>Which thing <lb/>being true, it is nece&longs;&longs;ary to make great account of every &longs;mall <lb/>ri&longs;ing, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> maketh towards the Sea-&longs;ide by fal­<lb/>ling into <emph type="italics"/>Serchio.<emph.end type="italics"/> For although the ri&longs;ing of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> by <lb/>being to di&longs;gorge its Waters into <emph type="italics"/>Serchio,<emph.end type="italics"/> towards the Sea, were <lb/>onely a quarter of a Brace; we might very well be &longs;ure, that fart <lb/>from the Sea, about <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and upon tho&longs;e fields the ri&longs;e &longs;hall be <lb/>much greater, and &longs;hall become two or three Braces: And be­<lb/>cau&longs;e the Countrey lyeth low, that &longs;ame ri&longs;e will cau&longs;e a conti­<lb/>nual Innundation of the Plains, like as it did before; I cau&longs;ed the <lb/>Mouth to be opened into the Sea. </s> <s>And therefore I conclude <lb/>that the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> ought by no means to be opened <lb/>into <emph type="italics"/>Serchio<emph.end type="italics"/>; but ought to be continued into the Sea, u&longs;ing all <lb/>diligence to keep it open after the manner afore&longs;aid, &longs;o &longs;oon as <lb/>ever the Wind &longs;hall be laid. </s> <s>And if they &longs;hall do otherwi&longs;e, I <lb/>confidently affirm, that there will daily follow greater damages; <lb/>not onely in the Plains, but al&longs;o in the whole&longs;omne&longs;s of the <lb/>Air; as hath been &longs;een in times pa&longs;t. </s> <s>And again, It ought with <lb/>all care to be procured, that no waters do by any means run or <lb/>fall from the Trench of <emph type="italics"/>Libra,<emph.end type="italics"/> into the Plain of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> for the&longs;e <lb/>Waters being to di&longs;charge into <emph type="italics"/>Fiume morto,<emph.end type="italics"/> they maintain it <lb/>much higher than is imagined, according to that which I have de­<lb/>mon&longs;trated in my con&longs;ideration upon the &longs;tate of the Lake of <lb/><emph type="italics"/>Venice.<emph.end type="italics"/> I have &longs;aid but little, but I &longs;peak to you, who under­<lb/>&longs;tandeth much, and I &longs;ubmit all to the mo&longs;t refined judgment of <lb/>our mo&longs;t Serene Prince <emph type="italics"/>Leopold,<emph.end type="italics"/> who&longs;e hands I be&longs;eech you in all <lb/>humility to ki&longs;s in my name, and implore the continuance of his <lb/>Princely favour to me; and &longs;o de&longs;iring your prayers to God for <lb/>me, I take my leave.</s></p><p type="main"> <s><emph type="italics"/>Rome<emph.end type="italics"/> 1. Feb. <lb/></s> <s>1642.</s></p><p type="main"> <s><emph type="italics"/>Your mo&longs;t affectionate Servant,<emph.end type="italics"/></s></p><p type="main"> <s>D. BENEDETTO CASTELLI.</s></p><pb xlink:href="040/01/649.jpg" pagenum="83"/><p type="head"> <s>The an&longs;wer to a Letter written by BAR­<lb/>TOLOTTI, touching the <lb/>difficultyes ob&longs;erved.</s></p><p type="head"> <s><emph type="italics"/>The former part of the Letter is omitted, and the di&longs;cour&longs;e <lb/>beginneth at the fir&longs;t Head.<emph.end type="italics"/></s></p><p type="main"> <s>And fir&longs;t I &longs;ay, Whereas I &longs;uppo&longs;e that the level of the <emph type="italics"/>Ser­<lb/>chio<emph.end type="italics"/> is higher than that of <emph type="italics"/>Fiume morto<emph.end type="italics"/>; this is mo&longs;t true, <lb/>at &longs;uch time as the waters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> are di&longs;charged in­<lb/>to the Sea; but I did never &longs;ay that things could never be brought <lb/>to that pa&longs;s, as that the level of <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hould be higher than <lb/><emph type="italics"/>Serchio<emph.end type="italics"/>: and &longs;o I grant that it will follow, that the waters of <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hall go into <emph type="italics"/>Serchio,<emph.end type="italics"/> and its very po&longs;&longs;ible, that the <lb/>Drain of <emph type="italics"/>Fiume morto<emph.end type="italics"/> into <emph type="italics"/>Serchio<emph.end type="italics"/> may be continuate; and I far­<lb/>ther grant, that its po&longs;&longs;ible, that the <emph type="italics"/>Serchio<emph.end type="italics"/> doth never di&longs;gorge <lb/>thorow <emph type="italics"/>Fiume morto<emph.end type="italics"/> towards <emph type="italics"/>Pi&longs;a<emph.end type="italics"/>; Nay, I will yet farther grant <lb/>that it might have happened, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> might have had <lb/>&longs;uch a fall into <emph type="italics"/>Serchio,<emph.end type="italics"/> as would have &longs;ufficed to have turned <lb/>Mills: But then I add withall, that the Plains of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and the <lb/>City it &longs;elf mu&longs;t be a meer Lake.</s></p><p type="main"> <s>2. <emph type="italics"/>Signore Bartololti<emph.end type="italics"/> &longs;aith confidently, that when the Sea &longs;wel­<lb/>leth by the South-We&longs;t, or other Winds, the level of <emph type="italics"/>Serchio<emph.end type="italics"/> in <lb/>the place marked A in the Platt, di&longs;tant about 200. Braces, ri&longs;eth <lb/>very little: But that <emph type="italics"/>Fiume morto<emph.end type="italics"/> in D, and in E, many miles <lb/>more up into Land ri&longs;eth very much, and that certain Fi&longs;hermen <lb/>confirm this, and &longs;hew him the &longs;ignes of the ri&longs;ing of the Water. <lb/></s> <s>I grant it to be very true, and I have &longs;een it with my own eyes: <lb/>But this cometh to pa&longs;s, when the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> is &longs;topt <lb/>up by the Sea; as I &longs;hall &longs;hew by and by. </s> <s>And this ri&longs;ing near <lb/>the Sea-&longs;ide, is of no con&longs;iderable prejudice to the fields. </s> <s>And <lb/>this is as much as I find to be true in the a&longs;&longs;ertion of <emph type="italics"/>Signore Bar­<lb/>tolotti,<emph.end type="italics"/> (without his confirming it by any other proof; as indeed <lb/>it needs none) That the level of <emph type="italics"/>Fiume morto<emph.end type="italics"/> ri&longs;eth in E, and ma­<lb/>ny miles farther upwards it ri&longs;eth much; nor did I ever affirm the <lb/>contrary.</s></p><p type="main"> <s>3. Concerning the difficulty of opening the Mouth of <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> into the Sea, that which <emph type="italics"/>Il Ca&longs;tellano<emph.end type="italics"/> &longs;aith is mo&longs;t certain; <lb/>namely, That at the entrance upon the opening of the Mouth, it <lb/>is nece&longs;&longs;ary to make a deep Trench: But I &longs;ay, that at that time <lb/>it is difficult to open it, unle&longs;s upon great occa&longs;ions; for that the <pb xlink:href="040/01/650.jpg" pagenum="84"/>difficulty proceedeth from the waters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> being low, <lb/>and the fields drained.</s></p><p type="main"> <s>4. As to the particular of the Cau&longs;es that you tell me men <lb/>pre&longs;s &longs;o much unto the mo&longs;t <emph type="italics"/>Serene Grand Duke,<emph.end type="italics"/> and to the <lb/>Prince, I have not much to &longs;ay, becau&longs;e it is not my profe&longs;&longs;ion; <lb/>nor have I con&longs;idered of the &longs;ame: Yet I believe, that when the <lb/>Prince and his Highne&longs;&longs;e &longs;ee the benefit of his People and Sub­<lb/>jects in one &longs;cale of the Ballance, and the accomodation of <lb/>Hunt&longs;men in the other, his Highne&longs;&longs;e will incline to the profit <lb/>of his &longs;ubjects; &longs;uch have I alwayes found his Clemency and <lb/>Noblene&longs;&longs;e of minde. </s> <s>But if I were to put in my vote upon <lb/>this bu&longs;ine&longs;&longs;e, I would &longs;ay, that the points of Spears, and the <lb/>mouths of Guns, the yelping of Dogs, the wilyne&longs;&longs;e of Hunt&longs;­<lb/>men, who run thorow and narrowly &longs;earch all tho&longs;e Woods, <lb/>Thickets and Heathes, are the true de&longs;troyers of Bucks and <lb/>Boares, and not a little Salt-water, which &longs;etleth at la&longs;t in &longs;ome <lb/>low places, and &longs;preadeth not very far. </s> <s>Yet neverthele&longs;&longs;e, I will <lb/>not enter upon any &longs;uch point, but confine my &longs;elf &longs;olely to the <lb/>bu&longs;ine&longs;&longs;e before me.</s></p><p type="main"> <s>5. That Experiment of joyning together the water of <emph type="italics"/>Fiume <lb/>morto,<emph.end type="italics"/> and that of <emph type="italics"/>Serchio<emph.end type="italics"/> by a little trench to &longs;ee what advan­<lb/>tage the Level E hath upon the Level I, doth not give me full <lb/>&longs;atisfaction, taken &longs;o particularly, for it may come to pa&longs;&longs;e, that <lb/>&longs;ometimes E may be higher, and &longs;ometimes A lower, and I do <lb/>not que&longs;tion but that when <emph type="italics"/>Serchio<emph.end type="italics"/> is low, and <emph type="italics"/>Fiume morto<emph.end type="italics"/> full <lb/>of Water, the level of <emph type="italics"/>Fiume morto<emph.end type="italics"/> will be higher than that of <lb/><emph type="italics"/>Serchio.<emph.end type="italics"/> But <emph type="italics"/>Serchio<emph.end type="italics"/> being full, and <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;cant of Wa­<lb/>ter, the contrary will follow, if the Mouth &longs;hall be opened to <lb/>the Sea. </s> <s>And here it &longs;hould &longs;eem to me, that it ought to be <lb/>con&longs;idered, that there is as much advantage from E to the Sea <lb/>through the little Trench opened anew into <emph type="italics"/>Serchio,<emph.end type="italics"/> as from E to <lb/>the Sea by the Mouth of <emph type="italics"/>Fiume morto.<emph.end type="italics"/> But the difficulty (which <lb/>is that we are to regard in our ca&longs;e) is, that the cour&longs;e of the <lb/>Waters thorow the Trench is three times longer than the cour&longs;e <lb/>of the Mouth of <emph type="italics"/>Fiums morto,<emph.end type="italics"/> as appeareth by the Draught or <lb/>Plat which you &longs;ent me, which I know to be very exactly drawn, <lb/>for that the &longs;ituation of tho&longs;e places are fre&longs;h in my memory. <lb/></s> <s>Here I mu&longs;t give notice, that the waters of <emph type="italics"/>Fiume morto<emph.end type="italics"/> determi­<lb/>ning thorow the Trench in <emph type="italics"/>Serchio<emph.end type="italics"/> (the waters of which <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> are, for certain, never &longs;o low as the Sea) their pendency or <lb/>declivity &longs;hall, for two cau&longs;es, be le&longs;&longs;e than the pendency of tho&longs;e <lb/>waters through the Mouth towards the Sea, that is, becau&longs;e of <lb/>the length of the line through the Trench, and becau&longs;e of the <lb/>height of their entrance into <emph type="italics"/>Serchio,<emph.end type="italics"/> a thing which is of very <lb/>great import in di&longs;charging the waters which come &longs;uddenly, as <pb xlink:href="040/01/651.jpg" pagenum="85"/>he &longs;hall plainly &longs;ee, who &longs;hall have under&longs;tood my Book of the <lb/>Mea&longs;ure of Running Waters And this was the Rea&longs;on why all <lb/>the Countrey did grow dry upon the opening of the Mouth into <lb/>the Sea. </s> <s>And here I propo&longs;e to con&longs;ideration that which the Pea­<lb/>&longs;ants about <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> relate, namely, That the Water in the Fields <lb/>doth no con&longs;iderable harm by continuing there five or &longs;ix, yea, or <lb/>eight dayes. </s> <s>And therefore the work of the Countrey is to o­<lb/>pen the Mouth of <emph type="italics"/>Fiume morto,<emph.end type="italics"/> in &longs;uch manner, that the Water <lb/>being come, they may have the Trench free and ready, when that <lb/>the Water cometh it may have a free drain, and may not &longs;tay <lb/>there above eight or nine dayes, for then the overflowings be­<lb/>come hurtful. </s> <s>It is to be de&longs;ired al&longs;o, that if any Propo&longs;ition is <lb/>produced touching the&longs;e affairs, it might be propounded the mo&longs;t <lb/>di&longs;tinctly that may be po&longs;&longs;ible, and not con&longs;i&longs;t in generals, e&longs;pe­<lb/>cially when the Di&longs;pute is of the ri&longs;ings, of velocity, of tardity, <lb/>of much and little water; things that are all to be &longs;pecified by <lb/>mea&longs;ures.</s></p><p type="main"> <s>6. Your Letter &longs;aith, in the next place, that <emph type="italics"/>Signore Barto­<lb/>lotti<emph.end type="italics"/> confe&longs;&longs;eth, that if the Mouth of the <emph type="italics"/>Fiume morto<emph.end type="italics"/> might al­<lb/>wayes be kept open, it would be better to let it continue as it is: <lb/>the which, that I may not yield to him in courte&longs;ie, I confe&longs;&longs;e, <lb/>for the keeping it &longs;topt on all &longs;ides would be a thing mo&longs;t per­<lb/>nicious. </s> <s>But admitting of his confe&longs;&longs;ion I again reply, that <emph type="italics"/>Fi­<lb/>ume morto<emph.end type="italics"/> ought not to be let into <emph type="italics"/>Serchio,<emph.end type="italics"/> but immediately in­<lb/>to the Sea; becau&longs;e although &longs;ometimes the Mouth to Sea­<lb/>wards be &longs;topt up, yet for all that, the rai&longs;ing of the Bank above <lb/>the Plains (which is all the bu&longs;ine&longs;&longs;e of importance) &longs;hall be ever <lb/>le&longs;&longs;er, if we make u&longs;e of the Mouth leading to the Sea, than u­<lb/>&longs;ing that of <emph type="italics"/>Serchio.<emph.end type="italics"/></s></p><p type="main"> <s>7. I will not omit to mention a kinde of &longs;cruple that I have <lb/>concerning the po&longs;ition of <emph type="italics"/>Sign. </s> <s>Bartolotti,<emph.end type="italics"/> that is, where he &longs;aith <lb/>that the two Mouths A and D are equal to the like Mouths into <lb/>the Sea; Now it &longs;eems to me, that the Mouth A of <emph type="italics"/>Fiume morto<emph.end type="italics"/><lb/>into <emph type="italics"/>Serchio<emph.end type="italics"/> is ab&longs;olutely within <emph type="italics"/>Serchio,<emph.end type="italics"/> nor can it be made low­<lb/>er, and is regulated by the height of <emph type="italics"/>Serchio<emph.end type="italics"/>: But the Mouth <lb/>of <emph type="italics"/>Fiume morto<emph.end type="italics"/> terminates, and ought to be under&longs;tood to ter­<lb/>minate in the Sea it &longs;elf, the lowe&longs;t place. </s> <s>And this I believe <lb/>was very well peroeived by <emph type="italics"/>Sig. </s> <s>Bartolotti,<emph.end type="italics"/> but I cannot tell why <lb/>he pa&longs;t it over without declaring it: and we &longs;ee not that the <lb/>Mouth D falleth far from the Sea, which Mouth ought to be let <lb/>into the Sea it &longs;elf, and &longs;o the advantage of the <emph type="italics"/>M<emph.end type="italics"/>outh into the <lb/>Sea more clearly appeareth.</s></p><p type="main"> <s>8. That which <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> addeth, that when it is high <lb/>Waters, at &longs;uch time as the Waters are out, and when Winds <lb/>choak up <emph type="italics"/>Fiume morto,<emph.end type="italics"/> they not only retard it, but return the <pb xlink:href="040/01/652.jpg" pagenum="86"/>cour&longs;e of the Waters upwards very lea&longs;urely, per&longs;wadeth me <lb/>more readily to believe that <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> knoweth very well, <lb/>that the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> let into <emph type="italics"/>Serchio<emph.end type="italics"/> is hurtful: for <lb/>by this he acknowledgeth that the Mouth towards the Sea doth <lb/>in &longs;uch &longs;ort drain the Countrey of the Waters, as that they be­<lb/>come very low; and therefore upon every little <emph type="italics"/>impetus<emph.end type="italics"/> the wa­<lb/>ters turn their cour&longs;e: And from the motions, being exceeding <lb/>&longs;low, is inferred, that the abundance of Sea-water that com­<lb/>eth into <emph type="italics"/>Fiume morto,<emph.end type="italics"/> is &longs;o much as is believed, and as <emph type="italics"/>Sig. </s> <s>Bat­<lb/>tolotti<emph.end type="italics"/> affirmeth.</s></p><p type="main"> <s>9. After that <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> hath &longs;aid what he promi&longs;eth a­<lb/>bove, namely, that when the Windes blowing &longs;trongly do &longs;top <lb/>up <emph type="italics"/>Fiume morto,<emph.end type="italics"/> and not onely retard but turn the cour&longs;e up­<lb/>wards, the time being Rainy, and the Mouth of <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hut <lb/>up, the Waves of the Sea pa&longs;&longs;e over the Bank of <emph type="italics"/>Fiume morto<emph.end type="italics"/>; at <lb/>that time, &longs;aith <emph type="italics"/>Signore Bartolotti,<emph.end type="italics"/> the Champain &longs;hall know the <lb/>benefit of <emph type="italics"/>Fiume morto<emph.end type="italics"/> di&longs;charged into <emph type="italics"/>Serchio,<emph.end type="italics"/> and the mouth A <lb/>&longs;hall &longs;tand alwayes open; and <emph type="italics"/>Fiume morto<emph.end type="italics"/> may alwayes con­<lb/>&longs;tantly run out, as al&longs;o the Rains and Rain-waters, although the <lb/>hurtful Tempe&longs;t &longs;hould la&longs;t many dayes, &c. </s> <s>And I reply, that <lb/>all the Art con&longs;i&longs;ts in this; for the benefit of tho&longs;e Fields doth <lb/>not depend on, or con&longs;i&longs;t in &longs;aying, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> is alwayes <lb/>open, and <emph type="italics"/>Fiume morto<emph.end type="italics"/> draineth continually; But all the bu&longs;i­<lb/>ne&longs;&longs;e of profit lyeth and con&longs;i&longs;teth in maintaining the Waters <lb/>low in tho&longs;e Plaines, and tho&longs;e Ditches, which &longs;hall never be ef­<lb/>fected whil&longs;t the World &longs;tands, if you let <emph type="italics"/>Fiume morto<emph.end type="italics"/> into <emph type="italics"/>Ser­<lb/>chio<emph.end type="italics"/>; but yet it may, by opening the mouth into the Sea: and <lb/>&longs;o much rea&longs;on and nature proveth, and (which importeth) Ex­<lb/>perience confirmeth.</s></p><p type="main"> <s>10. In the tenth place I come to con&longs;ider the an&longs;wer that <lb/>was made to another Propo&longs;ition in the Letter which I writ to <lb/>Father <emph type="italics"/>France&longs;co,<emph.end type="italics"/> which prudently of it &longs;elf alone might &longs;erve <lb/>to clear this whole bu&longs;ine&longs;&longs;e. </s> <s>I &longs;aid in my Letter, That great <lb/>account is to be made of every &longs;mall ri&longs;ing and ebbing of the <lb/>Waters neer to the Sea in <emph type="italics"/>Fiume morto,<emph.end type="italics"/> for that the&longs;e ri&longs;ings and <lb/>fallings, although that they be &longs;mall neer to the Sea-&longs;ide, yet ne­<lb/>verthele&longs;&longs;e, they operate and are accompanied by notable ri&longs;ings <lb/>and fallings within Land, and far from the Sea-&longs;ide, and I have <lb/>declared by an example of <emph type="italics"/>Arno,<emph.end type="italics"/> in which a Land-flood falling, <lb/>that made it increa&longs;e above its ordinary height within <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> &longs;ix or <lb/>&longs;even Braces, that this height of the &longs;ame Flood becometh &longs;till <lb/>le&longs;&longs;er, the neerer we approach to the Sea-coa&longs;ts. </s> <s>Nor &longs;hall the <lb/>&longs;aid River be rai&longs;ed hardly half a Brace; whereupon it nece&longs;&longs;­<lb/>rily followeth, that if I &longs;hould return to the Sea-&longs;ide, and not <lb/>knowing any think of that which happeneth at <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and &longs;eeing <pb xlink:href="040/01/653.jpg" pagenum="87"/>the River <emph type="italics"/>Arno<emph.end type="italics"/> rai&longs;ed by a Land-flood half a Brace, I might con­<lb/>fidently affirm the &longs;aid River to be rai&longs;ed in <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> tho&longs;e &longs;ix or &longs;e­<lb/>ven Braces, &c. </s> <s>From &longs;uch like accidents I conclude in the &longs;ame <lb/>Letter, that it is nece&longs;&longs;ary to make great account of every little <lb/>ri&longs;e that <emph type="italics"/>Fiume morto<emph.end type="italics"/> &longs;hall make towards the Sea. </s> <s>Now cometh <lb/><emph type="italics"/>Bartolotti<emph.end type="italics"/> (and perhaps becau&longs;e I knew not how to expre&longs;s my <lb/>&longs;elf better, under&longs;tandeth not my Propo&longs;ition) and &longs;peaketh that <lb/>which indeed is true, but yet be&longs;ides our ca&longs;e: Nor have I ever <lb/>&longs;aid the contrary; and withall doth not apply it to his purpo&longs;e. <lb/></s> <s>Nay I &longs;ay, that if he had well applyed it, this alone had been a­<lb/>ble to have made him change his opinion. </s> <s>And becau&longs;e he &longs;aith, <lb/>that I &longs;aid, that it is true, when the abatement proceedeth from <lb/>&longs;ome cau&longs;e above, as namely by Rain, or opening of Lakes; <lb/>But when the cau&longs;e is from below, that is, by &longs;ome &longs;top, as for <lb/>in&longs;tance &longs;ome Fi&longs;hers Wears or Locks, or &longs;ome impediment re­<lb/>mote from the Sea, although at the Level it &longs;hall ri&longs;e &longs;ome Braces <lb/>where the impediment is, yet that ri&longs;ing &longs;hall go upwards; and <lb/>here he fini&longs;heth his Di&longs;cour&longs;e, and concludeth not any thing <lb/>more. </s> <s>To which I &longs;ay fir&longs;t, that I have al&longs;o &longs;aid the &longs;ame in the <lb/>Propo&longs;ition, namely, that a Flood coming (which maketh <emph type="italics"/>Arno<emph.end type="italics"/><lb/>to ri&longs;e in <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> &longs;ix or &longs;even Braces (which I take to be a &longs;uperiour <lb/>cau&longs;e whether it be Rain or the opening of Lakes, as be&longs;t plea­<lb/>&longs;eth <emph type="italics"/>Bartolotti<emph.end type="italics"/>) in &longs;uch a ca&longs;e I &longs;ay, and in no other (for towards <lb/>the Sea-coa&longs;ts it &longs;hall not cau&longs;e a ri&longs;ing of full half a Brace; and <lb/>therefore &longs;eeing <emph type="italics"/>Arno<emph.end type="italics"/> at the Sea-&longs;ide to be rai&longs;ed by a Flood, whe­<lb/>ther of Rain, or of opening of Lakes half a Brace) it may be <lb/>inferred, that at <emph type="italics"/>Pi&longs;a<emph.end type="italics"/> it &longs;hall be rai&longs;ed tho&longs;e &longs;ix or &longs;even Braces; <lb/>which variety, well con&longs;idered, explaineth all this affair in favour <lb/>of my opinion: For the ri&longs;ing that is made by the impediment <lb/>placed below, of Fi&longs;hing Weares and Locks, operateth at the be­<lb/>ginning, rai&longs;ing the Waters that are neer to the impediment; <lb/>and afterwards le&longs;s and le&longs;s, as we retire upwards from the im­<lb/>pediment: provided yet that we &longs;peak not of a Flood that com­<lb/>meth by acce&longs;&longs;ion, but onely of the ordinary Water impeded. <lb/></s> <s>But there being a new acce&longs;&longs;ion, as in our ca&longs;e, then the Water <lb/>of the Flood, I &longs;ay, &longs;hall make a greater ri&longs;ing in the parts &longs;uperi­<lb/>our, far from the impediment; and the&longs;e impediments &longs;hall <lb/>come to be tho&longs;e that &longs;hall overflow the Plains, as happened <lb/>eighteen or nineteen years ago, before the opening of <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> into the Sea, The &longs;ame will certainly follow, if <emph type="italics"/>Fiume <lb/>morto<emph.end type="italics"/> be let into <emph type="italics"/>Serchio.<emph.end type="italics"/> Here I could alledge a very pretty <lb/>ca&longs;e that befell me in <emph type="italics"/>la ^{*} Campagna di Roma,<emph.end type="italics"/> neer to the Sea­<lb/><arrow.to.target n="marg975"></arrow.to.target><lb/>&longs;ide. </s> <s>where I drained a Bog or Fen, of the nature of the Wa­<lb/>ters of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> and I &longs;ucceeded in the enterprize, the Waters in their <lb/>&longs;ite towards the Sea abating only three Palmes, and yet in the <pb xlink:href="040/01/654.jpg" pagenum="88"/>Fen they fell more than fifteen Palmes. </s> <s>But the bu&longs;ine&longs;&longs;e <lb/>would be long, and not &longs;o ea&longs;ily to be declared, and I am cer­<lb/>tain that <emph type="italics"/>Sig. </s> <s>Bartolotti<emph.end type="italics"/> having con&longs;idered this, would alter his <lb/>judgment, and withall would know that remitting that impedi­<lb/>ment anew, which I had left for le&longs;&longs;e than three Palmes towards <lb/>the Sea, the Waters in the Fen would return with the fir&longs;t Floods <lb/>and Raines to the &longs;ame height as before, as likewi&longs;e <emph type="italics"/>Fiume morto<emph.end type="italics"/><lb/>will do if it &longs;hall be let again into <emph type="italics"/>Serchio.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg975"></margin.target>* The Countrey <lb/>or Province lying <lb/>round the City, <lb/>heretofore called <lb/><emph type="italics"/>Latium<emph.end type="italics"/></s></p><p type="main"> <s>Here I intreat your Honour to do me the favour to importune <lb/><emph type="italics"/>P. France&longs;co<emph.end type="italics"/> in my behalf, that he would be plea&longs;ed to deelare <lb/>my meaning in the afore&longs;aid Letter to <emph type="italics"/>Sig. </s> <s>Bartolotti,<emph.end type="italics"/> for I hope <lb/>that if he will under&longs;tand this point, he will be no longer &longs;o te­<lb/>nacious in his opinion.</s></p><p type="main"> <s>Next that the&longs;e Lords in the Commi&longs;&longs;ion of Sewers, with the <lb/>Right Honourable the Marque&longs;&longs;e of S. <emph type="italics"/>Angelo,<emph.end type="italics"/> and your Honour <lb/>do approve of my judgment, doth very much rejoyce me; but <lb/>becau&longs;e that I know that they do it not in de&longs;ign to complement <lb/>me, but onely to &longs;erve his Highne&longs;s our Grand Duke, I freely <lb/>profe&longs;s that I will pretend no farther obligations from them there­<lb/>in, than I account my &longs;elf to owe to tho&longs;e who&longs;e opinions are <lb/>contrary to mine, for that I know that they have the &longs;ame end. <lb/></s> <s>The definitive &longs;entence of this whole bu&longs;ine&longs;s is, that they give <lb/>the&longs;e Plains, the&longs;e Draines, and the&longs;e Waters farre fetcht ap­<lb/>pellations.</s></p><p type="main"> <s>11. As to the quantity of the Water that <emph type="italics"/>Fiume morto<emph.end type="italics"/> di&longs;­<lb/>chargeth into the Sea, there are very great di&longs;putes about it, and <lb/>I have been pre&longs;ent at &longs;ome of them. </s> <s>But let your Honour be­<lb/>lieve me, that as this is not continual, but only during a few <lb/>dayes, &longs;o it will never be of any great prejudice to the&longs;e Fields; <lb/>and if your Lord&longs;hip would be a&longs;certained thereof, you may <lb/>plea&longs;e to go to <emph type="italics"/>Fiume morto<emph.end type="italics"/> at about a mile's di&longs;tance from the <lb/>Sea, in the time of the&longs;e &longs;trong Windes, and ob&longs;erve the cur­<lb/>rent from thence upwards, for you &longs;hall finde it extream &longs;low, <lb/>and con&longs;equently will know that the quantity of the Water that <lb/>is repuls'd is very &longs;mall. </s> <s>And this &longs;eems to be contradicted by the <lb/>rule of Ri&longs;ings proceeding from cau&longs;es below, which occa&longs;ion no <lb/>con&longs;iderable alteration far from the Sea.</s></p><p type="main"> <s>I am nece&longs;&longs;itated to go to morrow out of <emph type="italics"/>Rome<emph.end type="italics"/> with his Emi­<lb/>nence Cardinal <emph type="italics"/>Gaetano<emph.end type="italics"/> about certain affairs touching Waters, <lb/>therefore I &longs;hall not farther inlarge, but for a clo&longs;e to this tedious <lb/>Di&longs;cour&longs;e, I conclude in few words, that <emph type="italics"/>Fiume morto<emph.end type="italics"/> is by no <lb/>means to be let into <emph type="italics"/>Serchio,<emph.end type="italics"/> nor are there any means intermedi­<lb/>ate cour&longs;es to be taken, for they will alwayes be prejudicial; but <lb/><emph type="italics"/>Fiume morto<emph.end type="italics"/> is to be di&longs;charged immediately into the Sea. </s> <s>When <lb/>it is &longs;topt up by the fury of the Sea waves, I affirm that it is a <pb xlink:href="040/01/655.jpg" pagenum="89"/>&longs;ign that there is no need of opening it; and if there be any oc­<lb/>ca&longs;ion to open it, it is ea&longs;ily done. </s> <s>As for the re&longs;t your Lord&longs;hip <lb/>may plea&longs;e to keep account of all the particulars that occur, for <lb/>the memory of things pa&longs;t is our Tutre&longs;&longs;e in tho&longs;e that are to <lb/>come. </s> <s>If occa&longs;ion &longs;hall offer, I intreat you to bow humbly in <lb/>my name to His Highne&longs;s the Grand Duke, and the mo&longs;t Serene <lb/>Prince <emph type="italics"/>Leopold<emph.end type="italics"/>; and to attend the &longs;ervice of Their Highne&longs;&longs;es, for <lb/>you &longs;erve I rinces of extraordinary merit; And to whom I my <lb/>&longs;elf am al&longs;o exceedingly obliged. </s> <s>In the controver&longs;ies that ari&longs;e <lb/>re&longs;pect the pious end of &longs;peaking the Truth, for then every <lb/>thing will &longs;ucceed happily. </s> <s>I ki&longs;s the hands of <emph type="italics"/>Padre France&longs;co,<emph.end type="italics"/><lb/>of <emph type="italics"/>Sig. </s> <s>Bartolotti,<emph.end type="italics"/> and of your Lord&longs;hip.</s></p><p type="main"> <s><emph type="italics"/>Rome, 14. March<emph.end type="italics"/> 1642.</s></p><p type="main"> <s><emph type="italics"/>Your Honours<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>most Obliged Servant<emph.end type="italics"/></s></p><p type="main"> <s>D. <emph type="italics"/>BENEDETTO CASTELLI.<emph.end type="italics"/></s></p><p type="main"> <s>Vpon this occa&longs;ion I will here in&longs;ert a Di&longs;cour&longs;e that I made <lb/>upon the Draining and improvement of the <emph type="italics"/>Pontine Fens,<emph.end type="italics"/><lb/>for that I think that what&longs;oever may be done well and to pur­<lb/>po&longs;e in this matter hath ab&longs;olute dependance on the perfect know­<lb/>ledge of that &longs;o important Propo&longs;ition, by me demon&longs;trated and <lb/>explained in my Treati&longs;e of the <emph type="italics"/>Men&longs;uration<emph.end type="italics"/> of <emph type="italics"/>Running Wa­<lb/>ters,<emph.end type="italics"/> namely, That the &longs;ame water of a River doth continually <lb/>change Mea&longs;ures, according as it altereth and changeth the ve­<lb/>locity of its cour&longs;e; &longs;o that the mea&longs;ure of the thickne&longs;&longs;e of a <lb/>River in one Site, to the mea&longs;ure of the &longs;ame River in another <lb/>Site, hath the &longs;ame proportion reciprocally that the velocity in <lb/>this &longs;ite hath to the velocity in the fir&longs;t &longs;ite. </s> <s>And this is a Truth <lb/>&longs;o con&longs;tant and unchangeable, that it altereth not in the lea&longs;t <lb/>point on any occurrences of the Waters that change: and <lb/>being well under&longs;tood, it openeth the way to the knowledge of <lb/>&longs;undry adverti&longs;ements in the&longs;e matters, which are all re&longs;olved by <lb/>this &longs;ole Principle; and from it are derived very con&longs;iderable be­<lb/>nefits; and without the&longs;e it is impo&longs;&longs;ible to do any thing with <lb/>ab&longs;olute perfection</s></p><pb xlink:href="040/01/656.jpg"/><pb xlink:href="040/01/657.jpg" pagenum="91"/><p type="head"> <s>A <lb/>CONSIDERATION <lb/>Upon the <lb/>DRAINING <lb/>OF THE <lb/>Pontine Fenns. <lb/></s> <s>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, Abbot <lb/>of S. BENEDETTO ALOISIO, and Profe&longs;&longs;or <lb/>of the <emph type="italics"/>Mathematicks<emph.end type="italics"/> to P. <emph type="italics"/>Urban<emph.end type="italics"/> VIII. in the <lb/>Univer&longs;ity of <emph type="italics"/>ROME.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>CONSIDERATION<emph.end type="italics"/> III.</s></p><p type="main"> <s>Among&longs;t the enterprizes by me e&longs;teemed, if not ab­<lb/>&longs;olutely impo&longs;&longs;ible, , at lea&longs;t exceeding difficult, <lb/>one was that famous one of Draining the <emph type="italics"/>Pontine <lb/>Fenns<emph.end type="italics"/>; and therefore I was thorowly re&longs;olved <lb/>never to apply my minde thereunto, although <lb/>by my Patrons I &longs;hould be commanded to the <lb/>&longs;ame: accounting that it was an occa&longs;ion rather of lo&longs;ing repu­<lb/>tation by the mi&longs;carriage of the attempt, than of gaining fame by <lb/>reducing things to a better pa&longs;s then they now are at. </s> <s>Yet never­<lb/>thele&longs;s, having of late years ob&longs;erved the place, and &longs;ailed through <lb/>tho&longs;e Chanels, and tho&longs;e Waters; after I had made &longs;ome reflection <lb/>thereupon, I thought that the enterprize was not &longs;o difficult as <lb/>I had at fir&longs;t conceited it to be; and I am the more confirmed in <lb/>this opinion, upon the inducement of that which I have written <pb xlink:href="040/01/658.jpg" pagenum="92"/>Geometrically in my Treati&longs;e of the Men&longs;uration of Running <lb/>Waters; &longs;o that talking with &longs;everal per&longs;ons, I adventured to <lb/>affirm, in di&longs;coures, that this improvement might po&longs;&longs;ibly be <lb/>brought into a good e&longs;tate.</s></p><p type="main"> <s>Now I have re&longs;olved to &longs;et down my thoughts in writing, and <lb/>to honour this my Paper with the Noble Name of your Lord&longs;hip, <lb/>to render it the more credible and con&longs;picuous at the fir&longs;t view, <lb/>if it &longs;hould chance that the Subject I treat of, were not of &longs;uch <lb/>moment, as that it did de&longs;erve to be valued for any other rea&longs;on. <lb/></s> <s>Pardon me, Sir, if I have been too bold, and continue me in the <lb/>number of your Servants.</s></p><p type="main"> <s>The enterprize of Draining a great part of the Territories of <lb/>the <emph type="italics"/>Pontine Fenns,<emph.end type="italics"/> hath been undertaken both in the time of <lb/>the antient <emph type="italics"/>Romans,<emph.end type="italics"/> and la&longs;t of all, in our days; yea in the late <lb/>times by <emph type="italics"/>Sixtus<emph.end type="italics"/> V. </s> <s>I do not doubt in the lea&longs;t, but that it will <lb/>be po&longs;&longs;ible yet to reduce things to a very good pa&longs;s; and if I be not <lb/>mi&longs;taken, with a very &longs;mall charge in compari&longs;on of the profit that <lb/>would be received from tho&longs;e rich Grounds. </s> <s>This improvement <lb/>was of great expence in the time of <emph type="italics"/>Sixtus Quintus,<emph.end type="italics"/> but by rea­<lb/>&longs;on the thing was not rightly under&longs;tood, there were made many <lb/>Drains; a great part of which were unprofitable and vain: and <lb/>among&longs;t &longs;o many operations, there hapned &longs;ome to be made that <lb/>&longs;ucceeded, as was de&longs;ired; but not being under&longs;tood, they were <lb/>held in no account; and thus the bu&longs;ine&longs;s being neglected, the <lb/>waters are returned into the &longs;ame &longs;tate as they were at fir&longs;t, be­<lb/>fore the improvement. </s> <s>Here I have by familiar di&longs;cour&longs;es <lb/>with my friends, explained this enterprize undertaken by <emph type="italics"/>Six­<lb/>tus<emph.end type="italics"/> V. and haply al&longs;o by &longs;ome more antient, with the example of <lb/>the Fable of <emph type="italics"/>Orilo,<emph.end type="italics"/> in <emph type="italics"/>Ario&longs;to.<emph.end type="italics"/> This Mon&longs;ter was made up with <lb/>&longs;uch enchantment, that men fought with him alwayes in vain; <lb/>for though in the Combate he were cut in pieces, tho&longs;e divided <lb/>Members pre&longs;ently re-united, and returned to the fight more <lb/>fierce then ever. </s> <s>But the <emph type="italics"/>Paladine A&longs;tolfo<emph.end type="italics"/> coming to undertake <lb/>him, after a long di&longs;pute, at the end he cut his head &longs;heer off <lb/>from the &longs;houlders at one blow; and nimbly alighting from his <lb/>Hor&longs;e, took the Mon&longs;trous head, and mounting again, as he rid <lb/>away he fell to &longs;have the Pole of that Mon&longs;ter, and &longs;o he lo&longs;t <lb/>the Lock of Hair, in which alone the enchantment lay; and then <lb/>the horrible Head in an in&longs;tant manife&longs;ted &longs;igns of death, and the <lb/>trunk which ran, &longs;eeking to reunite to it anew, gave the la&longs;t ga&longs;p, <lb/>and in this manner the enchantment ended. </s> <s>The Book of Fate <lb/>&longs;erved admirably to the <emph type="italics"/>Paladine,<emph.end type="italics"/> whereby he came to under­<lb/>&longs;tand that Charm; for by &longs;having his whole head, the enchanted <lb/>hairs came to be cut off among&longs;t the re&longs;t: In the &longs;ame manner, I <lb/>&longs;ay, that it hath &longs;ometimes happened in Draining tho&longs;e Fields; <pb xlink:href="040/01/659.jpg" pagenum="93"/>for that among&longs;t &longs;o many tryals as have been made, that al&longs;o <lb/>was light upon, on which the improvement and remedy to the <lb/>di&longs;order did depend. </s> <s>And to us my fore-named Treati&longs;e &longs;hall <lb/>&longs;erve for a Rule, which being well under&longs;tood, &longs;hall make us to <lb/>know wherein con&longs;i&longs;teth, and whereon dependeth this mi&longs;carri­<lb/>age, and con&longs;equently it will be ea&longs;ie to apply thereunto a &longs;ea&longs;o­<lb/>nable remedy.</s></p><p type="main"> <s>And fir&longs;t I &longs;ay, That there is no doubt but that the waters <lb/>continue &longs;o high on tho&longs;e Plains becau&longs;e they are &longs;o high in the <lb/>principal River, which ought to receive them, and carry them <lb/>into the Sea. </s> <s>Now the Cau&longs;es of the height of the River, may <lb/>in my judgement be reduced to one alone; which is that by me <lb/>&longs;o often mentioned for the mo&longs;t Potent one, and declared in my <lb/>afore-named Tractate; to wit, The tardity of the motion of the <lb/>waters, which doth alwayes infallibly, and preci&longs;ely cau&longs;e the <lb/>&longs;elf &longs;ame Running Water to change the mea&longs;ure of its thickne&longs;s <lb/>at &longs;uch a rate, that the more it encrea&longs;eth in velocity, the more <lb/>it decrea&longs;eth in mea&longs;ure; and the more it decrea&longs;eth in velocity, <lb/>the more it encrea&longs;eth in mea&longs;ure: As for example; If a River <lb/>run in &longs;uch a place with the velocity of moving a mile in the <lb/>&longs;pace of an hour, and afterwards the &longs;ame River in another place <lb/>doth encrea&longs;e in velocity, &longs;o as to make three miles an hour; <lb/>that &longs;ame River &longs;hall dimini&longs;h in thickne&longs;s two thirds: And on <lb/>the contrary, If it &longs;hall dimini&longs;h in velocity &longs;o, as that it runneth <lb/>but half a mile in the &longs;ame time, it &longs;hall encrea&longs;e the double in <lb/>thickne&longs;s and mea&longs;ure. </s> <s>And in a word, look what proportion <lb/>the velocity in the fir&longs;t place, hath to the velocity in the &longs;econd, <lb/>and &longs;uch hath reciprocally the mea&longs;ure of the thickne&longs;s in the <lb/>&longs;econd place, to the mea&longs;ure in the fir&longs;t; as I have clearly demon­<lb/>&longs;trated in my Treati&longs;e: Which I repeat &longs;o frequently, that I <lb/>fear the Profe&longs;&longs;ors of Polite Learning will charge me with Tua­<lb/>tologie, and vain Repetition. </s> <s>But I am &longs;o de&longs;irous in this mo&longs;t <lb/>important point to be well under&longs;tood, becau&longs;e it will then be <lb/>ea&longs;ie to comprehend all the re&longs;t; and without this it is impo&longs;&longs;ible <lb/>(I will not &longs;ay difficult, but ab&longs;olutely impo&longs;&longs;ible) to under&longs;tand, <lb/>or ever to effect any thing to purpo&longs;e. </s> <s>And the better to ex­<lb/>plain the example, let it be &longs;uppo&longs;ed, <lb/><figure id="id.040.01.659.1.jpg" xlink:href="040/01/659/1.jpg"/><lb/>That the water of a River A D, <lb/>runneth high at the level of A F, <lb/>with &longs;uch a certain velocity; and let <lb/>it, by the &longs;ame water, be velocitated <lb/>three times more; I &longs;ay, that it will <lb/>abate 1/3, and &longs;hall &longs;tand at the level <lb/>in B E; and if it &longs;hall more veloci­<lb/>tate, it will abate the more at the Sea; But if it &longs;hould retard <pb xlink:href="040/01/660.jpg" pagenum="94"/>more than it did at the level AF, it would ri&longs;e yet more above <lb/>the &longs;aid level A F; although that the &longs;elf &longs;ame quantity of water <lb/>runneth all the while. </s> <s>By the above-named &longs;olid Principle I <lb/>re&longs;olve extravagant Problems in my Treati&longs;e, and a&longs;&longs;ign the Rea­<lb/>&longs;ons of admirable effects of Running Waters: But as for what <lb/>concerneth our purpo&longs;e of the <emph type="italics"/>Pontine Fenns,<emph.end type="italics"/> we have the Cau­<lb/>&longs;es very plain and clear; for which, by the trampling of Cattle <lb/>which pa&longs;s thorow the <emph type="italics"/>Draining River,<emph.end type="italics"/> the waters abate &longs;o nota­<lb/>bly, that it is as it were a miracle for tho&longs;e Reeds, Flags, and <lb/>Weeds that &longs;pring up, encrea&longs;e, and &longs;pread all over the River, <lb/>&longs;top and impede that velocity of the waters which they would <lb/>have by means of their declivity. </s> <s>But that pa&longs;&longs;age of tho&longs;e Bea&longs;ts, <lb/>treading down tho&longs;e Weeds unto the bottom of the River, in &longs;uch <lb/>&longs;ort, as that they no longer hinder the Current of the Water; <lb/>and the &longs;ame Waters increa&longs;ing in their cour&longs;e, they do dimi­<lb/>ni&longs;h in mea&longs;ure and height; and by this meanes the Ditches of the <lb/>Plains empty into the &longs;ame &longs;ucce&longs;sfully, and leave them free <lb/>from Waters, and Drained. </s> <s>But the&longs;e Weeds in a &longs;hort <lb/>time &longs;prouting up anew, and rai&longs;ing their &longs;talkes thorow the <lb/>body of the Waters, they reduce things to the &longs;ame evil <lb/>&longs;tate, as before, retarding the velocity of the Water, ma­<lb/>king it to increa&longs;e in height, and perhaps do occa&longs;ion grea­<lb/>ter mi&longs;chiefs; &longs;eeing that tho&longs;e many knots which each plant <lb/>&longs;hoots forth, begets a greater multitude of Stalks, which much <lb/>more incumbering the Water of the River, are a greater impe­<lb/>diment unto its velocity, and con&longs;equently make the height <lb/>of the waters to encrea&longs;e &longs;o much the more, and do more mi&longs;chief <lb/>than before.</s></p><p type="main"> <s>Another head to which the&longs;e harms may be reduced, but pro­<lb/>ceeding from the &longs;ame Root, which hath a great part in this <lb/>di&longs;order, is the impediment of tho&longs;e Wears in the River which <lb/>are made by heightning the bed of the &longs;ame, for placing of fi&longs;h­<lb/>ing-nets; of which <emph type="italics"/>Pi&longs;caries<emph.end type="italics"/> I reckoned above ten, when I made <lb/>a voyage thorow tho&longs;e waters to <emph type="italics"/>Sandolo.<emph.end type="italics"/> And the&longs;e Fi&longs;hing­<lb/>Wears are &longs;uch impediments, that &longs;ome one of them makes the <lb/>water of the River in the upper part to ri&longs;e half a Palm, and <lb/>&longs;ometimes a whole Palm, and more; &longs;o that when they are all <lb/>gathered together, the&longs;e impediments amount to more than &longs;even, <lb/>or po&longs;&longs;ibly than eight Palms.</s></p><p type="main"> <s>There concurreth for a third mo&longs;t Potent Cau&longs;e of the waters <lb/>continuing high in the evacuating, or Draining Chanel, and con­<lb/>&longs;equently on the Plains; The great abundance of water that i&longs;&longs;u­<lb/>eth from <emph type="italics"/>Fiume Si&longs;to,<emph.end type="italics"/> the waters of which do not keep within its <lb/>Banks when they are abundant; but encrea&longs;ing above its Chanel, <lb/>they unite with tho&longs;e of the Evacuator, and di&longs;per&longs;ing thorow <pb xlink:href="040/01/661.jpg" pagenum="95"/>the Fens are rai&longs;ed with great prejudice, and much grea­<lb/>ter than is conceived, according to what hath been demon­<lb/>&longs;trated in the Second Con&longs;ideration upon the <emph type="italics"/>Lake of Venice.<emph.end type="italics"/><lb/>Nor is it to any purpo&longs;e to &longs;ay, that if we &longs;hould mea&longs;ure <lb/>all the Waters that disimbogue from <emph type="italics"/>Fiume Si&longs;to,<emph.end type="italics"/> and gather <lb/>them into one &longs;umme, we &longs;hould not finde them to be &longs;uch, <lb/>as that they &longs;hall be able to make the Waters of the Fens <lb/>to increa&longs;e, by rea&longs;on of the great expan&longs;ion of them, over <lb/>which that body of water is to di&longs;tend: for to this in&longs;tance we <lb/>an&longs;wer wich that which we have given notice of in the Fir&longs;t Con­<lb/>&longs;ideration touching the <emph type="italics"/>Lake of Venice,<emph.end type="italics"/> treating of the abate­<lb/>ment that is cau&longs;ed by the <emph type="italics"/>Brent<emph.end type="italics"/> let into the Lake. </s> <s>And more­<lb/>over, if I &longs;hall adde thereto that which I write in the Second <lb/>Con&longs;ideration, it will be very apparent how greatly harmfull <lb/>and prejudicial the&longs;e excurfions of Waters from <emph type="italics"/>Fiume Si&longs;to<emph.end type="italics"/><lb/>may be, which are not kept under, and confined within the <lb/>River: Therefore, proceeding to the provi&longs;ions, and ope­<lb/>rations that are to be accounted Principall, I reduce them to <lb/>three Heads.</s></p><p type="main"> <s>In the fir&longs;t place it is nece&longs;&longs;ary to throw down tho&longs;e Weares, <lb/>and to take the Pi&longs;ciaries quite away, ob&longs;erving a Maxime, in <lb/>my judgment, infallible, that Fi&longs;hing and Sowing are two things <lb/>that can never con&longs;i&longs;t together; Fi&longs;hing being on the Water, and <lb/>Sowing on land.</s></p><p type="main"> <s>Secondly, it will be nece&longs;&longs;ary to cut under Water in the bot­<lb/>tome of the River tho&longs;e Weeds and Plants that grow and in­<lb/>crea&longs;e in the River, and leave them to be carried into the Sea by <lb/>the Stream; for by this means the&longs;e Reeds &longs;hall not &longs;pring up <lb/>and di&longs;tend along the bottome of the River, by means of the <lb/>Bea&longs;ts treading upon them; And the &longs;ame ought to be done <lb/>often, and with care, and mu&longs;t not be delaied till the mi&longs;­<lb/>chief increa&longs;e, and the Champain Grounds be drowned, but <lb/>one ought to order matters &longs;o, as that they may not drown. <lb/></s> <s>And I will affirm, that otherwi&longs;e this principal point would be­<lb/>come a mo&longs;t con&longs;iderable inconvenience.</s></p><p type="main"> <s>Thirdly, it is nece&longs;&longs;ary to make good the Banks of <emph type="italics"/>Fiume Si&longs;to<emph.end type="italics"/><lb/>on the left hand, and to procure that tho&longs;e Waters may run in <lb/>the Chanel, and not break forth. </s> <s>And it is to be noted, that <lb/>it is not enough to do one or two of tho&longs;e things, but we are to <lb/>put them all in execution; for omitting any thing, the whole <lb/>machine will be out of tune, and &longs;poiled. </s> <s>But proceeding with <lb/>due care, you &longs;hall not only Drain the <emph type="italics"/>Pontine Fens,<emph.end type="italics"/> but by <lb/>means of this la&longs;t particular the Current of <emph type="italics"/>Fiums Sisto<emph.end type="italics"/> &longs;hall <lb/>&longs;cowr its own Chanel of its &longs;elf, even to the carrying part of it <lb/>away: and haply with this abundance of water that it &longs;hall <pb xlink:href="040/01/662.jpg" pagenum="96"/>bear, the Mouth <emph type="italics"/>della Torre<emph.end type="italics"/> may be opened, and kept open <lb/>into the Sea. </s> <s>And it would, la&longs;t of all, be of admirable bene­<lb/>fit to clean&longs;e <emph type="italics"/>Fiume Sisto<emph.end type="italics"/> from many Trees and Bu&longs;hes where­<lb/>with it is overgrown.</s></p><p type="main"> <s>And with this I conclude, that the Improvement or Drain <lb/>po&longs;&longs;ible to be made con&longs;i&longs;teth in the&longs;e three particulars. </s> <s>Fir&longs;t, <lb/>in taking away the Fi&longs;hing Weares, leaving the Cour&longs;e <lb/>of the Waters free. </s> <s>Secondly, in keeping the Principal <lb/>Rivers clear from Weeds and Plants. </s> <s>Thirdly, in keeping <lb/>the water of <emph type="italics"/>Fiume Sisto<emph.end type="italics"/> in its own Chanel. </s> <s>All which are <lb/>things that may be done with very little charge, and to the <lb/>manife&longs;t benefit of the whole Country, and to the rendering <lb/>the Air whol&longs;omer in all tho&longs;e Places adjoyning to the <emph type="italics"/>Pon­<lb/>tine Fens.<emph.end type="italics"/></s></p><figure id="id.040.01.662.1.jpg" xlink:href="040/01/662/1.jpg"/><pb xlink:href="040/01/663.jpg" pagenum="97"/><p type="head"> <s>A <lb/>CONSIDERATION <lb/>Upon the <lb/>DRAINING <lb/>Of the Territories of <lb/>Bologna, Ferrara, <lb/>AND <lb/>Romagna.</s></p><p type="head"> <s>BY <lb/>D. BENEDETTO CASTELLI, Abbot <lb/>of S. BENEDETTO ALOISIO, <emph type="italics"/>Mathematician<emph.end type="italics"/><lb/>to P. <emph type="italics"/>Vrban<emph.end type="italics"/> VIII. and Profe&longs;&longs;or in the <lb/>Univer&longs;ity of <emph type="italics"/>ROME.<emph.end type="italics"/></s></p><p type="main"> <s>The weghty bu&longs;ine&longs;&longs;e of the Draining of <lb/>the Territories of <emph type="italics"/>Bologna, Ferrara,<emph.end type="italics"/><lb/>and <emph type="italics"/>Romagna<emph.end type="italics"/> having been punctually <lb/>handled and declared in writing from <lb/>the excellent memory of the Right Ho­<lb/>nourable and Noble <emph type="italics"/>Mon&longs;ignore Cor&longs;ini,<emph.end type="italics"/><lb/>who was heretofore Deputed Commi&longs;­<lb/>&longs;ary General, and Vi&longs;itor of tho&longs;e Wa­<lb/>ters; I am not able to make &longs;uch ano­<lb/>ther Di&longs;cour&longs;e upon the &longs;ame Subject, but will only &longs;ay &longs;ome­<lb/>what for farther confirmation of that which I have &longs;aid in this <lb/>Book upon the <emph type="italics"/>Lake of Venice,<emph.end type="italics"/> upon the <emph type="italics"/>Pontine Fens,<emph.end type="italics"/> and up­<lb/>on the Draining of tho&longs;e Plains of <emph type="italics"/>Pi&longs;a,<emph.end type="italics"/> lying between the Ri­<lb/>vers <emph type="italics"/>Arno<emph.end type="italics"/> and <emph type="italics"/>Serchio<emph.end type="italics"/>; whereby it is manife&longs;t, that in all the <pb xlink:href="040/01/664.jpg" pagenum="98"/>aforementioned Ca&longs;es, and in the pre&longs;ent one that we are in hand <lb/>with, there have, in times pa&longs;t, very gro&longs;&longs;e Errours been com­<lb/>mitted, through the not having ever well under&longs;tood the true <lb/>mea&longs;ure of Running waters; and here it is to be noted, that the <lb/>bu&longs;ine&longs;&longs;e is, that in <emph type="italics"/>Venice,<emph.end type="italics"/> the diver&longs;ion of the waters of the <lb/>Lake, by diverting the <emph type="italics"/>Brent<emph.end type="italics"/> was debated, and in part executed, <lb/>without con&longs;ideration had how great abatement of water might <lb/>follow in the Lake, if the <emph type="italics"/>Brent<emph.end type="italics"/> were diverted, as I have &longs;hewn <lb/>in the fir&longs;t Con&longs;ideration upon this particular, from which act <lb/>there hath in&longs;ued very bad con&longs;equences, not only the difficulty <lb/>of Navigation, but it hath infected the whol&longs;omne&longs;&longs;e of the Air, <lb/>and cau&longs;ed the &longs;toppage of the Ports of <emph type="italics"/>Venice.<emph.end type="italics"/> And on the <lb/>contrary, the &longs;ame inadvertency of not con&longs;idering what ri&longs;ing of <lb/>the Water the <emph type="italics"/>Reno,<emph.end type="italics"/> and other Rivers being opened into the Val­<lb/>leys of <emph type="italics"/>Bologna<emph.end type="italics"/> and <emph type="italics"/>Ferrara,<emph.end type="italics"/> might cau&longs;e in the &longs;aid Valleys, is <lb/>the certain cau&longs;e that &longs;o many rich and fertile Fields are drown­<lb/>ed under water, converting the happy habitations and dwellings <lb/>of men into mi&longs;erable receptacles for Fi&longs;hes: Things which <lb/>doubtle&longs;&longs;e would never have happened, if tho&longs;e Rivers had been <lb/>kept at their height, and <emph type="italics"/>Reno<emph.end type="italics"/> had been turn'd into <emph type="italics"/>Main-Po,<emph.end type="italics"/><lb/>and the other Rivers into that of <emph type="italics"/>Argenta,<emph.end type="italics"/> and of <emph type="italics"/>Volano.<emph.end type="italics"/> Now <lb/>there having &longs;ufficient been &longs;poken by the above-named <emph type="italics"/>Mon&longs;ig. <lb/></s> <s>Cor&longs;ini<emph.end type="italics"/> in his Relation, I will only adde one conceit of my own, <lb/>which after the Rivers &longs;hould be regulated, as hath been &longs;aid, I <lb/>verily believe would be of extraordinary profit, I much doubt in­<lb/>deed that I &longs;hall finde it a hard matter to per&longs;wade men to be of <lb/>my mind, but yet neverthele&longs;s I will not que&longs;tion, but that tho&longs;e, <lb/>at lea&longs;t, who &longs;hall have under&longs;tood what I have &longs;aid and demon­<lb/>&longs;trated concerning the manners and proportions, according to <lb/>which the abatements and ri&longs;ings of Running waters proceed, <lb/>that are made by the Diver&longs;ions and Introductions of Waters, <lb/>will apprehend that my conjecture is grounded upon Rea&longs;on. <lb/></s> <s>And although I de&longs;cend not to the exactne&longs;&longs;e of particulars, I <lb/>will open the way to others, who having ob&longs;erved the requi&longs;ite <lb/>Rules of con&longs;idering the quantity of the waters that are intro­<lb/>duced, or that happen to be diverted, &longs;hall be able with punctu­<lb/>ality to examine the whole bu&longs;ine&longs;&longs;e, and then re&longs;olve on that <lb/>which &longs;hall be expedient to be done.</s></p><p type="main"> <s>Reflecting therefore upon the fir&longs;t Propo&longs;ition, that the <lb/>Ri&longs;ings of a Running Water made by the acce&longs;&longs;ion of new water <lb/>into the River, are to one another, as the Square-Roots of the <lb/>quantity of the water that runneth; and con&longs;equently, that the <lb/>&longs;ame cometh to pa&longs;s in the Diver&longs;ions: In&longs;omuch, that a River <lb/>running in height one &longs;uch a certain mea&longs;ure, to make it encrea&longs;e <lb/>double in height, the water is to be encrea&longs;ed to three times as <pb xlink:href="040/01/665.jpg" pagenum="99"/>much as it ran before; &longs;o that when the water &longs;hall be quadru­<lb/>ple, the height &longs;hall be double; and if the water were centuple, <lb/>the height would be decuple onely, and &longs;o from one quantity <lb/>to another: And on the contrary, in the Diver&longs;ions; If of the <lb/>100. parts of water that run thorow a River, there &longs;hall be di­<lb/>verted 19/160, the height of the River dimini&longs;heth onely 1/10, and con­<lb/>tinuing to divert 17/100, the height of the River abateth likewi&longs;e 1/10, <lb/>and &longs;o proceeding to divert 15/100 and then 13/100, and then 11/100, and <lb/>then 9/100, and then 7/100, and then 5/100, and then 3/106, alwaies by <lb/>each of the&longs;e diver&longs;ions, the height of the Running Water di­<lb/>mini&longs;heth the tenth part: although that the diver&longs;ions be &longs;o une. <lb/></s> <s>qual. </s> <s>Reflecting I &longs;ay upon this infallible Truth, I have had a <lb/>conceit, that though the <emph type="italics"/>Reno<emph.end type="italics"/> and other Rivers were diverted <lb/>from the Valleyes, and there was onely left the <emph type="italics"/>Chanel of Navi­<lb/>gation,<emph.end type="italics"/> which was onely the 1/20 part of the whole water that fal­<lb/>leth into the Valleys; yet neverthele&longs;s, the water in tho&longs;e &longs;ame <lb/>Valleyes would retain a tenth part of that height that became <lb/>conjoyned by the concour&longs;e of all the Rivers: And therefore I <lb/>&longs;hould think that it were the be&longs;t re&longs;olution to maintain the <emph type="italics"/>Gha­<lb/>nel of Navigation<emph.end type="italics"/> (if it were po&longs;&longs;ible) continuate unto the P<emph type="italics"/>o<emph.end type="italics"/> of <lb/><emph type="italics"/>Ferrara,<emph.end type="italics"/> and from thence to carry it into the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Volano<emph.end type="italics"/>; for <lb/>be&longs;ides that it would be of very great ea&longs;e in the Navigation of <lb/><emph type="italics"/>Bologna,<emph.end type="italics"/> and <emph type="italics"/>Ferrara,<emph.end type="italics"/> the &longs;aid water would render the P<emph type="italics"/>o<emph.end type="italics"/> o&longs; <lb/><emph type="italics"/>Volano<emph.end type="italics"/> navigable as far as to the very Walls of <emph type="italics"/>Ferrara,<emph.end type="italics"/> and con­<lb/>&longs;equently the Navigation would be continuate from <emph type="italics"/>Bologna<emph.end type="italics"/> to <lb/>the Sea-&longs;ide.</s></p><p type="main"> <s>But to manage this enterprize well, it is nece&longs;&longs;ary to mea&longs;ure <lb/>the quantity of the Water that the Rivers di&longs;charge into the Val­<lb/>leys, and that which the <emph type="italics"/>Chanel of Navigation<emph.end type="italics"/> carryeth, in man­<lb/>ner as I have demon&longs;trated at the beginning of this Book; for this <lb/>once known, we &longs;hall al&longs;o come to know, how profitable this di­<lb/>ver&longs;ion of the <emph type="italics"/>Chanel of Navigation<emph.end type="italics"/> from the Valleys is like to <lb/>prove; which yet would &longs;till be unprofitable, if &longs;o be that all <lb/>the Rivers that di&longs;charge their waters into the Valleys, &longs;hould <lb/>not &longs;ir&longs;t be Drained, according to what hath been above ad­<lb/>verti&longs;ed.</s></p><p type="main"> <s>Abbot CASTELLI, <emph type="italics"/>in the pre&longs;ent con&longs;ideration referring <lb/>himfelf to the Relation of<emph.end type="italics"/> Mon&longs;ig. </s> <s>Cor&longs;ini, <emph type="italics"/>grounded upon the Ob­<lb/>&longs;ervations and Precepts of the &longs;aid Abbot; as is &longs;een in the pre­<lb/>&longs;ent Di&longs;cour&longs;e. </s> <s>I thought it convenient for the compleating of the <lb/>Work of our Aulhour, upon the&longs;e &longs;ubjects, to in&longs;ert it in this <lb/>place.<emph.end type="italics"/></s></p><pb xlink:href="040/01/666.jpg" pagenum="100"/><p type="head"> <s>A <lb/>Relation of the Waters in the Territories <lb/>of <emph type="italics"/>Bologna<emph.end type="italics"/> and <emph type="italics"/>Ferrara.<emph.end type="italics"/><lb/>BY</s></p><p type="head"> <s>The Right Honourable and Illu&longs;trious, <emph type="italics"/>Mon&longs;ig­<lb/>nore<emph.end type="italics"/> CORSINI, a Native of <emph type="italics"/>Ju&longs;cany,<emph.end type="italics"/> Su­<lb/>perintendent of the general DRAINS, <lb/>and Pre&longs;ident of <emph type="italics"/>Romagna-<emph.end type="italics"/></s></p><p type="main"> <s>The <emph type="italics"/>Rheno,<emph.end type="italics"/> and other Brooks of <emph type="italics"/>Romagna,<emph.end type="italics"/> were by the <lb/>advice of <emph type="italics"/>P. </s> <s>Ago&longs;tino Spernazzati<emph.end type="italics"/> the Je&longs;uite, towards <lb/>the latter end of the time of <emph type="italics"/>Pope Clement<emph.end type="italics"/> VIII. notwith­<lb/>&longs;tanding the oppo&longs;ition of the <emph type="italics"/>Bologne&longs;i,<emph.end type="italics"/> and others concerned <lb/>therein, diverted from their Chanels, for the more commodious <lb/>clean&longs;ing of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Ferrara,<emph.end type="italics"/> and of its two Branches of <emph type="italics"/>Prima­<lb/>ro,<emph.end type="italics"/> and <emph type="italics"/>Volano<emph.end type="italics"/>; in order to the introducing the water of the <lb/><emph type="italics"/>Main-Po<emph.end type="italics"/> into them, to the end that their wonted Torrents being <lb/>re&longs;tored, they might carry the Muddy-water thence into the Sea, <lb/>and re&longs;tore to the City the Navigation which was la&longs;t, as is ma­<lb/>nife&longs;t by the Brief of the &longs;aid <emph type="italics"/>Pope Clement,<emph.end type="italics"/> directed to the <emph type="italics"/>Car­<lb/>dinal San Clemence,<emph.end type="italics"/> bearing date the 22. of <emph type="italics"/>Augu&longs;t,<emph.end type="italics"/> 1604.</s></p><p type="main"> <s>The work of the &longs;aid clean&longs;ing, and introducing of the &longs;aid <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> either as being &longs;uch in it &longs;elf, or by the contention of the <lb/><emph type="italics"/>Cardinal Legates<emph.end type="italics"/> then in the&longs;e parts; and the jarrings that hap­<lb/>ned betwixt them, proved &longs;o difficult, that after the expence of <lb/>va&longs;t &longs;umms in the &longs;pace of 21. years, there hath been nothing <lb/>done, &longs;ave the rendring of it the more difficult to be effected.</s></p><p type="main"> <s>Interim, the Torrents with their waters, both muddy and <lb/>clear, have damaged the Grounds lying on the right hand of the <lb/>P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> and the <emph type="italics"/>Rheno<emph.end type="italics"/> tho&longs;e on its Banks; of which I <lb/>will &longs;peak in the fir&longs;t place, as of that which is of greater impor­<lb/>tance, and from which the principal cau&longs;e of the mi&longs;chiefs that <lb/>re&longs;ult from the re&longs;t doth proceed.<lb/><arrow.to.target n="marg976"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg976"></margin.target>* Or Lord&longs;hip.</s></p><p type="main"> <s>This <emph type="italics"/>Rbeno<emph.end type="italics"/> having overflowed the ^{*} Tennency of <emph type="italics"/>Sanmartina,<emph.end type="italics"/><lb/>in circumference about fourteen miles given it before, and part <lb/>of that of <emph type="italics"/>Cominale<emph.end type="italics"/> given it afterwards, as it were, for a recepta­<lb/>cle; from whence, having depo&longs;ed the matter of its muddine&longs;s, <lb/>it i&longs;&longs;ued clear by the Mouths of <emph type="italics"/>Ma&longs;i,<emph.end type="italics"/> and of <emph type="italics"/>Lievaloro,<emph.end type="italics"/> into <lb/>the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro,<emph.end type="italics"/> and of <emph type="italics"/>Volano<emph.end type="italics"/>; did break down the encom­<pb xlink:href="040/01/667.jpg" pagenum="101"/>pa&longs;&longs;ing Bank or Dam towards S. <emph type="italics"/>Martino,<emph.end type="italics"/> and that of its new <lb/>Chanel on the right hand neer to <emph type="italics"/>Torre del Fondo.<emph.end type="italics"/></s></p><p type="main"> <s>By the breaches on this &longs;ide it &longs;treamed out in great abun­<lb/>dance from the upper part of <emph type="italics"/>Cominale,<emph.end type="italics"/> and in the parts about <lb/><emph type="italics"/>Raveda, Pioggio, Caprara, Chiare di Reno, Sant' Ago&longs;tino, San <lb/>Pro&longs;pero, San Vincenzo,<emph.end type="italics"/> and others, and made them to become <lb/>incultivable: it made al&longs;o tho&longs;e places above but little fruitful, <lb/>by rea&longs;on of the impediments that their Draines received, finding <lb/>the Conveyances called <emph type="italics"/>Riolo<emph.end type="italics"/> and <emph type="italics"/>Scor&longs;uro,<emph.end type="italics"/> not only filled by <emph type="italics"/>la <lb/>Motta<emph.end type="italics"/> and <emph type="italics"/>la Belletta,<emph.end type="italics"/> but that they turned backwards of them­<lb/>&longs;elves.</s></p><p type="main"> <s>But by the Mouths in the inclo&longs;ing Bank or Dam at <emph type="italics"/>Borgo di<emph.end type="italics"/><lb/>S. <emph type="italics"/>Martino<emph.end type="italics"/> i&longs;&longs;uing with violence, it fir&longs;t gave ob&longs;truction to the <lb/>ancient Navigation of <emph type="italics"/>la Torre del la Fo&longs;&longs;a,<emph.end type="italics"/> and afterwards to <lb/>the moderne of the mouth of <emph type="italics"/>Ma&longs;i,<emph.end type="italics"/> &longs;o that at pre&longs;ent the Com­<lb/>merce between <emph type="italics"/>Bologna<emph.end type="italics"/> and <emph type="italics"/>Ferrara<emph.end type="italics"/> is lo&longs;t, nor can it ever be <lb/>in any durable way renewed, whil&longs;t that this exceeds its due <lb/>bounds, and what ever moneys &longs;hall be imployed about the &longs;ame <lb/>&longs;hall be without any equivalent benefit, and to the manife&longs;t </s></p><p type="main"> <s><arrow.to.target n="marg977"></arrow.to.target><lb/>and notable prejudice of the ^{*} Apo&longs;tolick Chamber.</s></p><p type="margin"> <s><margin.target id="marg977"></margin.target>* The Popes <lb/>Exchequer.</s></p><p type="main"> <s>Thence pa&longs;&longs;ing into the Valley of <emph type="italics"/>Marzara,<emph.end type="italics"/> it &longs;welleth high­<lb/>er, not only by the ri&longs;ing of the water, but by the rai&longs;ing of the <lb/>bottome, by rea&longs;on of the matter &longs;unk thither after Land­<lb/>floods, and dilateth &longs;o, that it covereth all the Meadows there­<lb/>abouts, nor doth it receive with the wonted facility the Drains of <lb/>the upper Grounds, of which the next unto it lying under the wa­<lb/>ters that return upwards by the Conveyances, and the more re­<lb/>mote, not finding a pa&longs;&longs;age for Rain-waters that &longs;ettle, become <lb/>either altogether unpro&longs;itable or little better.</s></p><p type="main"> <s>From this Valley, by the Trench or Ditch of <emph type="italics"/>Marzara,<emph.end type="italics"/> or of <lb/><emph type="italics"/>la Duca<emph.end type="italics"/> by <emph type="italics"/>la Buova,<emph.end type="italics"/> or mouth of <emph type="italics"/>Ca&longs;taldo de Ro&longs;&longs;i,<emph.end type="italics"/> and by the <lb/>new pa&longs;&longs;age it falleth into the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> which being to re­<lb/>ceive it clear, that &longs;o it may &longs;ink farther therein, and receiving <lb/>it muddy, becau&longs;e it hath acquired a quicker cour&longs;e, there will <lb/>ari&longs;e a very contrary effect.</s></p><p type="main"> <s>Here therefore the &longs;uperficies of the water keeping high, until <lb/>it come to the Sea, hindereth the Valleys of <emph type="italics"/>Ravenna,<emph.end type="italics"/> where <lb/>the River <emph type="italics"/>Senio,<emph.end type="italics"/> tho&longs;e of <emph type="italics"/>San Bernardino<emph.end type="italics"/> where <emph type="italics"/>Santerno<emph.end type="italics"/> was <lb/>turned, tho&longs;e of <emph type="italics"/>Buon' acqui&longs;to,<emph.end type="italics"/> and tho&longs;e of <emph type="italics"/>Marmorto,<emph.end type="italics"/> where <lb/>the <emph type="italics"/>Idice, Quaderna, Sellero<emph.end type="italics"/> &longs;all in, from &longs;wallowing and taking <lb/>in their Waters by their u&longs;ual In-lets, yet many times, as I my <lb/>&longs;elf have &longs;een in the <emph type="italics"/>Vi&longs;itation,<emph.end type="italics"/> they drink them up plentifully, <lb/>whereupon, being conjoyned with the muddine&longs;&longs;e of tho&longs;e Ri­<lb/>vers that fall into the &longs;ame, they &longs;well, and dilate, and overflow <lb/>&longs;ome grounds, and deprive others of their Drains in like manner <pb xlink:href="040/01/668.jpg" pagenum="102"/>as hath been &longs;aid of that of <emph type="italics"/>Marrara,<emph.end type="italics"/> in&longs;omuch that from the <lb/>Point of S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> as far as S. <emph type="italics"/>Alberto<emph.end type="italics"/> all tho&longs;e that are between <lb/>the Valleys and P<emph type="italics"/>o<emph.end type="italics"/> are &longs;poiled, of tho&longs;e that are between Valley <lb/>and Valley many are in a very bad condition, and tho&longs;e that are <lb/>&longs;ome con&longs;iderable &longs;pace above not a little damnified.</s></p><p type="main"> <s>In fine, by rai&longs;ing the bottom or &longs;and of the Valleys, and the <lb/>bed of <emph type="italics"/>Reno,<emph.end type="italics"/> and the too great repletion of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro<emph.end type="italics"/><lb/>with waters, the Valleys of <emph type="italics"/>Comacchio<emph.end type="italics"/> (on which &longs;ide the Banks <lb/>are very bad) and ^{*} <emph type="italics"/>Pole&longs;ine di<emph.end type="italics"/> S. <emph type="italics"/>Giorgio<emph.end type="italics"/> are threatned with a <lb/><arrow.to.target n="marg978"></arrow.to.target><lb/>danger, that may in time, if it be not remedied, become irrepa­<lb/>rable, and at pre&longs;ent feeleth the incommodity of the Waters, <lb/>which penetrating thorow the pores of the Earth do &longs;pring up in <lb/>the &longs;ame, which they call <emph type="italics"/>Purlings,<emph.end type="italics"/> which is all likely to redound <lb/>to the prejudice of <emph type="italics"/>Ferrara,<emph.end type="italics"/> &longs;o noble a City of <emph type="italics"/>Italy,<emph.end type="italics"/> and &longs;o im­<lb/>portant to the <emph type="italics"/>Eccle&longs;ta&longs;tick State.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg978"></margin.target>+ <emph type="italics"/>Pole&longs;ine<emph.end type="italics"/> is a <lb/>plat of Ground al­<lb/>mo&longs;t &longs;urrounded <lb/>with Bogs or wa­<lb/>ters, like an I&longs;land</s></p><p type="main"> <s>Which particulars all appear to be atte&longs;ted under the hand of <lb/>a Notary in the <emph type="italics"/>Vi&longs;itation<emph.end type="italics"/> which I made upon the command of <lb/>His Holine&longs;&longs;e, and are withall known to be true by the ^{*}<emph type="italics"/>Ferrare&longs;t<emph.end type="italics"/><lb/><arrow.to.target n="marg979"></arrow.to.target><lb/>them&longs;elves, of whom (be&longs;ides the reque&longs;t of the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/>) the <lb/>greater part beg compa&longs;&longs;ion with &longs;undry <emph type="italics"/>Memorials,<emph.end type="italics"/> and reme­<lb/>dies, a&longs;well for the mi&longs;chiefs pa&longs;t, as al&longs;o for tho&longs;e in time to <lb/>come, from which I hold it a duty of Con&longs;cience, and of Cha­<lb/>rity to deliver them.</s></p><p type="margin"> <s><margin.target id="marg979"></margin.target>* People of <emph type="italics"/>Fer­<lb/>rara.<emph.end type="italics"/></s></p><p type="main"> <s>Pope <emph type="italics"/>Clement<emph.end type="italics"/> judged, that the &longs;ufficient means to effect this <lb/>was the &longs;aid Introduction of the <emph type="italics"/>Main Po<emph.end type="italics"/> into the Chancl of <lb/><emph type="italics"/>Ferrara<emph.end type="italics"/>; a re&longs;olution truly Heroical, and of no le&longs;&longs;e beauty <lb/>than benefit to that City, of which I &longs;peak not at pre&longs;ent, be­<lb/>cau&longs;e I think that there is need of a readier and more acco­<lb/>modate remedy.</s></p><p type="main"> <s>So that I &longs;ee not how any other thing can be &longs;o much con&longs;ide­<lb/>rable as the removal of <emph type="italics"/>Reno,<emph.end type="italics"/> omitting for this time to &longs;peak of <lb/><arrow.to.target n="marg980"></arrow.to.target><lb/>^{*} inclo&longs;ing it from Valley to Valley untill it come to the Sea, as <lb/>the Dukes of <emph type="italics"/>Ferrara<emph.end type="italics"/> did de&longs;ign, fora&longs;much as all tho&longs;e <emph type="italics"/>Ferra­<lb/>re&longs;i<emph.end type="italics"/> that have intere&longs;t in the <emph type="italics"/>Pole&longs;ine di<emph.end type="italics"/> S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> and on the <lb/>right hand of the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta<emph.end type="italics"/> do not de&longs;ire it, and do, but too <lb/>openly, prote&longs;t again&longs;t it; and becau&longs;e that before the Chanel <lb/>were made as far as the Sea, many hundreds of years would be <lb/>&longs;pent, and yet would not remedy the dammages of tho&longs;e who <lb/>now are agrieved, but would much increa&longs;e them, in regard the <lb/>Valleys would continue &longs;ubmerged, the Drains &longs;topped, and the <lb/>other Brooks ob&longs;tructed, which would of nece&longs;&longs;ity drown not a <lb/>few Lands that lie between Valley and Valley; and in fine, in <lb/>regard it hath not from <emph type="italics"/>San Martina<emph.end type="italics"/> to the Sea for a &longs;pace of &longs;if­<lb/>ty miles a greater fall then 19, 8, 6, feet, it would want that force <lb/>which they them&longs;elves who propound this project do require it to <pb xlink:href="040/01/669.jpg" pagenum="103"/>have, that &longs;o it may not depo&longs;e the matter of the muddine&longs;s when <lb/>it is intended to be let into <emph type="italics"/>Volana.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg980"></margin.target>* In Chanels <lb/>made by hand.</s></p><p type="main"> <s>So that making the Line of the bottome neer to <emph type="italics"/>Vigarano,<emph.end type="italics"/> it <lb/>would ri&longs;e to tho&longs;e prodigious termes that they do make bigger, <lb/>and they may thence expect tho&longs;e mi&longs;chiefs, for which they <lb/>will not admit of introducing it into the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Volana.<emph.end type="italics"/></s></p><p type="main"> <s>Among&longs;t the wayes therefore that I have thought of for effect­<lb/>ing that &longs;ame remotion, and which I have cau&longs;ed to be viewed by <lb/>skilful men that have taken a level thereof, (with the a&longs;&longs;i&longs;tance of <lb/>the venerable Father, <emph type="italics"/>D. </s> <s>Benedetto Ca&longs;telli<emph.end type="italics"/> of <emph type="italics"/>Ca&longs;ina,<emph.end type="italics"/> a man of <lb/>much fidelity and hone&longs;ty, and no le&longs;s expert in &longs;uch like affairs <lb/>touching waters, than perfect in the <emph type="italics"/>Mathematick<emph.end type="italics"/> Di&longs;ciplines) two <lb/>onely, the re&longs;t being either too tedious, or too dangerous to the <lb/>City, have &longs;eemed to me worthy, and one of them al&longs;o more than <lb/>the other, to offer to your Lord&longs;hip.</s></p><p type="main"> <s>The one is to remit it into the Chanel of <emph type="italics"/>Volana,<emph.end type="italics"/> thorow which <lb/>it goeth of its own accord to the Sea.</s></p><p type="main"> <s>The other is to turn it into <emph type="italics"/>Main-Po<emph.end type="italics"/> at <emph type="italics"/>Stellata,<emph.end type="italics"/> for, as at other <lb/>times it hath done, it will carry it to the Sea happily.</s></p><p type="main"> <s>As to what concerns the making choice of the fir&longs;t way, that <lb/>which &longs;eemeth to per&longs;wade us to it is, that we therein do nothing <lb/>that is new, in that it is but re&longs;tored to the place whence it was <lb/>removed in the year 1522. in the time of Pope <emph type="italics"/>Adrian,<emph.end type="italics"/> by an <lb/>agreement made in way of contract, between <emph type="italics"/>Alfon&longs;o,<emph.end type="italics"/> Duke of <lb/><emph type="italics"/>Ferrara,<emph.end type="italics"/> and the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/>; and that it was diverted for rea&longs;ons, <lb/>that are either out of date, or el&longs;e have been too long time <lb/>deferred.</s></p><p type="main"> <s>In like manner the facility wherewith it may be effected, let­<lb/>ting it run into the divided P<emph type="italics"/>o,<emph.end type="italics"/> whereby it will be turned to <emph type="italics"/>Fer­<lb/>rara,<emph.end type="italics"/> or el&longs;e carrying it by <emph type="italics"/>Torre del Fondo,<emph.end type="italics"/> to the mouth of <emph type="italics"/>Ma&longs;i,<emph.end type="italics"/><lb/>and from thence thorow the Trench made by the <emph type="italics"/>Ferrare&longs;i,<emph.end type="italics"/><lb/>along by <emph type="italics"/>Panaro,<emph.end type="italics"/> where al&longs;o finding an ample Bed, and high and <lb/>thick Banks, that will &longs;erve at other times for it, and for the wa­<lb/>ters of P<emph type="italics"/>o,<emph.end type="italics"/> there may a great expence be &longs;pared.</s></p><p type="main"> <s>That what ever its Fall be, it would maintain the &longs;ame, not <lb/>having other Rivers, which with their Floods can hinder it; and <lb/>that running confined between good Banks, without doubt it <lb/>would not leave <emph type="italics"/>la Motto<emph.end type="italics"/> by the way; but e&longs;pecially, that it <lb/>would be &longs;ufficient if it came to <emph type="italics"/>Codigoro,<emph.end type="italics"/> where being a&longs;&longs;i&longs;ted by <lb/>the Ebbing and Flowing of the Sea, it would run no hazard of <lb/>having its Chanel filled up from thence downwards.</s></p><p type="main"> <s>That there might thence many benefits be derived to the City, <lb/>by means of the Running Waters, and al&longs;o no mean Navigation <lb/>might be expected.</s></p><p type="main"> <s>On the contrary it is objected, That it is not convenient to <pb xlink:href="040/01/670.jpg" pagenum="104"/>think of returning this Torrent into the divided P<emph type="italics"/>o,<emph.end type="italics"/> by rea&longs;on of <lb/>the peril that would thence redound to this City.</s></p><p type="main"> <s>And that going by <emph type="italics"/>Torre del Fondo,<emph.end type="italics"/> through <emph type="italics"/>Sanmartina<emph.end type="italics"/> to <lb/>the Mouth <emph type="italics"/>de Ma&longs;i<emph.end type="italics"/> by the Chappel of <emph type="italics"/>Vigarano<emph.end type="italics"/> unto the Sea, it is <lb/>by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, &longs;o <lb/>that it would come to fall but 4. inches & an half, or thereabouts <lb/>in a mile; whereas the common opinion of the skilfull (to the <lb/>end that the Torrents may not depo&longs;e their &longs;and that they bring <lb/>with them in Land-Floods) requireth the twenty fourth part of <lb/>the hundredth part of their whole length, which in our ca&longs;e, <lb/>accounting according to the mea&longs;ure of the&longs;e places, is 16. inches <lb/><arrow.to.target n="marg981"></arrow.to.target><lb/>a ^{*} mile; whereupon the &longs;inking of the Mud and Sand would <lb/>mo&longs;t certainly follow, and &longs;o an immen&longs;e heightning of the Line <lb/>of the Bottom, and con&longs;equently a nece&longs;&longs;ity of rai&longs;ing the Banks, <lb/>the impo&longs;&longs;ibility of maintaining them, the danger of breaches <lb/>and decayes, things very prejudicial to the <emph type="italics"/>I&longs;lets<emph.end type="italics"/> of this City, and <lb/>of <emph type="italics"/>San Giorgio,<emph.end type="italics"/> the ob&longs;truction of the Drains, which from the <lb/>Tower of <emph type="italics"/>Tienne<emph.end type="italics"/> downwards, fall into the &longs;aid Chanel; to wit, <lb/>tho&longs;e of the Sluices of <emph type="italics"/>Goro,<emph.end type="italics"/> and the Drains, of the Meadows of <lb/><emph type="italics"/>Ferrara<emph.end type="italics"/>: And moreover, the damages that would ari&longs;e unto the <lb/>&longs;aid <emph type="italics"/>I&longs;let<emph.end type="italics"/> of S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> and the Valleys of <emph type="italics"/>Comachio,<emph.end type="italics"/> by the wa­<lb/>ters that &longs;hould enter into the <emph type="italics"/>Goro<emph.end type="italics"/> or Dam of the Mills of <emph type="italics"/>Belri­<lb/>guardo,<emph.end type="italics"/> thorow the Trenches of <emph type="italics"/>Quadrea,<emph.end type="italics"/> which cannot be &longs;topt, <lb/>becau&longs;e they belong to the Duke of <emph type="italics"/>Modena,<emph.end type="italics"/> who hath right of <lb/>diverting the waters of that place at his plea&longs;ure to the work of <lb/>turning Mills.</s></p><p type="margin"> <s><margin.target id="marg981"></margin.target>* The inch of <lb/>the&longs;e places is <lb/>&longs;omewhat bigger <lb/>than ours.</s></p><p type="main"> <s>The greater part of which Objections, others pretend to prove <lb/>frivolous, by &longs;aying, that its running there till at the la&longs;t it was <lb/>turned another way, is a &longs;ign that it had made &longs;uch an elevation <lb/>of the Line, of its Bed as it required; denying that it needeth <lb/>&longs;o great a declivity as is mentioned above; and that for the fu­<lb/>ture it would ri&longs;e no more.</s></p><p type="main"> <s>That the &longs;aid Dra ns and Ditches did empty into the &longs;ame, <lb/>whil&longs;t P<emph type="italics"/>o<emph.end type="italics"/> was there; &longs;o that they mu&longs;t needs be more able to do <lb/>&longs;o when onely <emph type="italics"/>Reno<emph.end type="italics"/> runs that way.</s></p><p type="main"> <s>That there would no Breaches follow, or if they did, they <lb/>would be onely of the water of <emph type="italics"/>Reno,<emph.end type="italics"/> which in few hours might <lb/>be taken away (in tho&longs;e parts they call damming up of Breaches, <lb/>and mending the Bank, <emph type="italics"/>taking away the Breaches<emph.end type="italics"/>) and its a que­<lb/>&longs;tion whether they would procure more inconvenience than bene­<lb/>fit, for that its Mud and Sand might in many places, by filling <lb/>them up, occa&longs;ion a &longs;ea&longs;onable improvement.</s></p><p type="main"> <s>Now omitting to di&longs;cour&longs;e of the &longs;olidity of the rea&longs;ons on the <lb/>one&longs;ide, or on the other, I will produce tho&longs;e that move me to <lb/>&longs;u&longs;pend my allowance of this de&longs;ign.</s></p><pb xlink:href="040/01/671.jpg" pagenum="105"/><p type="main"> <s>The fir&longs;t is, that although I dare not &longs;ub&longs;cribe to the opinion <lb/>of tho&longs;e that require 16. inches Declivity in a mile to <emph type="italics"/>Reno,<emph.end type="italics"/> to <lb/>prevent its depo&longs;ing of Mud; yet would I not be the Author that <lb/>&longs;hould make a trial of it with &longs;o much hazard, for having to &longs;a­<lb/>tisfie my &longs;elf in &longs;ome particulars cau&longs;ed a Level to be taken of <lb/>the Rivers <emph type="italics"/>L'amone, Senio,<emph.end type="italics"/> and <emph type="italics"/>Santerno,<emph.end type="italics"/> by <emph type="italics"/>Bernardino Aleotti,<emph.end type="italics"/><lb/>we found that they have more Declivity by much than Arti&longs;ts re­<lb/>quire, as al&longs;o the <emph type="italics"/>Reno<emph.end type="italics"/> hath from <emph type="italics"/>la Botta de Ghi&longs;lieri<emph.end type="italics"/> to the <lb/>Chappel of <emph type="italics"/>Vigarano,<emph.end type="italics"/> for in the &longs;pace of four miles its Bottom­<lb/>Line falleth five feet and five inches. </s> <s>So that I hold it greater <lb/>prudence to depend upon that example, than to go contrary to a <lb/>common opinion, e&longs;pecially &longs;ince, that the effects cau&longs;ed by <emph type="italics"/>Reno<emph.end type="italics"/><lb/>it &longs;elf do confirm me in the &longs;ame, for when it was for&longs;aken by <lb/>the P<emph type="italics"/>o,<emph.end type="italics"/> after a few years, either becau&longs;e it had choaked up its <lb/>Chanel with Sand, or becau&longs;e its too long journey did increa&longs;e <lb/>it, it al&longs;o naturally turned a&longs;ide, and took the way of the &longs;aid <lb/>P<emph type="italics"/>o<emph.end type="italics"/> towards <emph type="italics"/>Stellata.<emph.end type="italics"/> Nay, in tho&longs;e very years that it did run that <lb/>way, it only began (as relations &longs;ay) to make Breaches, an evi­<lb/>dent &longs;ign that it doth depo&longs;e Sand, and rai&longs;e its Bed; which a­<lb/>greeth with the te&longs;timony of &longs;ome that were examined in the <lb/><emph type="italics"/>Vi&longs;itation<emph.end type="italics"/> of the Publique Notary, who found great benefit by <lb/>having Running Water, and &longs;ome kind of pa&longs;&longs;age for Boats, <lb/>and yet neverthele&longs;s affirm that it for want of Running Water <lb/>had made too high Stoppages and Shelfes of Sand; &longs;o that if <lb/>it &longs;hould be re&longs;tored to the Cour&longs;e that it for&longs;ook, I much fear <lb/>that after a &longs;hort time, if not &longs;uddenly, it would leave it a­<lb/>again.</s></p><p type="main"> <s>The &longs;econd I take from the ob&longs;ervation of what happened to <lb/><emph type="italics"/>Panaro,<emph.end type="italics"/> when with &longs;o great applau&longs;e of the <emph type="italics"/>Ferare&longs;i,<emph.end type="italics"/> it was <lb/>brought by Cardinal <emph type="italics"/>Serra<emph.end type="italics"/> into the &longs;aid Chanel of <emph type="italics"/>Volana<emph.end type="italics"/>; for <lb/>that notwith&longs;tanding that it had Running Waters in much grea­<lb/>ter abundance than <emph type="italics"/>Reno<emph.end type="italics"/>; yet in the time that it continued in <lb/>that Chanel it rai&longs;ed its Bed well neer five feet, as is to be &longs;een <lb/>below the Sluice made by Cardinal <emph type="italics"/>Capponi<emph.end type="italics"/> to his new Chanel; <lb/>yea, the &longs;aid Cardinal <emph type="italics"/>Serra<emph.end type="italics"/> who de&longs;ired that this his under taking <lb/>&longs;hould appear to have been of no danger nor damage, was con­<lb/>&longs;trained at its Overflowings, to give it Vent into <emph type="italics"/>Sanmartina,<emph.end type="italics"/> that <lb/>it might not break in upon, and prejudice the City; which dan­<lb/>ger I &longs;hould more fear from <emph type="italics"/>Reno,<emph.end type="italics"/> in regard it carrieth a greater <lb/>abundance of Water and Sand</s></p><p type="main"> <s>Thirdly, I am much troubled (in the uncertainty of the &longs;uc­<lb/>ce&longs;s of the affair) at the great expence thereto required; For in <lb/>regard I do not approve of letting it in, neer to the Fortre&longs;&longs;e, <lb/>for many re&longs;pects, and carrying it by <emph type="italics"/>la Torre del Fondo<emph.end type="italics"/> to the <lb/>Month <emph type="italics"/>de Ma&longs;t,<emph.end type="italics"/> it will take up eight miles of double Banks, a <pb xlink:href="040/01/672.jpg" pagenum="106"/>thing not ea&longs;ie to be procured, by rea&longs;on that the Grounds lie <lb/>under Water; but from the Mouth <emph type="italics"/>de Ma&longs;i<emph.end type="italics"/> unto <emph type="italics"/>Codigoro,<emph.end type="italics"/> it <lb/>would al&longs;o be nece&longs;&longs;ary to make new Scowrings of the Chanel; <lb/>to the end, that the Water approaching (by wearing and carry­<lb/>ing away the Earth on both &longs;hores, might make a Bed &longs;ufficient <lb/>for its Body, the depth made for <emph type="italics"/>Panaro<emph.end type="italics"/> not &longs;erving the turn, as <lb/>I conceive; and if it &longs;hould &longs;uffice, when could the people of <lb/><emph type="italics"/>Ferrara<emph.end type="italics"/> hope to be re-imbur&longs;ed and &longs;atisfied for the charge <lb/>thereof?</s></p><p type="main"> <s>Fourthly, it &longs;erves as an Argument with me, to &longs;ee that the <lb/>very individual per&longs;ons concerned in the Remotion or Diver&longs;ion <lb/>of the &longs;aid Torrent, namely, the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/> do not incline unto it, <lb/>and that the whole City of <emph type="italics"/>Ferrara,<emph.end type="italics"/> even tho&longs;e very per&longs;ons who <lb/>at pre&longs;ent receive damage by it, cannot indure to hear thereof. <lb/></s> <s>The rea&longs;on that induceth the&longs;e la&longs;t named to be &longs;o aver&longs;e thereto, <lb/>is, either becau&longs;e that this undertaking will render the introducti­<lb/>on of the Water of <emph type="italics"/>Main-Po<emph.end type="italics"/> more difficult; or becau&longs;e they fear <lb/>the danger thereof; The others decline the Project, either for <lb/>that they know that <emph type="italics"/>Reno<emph.end type="italics"/> cannot long continue in that Cour&longs;e, <lb/>or becau&longs;e they fear that it is too much expo&longs;ed to tho&longs;e mens re­<lb/>vengeful Cutting of it who do not de&longs;ire it &longs;hould; and if a <lb/>man have any other wayes, he ought, in my opinion, to forbear <lb/>that, which to &longs;uch as &longs;tand in need of its Removal, is le&longs;&longs;e &longs;ati&longs;­<lb/>factory, and to &longs;uch as oppo&longs;e it, more prejudicial.</s></p><p type="main"> <s>To conclude, I exceedingly honour the judgment of Cardinal <lb/><emph type="italics"/>Capponi,<emph.end type="italics"/> who having to his Natural Ability and Prudence added <lb/>a particular Study, Ob&longs;ervation, and Experience of the&longs;e Wa­<lb/>ters for the &longs;pace of three years together, doth not think that <lb/><emph type="italics"/>Reno<emph.end type="italics"/> can go by <emph type="italics"/>Volana<emph.end type="italics"/>; to which agreeth the opinion of Car­<lb/>dinal S. <emph type="italics"/>Marcello,<emph.end type="italics"/> Legate of this City, of whom, for his exqui­<lb/>&longs;ite under&longs;tanding, we ought to make great account. </s> <s>But if e­<lb/>ver this &longs;hould be re&longs;olved on, it would be materially nece&longs;&longs;ary <lb/>to unite the Quick and Running Waters of the little Chanel of <lb/><emph type="italics"/>Cento,<emph.end type="italics"/> of the Chanel <emph type="italics"/>Navilio,<emph.end type="italics"/> of <emph type="italics"/>Guazzaloca,<emph.end type="italics"/> and at its very <lb/>beginning tho&longs;e of <emph type="italics"/>Dardagna,<emph.end type="italics"/> which at pre&longs;ent, is one of the <lb/>Springs or Heads of <emph type="italics"/>Panaro,<emph.end type="italics"/> that &longs;o they might a&longs;&longs;i&longs;t it in carry­<lb/>ing its Sand, and the matter of its Muddine&longs;s into the Sea; and <lb/>then there would not fail to be a greater evacuation and &longs;cowr­<lb/>ing; but withall the Proprietors in the I&longs;let of <emph type="italics"/>San Giorgio<emph.end type="italics"/> and <lb/>of <emph type="italics"/>Ferrara<emph.end type="italics"/> mu&longs;t prepare them&longs;elves to indure the inconveniences <lb/>of Purlings or Sewings of the Water from the River thorow <lb/>the Boggy Ground thereabouts.</s></p><p type="main"> <s>I &longs;hould more ea&longs;ily incline therefore to carry it into <emph type="italics"/>Main-Po<emph.end type="italics"/><lb/>at <emph type="italics"/>Stellata,<emph.end type="italics"/> for the Rea&longs;ons that Cardinal <emph type="italics"/>Capponi<emph.end type="italics"/> mo&longs;t ingeni­<lb/>ou&longs;ly enumerates in a &longs;hort, but well-grounded Tract of his: not <pb xlink:href="040/01/673.jpg" pagenum="107"/>becau&longs;e that indeed it would not both by Purlings and by Brea­<lb/>ches occa&longs;ion &longs;ome inconvenience; e&longs;pecially, in the beginning: <lb/>but becau&longs;e I hold this for the incomodities of it, to be a far le&longs;s <lb/>evil than any of the re&longs;t; and becau&longs;e that by this means there is <lb/>no occa&longs;ion given to them of <emph type="italics"/>Ferrara,<emph.end type="italics"/> to explain that they are <lb/>deprived of the hope of ever &longs;eeing the P<emph type="italics"/>o<emph.end type="italics"/> again under the Walls <lb/>of their City: To whom, where it may be done, it is but rea&longs;on <lb/>that &longs;atisfaction &longs;hould be given.</s></p><p type="main"> <s>It is certain that P<emph type="italics"/>o<emph.end type="italics"/> was placed by Nature in the mid&longs;t of this <lb/>great Valley made by the <emph type="italics"/>Appennine<emph.end type="italics"/> Hills, and by the Alps, to <lb/>carry, as the Ma&longs;ter-Drain to the Sea, that is the grand receptacle <lb/>of all Waters; tho&longs;e particular &longs;treams which de&longs;cend from <lb/>them.</s></p><p type="main"> <s>That the <emph type="italics"/>Reno<emph.end type="italics"/> by all Geographers, <emph type="italics"/>Strabo, Pliuy, Solimas, <lb/>Mella,<emph.end type="italics"/> and others is enumerated among the Rivers that fall into <lb/>the &longs;aid P<emph type="italics"/>o.<emph.end type="italics"/></s></p><p type="main"> <s>That although P<emph type="italics"/>o<emph.end type="italics"/> &longs;hould of it &longs;elf change its cour&longs;e, yet would <lb/><emph type="italics"/>Reno<emph.end type="italics"/> go to look it out, if the works erected by humane ind u&longs;try <lb/>did not ob&longs;truct its pa&longs;&longs;age; &longs;o that it neither is, nor ought to <lb/>&longs;eem &longs;trange, if one for the greater common good &longs;hould turn it <lb/>into the &longs;ame.</s></p><p type="main"> <s>Now at <emph type="italics"/>Stellata<emph.end type="italics"/> it may go &longs;everal waies into P<emph type="italics"/>o,<emph.end type="italics"/> as appeareth <lb/>by the levels that were taken by my Order; of all which I &longs;hould <lb/>be&longs;t like the turning of it to <emph type="italics"/>la Botta de' Ghi&longs;lieri,<emph.end type="italics"/> carrying it <lb/>above <emph type="italics"/>Bondeno<emph.end type="italics"/> to the Church of <emph type="italics"/>Gambarone,<emph.end type="italics"/> or a little higher or <lb/>lower, as &longs;hall be judged lea&longs;t prejudicial, when it cometh to the <lb/>execution, and this for two principal rea&longs;ons: The one becau&longs;e <lb/>that then it will run along by the confines of the Church P tri­<lb/>mony, without &longs;eparating <emph type="italics"/>Ferrara<emph.end type="italics"/> from the re&longs;t of it; The other <lb/>is, Becau&longs;e the Line is &longs;horter, and con&longs;equently the fall greater; <lb/>for that in a &longs;pace of ten miles and one third, it falleth twenty &longs;ix <lb/>feet, more by much than is required by Arti&longs;ts; and would go <lb/>by places where it could do but little hurt, notwith&longs;tanding that <lb/>the per&longs;ons interre&longs;&longs;ed &longs;tudy to amplifie it incredibly.</s></p><p type="main"> <s>On the contrary, there are but onely two objections that are <lb/>worthy to be examined; One, That the Drains and Ditches of <lb/>S. <emph type="italics"/>Bianca,<emph.end type="italics"/> of the Chanel of <emph type="italics"/>Cento,<emph.end type="italics"/> and of <emph type="italics"/>Burana,<emph.end type="italics"/> and all tho&longs;e <lb/>others that enter into P<emph type="italics"/>o,<emph.end type="italics"/> do hinder this diver&longs;ion of <emph type="italics"/>Reno,<emph.end type="italics"/> by the <lb/>encrea&longs;ing of the waters in the P<emph type="italics"/>o.<emph.end type="italics"/> The other is that P<emph type="italics"/>o<emph.end type="italics"/> ri&longs;ing <lb/>about the Tran&longs;om of the <emph type="italics"/>Pila&longs;ter<emph.end type="italics"/>-Sluice, very near 20 feet, the <lb/><emph type="italics"/>Reno<emph.end type="italics"/> would have no fall into the &longs;ame; whereupon it would ri&longs;e <lb/>to a terrible height, at which it would not be po&longs;&longs;ible to make, or <lb/>keep the Banks made, &longs;o that it would break out and drown <lb/>the Meadowes, and cau&longs;e mi&longs;chiefs, and damages un&longs;peakable <lb/>and irreparable; as is evident by the experiment made upon <pb xlink:href="040/01/674.jpg" pagenum="108"/><emph type="italics"/>Panaro,<emph.end type="italics"/> which being confined between Banks, that it might go <lb/>into P<emph type="italics"/>o,<emph.end type="italics"/> this not being neither in its greate&longs;t excre&longs;cen&longs;e, it broke <lb/>out into the territories of <emph type="italics"/>Final,<emph.end type="italics"/> and of <emph type="italics"/>Ferrara.<emph.end type="italics"/> And though <lb/>that might be done, it would thereupon en&longs;ue, that there being <lb/>let into the Chanel of P<emph type="italics"/>o,<emph.end type="italics"/> 2800, &longs;quare feet of water (for &longs;o much <lb/>we account tho&longs;e of <emph type="italics"/>Reno<emph.end type="italics"/> and <emph type="italics"/>Panaro,<emph.end type="italics"/> taken together in their <lb/>greate&longs;t heights) the &longs;uperficies of it would ri&longs;e at lea&longs;t four feet, <lb/>in&longs;omuch that either it would be requi&longs;ite to rai&longs;e its Banks all the <lb/>way unto the Sea, to the &longs;ame height, which the trea&longs;ures of the <lb/><emph type="italics"/>Indies<emph.end type="italics"/> would not &longs;uffice to effect; or el&longs;e there would be a nece&longs;­<lb/>&longs;ity of enduring exce&longs;&longs;ive Breaches. </s> <s>To the&longs;e two Heads are the <lb/>Arguments reduced, which are largely amplified again&longs;t our opi­<lb/>nion; and I &longs;hall an&longs;wer fir&longs;t to the la&longs;t, as mo&longs;t material.</s></p><p type="main"> <s>I &longs;ay therefore, that there are three ca&longs;es to be con&longs;idered: <lb/>Fir&longs;t, P<emph type="italics"/>o<emph.end type="italics"/> high, and <emph type="italics"/>Reno<emph.end type="italics"/> low. </s> <s>Secondly, <emph type="italics"/>Reno<emph.end type="italics"/> high, and P<emph type="italics"/>o<emph.end type="italics"/><lb/>low. </s> <s>Thirdly, <emph type="italics"/>Reno<emph.end type="italics"/> and P<emph type="italics"/>o<emph.end type="italics"/> both high together.</s></p><p type="main"> <s>As to the fir&longs;t and &longs;econd, there is no difficulty in them; for if <lb/>P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall not be at its greate&longs;t height, <emph type="italics"/>Reno<emph.end type="italics"/> &longs;hall ever have a fall <lb/>into it, and there &longs;hall need no humane Artifice about the Banks: <lb/>And if <emph type="italics"/>Reno<emph.end type="italics"/> &longs;hall be low, P<emph type="italics"/>o<emph.end type="italics"/> &longs;hall regurgitate and flow up into <lb/>the Chanel of it; and al&longs;o from thence no inconvenience &longs;hall <lb/>follow. </s> <s>The third remains, from which there are expected ma­<lb/>ny mi&longs;chiefs; but it is a mo&longs;t undoubted truth, that the excre&longs;cen­<lb/>cies of <emph type="italics"/>Reno,<emph.end type="italics"/> as coming from the adjacent <emph type="italics"/>Appennines<emph.end type="italics"/> and Rains, <lb/>are to continue but &longs;even, or eight hours at mo&longs;t, and &longs;o would <lb/>never, or very rarely happen to be at the &longs;ame time with tho&longs;e of <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> cau&longs;ed by the melting of the &longs;nowes of the Alps, at lea&longs;t 400. <lb/>miles di&longs;tance from thence. </s> <s>But becau&longs;e it &longs;ometimes may hap­<lb/>pen, I reply, that when it cometh to pa&longs;s, <emph type="italics"/>Reno<emph.end type="italics"/> &longs;hall not go into <lb/>P<emph type="italics"/>o,<emph.end type="italics"/> but it &longs;hall have allowed it one or two Vents; namely, into <lb/>the Chanel of <emph type="italics"/>Ferrara,<emph.end type="italics"/> as it hath ever had; and into <emph type="italics"/>Sanmartina,<emph.end type="italics"/><lb/>where it runneth at pre&longs;ent, and wherewith there is no doubt, but <lb/>that the per&longs;ons concerned will be well plea&longs;ed, it being a great <lb/>benefit to them, to have the water over-flow their grounds once <lb/>every four or five years, in&longs;tead of &longs;eeing it anoy them continu­<lb/>ally. </s> <s>Yea, the Vent may be regulated, re&longs;erving for it the Cha­<lb/>nel in which <emph type="italics"/>Reno<emph.end type="italics"/> at pre&longs;ent runneth; and in&longs;tead of turning it <lb/>by a Dam at <emph type="italics"/>la Betta de Chi&longs;lieri,<emph.end type="italics"/> perhaps, to turn it by help of <lb/>&longs;trong Sluices, that may upon all occa&longs;ions be opened and &longs;hut. <lb/></s> <s>And for my part, I do not que&longs;tion but that the Proprietors <lb/>them&longs;elves in <emph type="italics"/>Sanmartina<emph.end type="italics"/> would make a Chanel for it; which <lb/>receiving, and confining it in the time of the Vents, might carry <lb/>the Sand into the P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Primaro:<emph.end type="italics"/> Nor need there thence be fear­<lb/>ed any &longs;toppage by Mud and Sand, &longs;ince that it is &longs;uppo&longs;ed that <lb/>there will but very &longs;eldom be any nece&longs;&longs;ity of u&longs;ing it; &longs;o that <pb xlink:href="040/01/675.jpg" pagenum="109"/>time would be allowed, upon occa&longs;ion, to &longs;cowr and clean&longs;e <lb/>it.</s></p><p type="main"> <s>And in this manner all tho&longs;e Prodigies vani&longs;h that are rai&longs;ed <lb/>with &longs;o much fear from the enterance of the Water of <emph type="italics"/>Reno<emph.end type="italics"/><lb/>&longs;welled into P<emph type="italics"/>o,<emph.end type="italics"/> when it is high, to which there needeth no other <lb/>an&longs;wer; yet neverthele&longs;&longs;e we do not take that quantity of Wa­<lb/>ter, that is carried by <emph type="italics"/>Reno,<emph.end type="italics"/> and by <emph type="italics"/>Panaro,<emph.end type="italics"/> to be &longs;o great as is affir­<lb/>med: For that P. D. <emph type="italics"/>Benedetto Ca&longs;telli<emph.end type="italics"/> hath no le&longs;&longs;e accutely <lb/>than accurately ob&longs;erved the mea&longs;ures of this kind, noting that <lb/>the breadth and depth of a River is not enough to re&longs;olve the <lb/>que&longs;tion truly, but that there is re&longs;pect to be had to the velocity <lb/>of the Waters, and the term of time, things hitherto not con&longs;i­<lb/>dered by the Skilful in the&longs;e affairs; and therefore they are not <lb/>able to &longs;ay what quantity of Waters the &longs;aid Rivers carry, nor <lb/>to conclude of the ri&longs;ings that will follow thereupon. </s> <s>Nay, it <lb/>is mo&longs;t certain, that if all the Rivers that fall into <emph type="italics"/>Po,<emph.end type="italics"/> which are <lb/>above thirty, &longs;hould ri&longs;e at the rate that the&longs;e compute <emph type="italics"/>Reno<emph.end type="italics"/> to <lb/>do, an hundred feet of Banks would not &longs;uffice, and yet they <lb/>have far fewer: So that this confirmes the Rule of R. P. D. <emph type="italics"/>Bene­<lb/>detto,<emph.end type="italics"/> namely, that the proportion of the height of the Water <lb/>of <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno<emph.end type="italics"/> to the height of the Water of <emph type="italics"/>Reno<emph.end type="italics"/> in P<emph type="italics"/>o,<emph.end type="italics"/> is <lb/>compounded of the proportion of the breadth of the Chanel of <lb/><emph type="italics"/>Po<emph.end type="italics"/> to that of <emph type="italics"/>Reno,<emph.end type="italics"/> and of the velocity of the Water of <emph type="italics"/>Reno<emph.end type="italics"/><lb/>in <emph type="italics"/>Po<emph.end type="italics"/> to the velccity of the Water of <emph type="italics"/>Reno<emph.end type="italics"/> in <emph type="italics"/>Reno<emph.end type="italics"/>; a manife&longs;t <lb/>argument that there cannot in it, by this new augmentation of <lb/>Waters follow any alteration that nece&longs;&longs;itates the rai&longs;ing of its <lb/>Banks, as appeareth by the example of <emph type="italics"/>Panaro,<emph.end type="italics"/> which hath been <lb/>&longs;o far from &longs;welling P<emph type="italics"/>o,<emph.end type="italics"/> that it hath rather a&longs;&longs;waged it, for it hath <lb/>carried away many Shelfs and many I&longs;lets that had grown in its <lb/>Bed, for want of Waters &longs;ufficient to bear away the matter of <lb/>Land-floods in &longs;o broad a Chanel; and as is learnt by the trial <lb/>made by us in <emph type="italics"/>Panaro<emph.end type="italics"/> with the Water of <emph type="italics"/>Burana<emph.end type="italics"/>; for erecting <lb/>in the River &longs;tanding marks, and &longs;hutting the &longs;aid Sluice, we could <lb/>&longs;ee no &longs;en&longs;ible abatement, nor much le&longs;s after we had opened it <lb/>&longs;en&longs;ible increa&longs;ment; by which we judge that the &longs;ame is to &longs;uc­<lb/>ceed to P<emph type="italics"/>o,<emph.end type="italics"/> by letting in of <emph type="italics"/>Reno, Burana<emph.end type="italics"/> having greater pro­<lb/>portion to <emph type="italics"/>Panaro<emph.end type="italics"/> than <emph type="italics"/>Reno<emph.end type="italics"/> to P<emph type="italics"/>o,<emph.end type="italics"/> con&longs;idering the &longs;tate of tho&longs;e <lb/>Rivers in which the Ob&longs;ervation was made. </s> <s>So that there is no <lb/>longer any occa&longs;ion for tho&longs;e great rai&longs;ings of Banks, and the <lb/>danger of the ruptures as well of <emph type="italics"/>Reno<emph.end type="italics"/> as of P<emph type="italics"/>o<emph.end type="italics"/> do vani&longs;h, as al­<lb/>&longs;o the fear le&longs;t that the Sluices which empty into P<emph type="italics"/>o<emph.end type="italics"/> &longs;hould re­<lb/>ceive ob&longs;truction: which if they &longs;hould, yet it would be over in <lb/>a few hours. </s> <s>And as to the Breaches of <emph type="italics"/>Panaro<emph.end type="italics"/> which happened <lb/>in 1623. I know not why, &longs;eeing that it is confe&longs;&longs;ed that the P<emph type="italics"/>o<emph.end type="italics"/><lb/>was not, at that time, at its height, one &longs;hould rather charge it <pb xlink:href="040/01/676.jpg" pagenum="110"/>with the crime, than quit it thereof. </s> <s>The truth is, that the <lb/>Bank was not made of proof, &longs;ince that the &longs;ame now continu­<lb/>eth whole and good, and <emph type="italics"/>Panaro<emph.end type="italics"/> doth not break out; nay, there <lb/>was, when it brake more than a foot and half of its Banks above <lb/>the Water, and to &longs;pare; but it broke thorow by a Moles wor­<lb/>king, or by the hole of a Water-Rat, or &longs;ome &longs;uch vermine; <lb/>and by occa&longs;ion of the badne&longs;s of the &longs;aid Banks, as I finde by <lb/>the te&longs;timony of &longs;ome witne&longs;&longs;es examined by my command, that <lb/>I might know the truth thereof. </s> <s>Nor can I here forbear to &longs;ay, <lb/>that it would be better, if in &longs;uch matters men were more candid <lb/>and &longs;incere. </s> <s>But to &longs;ecure our &longs;elves neverthele&longs;&longs;e, to the ut­<lb/>mo&longs;t of our power, from &longs;uch like Breaches which may happen <lb/>at the fir&longs;t, by rea&longs;on of the newne&longs;&longs;e of the Banks, I pre&longs;uppo&longs;e <lb/>that from P<emph type="italics"/>o<emph.end type="italics"/> unto the place whence <emph type="italics"/>Reno<emph.end type="italics"/> is cut, there ought to <lb/>be a high and thick Fence made with its Banks, &longs;o that there <lb/>would be no cau&longs;e to fear any what&longs;oever acce&longs;&longs;ions of Water, <lb/>although that concurrence of three Rivers, which was by &longs;ome <lb/>more ingeniou&longs;ly aggravated than faithfully &longs;tated by that which <lb/>was &longs;aid above were true; to whom I think not my &longs;elf bound <lb/>to make any farther reply, neither to tho&longs;e who &longs;ay that <emph type="italics"/>Po<emph.end type="italics"/> will <lb/>a&longs;cend upwards into <emph type="italics"/>Reno,<emph.end type="italics"/> &longs;ince that the&longs;e are the &longs;ame per&longs;ons <lb/>who would introduce a &longs;mall branch of the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> into the <lb/>Chanel of <emph type="italics"/>Ferrara,<emph.end type="italics"/> that &longs;o it may conveigh to the Sea, not <emph type="italics"/>Reno<emph.end type="italics"/><lb/>onely, but al&longs;o all the other Brooks of which we complained; <lb/>and becau&longs;e that withal it is impo&longs;&longs;ible, that a River &longs;o capacious <lb/>as <emph type="italics"/>Po<emph.end type="italics"/> &longs;hould be incommoded by a Torrent, that, as I may &longs;ay, <lb/>hath no proportion to it.</s></p><p type="main"> <s>I come now to the bu&longs;ine&longs;&longs;e of the Ditches and Draines; and <lb/>as to the Conveyance of <emph type="italics"/>Burana,<emph.end type="italics"/> it hath heretofore been deba­<lb/>ted to turn it into <emph type="italics"/>Main-Po,<emph.end type="italics"/> &longs;o that in this ca&longs;e it will receive no <lb/>harm, and though it were not removed, yet would it by a Trench <lb/>under ground pur&longs;ue the cour&longs;e that it now holdeth, and al&longs;o <lb/>would be able to di&longs;-imbogue again into the &longs;aid new Chanel of <lb/><emph type="italics"/>Reno,<emph.end type="italics"/> which conforming to the &longs;uperficies of the Water of <emph type="italics"/>Po,<emph.end type="italics"/><lb/>would continue at a lower level than that which <emph type="italics"/>Panara<emph.end type="italics"/> had <lb/>when it came to <emph type="italics"/>Ferrara,<emph.end type="italics"/> into which <emph type="italics"/>Burana<emph.end type="italics"/> did neverthele&longs;&longs;e <lb/>empty it &longs;elf for &longs;ome time.</s></p><p type="main"> <s>The Conveyance or Drain of <emph type="italics"/>Santa Bianca,<emph.end type="italics"/> and the little <lb/>Chanel of <emph type="italics"/>Cento<emph.end type="italics"/> may al&longs;o empty them&longs;elves by two &longs;ubterranean <lb/>Trenches, without any prejudice where they run at pre&longs;ent, or <lb/>without any more works of that nature, they may be turned into <lb/>the &longs;aid new Chanel, although with &longs;omewhat more of incon­<lb/>venience; and withall, the Chanel of <emph type="italics"/>Ferrara,<emph.end type="italics"/> left dry, would <lb/>be a &longs;ufficient receptacle for any other Sewer or Drain what&longs;oe­<lb/>ver, that &longs;hould remain there.</s></p><pb xlink:href="040/01/677.jpg" pagenum="111"/><p type="main"> <s>All which Operations might be brought to perfection with <lb/>150. thou&longs;and Crowns, well and faithfully laid out; which &longs;umm <lb/>the <emph type="italics"/>Bologne&longs;i<emph.end type="italics"/> will not be unwilling to provide; be&longs;ides that tho&longs;e <lb/><emph type="italics"/>Ferrare&longs;i<emph.end type="italics"/> ought to contribute to it, who &longs;hall partake of the <lb/>benefit.</s></p><p type="main"> <s>Let me be permitted in this place to propo&longs;e a thing which I <lb/>have thought of, and which peradventure might occa&longs;ion two <lb/>benefits at once, although it be not wholly new. </s> <s>It was in the <lb/>time of <emph type="italics"/>Pope Paul<emph.end type="italics"/> V. propounded by one <emph type="italics"/>Cre&longs;cenzio<emph.end type="italics"/> an Ingi­<lb/>neer, to cut the <emph type="italics"/>Main-Po,<emph.end type="italics"/> above <emph type="italics"/>le Papozze<emph.end type="italics"/>; and having made a <lb/>&longs;ufficient evacuation to derive the water thereof into the P<emph type="italics"/>o<emph.end type="italics"/> of <lb/><emph type="italics"/>Adriano,<emph.end type="italics"/> and &longs;o to procure it to be Navigable, which was not at <lb/>that time effected, either by rea&longs;on of the oppo&longs;itions of tho&longs;e, <lb/>who&longs;e po&longs;&longs;e&longs;&longs;ions were to be cut thorow, or by rea&longs;on of the <lb/>great &longs;um of money that was nece&longs;&longs;ary for the effecting of it: But <lb/>in viewing tho&longs;e Rivers, we have ob&longs;erved, that the &longs;edge cutting <lb/>might ea&longs;ily be made below <emph type="italics"/>le Papozze,<emph.end type="italics"/> in digging thorow the <lb/>Bank called <emph type="italics"/>Santa Maria,<emph.end type="italics"/> & drawing a Trench of the bigne&longs;s that <lb/>skilful Arti&longs;ts &longs;hall judge meet unto the P<emph type="italics"/>o<emph.end type="italics"/> ^{*} of <emph type="italics"/>Ariano,<emph.end type="italics"/> below the <lb/><arrow.to.target n="marg982"></arrow.to.target><lb/><emph type="italics"/>Secche<emph.end type="italics"/> of the &longs;aid S. <emph type="italics"/>Maria<emph.end type="italics"/>; which as being a work of not <lb/>above 160. Perches in length, would be fini&longs;hed with onely <lb/>12000. Crowns.</s></p><p type="margin"> <s><margin.target id="marg982"></margin.target>* Of <emph type="italics"/>Adriano.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t; it is to be believed, that the waters running that way, <lb/>would not fail to open that Mouth into the Sea, which at pre­<lb/>&longs;ent is almo&longs;t choakt up by the Shelf of Sand, which the new <lb/>Mouth of <emph type="italics"/>Ponto Virro<emph.end type="italics"/> hath brought thither; and that it would <lb/>again bring into u&longs;e the Port <emph type="italics"/>Goro,<emph.end type="italics"/> and its Navigation.</s></p><p type="main"> <s>And haply experience might teach us, that the &longs;uperficies of <lb/>P<emph type="italics"/>o<emph.end type="italics"/> might come to fall by this a&longs;&longs;wagement of Water, &longs;o that the <lb/>acce&longs;&longs;ion of <emph type="italics"/>Reno<emph.end type="italics"/> would que&longs;tionle&longs;s make no ri&longs;ing in it: <lb/>Whereupon, if it &longs;hould &longs;o fall out, tho&longs;e Princes would have <lb/>no rea&longs;on to complain; who &longs;eem to que&longs;tion, le&longs;t by this new <lb/>acce&longs;&longs;ion of water into P<emph type="italics"/>o,<emph.end type="italics"/> the Sluices might be endangered. <lb/></s> <s>Which I thought not fit to omit to repre&longs;ent to your Lord&longs;hip; <lb/>not, that I propo&longs;e it to you as a thing ab&longs;olutely certain, but that <lb/>you might, if you &longs;o plea&longs;ed, lay it before per&longs;ons who&longs;e judge­<lb/>ments are approved in the&longs;e affairs.</s></p><p type="main"> <s>I return now from where I degre&longs;t, and affirm it as indubita­<lb/>ble, that <emph type="italics"/>Reno<emph.end type="italics"/> neither can, nor ought to continue longer where <lb/>it at this day is; and that it cannot go into any other place but <lb/>that, whither <emph type="italics"/>Cardinal Capponi<emph.end type="italics"/> de&longs;igned to carry it, and which <lb/>at pre&longs;ent plea&longs;eth me better than any other; or into <emph type="italics"/>Volana,<emph.end type="italics"/><lb/>whence it was taken away; the vigilance of Men being able to <lb/>obviate part of tho&longs;e mi&longs;chiefs, which it may do there.</s></p><p type="main"> <s>But from its Removal, be&longs;ides the alleviation of the harm <pb xlink:href="040/01/678.jpg" pagenum="112"/>which by it &longs;elf is cau&longs;ed, there would al&longs;o re&longs;ult the diminution <lb/>of that which is occa&longs;ioned by the other Brooks, to the right hand <lb/>of the <emph type="italics"/>Po<emph.end type="italics"/> of <emph type="italics"/>Argenta<emph.end type="italics"/>; fora&longs;much as the &longs;aid <emph type="italics"/>Po<emph.end type="italics"/> wanting all the <lb/>water of <emph type="italics"/>Reno,<emph.end type="italics"/> it would of nece&longs;&longs;ity come to ebb in &longs;uch man­<lb/>ner, that the Valleys would have a greater Fall into the &longs;ame, <lb/>and con&longs;equently it would take in, and &longs;wallow greater abun­<lb/>dance of water; and by this means the Ditches and Draines <lb/>of the Up-Lands would likewi&longs;e more ea&longs;ily Fall into them; e&longs;­<lb/>pecially if the &longs;couring of <emph type="italics"/>Zenzalino<emph.end type="italics"/> were brought to perfection, <lb/>by which the waters of <emph type="italics"/>Marrara<emph.end type="italics"/> would fall into <emph type="italics"/>Marmorta<emph.end type="italics"/>: And <lb/>if al&longs;o that of <emph type="italics"/>Ba&longs;tia<emph.end type="italics"/> were enlarged, and fini&longs;hed, by which there <lb/>might enter as much water into the &longs;aid P<emph type="italics"/>o<emph.end type="italics"/> of <emph type="italics"/>Argenta,<emph.end type="italics"/> as is taken <lb/>from it by the removal of <emph type="italics"/>Reno<emph.end type="italics"/>; although that by that meanes <lb/>the water of the Valleys would a&longs;&longs;wage double: Nor would the <lb/>people of <emph type="italics"/>Argenta,<emph.end type="italics"/> the I&longs;les of S. <emph type="italics"/>Giorgio,<emph.end type="italics"/> and <emph type="italics"/>Comacchio<emph.end type="italics"/> have any <lb/>cau&longs;e to complain; for that there would not be given to them <lb/>more water than was taken away: Nay &longs;ometimes whereas they <lb/>had Muddy waters, they would have clear; nor need they to fear <lb/>any ri&longs;ing: And furthermore, by this means a very great quan­<lb/>tity of ground would be re&longs;tored to culture; For the effecting of <lb/>all which, the &longs;umm of 50. thou&longs;and Crowns would go very far, <lb/>and would &longs;erve the turn at pre&longs;ent touching tho&longs;e Brooks, car­<lb/>rying them a little farther in the mean time, to fill up the greater <lb/>cavities of the Valleys, that we might not enter upon a va&longs;ter <lb/>and harder work, that would bring with it the difficulties of other <lb/>operations, and &longs;o would hinder the benefit which the&longs;e people <lb/>expect from the paternal charity of His Holine&longs;s.</s></p><pb xlink:href="040/01/679.jpg" pagenum="113"/><p type="head"> <s>TO <lb/>The Right Honourable, <lb/>MONSIGNORE <lb/>D. </s> <s>Ferrante Ce&longs;arini.</s></p><p type="main"> <s>My Treati&longs;e of the MENSURATION of RUN­<lb/>NING WATERS, Right Honourable, and <lb/>mo&longs;t Noble Sir, hath not a greater Preroga­<lb/>tive than its having been the production of the <lb/>command of Pope <emph type="italics"/>Vrban<emph.end type="italics"/> VIII. when His Ho­<lb/>line&longs;s was plea&longs;ed to enjoyn me to go with <lb/><emph type="italics"/>Mon&longs;ignore Cor&longs;ini,<emph.end type="italics"/> in the Vi&longs;itation that was <lb/>impo&longs;ed upon him in the year 1625. of the Waters of <emph type="italics"/>Ferrara, <lb/>Bologna, Romagna,<emph.end type="italics"/> and <emph type="italics"/>Romagnola<emph.end type="italics"/>; for that, on that occa&longs;ion <lb/>applying my whole Study to my &longs;ervice and duty, I publi&longs;hed in <lb/>that Treati&longs;e &longs;ome particulars till then not rightly under&longs;tood and <lb/>con&longs;idered (that I knew) by any one; although they be in them­<lb/>&longs;elves mo&longs;t important, and of extraordinary con&longs;equence. </s> <s>Yet <lb/>I mu&longs;t render thanks to Your Lord&longs;hip for the honour you have <lb/>done to that my Tract; but wi&longs;h withal, that your E&longs;teem of it <lb/>may not prejudice the univer&longs;al E&longs;teem that the World hath of <lb/>Your Honours mo&longs;t refined judgement.</s></p><p type="main"> <s>As to that Point which I touch upon in the Conclu&longs;ion, name­<lb/>ly, That the con&longs;ideration of the Velocity of Running Water &longs;up­<lb/>plyeth the con&longs;ideration of the ^{*} Length omitted in the common <lb/><arrow.to.target n="marg983"></arrow.to.target><lb/>way of mea&longs;uring Running Waters; Your Lord&longs;hip having com­<lb/>manded me that in favour of <emph type="italics"/>Practi&longs;e,<emph.end type="italics"/> and for the perfect di&longs;co­<lb/>very of the di&longs;order that commonly happeneth now adayes in <lb/>the di&longs;tribution of the Waters of Fountains, I &longs;hould demon­<lb/>&longs;trate that the knowledge of the Velocity &longs;erveth for the finding <lb/>of the Length: I have thought fit to &longs;atisfie your Command by <lb/>relating a Fable; which, if I do not deceive my &longs;elf, will make <lb/>out to us the truth thereof; in&longs;omuch that the re&longs;t of my Treati&longs;e <lb/>&longs;hall thereby al&longs;o become more manife&longs;t and intelligible, even to <pb xlink:href="040/01/680.jpg" pagenum="432"/>tho&longs;e who finde therein &longs;ome kinde of ob&longs;curity.</s></p><p type="margin"> <s><margin.target id="marg983"></margin.target>* Larghezza, but <lb/>mi&longs;printed.</s></p><p type="main"> <s>In the dayes of yore, before that the admirable Art of Wea­<lb/>ving was in u&longs;e, there was found in <emph type="italics"/>Per&longs;ia<emph.end type="italics"/> a va&longs;tand unvaluable <lb/>Trea&longs;ure, which con&longs;i&longs;ted in an huge multitude of pieces of Er­<lb/>me&longs;in, or Damask, I know not whether; which, as I take it, <lb/>amounted to near two thou&longs;and pieces; which were of &longs;uch a <lb/>nature, that though their Breadth and Thickne&longs;s were finite and <lb/>determinate, as they u&longs;e to be at this day; yet neverthele&longs;s, their <lb/>Length was in a certain &longs;en&longs;e infinite, for that tho&longs;e two thou&longs;and <lb/>pieces, day and night without cea&longs;ing, i&longs;&longs;ued out with their ends <lb/>at &longs;uch a rate, that of each piece there i&longs;&longs;ued 100. Ells a day, from <lb/>a deep and dark Cave, con&longs;ecrated by the Super&longs;tition of tho&longs;e <lb/>people, to the fabulous <emph type="italics"/>Arachne.<emph.end type="italics"/> In tho&longs;e innocent and early <lb/>times (I take it to have been, in that &longs;o much applauded and <lb/>de&longs;ired Golden age) it was left to the liberty of any one, to cut <lb/>off of tho&longs;e pieces what quantity they plea&longs;ed without any diffi­<lb/>culty: But that felicity decaying and degenerating, which was <lb/>altogether ignorant of <emph type="italics"/>Meum<emph.end type="italics"/> and <emph type="italics"/>Tuum<emph.end type="italics"/>; terms certainly mo&longs;t <lb/>pernicious, the Original of all evils, and cau&longs;e of all di&longs;cords; <lb/>there were by tho&longs;e people &longs;trong and vigilant Guards placed <lb/>upon the Cave, who re&longs;olved to make merchandize of the Stuffes; <lb/>and in this manner they began to &longs;et a price upon that ine&longs;tima­<lb/>ble Trea&longs;ure, &longs;elling the propriety in tho&longs;e pieces to divers Mer­<lb/>chants; to &longs;ome they &longs;old a right in one, to &longs;ome in two, and to <lb/>&longs;ome in more. </s> <s>But that which was the wor&longs;t of all, There was <lb/>found out by the in&longs;atiable avarice of the&longs;e men crafty inventions <lb/>to deceive the Merchants al&longs;o; who came to buy the afore&longs;aid <lb/>commodity, and to make them&longs;elves Ma&longs;ters, &longs;ome of one <lb/>&longs;ome of two, and &longs;ome of more ends of tho&longs;e pieces of &longs;tuff; <lb/>and in particular, there were certain ingenuous Machines placed <lb/>in the more &longs;ecret places of the Cave, with which at the plea&longs;ure <lb/>of the Guards, they did retard the velocity of tho&longs;e Stuffs, in <lb/>their i&longs;&longs;uing out of the Cave; in&longs;omuch, that he who ought to have <lb/>had 100. Ells of Stuff in a day, had not above 50, and he who <lb/>&longs;hould have had 400, enjoyed the benefit of 50. onely; and &longs;o all <lb/>the re&longs;t were defrauded of their Rights, the &longs;urplu&longs;age being &longs;old, <lb/>appropriated, and &longs;hared at the will of the corrupt Officers: So <lb/>that the bu&longs;ine&longs;s was without all order or ju&longs;tice, in&longs;omuch that <lb/>the Godde&longs;s <emph type="italics"/>Arachne<emph.end type="italics"/> being di&longs;plea&longs;ed at tho&longs;e people, deprived <lb/>every one of their benefit, and with a dreadful Earthquake for <lb/>ever clo&longs;ing the mouth of the Cave, in puni&longs;hment of &longs;o much <lb/>impiety and malice: Nor did it avail them to excu&longs;e them&longs;elves, <lb/>by &longs;aying that they allowed the Buyer the Breadth and Thick­<lb/>ne&longs;s bargained for; and that of the Length, which was infinite, <pb xlink:href="040/01/681.jpg" pagenum="115"/>there could no account be kept: For the wi&longs;e and prudent <lb/>Prie&longs;t of the Sacred <emph type="italics"/>Grotto<emph.end type="italics"/> an&longs;wered, That the deceit lay in the <lb/>length, which they were defrauded of, in that the velocity of the <lb/>ftuffe was retarded, as it i&longs;&longs;ued out of the Cave: and although <lb/>the total length of the Piece was infinite, for that it never cea­<lb/>&longs;ed coming forth, and &longs;o was not to be computed; yet never­<lb/>thele&longs;s its length con&longs;idered, part by part, as it came out of the <lb/>Cave, and was bargained for, continued &longs;till finite, and might <lb/>be one while greater, and another while le&longs;&longs;er, according as the <lb/>Piece was con&longs;tituted in greater or le&longs;&longs;er velocity; and he added <lb/>withall, that exact Ju&longs;tice required, that when they &longs;old a piece <lb/>of &longs;tuff, and the propriety or dominion therein, they ought not <lb/>only to have a&longs;certained the breadth and thickne&longs;&longs;e of the Piece, <lb/>but al&longs;o to have determined the length, determining its ve­<lb/>locity.</s></p><p type="main"> <s>The &longs;ame di&longs;order and confu&longs;ion, that was repre&longs;ented in the <lb/>Fable, doth come to pa&longs;&longs;e in the Hi&longs;tory of the Di&longs;tribution of <lb/>the Waters of Conduits and Fountains, &longs;eeing that they are &longs;old <lb/>and bought, having regard only to the two Dimen&longs;ions, I mean <lb/>of Breadth and Height of the Mouth that di&longs;chargeth the Wa­<lb/>ter; and to remedy &longs;uch an inconvenience, it is nece&longs;&longs;ary to de­<lb/>termine the length in the velocity; for never &longs;hall we be able to <lb/>make a gue&longs;&longs;e at the quantity of the Body of Running Water, <lb/>with the two Dimen&longs;ions only of Breadth and Height, without <lb/>Length.</s></p><p type="main"> <s>And to the end, that the whole bu&longs;ine&longs;s may be reduced <lb/>to a mo&longs;t ea&longs;ie practice, by which the waters of Aqueducts <lb/>may be bought and &longs;old ju&longs;tly, and with mea&longs;ures alwayes ex­<lb/>act and con&longs;tant.</s></p><p type="main"> <s>Fir&longs;t, the quantity of the Water ought diligently to be exa­<lb/>mined, which the whole principal ^{*} Pipe di&longs;chargeth in a time <lb/>certain, as for in&longs;tance, in an hour, in half an hour, or in a le&longs;&longs;e <lb/>interval of time, (for knowing which I have a mo&longs;t exact and <lb/>ea&longs;ie Rule) and finding that the whole principal pipe di&longs;char­<lb/>geth <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> a thou&longs;and Tuns of Water in the &longs;pace of one or <lb/>more hours, in &longs;elling of this water, it ought not to be uttered by <lb/>the ordinary and fal&longs;e mea&longs;ure, but the di&longs;tribution is to be <lb/>made with agreement to give and maintain to the buyer ten or <lb/>twenty, or a greater number of Tuns, as the bargain &longs;hall be <lb/>made, in the &longs;pace of an hour, or of &longs;ome other &longs;et and deter­<lb/>minate time. </s> <s>And here I adde, that if I were to undertake to <lb/>make &longs;uch an adju&longs;tment, I would make u&longs;e of a way to divide <lb/>and mea&longs;ure the time with &longs;uch accuratene&longs;&longs;e, that the &longs;pace of <lb/>an hour &longs;hould be divided into four, &longs;ix, or eight thou&longs;and parts <pb xlink:href="040/01/682.jpg" pagenum="116"/>without the lea&longs;t errour; which Rule was taught me by my <lb/>Ma&longs;ter <emph type="italics"/>Sign. </s> <s>Galilæo Galilæi,<emph.end type="italics"/> Chief Philo&longs;opher to the mo&longs;t Se­<lb/>rene <emph type="italics"/>Grand Duke<emph.end type="italics"/> of <emph type="italics"/>Tu&longs;cany.<emph.end type="italics"/> And this way will &longs;erve ea&longs;ily and <lb/>admirably to our purpo&longs;e and occa&longs;ion; &longs;o that we &longs;hall <lb/>thereby be able to know how many Quarts of Water an A­<lb/>queduct will di&longs;charge in a given time of hours, moneths, or <lb/>years. </s> <s>And in this manner we may con&longs;titute a Cock that &longs;hall <lb/>di&longs;charge a certain and determinate quantity of water in a time <lb/>given.</s></p><p type="main"> <s>And becau&longs;e daily experience &longs;hews us, that the Springs of A­<lb/>queducts do not maintain them alwayes equally high, and full <lb/>of Water, but that &longs;ometimes they increa&longs;e, and &longs;ometimes de­<lb/>crea&longs;e, which accident might po&longs;&longs;ibly procure &longs;ome difficulty in <lb/>our di&longs;tribution: Therefore, to the end that all manner of &longs;cru­<lb/>ple may be removed, I conceive that it would be convenient to <lb/>provide a Ci&longs;tern, according to the occa&longs;ion, into which there <lb/>might alwayes fall one certain quantity of water, which &longs;hould <lb/>not be greater than that which the principal pipe di&longs;chargeth in <lb/>times of drought, when the Springs are bare of water, that &longs;o in <lb/>this Ci&longs;tern the water might alwayes keep at one con&longs;tant height. <lb/></s> <s>Then to the Ci&longs;tern &longs;o prepared we are to fa&longs;ten the Cocks of <lb/>particular per&longs;ons, to whom the Water is &longs;old by the Reverend <lb/>Apo&longs;tolique Chamber, according to what hath been ob&longs;erved <lb/>before; and that quantity of Water which remaineth over and <lb/>above, is to be di&longs;charged into another Ci&longs;tern, in which the <lb/>Cocks of the Waters for publick &longs;ervices, and of tho&longs;e which <lb/>people buy upon particular occa&longs;ions are to be placed. </s> <s>And <lb/>when the bu&longs;ine&longs;&longs;e &longs;hall have been brought to this pa&longs;&longs;e, there <lb/>will likewi&longs;e a remedy be found to the &longs;o many di&longs;orders that <lb/>continually happen; of which, for brevity &longs;ake, I will in&longs;tance <lb/>in but four only, which concern both publique and private bene­<lb/>fit, as being, in my judgment, the mo&longs;t enormous and intole­<lb/>rable.</s></p><p type="main"> <s>The fir&longs;t inconvenience is, that in the common way of mea&longs;u­<lb/>ring, di&longs;pen&longs;ing, and &longs;elling the Waters of Aqueducts, it is not <lb/>under&longs;tood, neither by the Buyer nor Seller, what the quantity <lb/>truly is that is bought and &longs;old; nor could I ever meet with any <lb/>either Engineer or Architect, or Arti&longs;t, or other that was able to <lb/>decypher to me, what one, or two, or ten inches of water was. <lb/></s> <s>But by our above declared Rule, for di&longs;pen&longs;ing the Waters of <lb/>Aqueducts we may very ea&longs;ily know the true quantity of Water <lb/>that is bought or &longs;old, as that it is &longs;o many Tuns an hour, &longs;o ma­<lb/>ny a day, &longs;o many in a year, &c.</s></p><p type="main"> <s>The &longs;econd di&longs;order that happeneth, at pre&longs;ent, in the di&longs;tri­<pb xlink:href="040/01/683.jpg" pagenum="117"/>bution of Aqueducts is, that as the bu&longs;ine&longs;&longs;e is now governed, it <lb/>lieth in the power of a &longs;ordid Ma&longs;on to take unju&longs;tly from one, <lb/>and give unde&longs;ervedly to another more or le&longs;&longs;e Water than be­<lb/>longeth to them of right: And I have &longs;een it done, of my <lb/>own experience. </s> <s>But in our way of mea&longs;uring and di&longs;tri­<lb/>buting Waters, there can no fraud be committed; and put­<lb/>ting the ca&longs;e that they &longs;hould be committed, its an ea&longs;ie mat­<lb/>ter to know it, and amend it, by repairing to the Tribunal <lb/>appointed.</s></p><p type="main"> <s>Thirdly, it happens very often, (and we have examples there­<lb/>of both antient and modern) that in di&longs;pen&longs;ing the Water after <lb/>the common and vulgar way; there is &longs;ometimes more Water di&longs;­<lb/>pended than there is in the Regi&longs;ter, in which there will be regi­<lb/>&longs;tred, as they &longs;ay, two hundred inches (for example) and there <lb/>will be di&longs;pen&longs;ed two hundred and fifty inches, or more. </s> <s>Which <lb/>pa&longs;&longs;age happened in the time of <emph type="italics"/>Nerva<emph.end type="italics"/> the Emperour, as <emph type="italics"/>Giulio <lb/>Frontino<emph.end type="italics"/> writes, in his 2. Book, <emph type="italics"/>De Aquaductibus Vrbis Romæ,<emph.end type="italics"/><lb/>where he ob&longs;erveth that they had <emph type="italics"/>in Commentariis 12755. Qui­<lb/>naries<emph.end type="italics"/> of Water; and found that they di&longs;pen&longs;ed 14018. <emph type="italics"/>Qui­<lb/>naries.<emph.end type="italics"/> And the like Errour hath continued, and is in u&longs;e al&longs;o <lb/>modernly until our times. </s> <s>But if our Rule &longs;hall be ob&longs;erved, <lb/>we &longs;hall incur no &longs;uch di&longs;order, nay there will alwayes be given <lb/>to every one his &longs;hare, according to the holy end of exact ju&longs;tice, <lb/>which <emph type="italics"/>dat unicuique quod &longs;uum e&longs;t.<emph.end type="italics"/> As on the contrary, it is <lb/>manife&longs;t, that His Divine Maje&longs;ty hateth and abominateth <emph type="italics"/>Pon­<lb/>dus & pondus, Men&longs;ura & men&longs;ura,<emph.end type="italics"/> as the Holy Gho&longs;t &longs;peak­<lb/>eth by the mouth of <emph type="italics"/>Solomon<emph.end type="italics"/> in the <emph type="italics"/>Proverbs, Chap. </s> <s>20. Pondus <lb/>& Pondus, Men&longs;ura & Men&longs;ura, utrumque abominabile e&longs;t apud <lb/>Deum.<emph.end type="italics"/> And therefore who is it that &longs;eeth not that the way of <lb/>dividing and mea&longs;uring of Waters, commonly u&longs;ed, is expre&longs;ly <lb/>again&longs;t the Law of God. </s> <s>Since that thereby the &longs;ame mea&longs;ure <lb/>is made &longs;ometimes greater, and &longs;ometimes le&longs;&longs;er; A di&longs;order &longs;o <lb/>enormous and execrable, that I &longs;hall take the boldne&longs;s to &longs;ay, that <lb/>for this &longs;ole re&longs;pect it ought to be condemned and prohibited like­<lb/>wi&longs;e by human Law, which &longs;hould Enact that in this bu&longs;ine&longs;s there <lb/>&longs;hould be imployed either this our Rule, or &longs;ome other that <lb/>is more exqui&longs;ite and practicable, whereby the mea&longs;ure <lb/>might keep one con&longs;tant and determinate tenor, as we make it, <lb/>and not, as it is now, to make <emph type="italics"/>Pondus & Pondus, Men&longs;ur a & <lb/>Men&longs;ura.<emph.end type="italics"/></s></p><p type="main"> <s>And this is all that I had to offer to Your mo&longs;t Illu&longs;trious <lb/>Lord&longs;hip, in obedience to your commands, re&longs;erving to my &longs;elf <lb/>the giving of a more exact account of this my invention, when <lb/>the occa&longs;ion &longs;hall offer, of reducing to practice &longs;o holy, ju&longs;t, and <pb xlink:href="040/01/684.jpg" pagenum="118"/>nece&longs;&longs;ary a reformation of the Mea&longs;ure of Running Waters and <lb/>of Aqueducts in particular: which Rule may al&longs;o be of great <lb/>benefit in the divi&longs;ion of the greater Waters to over-flow <lb/>Grounds, and for other u&longs;es: I humbly bow,</s></p><p type="main"> <s><emph type="italics"/>Your Most Devoted,<emph.end type="italics"/><lb/>and <lb/><emph type="italics"/>Mo&longs;t Obliged Servant,<emph.end type="italics"/></s></p><p type="main"> <s>D. </s> <s>Benedetto Ca&longs;telli, <emph type="italics"/>Abb. </s> <s>Ca&longs;in.<emph.end type="italics"/></s></p><p type="head"> <s>FINIS.</s></p><pb xlink:href="040/01/685.jpg"/><p type="head"> <s>A TABLE</s></p><p type="head"> <s>Of the mo&longs;t ob&longs;ervable matters in this Treati&longs;e of the <lb/>MENSURATION of RUNNING <lb/>WATERS.<lb/><arrow.to.target n="table74"></arrow.to.target></s></p><table><table.target id="table74"></table.target><row><cell>A</cell><cell></cell></row><row><cell>Abatements <emph type="italics"/>of a River in different and unequal Diver&longs;ions, is alwaies equal, which is proved with<emph.end type="italics"/> 100. Syphons.</cell><cell><emph type="italics"/>Page<emph.end type="italics"/> 75</cell></row><row><cell>Arno <emph type="italics"/>River when it ri&longs;eth upon a Land-Flood near the Sea one third of a Brace, it ri&longs;eth about<emph.end type="italics"/> Pi&longs;a 6. <emph type="italics"/>or 7. Braces.<emph.end type="italics"/></cell><cell>82</cell></row><row><cell>B</cell><cell></cell></row><row><cell><emph type="italics"/>Banks near to the Sea lower, than far from thence. Corollary<emph.end type="italics"/> XIV.</cell><cell>16</cell></row><row><cell>Brent <emph type="italics"/>River diverted from the Lake o<emph.end type="italics"/>f Venice, <emph type="italics"/>and its effects.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell>Brent <emph type="italics"/>&longs;uppo&longs;ed in&longs;ufficient to remedy the inconveniences of the Lake, and the fal&longs;ity of that &longs;uppo&longs;ition.<emph.end type="italics"/></cell><cell>67</cell></row><row><cell>Brent, <emph type="italics"/>and its benefits in the Lake.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell><emph type="italics"/>Its Depo&longs;ition of Sand in the Lake, bow great it is.<emph.end type="italics"/></cell><cell>78, 79</cell></row><row><cell><emph type="italics"/>Bridges over Rivers, and how they are to be made. Appendix<emph.end type="italics"/> VIII.</cell><cell>20</cell></row><row><cell>Burana <emph type="italics"/>River, its ri&longs;ing, and falling in<emph.end type="italics"/> Panaro.</cell><cell>110</cell></row><row><cell>C</cell><cell></cell></row><row><cell>Ca&longs;telli <emph type="italics"/>applyed him&longs;elf to this Study by Order of<emph.end type="italics"/> Urban VIII.</cell><cell>2</cell></row><row><cell>Chanel of Navigation <emph type="italics"/>in the Valleys of<emph.end type="italics"/> Bologna, <emph type="italics"/>and its inconveniences.<emph.end type="italics"/></cell><cell>99</cell></row><row><cell><emph type="italics"/>Carried into the<emph.end type="italics"/> Po <emph type="italics"/>of<emph.end type="italics"/> Ferrara, <emph type="italics"/>and its benefits<emph.end type="italics"/></cell><cell>ibid.</cell></row><row><cell>Ciampoli <emph type="italics"/>alover of the&longs;e Ob&longs;ervations of Waters.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell>D</cell><cell></cell></row><row><cell><emph type="italics"/>Difficulty of this bu&longs;ine&longs;s of Mea&longs;uring Waters.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Di&longs;orders that happen in the di&longs;tribution of the Waters of Aqueducts, and their re-medies.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Di&longs;tribution of the Waters of Fountains, and Aqueducts. Appendix<emph.end type="italics"/> X.</cell><cell>22</cell></row><row><cell><emph type="italics"/>Di&longs;tribution of Water to over-flow Grounds. Appendix<emph.end type="italics"/> XI.</cell><cell>23, 69, 70</cell></row><row><cell><emph type="italics"/>Diver&longs;ion of<emph.end type="italics"/> Reno <emph type="italics"/>and other Brooks of<emph.end type="italics"/> Romagna, <emph type="italics"/>advi&longs;ed by<emph.end type="italics"/> P. Spernazzati <emph type="italics"/>to what end it was.<emph.end type="italics"/></cell><cell>100</cell></row><row><cell><emph type="italics"/>Drains and Ditches, the benefit they receive by cutting away the Weeds and Reeds. Appendix<emph.end type="italics"/> IX.</cell><cell>21</cell></row><row><cell><emph type="italics"/>Drains and Sewers ob&longs;tructed, in the Diver&longs;ion of<emph.end type="italics"/> Reno <emph type="italics"/>into<emph.end type="italics"/> Main Po, <emph type="italics"/>and a remedy for the &longs;ame.<emph.end type="italics"/></cell><cell>110</cell></row><row><cell>E</cell><cell></cell></row><row><cell><emph type="italics"/>Engineers unver&longs;'d in the matters of Waters.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Erour found in the common way of Mea&longs;uring Running Waters.<emph.end type="italics"/></cell><cell>68, 69</cell></row><row><cell><emph type="italics"/>Errour in deriving the Water of<emph.end type="italics"/> Acqua Paola. <emph type="italics"/>Appendix<emph.end type="italics"/> II.</cell><cell>17, 18</cell></row><pb xlink:href="040/01/686.jpg"/><row><cell><emph type="italics"/>Errour of<emph.end type="italics"/> Bartolotti.</cell><cell>86, 87</cell></row><row><cell><emph type="italics"/>Errours of Engineers in the Derivation of Chenels. Corollary<emph.end type="italics"/> XII.</cell><cell>12</cell></row><row><cell><emph type="italics"/>Errour of Engineers in Mea&longs;uring of<emph.end type="italics"/> Reno <emph type="italics"/>in<emph.end type="italics"/> Po. <emph type="italics"/>Appendix<emph.end type="italics"/> III.</cell><cell>ibid.</cell></row><row><cell><emph type="italics"/>Errour of other Engineers, contrary to the precedent. Appendix<emph.end type="italics"/> IV.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Errour of<emph.end type="italics"/> Giovanni Fontana <emph type="italics"/>in Mea&longs;uring Waters, Corollary<emph.end type="italics"/> XI.</cell><cell>9</cell></row><row><cell><emph type="italics"/>Errour of<emph.end type="italics"/> Giulio Frontino <emph type="italics"/>in Mea&longs;uring the Waters of Aqueducts. Appen-dix<emph.end type="italics"/> I.</cell><cell>17</cell></row><row><cell><emph type="italics"/>Errours committed in cutting the Bank at<emph.end type="italics"/> Bondeno, <emph type="italics"/>in the &longs;wellings of<emph.end type="italics"/> Po: <emph type="italics"/>Corollary<emph.end type="italics"/>XIII.</cell><cell>81</cell></row><row><cell>F</cell><cell></cell></row><row><cell><emph type="italics"/>Fenns<emph.end type="italics"/> Pontine, <emph type="italics"/>Drained by Pope<emph.end type="italics"/> Sixtus Quintus, <emph type="italics"/>with va&longs;t expence.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>The ruine and mi&longs;carriage thereof.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Tardity of the principal Chanel that Drains them, cau&longs;e of the Drowning.<emph.end type="italics"/></cell><cell>ibid.</cell></row><row><cell><emph type="italics"/>They are ob&longs;tructed by the Fi&longs;hing-Wears, which &longs;uell the River.<emph.end type="italics"/></cell><cell>94</cell></row><row><cell><emph type="italics"/>Waters of<emph.end type="italics"/> Fiume Si&longs;to, <emph type="italics"/>which flow in great abundance into the<emph.end type="italics"/> Evacuator <emph type="italics"/>of the &longs;aid Fenns.<emph.end type="italics"/></cell><cell>94, 95</cell></row><row><cell><emph type="italics"/>Remedies to the di&longs;orders of tho&longs;e Fenns.<emph.end type="italics"/></cell><cell>95, 96</cell></row><row><cell>Fontana Giovanni, <emph type="italics"/>his errours in Mea&longs;uring Waters. Corollary<emph.end type="italics"/> XI.</cell><cell>9</cell></row><row><cell>Fiume Morto, <emph type="italics"/>whether it ought to fall into the Sea, or into<emph.end type="italics"/> Serchio,</cell><cell>79</cell></row><row><cell><emph type="italics"/>Let into<emph.end type="italics"/> Serchio <emph type="italics"/>and its inconveniences.<emph.end type="italics"/></cell><cell>79, 80</cell></row><row><cell><emph type="italics"/>The dangerous ri&longs;ing of its Waters, when to be expected.<emph.end type="italics"/></cell><cell>81</cell></row><row><cell><emph type="italics"/>Its inconveniences when it is higher in level than<emph.end type="italics"/> Serchio, <emph type="italics"/>and why it ri&longs;eth mo&longs;t On the Sea-coa&longs;ts, at &longs;uch time as the Winds make the Sea to &longs;uell.<emph.end type="italics"/></cell><cell>83</cell></row><row><cell>G</cell><cell></cell></row><row><cell>Galilæo Galilæi. <emph type="italics"/>hoxourably mentioned.<emph.end type="italics"/></cell><cell><emph type="italics"/>Page<emph.end type="italics"/> 2, 28</cell></row><row><cell><emph type="italics"/>His Rule for mea&longs;uring the time.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell>H</cell><cell></cell></row><row><cell><emph type="italics"/>Height,<emph.end type="italics"/> vide <emph type="italics"/>Quick<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Heights different, made by the &longs;ame &longs;tream of a Brock or Torrent, according to the divers Velocities in the entrance of the River. Corollary<emph.end type="italics"/> I.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Heights different, made by the Torrent in the River, according to the different heights of the River. Corollary<emph.end type="italics"/> II.</cell><cell>ibid.</cell></row><row><cell>K</cell><cell></cell></row><row><cell><emph type="italics"/>Knowledge of Motion how much it importeth.<emph.end type="italics"/></cell><cell>1</cell></row><row><cell>L</cell><cell></cell></row><row><cell><emph type="italics"/>t<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Lake of<emph.end type="italics"/> Perugia, <emph type="italics"/>and, he Ob&longs;ervation made on it. Appendix<emph.end type="italics"/> XII.</cell><cell>42</cell></row><row><cell><emph type="italics"/>Lake of<emph.end type="italics"/> Thra&longs;imenus <emph type="italics"/>and Con&longs;iderations upon it, a Letter written to<emph.end type="italics"/> Sig. Galilæo Galilæi.</cell><cell>28</cell></row><row><cell><emph type="italics"/>Lake of<emph.end type="italics"/> Venice, <emph type="italics"/>and Con&longs;iderations upon it.<emph.end type="italics"/></cell><cell>63, 73</cell></row><row><cell><emph type="italics"/>Low Waters which let the bottom of it be di&longs;covered.<emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>The &longs;toppage and choaking of the Ports, a main cau&longs;e of the di&longs;orders of the Lake, and the grand remedy to tho&longs;e di&longs;orders what it is.<emph.end type="italics"/></cell><cell>66</cell></row><row><cell><emph type="italics"/>Lakes and Metrs along the Sea-coa&longs;ts, and the cau&longs;es thereof.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Length of Waters, how it is to be Mea&longs;ured.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell>M</cell><cell></cell></row><row><cell><emph type="italics"/>Mea&longs;ure and Di&longs;tributions of Waters. Appendix<emph.end type="italics"/> V.</cell><cell>18</cell></row><pb xlink:href="040/01/687.jpg"/><row><cell><emph type="italics"/>Mea&longs;ure of Rivers that fall into others difficult. Coroll.<emph.end type="italics"/> X:</cell><cell>9</cell></row><row><cell><emph type="italics"/>Mea&longs;ure of the Running Water of a Chanel of an height known by a<emph.end type="italics"/> Regulator <emph type="italics"/>of a Mea-&longs;ure given, in a time a&longs;&longs;igned. Propo&longs;ition<emph.end type="italics"/> I. <emph type="italics"/>Problem<emph.end type="italics"/> I.</cell><cell>50</cell></row><row><cell><emph type="italics"/>Mea&longs;ure of the Water of any River, of any greatne&longs;s, in a time given. Propo&longs;ition<emph.end type="italics"/> V. <emph type="italics"/>Problem<emph.end type="italics"/> III.</cell><cell>60</cell></row><row><cell><emph type="italics"/>Mea&longs;ure that &longs;hewes how much Water a River di&longs;chargeth in a time given.<emph.end type="italics"/></cell><cell>48</cell></row><row><cell><emph type="italics"/>Mole-holes,<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Motion the principal &longs;ubject of Philo&longs;ophy.<emph.end type="italics"/></cell><cell>1</cell></row><row><cell><emph type="italics"/>Mud.<emph.end type="italics"/> Vide <emph type="italics"/>Sand.<emph.end type="italics"/></cell><cell></cell></row><row><cell>N</cell><cell></cell></row><row><cell><emph type="italics"/>Navigation from<emph.end type="italics"/> Bologna <emph type="italics"/>to<emph.end type="italics"/> Ferrara, <emph type="italics"/>is become impo&longs;&longs;ible, till &longs;uch time as<emph.end type="italics"/> Reno <emph type="italics"/>be diverted.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Navigation in the Lake of<emph.end type="italics"/> Venice <emph type="italics"/>endangered, and how restored.<emph.end type="italics"/></cell><cell>65, 70</cell></row><row><cell>P</cell><cell></cell></row><row><cell><emph type="italics"/>Perpendicularity of the Banks of the River, to the upper &longs;uperficies of it.<emph.end type="italics"/></cell><cell>37</cell></row><row><cell><emph type="italics"/>Perpendicularity of the Banks to the bottom.<emph.end type="italics"/></cell><cell>37</cell></row><row><cell><emph type="italics"/>Perugia.<emph.end type="italics"/> Vide <emph type="italics"/>Lake.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Pontine.<emph.end type="italics"/> Vide <emph type="italics"/>Fenns.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Ports of<emph.end type="italics"/> Venice, Malamocco, Bondolo, <emph type="italics"/>and<emph.end type="italics"/> Chiozza, <emph type="italics"/>choaked up for want of Water in the Lake.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Proportions of unequal Sections of equal Velocity, and of equal Sections of unequal Velo-city. Axiome<emph.end type="italics"/> IV. <emph type="italics"/>and<emph.end type="italics"/> V.</cell><cell>38</cell></row><row><cell><emph type="italics"/>Proportions of equal and unequal quantities of Water, which pa&longs;s by the Sections of dif-ferent Rivers. Propo&longs;ition<emph.end type="italics"/> II.</cell><cell>39</cell></row><row><cell><emph type="italics"/>Proportions of unequal Sections that in equal times di&longs;charge equal quantities of Water. Propo&longs;ition<emph.end type="italics"/> III.</cell><cell>41</cell></row><row><cell><emph type="italics"/>Proportion wherewith one River falling into another, varieth in height. Propo-&longs;ition<emph.end type="italics"/> IV.</cell><cell>44</cell></row><row><cell><emph type="italics"/>Proportion of the Water di&longs;charged by a River in the time of Flood, to the Water di&longs;charged in an equal time by the &longs;aid River, before or after the Flood. Propo&longs;ition<emph.end type="italics"/> V.</cell><cell>44</cell></row><row><cell><emph type="italics"/>Proportion of the Heights made by two equal Brooks or Streams falling into the &longs;ame River. Propo&longs;ition<emph.end type="italics"/> VI.</cell><cell>45</cell></row><row><cell><emph type="italics"/>Proportion of the Water which a River di&longs;chargeth encrea&longs;ing in Quick-height by the ad-dition of new Water, to that which it di&longs;chargeth after the encrea&longs;e is made. Propo-&longs;ition<emph.end type="italics"/> IV. <emph type="italics"/>Theor.<emph.end type="italics"/> II.</cell><cell>54</cell></row><row><cell><emph type="italics"/>Proportion of a River when high, to it &longs;elf when low. Coroll.<emph.end type="italics"/> I.</cell><cell>55</cell></row><row><cell>Q</cell><cell></cell></row><row><cell><emph type="italics"/>Quantity of Running Waters is never certain, if with the Vulgar way of Mea&longs;uring them, their Velocities be not con&longs;idered.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Quantities of Waters which are di&longs;charged by a River, an&longs;wer in equality to the Velocities and times in which they are di&longs;charged. Axiome<emph.end type="italics"/> I, II, III.</cell><cell>38</cell></row><row><cell>Quick-Height <emph type="italics"/>of a River, what it is. Definition<emph.end type="italics"/> V.</cell><cell>48</cell></row><row><cell>R</cell><cell></cell></row><row><cell><emph type="italics"/>Rea&longs;on of the Proverb,<emph.end type="italics"/> Take heed of the &longs;till Waters. <emph type="italics"/>Coroll.<emph.end type="italics"/> VI.</cell><cell>7</cell></row><row><cell><emph type="italics"/>Rea&longs;ons of<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini <emph type="italics"/>again&longs;t the diver&longs;ion of<emph.end type="italics"/> Reno <emph type="italics"/>into the<emph.end type="italics"/> Po <emph type="italics"/>of<emph.end type="italics"/>Volano.</cell><cell>105</cell></row><row><cell><emph type="italics"/>Rea&longs;ons of<emph.end type="italics"/> Cardinal Capponi <emph type="italics"/>and<emph.end type="italics"/> Mon&longs;ig. Cor&longs;ini, <emph type="italics"/>for the turning of<emph.end type="italics"/> Reno <emph type="italics"/>into Main<emph.end type="italics"/> Po.</cell><cell>106</cell></row><pb xlink:href="040/01/688.jpg"/><row><cell><emph type="italics"/>Two objections on the contrary, and an&longs;wers to them.<emph.end type="italics"/></cell><cell>104 <emph type="italics"/>&<emph.end type="italics"/> 105</cell></row><row><cell><emph type="italics"/>What ought to be the proportion of the Heights of<emph.end type="italics"/> Reno <emph type="italics"/>in<emph.end type="italics"/> Reno, <emph type="italics"/>and of<emph.end type="italics"/> Reno <emph type="italics"/>in<emph.end type="italics"/>Po.</cell><cell>110</cell></row><row><cell><emph type="italics"/>Regulator what it is. Definition<emph.end type="italics"/> IV.</cell><cell>48</cell></row><row><cell><emph type="italics"/>Relation of the Waters of<emph.end type="italics"/> Bologna <emph type="italics"/>and<emph.end type="italics"/> Ferrara, <emph type="italics"/>by<emph.end type="italics"/> Mon&longs;ignore Cor&longs;ini</cell><cell>100</cell></row><row><cell>Reno <emph type="italics"/>in the Valleys, and its bad effects.<emph.end type="italics"/></cell><cell>100, 101</cell></row><row><cell><emph type="italics"/>Two wayes to divert it.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>The facility and utility of tho&longs;e wayes.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>The difficulties objected.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Reply to<emph.end type="italics"/> Bartolotti <emph type="italics"/>touching the dangers of turning<emph.end type="italics"/> Fiume Morto <emph type="italics"/>into<emph.end type="italics"/> Serchio.</cell><cell>83</cell></row><row><cell><emph type="italics"/>Retardment of the cour&longs;e of a River cau&longs;ed by its Banks. Appendix<emph.end type="italics"/> VII.</cell><cell>19</cell></row><row><cell><emph type="italics"/>Ri&longs;ings made by Flood-Gates but &longs;mall. Appendix<emph.end type="italics"/> XIII.</cell><cell>26</cell></row><row><cell><emph type="italics"/>Rivers that are &longs;hallow &longs;well much upon &longs;mall &longs;howers, &longs;uch as are deep ri&longs;e but little upon great Floods. Corollary<emph.end type="italics"/> III.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Rivers the higher they are, the &longs;wifter.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Rivers the higher they are, thele&longs;&longs;e they encrea&longs;e upon Floods.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell><emph type="italics"/>Rivers when they are to have equal and when like Velocity.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Rivers in falling into the Sea, form a Shelf of Sand called<emph.end type="italics"/> Cavallo.</cell><cell>65</cell></row><row><cell><emph type="italics"/>Five Rivers to be diverted from the Lake of<emph.end type="italics"/> Venice, <emph type="italics"/>and the inconveniences that would en&longs;ue thereupon.<emph.end type="italics"/></cell><cell>74, 75</cell></row><row><cell><emph type="italics"/>A River of Quick-height, and Velocity in its Regulator being given, if the Height be redoubled by new Water, it redoubleth al&longs;o in Velocity. Propo&longs;ition<emph.end type="italics"/> II. <emph type="italics"/>The-orem<emph.end type="italics"/> I.</cell><cell>51</cell></row><row><cell><emph type="italics"/>Keepeth the proportion of the heights, to the Velocities. Corollary<emph.end type="italics"/></cell><cell>52</cell></row><row><cell>S</cell><cell></cell></row><row><cell><emph type="italics"/>Sand and Mud that entereth into the Lake of<emph.end type="italics"/> Venice, <emph type="italics"/>and the way to examine it.<emph.end type="italics"/></cell><cell>76</cell></row><row><cell><emph type="italics"/>Seas agitated and driven by the Winds &longs;top up the Ports.<emph.end type="italics"/></cell><cell>64, 65</cell></row><row><cell><emph type="italics"/>Sections of a River what they are. Definition<emph.end type="italics"/> I.</cell><cell>37</cell></row><row><cell><emph type="italics"/>Sections equally &longs;wift what they are. Definition<emph.end type="italics"/> II.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Sections of a River being given, to conceive others equal to them, of different breadth, height and Velocity. Petition.<emph.end type="italics"/></cell><cell>38</cell></row><row><cell><emph type="italics"/>Sections of the &longs;ame River, and their Proportions to their Velocities. Coroll.<emph.end type="italics"/> I.</cell><cell>42</cell></row><row><cell><emph type="italics"/>Sections of a River di&longs;charge in any what&longs;oever place of the &longs;aid River, equal quantities of Water in equal times. Propo&longs;ition<emph.end type="italics"/> I.</cell><cell>39</cell></row><row><cell>Sile <emph type="italics"/>River what mi&longs;chiefes it threatneth, diverted from the Lake.<emph.end type="italics"/></cell><cell>74</cell></row><row><cell><emph type="italics"/>Spirtings of Waters grow bigger the higher they go. Coroll.<emph.end type="italics"/> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"/>Sreams of Rivers how they encrea&longs;e and vary. Coroll.<emph.end type="italics"/> I.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Streams retarded, and the effects thereof. Coroll.<emph.end type="italics"/> IX.</cell><cell>8</cell></row><row><cell>T</cell><cell></cell></row><row><cell><emph type="italics"/>Table of the Heights, Additions, and Quantities of Waters, and its u&longs;e.<emph.end type="italics"/></cell><cell>56</cell></row><row><cell><emph type="italics"/>Thra&longs;imenus.<emph.end type="italics"/> Vide <emph type="italics"/>Lake.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>Time how its mea&longs;ured in the&longs;e Operations of the Waters.<emph.end type="italics"/></cell><cell>49</cell></row><row><cell><emph type="italics"/>Torrents encrea&longs;e at the encrea&longs;ing of a River, though they carry no more Water than before: Coroll.<emph.end type="italics"/> IV.</cell><cell>6</cell></row><row><cell><emph type="italics"/>Torrents when they depo&longs;e and carry away the Sand. Coroll.<emph.end type="italics"/> V.</cell><cell>7</cell></row><row><cell><emph type="italics"/>Torrents and their effects in a River.<emph.end type="italics"/></cell><cell>6, 7</cell></row><row><cell><emph type="italics"/>Torrents that fall into the Valleys, or into<emph.end type="italics"/> Po <emph type="italics"/>of<emph.end type="italics"/> Volano, <emph type="italics"/>and their mi&longs;chiefs prevent-ed, by the diverting of<emph.end type="italics"/> Reno <emph type="italics"/>into<emph.end type="italics"/> Main Po.</cell><cell>100</cell></row><row><cell><emph type="italics"/>Tyber and the cau&longs;es of its inundations. Coroll.<emph.end type="italics"/> VIII.</cell><cell>8</cell></row><pb xlink:href="040/01/689.jpg"/><row><cell>V</cell><cell></cell></row><row><cell><emph type="italics"/>Valleys of<emph.end type="italics"/> Bologna <emph type="italics"/>and<emph.end type="italics"/> Ferrara, <emph type="italics"/>their inundations and di&longs;orders, whence they pro-ceed.<emph.end type="italics"/></cell><cell>97</cell></row><row><cell><emph type="italics"/>Velocity of the Water &longs;hewn by &longs;everal Examples.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Its proportion to the Mea&longs;ure.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Velocities equal, what they are.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Velocities like, what they are.<emph.end type="italics"/></cell><cell>47, 48</cell></row><row><cell><emph type="italics"/>Velocities of Water known, how they help us in finding the Lengths.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>A Fable to explain the truth thereof.<emph.end type="italics"/></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"/>Venice.<emph.end type="italics"/> Vide <emph type="italics"/>Lake.<emph.end type="italics"/></cell><cell></cell></row><row><cell><emph type="italics"/>V&longs;e of the<emph.end type="italics"/> Regulator <emph type="italics"/>in mea&longs;uring great Rivers. Con&longs;ideration I.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell>W</cell><cell></cell></row><row><cell><emph type="italics"/>Waters falling, why they di&longs;groß. Coroll.<emph.end type="italics"/> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"/>Waters, how the Length of them is Mea&longs;ured.<emph.end type="italics"/></cell><cell>70</cell></row><row><cell><emph type="italics"/>Waters that are imployed to flow Grounds, how they are to be di&longs;tributed.<emph.end type="italics"/></cell><cell>19, 53, 54</cell></row><row><cell><emph type="italics"/>Waters to be carryed in Pipes, to &longs;erve Aquaducts and Conduits, how they are to be Mea-&longs;ured.<emph.end type="italics"/></cell><cell>115, 116</cell></row><row><cell><emph type="italics"/>Way to know the ri&longs;ing of Lakes by Raines.<emph.end type="italics"/></cell><cell>28</cell></row><row><cell><emph type="italics"/>Way of the Vulgar to Mea&longs;ure the Waters of Rivers.<emph.end type="italics"/></cell><cell>68</cell></row><row><cell><emph type="italics"/>Wind Gun, and Tortable Fountain of<emph.end type="italics"/> Vincenzo Vincenti <emph type="italics"/>of<emph.end type="italics"/> Urbin.</cell><cell>11</cell></row><row><cell><emph type="italics"/>Windes contrary, retard, and make Rivers encrea&longs;e. Coroll.<emph.end type="italics"/> VII.</cell><cell>8</cell></row></table><p type="head"> <s>The END of the TABLE of the Second Part <lb/>of the Fir&longs;t TOME.</s></p> </chap> <chap> <p type="head"><s>MATHEMATICAL <lb/>Collections and Tran&longs;lations: <lb/>THE SECOND <lb/>TOME: <lb/>IN TWO PARTS.</s></p><p type="head"> <s><emph type="italics"/>THE FIRST PART,<emph.end type="italics"/></s></p><p type="head"> <s>Containing,</s></p><p type="main"> <s><emph type="italics"/>I.<emph.end type="italics"/> GALILEUS GALILEUS His <emph type="italics"/>MATHEMATI­<lb/>CAL Di&longs;cour&longs;es<emph.end type="italics"/> and <emph type="italics"/>Demon&longs;trations,<emph.end type="italics"/> touching two <lb/><emph type="italics"/>NEW SCIENCES,<emph.end type="italics"/> pertaining to the <emph type="italics"/>MECHA­<lb/>NICKS<emph.end type="italics"/> and <emph type="italics"/>LOCAL MOTIONS:<emph.end type="italics"/> With an <lb/><emph type="italics"/>Appendix<emph.end type="italics"/> of the <emph type="italics"/>CENTRE of GRAVITY<emph.end type="italics"/> of &longs;ome <lb/><emph type="italics"/>SOLIDS.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>II.<emph.end type="italics"/> GALILEUS His <emph type="italics"/>MECHANICKS:<emph.end type="italics"/> with &longs;ome <lb/>Additionall <emph type="italics"/>Pieces.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>III.<emph.end type="italics"/> RHENATUS DES CARTES His <emph type="italics"/>MECHA­<lb/>NICKS,<emph.end type="italics"/> Tran&longs;lated from the FRENCH <emph type="italics"/>Manu&longs;cript.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>IV.<emph.end type="italics"/> ARCHIMEDES His Tract <emph type="italics"/>De Insidentibus Humido,<emph.end type="italics"/> or of <lb/>the <emph type="italics"/>NATATION<emph.end type="italics"/> of <emph type="italics"/>BODIES:<emph.end type="italics"/> With the Notes <lb/>and Demon&longs;trations of NICHOLAUS TARTALEA, and <lb/>FEDERICUS COMMANDINUS.</s></p><p type="main"> <s><emph type="italics"/>V.<emph.end type="italics"/> GALILEUS His <emph type="italics"/>Di&longs;cour&longs;e<emph.end type="italics"/> of <emph type="italics"/>NATATION.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>VI.<emph.end type="italics"/> NICOLAUS TARTALEA, His <emph type="italics"/>Inventions<emph.end type="italics"/> for <emph type="italics"/>Diving<emph.end type="italics"/> un­<lb/>der <emph type="italics"/>Water, Rai&longs;ing<emph.end type="italics"/> of <emph type="italics"/>Ships<emph.end type="italics"/> &longs;unk, &c.</s></p><p type="head"> <s><emph type="italics"/>By THOMAS SALUSBURY, E&longs;q<emph.end type="italics"/>;</s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, <emph type="italics"/>Anno Dom. <lb/>MD CLXV.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/690.jpg"/> </chap><pb xlink:href="040/01/691.jpg"/> <chap> <p type="head"> <s>MATHEMATICAL <lb/>DISCOURSES <lb/>AND <lb/>DEMONSTRATIONS, <lb/>TOVCHING <lb/>Two <emph type="italics"/>NEW SCIENCES<emph.end type="italics"/>; pertaining to <lb/>THE <lb/>MECHANICKS <lb/>AND <lb/>LOCAL MOTION:</s></p><p type="head"> <s>BY <lb/><emph type="italics"/>GALILÆVS GALILÆVS LYNCEVS,<emph.end type="italics"/><lb/>Chiefe <emph type="italics"/>Phylo&longs;opher<emph.end type="italics"/> and <emph type="italics"/>Mathematitian<emph.end type="italics"/> to the mo&longs;t <lb/>Serene <emph type="italics"/>GRAND DVKE<emph.end type="italics"/> of <emph type="italics"/>TVSCANY.<emph.end type="italics"/><lb/>WITH <lb/><emph type="italics"/>AN APPENDIX OF THE<emph.end type="italics"/><lb/>Centre of Gravity <lb/>Of &longs;ome <emph type="italics"/>SOLIDS.<emph.end type="italics"/></s></p><p type="head"> <s>Engli&longs;hed from the Originall <emph type="italics"/>Latine<emph.end type="italics"/> and <emph type="italics"/>Italian, <lb/>By THOMAS SALUSBURY, E&longs;q<emph.end type="italics"/>;</s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, <emph type="italics"/>Anno Dom. <lb/> MDCLXV.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/692.jpg" pagenum="1"/><p type="head"> <s>GALILEUS, <lb/>HIS <lb/>DIALOGUES <lb/>OF <lb/>MOTION.</s></p> </chap> <chap> <pb xlink:href="040/01/693.jpg"/><p type="head"> <s>The Fir&longs;t Dialogue.</s></p><p type="head"> <s><emph type="italics"/>INTERLOCUTORS,<emph.end type="italics"/></s></p><p type="head"> <s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"> <s>SALVIATUS.</s></p><p type="main"> <s>The frequent re&longs;ort (Gentlemen) to <lb/><arrow.to.target n="marg984"></arrow.to.target><lb/>your Famous Ar&longs;enal of <emph type="italics"/>Venice,<emph.end type="italics"/> pre&longs;en­<lb/>teth, in my thinking, to your Speculative <lb/><arrow.to.target n="marg985"></arrow.to.target><lb/>Wits, a large field to Philo&longs;ophate in: <lb/>and more particularly, as to that part <lb/>which is called the <emph type="italics"/>Mechanicks:<emph.end type="italics"/> in re­<lb/>gard that there all kinds of Engines, and <lb/>Machines are continually put in u&longs;e, by a <lb/>huge number of Artificers of all &longs;orts; <lb/>among&longs;t whom, as well through the ob&longs;ervations of their Prede­<lb/>ce&longs;&longs;ors, as tho&longs;e, which through their own care they continually <lb/>are making, it's probable, that there are &longs;ome very learned, and <lb/>bravely di&longs;cours'd Men.</s></p><p type="margin"> <s><margin.target id="marg984"></margin.target><emph type="italics"/>A De&longs;cription of <lb/>the Ar&longs;enal of<emph.end type="italics"/><lb/>Venice.</s></p><p type="margin"> <s><margin.target id="marg985"></margin.target><emph type="italics"/>It is a large field <lb/>for Wits to Philo­<lb/>&longs;ophate in.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. Sir, you are not therein mi&longs;taken: and I my &longs;elf, out of <pb xlink:href="040/01/694.jpg" pagenum="2"/>a natural Curio&longs;itie, do frequentlie for my Recreation vi&longs;it that <lb/>place, and confer with the&longs;e per&longs;ons; which for a certain prehe­<lb/><arrow.to.target n="marg986"></arrow.to.target><lb/>minence that they have above the re&longs;t we call ^{*} <emph type="italics"/>Over&longs;eers<emph.end type="italics"/>: who&longs;e <lb/>di&longs;cour&longs;e hath oft helped me in the inve&longs;tigation of not only won­<lb/>derful, but ab&longs;truce, and incredible Effects: and indeed I have been <lb/>at a lo&longs;&longs;e &longs;ometimes, and de&longs;paired to penetrate how that could <lb/>po&longs;&longs;ibly come to pa&longs;&longs;e, which far from all expectation my &longs;en&longs;es <lb/>demon&longs;trated to be true; and yet that which not long &longs;ince that <lb/>good Old man told us, is a &longs;aying and propo&longs;ition, though com­<lb/><arrow.to.target n="marg987"></arrow.to.target><lb/>mon enough, yet in my opinion wholly vain, as are many others, <lb/>often in the mouths of unskilful per&longs;ons; introduced by them, as <lb/>I &longs;uppo&longs;e, to &longs;hew that they under&longs;tand how to &longs;peak &longs;omething <lb/>about that, of which neverthele&longs;&longs;e they are incapable.</s></p><p type="margin"> <s><margin.target id="marg986"></margin.target>* Proti.</s></p><p type="margin"> <s><margin.target id="marg987"></margin.target><emph type="italics"/>The Opinion of <lb/>Common Artificers <lb/>are often fal&longs;e.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>It may be Sir, you &longs;peak of that la&longs;t propo&longs;ition which <lb/>he affirmed, when we de&longs;ired to under&longs;tand, why they made <lb/><arrow.to.target n="marg988"></arrow.to.target><lb/>&longs;o much greater provi&longs;ion of &longs;upporters, and other provi&longs;ions, <lb/>and reinforcements about that Galea&longs;&longs;e, which was to be launcht <lb/>than is made about le&longs;&longs;er Ve&longs;&longs;els, and he an&longs;wered us, that they did <lb/>&longs;o to avoid the peril of breaking its Keel, through the mighty <lb/>weight of its va&longs;t bulk, an inconvenience to which le&longs;&longs;er &longs;hips are <lb/>not subject.</s></p><p type="margin"> <s><margin.target id="marg988"></margin.target><emph type="italics"/>Great Ships apter <lb/>than others to break <lb/>their Keels in <lb/>Launching, accor­<lb/>ding to &longs;ome.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>I do intend the &longs;ame, and chiefly that la&longs;t conclu&longs;ion, <lb/>which he added to his others, and which I alwaies e&longs;teemed a vain <lb/>conceit of the Vulgar, namely, That in the&longs;e and other Machines <lb/>we mu&longs;t not argue from the le&longs;&longs;e to the greater, becau&longs;e many <lb/>Mechanical Inventions take in little, which hold not in great. </s> <s>But <lb/>being that all the Rea&longs;ons of the Mechanicks, have their founda­<lb/>tions from Geometry; in which I &longs;ee not that greatne&longs;&longs;e and <lb/>&longs;malne&longs;&longs;e make Circles, Triangles, Cilinders, Cones, or any other <lb/>&longs;olid Figures &longs;ubject to different pa&longs;&longs;ions: when the great Ma­<lb/>chine is conformed in all its members to the proportions of the <lb/>le&longs;&longs;e that is u&longs;eful, and fit for exerci&longs;e to which it is de&longs;igned; I <lb/>cannot &longs;ee why it al&longs;o &longs;hould not be exempt from the unlucky, <lb/>&longs;ini&longs;ter, and de&longs;tructive accidents that may befall it.</s></p><p type="main"> <s>SALV The &longs;aying of the Vulgar is ab&longs;olutely vain, and &longs;o <lb/>fal&longs;e, that its contrary may be affirmed with equal truth, &longs;aying, <lb/><arrow.to.target n="marg989"></arrow.to.target><lb/>That many Machines may be made more perfect in great than lit­<lb/>tle: As for in&longs;tance, a Clock that &longs;hews and &longs;trikes the Houres, <lb/>may be made more exact in one certain &longs;ize, than in another le&longs;&longs;e. <lb/></s> <s>With better ground is that &longs;ame conclu&longs;ion u&longs;urped by other more <lb/>intelligent per&longs;ons, who refer the cau&longs;e of &longs;uch effects in the&longs;e <lb/>great Machines different from what is collected from the pure, and <lb/>ab&longs;tracted Demon&longs;trations of Geometry, to the imperfection of <lb/>the matter, which is &longs;ubject to many alterations, and defects. <lb/></s> <s>But here, I know not whether I may without contracting &longs;ome <pb xlink:href="040/01/695.jpg" pagenum="3"/>&longs;u&longs;pition of Arrogance &longs;ay, that thither al&longs;o doth the recour&longs;e to <lb/>the defects of the matter (able to blemi&longs;h the perfecte&longs;t Mathe­<lb/>matical Demon&longs;trations) &longs;uffice to excu&longs;e the di&longs;obedience of <lb/><arrow.to.target n="marg990"></arrow.to.target><lb/>Machines in concrete, to the &longs;ame ab&longs;tracted and Ideal: yet not­<lb/>with&longs;tanding I will &longs;peak it, affirming, That ab&longs;tracting all imper­<lb/>fections from the Matter, and &longs;uppo&longs;ing it mo&longs;t perfect, and unal­<lb/>terable, and from all accidental mutation exempt, yet neverthe­<lb/>le&longs;&longs;e its only being Material, cau&longs;eth, that the greater Machine, <lb/>made of the &longs;ame matter, and with the &longs;ame proportions, as the <lb/>le&longs;&longs;er; &longs;hall an&longs;wer in all other conditions to the le&longs;&longs;er in exact <lb/>Symetry, except in &longs;trength, and re&longs;i&longs;tance again&longs;t violent inva&longs;i­<lb/>ons: but the greater it is, &longs;o much in proportion &longs;hall it be wea­<lb/>ker. </s> <s>And becau&longs;e I &longs;uppo&longs;e the Matter to be unalterable, that is <lb/>alwaies the &longs;ame, it is manife&longs;t, that one may produce Demon&longs;tra­<lb/>tions of it, no le&longs;&longs;e &longs;imply and purely Mathematical, then of eter­<lb/>nal, and nece&longs;&longs;ary Affections: Therefore, <emph type="italics"/>Sagredus,<emph.end type="italics"/> Revoke the <lb/>opinion which you, and, it may be, all the re&longs;t hold, that have &longs;tu­<lb/>died the Mechanicks; that Machines, and Frames compo&longs;ed of the <lb/>&longs;ame Matter, with punctual ob&longs;ervation of the &longs;elf &longs;ame proporti­<lb/>on between their parts, ought to be equally, or to &longs;ay better, pro­<lb/>portionally di&longs;po&longs;ed to Re&longs;i&longs;t; and to yield to External injuries <lb/>and a&longs;&longs;aults: For if it may be Geometrically demon&longs;trated, that <lb/>the greater are alwaies in proportion le&longs;s able to re&longs;i&longs;t, than the <lb/>le&longs;&longs;e; &longs;o that in fine there is not only in all Machines & Fabricks <lb/>Arti&longs;icial, but Natural al&longs;o, a term nece&longs;&longs;arily a&longs;cribed, beyond <lb/>which neither Art, nor Nature may pa&longs;&longs;e; may pa&longs;&longs;e, I &longs;ay, al­<lb/>waies ob&longs;erving the &longs;ame proportions with the Identity of the <lb/>Matter.</s></p><p type="margin"> <s><margin.target id="marg989"></margin.target><emph type="italics"/>Many Machines <lb/>may be made more <lb/>exact in great than <lb/>in little.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg990"></margin.target><emph type="italics"/>Great Material <lb/>Machines, al­<lb/>though framed In <lb/>the &longs;ame proportion <lb/>as others of the <lb/>&longs;ame Matter that <lb/>are le&longs;&longs;er, are le&longs;&longs;e <lb/>&longs;trong and able to <lb/>re&longs;i&longs;t external Im­<lb/>petu&longs;s's than the <lb/>le&longs;&longs;er.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>I already feel my Brains to turn round, and my Mind, <lb/>(like a Cloud unwillingly opened by the Lightning,) I perceive <lb/>to be &longs;urprized with a tran&longs;cient, and unu&longs;ual Light, which from <lb/>affar off twinkleth, and &longs;uddenly a&longs;toni&longs;heth me; and with ab­<lb/>&longs;truce, &longs;trange, and indige&longs;ted imaginations. </s> <s>And from what hath <lb/>been &longs;poken, it &longs;eems to follow, that, it is a thing impo&longs;&longs;ible to <lb/>frame two Fabricks of the &longs;ame Matter, alike, and unequal, and <lb/>between them&longs;elves in proportion equally able to Re&longs;i&longs;t; and <lb/>were it to be done, yet it would be impo&longs;&longs;ible to find two only <lb/>Launces of the &longs;ame wood, alike between them&longs;elves in &longs;trength, <lb/><arrow.to.target n="marg991"></arrow.to.target><lb/>and toughne&longs;&longs;e, but unequal in bigne&longs;&longs;e.</s></p><p type="margin"> <s><margin.target id="marg991"></margin.target><emph type="italics"/>A Wooden Launce <lb/>fixed in a Wall at <lb/>Right-Angles, and <lb/>reduced to &longs;uch a <lb/>length and thick­<lb/>ne&longs;&longs;e as that it may <lb/>endure, but made a <lb/>hairs breadth big­<lb/>ger, breaketh with <lb/>its own weight, is <lb/>&longs;ingly one and no <lb/>more.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>So it is Sir; and the better to a&longs;&longs;ure you that we con­<lb/>cur in opinion, I &longs;ay, that if we take a Launce of wood of &longs;uch a <lb/>length and thickne&longs;&longs;e, that being fixed fa&longs;t <emph type="italics"/>(v. </s> <s>g.)<emph.end type="italics"/> in a Wall at <lb/>Right Angles, that is parallel to the Horizon, it is reduced to the <lb/>utmo&longs;t length, that it will hold at, &longs;o that lengthened never­<lb/>&longs;o-little more, it would break, being over-burthened with its own <pb xlink:href="040/01/696.jpg" pagenum="4"/>weight, there could not be another &longs;uch-a-one in the World: So <lb/>that if its length (for example) were Centuple to its thickne&longs;&longs;e, <lb/>there cannot be found another Launce of the &longs;ame Matter, that <lb/>being in length Centuple to its thickne&longs;&longs;e, &longs;hall be able to &longs;u&longs;tain <lb/>it &longs;elf preci&longs;ely, as that did, and no more: for all that are bigger <lb/>&longs;hall break, and the le&longs;&longs;er &longs;hall be able, be&longs;ides their own, to &longs;u&longs;tain <lb/>&longs;ome additional weight. </s> <s>And this that I &longs;ay of the <emph type="italics"/>State of bear­<lb/>ing it &longs;elf,<emph.end type="italics"/> I would have under&longs;tood to be &longs;poken of every other <lb/>Con&longs;titution, and thus if one Tran&longs;ome bear or &longs;u&longs;tain the force <lb/>often Tran&longs;omes equal to it, &longs;uch another Beam cannot bear the <lb/>weight of ten that are equal to it. </s> <s>Now be plea&longs;ed, Sir, and you <lb/><arrow.to.target n="marg992"></arrow.to.target><lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> to ob&longs;erve, how true Conclu&longs;ions, though at the fir&longs;t <lb/>&longs;ight they &longs;eem improbable, yet never &longs;o little glanced at, do depo&longs;e <lb/>the Vailes which ob&longs;cure them, and make a voluntary &longs;hew of their <lb/>&longs;ecrets nakedly, and &longs;imply. </s> <s>Who &longs;ees not, that a Hor&longs;e falling <lb/><arrow.to.target n="marg993"></arrow.to.target><lb/>from a height of three or four yards, will break his bones, but a <lb/>Dog falling &longs;o many yards, or a Cat eight or ten, will receive no <lb/>hurt; nor likewi&longs;e a Gra&longs;hopper from a Tower, nor an Ant thrown <lb/>from the Orbe of the Moon? </s> <s>Little Children e&longs;cape all harm in <lb/>their falls, whereas per&longs;ons grown up break either their &longs;hins or <lb/>faces. </s> <s>And as le&longs;&longs;er Animals are in proportion more robu&longs;tious, <lb/>and &longs;trong than greater, &longs;o the le&longs;&longs;er Plants better &longs;upport them­<lb/>&longs;elves: and I already believe, that both of you think, that an Oake <lb/>two hundred foot high could not &longs;upport its branches &longs;pread like <lb/><arrow.to.target n="marg994"></arrow.to.target><lb/>one of an indifferent &longs;ize; and that Nature could not have made <lb/>an Hor&longs;e as big as twenty Hor&longs;es, nor a Giant ten times as tall as a <lb/>Man, unle&longs;&longs;e &longs;he did it either miraculou&longs;ly, or el&longs;e by much alte­<lb/>ring the proportion of the Members, and particularly of the Bones, <lb/>enlarging them very much above the Symetry of common Bones. <lb/></s> <s>To &longs;uppo&longs;e likewi&longs;e, that in Artificial Machines, the greater and <lb/>le&longs;&longs;er are with equal facility made, and pre&longs;erved, is a manife&longs;t Er­<lb/>rour: and thus for in&longs;tance, &longs;mall Spires, Pillars, and other &longs;olid <lb/>figures may be &longs;afely moved, laid along, and reared upright, with­<lb/>out danger of breaking them; but the very great upon every &longs;ini­<lb/>&longs;ter accident fall in pieces, and for no other rea&longs;on but their own <lb/>weight. </s> <s>And here it is nece&longs;&longs;ary that I relate an accident, worthy <lb/>of notice, as are all tho&longs;e events that occur unexpectedly, e&longs;pecial­<lb/>ly when the means u&longs;ed to prevent an inconvenience, proveth in <lb/><arrow.to.target n="marg995"></arrow.to.target><lb/>fine the mo&longs;t potent cau&longs;e of the di&longs;order. </s> <s>There was a very great <lb/>Pillar of Marble laid along, and two Rowlers were put under the <lb/>&longs;ame neer to the ends of it; it came into the mind of a certain In­<lb/>gineer &longs;ome time after, that it would be expedient, the better to <lb/>&longs;ecure it from breaking in the mid&longs;t through its own weight, to <lb/>put under it in that part yet another Rowler: the coun&longs;el &longs;eemed <lb/>generally very &longs;ea&longs;onable, but the &longs;ucce&longs;&longs;e demon&longs;trated it to be <pb xlink:href="040/01/697.jpg" pagenum="5"/>wholly contrary: for many moneths had not pa&longs;t, before the Pil­<lb/>lar crackt, and broke in the middle ju&longs;t upon the new Rowler.</s></p><p type="margin"> <s><margin.target id="marg992"></margin.target><emph type="italics"/>Truth upon a little <lb/>Courting, throweth <lb/>off her Vail, and <lb/>&longs;hews her Secrets <lb/>maked.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg993"></margin.target><emph type="italics"/>Great Animals <lb/>receive more harm <lb/>by a fall than le&longs;­<lb/>&longs;er.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg994"></margin.target><emph type="italics"/>Nature could not <lb/>have made of mea­<lb/>ner Hor&longs;es bigger, <lb/>and have retained <lb/>the &longs;ame &longs;trength, <lb/>but by altering <lb/>their Symetry.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg995"></margin.target><emph type="italics"/>A great Marble <lb/>Pillar broken by <lb/>its own weight, <lb/>and why.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>This was an accident truly &longs;trange, and indeed <emph type="italics"/>preter <lb/>&longs;pem,<emph.end type="italics"/> e&longs;pecially if it were derived from the addition of new &longs;up­<lb/>port in the middle.</s></p><p type="main"> <s>SALV. </s> <s>From that doubtle&longs;s it did proceed; and the known cau&longs;e <lb/>of the Effect removeth the wonder: for the two pieces of the Pillar <lb/>being taken from off the Rowlers, one of tho&longs;e bearers on which <lb/>one end of the Column had re&longs;ted, was by length of time rotten, and <lb/>&longs;unk away; and that in the mid&longs;t continuing &longs;ound, and &longs;trong, <lb/>occa&longs;ioned that half the Column lay hollow in the air without any <lb/>&longs;upport at the end; &longs;o that its own unweildy weight, made it do <lb/>that, which it would not have done, if it had re&longs;ted only upon the <lb/>two fir&longs;t Bearers, for as they had &longs;hrunk away it would have fol­<lb/>lowed. </s> <s>And here none can think that this would have faln out in <lb/>a little Column, though of the &longs;ame &longs;tone, and of a length an&longs;we­<lb/>rable to its thickne&longs;&longs;e, in the very &longs;ame proportion as the thick­<lb/>ne&longs;s, and length of the great Pillar.</s></p><p type="main"> <s>SAGR. </s> <s>I am now a&longs;&longs;ured of the effect, but do not yet compre­<lb/>hend the cau&longs;e, how in the augmentation of Matter, the Re&longs;i&longs;tance <lb/>and Strength ought not al&longs;o to multiply at the &longs;ame rate. </s> <s>And I <lb/>admire at it &longs;o much the more, in regard I &longs;ee, on the contrary, in <lb/>other ca&longs;es the &longs;trength of Re&longs;i&longs;tance again&longs;t Fraction to encrea&longs;e <lb/>much more than the enlargement of the matter encrea&longs;eth. </s> <s>For if <lb/>(for example) there be two Nailes fa&longs;tned in a Wall, the one twice <lb/>asthick as the other, that &longs;hall bear a weight not only double to this, <lb/>but triple, and quadruple.</s></p><p type="main"> <s>SALV. </s> <s>You may &longs;ay octuple, and not be wide of the truth: <lb/><arrow.to.target n="marg996"></arrow.to.target><lb/>nor is this effect contrary to the former, though in appearance it <lb/>&longs;eemeth &longs;o different.</s></p><p type="margin"> <s><margin.target id="marg996"></margin.target><emph type="italics"/>A Naile double <lb/>in thickne&longs;&longs;e to <lb/>another being fa&longs;t­<lb/>ned in a Wall, &longs;u­<lb/>&longs;tains a Weight <lb/>octuple to that of <lb/>the le&longs;&longs;er.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>Therefore <emph type="italics"/>Salviatus,<emph.end type="italics"/> explain unto us the&longs;e Riddles, and <lb/>level us the&longs;e Rocks, if you can do it: for indeed I gue&longs;&longs;e this mat­<lb/>ter of Re&longs;i&longs;tance to be a field repleni&longs;hed with rare, and u&longs;eful Con­<lb/>templations, and if you be content that this be the &longs;ubject of our <lb/>this-daies di&longs;cour&longs;e, it will be to me, and I believe to <emph type="italics"/>Simplicius,<emph.end type="italics"/><lb/>very acceptable.</s></p><p type="main"> <s>SALV. </s> <s>I cannot refu&longs;e to &longs;erve you, &longs;ince my Memory &longs;erveth <lb/><arrow.to.target n="marg997"></arrow.to.target><lb/>me, in minding me of that which I formerly learnt of our <emph type="italics"/>Accade­<lb/>mick,<emph.end type="italics"/> who hath made many Speculations on this &longs;ubject, and all <lb/>conformable (as his manner is) to Geometrical Demon&longs;tration: <lb/>in&longs;omuch that, not without rea&longs;on, this of his may be called a <emph type="italics"/>New <lb/>Science<emph.end type="italics"/>; for though &longs;ome of the Conclu&longs;ions have been ob&longs;erved <lb/><arrow.to.target n="marg998"></arrow.to.target><lb/>by others, and in the fir&longs;t place by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> yet neverthele&longs;&longs;e are <lb/>they not any of the mo&longs;t curious, or (which more importeth) <lb/>proved by nece&longs;&longs;ary Demon&longs;trations deduced from their primary, <pb xlink:href="040/01/698.jpg" pagenum="6"/>and indubitable fundamentals. </s> <s>And becau&longs;e, as I &longs;ay, I de&longs;ire de­<lb/>mon&longs;tratively to a&longs;&longs;ure you, and not with only probable di&longs;cour­<lb/>&longs;es to per&longs;wade you; pre&longs;uppo&longs;ing, that you have &longs;o much know­<lb/>ledge of the Mechanical Conclu&longs;ions, by others heretofore funda­<lb/>mentally handled, as &longs;ufficeth for our purpo&longs;e; it is requi&longs;ite, that <lb/>before we proceed any further, we con&longs;ider what effect that is which <lb/>opperates in the Fraction of a Beam of Wood, or other Solid, who&longs;e <lb/>parts are firmly connected; becau&longs;e this is the fir&longs;t <emph type="italics"/>Notion,<emph.end type="italics"/> where­<lb/>on the fir&longs;t and &longs;imple principle dependeth, which as familiarly <lb/>known, we may take for granted. </s> <s>For the clearer explanation <lb/>whereof; let us take the Cilinder, or Pri&longs;me, <emph type="italics"/>A. B.<emph.end type="italics"/> of Wood, or <lb/>other &longs;olid and coherent matter, fa&longs;tned above in <emph type="italics"/>A,<emph.end type="italics"/> and hanging <lb/>perpendicular; to which, at the other end <emph type="italics"/>B,<emph.end type="italics"/> let there hang the <lb/>Weight <emph type="italics"/>C<emph.end type="italics"/>: It is manife&longs;t, that how great &longs;oever the Tenacity and <lb/>coherence of the parts of the &longs;aid Solid to one another be, &longs;o it be <lb/>not infinite, it may be overcome by the <lb/>Force of the drawing Weight C: who&longs;e <lb/>Gravity I &longs;uppo&longs;e may be encrea&longs;ed as much <lb/><figure id="id.040.01.698.1.jpg" xlink:href="040/01/698/1.jpg"/><lb/>as we plea&longs;e; by the encrea&longs;e whereof the <lb/>&longs;aid Solid in fine &longs;hall break, like as if it had <lb/>been a Cord. </s> <s>And, as in a Cord, we under­<lb/>&longs;tand its re&longs;i&longs;tance to proceed from the mul­<lb/>titude of the &longs;trings or threads in the Hemp <lb/>that compo&longs;e it, &longs;o in Wood we &longs;ee its veins, <lb/>and grain di&longs;tended lengthwaies, that render <lb/>it far more re&longs;i&longs;ting again&longs;t Fraction, then any <lb/>Rope would be, of the &longs;ame thickne&longs;&longs;e: but <lb/>in a Cylinder of &longs;tone or Metal the Tenacity <lb/>of its parts, (which yet &longs;eemeth greater) de­<lb/>pendeth on another kind of Cement, <lb/>than of &longs;trings, or grains, and yet they al&longs;o <lb/>being drawn with equivalent force, break.</s></p><p type="margin"> <s><margin.target id="marg997"></margin.target><emph type="italics"/>By Accademick <lb/>here, as in his <lb/>Dialogues of the <lb/>Sy&longs;teme,<emph.end type="italics"/> Galile­<lb/>us <emph type="italics"/>meaneth him­<lb/>&longs;elf.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg998"></margin.target>Ari&longs;totle <emph type="italics"/>the fir&longs;t <lb/>Ob&longs;erver of Me­<lb/>chanical Conclu&longs;i­<lb/>ons, but they nei­<lb/>ther not the mo&longs;t <lb/>curious nor &longs;olidly <lb/>demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>If the thing &longs;ucceed as you &longs;ay, I under&longs;tand well <lb/>enough, that the thread or grain of the Wood which is as long as <lb/>the &longs;aid Wood may make it &longs;trong and able to Re&longs;i&longs;t a great vio­<lb/>lence done to it to break it: But a Cord compo&longs;ed of &longs;trings of <lb/>Hemp, no longer than two, or three foot a piece, how can it be &longs;o <lb/>&longs;trong when it is &longs;pun out, it may be, to a hundred times that <lb/>length? </s> <s>Now I would farther under&longs;tand your opinion concern­<lb/>ing the Connection of the parts of Metals, Stones, and other mat­<lb/>ters deprived of &longs;uch Ligatures, which neverthele&longs;&longs;e, if I be not <lb/>deceived, are yet more tenacious.</s></p><p type="main"> <s>SALV. </s> <s>We mu&longs;t be nece&longs;&longs;itated to digre&longs;&longs;e into new Specu­<lb/>lations, and not much to our purpo&longs;e, if we &longs;hould re&longs;olve tho&longs;e <lb/>difficulties you &longs;tart.</s></p><pb xlink:href="040/01/699.jpg" pagenum="7"/><p type="main"> <s>SAGR. </s> <s>But if Digre&longs;&longs;ions may lead us to the knowledge of <lb/>new Truths, what prejudice is it to us, that are not obliged to a <lb/>&longs;trict and conci&longs;e method, but that make our Congre&longs;&longs;ions only <lb/>for our diverti&longs;ement to digre&longs;&longs;e &longs;ometimes, le&longs;t we let &longs;lip tho&longs;e <lb/>Notions, which perhaps the offered occa&longs;ion being pa&longs;t, may never <lb/>meet with another opportunity of remembrance? </s> <s>Nay, who knows <lb/>not, that many times curio&longs;ity may thereby di&longs;cover hints of more <lb/>worth, than the primarily intended Conclu&longs;ions? </s> <s>Therefore I <lb/>entreat you to give &longs;atisfaction to <emph type="italics"/>Simplicius,<emph.end type="italics"/> and my &longs;elf al&longs;o, <lb/>no le&longs;&longs;e curious than he, and de&longs;irous to under&longs;tand what that <lb/>Cement is, that holdeth the parts of tho&longs;e Solids &longs;o tenaciou&longs;ly <lb/>conjoyned, which yet neverthele&longs;&longs;e in conclu&longs;ion are di&longs;&longs;oluble: <lb/>a knowledge which furthermore is nece&longs;&longs;ary for the under&longs;tanding <lb/>of the coherence of the parts of tho&longs;e very ligaments, whereof <lb/>&longs;ome Solids are compo&longs;ed.</s></p><p type="main"> <s>SALV. Well, &longs;ince it is your plea&longs;ure, I will herein &longs;erve you. <lb/><arrow.to.target n="marg999"></arrow.to.target><lb/>And the fir&longs;t difficulty is, how the threads of a Cord or Rope <lb/>an hundred foot long &longs;hould &longs;o clo&longs;ely connect together (none <lb/>of them exceeding two or three foot) that it requireth a great <lb/>violence to break them. </s> <s>But tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> cannot you hold <lb/>one &longs;ingle &longs;tring of Hemp &longs;o fa&longs;t between your fingers by one <lb/><arrow.to.target n="marg1000"></arrow.to.target><lb/>end, that I pulling by the other end &longs;hould break it &longs;ooner than <lb/>get it from you? </s> <s>Que&longs;tionle&longs;&longs;e you might: when then, tho&longs;e <lb/>threads are not only at the end, but al&longs;o in every part of their <lb/>length, held fa&longs;t with much &longs;trength by him that gra&longs;peth them, is <lb/>it not apparent, that it is a much harder matter to pluck them <lb/>from him that holds them, then to break them? </s> <s>Now in the Cord, <lb/><arrow.to.target n="marg1001"></arrow.to.target><lb/>the &longs;ame act of twi&longs;ting, binds the threads mutually within one <lb/>another, in &longs;uch &longs;ort, that pulling the Cord with great force, the <lb/>threads of it break in&longs;under, but &longs;eparate and part not from one <lb/>another; as is plainly &longs;een by viewing the &longs;hort ends of the &longs;aid <lb/>threads in the broken place, that are not a &longs;pan long; as they <lb/>would be, if the divi&longs;ion of the Cord had been made by the &longs;ole <lb/>&longs;eperating of them in drawing the Cord, and not by breaking <lb/>them.</s></p><p type="margin"> <s><margin.target id="marg999"></margin.target><emph type="italics"/>What that Cement <lb/>is that Connecteth <lb/>the parts of Solids.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1000"></margin.target><emph type="italics"/>How a Rope or <lb/>Cord re&longs;i&longs;teth Fra­<lb/>ction.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1001"></margin.target><emph type="italics"/>In breaking a Rope <lb/>the parts are not <lb/>&longs;eparated, but bro­<lb/>kon.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>For confirmation of this, let me add, that the Cord is <lb/>&longs;ometimes &longs;een to break, not by pulling it length-waies, but by <lb/>over-twi&longs;ting it: an argument, in my judgment, concluding that <lb/>the threads are &longs;o enterchangeably compre&longs;t by one another, that <lb/>tho&longs;e compre&longs;&longs;ings permit not the compre&longs;&longs;ed to &longs;lip &longs;o very little, <lb/>as is requi&longs;ite to lengthen it out that it wind about the Cord, <lb/>which in the twining breaketh, and con&longs;equently in &longs;ome &longs;inall <lb/>mea&longs;ure &longs;wels in thickne&longs;&longs;e.</s></p><p type="main"> <s>SALV. </s> <s>You &longs;ay very well; but con&longs;ider by the way, how one <lb/>truth draweth on another. </s> <s>That thread, which griped between the <pb xlink:href="040/01/700.jpg" pagenum="8"/>fingers, did not yield to follow him that would have forceably <lb/>drawn it from between them, re&longs;i&longs;ted, becau&longs;e it was &longs;tayed by a <lb/>double compre&longs;&longs;ion, &longs;ince the upper finger pre&longs;t no le&longs;&longs;e again&longs;t <lb/>the nether, than it pre&longs;&longs;ed again&longs;t that. </s> <s>And there is no que&longs;tion, <lb/>that if of the&longs;e two pre&longs;&longs;ures, one alone might be retained, there <lb/>would remain half of that Re&longs;i&longs;tance, which depended conjunctive­<lb/>ly on them both: but becau&longs;e you cannot with removing, <emph type="italics"/>v.g.<emph.end type="italics"/> the <lb/>upper finger take away its pre&longs;&longs;ion, without taking away the other <lb/>part al&longs;o; it will be nece&longs;&longs;ary by &longs;ome new Artifice to retain one <lb/>of them, and to find a way that the &longs;ame thread may compre&longs;&longs;e it <lb/>&longs;elf again&longs;t the finger or other &longs;olid body upon which it is put; and <lb/>this is done by winding the &longs;ame thread about the Solid. </s> <s>For the <lb/>better under&longs;tanding whereof, I will briefly give it you in Figure; <lb/>and let <emph type="italics"/>A B<emph.end type="italics"/> and C<emph type="italics"/>D<emph.end type="italics"/> be two Cilinders, and between them let there <lb/>be di&longs;tended the thread <emph type="italics"/>E F,<emph.end type="italics"/> which for greater plainne&longs;&longs;e I will <lb/>repre&longs;ent to be a &longs;mall Cord: there is no doubt but that the two <lb/>Cylinders being pre&longs;&longs;ed hard one again&longs;t the other, the Cord <lb/><emph type="italics"/>E F<emph.end type="italics"/> pulled by the end <emph type="italics"/>F<emph.end type="italics"/> will Re&longs;i&longs;t no &longs;mal force before <lb/>it will &longs;lip from between the two Solids compre&longs;&longs;ing it: but if <lb/>we remove one of them, though the Cord <lb/><figure id="id.040.01.700.1.jpg" xlink:href="040/01/700/1.jpg"/><lb/>continue touching the other, yet &longs;hall it not <lb/>by &longs;uch contact be hindered from &longs;lipping <lb/>away. </s> <s>But if holding it fa&longs;t, though but <lb/>gently in the point A, towards the top of the <lb/>Cylinder, we wind, or belay it about the <lb/>&longs;ame &longs;pirally in A F L O T R, and pull it by <lb/>the end R: it is manife&longs;t, that it will begin <lb/>to pre&longs;&longs;e the Cylinder, and if the windings <lb/>and wreathes be many, it &longs;hall in its effectual <lb/>drawing alwaies pre&longs;&longs;e it &longs;o much the &longs;trai­<lb/>ter about the Cylinder: and by multiplying <lb/>the wreathes if you make the contact longer, <lb/>and con&longs;equently more invincible, the more <lb/>difficult &longs;till &longs;hall it be to withdraw the <lb/>Cord, and make it yield to the force that <lb/>pulls it. </s> <s>Now who &longs;eeth not, that the &longs;ame <lb/>Re&longs;i&longs;tance is in the threads, which with many thou&longs;and &longs;uch <lb/>twinings &longs;pin the thick Cord? </s> <s>Yea, the &longs;tre&longs;&longs;e of &longs;uch twi&longs;ting <lb/>bindeth with &longs;uch Tenacity, that a few Ru&longs;hes, and of no great <lb/>length, (&longs;o that the wreaths and windings are but few where­<lb/>with they entertwine) make very &longs;trong bands, called, as I take it, <lb/><arrow.to.target n="marg1002"></arrow.to.target><lb/>^{*} Thum-ropes.</s></p><p type="margin"> <s><margin.target id="marg1002"></margin.target>* Fu&longs;ta.</s></p><p type="main"> <s>SAGR. </s> <s>Your Di&longs;cour&longs;e hath removed the wonder out of my <lb/>mind at two effects, whereof I did not well under&longs;tand the rea­<lb/>&longs;on; One was to &longs;ee, how two, or at the mo&longs;t three twines of the <pb xlink:href="040/01/701.jpg" pagenum="9"/>Rope about the Axis of a Crane did not only hold it, that be­<lb/>ing drawn by the immen&longs;e force of the weight, which it held, it <lb/>&longs;lipt nor &longs;hrunk not; but that moreover turning the Crane about, <lb/>the &longs;aid Axis with the &longs;ole touch of the Rope which begirteth it, <lb/>did in the after-turnings, draw and rai&longs;e up va&longs;t &longs;tones, whil&longs;t the <lb/>&longs;trength of a little Boy &longs;ufficed to hold and &longs;tay the other end of <lb/>the &longs;ame Cord. </s> <s>The other is at a plain, but cunning, In&longs;trument found <lb/>out by a young Kin&longs;man of mine, by which with a Cord he could <lb/>let him&longs;elf down from a window without much gauling the palmes <lb/>of his hands, as to his great &longs;mart not long before he had done. </s> <s>For <lb/><arrow.to.target n="marg1003"></arrow.to.target><lb/>the better under&longs;tanding whereof, rake this Scheame: About &longs;uch <lb/>a Cylinder of Wood as A B, two Inches <lb/>thick, and &longs;ix or eight Inches long, he cut a <lb/>hollow notch &longs;pirally, for one turn and a <lb/><figure id="id.040.01.701.1.jpg" xlink:href="040/01/701/1.jpg"/><lb/>half and no more, and of widene&longs;&longs;e fit for <lb/>the Cord he would u&longs;e; which he made to <lb/>enter through the notch at the end A, and <lb/>to come out at the other B, incircling after­<lb/>wards the Cylinder in a barrel or &longs;ocket of <lb/>Wood, or rather Tin, but divided length­<lb/>waies, and made with Cla&longs;pes or Hinges to <lb/>open and &longs;hut at plea&longs;ure: and then gra&longs;p­<lb/>ing and holding the &longs;aid Barrel or Ca&longs;e with <lb/>both his hands, the rope being made fa&longs;t <lb/>above, he hung by his arms; and &longs;uch was <lb/>the compre&longs;&longs;ion of the Cord between the <lb/>moving Socket and the Cylinder, that at <lb/>plea&longs;ure griping his hands clo&longs;er he could <lb/>&longs;tay him&longs;elf without de&longs;cending, and &longs;lacking his hold a little, he <lb/>could let him&longs;elf down as he plea&longs;ed.</s></p><p type="margin"> <s><margin.target id="marg1003"></margin.target><emph type="italics"/>An Hand-Pully <lb/>or In&longs;trument in­<lb/>vented by an ama­<lb/>rous per&longs;on to let <lb/>him&longs;elf down from <lb/>any great height <lb/>with a Cord with­<lb/>out gauling his <lb/>hands.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Aningenious invention verily, and for a full explanati­<lb/>on of its nature, me-thinks I di&longs;cover, as it were by a &longs;hadow, the <lb/>light of &longs;ome other additional di&longs;coveries: but I will not at this <lb/>time deviate any more from my purpo&longs;e upon this particular: and <lb/>the rather in regard you are de&longs;irous to hear my opinion of the <lb/>Re&longs;i&longs;tance of other Bodies again&longs;t Fraction, who&longs;e texture is not <lb/><arrow.to.target n="marg1004"></arrow.to.target><lb/>with threads, and fibrous &longs;trings, as is that of Ropes, and mo&longs;t <lb/>kinds of Wood: but the connection of their parts &longs;eem to de­<lb/>pend on other Cau&longs;es; which in my judgment may be reduced to <lb/>two heads; one is the much talked-of Repugnance that Nature <lb/>hath again&longs;t the admi&longs;&longs;ion of Vacuity: for another (this of Va­<lb/>cuity not &longs;ufficing) there mu&longs;t be introduced &longs;ome glue, vi&longs;cous <lb/>matter, or Cement, that tenaciou&longs;ly connecteth the Corpu&longs;cles of <lb/>which the &longs;aid Body is compacted.</s></p><p type="margin"> <s><margin.target id="marg1004"></margin.target><emph type="italics"/>Why &longs;uch Bodies <lb/>re&longs;i&longs;t Fraction that <lb/>are not connected <lb/>with Fibrous fila­<lb/>ments.<emph.end type="italics"/></s></p><p type="main"> <s>I will fir&longs;t &longs;peak of <emph type="italics"/>Vacuity,<emph.end type="italics"/> &longs;hewing by plain experiments, <pb xlink:href="040/01/702.jpg" pagenum="10"/><arrow.to.target n="marg1005"></arrow.to.target><lb/>what and how great its virtue is. </s> <s>And fir&longs;t of all the &longs;eeing at <lb/>plea&longs;ure two flat pieces of either Marble, Metal, or Gla&longs;&longs;e, exqui­<lb/>&longs;itely planed, &longs;lickt, and poli&longs;hed, that being laid upon one the <lb/>other, without any difficulty &longs;lide along upon each other, if drawn <lb/><arrow.to.target n="marg1006"></arrow.to.target><lb/>&longs;idewaies, (a certain argument that no glue connects them,) but <lb/>that going about to &longs;eperate them, keeping them equidi&longs;tant, <lb/>there is found &longs;uch repugnance, that the uppermo&longs;t will be lif­<lb/>ted up, and will draw the other after it, and keep it perperually <lb/>rai&longs;ed, though it be pretty thick, and heavy, evidently proveth to <lb/>us, how much Nature abhorreth to admit, though for a &longs;hort mo­<lb/>ment of time, the void &longs;pace, that would be between them, till <lb/>the concour&longs;e of the parts of the Circum-Ambient Air &longs;hould have <lb/>po&longs;&longs;e&longs;t, and repleated it. </s> <s>We &longs;ee likewi&longs;e, that if tho&longs;e two Plates <lb/>be not exactly poli&longs;hed, and con&longs;equently their contact not every <lb/>where exqui&longs;ite; in going about to &longs;eparate them gently, there will <lb/>be found no Renitence more than that of their meer weight, but in <lb/>the &longs;udden rai&longs;ing, the nether Stone will ri&longs;e, and in&longs;tantly fall <lb/>down again, following the upper only for that very &longs;mall time <lb/>which &longs;erveth for the expan&longs;ion of that little Air which interpo­<lb/>&longs;eth betwixt the Plates, that did not every where touch, and for <lb/>the ingre&longs;&longs;ion of the other circumfu&longs;ed. </s> <s>The like Re&longs;i&longs;tance, which <lb/>&longs;o &longs;en&longs;ibly di&longs;covers it &longs;elf betwixt the two Plates, cannot be <lb/>doubted to re&longs;ide al&longs;o between the parts of a Solid, and that it en­<lb/>tereth into their connection, at lea&longs;t in part, and as their Concomi­<lb/>tant Cau&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1005"></margin.target><emph type="italics"/>The fir&longs;t Cau&longs;e of <lb/>the Cohorence of <lb/>Bodies is their Re­<lb/>pugnance to Vacu­<lb/>ity.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1006"></margin.target><emph type="italics"/>This is proved by <lb/>the Coherence of <lb/>two poli&longs;hed Mar­<lb/>bles.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. Hold, I pray you, and permit me to impart unto you a <lb/>particular Con&longs;ideration, ju&longs;t now come into my Mind, and this it <lb/>is; That &longs;eeing how the lower Plate followeth the upper, and is <lb/>by a &longs;peedy motion rai&longs;ed, we are thereby a&longs;certained that (con­<lb/>trary to the &longs;aying of many Philo&longs;ophers, and perchance of <emph type="italics"/>Ari­<lb/>&longs;totle<emph.end type="italics"/> him&longs;elf) the Motion in <emph type="italics"/>Vacuity<emph.end type="italics"/> would not be In&longs;tantaneous; <lb/>for &longs;hould in be &longs;uch, the propo&longs;ed Plates without the lea&longs;t repug­<lb/>nance would Seperate; &longs;ince the &longs;elf &longs;ame in&longs;tant of time would <lb/>&longs;uffice for their &longs;eparation, and for the concour&longs;e of the Ambient <lb/>Air to repleat that <emph type="italics"/>Vacuity,<emph.end type="italics"/> which might remain between them. <lb/></s> <s>By the Inferiour Plates following the Superiour therefore may be <lb/>gathered, that in the <emph type="italics"/>Vacuity<emph.end type="italics"/> the Motion would not be In&longs;tanta­<lb/><arrow.to.target n="marg1007"></arrow.to.target><lb/>neous. </s> <s>And al&longs;o it may be inferred, that even betwixt tho&longs;e Plates <lb/>there re&longs;teth &longs;ome <emph type="italics"/>Vacuity,<emph.end type="italics"/> at lea&longs;t for &longs;ome very &longs;hort time; that <lb/>is, for &longs;o long as the Ambient Air is moving whil&longs;t it concurreth to <lb/>replete the <emph type="italics"/>Vacuum:<emph.end type="italics"/> for if there did no <emph type="italics"/>Vacuity<emph.end type="italics"/> remain, there <lb/>would be no need either of the Concour&longs;e, or Motion of the Am­<lb/>bient We mu&longs;t therefore &longs;ay that <emph type="italics"/>Vacuity<emph.end type="italics"/> &longs;ometimes is admit­<lb/>ted, though by Violence or again&longs;t Nature, (albeit it is my opi­<lb/>nion, that nothing is contrary to Nature, but that which is im­<pb xlink:href="040/01/703.jpg" pagenum="11"/>po&longs;&longs;ible, which again never is.) But here &longs;tarts up another diffi­<lb/>culty, and it is, That though Experience a&longs;&longs;ures me of the truth of <lb/>the Conclu&longs;ion, yet my Judgment is not thorowly &longs;atisfied of the <lb/>Cau&longs;e, to which &longs;uch an effect may be a&longs;cribed. </s> <s>For as much as <lb/>the effect of the Seperation of the two Plates, is in time before the <lb/>Vacuity which &longs;hould &longs;ucceed by con&longs;equence upon the Separa­<lb/>tion. </s> <s>And becau&longs;e, in my opinion, the Cau&longs;e ought, if not in <lb/><arrow.to.target n="marg1008"></arrow.to.target><lb/>Time, at lea&longs;t in Nature, to precede the Effect: and that of a Po­<lb/>&longs;itive Effect, the Cau&longs;e ought al&longs;o to be Po&longs;itive; I cannot con­<lb/>ceive, how the Cau&longs;e of the Adhe&longs;ion of the two Plates, and of <lb/>their Repugnance to Separation, (Effects that are already in <lb/>Act) &longs;hould be a&longs;&longs;igned to Vacuity, which yet is not, but &longs;hould <lb/>follow. </s> <s>And of things that are not in being, there can be no Ope­<lb/><arrow.to.target n="marg1009"></arrow.to.target><lb/>ration; according to the infallible Maxime of Philo&longs;ophy.</s></p><p type="margin"> <s><margin.target id="marg1007"></margin.target><emph type="italics"/>Vacuity partly the <lb/>cau&longs;e of the Cohe­<lb/>rence between the <lb/>parts of Solids.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1008"></margin.target><emph type="italics"/>Of a Po&longs;itive Ef­<lb/>fect the Cau&longs;e is <lb/>Po&longs;itive.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1009"></margin.target><emph type="italics"/>Non-entity is at­<lb/>tended with Non­<lb/>operation.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>But &longs;ince you grant <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> this Axiome, I do not <lb/>think you will deny another that is mo&longs;t excellent, and true; to <lb/><arrow.to.target n="marg1010"></arrow.to.target><lb/>wit, That Nature doth not attempt Impo&longs;&longs;ibilities: Upon which <lb/>Axiom I think the Solution of our doubt depends: becau&longs;e there­<lb/>fore a void &longs;pace is of it &longs;elf impo&longs;&longs;ible, Nature forbids the doing <lb/>that, in con&longs;equence of which Vacuity would nece&longs;&longs;arily &longs;ucceed; <lb/>and &longs;uch an act is the &longs;eparation of the two Plates.</s></p><p type="margin"> <s><margin.target id="marg1010"></margin.target><emph type="italics"/>Nature doth not <lb/>attempt Impo&longs;&longs;ibi­<lb/>lities.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. Now, (admitting this which <emph type="italics"/>Simplicius<emph.end type="italics"/> alledgeth is a <lb/>&longs;ufficient Solution of my Doubt) in per&longs;uance of the di&longs;cour&longs;e <lb/>with which I began, it &longs;eemeth to me, that this &longs;ame Repugnance <lb/>to Vacuity &longs;hould be a &longs;ufficient Cement in the parts of a Solid of <lb/>Stone, Metal, or what other &longs;ub&longs;tance is more firmly conjoyned, <lb/>and aver&longs;e to Divi&longs;ion. </s> <s>For if a &longs;ingle Effect, hath but one &longs;ole <lb/>Cau&longs;e, as I under&longs;tand, and think; or if many be a&longs;&longs;igned, they <lb/>are reducible to one alone: why &longs;hould not this of Vacuity, which <lb/>certainly is one, be &longs;ufficient to an&longs;wer all Re&longs;i&longs;tances?</s></p><p type="main"> <s>SALV. </s> <s>I will not at this time enter upon this conte&longs;t, whether <lb/>Vacuity, without other Cement, be in it &longs;elf alone &longs;ufficient to <lb/>keep together the &longs;eparable parts of firm Bodies; but yet this I <lb/>&longs;ay, that the Rea&longs;on of the Vacuity, which is of force, and con­<lb/>oluding in the two Plates, &longs;ufficeth not of it &longs;elf alone for the <lb/>firm connection of the parts of a &longs;olid Cylinder of Marble, or <lb/>Metal, the which forced with great violence, pulling them &longs;treight <lb/>out, in fine, divide and &longs;eparate. </s> <s>And in ca&longs;e I have found a way <lb/>to di&longs;tingui&longs;h this already-known Re&longs;i&longs;tance dependent on Va­<lb/>ouity, from all others what&longs;oever that may concur with it in <lb/>&longs;trengthening the Connection, and make you &longs;ee how that it alone <lb/>is not neer &longs;ufficient for &longs;uch an Effect, would not you grant that <lb/>it would be nece&longs;&longs;ary to introduce &longs;ome other? </s> <s>Help him out, <emph type="italics"/>Sim­<lb/>plicius,<emph.end type="italics"/> for he &longs;tands &longs;tudying what to an&longs;wer.</s></p><p type="main"> <s>SIMP. </s> <s>The Su&longs;pen&longs;ion of <emph type="italics"/>Sagredus<emph.end type="italics"/> mu&longs;t needs be upon ano­<pb xlink:href="040/01/704.jpg" pagenum="12"/>ther account, there being no place left for doubting of &longs;o clear, and <lb/>nece&longs;&longs;ary a Con&longs;equence.</s></p><p type="main"> <s>SAGR. </s> <s>You Divine <emph type="italics"/>Simplicius,<emph.end type="italics"/> I was thinking if a Million of <lb/>Gold <emph type="italics"/>per annum,<emph.end type="italics"/> coming from <emph type="italics"/>Spaine,<emph.end type="italics"/> not being &longs;ufficient to pay <lb/>the Army, whether it was nece&longs;&longs;ary to make any other provi&longs;ion <lb/>than of Money to pay the Souldiers. </s> <s>But proceed, <emph type="italics"/>Salviatus,<emph.end type="italics"/> and <lb/>&longs;uppo&longs;ing that I admit of your Con&longs;equence, &longs;hew us how to &longs;e­<lb/>parate the opperation of Vacuity from the other, that mea&longs;uring <lb/>it we may &longs;ee how it's in&longs;ufficient for the Effect of which we &longs;peak.</s></p><p type="main"> <s>SALV. </s> <s>Your Genius hath prompted you. </s> <s>Well, I will tell you <lb/>the way to part the Virtue of Vacuity from the re&longs;t, and then how <lb/>to mea&longs;ure it. </s> <s>And to &longs;ever it, we will take a continuate matter, <lb/><arrow.to.target n="marg1011"></arrow.to.target><lb/>who&longs;e parts are de&longs;titute of all other Re&longs;i&longs;tance to Separation, &longs;ave <lb/>only that of Vacuity, &longs;uch as Water at large hath been demon­<lb/>&longs;trated to be in a certain Tractate of our <emph type="italics"/>Accademick.<emph.end type="italics"/> So that <lb/>when ever a Cylinder of Water is &longs;o di&longs;po&longs;ed, that being drawn <lb/>we find a Re&longs;i&longs;tance again&longs;t the &longs;eparation of its parts, this mu&longs;t <lb/>be acknowledged to proceed from no other cau&longs;e, but from re­<lb/>pugnance to Vacuity. </s> <s>But to make &longs;uch an experiment, I have <lb/>imagined a device, which with the help of a &longs;mall Diagram, may <lb/>be better expre&longs;t than by my bare words. </s> <s>Let this Figure C A B D <lb/>be the Profile of a Cylinder of Metal, or of Gla&longs;s, which mu&longs;t <lb/>be made hollow within, but turned exactly round; into who&longs;e <lb/>Concave mu&longs;t enter a Cylinder of Wood, exqui&longs;itely fitted to <lb/>touch every where, who&longs;e Profile is noted by <lb/>E G H F, which Cylinder may be thru&longs;t up­<lb/><figure id="id.040.01.704.1.jpg" xlink:href="040/01/704/1.jpg"/><lb/>wards, and downwards: and this I would <lb/>have bored in the middle, &longs;o that there may <lb/>a rod of Iron pa&longs;s thorow, hooked in the end <lb/>K, and the other end I, &longs;hall grow thicker in <lb/>fa&longs;hion of a Cone, or Top; and let the <lb/>hole made for the &longs;ame thorow the Cylinder <lb/>of Wood be al&longs;o cut hollow in the upper <lb/>part, like a Conical Superficies, and exactly <lb/>fitted to receive the Conick end I, of the <lb/>Iron I K, as oft as it is drawn down by the <lb/>part K. </s> <s>Then I put the Cylinder of Wood <lb/>E H into the Concave Cylinder A D, and <lb/>would not have it come to touch the upper­<lb/>mo&longs;t Superficies of the &longs;aid hollow Cylinder, <lb/>but that it &longs;tay two or three fingers breadth <lb/>from it: and I would have that &longs;pace filled with Water; which <lb/>&longs;hould be put therein, holding the Ve&longs;&longs;el with the mouth C D up­<lb/>wards; and thereupon pre&longs;s down the Stopper E H, holding the <lb/>Conical part I &longs;omewhat di&longs;tant from the hollow that was made <pb xlink:href="040/01/705.jpg" pagenum="13"/>for it in the Wood, to leave way for the Air to go out, which in <lb/>thru&longs;ting down the Stopper will i&longs;&longs;ue out by the hole of the <lb/>Wood, which therefore &longs;hould be made a little wider than the <lb/>thickne&longs;s of the Hook of Iron I K. </s> <s>The Air being let out, and the <lb/>Iron pull'd back, which clo&longs;e &longs;toppeth the wood with its Conick <lb/>part I, then turn the ve&longs;&longs;el with its mouth downwards, and fa&longs;ten to <lb/>the hook K a Bucket that may receive into it &longs;and, or other weigh­<lb/>ty matter, and you may hang &longs;o much weight thereat, that at length <lb/>the Superiour &longs;urface of the Stopper E F will &longs;eparate and for&longs;ake <lb/>the inferiour part of the Water; to which nothing el&longs;e held it con­<lb/>nected but the Repugnance again&longs;t Vacuity: afterwards weighing <lb/>the Stopper with the Iron, the Bucket, and all that was in it, you <lb/>will have the quantity of the Force of the Vacuity. </s> <s>And if affixing <lb/>to a Cylinder of Marble, or Chri&longs;tal, as thick as the Cylinder of <lb/>Water, &longs;uch a weight, that together with the proper weight of the <lb/>Marble or Chri&longs;tal it &longs;elf, equalleth the gravity of all tho&longs;e fore­<lb/>named things, a Rupture follow thereupon; we may without <lb/>doubt affirm, that the only rea&longs;on of Vacuity holdeth the parts of <lb/>Marble and Chri&longs;tal conjoyned: but not &longs;ufficing; and &longs;eeing <lb/>that to break it there mu&longs;t be added four times as much weight, <lb/>it mu&longs;t be confe&longs;&longs;ed, that the Re&longs;i&longs;tance of Vacuity is one part of <lb/>&longs;ive, and that the other Re&longs;i&longs;tance is quadruple to that of Vacuity.</s></p><p type="margin"> <s><margin.target id="marg1011"></margin.target><emph type="italics"/>How to mea&longs;ure <lb/>the Virtue of Va­<lb/>cuity in Solids di­<lb/>&longs;tinct from other <lb/>convenient Cau&longs;es <lb/>of their Coherence. <lb/></s> <s>Water a Continu­<lb/>ate Matter, and <lb/>void of all other a­<lb/>ver&longs;ion to &longs;eparati­<lb/>on, &longs;ave that of Va­<lb/>cuity.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>It cannot be denied, but that the Invention is Ingen­<lb/>ous: but I hold it to be &longs;ubject to many difficulties, which makes <lb/>me que&longs;tion it; for who &longs;hall a&longs;&longs;ure us, that the Air cannot pene­<lb/>trate between the Gla&longs;s, and the Stopper, though it be clo&longs;e &longs;topt <lb/>with Flax, or other pliant matter? </s> <s>And al&longs;o it's a Que&longs;tion, whe­<lb/>ther Wax or Turpentine will &longs;erve to make the Cone I, &longs;top the <lb/>hole clo&longs;e: Again, Why may not the parts of the Water with­<lb/>draw and rarefie them&longs;elves? </s> <s>Why may not the Air, or Exhalati­<lb/>ons, or other more &longs;ubtil Sub&longs;tances penetrate through the Poro&longs;i­<lb/>ties of the Wood, or Gla&longs;s it &longs;elf?</s></p><p type="main"> <s>SALV. <emph type="italics"/>Simplicius<emph.end type="italics"/> is very nimble at rai&longs;ing doubts, and, in part, <lb/>helping us to re&longs;olve them, as to the Penetration of the Air through <lb/>the Wood, or between the Wood and Gla&longs;s. </s> <s>But I moreover <lb/>ob&longs;erve, that we may at the &longs;ame time &longs;ecure our &longs;elves, and with­<lb/>all acquire new Notions, if the fore-named doubts take place; for <lb/>if the Water be by Nature, howbeit with violence, capable of ex­<lb/>tention, as it falleth out in Air, you &longs;hall &longs;ee the Stopper to de­<lb/>&longs;cend: and if in the upper part of the Gla&longs;s we make a &longs;mall pro­<lb/>minent Bo&longs;s, as this V; in ca&longs;e any Air, or other more Tenuous or <lb/>Spirituous Matter &longs;hould penetrate thorow the Sub&longs;tance, or Poro&longs;i­<lb/>ty of the Gla&longs;s, or Wood, it would be &longs;een to reunite (the water <lb/>giving place) in the eminence V: which things not being percei­<lb/>ved, we re&longs;t a&longs;&longs;ured that the Experiment was made with due <pb xlink:href="040/01/706.jpg" pagenum="14"/>caution: and &longs;ee that the Water is not capable o&longs; exten&longs;ion, nor <lb/>the Gla&longs;s permeable by any matter, though never &longs;o &longs;ubtil.</s></p><p type="main"> <s>SAGR. </s> <s>And I, by means of the&longs;e Di&longs;cour&longs;es have found the <lb/>Cau&longs;e of an Effect, that hath for a long time puzled my mind <lb/><arrow.to.target n="marg1012"></arrow.to.target><lb/>with wonder, and kept it in Ignorance. </s> <s>I have heretofore ob­<lb/>&longs;erved a Ci&longs;tern, wherein, for the drawing thence of Water, there <lb/>was made a Pump, by &longs;ome one that thought, perhaps, (but in <lb/>vain) to be thereby able to draw, with le&longs;s labour, the &longs;ame, or <lb/>greater quantity of Water, than with the ordinary Buckets; and <lb/>this Pump had its Sucker and Value on high, &longs;o that the Water <lb/>was made to a&longs;cend by Attraction, and not by Impul&longs;e, as do the <lb/>Pumps that work below. </s> <s>This, whil&longs;t there is any Water in the <lb/>Ci&longs;tern to &longs;uch a determinate height, will draw it plentifully; but <lb/>when the Water ebbeth below a certain Mark, the Pump will <lb/>work no more. </s> <s>I conceited, the fir&longs;t time that I ob&longs;erved this ac­<lb/>cident, that the Engine ____ had been &longs;poyled, and looking for <lb/>the Workman, that he might amend it; he told me, that there was <lb/>no defect at all, other than what was in the Water, which being <lb/>fallen too low, permitted not it &longs;elf to be rai&longs;ed to &longs;uch a height; <lb/><arrow.to.target n="marg1013"></arrow.to.target><lb/>and farther &longs;aid, that neither Pump, or other Machine, that rai&longs;eth <lb/>the water by Attraction, was po&longs;&longs;ibly able to make it ri&longs;e a hair <lb/>more than eighteen Braces, and be the Pumps wide or narrow, this <lb/>is the utmo&longs;t limited mea&longs;ure of their height. </s> <s>And I have hitherto <lb/>been &longs;o dull of apprehen&longs;ion, that though I knew that a Rope, a <lb/>Stick, and a Rod of Iron might be &longs;o and &longs;o lengthened, that at <lb/>la&longs;t, holding it up on high in the Air, its own weight would break <lb/>it, yet I never remembred, that the &longs;ame would much more ea&longs;ily <lb/>happen in a Rope, or Thread of Water. </s> <s>And what other is that <lb/>which is attracted in the Pump than a Cylinder of Water, which <lb/>having its contraction above, prolonged more and more, in the end <lb/>arriveth to that term, beyond which being drawn, it breaketh by <lb/>its foregoing over-weight, ju&longs;t as if it was a Rope.</s></p><p type="margin"> <s><margin.target id="marg1012"></margin.target><emph type="italics"/>The Nature of the <lb/>attraction of Wa­<lb/>ter by Pumps.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1013"></margin.target><emph type="italics"/>Water rai&longs;ed or at­<lb/>tracted by a Pump <lb/>ri&longs;eth not above <lb/>eleven yards.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>It is even &longs;o as you &longs;ay; and becau&longs;e the &longs;aid height of <lb/>eighteen Braces is the prefixed term of the Elevation, to which any <lb/>quantity of Water, be it (that is to &longs;ay, be the Pump) broad, <lb/>narrow, or even, &longs;o narrow as to the thickne&longs;s of a &longs;traw, can &longs;u­<lb/>&longs;tain it &longs;elf; when ever we weigh the water contained in eighteen <lb/>Braces of Pipe, be it broad or narrow, we have the value of Re&longs;i­<lb/>&longs;tance of Vacuity in Cylinders of what&longs;oever &longs;olid matter, of the <lb/>thickne&longs;s of the propo&longs;ed Pipes. </s> <s>And &longs;ince I have &longs;aid &longs;o much, <lb/><arrow.to.target n="marg1014"></arrow.to.target><lb/>we will &longs;hew, that a man may ea&longs;ily find in all Metals, Stones, Tim­<lb/>bers, Gla&longs;&longs;es, <emph type="italics"/>&c.<emph.end type="italics"/> How far one may lengthen out Cylinders, <lb/>&longs;trings, or rods of any thickne&longs;s, beyond which, being oppre&longs;t with <lb/>their own weight, they can no longer hold, but break in pieces. <lb/></s> <s>Take for example a Bra&longs;s wyer of any certain thickne&longs;s, and length, <pb xlink:href="040/01/707.jpg" pagenum="15"/>and fixing one of its ends on high, add gradually more and more <lb/>weight to the other, till at la&longs;t it break, and let the greate&longs;t weight <lb/>that it can bear be <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> fifty pounds. </s> <s>It is manife&longs;t that fifty <lb/>pound of Bra&longs;s more than its own weight, which let us &longs;uppo&longs;e, <lb/>for example, to be one eighth of an Ounce, drawn out into a <lb/>Wyer of the like thickne&longs;s, would be the greate&longs;t length of the <lb/>Wyer that could bear it &longs;elf. </s> <s>Then mea&longs;ure how long the Wyer <lb/>was which brake, and let it be for in&longs;tance a y ard; and becau&longs;e it <lb/>weighed one eighth of an Ounce; and poi&longs;ed, or bore it &longs;elf, and <lb/>fifty pounds more; which are Four Thou&longs;and Eight Hundred <lb/>eighths of Ounces; we &longs;ay, that all Wyers of Bra&longs;s, whatever <lb/>thickne&longs;s they be of, can hold, at the length of Four Thou&longs;and <lb/>Eight Hundred and one yards, and no more: and &longs;o, a Bra&longs;s Wyer <lb/>being able to hold to the length of 4801 yards; the Re&longs;i&longs;tance it <lb/>findeth dependent on Vacuity, in re&longs;pect of the remainder, is as <lb/>much as is equivalent to the weight of a Rope of Water eighteen <lb/>Braces long, and of the &longs;ame thickne&longs;s with the &longs;aid Bra&longs;s Wyer: <lb/>and finding Bra&longs;s to be <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> nine times heavier than Water, in <lb/>any Wyer of Bra&longs;s, the Re&longs;i&longs;tance again&longs;t Fraction dependent on <lb/>the rea&longs;on of Vacuity, importeth as much as two Braces of the <lb/>&longs;ame Wyer weigheth. </s> <s>And thus arguing, and operating, we may <lb/>find the length of the Wyers, or Threads of all Solid Matters re­<lb/>duced to the utmo&longs;t length that they can &longs;ub&longs;i&longs;t of, and al&longs;o what <lb/>part Vacuity hath in their Re&longs;i&longs;tance.</s></p><p type="margin"> <s><margin.target id="marg1014"></margin.target><emph type="italics"/>To what length Cy­<lb/>linders or Ropes of <lb/>any Matter may <lb/>be prolonged, be­<lb/>yond which being <lb/>charged they break <lb/>by their own weight<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>It re&longs;teth now, that you declare to us wherein con&longs;i&longs;ts <lb/>the remainder of that Tenacity, that is, what that Glue or Reni­<lb/>tence is, which connecteth together the parts of a Solid, be&longs;ides <lb/>that which is derived from Vacuity; becau&longs;e I cannot imagine <lb/>what that Cement is, that cannot be burnt, or con&longs;umed in a ve­<lb/>ry hot Furnace in two, three, or four Moneths, nor ten, nor an hun­<lb/>dred; and yet Gold, Silver, and Gla&longs;s, &longs;tanding &longs;o long Liqui&longs;i­<lb/>ed, when it is taken out, its parts return, upon cooling, to reunite, <lb/>and conjoyn, as before. </s> <s>And again, becau&longs;e the &longs;ame difficulty <lb/>which I meet within the Connection of the parts of the Gla&longs;s, I <lb/>find al&longs;o in the parts of the Cement, that is, what thing that <lb/>&longs;hould be which maketh them cleave &longs;o clo&longs;s together.</s></p><p type="main"> <s>SALV. </s> <s>I told you but even now, that your Genius prompted <lb/>you: I am al&longs;o in the &longs;ame &longs;trait: and al&longs;o whereas I have in gene­<lb/>ral told you, how that Repugnance again&longs;t Vacuity is unque&longs;ti­<lb/>onably that which permits not, nnle&longs;s with great violence, the &longs;e­<lb/>paration of the two Plates, and moreover of the two great pieces of <lb/>the Pillar of Marble, or Bra&longs;s, I cannot &longs;ee why it &longs;hould not al&longs;o <lb/>take place, and be likewi&longs;e the Cau&longs;e of the Coherence of the le&longs;­<lb/>&longs;er parts, and even of the very lea&longs;t and la&longs;t, of the &longs;ame Matters: <lb/><arrow.to.target n="marg1015"></arrow.to.target><lb/>and being that of one &longs;ole Effect, there is but one only true, and <pb xlink:href="040/01/708.jpg" pagenum="16"/>mo&longs;t potent Cau&longs;e; if I can find no other Cement, why may I not <lb/>try whether this of Vacuity, which I have already found, may be <lb/>&longs;ufficient?</s></p><p type="margin"> <s><margin.target id="marg1015"></margin.target><emph type="italics"/>There is but one <lb/>&longs;ole Cau&longs;e of one <lb/>&longs;ole Effect.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>But when you have already demon&longs;trated the Re&longs;i­<lb/>&longs;tance of the great Vacuity in the &longs;eparation of the two great <lb/>parts of a Solid to be very &longs;mall in compari&longs;on of that which con­<lb/>necteth, and con&longs;olidates the little Particles, or Atomes, why will <lb/>you not &longs;till hold, for certain, that this is extreamly differing from <lb/>that?</s></p><p type="main"> <s>SALV. </s> <s>To this <emph type="italics"/>Sagredus<emph.end type="italics"/> an&longs;wereth, That every particular <lb/>Souldier is &longs;till paid with money collected by the general Impo&longs;i­<lb/>tions of Shillings and Pence, although a Million of Gold &longs;ufficeth <lb/>not to pay the whole Army. </s> <s>And who knows, but that other ex­<lb/>ceeding &longs;mall Vacuities may operate among&longs;t tho&longs;e &longs;mall Atomes, <lb/>(even like as that was of the &longs;elf-&longs;ame money) wherewith all <lb/>the parts are connected? </s> <s>I will tell you what I have &longs;ometimes <lb/>fancied: and I give it you, not as an unque&longs;tionable Truth, but as a <lb/>kind of Conjecture very undige&longs;ted, &longs;ubmitting it to exacter con­<lb/>&longs;iderations: Pick out of it what plea&longs;eth you, and judge of the re&longs;t <lb/><arrow.to.target n="marg1016"></arrow.to.target><lb/>as you think fit. </s> <s>Con&longs;idering &longs;ometimes how the Fire, penetra­<lb/>ting and in&longs;inuating between the &longs;mall Atomes of this or that Me­<lb/>tal, which were before &longs;o clo&longs;ely con&longs;olidated, in the end &longs;epa­<lb/>rates, and di&longs;unites them; and how, the Fire being gone, they re­<lb/>turn with the &longs;ame Tenacity as before to Con&longs;olidation, without <lb/>dimini&longs;hing in quantity, (at all in Gold, and very little in other <lb/>Metals,) though they continue a long time melted; I have thought <lb/>that that might happen, by rea&longs;on the extream &longs;mall parts of the <lb/>Fire, penetrating through the narrow pores of the Metal (through <lb/>which the lea&longs;t parts of Air, or of many other Fluids, could not <lb/>for their clo&longs;ene&longs;s perforate) by repleating the &longs;mall interpo&longs;ing <lb/>Vacuities might free the minute parts of the &longs;ame from the vio­<lb/>lence, wherewith the &longs;aid Vacuities attract them one to another, <lb/>prohibiting their &longs;eparation: and thus becoming able to move <lb/>freely, their Ma&longs;s might become fluid, and continue &longs;uch, as long <lb/>as the &longs;mall parts of the Fire &longs;hould abide betwixt them: and that <lb/>tho&longs;e departing, and leaving the former Vacuities, their wonted <lb/>attractions might return, and con&longs;equently the Cohe&longs;ion of the <lb/>parts. </s> <s>And, as to the Allegation made by <emph type="italics"/>Simplicius,<emph.end type="italics"/> it may, in <lb/>my opinion, be thus re&longs;olved; That although &longs;uch Vacuities &longs;hould <lb/>be very &longs;mall, and con&longs;equently each of them ea&longs;ie to be over­<lb/>come, yet neverthele&longs;s their innumerable multitude innumerably <lb/><arrow.to.target n="marg1017"></arrow.to.target><lb/>(if it be proper &longs;o to &longs;peak) multiplieth the Re&longs;i&longs;tances: and we <lb/>have an evident proof what, and how great is the Force that re&longs;ul­<lb/>teth from the conjunction of an immen&longs;e number of very weak <lb/>Moments, in &longs;eeing a Weight of many thou&longs;ands of pounds, held <pb xlink:href="040/01/709.jpg" pagenum="17"/>by mighty Cables, to yield, and &longs;uffer it &longs;elf at la&longs;t to be over­<lb/>come by the a&longs;&longs;ault of the innumerable Atomes of Water; which, <lb/>either carryed by the South-wind, or el&longs;e by being di&longs;tended into <lb/>very thin Mi&longs;ts that move to and fro in the Air, in&longs;inuate them­<lb/>&longs;elves between &longs;tring and &longs;tring of the Hemp of the harde&longs;t twi­<lb/>&longs;ted Cables; nor can the immen&longs;e force of the pendent Weight <lb/>prohibit their enterance; &longs;o that perforating the &longs;trict pa&longs;&longs;ages be­<lb/>tween the Pores, they &longs;well the Ropes, and by con&longs;equence &longs;hor­<lb/>ten them, whereupon that huge Ma&longs;s is forcibly rai&longs;ed.</s></p><p type="margin"> <s><margin.target id="marg1016"></margin.target><emph type="italics"/>Mo&longs;t &longs;mall Va­<lb/>cuities di&longs;&longs;emina­<lb/>ted and interpo&longs;ed <lb/>between the &longs;mall <lb/>Corpu&longs;cles of So­<lb/>lids the probable <lb/>cau&longs;e of the con&longs;i­<lb/>&longs;tence or connecti­<lb/>on of tho&longs;e Corpu&longs;­<lb/>cles to one another,<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1017"></margin.target><emph type="italics"/>Innumerable A­<lb/>tomes of Water in­<lb/>&longs;inuating into Ca­<lb/>bles draw and rai&longs;e <lb/>an immen&longs;e weight<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. There's no doubt but that &longs;o long as a Re&longs;i&longs;tance is not <lb/><arrow.to.target n="marg1018"></arrow.to.target><lb/>infinite, it may by a multitude of mo&longs;t minute Forces be over­<lb/>come; in&longs;omuch that a competent number even of Ants would <lb/>be able to carry to &longs;hore a whole &longs;hips lading of Corn: for Sen&longs;e <lb/>giveth us quotidian examples, that an Ant carrieth a &longs;ingle grain <lb/>with ea&longs;e; and its cleer, that in the Ship there are not infinite <lb/>grains, but that they are compri&longs;ed in a certain number; and if you <lb/>take another number four or &longs;ix times bigger than that, and take <lb/>al&longs;o another of Ants equal to it, and &longs;et them to work, they &longs;hall <lb/>carry the Corn, and the Ship al&longs;o. </s> <s>It is true indeed, that it will be <lb/>needful that the number be great, as al&longs;o in my judgment that of <lb/>the <emph type="italics"/>Vacuities,<emph.end type="italics"/> which hold together the &longs;inall parts of the <lb/>Mettal.</s></p><p type="margin"> <s><margin.target id="marg1018"></margin.target><emph type="italics"/>Any finite Re&longs;i­<lb/>&longs;tance is &longs;uperable <lb/>by any the lea&longs;t <lb/>Force, multiplied.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>But though they were required to be infinite, do you <lb/>think it impo&longs;&longs;ible?</s></p><p type="main"> <s>SAGR. </s> <s>Not if the Mettal were of an infinite ma&longs;&longs;e; other­<lb/>wi&longs;e ----</s></p><p type="main"> <s>SALV. </s> <s>Otherwi&longs;e what? </s> <s>Go to, feeing we are faln upon <lb/>Paradoxes, let us &longs;ee if we can any way demon&longs;trate, how that <lb/>in a continuate finite exten&longs;ion, it is not impo&longs;&longs;ible to finde infi­<lb/>nite <emph type="italics"/>Vacuities:<emph.end type="italics"/> and then, if we gain nothing el&longs;e, yet at lea&longs;t we <lb/><arrow.to.target n="marg1019"></arrow.to.target><lb/>&longs;hall finde a &longs;olution of that mo&longs;t admirable Problem propound­<lb/>ed by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> among&longs;t tho&longs;e which he him&longs;elf calleth admirable, <lb/>I mean among&longs;t his <emph type="italics"/>Mechanical Que&longs;tions<emph.end type="italics"/>; and the Solution may <lb/>haply be no le&longs;&longs;e plain and concluding, than that which he him&longs;elf <lb/>brings thereupon, and different al&longs;o from that which Learned <lb/><arrow.to.target n="marg1020"></arrow.to.target><lb/><emph type="italics"/>Mon&longs;ig. </s> <s>di Guevara<emph.end type="italics"/> very acutely di&longs;cu&longs;&longs;eth. </s> <s>But it is fir&longs;t requi&longs;ite <lb/>to declare a Propo&longs;ition not toucht by others, on which the &longs;olution <lb/>of the que&longs;tion dependeth, which afterwards, if I deceive not my <lb/>&longs;elf, will draw along with it other new and admirable Notions; for <lb/>under&longs;tanding whereof the more exactly, we will give it you in <lb/>a Scheme: We &longs;uppo&longs;e, therefore an equilateral, and equian­<lb/>gled Poligon of any number of Sides at plea&longs;ure, de&longs;cribed <lb/>about this Center G; and in this example let it be a Hexagon <lb/>A B C D E F; like to which, and concentrick with the &longs;ame <lb/>mu&longs;t be di&longs;tributed another le&longs;&longs;er, which we mark H I K L M N; <pb xlink:href="040/01/710.jpg" pagenum="18"/>and let one Side of the greater A B be prolonged indeterminately <lb/>towards S, and of the le&longs;&longs;e the corre&longs;pondent Side H I is to be <lb/>produced in like manner towards the &longs;ame part, repre&longs;enting the <lb/>Line H T, parallel to A S; and let another pa&longs;&longs;e by the Center <lb/>equidi&longs;tant from the former, namely G V. </s> <s>This done, we &longs;uppo&longs;e <lb/>the greater Poligon to turn about upon the Line A S, carrying <lb/>with it the other le&longs;&longs;er Poligon. </s> <s>It is manife&longs;t, that the point B, <lb/>the term of the Side A B, &longs;tanding &longs;till, whil&longs;t the Revolution <lb/>begins, the angle A ri&longs;eth, and the point C de&longs;cendeth, de&longs;cribing <lb/>the arch C <expan abbr="q;">que</expan> &longs;o that the Side B C is applyed to the line B Q, <lb/>equal to it &longs;elf: but in &longs;uch conver&longs;ion the angle I of the le&longs;&longs;er <lb/>Poligon ri&longs;eth above the Line I T. for that I B is oblique upon <lb/>A S: nor will the point I fall upon the parallel I T, before the <lb/>point C come to Q: and by that time I &longs;hall be de&longs;cended unto <lb/>O after it had de&longs;cribed the Arch I O, without the Line H T: and <lb/>at the &longs;ame time the Side I K &longs;hall have pa&longs;s'd to O P. </s> <s>But the Cen­<lb/>ter G &longs;hall have gone all this time out of the Line G V, on which it <lb/>&longs;hal not fall, until it &longs;hall fir&longs;t have de&longs;cribed the Arch G C. </s> <s>Having <lb/>made this fir&longs;t &longs;tep, the greater Poligon &longs;hall be tran&longs;po&longs;ed to re&longs;t <lb/>with the Side B C upon the Line B <expan abbr="q;">que</expan> the Side I K of the le&longs;&longs;er <lb/>upon the Line O P, having skipt all the Line I O without touching <lb/><figure id="id.040.01.710.1.jpg" xlink:href="040/01/710/1.jpg"/><lb/>it; and the Center G &longs;hall be removed to C, making its whole <lb/>cour&longs;e without the Parallel G V: And in fine all the Figure &longs;hall <lb/>be remitted into a Po&longs;ition like the fir&longs;t; &longs;o that the Revolution <lb/>being continued, and coming to the &longs;econd &longs;tep, the Side of the <lb/>greater Poligon D C &longs;hall remove to Q X; K L of the le&longs;&longs;er (ha­<lb/>ving fir&longs;t skipt the Arch P Y) &longs;hall fall upon Y Z, and the Center <lb/>proceeding evermore without G V &longs;hall fall on it in R, after the <lb/>great skip C R. </s> <s>And in the la&longs;t place, having fini&longs;hed an entire <lb/>Conver&longs;ion, the greater Poligon will have impre&longs;&longs;ed upon A S, &longs;ix <pb xlink:href="040/01/711.jpg" pagenum="19"/>Lines equal to its Perimeter without any interpo&longs;itions or skips: <lb/>the le&longs;&longs;er Poligon likewi&longs;e &longs;hall have traced &longs;ix Lines equal to its <lb/>Perimeter, but di&longs;continued by the interpo&longs;ition of five Arches, <lb/>under which are the Chords, parts of the parallel H T not toucht <lb/>by the Poligon: And la&longs;tly, the Center G never hath toucht the <lb/>Parallel G V except in &longs;ix points. </s> <s>From hence you may compre­<lb/>hend, how that the Space pa&longs;&longs;ed by the le&longs;&longs;er Poligon, is almo&longs;t <lb/>equal to that pa&longs;&longs;ed by the greater, that is the Line H T is almo&longs;t <lb/>equal to A S, then which it is le&longs;&longs;er only the quantity of one of <lb/>the&longs;e Arches, taking the Line H T, together with all its Arches. <lb/></s> <s>Now, this which I have declared and explained to you in the exam­<lb/>ple of the&longs;e Hexagons, I would have you under&longs;tand to hold true <lb/>in all other Poligons, of what number of Sides &longs;oever they be, &longs;o <lb/>that they be like Concentrick, and Conjoyned; and that at the <lb/>Conver&longs;ion of the greater, the other, how much &longs;oever le&longs;&longs;er, be <lb/>&longs;uppo&longs;ed to revolve therewith: that is, you mu&longs;t under&longs;tand, I &longs;ay, <lb/>that the Lines by them pa&longs;&longs;ed are very near equal, computing in­<lb/>to the Space pa&longs;t by the le&longs;&longs;er, the Intervals under the little Ar­<lb/>ches not toucht by any part of the Perimeter of the &longs;aid le&longs;&longs;er Po­<lb/>ligon. </s> <s>Let therefore the greater Poligon, of a thou&longs;and Sides, pa&longs;s <lb/>round, and mea&longs;ure out a continued Line equal to its Perimeter; <lb/>and in the &longs;ame time the le&longs;s pa&longs;&longs;eth a Line almo&longs;t as long, but <lb/>compounded of a thou&longs;and Particles equal to its thou&longs;and Sides, <lb/>but di&longs;continued with the interpo&longs;ition of a thou&longs;and void Spaces: <lb/>for &longs;uch may we call them, in relation to the thou&longs;and little Lines <lb/>toucht by the Sides of the Poligon. </s> <s>And what hath been &longs;poken <lb/>hitherto admits of no doubt or &longs;cruple. </s> <s>But tell me, in ca&longs;e that <lb/>about a Center, as &longs;uppo&longs;e the point A, (in the former Scheme) <lb/>we &longs;hould de&longs;cribe two Circles concentrick, and united together; <lb/>and that from the points C and B of their Semi-Diameters, there <lb/>be drawn the Tangents C E, and B F, and by the Center A the Pa­<lb/>rallel A D; &longs;uppo&longs;ing the greater Circle to be turned upon the <lb/>Line B F, (drawn equal to its Circumference, as likewi&longs;e the other <lb/>two C E, and A D;) when it hath compleated one Revolution, <lb/>what &longs;hall the le&longs;&longs;er Circle, and Center have done? </s> <s>The Center <lb/>&longs;hall doubtle&longs;s have run over, and touched the whole Line A D, <lb/>and the le&longs;s Circumference &longs;hall with its touches have mea&longs;ured <lb/>all C E, doing the &longs;ame as did the Poligons above; and different <lb/>only in this, that the Line H T was not touched in all its Parts by <lb/>the Perimeter of the le&longs;&longs;er Poligon, but there were as many parts <lb/>left untoucht with the interpo&longs;ition of &longs;alts, or skipped &longs;paces; as <lb/>were the&longs;e parts touched by the Sides: but here in the Circles, <lb/>the Circumference of the le&longs;&longs;er Circle, never &longs;eparates from the <lb/>Line C E, &longs;o as to leave any of its parts untou cht; nor is the parts <lb/>touching of the Circumference, le&longs;s than the part toucht of the <pb xlink:href="040/01/712.jpg" pagenum="20"/>Right-line. </s> <s>Now how is it po&longs;&longs;ible that the le&longs;&longs;er Circle &longs;hould <lb/>without skips run a Line &longs;o much bigger than its Circumfe­<lb/>rence?</s></p><p type="margin"> <s><margin.target id="marg1019"></margin.target>Ari&longs;totles <emph type="italics"/>admi­<lb/>rable Problem of <lb/>two Concentrick <lb/>Circles that turn <lb/>round, and its true <lb/>re&longs;olution.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1020"></margin.target>Mon&longs;ig. </s> <s>Gueva <lb/>ra <emph type="italics"/>honourably men­<lb/>tioned.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>I was con&longs;idering whether one might not &longs;ay, that like <lb/>as the Center of the Circle trailed alone upon A D toucht, it all <lb/>being yet but one &longs;ole Point; &longs;o likewi&longs;e might the Points of the <lb/>le&longs;&longs;er Circumference, drawn by the revolution of the greater, go <lb/>gliding along &longs;ome &longs;mall part of the Line C E.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>This cannot be, for two rea&longs;ons; fir&longs;t, becau&longs;e there is <lb/>no rea&longs;on why &longs;ome of the touches like to C &longs;hould go gliding <lb/>along &longs;ome part of the Line C E, more than others: and though <lb/>there &longs;hould; &longs;uch touches being (becau&longs;e they are points) in&longs;i­<lb/>nite, the glidings along upon C E would be infinite; and &longs;o being, <lb/>they would make an infinite Line, but the Line C E is finite. </s> <s>The <lb/>other rea&longs;on is, that the greater Circle, in its Revolution continu­<lb/>ally changing contact, the le&longs;&longs;er Circle mu&longs;t of nece&longs;&longs;ity do the <lb/>like; there being no other Point but B, by which a Right Line can <lb/>be drawn to the Center A, and pa&longs;&longs;ing through C; &longs;o that the <lb/>greater Circumference changing Contact, the le&longs;s doth change it <lb/>al&longs;o; nor doth any Point of the le&longs;s touch more than one Point of <lb/>its Right-Line C E: be&longs;ides, that al&longs;o in the conver&longs;ion of the Po­<lb/>ligons, no Point of the Perimeter of the le&longs;s falls on more than one <lb/>Point of the Line, which was by the &longs;aid Perimeter traced, as may <lb/>be ea&longs;ily under&longs;tood, con&longs;idering the Line I K is parallel to B C, <lb/>whereupon, till ju&longs;t that B C fall on B R, I K continueth elevated <lb/>above I P, and toucheth it not before B C is on the very Point of <lb/>uniting with B Q, and then all in the &longs;ame in&longs;tant I K uniteth <lb/>with O P, and afterwards immediately ri&longs;eth above it again.</s></p><p type="main"> <s>SAGR. </s> <s>The bu&longs;ine&longs;s is really very intricate, nor can I think on <lb/>any Solution of it, therefore do you explain it to us as far as you <lb/>judge needful.</s></p><p type="main"> <s>SALV. </s> <s>I &longs;hould, for the evincing hereof, have recour&longs;e to the <lb/>con&longs;ideration of the fore-de&longs;cribed Poligons, the effect of which is <lb/>intelligible and already comprehended, and would &longs;ay, that like as <lb/>in the Poligons of an hundred thou&longs;and Sides, the Line pa&longs;&longs;ed and <lb/>mea&longs;ured by the Perimeter of the greater, that is by its hundred <lb/>thou&longs;and Sides continually di&longs;tended, is not con&longs;iderably bigger <lb/>than that mea&longs;ured by the hundred thou&longs;and Sides of the le&longs;s, but <lb/>with the interpo&longs;ition of an hundred thou&longs;and void &longs;paces interve­<lb/>ning; fo I would &longs;ay in the Circles (which are Poligons of innu­<lb/>merable Sides) that the Line mea&longs;ured by the infinite Sides of the <lb/>great Circle, lying continued one with another, to be equalled in <lb/>length by the Line traced by the infinite Sides of the le&longs;s, but by <lb/>the&longs;e including the interpo&longs;ition of the like number of intervening <lb/>Spaces: and like as the Sides are not quantitative, but yet infinite <pb xlink:href="040/01/713.jpg" pagenum="21"/>in number, &longs;o the interpo&longs;ing Vacuitics are not quantitative, but <lb/>infinite in number; that is, tho&longs;e are infinite Points all filled, and <lb/>the&longs;e are infinite points, part filled, and part empty. </s> <s>And here I <lb/>would have you note, that re&longs;olving, and dividing a Line into quan­<lb/>titative parts, and con&longs;equently of a finite number, it is not po&longs;&longs;ible <lb/>to di&longs;po&longs;e them into a greater extention than that which they po&longs;­<lb/>&longs;e&longs;t whil&longs;t they were continued, and connected, without the inter­<lb/>po&longs;ition of a like number of void Spaces; but imagining it to be <lb/>re&longs;olved into parts not quantitative, namely, into its infinite indivi­<lb/>&longs;ibles, we may conceive it produced to immen&longs;ity without the in­<lb/>terpo&longs;ition of quantitative void &longs;paces, but yet of infinite indivi&longs;i­<lb/>ble Vacuities. </s> <s>And this which is &longs;poken of &longs;imple lines, &longs;hould al&longs;o <lb/>be under&longs;tood of Superficies, and Solid Bodies, con&longs;idering that they <lb/>are compo&longs;ed of infinite Atomes not non-quantitative; if we would <lb/>divide them into certain quantitative parts, there's no que&longs;tion, but <lb/>that we cannot di&longs;po&longs;e them into Spaces more ample than the Solid <lb/>before occupied, unle&longs;s with the interpo&longs;ition of a certain number <lb/>of quantitative void Spaces; void, I &longs;ay, at lea&longs;t of the matter of the <lb/>Solid: but if we &longs;hould propo&longs;e the highe&longs;t, and ultimate re&longs;olution <lb/>made into the fir&longs;t, non-quantitative, but infinite fir&longs;t compoun­<lb/>ding parts, we may be able to conceive &longs;uch compounding parts <lb/>extended unto an immen&longs;e Space without the interpo&longs;ition of <lb/>quantitative void Spaces; but only of infinite non-quantitative Va­<lb/>cuities: and in this manner a man may draw out, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> a little Ball <lb/>of Gold into a very va&longs;t expan&longs;ion without admitting any quan­<lb/>titative void Spaces; yet neverthele&longs;s we may admit the Gold to <lb/>be compounded of infinite induci&longs;&longs;ible ones.</s></p><p type="main"> <s>SIMP. </s> <s>Me thinks that in this point you go the way of tho&longs;e di&longs;­<lb/>&longs;eminated Vacuities of a certain <emph type="italics"/>Ancient Philo&longs;opher<emph.end type="italics"/> ------</s></p><p type="main"> <s>SALV. </s> <s>But you add not: [<emph type="italics"/>who denied Divine Providence:)<emph.end type="italics"/><lb/>as on &longs;uch another occa&longs;ion, &longs;ufficiently be&longs;ides his purpo&longs;e, a cer­<lb/>tain Antagoni&longs;t of our <emph type="italics"/>Accademick<emph.end type="italics"/> did &longs;ubjoyn.</s></p><p type="main"> <s>SIMP. </s> <s>I &longs;ee very well, and not without indignation, the malice <lb/>of &longs;uch contradictors; but I &longs;hall forbear the&longs;e Cen&longs;ures, not only <lb/>upon the &longs;core of Good-Manners, but becau&longs;e I know how di&longs;a­<lb/>greeing &longs;uch Tenets are to the well-tempered, and well-di&longs;po&longs;ed <lb/>mind of a per&longs;on, &longs;o Religious and Pious, yea, Orthodox and Ho­<lb/>ly, as you, Sir. </s> <s>But returning to my purpo&longs;e; I find many &longs;cruples <lb/>to ari&longs;e in my mind about your la&longs;t Di&longs;cour&longs;e, which I know not <lb/>how to re&longs;olve. </s> <s>And this pre&longs;ents its &longs;elf for one, that if the Cir­<lb/>cumferences of two Circles are equall to the two Right Lines <lb/>C E, and B F, this taken continually, and that, with the interpo&longs;i­<lb/>tion of infinite void Points; how can A D, de&longs;cribed by the Center, <lb/>which is but one &longs;ole Point, be &longs;aid to be equal to the &longs;ame, it con­<lb/>taining infinite of them? </s> <s>Again, that &longs;ame compo&longs;ing the Line of <pb xlink:href="040/01/714.jpg" pagenum="22"/>Points, the divi&longs;ible of indivi&longs;ibles, the quantitative of non-quan­<lb/>titative, is a rock very hard, in my judgment, to pa&longs;s over: And <lb/>the very admitting of Vacuity, &longs;o thorowly confuted by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/><lb/>no le&longs;s puzleth me than tho&longs;e difficulties them&longs;elves.</s></p><p type="main"> <s>SALV. </s> <s>There be, indeed, the&longs;e and other difficulties; but re­<lb/>member, that we are among&longs;t Infinites, and Indivi&longs;ibles: tho&longs;e in­<lb/>comprehen&longs;ible by our finite under&longs;tanding for their Grandure; <lb/>and the&longs;e for their minutene&longs;s: neverthele&longs;s we &longs;ee that Humane <lb/>Di&longs;cour&longs;e will not be beat off from ruminating upon them, in <lb/>which regard, I al&longs;o a&longs;&longs;uming &longs;ome liberty, will produce &longs;ome of <lb/>my conceits, if not nece&longs;&longs;arily concluding, yet for novelty &longs;ake, <lb/>which is ever the me&longs;&longs;enger of &longs;ome wonder: but perhaps the car­<lb/>rying you &longs;o far out of your way begun, may &longs;eem to you imper­<lb/>tinent, and con&longs;equently little plea&longs;ing.</s></p><p type="main"> <s>SAGR. </s> <s>Pray you let us enjoy the benefit, and priviledge, of free <lb/>&longs;peaking which is allowed to the living, and among&longs;t friends; e&longs;pe­<lb/>cially, in things arbitrary, and not nece&longs;&longs;ary; different from Di&longs;cour&longs;e <lb/>with dead Books, which &longs;tart us a thou&longs;and doubts, and re&longs;olve not <lb/>one of them. </s> <s>Make us therefore partakers of tho&longs;e Con&longs;iderations, <lb/>which the cour&longs;e of our Conferences &longs;ugge&longs;t unto you; for we <lb/>want no time, &longs;eeing we are di&longs;engaged from urgent bu&longs;ine&longs;&longs;es, to <lb/>continue and di&longs;cu&longs;&longs;e the other things mentioned; and particular­<lb/>ly, the doubts, hinted by <emph type="italics"/>Simplicius,<emph.end type="italics"/> mu&longs;t by no means e&longs;cape us.</s></p><p type="main"> <s>SAIV. </s> <s>It &longs;hall be &longs;o, &longs;ince it plea&longs;eth you: and beginning at <lb/>the fir&longs;t, which was, how it's po&longs;&longs;ible to imagine that a &longs;ingle Point <lb/>is equal to a Line; in regard I can do no more for the pre&longs;ent, I <lb/>will attempt to &longs;atisfie, or, at lea&longs;t, qualifie one improbability with <lb/>another like it, or greater; as &longs;ome times a Wonder is &longs;wallowed <lb/>up in a Miracle. </s> <s>And this &longs;hall be by &longs;hewing you two equal Su­<lb/>perficies, and at the &longs;ame time two Bodies, likewi&longs;e equal, and <lb/>placed upon tho&longs;e Superficies as their Ba&longs;es; and that go (both <lb/>the&longs;e and tho&longs;e) continually and equally dimini&longs;hing in the &longs;elf­<lb/><arrow.to.target n="marg1021"></arrow.to.target><lb/>&longs;ame time, and that in their remainders re&longs;t alwaies equal between <lb/>them&longs;elves, and (la&longs;tly) that, as well Super&longs;icies, as Solids, deter­<lb/>mine their perpetual precedent equalities, one of the Solids with <lb/>one of the Superficies in a very long Line; and the other Solid <lb/>with the other Superficies in a &longs;ingle Point: that is, the latter in <lb/>one Point alone, the other in infinite.</s></p><p type="margin"> <s><margin.target id="marg1021"></margin.target><emph type="italics"/>The equal Super­<lb/>ficies of two Solids <lb/>continually &longs;ub­<lb/>&longs;tracting from <lb/>them both equal <lb/>parts, are reduced, <lb/>the one into the <lb/>Circumference of a <lb/>Circle, and the o­<lb/>ther into a Point.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>AGR. </s> <s>An admirable propo&longs;al, really, yet let us hear you ex­<lb/>plain and demon&longs;trate it.</s></p><p type="main"> <s>SALV. </s> <s>It is nece&longs;&longs;ary to give you it in Figure, becau&longs;e the proof <lb/>is purely Geometrical. </s> <s>Therefore &longs;uppo&longs;e the Semicircle A F B, <lb/>and its Center to be C, and about it de&longs;cribe the Rectangle <lb/>A D E B, and from the Center unto the Points D and E let there <lb/>be drawn the Lines C D, and C E; Then drawing the Semi-Dia­<pb xlink:href="040/01/715.jpg" pagenum="23"/>meter C F, perpendicular to one of the two Lines A B, or D E <lb/>and immoveable; we &longs;uppo&longs;e all this Figure to turn round about <lb/>that Perpendicular: It is manife&longs;t, that there will be de&longs;cribed by <lb/>the Parallelogram A D E B, a Cylinder; by the Semi-circle A F B, <lb/>an Hemi-Sphære; and by the Triangle C D E a Cone. </s> <s>This pre­<lb/>&longs;uppo&longs;ed, I would have you imagine the Hemi&longs;phære to be taken <lb/>away, leaving behind the Cone, and that which &longs;hall remain of <lb/>the Cylinder; which for the Figure, which it &longs;hall retain like to a <lb/>Di&longs;h, we will hereafter call a Di&longs;h: touching which, and the <lb/>Cone, we will &longs;ir&longs;t demon&longs;trate that they are equal; and next <lb/>a Plain being drawn parallel to the Circle, which is the foot or <lb/>Ba&longs;e of the Di&longs;h, who&longs;e Diameter is the Line D E, and its Center <lb/>F; we will demon&longs;trate, that &longs;hould the &longs;aid Plain pa&longs;s, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> by <lb/>the Line G H, cutting the Di&longs;h in the points G I, and O N; and <lb/>the Cone in the points H and L; it would cut the part of the <lb/>Cone C H L, equal alwaies to the part of the Di&longs;h, who&longs;e Profile <lb/>is repre&longs;ented to us by the Triangles G A I, and B O N: and more­<lb/>over we will prove the Ba&longs;e al&longs;o of the &longs;ame Cone, (that is the <lb/>Circle, who&longs;e Diameter is H L) to be equal to that circular Su­<lb/>perficies, which is Ba&longs;e of the part of the Di&longs;h; which is, as we <lb/>may &longs;ay, a Rimme as broad as G I; (note here by the way what <lb/>Mathematical Definitions are: they be an impo&longs;ition of names, or, <lb/>we may &longs;ay, abreviations of &longs;peech, ordain'd and introduced to <lb/>prevent the trouble and pains, which you and I meet with, at pre­<lb/>&longs;ent, in that we have not agreed together to call <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> this Super­<lb/>ficies a circular Rimme, and that very &longs;harp Solid of the Di&longs;h a <lb/>round Razor:) now how&longs;oever you plea&longs;e to call them, it &longs;ufficeth <lb/>you to know, that the Plain produced to any di&longs;tance at plea&longs;ure, <lb/>&longs;o that it be parallel to the Ba&longs;e, <emph type="italics"/>viz.<emph.end type="italics"/> to the Circle who&longs;e Diame­<lb/>ter D E cuts alwaies the two Solids, namely, the part of the Cone <lb/>C H L, and the upper part of the Di&longs;h equal to one another: and <lb/>likewi&longs;e the two Superficies, Ba&longs;is of the &longs;aid Solids, <emph type="italics"/>viz.<emph.end type="italics"/> the &longs;aid <lb/>Rimme, and the Circle H L, equal al&longs;o to one another. </s> <s>Whence <lb/>followeth the forementioned Wonder; namely, that if we &longs;hould <lb/>&longs;uppo&longs;e the cutting-plain to be <lb/>&longs;ucce&longs;&longs;ively rai&longs;ed towards the <lb/><figure id="id.040.01.715.1.jpg" xlink:href="040/01/715/1.jpg"/><lb/>Line A B, the parts of the Solid <lb/>cut are alwaies equall, as al&longs;o the <lb/>Superficies, that are their Ba&longs;es, <lb/>are evermore equal; and, in <lb/>fine, rai&longs;ing the &longs;aid Plain higher <lb/>and higher, the two Solids (ever <lb/>equal) as al&longs;o their Ba&longs;es, (Su­<lb/>perficies ever equal) &longs;hall one couple of them terminate in a Cir­<lb/>cumference of a Circle, and the other couple in one &longs;ole point; <pb xlink:href="040/01/716.jpg" pagenum="24"/>for &longs;uch are the upper Verge or Rim of the Di&longs;h, and the Vertex <lb/>of the Cone. </s> <s>Now whil&longs;t that in the diminution of the two So­<lb/>lids, they till the very la&longs;t maintain their equality to one another, it <lb/>is, in my thoughts, proper to &longs;ay, that the highe&longs;t and ultimate terms <lb/>of &longs;uch Diminutions are equal, and not one infinitely bigger than <lb/>the other. </s> <s>It &longs;eemeth therefore, that the Circumference of an im­<lb/>men&longs;e Circle may be &longs;aid to be equal to one &longs;ingle point; and <lb/>this that befalls in Solids, holdeth likewi&longs;e in the Superficies their <lb/>Ba&longs;es; that they al&longs;o in the common Diminution con&longs;erving al­<lb/>waies equality, in fine, determine at the in&longs;tant of their ultimate <lb/>Diminution the one, (that is, that of the Di&longs;h) in their Circum­<lb/>ference of a Circle, the other (to wit, that of the Cone) in one <lb/>&longs;ole point. </s> <s>And why may not the&longs;e be called equal, if they be the <lb/>la&longs;t remainders, and foot&longs;teps left by equal Magnitudes? </s> <s>And note <lb/>again, that were &longs;uch Ve&longs;&longs;els capable of the immen&longs;e Cœle&longs;tial <lb/>Hemi&longs;pheres: both their upper Rims, and the points of the contai­<lb/>ned Cones (keeping evermore equally to one another) would fi­<lb/>nally determine, tho&longs;e, in Circumferences equal to tho&longs;e of the <lb/>greate&longs;t Circles of the Cœle&longs;tial Orbes, and the&longs;e in &longs;implo points. <lb/></s> <s>Whence, according to that which &longs;uch Speculations per&longs;wade us <lb/>to, all Circumferences of Circles, how unequal &longs;oever, may be <lb/>&longs;aid to be equal to one another, and each of them equal to one &longs;ole <lb/>point.</s></p><p type="main"> <s>SAGR. </s> <s>The Speculation is, in my e&longs;teem, &longs;o quaint and curi­<lb/>ous, that, for my part, though I could, yet would I not oppo&longs;e it, <lb/>for I take it for a piece of Sacriledge to deface &longs;o fine a Structure, <lb/>by &longs;purning at it with any pedantick contradiction; yet for our en­<lb/>tire &longs;atisfaction, give us the proof (which you &longs;ay is Geometrical) <lb/>of the equality alwaies retained between tho&longs;e Solids, and tho&longs;e <lb/>their Ba&longs;es, which I think mu&longs;t needs be very &longs;ubtil, the philo&longs;o­<lb/>phical Contemplation being &longs;o nice, which depends on the &longs;aid <lb/>Conclu&longs;ion.</s></p><p type="main"> <s>SALV. </s> <s>The Demon&longs;tration is but &longs;hort, and ea&longs;ie. </s> <s>Let us keep <lb/>to the former Figure, in which the Angle I P C being a Right An­<lb/>gle, the Square of the Semi-Diameter I C is equal to the two <lb/>Squares of the Sides I P, and P C. </s> <s>But the Semi-Diameter I C, is <lb/>equal to A C, and this to G P; and C P is equal to P H; therefore <lb/>the Square of the Line G P is equal to the two Squares of I P, and <lb/>P H, and the Quadruple to the Quadruples; that is, the Quadrate <lb/>of the Diameter G N is equal to the two Quadrates I O, and H L: <lb/>and becau&longs;e Circles are to each other, as the Squares of their Dia­<lb/>meters; the Circle who&longs;e Diameter is G N, &longs;hall be equall to the <lb/>two Circles who&longs;e Diameters are I O, and H L; and taking away <lb/>the Common Circle, who&longs;e Diameter is I O; the re&longs;idue of the <lb/>Circle G N &longs;hall be equal to the Circle, who&longs;e Diameter is H L. <pb xlink:href="040/01/717.jpg" pagenum="25"/>And this is as to the fir&longs;t part: Now as for the other part, we will, <lb/>for the pre&longs;ent, omit its Demon&longs;tration, as well becau&longs;e that if you <lb/>would &longs;ee it, you &longs;hall find it in the twelfth Propo&longs;ition of the Se­<lb/><arrow.to.target n="marg1022"></arrow.to.target><lb/>cond Book <emph type="italics"/>De centro Gravitatis Solidorum,<emph.end type="italics"/> publi&longs;hed by <emph type="italics"/>Signeur <lb/>Lucas Valerius,<emph.end type="italics"/> the new <emph type="italics"/>Archimedes<emph.end type="italics"/> of our Age; who upon ano­<lb/>ther occa&longs;ion hath made u&longs;e of it; as becau&longs;e in our ca&longs;e it &longs;uffi­<lb/>ceth to have &longs;een, how the Superficies, already explained, are ever­<lb/>more equal; and that alwaies dimini&longs;hing equally, they in the end <lb/>determine, one in a &longs;ingle point, and the other in the Circumfe­<lb/>rence of a Circle, be it never-&longs;omuch bigger, for in this lyeth our <lb/>Wonder.</s></p><p type="margin"> <s><margin.target id="marg1022"></margin.target>Lucas Valerius, <lb/><emph type="italics"/>the other<emph.end type="italics"/> Archi­<lb/>chimedes <emph type="italics"/>of our <lb/>Age, hath written <lb/>admirably,<emph.end type="italics"/> De <lb/>Centro Gravita­<lb/>tis Solidorum.</s></p><p type="main"> <s>SAGR. </s> <s>The Demon&longs;tration is as ingenious, as the reflection <lb/>grounded upon it is admirable. </s> <s>Now let us hear &longs;omewhat about <lb/>the other Doubt &longs;ugge&longs;ted by <emph type="italics"/>Simplicius,<emph.end type="italics"/> if you have any particu­<lb/>lars worth note to hint thereupon, but I &longs;hould incline to think it <lb/>impo&longs;&longs;ible to be, in regard it is a Controver&longs;ie that hath been &longs;o <lb/>canva&longs;&longs;ed.</s></p><p type="main"> <s>SALV. </s> <s>You &longs;hall have &longs;ome of my particular thoughts thereon; <lb/>fir&longs;t repeating what but even now I told you, namely, that Infini­<lb/>ty alone, as al&longs;o Indivi&longs;ibility, are things incompre hen&longs;ible to us: <lb/>now think how they will be conjoyned together: and yet if you <lb/>would compound the Line of indivi&longs;ible points, you mu&longs;t make <lb/>them infinite; and thus it will be requi&longs;ite to apprehend in the <lb/>&longs;ame in&longs;tant both Infinite, and Indivi&longs;ible. </s> <s>The things that ar &longs;e­<lb/>veral times have come into my mind, on this occa&longs;ion, are many; <lb/>part whereof, and the more con&longs;iderable, it may be, I cannot upon <lb/>&longs;uch a &longs;udden remember; but it may happen, that in the &longs;equal <lb/>of the Di&longs;cour&longs;e, coming to put que&longs;tions and doubts to you, and <lb/>particularly to <emph type="italics"/>Simplicius,<emph.end type="italics"/> they may, on the other &longs;ide, re-mind <lb/>me of that, which without &longs;uch excitement would have lain dor­<lb/>mant in my Fancy: and therefore, with my wonted freedom, per­<lb/>mit me that I produce any wild conjectures, for &longs;uch may we fitly <lb/>call them in compari&longs;on of &longs;upernatural Doctrines, the only true <lb/>and certain determiners of our Controver&longs;ies, and unerring guides <lb/>in our ob&longs;cure, and dubious paths, or rather Laberinths.</s></p><p type="main"> <s>Among&longs;t the fir&longs;t In&longs;tances that are wont to be produced <lb/><arrow.to.target n="marg1023"></arrow.to.target><lb/>again&longs;t tho&longs;e that compound <emph type="italics"/>Continuum<emph.end type="italics"/> of Indivi&longs;ibles, this is u&longs;u­<lb/>ally one; That an Indivi&longs;ible, added to another Indivi&longs;ible, produ­<lb/>ceth not a thing divi&longs;ible; for if that were &longs;o, it would follow, that <lb/>even the Indivi&longs;ibles were divi&longs;ible: for if two Indivi&longs;ibles, as for <lb/>example, two Points conjoyned, &longs;hould make a Quantity that <lb/>&longs;hould be a divi&longs;ible Line, much more &longs;uch &longs;hould one be that is <lb/>compounded of three, five, &longs;even, or others, that are odd num­<lb/>bers; the which Lines, being to be cut in two equal parts, render <lb/>divi&longs;ible that Indivi&longs;ible which was placed in the middle. </s> <s>In this <pb xlink:href="040/01/718.jpg" pagenum="26"/>and other Objections of this kind you may &longs;atisfie the propo&longs;er of <lb/>them, telling him, that neither two Indivi&longs;ibles, nor ten, nor an <lb/>hundred, no, nor a thou&longs;and can compound a Magnitude divi&longs;ible, <lb/>and quantitative, but being infinite they may.</s></p><p type="margin"> <s><margin.target id="marg1023"></margin.target>Continuum <emph type="italics"/>com­<lb/>pounded of Indivi­<lb/>&longs;ibles.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>Here already ri&longs;eth a doubt, which I think unre&longs;olvable; <lb/>and it is, that we being certain to find Lines one bigger than ano­<lb/>ther, although both contain infinite Points, we mu&longs;t of nece&longs;&longs;ity <lb/>confe&longs;s, that we have found in the &longs;ame Species a thing bigger than <lb/>infinite; becau&longs;e the Infinity of the Points of the greater Line, &longs;hall <lb/>exceed the Infinity of the Points of the le&longs;&longs;er. </s> <s>Now this a&longs;&longs;igning <lb/>of an Infinite bigger than an Infinite is, in my opinion, a conceit <lb/>that can never by any means be apprehended.</s></p><p type="main"> <s>SALV. </s> <s>The&longs;e are &longs;ome of tho&longs;e difficulties, which re&longs;ult from <lb/>the Di&longs;cour&longs;es that our finite Judgments make about Infinites, gi­<lb/>ving them tho&longs;e attributes which we give to things finite and ter­<lb/>minate; which I think is inconvenient; for I judge that the&longs;e <lb/>terms of Majority, Minority, and Equality &longs;ute not with Infinites, <lb/>of which we cannot &longs;ay that one is greater, or le&longs;s, or equal to ano­<lb/>ther: for proof of which there cometh to my mind a Di&longs;cour&longs;e, <lb/>which, the better to explain, I will propound by way of Interroga­<lb/>tories to <emph type="italics"/>Simplicius<emph.end type="italics"/> that &longs;tarted the que&longs;tion.</s></p><p type="main"> <s>I &longs;uppo&longs;e that you very well under&longs;tand which are Square Num­<lb/>bers, and which not Square.</s></p><p type="main"> <s>SIMP. </s> <s>I know very well, that the Square Number is that which <lb/>proceeds from the multiplication of another Number into it &longs;elf; <lb/>and &longs;o four, and nine, are Square Numbers, that ari&longs;ing from two, <lb/>and this from three multiplied into them&longs;elves.</s></p><p type="main"> <s>SALV. </s> <s>Very well; And you know al&longs;o, that as the Products are <lb/>called Squares: the Produ&longs;ors, that is, tho&longs;e that are multiplied, are <lb/>called Sides, or Roots; and the others, which proceed not from <lb/>Numbers multiplied into them&longs;elves, are not Squares. </s> <s>So that if I <lb/>&longs;hould &longs;ay, all Numbers comprehending the Square, and the not <lb/>Square Numbers, are more than the Square alone, I &longs;hould &longs;peak a <lb/>mo&longs;t unque&longs;tionable truth: Is it not &longs;o?</s></p><p type="main"> <s>SIMP. </s> <s>It cannot be denied.</s></p><p type="main"> <s>SALV. </s> <s>Farther que&longs;tioning, if I ask you how many are the <lb/>Numbers Square, you can an&longs;wer me truly, that they be as many, <lb/>as are their propper Roots; &longs;ince every Square hath its Root, and <lb/>every Root its Square, nor hath any Square more than one &longs;ole <lb/>Root, or any Root more than one &longs;ole Square.</s></p><p type="main"> <s>SIMP. True.<lb/><arrow.to.target n="marg1024"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1024"></margin.target><emph type="italics"/>An Infinite Num­<lb/>ber, as it contains <lb/>infinite Square <lb/>and Cupe Roots, &longs;o <lb/>it conta neth infi­<lb/>nite Square and <lb/>Cube Numbers.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>But if I &longs;hall demand how many Roots there be, you <lb/>cannot deny but that they be as many as all Numbers, &longs;ince there <lb/>is no Number that is not the Root of &longs;ome Square: And this be­<lb/>ing granted, it is requi&longs;ite to affirm, that Square Numbers are as <pb xlink:href="040/01/719.jpg" pagenum="27"/>many as their Roots, and Roots are all Numbers: and yet in the <lb/>beginning we &longs;aid, that all Numbers are far more than all Squares, <lb/>the greater part not being Squares: and yet neverthele&longs;s the num­<lb/>ber of the Squares goeth dimini&longs;hing alwaies with greater propor­<lb/>tion, by how much the greater number it ri&longs;eth to; for in an hun­<lb/>dred there are ten Squares, which is as much as to &longs;ay, the tenth <lb/>part are Squares: in ten thou&longs;and only the hundredth part are <lb/>Squares: in a Million only the thou&longs;andth, and yet in an Infinite <lb/>Number, if we are able to comprehend it, we may &longs;ay the Squares <lb/>are as many, as all Numbers put together.</s></p><p type="main"> <s>SAGR. </s> <s>What is to be re&longs;olved then on this occa&longs;ion?</s></p><p type="main"> <s>SALV. </s> <s>I &longs;ee no other deci&longs;ion that it may admit, but to &longs;ay, <lb/>that all Numbers are infinite, Squares are infinite, their Roots are <lb/>infinite; and that neither is the multitude of Squares le&longs;s than all <lb/>Numbers, nor this greater than that: and in conclu&longs;ion, that the <lb/>Attributes of Equality, Majority, and Minority, have no place <lb/>in Infinites, but only in terminate quantities. </s> <s>And therefore when <lb/><emph type="italics"/>Simplicius<emph.end type="italics"/> propoundeth to me many unequal <emph type="italics"/>L<emph.end type="italics"/>ines, and demand­<lb/>eth of me, how it can be, that in the greater there are no more <lb/>Points than in the le&longs;s: I an&longs;wer him, That there are neither more, <lb/>nor le&longs;s, nor ju&longs;t &longs;o many; but in each of them infinite. </s> <s>Or if I <lb/>had an&longs;wered him, that the Points in one, are as many as there are <lb/>Square Numbers; in another bigger, as many as all Numbers; in <lb/>a le&longs;s, as many as the Cubick Numbers, might not I have given &longs;a­<lb/>tisfaction, by a&longs;&longs;igning more to one, than to another, and yet to <lb/>every one infinite? </s> <s>And thus much as to the fir&longs;t difficulty.</s></p><p type="main"> <s>SAGR. Hold, I pray you, and give me leave to add unto what hath <lb/>been &longs;poken hitherto, a thought which I ju&longs;t now light on, and it <lb/>is this, that granting what hath been &longs;aid, me-thinks, that not on­<lb/>ly it's improper to &longs;ay, one Infinite is greater than another Infinite, <lb/>but al&longs;o, that it's greater than a Finite; for if an Infinite Number <lb/>were greater, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> than a Million; it would thereupon follow, <lb/>that pa&longs;&longs;ing from the Million to others, and &longs;o to others continual­<lb/>ly greater, one &longs;hould pa&longs;s on towards Infinity; which is not &longs;o: but <lb/>on the contrary, to how much the greater Numbers we go, &longs;o <lb/>much the more we depart from Infinite Number; becau&longs;e in Num­<lb/>bers, the greater you take, &longs;o much the rarer and rarer alwaies are <lb/>Square Numbers contained in them; but in Infinite Number the <lb/>Squares can be no le&longs;s than all Numbers, as but ju&longs;t now was con­<lb/>cluded: therefore the going towards Numbers alwaies greater, and <lb/>greater, is a departing farther from Infinite Number.</s></p><p type="main"> <s>SALV. </s> <s>And &longs;o by your ingenious Di&longs;cour&longs;e we may conclude, <lb/>that the Attributes of Greater, Le&longs;&longs;er, or Equal, have no place, <lb/>not only among&longs;t Infinites; but al&longs;o betwixt Infinites, and Fi­<lb/>nites.</s></p><pb xlink:href="040/01/720.jpg" pagenum="28"/><p type="main"> <s>I pa&longs;s now to another Con&longs;ideration; and it is, that in regard <lb/>that the Line, and every continued quantity are divideable conti­<lb/>nually into divi&longs;ibles, I &longs;ee not how we can avoid granting that the <lb/>compo&longs;ition is of infinite Indivi&longs;ibles: becau&longs;e a divi&longs;ion and &longs;ub­<lb/>divi&longs;ion that may be pro&longs;ecuted perpetually &longs;uppo&longs;eth that the <lb/>parts are infinite; for otherwi&longs;e the &longs;ubdivi&longs;ion would be termina­<lb/>ble: and the parts being Infinite, it followeth of con&longs;equence <lb/>that they be non-quantitative; for infinite quantitative parts make <lb/>an infinite exten&longs;ion: and thus we have a <emph type="italics"/>Continuum<emph.end type="italics"/> compoun­<lb/>ded of infinite Indivi&longs;ibles.</s></p><p type="main"> <s>SIMP. </s> <s>But if we may continually pro&longs;ecute the divi&longs;ion in <lb/>quantitative parts, what need have we, for &longs;uch re&longs;pect, to intro­<lb/>duce the non-quantitative?</s></p><p type="main"> <s>SALV. </s> <s>The very po&longs;&longs;ibility of perpetually pro&longs;ecuting the di­<lb/>vi&longs;ion in quantitative parts induceth the nece&longs;&longs;ity of the compo&longs;iti­<lb/>on of infinite non-quantitative. </s> <s>Therefore, coming clo&longs;er to you, <lb/>I demand you to tell me re&longs;olutely, whether the quantitative parts <lb/>in <emph type="italics"/>Continuum<emph.end type="italics"/> be in your judgment finite or infinite?</s></p><p type="main"> <s>SIMP. </s> <s>I reply, that they are both Infinite, and Finite; Infinite <lb/>in Power, and Finite in Act. </s> <s>Infinite in Power, that is, before the <lb/>Divi&longs;ion; but Finite in Act, that is, after they are divided: for the <lb/>parts are not actually under&longs;tood to be in the whole, till it is di­<lb/>vided, or at lea&longs;t marked; otherwi&longs;e we &longs;ay that they are in <lb/>Power.</s></p><p type="main"> <s>SALV. </s> <s>So that a Line <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> twenty foot long, is not &longs;aid to <lb/>contain twenty Lines of one foot a piece, actually, but only after <lb/>it is divided into twenty equal parts: but is till then &longs;aid to contain <lb/>them only in power. </s> <s>Now be it as you plea&longs;e; and tell me whe­<lb/>ther, when the actual Divi&longs;ion of &longs;uch parts is made, that fir&longs;t <lb/>whole encrea&longs;eth or dimini&longs;heth, or el&longs;e continueth of the &longs;ame <lb/>bigne&longs;s?</s></p><p type="main"> <s>SIMP. </s> <s>It neither encrea&longs;eth, nor dimini&longs;heth.</s></p><p type="main"> <s>SALV. </s> <s>So I think al&longs;o. </s> <s>Therefore the quantitative parts in <emph type="italics"/>Con­<lb/>tinuum<emph.end type="italics"/> quantity, be they in Act, or be they in Power, make not its <lb/>quantity bigger or le&longs;&longs;er: but it is very plain that the&longs;e quantita­<lb/>tive parts, actually contained in their whole, if they be infinite, <lb/>make it an infinite Magnitude; therefore quantitative parts, <lb/>though infinite only in power, cannot be contained, but only in an <lb/>infinite Magnitude: therefore in a finite Magnitude infinite quan­<lb/>titative parts can be contained neither in Act, nor Power.</s></p><p type="main"> <s>SAGR. </s> <s>How then can it be true, that the <emph type="italics"/>Continuum<emph.end type="italics"/> may be <lb/>ince&longs;&longs;antly divided into parts &longs;till capable of new divi&longs;ions?</s></p><p type="main"> <s>SALV. </s> <s>It &longs;eems that that di&longs;tinction of Power, and Act, makes <lb/>that fea&longs;ible one way, which another way would be impo&longs;&longs;ible. <lb/></s> <s>But I will &longs;ee to adju&longs;t the&longs;e matters by making another account: <pb xlink:href="040/01/721.jpg" pagenum="29"/>And to the Que&longs;tion, which was put, Whether the quantitative <lb/>parts in a terminated <emph type="italics"/>Continuum<emph.end type="italics"/> be finite or infinite; I will an&longs;wer <lb/>directly contrary to that which <emph type="italics"/>Simplicius<emph.end type="italics"/> replied, namely, that <lb/>they be neither finite, nor infinite.</s></p><p type="main"> <s>SIMP. </s> <s>I &longs;hould never have found &longs;uch an an&longs;wer, not imagi­<lb/>ning that there was any mean term between finite and infinite; <lb/>&longs;o that the divi&longs;ion or di&longs;tinction which makes a thing to be either <lb/>Finite, or Infinite, is imperfect and deficient.</s></p><p type="main"> <s>SALV. </s> <s>In my opinion it is; and &longs;peaking of ^{*} Di&longs;crete Quan­</s></p><p type="main"> <s><arrow.to.target n="marg1025"></arrow.to.target><lb/>tities, me thinks that there is a third mean term between Finite and <lb/>Infinite, which is that which an&longs;wereth to every a&longs;&longs;igned Number: <lb/>So that being demanded in our pre&longs;ent ca&longs;e, Whether the quanti­<lb/>tative parts in <emph type="italics"/>Continuum<emph.end type="italics"/> be Finite, or Infinite, the mo&longs;t congru­<lb/>ous reply is to &longs;ay, that they are neither Finite, nor Infinite, but &longs;o <lb/>many, as that they <emph type="italics"/>An&longs;wer<emph.end type="italics"/> to any number a&longs;&longs;igned: the which to <lb/>do, it is nece&longs;&longs;ary that they be not comprehended in a limited <lb/>Number, for then they would not an&longs;wer to a greater: nor, again, <lb/>is it nece&longs;&longs;ary, that they be infinite, for no a&longs;&longs;igned Number is infi­<lb/>nite. </s> <s>And thus at the plea&longs;ure of the Demander, a Line being <lb/>propounded, we may be able to a&longs;&longs;ign in it an hundred quantita­<lb/>tive parts, or a thou&longs;and, or an hundred thou&longs;and, according to <lb/>the number which he be&longs;t likes; &longs;o that it be not divided into in­<lb/>finite. </s> <s>I grant therefore to the Philo&longs;ophers, that <emph type="italics"/>Continuum<emph.end type="italics"/> con­<lb/>taineth as many quantitative parts as they plea&longs;e, and grant them <lb/>that it containeth the &longs;ame either in Act, or in Power, which they <lb/>be&longs;t like: but this I add again, that in like manner, as in a Line of <lb/>ten yards, there are contained ten Lines of one yard a piece, and <lb/>thirty Lines of a foot a piece, and three hundred and &longs;ixty Lines <lb/>of an inch a piece, &longs;o it contains infinite Points; denominate them <lb/>in Act, or in Power, as you will: and I remit my &longs;elf in this matter <lb/>to your opinion and judgment, <emph type="italics"/>Simplicius.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1025"></margin.target><emph type="italics"/>Quantitative parts <lb/>in Di&longs;crete Quan­<lb/>tity are neither fi­<lb/>nite nor infinite, <lb/>but an&longs;werable to <lb/>every given Num­<lb/>ber.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>I cannot but commend your Di&longs;cour&longs;e: but am great­<lb/>ly afraid, that this parity of the Points, being contained in the like <lb/>manner as the quantitative parts, will not agree with ab&longs;olute ex­<lb/>actne&longs;s; nor &longs;hall it be &longs;o ea&longs;ie a matter for you to divide the gi­<lb/>ven Line into infinite Points, as for tho&longs;e Philo&longs;ophers to divide it <lb/>into ten yards, or thirty feet, nay, I hold it wholly impo&longs;&longs;ible to <lb/>effect &longs;uch a divi&longs;ion: &longs;o that this will be one of tho&longs;e Powers that <lb/>are never reduced to Act.</s></p><p type="main"> <s>SALV. </s> <s>The trouble, pains, and long time without which a <lb/>thing is not fea&longs;ible, render it not impo&longs;&longs;ible; for I think al&longs;o, that <lb/>you cannot &longs;o ea&longs;ily effect a divi&longs;ion to be made of a Line into a <lb/>thou&longs;and parts; and much le&longs;s being to divide it into 937, or &longs;ome <lb/>other great Prime Number. </s> <s>But if I di&longs;patch this, which you, it may <lb/>be, judge an impo&longs;&longs;ible divi&longs;ion, in as &longs;hort a time, as another <pb xlink:href="040/01/722.jpg" pagenum="30"/>would require to divide it into forty, you will be content more <lb/>willingly to admit of it in our future Di&longs;cour&longs;e?</s></p><p type="main"> <s>SIMP. </s> <s>I am plea&longs;ed with your way of arguing, as you now do <lb/>mix it with &longs;ome plea&longs;antne&longs;s: and to your que&longs;tion I reply, that <lb/>the facility would &longs;eem more than &longs;ufficient, if the re&longs;olving it into <lb/>Points were but as ea&longs;ie, as to divide it into a thou&longs;and parts.</s></p><p type="main"> <s>SALV. </s> <s>Here I will tell you a thing, which haply will make you <lb/>wonder in this matter of going about, or being able to re&longs;olve the <lb/>Line into its Infinites, keeping that order which others ob&longs;erve in <lb/>dividing it into forty, &longs;ixty, or an hundred parts; namely, by di­<lb/>viding it fir&longs;t into two, then into four: in which order he that <lb/>&longs;hould think to find its infinite Points would gro&longs;ly delude him&longs;elf; <lb/>for by that progre&longs;&longs;ion, though continued to eternity, he &longs;hould <lb/>never arrive to the divi&longs;ion of all its quantitative parts: yea, he is <lb/>in that way &longs;o far from being able to arrive at the intended term <lb/>of Indivi&longs;ibility, that he rather goeth farther from it; and whil&longs;t <lb/>he thinks by continuing the divi&longs;ion, and multiplying the multi­<lb/>tudes of the parts, to approach to Infinite, I am of opinion, that he <lb/>more and more removes from it: and my rea&longs;on is this; In the <lb/>Di&longs;cour&longs;e, we had even now, we concluded, that, in an infinite <lb/>Number, there was, of nece&longs;&longs;ity, as many Square, or Cube Num­<lb/>bers, as there were Numbers; &longs;ince that tho&longs;e and the&longs;e were as ma­<lb/>ny as their Roots, and Roots comprehend all Numbers: Next we <lb/>did &longs;ee, that the greater the Numbers were that were taken, the <lb/>&longs;eldomer are their Squares to be found in them, and &longs;eldomer yet <lb/>their Cubes: Therefore it is manife&longs;t, that the greater the Number <lb/>is to which you pa&longs;s, the farther you remove from Infinite Num­<lb/>ber: from whence it followeth, that turning backwards, (&longs;eeing <lb/>that &longs;uch a progre&longs;&longs;ion more removes us from the de&longs;ired term) if <lb/><arrow.to.target n="marg1026"></arrow.to.target><lb/>any number may be &longs;aid to be infinite it is the Unite: and, indeed, <lb/>there are in it tho&longs;e conditions, and nece&longs;&longs;ary qualities of the Infi­<lb/>nite Number, I mean, of containing in it as many Squares as Cubes, <lb/>and as Numbers.</s></p><p type="margin"> <s><margin.target id="marg1026"></margin.target><emph type="italics"/>The Unite of all <lb/>Numbers may <lb/>mo&longs;t properly be <lb/>&longs;aid to be Infinite.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>I do not apprehend very well, how this bu&longs;ine&longs;s &longs;hould <lb/>be under&longs;tood.</s></p><p type="main"> <s>SALV. </s> <s>The thing hath no difficulty at all in it, for the Unite <lb/>is a Square, a Cube, a Squared Square, and all other Powers; nor <lb/>is there any particular what&longs;oever e&longs;&longs;ential to the Square, or to the <lb/>Cube, which doth not agree with the Unite; as <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> one proper­<lb/>ty of two Square-numbers is to have between them a Number <lb/>mean-proportional; take any Square number for one of the terms, <lb/>and the Unite for the other, and you &longs;hall likewi&longs;e ever find be­<lb/>tween them a Number Mean-proportional. </s> <s>Let the two Square <lb/>Numbers be 9 and 4, you &longs;ee that between 9 and 1 the Mean­<lb/>proportional is 3, and between 4 and 1 the Mean-proportional <pb xlink:href="040/01/723.jpg" pagenum="31"/>is 2, and between the two Squares 9 and 4, 6 is the Mean. </s> <s>The <lb/>property of Cubes is to have nece&longs;&longs;arily between them two Num­<lb/>bers Mean-proportional. </s> <s>Suppo&longs;e 8, and 27, the Means between <lb/>them are 12 and 18; and between the Unite and 8 the Means <lb/>are 2 and 4; betwixt the Unite and 27 there are 3, and 9. We <lb/>therefore conclude, <emph type="italics"/>That there is no other Infinite Number but the <lb/>Vnite.<emph.end type="italics"/> And the&longs;e be &longs;ome of tho&longs;e Wonders, that &longs;urmount the <lb/>comprehen&longs;ion of our Imagination, and that advertize us how ex­<lb/>ceedingly they err, who di&longs;cour&longs;e about Infinites with tho&longs;e very <lb/>Attributes, that are u&longs;ed about Finites; the Natures of which have <lb/>no congruity with each other. </s> <s>In which affair I will not conceal <lb/>from you an admirable accident, that I met with &longs;ome time &longs;ince, <lb/>explaining the va&longs;t difference, yea, repugnance and contrariety of <lb/>Nature, that a terminate quantity would incur by changing or pa&longs;­<lb/>&longs;ing into Infinite. </s> <s>We a&longs;&longs;ign this Right Line A B, of any length at <lb/>plea&longs;ure, and any point in the &longs;ame, as C being taken, dividing it <lb/>into two unequal parts: I &longs;ay, that many couples Lines, (hold­<lb/>ing the &longs;ame proportion between them&longs;elves as have the parts <lb/>A C, and B C,) departing from the terms A and B to meet with <lb/>one another; the points of their Inter&longs;ection &longs;hall all fall in the <lb/>Circumference of one and the &longs;ame Circle: as for example, A L <lb/>and B L departing [or <emph type="italics"/>being drawn<emph.end type="italics"/>] from the Points A and B, and <lb/>having between them&longs;elves the &longs;ame proportion, as have the parts <lb/>A C and B C, and concurring in the point L: and the &longs;ame pro­<lb/>portion being between two others A K, and B K, concurring in K, <lb/>al&longs;o others as A I, and B I; A H, and B H; A G, and B G; A F, <lb/>and B F; A E, and B E: I &longs;ay, that the points of their Inter&longs;ecti­<lb/>on L, K, I, H, G, F, E, do all fall in the Circumference of one <lb/>and the &longs;ame Semi-circle: &longs;o that we &longs;hould imagine the point <lb/>C to mve conti­<lb/><figure id="id.040.01.723.1.jpg" xlink:href="040/01/723/1.jpg"/><lb/>nuallyafter &longs;uch <lb/>a &longs;ort, that the <lb/>Lines produced <lb/>from it to the fix­<lb/>ed terms A and <lb/>B retain alwaies <lb/>the &longs;ame propor­<lb/>tion that is be­<lb/>tween the fir&longs;t <lb/>parts A C and C B, that point C &longs;hall decribe the Circumference <lb/>of a Circle, as we &longs;hall &longs;hew you pre&longs;ently. </s> <s>And the Circle in &longs;uch <lb/>&longs;ort de&longs;cribed &longs;hall be alwaies greater and greater &longs;ucce&longs;&longs;ively, <lb/>according as the point C is taken nearer to the middle point <lb/>which is O; and the Circle &longs;hall be le&longs;&longs;er which &longs;hall be de&longs;cribed <lb/>from a point nearer to the extremity B, in&longs;omuch, that from the <pb xlink:href="040/01/724.jpg" pagenum="32"/>infinite Points which may be taken in the Line O B, there may be <lb/>de&longs;cribed Circles (moving them in &longs;uch &longs;ort as above is pre&longs;cri­<lb/>bed) of any Magnitude; le&longs;&longs;er than the Pupil of the eye of a <lb/>Flea, and bigger than the Equinoctial of the <emph type="italics"/>Primum Mobile.<emph.end type="italics"/><lb/>Now, if rai&longs;ing any of the Points comprehended betwixt the terms <lb/>O and B, from every one we may de&longs;cribe Circles, and va&longs;t ones <lb/>from the Points nearer to O; then if we rai&longs;e the Point O it &longs;elf, <lb/>and continue to move it in &longs;uch &longs;ort as afore&longs;aid, that is, that the <lb/>Lines drawn from it to the terms A and B keep the &longs;ame proporti­<lb/>on as have the fir&longs;t Lines A O, and O B, what Line &longs;hall be de&longs;cri­<lb/>bed? </s> <s>There would be de&longs;cribed the Circumference of a Circle, <lb/>but of a Circle bigger than the bigge&longs;t of all Circles, therefore of <lb/>a Circle that is infinite: but it doth al&longs;o de&longs;cribe a Right Line, and <lb/>perpendicular upon A B, erected from the Point O, and produced <lb/><emph type="italics"/>in infinitum<emph.end type="italics"/> without ever turning to reunite its la&longs;t term with the <lb/>fir&longs;t, as the others did; for the limited motion of the Point C, after <lb/>it had de&longs;igned the upper Semi-circle C H E, continued to de­<lb/>&longs;cribe the Lower E M C, reuniting its extream terms in the point <lb/>C: But the Point O being moved to de&longs;ign (as all the other Points <lb/>of the Line A B, for the Points taken in the other part O A <lb/>&longs;hall de&longs;ign their Circles, and tho&longs;e Points neare&longs;t to O the <lb/>greate&longs;t) its Circle; to make it the bigge&longs;t of all, and con&longs;e­<lb/>quently infinite, it can never return any more to its fir&longs;t term, and <lb/><arrow.to.target n="marg1027"></arrow.to.target><lb/>in a word de&longs;igneth an Infinite Right-Line for the Circumference <lb/>of its Infinite Circle. </s> <s>Con&longs;ider now, what difference there is be­<lb/>tween a finite Circle, and an infinite; &longs;eeing that this in &longs;uch man­<lb/>ner changeth its being that it wholly lo&longs;eth both its being, and <lb/>power of being; for we have already well comprehended, that <lb/>there cannot be a&longs;&longs;igned an infinite Circle; by which we may <lb/>con&longs;equently know that there can be no infinite Sphære, or other <lb/>Body, or figured Superficies. </s> <s>Now what &longs;hall we &longs;ay to this Meta­<lb/>morpho&longs;is in pa&longs;&longs;ing from Finite to Infinite? </s> <s>And why &longs;hould we <lb/>find greater repugnance, whil&longs;t &longs;eeking Infinity in Numbers, we <lb/><arrow.to.target n="marg1028"></arrow.to.target><lb/>come to conclude it to be in the Unite? </s> <s>And whil&longs;t that breaking <lb/>a Solid into many pieces, and pur&longs;uing to reduce it into very &longs;mall <lb/>powder, it were re&longs;olved into its infinite Atomes, admitting no far­<lb/>ther divi&longs;ion, why may we not &longs;ay that it is returned into one &longs;ole <lb/><emph type="italics"/>Continuum,<emph.end type="italics"/> but perhaps fluid, as the Water, or Quick&longs;ilver, or <lb/>other Metall melted? </s> <s>And do we not &longs;ee Stones liquified into <lb/>Gla&longs;s, and Gla&longs;s it &longs;elf with much Fire to become more fluid than <lb/>Water?</s></p><p type="margin"> <s><margin.target id="marg1027"></margin.target><emph type="italics"/>The difference be­<lb/>twixt a finite and <lb/>infinite Circle.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1028"></margin.target><emph type="italics"/>Vnity participates <lb/>of Infinity.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>Should we therefore think Fluids to be &longs;o called, be­<lb/>cau&longs;e they are re&longs;olved into their fir&longs;t, infinite, indivi&longs;ible com­<lb/>pounding parts?</s></p><p type="main"> <s>SALV. </s> <s>I know not how to find a better an&longs;wer to re&longs;olve cer­<pb xlink:href="040/01/725.jpg" pagenum="33"/>tain &longs;en&longs;ible appearances, among&longs;t which this is one: When I take <lb/>a hard Body, be it either Stone, or Metal, and with a Hammer, or <lb/>very fine File, endeavour to divide it, as much as is po&longs;&longs;ible, into <lb/>its mo&longs;t minute and impalpable powder; it is very clear, that its <lb/>lea&longs;t Atomes, albeit for their &longs;malne&longs;s they are imperceptible, one by <lb/>one, to our &longs;ight and touch; yet are they quantitative, figured, and <lb/>numerable: and it happens in them, that being accumulated to­<lb/>gether, they continue in heap; and being laid hollow, or with a <lb/>pit in the mid&longs;t, the hollowne&longs;s or pit remains, the parts heaped <lb/>about it not returning to fill it up; and being &longs;tirr'd, or &longs;haken, <lb/>they &longs;uddenly &longs;ettle &longs;o &longs;oon as their external mover leaves them, <lb/>And the like effects are &longs;een in all the Aggregates of &longs;mall Bodies, <lb/>bigger, and bigger, and of any kind of Figure, although Sphærical; <lb/>as we &longs;ee in heaps of Pea&longs;e, Wheat, Bird &longs;hot, and other matters. </s> <s>But <lb/>if we try to find the like accidents in Water, you will meet with <lb/>none of them; but, being rai&longs;ed, it in&longs;tantly returns to a level, if <lb/>it be not by a ve&longs;&longs;el, or &longs;ome other external &longs;tay upheld; being <lb/>made hollow, it pre&longs;ently diffu&longs;eth to fill up the Cavity; and be­<lb/>ing long moved, it continually undulates, and &longs;preads its waves very <lb/>far. </s> <s>From this, I think, we may very rationally infer, that the minute <lb/><arrow.to.target n="marg1029"></arrow.to.target><lb/>parts of Water, into which it &longs;eemeth to be re&longs;olved, (&longs;ince it hath <lb/>le&longs;s con&longs;i&longs;tence than any the fine&longs;t powder, yea, hath no con&longs;i­<lb/>&longs;tence at all) are va&longs;tly differing from Atomes quantitative and <lb/>divi&longs;ible; nor know I how to find any other difference therein <lb/>than that of being indivi&longs;ible. </s> <s>Methinks, al&longs;o, that its mo&longs;t exqui­<lb/>&longs;ite tran&longs;parency, affords us &longs;ufficient grounds to conjecture there­<lb/>of; for if we take the mo&longs;t diaphanous Chri&longs;tal that is, and begin <lb/>to break, and pound it to powder, when it is in powder it lo&longs;eth <lb/>its tran&longs;parency, and &longs;o much the more, the &longs;maller it is pounded; <lb/>but yet Water which is ground to the highe&longs;t degree, hath al&longs;o the <lb/>highe&longs;t degree of Diaphaneity Gold and Silver, reduced by <emph type="italics"/>Aqua­<lb/>fortis<emph.end type="italics"/> into a &longs;maller Powder than any File can make, yet they con­<lb/>tinue powder, and become not fluid; nor do they liquifie till the <lb/>Indivi&longs;ibles of the Fire, or of the Sun-beams di&longs;&longs;olve them, as, I be­<lb/>lieve, into their fir&longs;t and highe&longs;t infinite and indivi&longs;ible compoun­<lb/>ding parts.</s></p><p type="margin"> <s><margin.target id="marg1029"></margin.target><emph type="italics"/>Fluid Bodies are <lb/>&longs;uch, for that they <lb/>are re&longs;olved into <lb/>their fir&longs;t Indivi&longs;i­<lb/>ble Atomes.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>This which you have hinted of the Light I have many <lb/>times ob&longs;erved with admiration: I have &longs;een, I &longs;ay, a burning­<lb/>Gla&longs;s, of a foot Diameter, liquifie or melt lead in an in&longs;tant; <lb/>whence I came to be of opinion, that if the Gla&longs;&longs;es were very big, <lb/>and very polite, and of Parabolical Figure, they would no le&longs;s melt <lb/>every other Metal in a very &longs;hort time; &longs;eeing that that, not very <lb/>big, nor very clear, and of a Sphærical Concave, with &longs;uch force <lb/>melted Lead, and burnt every combu&longs;tible matter: effects, that <lb/>make the wonders, reported of the Burning-gla&longs;&longs;es of <emph type="italics"/>Archimedes,<emph.end type="italics"/><lb/>credible to me.<pb xlink:href="040/01/726.jpg" pagenum="34"/><arrow.to.target n="marg1030"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1030"></margin.target>Archimedes <emph type="italics"/>his <lb/>Burning — Gla&longs;&longs;es <lb/>admirable.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Touching the Effects of the Gla&longs;&longs;es, invented by <emph type="italics"/>Ar­<lb/>chimedes,<emph.end type="italics"/> all the Miracles, that &longs;everal Writers record of them, <lb/>are to me rendred credible by the reading of <emph type="italics"/>Archimedes<emph.end type="italics"/> his own <lb/>Books, which I have with infinite amazement peru&longs;ed and &longs;tudied: <lb/>and if any doubts had been left me; that which la&longs;t of all Father </s></p><p type="main"> <s><arrow.to.target n="marg1031"></arrow.to.target><lb/><emph type="italics"/>Buonaventura Cavalieri<emph.end type="italics"/> hath publi&longs;hed, touching <emph type="italics"/>Lo Specehio <lb/>V&longs;torio,<emph.end type="italics"/> (or the Burning gla&longs;s) and which I have read with ad­<lb/>miration, is &longs;ufficient to re&longs;olve them all.</s></p><p type="margin"> <s><margin.target id="marg1031"></margin.target>Buonaventura <lb/>Cavalieri, <emph type="italics"/>the Je­<lb/>&longs;uate, a famous <lb/>Mathematician, <lb/>and his Book en­<lb/>titled,<emph.end type="italics"/> Lo Spec­<lb/>chio U&longs;torio.</s></p><p type="main"> <s>SAGR. </s> <s>I have al&longs;o &longs;een that Tract, and peru&longs;ed it with much <lb/>delight and wonder; and becau&longs;e I formerly had knowledge of <lb/>the Author, I was confirmed in the opinion which I had conceived <lb/>of him, that he was like to prove one of the principal Mathemati­<lb/>cians of our Age. </s> <s>But returning to the admirable effects of the <lb/>Sun-Beams in melting of Metals, are we to believe that &longs;uch, and <lb/>&longs;o violent an operation is without Motion, or el&longs;e that it is with <lb/>Motion, but extream &longs;wift?<lb/><arrow.to.target n="marg1032"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1032"></margin.target><emph type="italics"/>Burnings are per­<lb/>formed with a mo&longs;t <lb/>&longs;wift Motion.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>We &longs;ee other burnings, and meltings to be performed <lb/>with Motion, and with a mo&longs;t &longs;wift Motion. </s> <s>Ob&longs;erve the ope­<lb/>rations of Lightnings, of Powder in Mines, and in Petards, <lb/>and, in &longs;um, how by quickning the flame of Coles, mixt with <lb/>gro&longs;s and impure vapours, by Bellows, encrea&longs;eth its force in <lb/>the melting of Metals: &longs;o that I cannot &longs;ee how the Action of <lb/>Light, albeit mo&longs;t pure, can be without Motion, and that al&longs;o ve­<lb/>ry &longs;wift.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>AGR. </s> <s>But what and how great ought we to judge this Velo­<lb/>city of the Light? </s> <s>Is it haply <emph type="italics"/>In&longs;tantaneous,<emph.end type="italics"/> and done in a moment, <lb/>or, as the re&longs;t of Motions, performed in Time? </s> <s>May we not by <lb/>Experiment be a&longs;&longs;ured what it is?</s></p><p type="main"> <s>SIMP. </s> <s>Quotidian experience &longs;hews the expan&longs;ion of Light to <lb/>be <emph type="italics"/>In&longs;tantaneous<emph.end type="italics"/>; in that beholding a Cannon, let off at a great <lb/>di&longs;tance, the fla&longs;h of the fire, without interpo&longs;ition of time, is tran&longs;­<lb/>mitted to our eye, but &longs;o is not the Report to our ear untill a con­<lb/>&longs;iderable time after.</s></p><p type="main"> <s>SAGR. True, but, I pray you, what doth this obvious experi­<lb/>ment evince; but only this, that the Report is longer in arriving at <lb/>our Ear, than the Fla&longs;h at our Eye; but it a&longs;&longs;ures me not, that the <lb/>tran&longs;mi&longs;&longs;ion of the Light is therefore <emph type="italics"/>In&longs;tantaneous<emph.end type="italics"/> rather than in <lb/>Time, but only mo&longs;t &longs;wift. </s> <s>Nor doth &longs;uch an ob&longs;ervation con­<lb/>clude more than that other, of &longs;uch who &longs;ay, that as &longs;oon as the <lb/>Sun cometh to the Horizon, its Light arriveth at our eye: for who <lb/>&longs;hall a&longs;&longs;ure me, that its beams arrive not at the &longs;aid term, afore they <lb/>reach our &longs;ight?</s></p><p type="main"> <s>SALV. </s> <s>The inconcludency of the&longs;e, and other ob&longs;ervations of <lb/>the like Nature, made me once think of &longs;ome other way, whereby <lb/>we may without errour be a&longs;certained whether the illumination, <pb xlink:href="040/01/727.jpg" pagenum="35"/>that is, whether the expan&longs;ion of the Light were really <emph type="italics"/>In&longs;tantane­<lb/>ous<emph.end type="italics"/>; &longs;eeing that the very &longs;wift Motion of Sound, a&longs;&longs;ureth us, that <lb/>that of Light cannot but be extream &longs;wift. </s> <s>And the experiment I </s></p><p type="main"> <s><arrow.to.target n="marg1033"></arrow.to.target><lb/>hit upon, was this; I would have two per&longs;ons take each of them a <lb/>Light, which, by holding it in a Lanthorn, or other coverture, they <lb/>may cover, and di&longs;cover at plea&longs;ure by interpo&longs;ing their hand to the <lb/>fight of each other; and, that placing them&longs;elvs again&longs;t one another, <lb/>&longs;ome few paces di&longs;tance, they may practice the &longs;peedy di&longs;covery, <lb/>and occultation of their Lights from the &longs;ight of each other: So <lb/>that when one &longs;eeth the others Light, he immediatly di&longs;clo&longs;e his: <lb/>which corre&longs;pondence, after &longs;ome Re&longs;pon&longs;es mutually made, will <lb/>become &longs;o exactly In&longs;tantaneous, that, without &longs;en&longs;ible variation, <lb/>at the di&longs;covery of the one, the other &longs;hall at the &longs;ame time ap­<lb/>pear to the &longs;ight of him that di&longs;clos'd the fir&longs;t. </s> <s>Having adju&longs;ted <lb/>this practice at this &longs;mall di&longs;tance, let us place the two per&longs;ons with <lb/>two &longs;uch Lights at two or three miles di&longs;tance; and by night re­<lb/>newing the &longs;ame experiment; Let them inten&longs;ely ob&longs;erve if the <lb/>Re&longs;pon&longs;es of the di&longs;clo&longs;ures, and occultations do follow the &longs;ame <lb/>tenour which they did near hand: for if they keep the &longs;ame pro­<lb/>portion, it may be with certainty enough concluded, that the ex­<lb/>pan&longs;ion of Light is In&longs;tantaneous; but if it &longs;hould require time in <lb/>a di&longs;tance of three miles, which importeth &longs;ix for the going of <lb/>one, and return of the other, the &longs;tay would be &longs;ufficiently ob&longs;er­<lb/>vable. </s> <s>And if this Experiment be made at greater di&longs;tances, <lb/>namely, at eight or ten miles, we may make u&longs;e of the <emph type="italics"/>Tele&longs;cope,<emph.end type="italics"/><lb/>the Ob&longs;ervators accommodating each of them one at the places, <lb/>where by night the Lights are to be ob&longs;erved; which though not <lb/>very big, and &longs;o not vi&longs;ible, at that great di&longs;tance, to the eye at <lb/>large; (though ea&longs;ie to be di&longs;clo&longs;ed, and hid) by help of the <lb/><emph type="italics"/>Tele&longs;copes<emph.end type="italics"/> before admitted, and fixed they may commodiou&longs;ly be <lb/>di&longs;cerned.</s></p><p type="margin"> <s><margin.target id="marg1033"></margin.target><emph type="italics"/>The Velocity of <lb/>Light, how to find <lb/>by Experiment <lb/>whether it be In­<lb/>&longs;tantaneosu or not.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>The Invention &longs;eems to me no le&longs;s certain than ingenu­<lb/>ous; but tell us what upon experimenting it you concluded.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. Really, I have not tryed it, &longs;ave only at a &longs;mall di&longs;tance, <lb/>namely, le&longs;s than a Mile: whereby I could come to no certainty <lb/>whether the apparence of the oppo&longs;ite Light was truly In&longs;tantane­<lb/>ous; But if not In&longs;tantaneous, yet it was of exceeding great Velo­<lb/>city, and I may &longs;ay Momentary: and for the pre&longs;ent, I would re­<lb/>&longs;emble it to that Motion which we &longs;ee a fla&longs;h of Lightning make <lb/>in the Clouds ten or more Miles off: of which Light we di&longs;tin­<lb/>gui&longs;h the beginning, and, I may fay, the &longs;ource and ri&longs;e of it, in a <lb/>particular place in tho&longs;e Clouds; but yet its wide expan&longs;ion imme­<lb/>diatly &longs;ucceeds among&longs;t tho&longs;e adjacent: which to me &longs;eems an ar­<lb/>gument that it is &longs;ome &longs;mall time in doing; becau&longs;e had the illu­<lb/>mination been made all at once, and not by degrees, it feems to <pb xlink:href="040/01/728.jpg" pagenum="36"/>me that we could not have di&longs;tingui&longs;hed its original, or rather the <lb/>Center of its flake, and extream Dilatations. </s> <s>But into what Oceans <lb/>do we by degrees engage our &longs;elves? </s> <s>Among&longs;t <emph type="italics"/>Vacuities, Infinites, <lb/>Indivi&longs;ibles,<emph.end type="italics"/> and <emph type="italics"/>Instantaneous Motions<emph.end type="italics"/>; &longs;o that we &longs;hall not be <lb/>able by a thou&longs;and Di&longs;cour&longs;es to recover the Shore?</s></p><p type="main"> <s>SAGR. </s> <s>They are things, indeed, very di&longs;proportionate to our <lb/>under&longs;tanding. </s> <s>Behold Infinite, &longs;ought among&longs;t Numbers, &longs;eemeth <lb/>to determine in the Unite: From Indivi&longs;ibles ari&longs;eth things that <lb/>are continually divi&longs;ible: Vacuity &longs;eems only to re&longs;ide indivi&longs;ibly <lb/>mixt with Repletion: and, in brief, the&longs;e things &longs;o change the <lb/>nature of tho&longs;e under&longs;tood by us, that even the Circumference of <lb/>a Circle becometh an Infinite Right-Line; which, if I well re­<lb/>member, is that Propo&longs;ition which you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> are to mani­<lb/>fe&longs;t by Geometrical Demon&longs;tration. </s> <s>Therefore, if you think fit, <lb/>it would be well, without any more digre&longs;&longs;ions, to make it out <lb/>to us.</s></p><p type="main"> <s>SALV. </s> <s>I am ready to &longs;erve you in demon&longs;trating the en&longs;uing <lb/>Problem for your fuller information.</s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"/>A Right-Line being given, divided, according to any <lb/>proportion, into unequal parts, to de&longs;cribe a Circle, to <lb/>the Circumference of which, at any point of the &longs;ame, <lb/>two Right-Lines being produced from the terms of <lb/>the given Right Line, they may retain the &longs;ame pro­<lb/>portion that the parts of the &longs;aid Line given have to <lb/>one another, &longs;o that tho&longs;e be Homologous which de­<lb/>part &longs;rom the &longs;ame terms.<emph.end type="italics"/></s></p><p type="main"> <s>Let the given Right-Line be AB, unequally divided ac­<lb/>cording to any proportion in the point C; it is required to <lb/>de&longs;cribe a Circle at any point of who&longs;e Circumference two <lb/>Right Lines, produced from the terms A and B, concurring, have <lb/>the &longs;ame proportion to each other, that A C, hath to B C, &longs;o that <lb/>tho&longs;e be Homologous which depart from the &longs;ame term. </s> <s>Upon <lb/>the Center C, at the di&longs;tance of the le&longs;&longs;er part C B, let a Circle be <lb/>&longs;uppo&longs;ed to be de&longs;cribed, to the Circumference of which from the <lb/>point A the Right-line A D is made a Tangent, and indetermi­<lb/>nately prolonged towards E: and let the Contact be in D, and <lb/>draw a Line from C to D, which &longs;hall be perpendicular to A E; <lb/>and let B E be perpendicular to B A, which produced, &longs;hall inter­<pb xlink:href="040/01/729.jpg" pagenum="37"/>&longs;ect A E, the Angle A being acute: Let the inter&longs;ection be in E, <lb/>from whence let fall a Perpendicular to A E, which produced, will <lb/>meet with A B infinitely prolonged in F. </s> <s>I &longs;ay, fir&longs;t, that the <lb/>Right-lines F E, and F C are equal: &longs;o that drawing the Line <lb/>E C, we &longs;hall, in the <lb/><figure id="id.040.01.729.1.jpg" xlink:href="040/01/729/1.jpg"/><lb/>two Triangles D E C, <lb/>B E C, have the two <lb/>Sides of the one, D E, <lb/>and C E, equal to the <lb/>two Sides of the other <lb/>B E, and E C; the <lb/>two Sides, D E, and <lb/>E B, being Tangents <lb/>to the Circle D B, <lb/>and the Ba&longs;es D C, <lb/>and C B, are likewi&longs;e <lb/>equal: wherefore the <lb/>two Angles D E C, <lb/>and B E C, &longs;hall be <lb/>equal. </s> <s>And becau&longs;e the Angle B C E wanteth of being a Right­<lb/>Angle, as much as the Angle B E C; and the Angle C E F, to <lb/>make it a Right-Angle, wants the Angle C E D, tho&longs;e Supple­<lb/>ments being equal, the Angles F C E, and F E C &longs;hall be equal, <lb/>and &longs;o con&longs;equently the Sides F E, and F C; wherefore making <lb/>the point F a Center, and at the di&longs;tance F E, de&longs;cribing a Circle, <lb/>it &longs;hall pa&longs;s by the point C. </s> <s>De&longs;cribe it, and let it be C E G. </s> <s>I &longs;ay, <lb/>that this is the Circle required, by any point of the Circumfe­<lb/>rence of which, any two Lines that &longs;hall inter&longs;ect, departing from <lb/>the terms A and B, &longs;hall be in proportion to each other, as are the <lb/>two parts A C, and B C, which be&longs;ore did concur in the point C. <lb/></s> <s>This is manife&longs;t in the two that concur or inter&longs;ect in the point E, <lb/>that is A E, and B E; the Angle E of the Triangle A E B being <lb/>divided in the mid&longs;t by C E; &longs;o that as A C is to C B, &longs;o is A E <lb/>to B E. </s> <s>The &longs;ame we prove in the two A G, and B G, determined <lb/>in the point G. </s> <s>Therefore being (by the Similitude of the Tri­<lb/>angles A F E, and E F B) that as A F is to E F, &longs;o is E F to F B; <lb/>that is, as A F is to F C, &longs;o is C F to F B: So by Divi&longs;ion; as A C <lb/>is to C F, (that is, to F G) &longs;o is C B to B F; and the whole A B <lb/>is to the whole B G, as the part C B to the part B F: and by Com­<lb/>po&longs;ition; as A G is to G B, &longs;o is C F to F B; that is, as E F to <lb/>F B, that is, as A E to E B, and A C to C B: Which was to be de­<lb/>mon&longs;trated. </s> <s>Again, let any other Point be taken in the Circum­<lb/>ference, as H; in which the two Lines A H and B H concur. </s> <s>I &longs;ay, in <lb/>like manner as before, that as A C is to C B, &longs;o is A H to B H. <lb/></s> <s>Continue H B untill it inter&longs;ect the Circumference in I, and draw <pb xlink:href="040/01/730.jpg" pagenum="38"/>a Line joyning I to F. </s> <s>And becau&longs;e it hath been proved already <lb/>that as A B is to B G, &longs;o is C B to B F, the Rectangle A B F &longs;hall be <lb/>equall to the Rectangle C B G, that is I B H: and therefore, as <lb/>A B is to B H, &longs;o is I B to B F, and the Angles at B are equal: <lb/>Therefore A H is to H B, as I F, that is E F, to F B, and as A E <lb/>to E B.</s></p><p type="main"> <s>I &longs;ay moreover, that it is impo&longs;&longs;ible, that the Lines, which have <lb/>this &longs;ame proportion, departing from the terms A and B, &longs;hould <lb/>meet in any point, either within or without the &longs;aid Circle: For­<lb/>a&longs;much as if it be po&longs;&longs;ible that two Lines &longs;hould concur in the <lb/>point L, placed without; let them be A L, and B L; and continue <lb/>L B to the Circumference in M, and conjoyn M to F. </s> <s>If therefore <lb/>A L is to B L, as A C to B C, that is, as M F to F B, we &longs;hall have <lb/>two Triangles A L B, and M F B, which about the two Angles <lb/>A L B and M F B have their Sides proportional, their upper Angles <lb/>in the point B equal, and the two remaining Angles F M B and <lb/>L A B le&longs;s than Right Angles (for that the Right-angle at the <lb/>point M hath for its Ba&longs;e the whole Diameter C G, and not the <lb/>&longs;ole part B F, and the other at the point A is acute by rea&longs;on the <lb/>Line A L Homologous to A C, is greater than B L Homologous to <lb/>B C) Therefore the Triangles A B L, and M B F are like: and <lb/>therefore as A B is to B L, &longs;o is M B to B F; Wherefore the <lb/>Rectangle A B F &longs;hall be equall to the Rectangle M B L. </s> <s>But the <lb/>Rectangle A B F hath been demon&longs;trated to be equal to that of <lb/>C B G: Therefore the Rectangle M B L is equal to the Rectangle <lb/>C B G, which is impo&longs;&longs;ible: Therefore the Concour&longs;e of the Lines <lb/>cannot fall without the Circle. </s> <s>And in like manner it may be de­<lb/>mon&longs;trated that it cannot fall within; Therefore all the Concour­<lb/>&longs;es fall in the Circumference it &longs;elf.</s></p><p type="main"> <s>But it is time that we return to give &longs;atisfaction to the Intreaty <lb/>of <emph type="italics"/>Simplicius,<emph.end type="italics"/> &longs;hewing him that the re&longs;olving the Line into its in­<lb/>finite Points is not only not impo&longs;&longs;ible, but that it hath in it no <lb/>more difficulty than to di&longs;tingui&longs;h its quantitative parts; pre&longs;up­<lb/>po&longs;ing one thing (notwith&longs;tanding) which I think, <emph type="italics"/>Simplicius,<emph.end type="italics"/><lb/>you will not deny me, and that is this; that you will not require me <lb/>to &longs;ever the Points one from another, and &longs;hew you them one by <lb/>one di&longs;tinctly upon this paper: for I my &longs;elfe &longs;hould be content, <lb/>if without enjoyning to pull the four or &longs;ix parts of a Line from <lb/>one another, you &longs;hould but &longs;hew me its divi&longs;ions marked, or at <lb/>mo&longs;t inclined to Angles, framing them into a Square, or a Hexa­<lb/>gon; therefore I per&longs;wade my &longs;elf, that for the pre&longs;ent you will <lb/>grant them then &longs;ufficiently, and actually di&longs;tingui&longs;hed.</s></p><p type="main"> <s>SIMP. </s> <s>I &longs;hall indeed.</s></p><p type="main"> <s>SALV. </s> <s>Now if the inclining of a Line to Angles, framing <lb/><arrow.to.target n="marg1034"></arrow.to.target><lb/>therewith &longs;ometimes a Square &longs;ometimes an Octagon, &longs;ometimes <pb xlink:href="040/01/731.jpg" pagenum="39"/>a Poligon of Forty, of an <emph type="italics"/>H<emph.end type="italics"/>undred, of a Thou&longs;and Angles be a <lb/>mutation &longs;ufficient to reduce into Act tho&longs;e four, eight, forty, <lb/>hundred, or thou&longs;and parts, which were, as you &longs;ay, Potentially <lb/>in the &longs;aid Line at fir&longs;t: if I make thereof a Poligon of infinite <lb/>Sides, namely, when I bend it into the Circumference of a Circle, <lb/>may not I, with the like leave, &longs;ay, that I have reduced tho&longs;e infi­<lb/>nite parts into Act, which you before, whil&longs;t it was &longs;traight, &longs;aid <lb/>were Potentially contained in it? </s> <s>Nor may &longs;uch a Re&longs;olution be <lb/>denied to be made into its Infinite Points, as well as that of its four <lb/>parts in forming thereof a Square, or into its thou&longs;and parts in <lb/>forming thereof a Mill-angular Figure; by rea&longs;on that there wants <lb/>not in it any of the Conditions found in the Poligon of a thou­<lb/>&longs;and, or of an hundred thou&longs;and Sides. </s> <s>This applied or layed to a <lb/>Right-Line covereth it, touching it with one of its Sides, that is, <lb/>with one of its hundred thou&longs;andth parts; the Circle, which is a <lb/>Poligon of infinite Sides, toucheth the &longs;aid Right-line with one of <lb/>its Sides, that is one &longs;ingle Point divers from all its Colaterals, and <lb/>therefore divided, and di&longs;tinct from them, no le&longs;s than a Side of <lb/>the Poligon from its Conterminals. </s> <s>And as the Poligon turned <lb/>round upon a Plane de&longs;cribes, with the con&longs;equent tacts of its Sides, <lb/>a Right-line equal to its Perimeter: &longs;o the Circle, rowled upon <lb/>&longs;uch a Plane, de&longs;cribes or &longs;tamps upon it, by its infinite &longs;ucce&longs;&longs;ive <lb/>Contacts, a Right-line, equall to its own Circumference. </s> <s>I know <lb/>not at pre&longs;ent, <emph type="italics"/>Simplicius,<emph.end type="italics"/> whether or no the Peripateticks, (to <lb/>whom I grant, as a thing mo&longs;t certain, that <emph type="italics"/>Continuum<emph.end type="italics"/> may be di­<lb/>vided into parts alwaies divi&longs;ible, &longs;o that continuing the divi&longs;ion <lb/>and &longs;ubdivi&longs;ion there can be no end thereof) will be content to <lb/>yield to me, that none of tho&longs;e divi&longs;ions are the ultimate, as in­<lb/>deed they be not, &longs;ince that there alwaies remains another; but <lb/>that only to be the la&longs;t, which re&longs;olves it into infinite Indivi&longs;ibles; <lb/>to which I yield we can never attain, dividing and &longs;ubdividing it <lb/>&longs;ucce&longs;&longs;ively into a greater, and greater multitude of parts: but <lb/>making u&longs;e of the way which I propound to di&longs;tingui&longs;h and re­<lb/>&longs;olve all the infinite parts at one only draught, (an Artifice which <lb/>ought not to be denied me) I could per&longs;wade my &longs;elf they <lb/>would &longs;atisfie them&longs;elves, and admit this compo&longs;ition of <emph type="italics"/>Continu-<emph.end type="italics"/><lb/><arrow.to.target n="marg1035"></arrow.to.target><lb/><emph type="italics"/>um<emph.end type="italics"/> to con&longs;i&longs;t of Atomes ab&longs;olutely indivi&longs;ible: And e&longs;pecially, <lb/>this one path being more current than any other to extricate us <lb/>out of very intricate Laberinths; &longs;uch as are, (be&longs;ides that alrea­<lb/>dy touched of the Coherence of the parts of Solids) the concei­<lb/>ving the bu&longs;ine&longs;s of Rarefaction and Conden&longs;ation, without <lb/>running into the inconvenience of being forced to admit forth of <lb/>void Spaces or Vacuities; and for this a Penetration of Bodies: in­<lb/>conveniences, which both, in my opinion, may ea&longs;ily be avoided, <lb/>by granting the fore&longs;aid Compo&longs;ition of Indivi&longs;ibles.</s></p><pb xlink:href="040/01/732.jpg" pagenum="40"/><p type="margin"> <s><margin.target id="marg1034"></margin.target><emph type="italics"/>How infinite points <lb/>are a&longs;&longs;igned in a <lb/>finite Line.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1035"></margin.target>Continuum <emph type="italics"/>com­<lb/>pounded of Indivi­<lb/>&longs;ibles.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>I know not what the Peripateticks would &longs;ay, in regard <lb/>that the Con&longs;iderations you have propo&longs;ed would be, for the mo&longs;t <lb/>part, new unto them, and as &longs;uch, it is requi&longs;ite that they be exa­<lb/>mined: and it may be, that they would find you an&longs;wers, and <lb/>powerful Solutions, to unty the&longs;e knots, which I, by rea&longs;on of the <lb/>want of time and ingenuity proportionate, cannot for the pre&longs;ent <lb/>re&longs;olve. </s> <s>Therefore, &longs;u&longs;pending this particular for this time, I <lb/>would gladly under&longs;tand how the introduction of the&longs;e Indivi&longs;i­<lb/>bles facilitateth the knowledge of Conden&longs;ation, and Rarefa­<lb/>ction, avoiding at the &longs;ame time a <emph type="italics"/>Vacuum,<emph.end type="italics"/> and the Penetration of <lb/>Bodies.</s></p><p type="main"> <s>SAGR. </s> <s>I al&longs;o much long to under&longs;tand the &longs;ame, it being to <lb/>my Capacity &longs;o ob&longs;cure: with this <emph type="italics"/>provi&longs;o,<emph.end type="italics"/> that I be not couzen­<lb/>ed of hearing (as <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;aid but even now) the Rea&longs;ons of <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in confutation of a <emph type="italics"/>Vacuum,<emph.end type="italics"/> and con&longs;equently the Solu­<lb/>tions which you bring, as ought to be done, whil&longs;t that you ad­<lb/>mit what he denieth.</s></p><p type="main"> <s>SALV. </s> <s>I will do both the one and the other. </s> <s>And as to the fir&longs;t <lb/>it's nece&longs;&longs;ary, that like as in favour of Rarefaction, we make u&longs;e of <lb/>the Line de&longs;cribed by the le&longs;&longs;er Circle bigger than its own Cir­<lb/>cumference, whil&longs;t it was moved at the Revolution of the greater; <lb/>&longs;o, for the under&longs;tanding of Conden&longs;ation, we &longs;hall &longs;hew, how that, <lb/>at the conver&longs;ion made by the le&longs;&longs;er Circle, the greater de&longs;cribeth <lb/>a Right-line le&longs;s than its Circumference; for the clearer explicati­<lb/>on of which, let us &longs;et before us the con&longs;ideration of that which <lb/>befalls in the Poligons. </s> <s>In a de&longs;cription like to that other; &longs;up­<lb/>po&longs;e two Hexagons about the common Center L, which let be <lb/>A B C, and H I K, with the Parallel-lines H O M, and A B C, up­<lb/>on which they are to make their Revolutions; and the Angle I, of <lb/>the le&longs;&longs;er Poligon, re&longs;ting at a &longs;tay, turn the &longs;aid Poligon till &longs;uch <lb/>time as I K fall upon the Parallel, in which motion the point K <lb/>&longs;hall de&longs;cribe the Arch K M, and the Side K I, &longs;hall unite with the <lb/>part I M; while this is in doing, you mu&longs;t ob&longs;erve what the Side <lb/>C B of the greater Poligon will do. </s> <s>And becau&longs;e the Revolution <lb/>is made upon the Point I, the Line I B with its term B &longs;hall de­<lb/>&longs;cribe, turning backward the Arch B b, below the Parallel c A, &longs;o <lb/>that when the Side K I &longs;hall fall upon the Line M I, the Line B C <lb/>&longs;hall fall upon the Line b c, advancing forwards only &longs;o much as <lb/>is the Line B c, and retiring back the part &longs;ubtended by the Arch <lb/>B b, which falls upon the Line B A, and intending to continue af­<lb/>ter the &longs;ame manner the Revolution of the le&longs;&longs;er Poligon, this will <lb/>de&longs;cribe, and pa&longs;s upon its Parallel, a Line equal to its Perimeter; <lb/>but the greater &longs;hall pa&longs;s a Line le&longs;s than its Perimeter, the quan­<lb/>tity of &longs;o many of the lines <emph type="italics"/>B<emph.end type="italics"/> b as it hath Sides, wanting one; <lb/>and that &longs;ame line &longs;hall be very near equal to that de&longs;cribed by <pb xlink:href="040/01/733.jpg" pagenum="41"/>the le&longs;&longs;er Poligon, exceeding it only the quantity of b B. </s> <s>Here <lb/>then, without the lea&longs;t repugnance the cau&longs;e is &longs;een, why the grea­<lb/>ter Poligon pa&longs;&longs;eth or moveth not (being carried by the le&longs;s) <lb/>with its Sides a greater Line than that pa&longs;&longs;ed by the le&longs;s; that is, <lb/>becau&longs;e that one part of each of them falleth upon its next coter­<lb/>minal and precedent.</s></p><p type="main"> <s>But if we &longs;hould con&longs;ider the two Circles about the Center A, <lb/>re&longs;ting upon their Parallels, the le&longs;&longs;er touching his in the point B, <lb/>and the greater his in the <lb/><figure id="id.040.01.733.1.jpg" xlink:href="040/01/733/1.jpg"/><lb/>point C; here, in begin­<lb/>ning to make the Revolu­<lb/>tion of the le&longs;s, it &longs;hall not <lb/>occur as before, that the <lb/>point B re&longs;t for &longs;ome time <lb/>immoveable, &longs;o that the <lb/>Line B C giving back, <lb/>carry with it the point C, <lb/>as it befell in the Poligons, <lb/>which re&longs;ting fixed in the <lb/>point I till that the Side <lb/>K I falling upon the Line <lb/>I M, the Line I B carried <lb/>back B, the term of the <lb/>Side C B, as far as b, by <lb/>which means the Side B C <lb/>fell on b c, &longs;uper-po&longs;ing or <lb/>re&longs;ting the part B b upon <lb/>the Line B A, and advancing forwards only the part <emph type="italics"/>B<emph.end type="italics"/> c, equal to <lb/>I M, that is to one Side of the le&longs;&longs;er Poligon: by which &longs;uperpo&longs;i­<lb/>tions, which are the exce&longs;&longs;es of the greater Sides above the le&longs;s, the <lb/>advancements which remain equal to the Sides of the le&longs;&longs;er Poli­<lb/>gon come to compo&longs;e in the whole Revolution the Right-line <lb/>equal to that traced, and mea&longs;ured by the le&longs;&longs;er Poligon. </s> <s>But <lb/><arrow.to.target n="marg1036"></arrow.to.target><lb/>now, I &longs;ay, that if we would apply this &longs;ame di&longs;cour&longs;e to the ef­<lb/>fect of the Circles, it will be requi&longs;ite to confe&longs;s, that whereas the <lb/>Sides of what&longs;oever Poligon are comprehended by &longs;ome Number, <lb/>the Sides of the Circle are infinite; tho&longs;e are quantitative and di­<lb/>vi&longs;ible, the&longs;e non-quantitative and Indivi&longs;ible: the terms of the <lb/>Sides of a Poligon in the Revolution &longs;tand &longs;till for &longs;ome time, that <lb/>is, each &longs;uch part of the time of an entire Conver&longs;ion, as it is of <lb/>the whole Perimeter: in the Circles likewi&longs;e the &longs;tay o&longs; the terms <lb/><arrow.to.target n="marg1037"></arrow.to.target><lb/>of its infinite Sides are momentary, for a Moment is &longs;uch part of a <lb/>limited Time, as a Point is of a Line, which containeth infinite of <lb/>them; the regre&longs;&longs;ions made by the Sides of the greater Poligon, are <lb/>not of the whole Side, but only of its exce&longs;s above the Side of the <pb xlink:href="040/01/734.jpg" pagenum="42"/>le&longs;&longs;er, getting forwards as much &longs;pace as the &longs;aid le&longs;&longs;er Side: in <lb/>Circles, the Point, or Side C in the in&longs;tantaneous re&longs;t of B recedeth <lb/>as much as is its exce&longs;s above the Side B, advancing forward as <lb/>much as the quantity of the &longs;ame B: And in &longs;hort, the infinite <lb/>indivi&longs;ible Sides of the greater Circle with their infinite indivi&longs;ible <lb/>Regre&longs;&longs;ions, made in the infinite in&longs;tantaneous &longs;taies of the infi­<lb/>nite terms of the infinite Sides of the le&longs;&longs;er Circle, and with their <lb/>infinite Progre&longs;&longs;es, equal to the infinite Sides of the &longs;aid le&longs;&longs;er <lb/>Circle, they compo&longs;e and mea&longs;ure a Line equall to that de&longs;cribed <lb/>by the le&longs;&longs;er Circle, containing in it &longs;elf infinite &longs;uperpo&longs;itious <lb/>non-quantitative, which make a Con&longs;tipation and Conden&longs;ation <lb/>without any penctration of quantitative parts: which cannot be <lb/>contrived to be done in the Line divided into quantitative parts, <lb/>as is the Perimeter of any Poligon, which being di&longs;tended in a <lb/>Right-line at length, cannot be reduced to a le&longs;&longs;er length, unle&longs;s <lb/>the Sides fall upon and Penetrate one the other. </s> <s>This Con&longs;tipati­<lb/>on of parts non-quantitative, but infinite without Penetration of <lb/>quantitative parts, and the former Di&longs;traction above declared of <lb/><arrow.to.target n="marg1038"></arrow.to.target><lb/>infinite Indivi&longs;ibles by the interpo&longs;ition of indivi&longs;ible Vacui­<lb/>ties, I believe, is the mo&longs;t that can be &longs;aid for the Conden&longs;ation <lb/>and Rarefaction of Bodies, without being driven to introduce Pe­<lb/>netration of Bodies, or quantitative Void Spaces. </s> <s>If there be any <lb/>thing therein that plea&longs;eth you, make u&longs;e of it, if not, account it <lb/><arrow.to.target n="marg1039"></arrow.to.target><lb/>vain, and my di&longs;cour&longs;e al&longs;o; and &longs;eek out &longs;ome other explanation <lb/>that may better &longs;atisfie your Judgment. </s> <s>Only the&longs;e two words <lb/>by the way, let us remember that we are among&longs;t Infinites, and In­<lb/>divi&longs;ibles.</s></p><p type="margin"> <s><margin.target id="marg1036"></margin.target><emph type="italics"/>A Circle is a Poli­<lb/>gon of infinite in­<lb/>divi&longs;ible quantita­<lb/>tive Sides.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1037"></margin.target><emph type="italics"/>An In&longs;tant or Mo­<lb/>ment of quantita­<lb/>tive Time, is the <lb/>&longs;ame as a Point of <lb/>a quantitative <lb/>Line.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1038"></margin.target><emph type="italics"/>Rarefaction is the <lb/>di&longs;traction of infi­<lb/>nite Indivi&longs;ibles <lb/>by the interpo&longs;ition <lb/>of infinite indivi&longs;i­<lb/>ble Vaeuities.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1039"></margin.target><emph type="italics"/>Conden&longs;ation, ac­<lb/>cording to the ope­<lb/>ration of the Au­<lb/>thor, proceeds from <lb/>the Con&longs;tipation of <lb/>quantitative and <lb/>indivi&longs;ible parts.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>That the Conceit is ingenious, and to my eares wholly <lb/>new, and &longs;trange, I freely confe&longs;s, but whether or no Nature pro­<lb/>ceed in this order, I know not how to re&longs;olve; Truth is, that till <lb/>&longs;uch time as I hear &longs;omething that may better &longs;atisfie me, that I <lb/>may not &longs;tand &longs;ilent, I will adhere to this. </s> <s>But haply <emph type="italics"/>Simplicius<emph.end type="italics"/><lb/>may have &longs;omwhat, which I have not yet met with, to explicate <lb/>the explication, which is produced by Philo&longs;ophers in &longs;o ab&longs;truce <lb/>a matter; for, indeed, what I have hitherto read about Conden&longs;a­<lb/>tion, is to me &longs;o den&longs;e, and that of Rarefaction &longs;o &longs;ubtill, that <lb/>my weak &longs;ight neither penetrates the one, nor comprehends the <lb/>other.</s></p><p type="main"> <s>SIMP. </s> <s>I am full of confu&longs;ion, and find great Rubbs in the one <lb/>path, and in the other, and more particularly in this new one: for <lb/>according to this Rule, an Ounce of Gold might be rarefied and <lb/>drawn forth into a Ma&longs;s bigger than the whole Earth, and the <lb/>whole Earth conden&longs;ed and reduced into a le&longs;s Ma&longs;s than a Nut; <lb/>which I neither believe, nor think that you your &longs;elf do believe: <lb/>and the Con&longs;iderations and Demon&longs;trations by you hitherto de­<pb xlink:href="040/01/735.jpg" pagenum="43"/>livered, as they are things Mathematical, ab&longs;tract and &longs;eparate <lb/>from Sen&longs;ible Matter, I believe, that when they come to be apply­<lb/>ed to Matters Phy&longs;ical and Natural, they will not exactly comply <lb/>with the&longs;e Rules.</s></p><p type="main"> <s>SALV. </s> <s>It is not in my power, nor, as I believe, do you de&longs;ire, <lb/>that I &longs;hould make that vi&longs;ible which is invi&longs;ible; but as to &longs;uch <lb/>things as may be comprehended by our Sen&longs;es, in regard that you <lb/><arrow.to.target n="marg1040"></arrow.to.target><lb/>have in&longs;tanced in Gold, do we not &longs;ee an immen&longs;e exten&longs;ion to <lb/>be made of its parts? </s> <s>I know not whether you may have &longs;een the <lb/>Method that Wyer-drawers ob&longs;erve in di&longs;gro&longs;&longs;ing Gold Wyer: <lb/>which in reality is not Gold, &longs;ave only in the Superficies, for the <lb/>internal &longs;ub&longs;tance is Silver; and the way of di&longs;gro&longs;&longs;ing it is this. <lb/></s> <s>They take a Cylinder, or, if you will, Ingot of Silver, about half <lb/>a yard long, and about three or four Inches thick, and this they <lb/><arrow.to.target n="marg1041"></arrow.to.target><lb/>gild or over-lay with Leaves of beaten Gold, which, you know, <lb/>is &longs;o thin that the Wind will blow it to and again, and of the&longs;e <lb/>Leaves they lay on eight or ten, and no more. </s> <s>So &longs;oon as it is <lb/>gilded, they begin to draw it forth with extraordinary force, ma­<lb/>king it to pa&longs;s thorow the hole of the Drawing Iron, and then <lb/>reiterate this forceable di&longs;gro&longs;sment again and again thorow holes <lb/>&longs;ucce&longs;&longs;ively narrower, &longs;o that, after &longs;everal of the&longs;e di&longs;gro&longs;ments, <lb/>they bring it to the &longs;malne&longs;s of the hair of a womans head, if not <lb/>&longs;maller, and yet it &longs;till continueth gilded in its Superficies or out­<lb/>&longs;ide: Now I leave you to con&longs;ider to what a finene&longs;s and di&longs;ten&longs;i­<lb/>on the &longs;ub&longs;tance of the Gold is brought.</s></p><p type="margin"> <s><margin.target id="marg1040"></margin.target><emph type="italics"/>Gold in the gilding <lb/>of Silver is drawn <lb/>forth and di&longs;gro&longs;­<lb/>&longs;ed immen&longs;ly.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1041"></margin.target>* Or Thumb­<lb/>breadths.</s></p><p type="main"> <s>SIMP. </s> <s>I do not &longs;ee how it can be inferred from this Experi­<lb/>ment, that there may be a di&longs;gro&longs;ment of the matter of the Gold <lb/>&longs;ufficient to effect tho&longs;e wonders which you &longs;peak of: Fir&longs;t, For <lb/>that the fir&longs;t gilding was with ten Leaves of Gold, which make a <lb/>con&longs;iderable thickne&longs;s: Secondly, howbeit in the exten&longs;ion and <lb/>di&longs;gro&longs;ment that Silver encrea&longs;eth in length, it yet withall dimi­<lb/>ni&longs;heth &longs;o much in thickne&longs;s, that compen&longs;ating the one dimen&longs;i­<lb/>on with the other, the Superficies doth not &longs;o enlarge, as that for <lb/>overlaying the Silver with Gold, the &longs;aid Gold need to be reduced <lb/>to a greater thinne&longs;s than that of its fir&longs;t Leaves.</s></p><p type="main"> <s>SALV. </s> <s>You much deceive your &longs;elf, <emph type="italics"/>Simplicius,<emph.end type="italics"/> for the en­<lb/>crea&longs;e of the Superficies is Subduple to the exten&longs;ion in length, as <lb/>I could Geometrically demon&longs;trate to you.</s></p><p type="main"> <s>SAGR. </s> <s>I be&longs;eech you, both in the behalf of my &longs;elf, and of <lb/><emph type="italics"/>Simplicius,<emph.end type="italics"/> to favour us with that Demon&longs;tration, if &longs;o be you <lb/>think that we can comprehend it.</s></p><p type="main"> <s>SALV. </s> <s>I will &longs;ee whether I can, thus upon the &longs;udden, recall <lb/>it to mind. </s> <s>It is already manife&longs;t, that that &longs;ame fir&longs;t gro&longs;s Cylin­<lb/>der of Silver, and the Wyer di&longs;tended to &longs;o great a length are two <lb/>equal Cylinders, in regard that they are the &longs;ame Silver; &longs;o that <pb xlink:href="040/01/736.jpg" pagenum="44"/>if I &longs;hall &longs;hew you what proportion the Superficies of equall Cy­<lb/>linders have to one another, we &longs;hall obtain our de&longs;ire. </s> <s>I &longs;ay there­<lb/>fore, that</s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"/>The Superficies of Equal Cylinders, their Ba&longs;es being <lb/>&longs;ub&longs;tracted, are to one another in &longs;ubduple proportion <lb/>of their lengths.<emph.end type="italics"/></s></p><p type="main"> <s>Take two equall Cylinders, the heights of which let be A B, <lb/>and C D: and let the Line E be a Mean-proportional <lb/>between them. </s> <s>I &longs;ay, the Superficies of the Cylinder A B, <lb/>the Ba&longs;es &longs;ub&longs;tracted, hath the &longs;ame proportion to the Superficies <lb/>of the Cylinder C D, the Ba&longs;es in like manner &longs;ub&longs;tracted, as the <lb/>Line A B hath to the Line E, which is &longs;ubduple of the proportion <lb/>of A B to C D. </s> <s>Cut the part of the Cylinder A B in F, and let the <lb/>height A F be equal to C D: And becau&longs;e the Ba&longs;es of equal Cy­<lb/>linders an&longs;wer Reciprocally to their heights, the Circle, Ba&longs;e of <lb/>the Cylinder C D, to the Circle, Ba&longs;e of the <lb/><figure id="id.040.01.736.1.jpg" xlink:href="040/01/736/1.jpg"/><lb/>Cylinder A B, &longs;hall be as the height B A to <lb/>D C: And becau&longs;e Circles are to one ano­<lb/>ther as the Squares of their Diameters, the <lb/>&longs;aid Squares &longs;hall have the &longs;ame proportion, <lb/>that B A hath to C D: But as B A, is to <lb/>C D, &longs;o is the Square B A to the Square of <lb/>E: Therefore tho&longs;e four Squares are Pro­<lb/>portionals: And therefore their Sides &longs;hall <lb/>be Proportionals. </s> <s>And as the Line A B is to <lb/>E, &longs;o is the Diameter of the Circle C to the <lb/>Diameter of the Circle A: But as are the <lb/>Diameters, &longs;o are the Circumferences; and <lb/>as are the Circumferences, &longs;o likewi&longs;e are the Superficies of Cylin­<lb/>ders equal in Height. </s> <s>Therefore as the Line A B is to E, &longs;o is the <lb/>Superficies of the Cylinder C D to the Superficies of the Cylinder <lb/>A F. </s> <s>Becau&longs;e therefore the height A F to the height A B, is as the <lb/>Superficies A F to the Superficies A B: And as is the height A B <lb/>to the Line E, &longs;o is the Superficies C D to the Superficies A F: <lb/>Therefore by Perturbation of Proportion as the height A F is to <lb/>E, &longs;o is the Superficies C D to the Superficies A B: And, by Con­<lb/>ver&longs;ion, as the Superficies of the Cylinder A B is to the Superficies <lb/>of the Cylinder C D, &longs;o is the Line E to the Line A F; that is, to <lb/>the Line C D: or as A B to E: Which is in &longs;ubduple proportion <lb/>of A B to C D: Which is that which was to be proved.</s></p><pb xlink:href="040/01/737.jpg" pagenum="45"/><p type="main"> <s>Now if we apply this, that hath been demon&longs;trated, to our <lb/>purpo&longs;e; pre&longs;uppo&longs;ing that that &longs;ame Cylinder of Silver, that was <lb/>gilded whil&longs;t it was no more than half a yard long, and four or five <lb/>Inches thick, being di&longs;gro&longs;&longs;ed to the &longs;inene&longs;s of an hair, is prolon­<lb/>ged unto the exten&longs;ion of twenty thou&longs;and yards (for its length <lb/>would be much greater) we &longs;hall find its Superficies augmented <lb/>to two hundred times its former greatne&longs;s: and con&longs;equently, tho&longs;e <lb/>Leaves of Gold, which were laid on ten in number, being di&longs;ten­<lb/>ded on a Superficies two hundred times bigger, a&longs;&longs;ure us that the <lb/>Gold which covereth the Superficies of the &longs;o many yards of Wyer <lb/>is left of no greater thickne&longs;s than the twentieth part of a Leaf of <lb/>ordinary Beaten-Gold. </s> <s>Con&longs;ider, now, how great its thinne&longs;s is, and <lb/>whether it is po&longs;&longs;ible to imagine it done without an immen&longs;e di­<lb/>&longs;tention of its parts: and whether this &longs;eem to you an Experi­<lb/>ment, that tendeth likewi&longs;e towards a compo&longs;ition of infinite In­<lb/>divi&longs;ibles in Phy&longs;ical Matters: Howbeit there want not other more <lb/>&longs;trong and nece&longs;&longs;ary proofs of the &longs;ame.</s></p><p type="main"> <s>SAGR. </s> <s>The Demon&longs;tration &longs;eemeth to me &longs;o ingenuous, that <lb/>although it &longs;hould not be of force enough to prove that fir&longs;t intent <lb/>for which it was produced, (and yet, in my opinion, it plainly <lb/>makes it out) yet neverthele&longs;s that &longs;hort &longs;pace of time was well <lb/>&longs;pent which hath been employed in hearing of it.</s></p><p type="main"> <s>SALV. </s> <s>In regard I &longs;ee, that you are &longs;o well plea&longs;ed with the&longs;e <lb/>Geometrical Demon&longs;trations, which bring with them certain pro. <lb/></s> <s>fit, I will give you the fellow to this, which &longs;atisfieth to a very cu­<lb/>rious Que&longs;tion. </s> <s>In the former we have that which hapneth in <lb/>Cylinders that are equall, but of different heights or lengths: it <lb/>will be convenient, that you al&longs;o hear that which occurreth in Cy­<lb/>linders equal in Superficies, but unequal in heights; my meaning <lb/>alwaies is, in tho&longs;e Superficies only that encompa&longs;s them about, <lb/>that is, not comprehending the two Ba&longs;es &longs;uperiour and inferiour. <lb/></s> <s>I &longs;ay, therefore, that</s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"/>Upon Cylinders, the Superficies of which the Ba&longs;es be­<lb/>ing &longs;ub&longs;tracted are equal, have the &longs;ame proportion <lb/>to one another as their heights Reciprocally taken.<emph.end type="italics"/></s></p><p type="main"> <s>Let the Superficies of the two Cylinders A E and C F be <lb/>equall; but the height of this C D greater than the height <lb/>of the other A B. </s> <s>I &longs;ay, that the Cylinder A E hath the <lb/>&longs;ame proportion to the Cylinder C F, that the height C D hath <lb/>to A B. </s> <s>Becau&longs;e therefore the Superficies C F is equall to the <pb xlink:href="040/01/738.jpg" pagenum="46"/>&longs;uperficies A E, the Cylinder C F &longs;hall be le&longs;&longs;e than A E: For <lb/>if they were equal, its Superficies, by the la&longs;t Propo&longs;ition would <lb/>be greater than the Superficies A E, and <lb/><figure id="id.040.01.738.1.jpg" xlink:href="040/01/738/1.jpg"/><lb/>much the more, if the &longs;aid Cylinder C F <lb/>were greater than A E. </s> <s>Let the Cylinder <lb/>I D be &longs;uppo&longs;ed equal to A E: There­<lb/>fore, by the precedent Propo&longs;ition, the <lb/>Superficies of the Cylinder I D &longs;hall be <lb/>to the Superficies A E, as the height I F <lb/>to the Mean-proportional betwixt I F & <lb/>A B. </s> <s>But the Superficies A E being by <lb/>Suppo&longs;ition equal to C F and I D, ha­<lb/>ving the &longs;ame proportion to C F that the <lb/>height I F hath to C D: Therefore <lb/>C D is the Mean-Proportional between <lb/>I F and A B. Moreover, the Cylinder <lb/>I D being equal to the Cylinder A E, <lb/>they &longs;hall both have the &longs;ame proporti­<lb/>on to the Cylinder C F: But I D is to <lb/>C F, as the height I F is to C D: Therefore the Cylinder A E <lb/>&longs;hall have the &longs;ame proportion to the Cylinder C F, that the line <lb/>I F hath to C D; that is, that C D hath to A B: Which was to be <lb/>demon&longs;trated.<lb/><arrow.to.target n="marg1042"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1042"></margin.target><emph type="italics"/>Of Corn-&longs;acks <lb/>with a Board at <lb/>the Bottom, made <lb/>of the &longs;ame Stuffe, <lb/>but different in <lb/>height, which are <lb/>the more capa­<lb/>cious.<emph.end type="italics"/></s></p><p type="main"> <s>From hence is collected the Cau&longs;e of an Accident, which the <lb/>Vulgar do not hearken to without admiration; and it is, how it <lb/>is po&longs;&longs;ible that the &longs;ame piece of ^{*}Cloth, being longer one way than <lb/>another, if a Sack be made thereof to hold Corn, as the u&longs;ual <lb/>manner is, with a Board at the bottom, will hold more, making <lb/>u&longs;e of the le&longs;&longs;er breadth of the Cloth, for the height of the Sack, </s></p><p type="main"> <s><arrow.to.target n="marg1043"></arrow.to.target><lb/>and with the other encompa&longs;&longs;ing the Board at the bottom, than if <lb/>it be made up the other way: As if for Example, the Cloth were <lb/>one way &longs;ix foot, and the other way twelve, it will hold more, <lb/>when with the length of twelve one encompa&longs;&longs;eth the Board at the <lb/>bottom, the Sack being &longs;ix foot high, than if it encompa&longs;&longs;ed a <lb/>bottom of &longs;ix foot, having twelve for its height. </s> <s>Now, by what <lb/>hath been demon&longs;trated, there is added to the Knowledge in ge­<lb/>neral that it holds more that way than this, the Specifick, and <lb/>particular Knowledge of how much it holdeth more: which is, <lb/>That it will hold more in proportion as it is lower, and le&longs;&longs;er, as <lb/>it is higher. </s> <s>And thus in the mea&longs;ures afore taken, the Cloth be­<lb/>ing twice as long as broad, when it is &longs;ewed the length-ways it will <lb/>hold but half &longs;o much, as it will do the other way. </s> <s>And likewi&longs;e <lb/><arrow.to.target n="marg1044"></arrow.to.target><lb/>having a Mat to make a ^{*} Frale or Basket twenty five foot long, <lb/>and &longs;uppo&longs;e &longs;even broad; made up the long-way it will hold but <lb/>onely &longs;even of tho&longs;e mea&longs;ures, whereof the other way it will hold <lb/>five and twenty.</s></p><pb xlink:href="040/01/739.jpg" pagenum="47"/><p type="margin"> <s><margin.target id="marg1043"></margin.target>* Or Sacking.</s></p><p type="margin"> <s><margin.target id="marg1044"></margin.target>* Bugnola, any <lb/>Ve&longs;&longs;el made of <lb/>Rushes or Wick­<lb/>er.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>AGR. </s> <s>And thus to our particular content we continually di&longs;­<lb/>cover new Notions of great Curio&longs;ity, and not unaccompanyed <lb/>with Utility. </s> <s>But in the particular glanced at but even now, I <lb/>really believe, that among&longs;t &longs;uch as are altogether void of the <lb/>knowledge of Geometry, there would not be found one in twen­<lb/>ty, but at the fir&longs;t da&longs;h would not be mi&longs;taken, and wonder <lb/>that tho&longs;e Bodies that are contained within equal Superficies, <lb/>&longs;hould not likewi&longs;e be in every re&longs;pect equal; like as they run in­<lb/>to the &longs;ame errour, &longs;peaking of the Superficies, when for deter­<lb/>mining, as it frequently falls out, of the amplene&longs;&longs;e of &longs;everal <lb/>Cities, they think they have obtained their de&longs;ire &longs;o &longs;oon as they <lb/>know the &longs;pace of their Circuits, not knowing that one Circuit <lb/>may be equal to another, and yet the place conteined by this <lb/>much larger than the place of that: which befalleth not onely in <lb/>irregular Superficies, but in the regular; among&longs;t which tho&longs;e <lb/>of more Sides are alwayes more capacious than tho&longs;e of fewer; <lb/>&longs;o that in fine, the Circle, as being a Poligon of infinite Sides, is <lb/>more capacious than all other Poligons of equal Perimeter; of <lb/>which I remember, that I with particular delight &longs;aw the Demon­<lb/>&longs;tration on a time when I &longs;tudied the Sphere of <emph type="italics"/>Sacrobo&longs;co,<emph.end type="italics"/> with <lb/>a very learned Commentary upon the &longs;ame.</s></p><p type="main"> <s>SALV. </s> <s>It is mo&longs;t certain; and I having likewi&longs;e light upon <lb/>that very place, it gave me occa&longs;ion to inve&longs;tigate, how it may <lb/>with one &longs;ole Demon&longs;tration be concluded, that the Circle is <lb/>greater than all the re&longs;t of regular I&longs;operemitral Figures, and of <lb/>others, tho&longs;e of more Sides bigger than tho&longs;e of fewer.</s></p><p type="main"> <s>SAGR. </s> <s>And I that take great plea&longs;ure in certain &longs;elect and no­<lb/>wi&longs;e-trivial Demon&longs;trations, entreat you with all importunity to <lb/>make me a partaker therein.</s></p><p type="main"> <s>SALV. </s> <s>I &longs;hall di&longs;patch the &longs;ame in few words, demon&longs;trating <lb/>the following Theorem, namely;</s></p><pb xlink:href="040/01/740.jpg" pagenum="48"/><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"/>The Circle is a Mean-Proportional betwixt any two <lb/>Regular Homogeneal Poligons, one of which is cir­<lb/>cum&longs;cribed about it, and the other I&longs;operimetral to <lb/>it: Moreover, it being le&longs;&longs;e than all the circum&longs;cri­<lb/>bed, it is, on the contrary, bigger than all the I&longs;operi­<lb/>metral. </s> <s>And, again of the circum&longs;cribed, tho&longs;e that <lb/>have more angles are le&longs;&longs;er than tho&longs;e that have <lb/>fewer; and on the other &longs;ide of the I&longs;operimetral, <lb/>tho&longs;e of more angles are bigger.<emph.end type="italics"/></s></p><p type="main"> <s>Of the two like Poligons A and B, let A be circum&longs;cribed <lb/>about the Circle A, and let the other B, be I&longs;operime­<lb/>tral to the &longs;aid Circle: I &longs;ay, that the Circle is the Mean­<lb/>proportional betwixt them. </s> <s>For that (having drawn the Semidi­<lb/>ameter A C) the Circle being equal to that Right-angled Trian­<lb/>gle, of who&longs;e Sides including the Right angle, the one is equal <lb/><figure id="id.040.01.740.1.jpg" xlink:href="040/01/740/1.jpg"/><lb/>to the Semidiameter A C, and the other to the Circumference: <lb/>And likewi&longs;e the Poligon A being equal to the right angled Tri­<lb/>angle, that about the right angle hath one of its Sides equal to <lb/>the &longs;aid right line A C, and the other to the Perimeter of the &longs;aid <lb/>Poligon: It is manife&longs;t, that the circum&longs;cribed Poligon hath the <lb/>&longs;ame proportion to the Circle, that its Perimeter hath to the Cir­<lb/>cumference of the &longs;aid Circle; that is, to the Perimeter of the <lb/>Poligon B, which is &longs;uppo&longs;ed equal to the &longs;aid Circumference: <lb/>But the Poligon A hath a proportion to the Poligon B, double to <lb/>that of its Perimeter, to the Perimeter of B (they being like Fi­<lb/>gures:) Therefore the Circle A is the Mean-proportional be­<lb/>tween the two Poligons A and B. </s> <s>And the Poligon A being <lb/>bigger than the Circle A, it is manife&longs;t that the &longs;aid Circle <lb/>A is bigger than the Poligon B, its I&longs;operimetral, and con&longs;e­<lb/>quently the greate&longs;t of all Regular Poligons that are I&longs;operimetral <pb xlink:href="040/01/741.jpg" pagenum="49"/>to it. </s> <s>As to the other particular, that is to prove, that of the <lb/>Poligons circum&longs;cribed about the &longs;ame Circle, that of fewer <lb/>Sides is bigger than that of more Sides; but that, on the contrary, of <lb/>the I&longs;operimetral Poligons, that of more Sides is bigger than that <lb/>of fewer Sides, we will thus demon&longs;trate. </s> <s>In the Circle who&longs;e <lb/>Center is O, and Semidiameter O A, let there be a Tangent <lb/>A D, and in it let it be &longs;uppo&longs;ed, for example, that A D is the <lb/>half of the Side of the Pentagon circum&longs;cribed, and A C the half <lb/>of the Side of the Heptagon, and draw the right lines O G C, <lb/>and O F D; and on the Center O, at the di&longs;tance O C, draw the <lb/>Arch E C I: And becau&longs;e the Triangle D O C is greater than the <lb/>Sector E O C, and the Sector C O I greater than the Triangle <lb/>C O A; the Triangle D O C &longs;hall have greater proportion to <lb/>the Triangle C O A, than the Sector E O C, to the Secant C O I, <lb/>that is, than the Secant F O G to the Secant G O A. And, by <lb/>Compo&longs;ition, Permutation of Proportion, the Triangle D O A <lb/>&longs;hall have greater proportion to the Secant F O A, than the Tri­<lb/>angle C O A to the Secant G O A: And ten Triangles D O A <lb/>&longs;hall have greater proportion to ten Secants F O A, than four­<lb/>teen Triangles C O A to fourteen Sectors G O A: That is the <lb/>circum&longs;cribed Pentagon &longs;hall have greater proportion to the Cir­<lb/>cle, than hath the Heptagon: And therefore the Pentagon &longs;hall <lb/>be greater than the Heptagon. </s> <s>Let us now &longs;uppo&longs;e an Hep­<lb/>tagon and a Pentagon I&longs;operimetral to the &longs;ame Circle. </s> <s>I &longs;ay, that <lb/>the Heptagon is bigger than the Pentagon. </s> <s>For that the &longs;aid Cir­<lb/>cle being the Mean proportional between the Pentagon circum­<lb/>&longs;cribed and the Pentagon its I&longs;operimetral, and likewi&longs;e the Mean <lb/>between the Circum&longs;cribed and I&longs;operimetral Heptagon: It ha­<lb/>ving been proved that the Circum&longs;cribed Pentagon is greater then <lb/>the Circum&longs;cribed Heptagon, the &longs;aid Pentagon &longs;hall have greater <lb/>proportion to the Circle, than the Heptagon: that is, the Circle <lb/>&longs;hall have greater proportion to its I&longs;operimetral Pentagon, than <lb/>to its I&longs;operimetral Heptagon: Therefore the Pentagon is le&longs;&longs;er <lb/>than the I&longs;operimetral Heptagon. </s> <s>Which was to be demon­<lb/>&longs;trated</s></p><p type="main"> <s>SAGR. </s> <s>A mo&longs;t ingenious Demon&longs;tration, and very acute. </s> <s>But <lb/>whither are we run to ingulph our &longs;elves in Geometry, when as <lb/>we were about to con&longs;ider the Difficulties propo&longs;ed by <emph type="italics"/>Simpli­<lb/>cius,<emph.end type="italics"/> which indeed are very con&longs;iderable, and in particular, that <lb/>of Conden&longs;ation, is in my opinion, very ab&longs;truce.</s></p><p type="main"> <s>SALV. </s> <s>If Conden&longs;ation and Rarefaction are oppo&longs;ite Motions, <lb/>where there is &longs;een an immen&longs;e Rarefaction, one cannot deny an <lb/>extraordinary Conden&longs;ation: but immen&longs;e Rarefactions, and, <lb/>which encrea&longs;eth the wonder, almo&longs;t Momentary, we &longs;ee every <lb/>day: for what a boundle&longs;&longs;e Rarefaction is that of a little quan­<pb xlink:href="040/01/742.jpg" pagenum="50"/><arrow.to.target n="marg1045"></arrow.to.target><lb/>tity of Gunpowder re&longs;olved into a va&longs;t ma&longs;&longs;e of Fire? </s> <s>And what, <lb/>beyond this, the (I could almo&longs;t &longs;ay) indeterminate Expan&longs;ion <lb/>of its Light? </s> <s>And if that Fire and this Light &longs;hould reunite toge­<lb/>ther, which yet is no impo&longs;&longs;ibility, in regard, that at the fir&longs;t <lb/>they lay in that little room, what a Conden&longs;ation would this be? <lb/></s> <s>If you &longs;tudy for them, you will find hundreds of &longs;uch Rarefacti­<lb/>ons, which are much more readily ob&longs;erved, than Conden&longs;ati­<lb/>ons: for Den&longs;e matters are more tractable, and &longs;ubject to our <lb/>Sen&longs;es. </s> <s>For we can ea&longs;ily order Wood at plea&longs;ure, and we &longs;ee <lb/>it re&longs;olved into Fire, and into Light, but we do not in the &longs;ame <lb/>manner &longs;ee the Fire and the Light Conden&longs;e to the making of <lb/>Wood: We &longs;ee Fruits, Flowers, and many other &longs;olid matters <lb/>re&longs;olved in a great mea&longs;ure into Odors, but we do not after the <lb/>&longs;ame manner &longs;ee the odoriferous Atomes concurre to the con&longs;titu­<lb/>tion of the Oderate Solids; but where Sen&longs;ible Ob&longs;ervation is <lb/>wanting, we are to &longs;upply it with Rea&longs;on, which will &longs;uffice to <lb/>make us apprehen&longs;ive, no le&longs;&longs;e of the Motion to the Rarefaction <lb/>and re&longs;olution of Solids, than, to the Conden&longs;ation of rare and <lb/>mo&longs;t tenuous Sub&longs;tances. </s> <s>Moreover, we que&longs;tion how to effect <lb/>the Conden&longs;ation and Rarefaction of the Bodies which may be <lb/>rarefied and conden&longs;ed, &longs;tudying in what manner it may be done <lb/>without introducing of a <emph type="italics"/>Vacuum,<emph.end type="italics"/> and Penetration of Bodies; <lb/>which doth not hinder, but that in Nature there may be matters <lb/>which admit no &longs;uch accidents, and con&longs;equently do not allow <lb/>roome for tho&longs;e things which you phra&longs;e inconvenient and im­<lb/>po&longs;&longs;ible. </s> <s>And la&longs;tly, <emph type="italics"/>Simplicius,<emph.end type="italics"/> I have on the the &longs;core of &longs;atis­<lb/>fying you, and tho&longs;e Philo&longs;ophers that hold with you, taken <lb/>&longs;ome pains in con&longs;idering how Conden&longs;ation and Rarefaction <lb/>may be under&longs;tood to be performed without admitting Penetra­<lb/>tion of Bodies, and introducing the Void Spaces called Vacuities, <lb/>Effects which you deny and abhorre: for if you would but grant <lb/>them, I would no longer &longs;o re&longs;olutely contradict you. </s> <s>There­<lb/>fore either admit the&longs;e Inconveniences, or accept of my Spe­<lb/>culations, or el&longs;e finde out others more conducing to the <lb/>purpo&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1045"></margin.target><emph type="italics"/>Rarefaction im­<lb/>min&longs;e is that of <lb/>a little Gunpow­<lb/>der into a va&longs;t <lb/>ma&longs;s of Fire.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>As to the denying of Penetration, I am wholly of opi­<lb/>nion with the Peripatetick Philo&longs;ophers; as to that of a <emph type="italics"/>Vacuum,<emph.end type="italics"/><lb/>I would &longs;ee the Demon&longs;tration of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> thorowly examined, <lb/>wherewith he oppo&longs;eth the &longs;ame, and what you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> will <lb/>an&longs;wer to it. <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;hall do me the favour punctually to <lb/>recite the proof of the Philo&longs;opher; and you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> to an­<lb/>&longs;wer it.</s></p><p type="main"> <s>SIMP. <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> as neer as I can remember, breaks out again&longs;t <lb/>certain of the Ancients, who introduced Vacuity, as nece&longs;&longs;ary <lb/>to Motion, &longs;aying, that this without that could not be effected; <pb xlink:href="040/01/743.jpg" pagenum="51"/>to this <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> making oppo&longs;ition, demon&longs;trateth, that on the <lb/>contrary, the effecting of Motion (as we &longs;ee) de&longs;troyeth the Po&longs;iti­<lb/>on of <emph type="italics"/>Vacuum<emph.end type="italics"/>; and his method therein is this. </s> <s>He maketh two <lb/>Suppo&longs;itions, one is touching Moveables different in Gravity <lb/>moved in the &longs;ame <emph type="italics"/>Medium:<emph.end type="italics"/> the other is concerning the &longs;ame <lb/>Moveable moved in &longs;everal <emph type="italics"/>Medium's.<emph.end type="italics"/> As to the fir&longs;t, he &longs;uppo­<lb/>&longs;eth that Moveables different in Gravity, move in the &longs;ame <lb/><emph type="italics"/>Medium<emph.end type="italics"/> with unequal Velocities, which bear to each other the <lb/>&longs;ame proportion as their Gravities: &longs;o that, for example, a Move­<lb/>able ten times heavier than another, moveth ten times more &longs;wift­<lb/>ly. </s> <s>In the other Po&longs;ition he a&longs;&longs;umes, that the Velocity of the <lb/>&longs;ame Moveable in different <emph type="italics"/>Medium's<emph.end type="italics"/> are in Reciprocal to that of <lb/>the thickne&longs;&longs;e or Den&longs;ity of the &longs;aid <emph type="italics"/>Medium's<emph.end type="italics"/>: &longs;o that &longs;uppo­<lb/>&longs;ing <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> that the Cra&longs;&longs;itude of the Water was ten times as great <lb/>as that of the Air, he will have the Velocity in the Air to be <lb/>ten times more than the Velocity in the Water. </s> <s>And from this &longs;e­<lb/>cond A&longs;&longs;umption he draweth his Demon&longs;tration in this manner. <lb/></s> <s>Becau&longs;e the tenuity of <emph type="italics"/>Vacuum<emph.end type="italics"/> infinitely &longs;urpa&longs;&longs;eth the corpu­<lb/>lence, though never &longs;o &longs;ubtil, of any whatever Replete <emph type="italics"/>Medi­<lb/>um,<emph.end type="italics"/> every Moveable that in the Replete <emph type="italics"/>Medium<emph.end type="italics"/> moveth a cer­<lb/>tain &longs;pace in a certain time, in a <emph type="italics"/>Vacuum<emph.end type="italics"/> would pa&longs;&longs;e the &longs;ame <lb/>in an in&longs;tant: But to make a Motion in an in&longs;tant is impo&longs;&longs;ible: <lb/>Therefore to introduce Vacuity in the accompt of Motion is im­<lb/>po&longs;&longs;ible.</s></p><p type="main"> <s>SALV. </s> <s>The Argument one may &longs;ee to be <emph type="italics"/>ad hominem,<emph.end type="italics"/> that is, <lb/><arrow.to.target n="marg1046"></arrow.to.target><lb/>again&longs;t tho&longs;e who would make a <emph type="italics"/>Vacuum<emph.end type="italics"/> nece&longs;&longs;ary to Motion; <lb/>but if I &longs;hall admit of the Argument as concludent, granting <lb/>withal, that in Vacuity there would be no Motion; yet the Po&longs;i­<lb/>tion of Vacuity taken ab&longs;olutely, and not in relation to Motion, <lb/>is not thereby overthrown. </s> <s>But to tell you what tho&longs;e Ancients, <lb/>peradventure, might an&longs;wer, that &longs;o we may the better di&longs;cover <lb/>how far the Demon&longs;tration of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> holds good, methinks that <lb/>one might oppo&longs;e his A&longs;&longs;umptions, denying them both. </s> <s>And as <lb/>to the fir&longs;t: I greatly doubt that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> never experimented <lb/>how true it is, that two &longs;tones, one ten times heavier than the o­<lb/>ther, let fall in the &longs;ame in&longs;tant from an height, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> of an hun­<lb/>dred yards, were &longs;o different in their Velocity, that upon the <lb/>arrival of the greater to the ground, the other was found not to <lb/>have de&longs;cended &longs;o much as ten yards.</s></p><p type="margin"> <s><margin.target id="marg1046"></margin.target>Ari&longs;totle's <emph type="italics"/>Argu­<lb/>ment again&longs;t a<emph.end type="italics"/><lb/>Vacuum <emph type="italics"/>is<emph.end type="italics"/> ad <lb/>hominem.</s></p><p type="main"> <s>SIMP. Why, it may be &longs;een by his own words, that he confe&longs;­<lb/>&longs;eth he had made the Experiment, for he &longs;aith, [<emph type="italics"/>We &longs;ee the more <lb/>grave<emph.end type="italics"/>] now that <emph type="italics"/>Seeing<emph.end type="italics"/> implieth that he had tried the Experi­<lb/>ment.</s></p><p type="main"> <s>SAGR. </s> <s>But I, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that have made proof thereof, do a&longs;­<lb/>&longs;ure you, that a Cannon bullet that weigheth one hundred, rwo <pb xlink:href="040/01/744.jpg" pagenum="52"/>hundred, and more pounds, will not one Palme anticipate the ar­<lb/>rival of a Musket-bullet to the ground, that weigheth but half <lb/>a pound, falling likewi&longs;e from an height of two hundred yards.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>But without any other Experiments, we may by &longs;hort <lb/>and nece&longs;&longs;ary Demon&longs;trations cleerly prove, that it is not true that <lb/>a Moveable more grave moveth more &longs;wiftly than another le&longs;&longs;e <lb/>grave, confining our meaning &longs;till to Moveables of the &longs;ame Mat­<lb/>ter; and, in &longs;hort, to tho&longs;e of which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;peaketh. </s> <s>For tell <lb/>me, <emph type="italics"/>Simplicius<emph.end type="italics"/> whether you admit, that to every cadent grave <lb/>Body there belongeth by nature one determinate Velocity; &longs;o <lb/>as that it cannot be encrea&longs;ed or dimini&longs;hed in it without u&longs;ing vi­<lb/>olence to it, or impo&longs;ing &longs;ome impediment upon it?</s></p><p type="main"> <s>SIMP. </s> <s>It cannot be doubted, but that the &longs;ame Moveable in <lb/>the &longs;ame <emph type="italics"/>Medium<emph.end type="italics"/> hath one e&longs;tabli&longs;hed and by-nature-determinate <lb/>Velocity, which cannot be increa&longs;ed, unle&longs;&longs;e with new <emph type="italics"/>Impetus<emph.end type="italics"/><lb/>conferred on it, or dimini&longs;hed, &longs;ave onely by &longs;ome impediment <lb/>that retards it.</s></p><p type="main"> <s>SALV. </s> <s>If therefore we had two Moveables, the natural Velo­<lb/>cities of which were unequal, it is manife&longs;t, that if we joyned the <lb/>&longs;lower with the &longs;wifter, this would be in part retarded by the <lb/>&longs;lower, and that in part accelerated by the other more &longs;wift. </s> <s>Do <lb/>not you concur with me in this opinion?</s></p><p type="main"> <s>SIMP. </s> <s>I think that it ought undoubtedly &longs;o to &longs;ucceed.</s></p><p type="main"> <s>SALV. </s> <s>But if this be &longs;o, and, it be likewi&longs;e true that a great <lb/>Stone moveth with (&longs;uppo&longs;e) eight degrees of Velocity, and a le&longs;­<lb/>&longs;er with fewer, then joyning them both together, the compound <lb/>of them will move with a Velocity le&longs;&longs;e than eight Degrees: But <lb/>the two Stones joyned together make one Stone greater than <lb/>that before, which moved with eight degrees of Velocity: There­<lb/>fore this greater Stone moveth le&longs;&longs;e &longs;wiftly than the le&longs;&longs;er, which <lb/>is contrary to your Suppo&longs;ition. </s> <s>You &longs;ee therefore, that from the <lb/>&longs;uppo&longs;ing that the more grave Moveable moveth more &longs;wiftly <lb/>than the le&longs;&longs;e grave, I prove unto you that the more grave mo­<lb/>veth le&longs;&longs;e &longs;wiftly.</s></p><p type="main"> <s>SIMP. </s> <s>I find my &longs;elf at a lo&longs;&longs;e, for the truth is, that the le&longs;­<lb/>&longs;er Stone being joyned to the greater, weight is added unto it, and <lb/>weight being added to it, I cannot &longs;ee why there &longs;hould not Ve­<lb/>locity be added to it, or at lea&longs;t why it &longs;hould be dimini&longs;hed <lb/>in it.</s></p><p type="main"> <s>SALV. </s> <s>Here you run into another errour, <emph type="italics"/>Simplicius,<emph.end type="italics"/> for it <lb/>is not true, that that &longs;ame le&longs;&longs;er Stone encrea&longs;eth the weight of <lb/>the greater.</s></p><p type="main"> <s>SIMP. </s> <s>Oh wonderful! this quite &longs;urpa&longs;&longs;eth my apprehen&longs;ion.</s></p><p type="main"> <s>SALV. </s> <s>Not at all, if you will but &longs;tay till I have di&longs;covered <lb/>to you the Equivokes, of which you are in doubt: Therefore <pb xlink:href="040/01/745.jpg" pagenum="53"/>you mu&longs;t know that it is nece&longs;&longs;ary to di&longs;tingui&longs;h betwixt grave <lb/>Bodies &longs;et on Moving, and the &longs;ame con&longs;tituted in Re&longs;t; a Stone <lb/>put into the Ballance not onely acquireth greater weight, by lay­<lb/>ing another Stone upon it, but al&longs;o the addition of, a Flake of <lb/>Hemp will make it weigh more by tho&longs;e &longs;ix or ten ounces that <lb/>the Hemp &longs;hall weigh; but if you &longs;hould freely let fall the Stone <lb/>tied to the Hemp from an high place, do you think that in the <lb/>Motion the Hemp weigheth down the Stone, &longs;o as to accelerate <lb/>its Motion; or el&longs;e do you believe that it will retard it, &longs;u&longs;tain­<lb/>ing it in part? </s> <s>We indeed feel our &longs;houlders laden, &longs;o long as we <lb/>will oppo&longs;e the Motion that the weight would make which lyeth <lb/>upon our backs; but if we &longs;hould de&longs;cend with the &longs;ame Velocity <lb/>wherewith that &longs;ame grave Body would naturally de&longs;cend, in what <lb/>manner will you that it pre&longs;&longs;e or bear upon us? </s> <s>Do not you &longs;ee <lb/>that this would be a wounding one with a Lance that runneth <lb/>before you, with as much or more &longs;peed than you pur&longs;ue him. <lb/></s> <s>You may conclude therefore that in the free and natural fall, the <lb/>le&longs;&longs;er Stone doth not bear upon the greater, and con&longs;equently doth <lb/>not encrea&longs;e their weight, as it doth in Re&longs;t.</s></p><p type="main"> <s>SIMP. </s> <s>But what if the greater was put upon the le&longs;&longs;er?</s></p><p type="main"> <s>SALV. </s> <s>It would encrea&longs;e their weight, in ca&longs;e its Motion were <lb/>more &longs;wift; but it hath been already concluded, that in ca&longs;e the <lb/>le&longs;&longs;er &longs;hould be more &longs;low it would in part retard the Velocity of <lb/>the greater, &longs;o that there Compound would move le&longs;&longs;e &longs;wiftly; <lb/>being greater than the other, which is contrary to your A&longs;&longs;umpti­<lb/>on: Let us conclude therefore, that great Moveables, and like­<lb/>wi&longs;e little, being of the &longs;ame Specifical Gravity, move with like <lb/>Velocity.</s></p><p type="main"> <s>SIMP. </s> <s>Your di&longs;cour&longs;e really is full of ingenuity, yet methinks <lb/>it is hard to conceive that a drop of Bird-&longs;hot, &longs;hould move as <lb/>&longs;wiftly as a Canon-bullet.</s></p><p type="main"> <s>SALV. </s> <s>You may &longs;ay a grain of Sand as fa&longs;t as a Mill-&longs;tone. <lb/></s> <s>I would not have you, <emph type="italics"/>Simplicius,<emph.end type="italics"/> to do as &longs;ome others are wont <lb/>to do, and diverting the di&longs;cour&longs;e from the principal de&longs;ign, fa­<lb/>&longs;ten upon &longs;ome one &longs;aying of mine that may want an hairs-breadth <lb/>of the truth, and under this hair hide a defect of another man as <lb/>big as the Cable of a Ship. <emph type="italics"/>Aristotle<emph.end type="italics"/> &longs;aith, a Ball of Iron of an <lb/>hundred pounds weight falling, from an height of an hundred yards, <lb/>commeth to the ground before that one of one pound is de&longs;cended <lb/>one &longs;ole yard: I &longs;ay, that they arrive at the earth both in the &longs;ame <lb/>time: You find, that the bigger anticipates the le&longs;&longs;er two Inches, <lb/>that is to &longs;ay, that when the great one falls to the ground, the o­<lb/>ther is di&longs;tant from it two inches: you go about to hide under <lb/>the&longs;e two inches the ninety nine yards of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and &longs;peaking <lb/>onely to my &longs;mall errour, pa&longs;&longs;e over in &longs;ilence the other great one. <pb xlink:href="040/01/746.jpg" pagenum="54"/><emph type="italics"/>Ari&longs;totlee<emph.end type="italics"/> affirmeth, that Moveables of different Gravities in the <lb/>&longs;ame <emph type="italics"/>Medium<emph.end type="italics"/> move (as far as concerneth Gravity) with Veloci­<lb/>ties proportionate to their Weights; and exemplifieth it by <lb/>Moveables, wherein one may di&longs;cover the pure and ab&longs;olute effect <lb/>of Weight, omitting the other Con&longs;iderations, as well of Figures, <lb/>as of the minute Motions; which things receive great alteration <lb/>from the <emph type="italics"/>Medium,<emph.end type="italics"/> which altereth the &longs;imple effect of the &longs;ole <lb/>Gravity; wherefore we &longs;ee Gold, that is heavier than any other <lb/>matter, being reduced into a very thin Leaf, to go flying to and <lb/>again through the Air, the like do Stones beaten to very &longs;mall <lb/>Powder. </s> <s>But if you would maintain the Univer&longs;al Propo&longs;ition, it <lb/>is requi&longs;ite that you &longs;hew the proportion of the Velocities to be <lb/>ob&longs;erved in all grave Bodies, and that a Stone of twenty pounds <lb/>moveth ten times &longs;wifter than one of two: which, I tell you, is <lb/>fal&longs;e, and that falling from an height of fifty or an hundred yards, <lb/>they come to the ground in the &longs;ame in&longs;tant.</s></p><p type="main"> <s>SIMP. </s> <s>Perhaps in very great heights of Thou&longs;ands of yards <lb/>that would happen, which is not &longs;een to occur in the&longs;e le&longs;&longs;er <lb/>heights.</s></p><p type="main"> <s>SALV. </s> <s>If this was the Meaning of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> you have in­<lb/>volved him in another Errour, which will be found a Lie; for <lb/>there being no &longs;uch perpendicular altitudes found on the Earth, <lb/>its a clear ca&longs;e, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> was not able to have made an Experi­<lb/>ment thereof; and yet would per&longs;wade us that he had, whil&longs;t he <lb/>&longs;aith, that the &longs;aid effect is <emph type="italics"/>&longs;een.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> indeed makes no u&longs;e of this Principle, but of <lb/>that other, which I believe is not obnoxious to the&longs;e doubts.</s></p><p type="main"> <s>SALV. </s> <s>Why that al&longs;o is no le&longs;&longs;e fal&longs;e than this; and I admire <lb/>that you do not of your &longs;elf perceive the fallacy, and di&longs;cern, that <lb/>&longs;hould it be true, that the &longs;ame Moveable in <emph type="italics"/>Medium's<emph.end type="italics"/> of dif­<lb/>ferent Subtilty and Rarity, and, in a word, of different Ce&longs;&longs;ion, <lb/>&longs;uch, for example, as are Water and Air, move with a greater <lb/>Velocity in the Air than in the Water, according to the propor­<lb/>tion of the Airs Rarity to the Rarity of the Water, it would <lb/>follow that every Moveable that de&longs;cendeth in the Air would <lb/>de&longs;cend al&longs;o in the Water: Which is &longs;o fal&longs;e, that very many <lb/>Bodies de&longs;cend in the Air, that in the Water do not onely not <lb/>de&longs;cend, but al&longs;o ri&longs;e upwards.</s></p><p type="main"> <s>SIMP I do not under&longs;tand the nece&longs;&longs;ity of your Con&longs;equence: <lb/>and I will &longs;ay farther, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;peaketh of tho&longs;e Grave­<lb/>bodies that de&longs;cend in the one <emph type="italics"/>Medium<emph.end type="italics"/> and in the other, and not <lb/>of tho&longs;e that de&longs;cend in the Air and a&longs;cend in the Water.</s></p><p type="main"> <s>SALV. </s> <s>You produce for the Phil&longs;opher &longs;uch Pleas as he, with­<lb/>out all doubt, would never alledge, for that they aggravate the <lb/>fir&longs;t mi&longs;take. </s> <s>Therefore tell me, if the Cra&longs;situde of the Water, <pb xlink:href="040/01/747.jpg" pagenum="55"/>or whatever it be that retardeth the Motion, hath any proporti­<lb/>on to the Cra&longs;&longs;itude of the Air that le&longs;&longs;e retards it; and if it have; <lb/>do you a&longs;&longs;ign it us, at plea&longs;ure.</s></p><p type="main"> <s>SIMP. </s> <s>It hath &longs;uch a proportion, and we will &longs;uppo&longs;e it to be <lb/>decuple; and that therefore the Velocity of a Grave Body, that <lb/>de&longs;cends in both the Elements, &longs;hall be ten times &longs;lower in the Wa­<lb/>ter than in the Air.</s></p><p type="main"> <s>SALV. </s> <s>I will take one of tho&longs;e Grave-Bodies that de&longs;cend in <lb/>the Air, but not in the Water; as for in&longs;tance, a Ball of Wood, <lb/>and de&longs;ire that you will a&longs;&longs;ign it what Velocity you plea&longs;e, whil&longs;t it <lb/>de&longs;cends through the Air.</s></p><p type="main"> <s>SIMP. </s> <s>Suppo&longs;e we, that it move with twenty degrees of Velo­<lb/>city.</s></p><p type="main"> <s>SALV. </s> <s>Very well: And it is manife&longs;t, that that Velocity to <lb/>&longs;ome other le&longs;&longs;er, may have the &longs;ame proportion, that the Cra&longs;&longs;i­<lb/>tude of the Water hath to that of the Air; and that this &longs;hall be <lb/>the Velocity of the two only degrees: &longs;o that exactly to an hair, <lb/>and in direct conformity to the A&longs;&longs;umption of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> it &longs;hould <lb/>be concluded, That the Ball of Wood, which in the Air, ten times <lb/>more yielding, moveth de&longs;cending with twenty degrees of Veloci­<lb/>ty, in the Water &longs;hould de&longs;cend with two, and not return from the <lb/>bottom to flote a-top, as it doth: unle&longs;s you will &longs;ay, that the <lb/>a&longs;cending of the Wood to the top is the &longs;ame in the Water, as its <lb/>&longs;inking to the bottom with two degrees of Velocity; which I do <lb/>not believe. </s> <s>But &longs;eeing that the Ball of Wood de&longs;cends not to the <lb/>bottom, I rather think that you will grant me, that &longs;ome other Ball, <lb/>of other matter different from Wood, might be found that de&longs;cends <lb/>in the Water with two degrees of Velocity.</s></p><p type="main"> <s>SIMP. </s> <s>Que&longs;tionle&longs;&longs;e there might; but it mu&longs;t be of a matter <lb/>con&longs;iderably more grave than Wood.</s></p><p type="main"> <s>SALV. </s> <s>This is that which I de&longs;ired to know. </s> <s>But this &longs;econd <lb/>Ball, which in the Water de&longs;cendeth with two degrees of Velocity, <lb/>with what Velocity will it de&longs;cend in the Air? </s> <s>It is requi&longs;ite (if <lb/>you will maintain <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> Rule) that you an&longs;wer that it will <lb/>move with twenty degrees: But you your &longs;elf have a&longs;&longs;igned twen­<lb/>ty degrees of Velocity to the Ball of Wood; Therefore this, and <lb/>the other that is much more grave, will move thorow the Air with <lb/>equall Velocity. </s> <s>Now how doth the Philo&longs;opher reconcile this <lb/>Conclu&longs;ion with that other of his, that the Moveables of different <lb/>Gravity, move in the &longs;ame <emph type="italics"/>Medium<emph.end type="italics"/> with different Velocities, and <lb/>&longs;o different as are their Gravities? </s> <s>But, without any deep &longs;tudies, <lb/>how comes it to pa&longs;s that you have not ob&longs;erved very frequent, <lb/>and very palpable Accidents, and not con&longs;idered two Bodies, that in <lb/>the Water will move one an hundred times more &longs;wiftly than the <lb/>other, but that again in the Air that &longs;wifter one will not out-go the <pb xlink:href="040/01/748.jpg" pagenum="56"/>other, one &longs;ole Cente&longs;m? </s> <s>As for example, an Egge of Marble will <lb/>de&longs;cend in the Water an hundred times fa&longs;ter than one of an Hen, <lb/>when as in the Air, at the height of twenty Yards it will not anti­<lb/>cipate it four Inches: and, in a word, &longs;uch a certain Grave Body <lb/>will &longs;ink to the bottom in three hours in ten fathom Water, that <lb/>in the Air will pa&longs;s the &longs;ame &longs;pace in one or two pul&longs;es, and &longs;uch <lb/>another (as for in&longs;tance a Ball of Lead) will pa&longs;s that number of <lb/>fathoms with ea&longs;e in le&longs;s than double the time. </s> <s>And here I &longs;ee <lb/>plainly, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that you find, that herein there is no place left <lb/>for any di&longs;tinction, or reply. </s> <s>Conclude we therefore, that that <lb/>&longs;ame Argument concludeth nothing again&longs;t <emph type="italics"/>Vacuum<emph.end type="italics"/>; and if it <lb/>&longs;hould, it would only overthrow Spaces con&longs;iderably great, which <lb/>neither I, nor, as I take it, tho&longs;e <emph type="italics"/>Ancients<emph.end type="italics"/> did &longs;uppo&longs;e to be natu­<lb/>rally allowed, though, perhaps, with violence they may be effe­<lb/>cted, as, me thinks, one may collect from &longs;everal Experiments, which <lb/>it would be two tedious to go about at pre&longs;ent to produce.</s></p><p type="main"> <s>SAGR. </s> <s>Seeing that <emph type="italics"/>Simplicius<emph.end type="italics"/> is &longs;ilent, I will take leave to &longs;ay <lb/>&longs;omething. </s> <s>In regard you have with &longs;ufficient plainne&longs;&longs;e demon­<lb/>&longs;trated, that it is not true, That Moveables unequally grave move in <lb/>the &longs;ame <emph type="italics"/>Medium<emph.end type="italics"/> with Velocities proportionate to their Gravities, <lb/>but with equal: de&longs;iring to be under&longs;tood to &longs;peak of Bodies of the <lb/>&longs;ame Matter, or of the &longs;ame Specifick Gravity, but not (as I con­<lb/>ceive) of Gravities different <emph type="italics"/>in Spetie,<emph.end type="italics"/> (for I do not think that <lb/>you intend to prove unto us, that a Ball of Cork moveth with like <lb/>Velocity to one of Lead;) and having moreover very manife&longs;tly <lb/>demon&longs;trated, that it is not true, That the &longs;ame Moveable in <emph type="italics"/>Me­<lb/>diums<emph.end type="italics"/> of different Re&longs;i&longs;tances retain in their Velocities and Tardi­<lb/>ties the &longs;ame proportion as have their Re&longs;i&longs;tances: to me it would <lb/>be a very plea&longs;ing thing to hear, what tho&longs;e be which are ob&longs;erved <lb/>as well in the one ca&longs;e as in the other.</s></p><p type="main"> <s>SALV. </s> <s>The Que&longs;tions are ingenuous, and I have many times <lb/>thought of them: I will relate unto you the Contemplations made <lb/>upon them, and what at length I did from thence infer. </s> <s>After I <lb/>had a&longs;&longs;ured my &longs;elf that it was not true, That the &longs;ame Moveable <lb/>in <emph type="italics"/>Medium's<emph.end type="italics"/> of different Re&longs;i&longs;tance ob&longs;erveth in its Velocity the <lb/>proportion of the Ce&longs;&longs;ion of tho&longs;e <emph type="italics"/>Media<emph.end type="italics"/>; nor yet, again, That in <lb/>the &longs;ame <emph type="italics"/>Medium<emph.end type="italics"/> Moveables of different Gravity retain in their <lb/>Velocities the proportion of tho&longs;e Gravities (&longs;peaking alwaies of <lb/>Gravitles different <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>) I began to put both the&longs;e Accidents <lb/>together, ob&longs;erving that which befell the Moveables different in <lb/>Gravity put into <emph type="italics"/>Mediums<emph.end type="italics"/> of different Re&longs;i&longs;tance, and I perceived <lb/>that the inequality of the Velocities were found to be alwaies <lb/>greater in the more re&longs;i&longs;ting <emph type="italics"/>Medium's,<emph.end type="italics"/> than in the more yielding; <lb/>and that with &longs;uch a diver&longs;ity, that of two Moveables that, de­<lb/>&longs;cending thorow the Air, differ very little in Velocity of Motion, <pb xlink:href="040/01/749.jpg" pagenum="57"/>one will, in the Water, move ten times fa&longs;ter than the other; <lb/>yea: that &longs;uch, as in the Air do &longs;wiftly de&longs;cend, in the Water not <lb/>only will not de&longs;cend, but will be wholly deprived of Motion, <lb/>and, which is yet more, will move upwards: for one &longs;hall &longs;ome­<lb/>times find &longs;ome kind of Wood, or &longs;ome knot, or root of the &longs;ame, <lb/>that in the Water will lye &longs;till, when as in the Air it will &longs;wiftly <lb/>de&longs;cend.</s></p><p type="main"> <s>SAGR. </s> <s>I have many times &longs;et my &longs;elf with an extream patience <lb/>to &longs;ee if I could reduce a Ball of Wax, (which of it &longs;elf doth not <lb/>go to the bottom) by adding to it grains of &longs;and, to &longs;uch a degree <lb/>of Gravity like to the Water, as to make it &longs;tand &longs;till in the <lb/>mid&longs;t of that Element; but I could never, by all the care I <lb/>u&longs;ed, &longs;ucceed in my attempt; &longs;o that I cannot tell, whether any <lb/>Solid matter may be found &longs;o naturally alike in Gravity to Wa­<lb/>ter, as that being put into any place of the &longs;ame, it can re&longs;t or lye <lb/>&longs;till.</s></p><p type="main"> <s>SALV. </s> <s>In this, as well as in a thou&longs;and other actions, many <lb/>Animals are more ingenuous than we. </s> <s>And, in this ca&longs;e, Fi&longs;hes <lb/><arrow.to.target n="marg1047"></arrow.to.target><lb/>would have been able to have given you &longs;ome light, being in this <lb/>affair &longs;o skilful, that at their plea&longs;ure they ^{*} equilibrate them&longs;elves, <lb/><arrow.to.target n="marg1048"></arrow.to.target><lb/>not only with one kind of Water, but with &longs;uch, as, either of their <lb/>own nature, or by means of &longs;ome &longs;upervenient muddine&longs;s, or for <lb/>their &longs;altne&longs;s (which maketh a great alteration) are very diffe­<lb/>rent; equilibrate them&longs;elves, I &longs;ay, &longs;o exactly, that without &longs;tir­<lb/>ring in the lea&longs;t they lye &longs;till in every place: and this, in my opi­<lb/>nion, they do, by making u&longs;e of the In&longs;trument given them by Na­<lb/>ture to that end, <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> of that Bladder which they have in their <lb/>Bodies, which by a very narrow neck an&longs;wereth to their mouth; <lb/>and by that they either, when they would &longs;tand &longs;till, &longs;end forth <lb/>part of the Air that is contained in the &longs;aid Bladders, or, &longs;wimming <lb/>to the top they draw in more, making them&longs;elves by that art one <lb/>while more, another while le&longs;s heavy than the Water, and at their <lb/>plea&longs;ures equilibrating them&longs;elves to the &longs;ame.</s></p><p type="margin"> <s><margin.target id="marg1047"></margin.target><emph type="italics"/>Fi&longs;hes equilibrate <lb/>them&longs;elves admi­<lb/>rably in the Water.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1048"></margin.target>* Or poi&longs;e.</s></p><p type="main"> <s>SAGR I deceived &longs;ome of my Friends with another device; <lb/>for I had made my boa&longs;t unto them, that I would reduce that Ball <lb/>of Wax to an exact <emph type="italics"/>equilibrium<emph.end type="italics"/> with the Water, and having put <lb/>&longs;ome &longs;alt Water in the bottom of the Ve&longs;&longs;el, and a-top of that &longs;ome <lb/>fre&longs;h, I &longs;hewed them the Ball, which in the mid&longs;t of the Water <lb/>&longs;tood &longs;till, and being thru&longs;t to the bottom, or to the top, &longs;taid nei­<lb/>ther in this nor that &longs;cituation, but returned to the mid&longs;t.</s></p><p type="main"> <s>SALV. </s> <s>This &longs;ame Experiment is not void of utility; for Phy&longs;i­<lb/><arrow.to.target n="marg1049"></arrow.to.target><lb/>cians, in particular, treating of &longs;undry qualities of Waters, and <lb/>among&longs;t other things, principally of the more or le&longs;s Gravity or <lb/>Levity of this or that: by &longs;uch a Ball, in &longs;uch manner poi&longs;ed and <lb/>adju&longs;ted that it may re&longs;t ambiguous, if I may &longs;o &longs;ay, between <pb xlink:href="040/01/750.jpg" pagenum="58"/>a&longs;cending and de&longs;cending in a Water, upon the lea&longs;t difference <lb/>of weight between two Waters, if that Ball &longs;hall de&longs;cend in the <lb/>one; in the other, that is more grave, it &longs;hall a&longs;cend. </s> <s>And the <lb/>Experiment is &longs;o exact, that the addition of but only two grains <lb/>of Salt, put into &longs;ix pounds of Water, &longs;hall make that Ball to <lb/>a&longs;cend from the bottom to the &longs;urface, which was but a little be­<lb/><arrow.to.target n="marg1050"></arrow.to.target><lb/>fore de&longs;cended thither. </s> <s>And moreover, I will tell you this in con­<lb/>firmation of the exactne&longs;s of this Experiment, and withall for a <lb/>clear proof of the Non-re&longs;i&longs;tance of Water to divi&longs;ion, that not <lb/>only the ingravitating it with the mixture of &longs;ome matter heavier <lb/>than it, maketh that &longs;o notable difference, but the warming or <lb/>cooling of it a little produceth the &longs;ame effect, and with &longs;o &longs;ubtil <lb/>an operation, that the infu&longs;ing four diops of other Water, a lit­<lb/>tle warmer, or a little colder, than the &longs;ix pounds, &longs;hall cau&longs;e the <lb/>Ball to ri&longs;e or &longs;ink in the &longs;ame; to &longs;ink in it upon the infu&longs;ion of <lb/>the warm, and to ri&longs;e at the infu&longs;ion of the cold. </s> <s>Now &longs;ee how <lb/>much tho&longs;e Philo&longs;ophers are deceived, who would introduce in <lb/>Water vi&longs;co&longs;ity, or other conjunction of parts which make it to <lb/>re&longs;i&longs;t Divi&longs;ion or Penetration.</s></p><p type="margin"> <s><margin.target id="marg1049"></margin.target><emph type="italics"/>A Ball of Wax <lb/>prepared to make <lb/>the Experiment of <lb/>the different Gra­<lb/>vities of Waters.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1050"></margin.target><emph type="italics"/>Water bath no <lb/>Re&longs;i&longs;tance to Di­<lb/>vi&longs;ion.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>I have &longs;een many Convincing Di&longs;cour&longs;es touching <lb/><arrow.to.target n="marg1051"></arrow.to.target><lb/>this Argument in a ^{*} Treati&longs;e of our <emph type="italics"/>Accademick<emph.end type="italics"/>; yet never the le&longs;s <lb/>there is re&longs;ting in me a &longs;trong &longs;cruple, which I know not how to <lb/>remove: For if nothing of Tenacity, or Coherence re&longs;ides among&longs;t <lb/>the parts of Water, how can it bear it &longs;elf up in rea&longs;onable big <lb/>and high Tumours; in particular, upon the leaves of Cole-worts <lb/>without di&longs;per&longs;ing or levelling?</s></p><p type="margin"> <s><margin.target id="marg1051"></margin.target>* The Tract cited <lb/>in this place is <lb/>that which we <lb/>di&longs;po&longs;e fir&longs;t in <lb/>Order, in the <lb/>fir&longs;t part of this <lb/>Tome,</s></p><p type="main"> <s>SALV. </s> <s>Although it be true, that he who is Ma&longs;ter of a true <lb/>Conclu&longs;ion, may re&longs;olve all Objections that can be brought again&longs;t <lb/>it, yet will not I arrogate to my &longs;elf the power &longs;o to do; nor <lb/>ought my in&longs;ufficiency becloud the &longs;plendour of Truth. </s> <s>Fir&longs;t, <lb/>therefore, I confe&longs;s that I know not how it cometh to pa&longs;s, that <lb/>tho&longs;e Globes of Water &longs;u&longs;tain them&longs;elves at &longs;uch an height and <lb/>bigne&longs;s, albeit I certainly know that it doth not proceed from any <lb/><arrow.to.target n="marg1052"></arrow.to.target><lb/>internal Tenacity that is between its parts; &longs;o that it remaineth <lb/>neœ&longs;&longs;ary, that the Cau&longs;e of that Effect do re&longs;ide without. </s> <s>That it <lb/>is not Internal, be&longs;ides tho&longs;e Experiments already &longs;hewn you, I can <lb/>prove by another mo&longs;t convincing one. </s> <s>If the parts of that Wa­<lb/>ter, which con&longs;erveth it &longs;elf in a Globe or Tumour whil&longs;t it is en­<lb/>compa&longs;&longs;ed by the Air, had an internal Cau&longs;e for &longs;o doing, they <lb/>would much better &longs;u&longs;tain them&longs;elves being environed by a <emph type="italics"/>Medi­<lb/>um,<emph.end type="italics"/> in which they had le&longs;s propen&longs;ion to de&longs;cend, than they have <lb/>in the Ambient Air: But every Fluid Body more grave than the <lb/>Air would be &longs;uch a <emph type="italics"/>Medium<emph.end type="italics"/>; as, for in&longs;tance, Wine: And there­<lb/>fore, infu&longs;ing Wine about that Globe of Water, it might rai&longs;e it <lb/>&longs;elf on every &longs;ide, and yet the parts of the Water, conglutinated <pb xlink:href="040/01/751.jpg" pagenum="59"/>by the internal Vi&longs;co&longs;ity, never di&longs;&longs;olve: But it doth not happen <lb/>&longs;o; nay, no &longs;ooner doth the circumfu&longs;ed liquor approach thereto, <lb/>but, without &longs;taying till it ri&longs;e much about it, the little globes of <lb/>Water will di&longs;&longs;olve and become flat, re&longs;ting under the Wine, if it <lb/>was red. </s> <s>The Cau&longs;e therefore of this Effect is External, and per­<lb/>haps in the Ambient Air: and, indeed, one may ob&longs;erve a great <lb/>di&longs;&longs;ention between the Air and Water; which I have ob&longs;erved <lb/>in another Experiment; and this it is: If I fill a ^{*} Ball of Chri&longs;tal, <lb/><arrow.to.target n="marg1053"></arrow.to.target><lb/>that hath a mouth as narrow as the hollow of a &longs;traw, with water, <lb/>and when it is thus full, turn it with its mouth downwards, yet will <lb/>not the Water, although very heavy, and prone to de&longs;cend tho­<lb/>row the Air, nor the Air, as much di&longs;po&longs;ed on the other hand, as <lb/>being very light, to a&longs;cend thorow the Waters, yet will they not <lb/>(I &longs;ay) agree that that &longs;hould de&longs;cend, i&longs;&longs;uing out at the mouth, <lb/>and this a&longs;cend, entering in at the &longs;ame: but they both continue <lb/>aver&longs;e and contumacious. </s> <s>Again, on the contrary, if I pre&longs;ent to <lb/>that mouth a ve&longs;&longs;el of red Wine, which is almo&longs;t in&longs;en&longs;ibly le&longs;s <lb/>grave than Water, we &longs;hall &longs;ee it in an in&longs;tant gently to a&longs;cend by <lb/>red &longs;treams thorow the Water, and the Water with like Tardity to <lb/>de&longs;cend through the Wine, without ever mixing with each other, <lb/>till that in the end, the Ball will be full of Wine, and the Water <lb/>Will all &longs;ink unto the bottom of the Ve&longs;&longs;el underneath. </s> <s>Now <lb/>what are we to &longs;ay, or what are we to infer, but a di&longs;agreement <lb/>between the Water and Air, occult to me, but perhaps -----</s></p><p type="margin"> <s><margin.target id="marg1052"></margin.target><emph type="italics"/>Water formed into <lb/>great drops upon <lb/>the Leaves of Col­<lb/>worts, how they <lb/>con&longs;i&longs;t.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1053"></margin.target>* Or bottle.</s></p><p type="main"> <s>SIMP. </s> <s>I can &longs;carce refrain my laughter to &longs;ee the great Anti­<lb/>pathy that <emph type="italics"/>Salviatus<emph.end type="italics"/> hath to Antipathy, &longs;o that he will not &longs;o much <lb/>as name it, and yet it is &longs;o accommodate to re&longs;olve the doubt.</s></p><p type="main"> <s>SALV. </s> <s>Now let this, for the &longs;ake of <emph type="italics"/>Simplicius<emph.end type="italics"/> be the &longs;oluti­<lb/>on of our &longs;cruple; and leaving the Digre&longs;&longs;ion, let us return to our <lb/>purpo&longs;e. </s> <s>Seeing that the difference of Velocity in Moveables of <lb/>divers Gravities is found to be more and more, as the <emph type="italics"/>Mediums<emph.end type="italics"/> are <lb/>more and more Re&longs;i&longs;ting: And withall, that in a <emph type="italics"/>Medium<emph.end type="italics"/> of <lb/>Quick&longs;ilver, Gold doth not only go to the bottom more &longs;wiftly <lb/>than Lead, but it alone de&longs;cends in it, and all other Metals and <lb/>Stones move upwards therein, and flote thereon; whereas between <lb/>Balls of Gold, Lead, Bra&longs;s, Porphiry, or other grave matters, the in­<lb/>equality of motion in the Air &longs;hall be almo&longs;t wholly in&longs;en&longs;ible, for <lb/>it is certain, that a Ball of Gold in the end of the de&longs;cent of an <lb/><arrow.to.target n="marg1054"></arrow.to.target><lb/>hundred yards &longs;hall not out-&longs;trip one of Bra&longs;s four Inches: &longs;eeing <lb/>this, I &longs;ay, I have thought, that if we wholly took away the <lb/>Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> all Matters would de&longs;cend with equall <lb/>Velocity.</s></p><p type="margin"> <s><margin.target id="marg1054"></margin.target><emph type="italics"/>Re&longs;i&longs;tance of the<emph.end type="italics"/><lb/>Medium <emph type="italics"/>remo­<lb/>ved, all Matters, <lb/>though of different <lb/>Gravities would <lb/>move with like <lb/>Velocity.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>This is a bold &longs;peech, <emph type="italics"/>Salviatus,<emph.end type="italics"/> I &longs;hall never believe <lb/>that in <emph type="italics"/>Vacuity<emph.end type="italics"/> it &longs;elf, if &longs;o be one &longs;hould allow Motion in it, a lock <lb/>of Wooll would move as &longs;wiftly as a piece of Lead.</s></p><pb xlink:href="040/01/752.jpg" pagenum="60"/><p type="main"> <s>SALV. </s> <s>Fair and &longs;oftly, <emph type="italics"/>Simplicius,<emph.end type="italics"/> your &longs;cruple is not &longs;o ab­<lb/>&longs;truce, nor I &longs;o incautelous, that you &longs;hould need to think that I <lb/>was not advi&longs;ed of it, and that con&longs;equently I have not found a re­<lb/>ply to it. </s> <s>Therefore, for my explanation, and your information, <lb/>hearken to what I &longs;hall &longs;ay. </s> <s>We are upon the examination of <lb/>what would befall Moveables exceeding different in weight in a <lb/><emph type="italics"/>Medium,<emph.end type="italics"/> in ca&longs;e it &longs;hould have no Re&longs;i&longs;tance, &longs;o that all the diffe­<lb/>rence of Velocity that is found between the &longs;aid Moveables ought <lb/>to be referred to the &longs;ole inequality of Weight. </s> <s>And becau&longs;e on­<lb/>ly a Space altogether void of Air, and of every other, though te­<lb/>nuous and yielding Body, would be apt &longs;en&longs;ibly to &longs;hew us what <lb/>we &longs;eek, &longs;ince we want &longs;uch a Space, let us &longs;ucce&longs;&longs;ively ob&longs;erve that <lb/>which happeneth in the more &longs;ubtill and le&longs;&longs;e re&longs;i&longs;ting <emph type="italics"/>Mediums,<emph.end type="italics"/><lb/>in compari&longs;on of that which we &longs;ee to happen in others le&longs;&longs;e &longs;ubtill <lb/>and more re&longs;i&longs;ting: for if we &longs;hould really find the Moveables <lb/>different in Gravity to differ le&longs;&longs;e and le&longs;&longs;e in Velocity, according <lb/>as the <emph type="italics"/>Mediums<emph.end type="italics"/> are found more and more yielding; and that, <lb/>finally, although extreamly unequal in weight, in a <emph type="italics"/>Medium<emph.end type="italics"/> more <lb/>tenuous than any other, though not void, the difference of Velo­<lb/>city di&longs;covers it &longs;elf to be very &longs;mall, and almo&longs;t unob&longs;ervable, I <lb/>conceive that we may, and that upon very probable conjecture, <lb/>believe, that in a <emph type="italics"/>Vacuum<emph.end type="italics"/> their Velocities would be exactly equal. <lb/></s> <s>Therefore let us con&longs;ider that which hapneth in the Air; wherein <lb/>to have a Figure of an uniform Superficies, and very light Matter, <lb/>I will that we take a blown Bladder, in which the included Air <lb/>will weigh little or nothing in a <emph type="italics"/>Medium<emph.end type="italics"/> of the Air it &longs;elf, becau&longs;e <lb/>it can make but very &longs;mall Compre&longs;&longs;ion therein, &longs;o that the Gravi­<lb/>ty is only that little of the &longs;aid film, which would not be the thou­<lb/>&longs;andth part of the weight of a lump of Lead of the bigne&longs;s of <lb/>the &longs;aid Bladder when blown. </s> <s>The&longs;e, <emph type="italics"/>Simplicius,<emph.end type="italics"/> being let fall <lb/>from the height of four or &longs;ix yards, how great a &longs;pace, do you <lb/>judge, that the Lead would anticipate the Bladder in its de&longs;cent? <lb/></s> <s>A&longs;&longs;ure your &longs;elf that would not move thrice, no nor twice as fa&longs;t, <lb/>although even now you would have had it to have been a thou­<lb/>&longs;and times more &longs;wift.</s></p><p type="main"> <s>SIMP. </s> <s>It is po&longs;&longs;ible that at the beginning of the Motion, that <lb/>is, in the fir&longs;t five or &longs;ix yards this might happen that you &longs;ay; but <lb/>in the progre&longs;&longs;e, and in a long continuation I believe, that the Lead <lb/>would leave it behind, not only &longs;ix, but al&longs;o eight and ten parts of <lb/>twelve.</s></p><p type="main"> <s>SALV. </s> <s>And I al&longs;o believe the &longs;ame: and make no que&longs;tion, <lb/>but that in very great di&longs;tances the Lead will have pa&longs;&longs;ed an hun­<lb/>dred miles of <emph type="italics"/>way,<emph.end type="italics"/> ere the Bladder will have pa&longs;&longs;ed &longs;o much as one. <lb/></s> <s>But this, <emph type="italics"/>Simplicius,<emph.end type="italics"/> which you propound, as an effect contrary to <lb/>my A&longs;&longs;ertion, is that which mo&longs;t e&longs;pecially confirmeth it. </s> <s>It is (I <pb xlink:href="040/01/753.jpg" pagenum="61"/>once more tell you) my intent to declare, That the difference of <lb/>Gravity is in no wi&longs;e the cau&longs;e of the divers velocities of Movea­<lb/>bles of different Gravity, but that the &longs;ame dependeth on exteri­<lb/>our accidents, & in particular, on the Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> &longs;o <lb/>that, this being removed, all Moveables move with the &longs;ame de­<lb/>grees of Velocity. </s> <s>And this I chiefly deduce from that which but <lb/>now you your &longs;elf did admit, and which is very true, namely, that <lb/>of two Moveables, very different in weight, the Velocities more and <lb/>more differ, according as the ^{*} Spaces are greater and greater that <lb/><arrow.to.target n="marg1055"></arrow.to.target><lb/>they pa&longs;&longs;e: an Effect which would not follow, if it did depend on <lb/>the different Gravities: for they being alwaies the &longs;ame, the pro­<lb/>portion betwixt the Spaces would likewi&longs;e alwaies continue the <lb/>&longs;ame, which proportion we &longs;ee &longs;till &longs;ucce&longs;&longs;ively to encrea&longs;e in the <lb/>continuance of the Motion; for that the heavie&longs;t Moveable in the <lb/>de&longs;cent of one yard will not anticipate the lighte&longs;t the tenth part <lb/>of that Space or Way, but in the fall of twelve yards will out-go <lb/>it a third part, in that of an hundred will out&longs;trip it 90/100.</s></p><p type="margin"> <s><margin.target id="marg1055"></margin.target>* Or Waies.</s></p><p type="main"> <s>SIMP. </s> <s>Very well: But following you &longs;tep by &longs;tep, if the dif­<lb/>ference of weight in Moveables of different Gravities cannot <lb/>cau&longs;e the difference of proportion in their Velocities, for that the <lb/>Gravities do not alter; neither then can the <emph type="italics"/>Medium,<emph.end type="italics"/> which is <lb/>&longs;uppo&longs;ed alwaies to continue the &longs;ame, cau&longs;e any alteration in the <lb/>proportion of the Velocities.</s></p><p type="main"> <s>SALV. </s> <s>You wittily bring an in&longs;tance again&longs;t my Po&longs;ition, that <lb/><arrow.to.target n="marg1056"></arrow.to.target><lb/>it is very nece&longs;&longs;ary to remove. </s> <s>I &longs;ay therefore, that a Grave Body <lb/>hath, by Nature, an intrin&longs;ick Principle of moving towards the <lb/>Common Center of heavy things, that is to that of our Terre&longs;trial <lb/>Globe, with a Motion continually accelerated, and accelerated <lb/>alwaies equally, <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> that in equal times there are made equal <lb/>^{*} additions of new Moments, and degrees of Velocities: and this <lb/>ought to be under&longs;tood to hold true at all times when all acciden­<lb/><arrow.to.target n="marg1057"></arrow.to.target><lb/>tal and external impediments are removed; among&longs;t which there <lb/>is one that we cannot obviate, that is the Impediment of the <emph type="italics"/>Me­<lb/>dium,<emph.end type="italics"/> which is Repleat, when as it &longs;hould be opened and latterally <lb/>moved by the falling Moveable, to which tran&longs;ver&longs;e Motion the <lb/><emph type="italics"/>Medium,<emph.end type="italics"/> though fluid, yielding and tranquile, oppo&longs;eth it &longs;elf <lb/>with a Re&longs;i&longs;tance one while le&longs;&longs;er, and another while greater and <lb/>greater, according as it is more &longs;lowly or ha&longs;tily to open to give <lb/>pa&longs;&longs;age to the Moveable, which, becau&longs;e, as I have &longs;aid, it goeth <lb/>of its own nature continually accelerating, it cometh of con&longs;e­<lb/>quence to encounter continually greater Re&longs;i&longs;tance in the <emph type="italics"/>Medi­<lb/>um,<emph.end type="italics"/> and therefore Retardment, and diminution in the acqui&longs;t of <lb/>new degrees of Velocity; &longs;o that in the end, the Velocity arriveth <lb/>to that &longs;wiftne&longs;&longs;e, and the Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> to that <lb/>&longs;trength, that ballancing each other, they take away all further <pb xlink:href="040/01/754.jpg" pagenum="62"/>Acceleration, and reduce the Moveable to an Equable and Uni­<lb/>form Motion, in which it afterwards continually abides. </s> <s>There is <lb/>therefore in the <emph type="italics"/>Medium<emph.end type="italics"/> augmentation of Re&longs;i&longs;tance, not becau&longs;e <lb/>it changeth its E&longs;&longs;ence, but becau&longs;e the Velocity altereth where­<lb/>with it ought to open, and laterally move, to give pa&longs;&longs;age to the <lb/>falling Body, which goeth continually accelerating. </s> <s>Now the <lb/>ob&longs;erving, that the Re&longs;i&longs;tance of the Air to the &longs;mall Moment or <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> of the Bladder is very great, and to the great weight of <lb/>the Lead is very &longs;mall, makes me hold for certain, that if one &longs;hould <lb/>wholly remove it, by adding to the Bladder great a&longs;&longs;i&longs;tance, and <lb/>but very little to the Lead, their Velocities would equalize each <lb/>other. </s> <s>Taking this Principle therefore for granted, That in the <lb/><emph type="italics"/>Medium<emph.end type="italics"/> wherein, either by rea&longs;on of Vacuity, or otherwi&longs;e, there <lb/>were no Re&longs;i&longs;tance that might abate the Velocity of the Motion, <lb/>&longs;o that of all Moveables the Velocities were alike, we might con­<lb/><arrow.to.target n="marg1058"></arrow.to.target><lb/>gruou&longs;ly enough a&longs;&longs;ign the proportions of the Velocities of like <lb/>and unlike Moveables, in the &longs;ame and in different, Replear, and <lb/>therefore Re&longs;i&longs;ting <emph type="italics"/>Medium's.<emph.end type="italics"/> And this we might effect by &longs;tudy­<lb/>ing how much the Gravity of the <emph type="italics"/>Medium<emph.end type="italics"/> abateth from the Gra­<lb/>vity of the Moveable, which Gravity is the In&longs;trument wherewith <lb/>the Moveable makes its Way, repelling the parts of the <emph type="italics"/>Medium<emph.end type="italics"/><lb/>on each Side: an operation that doth not occur in void <emph type="italics"/>Mediums<emph.end type="italics"/>; <lb/>and therefore there is no difference to be expected from the di­<lb/>ver&longs;e Gravity: and becau&longs;e it is manife&longs;t, that the <emph type="italics"/>Medium<emph.end type="italics"/> abateth <lb/>from the Gravity of the Body by it contained, as much as is the <lb/>weight of &longs;uch another ma&longs;s of its own Matter, if the Velocities of <lb/>the Moveables that in a non-re&longs;i&longs;ting <emph type="italics"/>Medium<emph.end type="italics"/> would be (as hath <lb/>been &longs;uppo&longs;ed) equal, &longs;hould dimini&longs;h in that proportion, we <lb/>&longs;hould have what we de&longs;ired. </s> <s>As for example; &longs;uppo&longs;ing that <lb/>Lead be ten thou&longs;and times more grave than Air, but Ebony a <lb/>thou&longs;and times only; of the Velocities of the&longs;e two Matters, which <lb/>ab&longs;olutely taken, that is, all Re&longs;i&longs;tance being removed, would be <lb/>equal, the Air &longs;ub&longs;tracts from the ten thou&longs;and degrees of the <lb/>Lead one, and from the thou&longs;and degrees of the Ebony likewi&longs;e <lb/>abateth one, or, if you will, of its ten thou&longs;and, ten. </s> <s>If there­<lb/>fore the Lead and the Ebony &longs;hall de&longs;cend thorow the Air from <lb/>any height, which, the retardment of the Air removed, they would <lb/>have pa&longs;&longs;ed in the &longs;ame time, the Air will abate from the ten <lb/>thou&longs;and degrees of the Leads Velocity one, but from the ten <lb/>thou&longs;and degrees of Ebony's Velocity it will abate ten: which is <lb/>as much as to &longs;ay, that dividing that Altitude, from which tho&longs;e <lb/>Moveables departed into ten thou&longs;and parts, the Lead will arrive <lb/>at the Earth, the Ebony being left behind, ten, nay, nine of tho&longs;e <lb/>&longs;ame ten thou&longs;and parts. </s> <s>And what el&longs;e is this, but that a Ball of <lb/>Lead, falling from a Tower two hundred yards high, to find how <pb xlink:href="040/01/755.jpg" pagenum="63"/>much it will anticipate one of Ebony of le&longs;&longs;e than four Inches? <lb/></s> <s>The Ebony weigheth a thou&longs;and times more than the Air, but that <lb/>Bladder &longs;o blown, weigheth only four times &longs;o much; the Air <lb/>therefore from the intrin&longs;ick and natural Velocity of the Ebony <lb/>&longs;ubducteth one degree of a thou&longs;and, but from that, which al&longs;o in <lb/>the Bladder would ab&longs;olutely have been the &longs;ame, the Air &longs;ub­<lb/>ducts one part of four: &longs;o that by that time the Ball of Ebony <lb/>falling from the Tower, &longs;hall come to the ground, the Bladder <lb/>&longs;hall have pa&longs;&longs;ed but three quarters of that height. </s> <s>Lead is twelve <lb/>times heavier than Water, but Ivory only twice as heavy; the <lb/>Water therefore, from their ab&longs;olute Velocities which would be <lb/>equal, &longs;hall abate in the Lead the twelfth part, but in the Ivory <lb/>the half: when therefore, in the Water, the Lead &longs;hall have de­<lb/>&longs;cended eleven fathom, the Ivory &longs;hall have de&longs;cended &longs;ix. </s> <s>And, <lb/>arguing by this Rule, I believe, that we &longs;hall find the Experiment <lb/>much more exactly agree with this &longs;ame Computation, than with <lb/>that of <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/> By the like method we might find the Veloci­<lb/>ties of the &longs;ame Moveable in different fluid <emph type="italics"/>Mediums,<emph.end type="italics"/> not compa­<lb/>ring the different Re&longs;i&longs;tances of the <emph type="italics"/>Mediums,<emph.end type="italics"/> but con&longs;idering the <lb/>exce&longs;&longs;es of the Gravity of the Moveable over and above the Gra­<lb/>vities of the <emph type="italics"/>Mediums: v. </s> <s>gr.<emph.end type="italics"/> ^{*} Tin is a thou&longs;and times heavier than <lb/><arrow.to.target n="marg1059"></arrow.to.target><lb/>Air, and ten times heavier than Water; therefore dividing the ab­<lb/>&longs;olute Velocity of the Tin into a thou&longs;and degrees, it &longs;hall move <lb/>in the Air, (which deducteth from it the thou&longs;andth part,) with nine <lb/>hundred ninety nine, but in the Water with nine hundred only; <lb/>being that the Water abateth the tenth part of its Gravity, and <lb/>the Air the thou&longs;andth part. </s> <s>Take a Solid &longs;omewhat heavier than <lb/>Water, as for in&longs;tance, the Wood called Oake, a Ball of which <lb/>weighing, as we will &longs;uppo&longs;e, a thou&longs;and drams, a like quantity <lb/>of Water will weigh nine hundred and fifty, but &longs;o much Air will <lb/>weigh but two drams,: it is manife&longs;t, that &longs;uppo&longs;ing that its ab&longs;o­<lb/>lute Velocity were of a thou&longs;and degrees, in Air there would re­<lb/>main nine hundred ninety eight, but in the Water only fifty; be­<lb/>cau&longs;e that the Water of the thou&longs;and degrees of Gravity taketh <lb/>away nine hundred and fifty, and leaves fifty only; that Solid there­<lb/>fore would move well-near twenty times as fa&longs;t in the Air as Wa­<lb/>ter; like as the exce&longs;&longs;e of its Gravity above that of the Water is <lb/>the twentieth part of its own. </s> <s>And here I de&longs;ire that we may con­<lb/>&longs;ider, that no matters, having a power to move downwards in the <lb/>Water, but &longs;uch as are more grave in Species than it; and con&longs;e­<lb/>quently many hundreds of times, more grave than the Air, in <lb/>&longs;eeking what the proportions of their Velocities are in the Air and <lb/>Water, we may, without any con&longs;iderable errour, make account <lb/>that the Air doth not deduct any thing of moment from the ab&longs;o­<lb/>lute Gravity, and con&longs;equently, from the ab&longs;olute Velocity of &longs;uch <pb xlink:href="040/01/756.jpg" pagenum="66"/>matters: &longs;o that having ea&longs;ily found the exce&longs;&longs;e of their Gravi­<lb/>ty above the Gravity of the Water, we may &longs;ay that their Velo­<lb/>city in the Air, to their Velocity in the Water hath the &longs;ame propor­<lb/>tion, that their total Gravity hath to the exce&longs;&longs;e of this above <lb/>the Gravity of the Water. </s> <s>For example, a Ball of Ivory weigh­<lb/>eth twenty ounces, a like quantity of Water weigheth &longs;eventeen <lb/>ounces: therefore the Velocity of the Ivory in Air, to its Velocity <lb/>in Water is very neer as twenty to three.</s></p><p type="margin"> <s><margin.target id="marg1056"></margin.target><emph type="italics"/>The Velocity of <lb/>Grave Bodies de­<lb/>&longs;cending Natural­<lb/>ly to the Center do <lb/>go continually en­<lb/>crea&longs;ing till that <lb/>by the encrea&longs;e of <lb/>the Re&longs;i&longs;tance of <lb/>the<emph.end type="italics"/> Medium <emph type="italics"/>it <lb/>becometh uniform.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1057"></margin.target>* Or aqui&longs;ts.</s></p><p type="margin"> <s><margin.target id="marg1058"></margin.target><emph type="italics"/>To find the Pro­<lb/>portions of the Ve­<lb/>locities of different <lb/>Moveables in the <lb/>&longs;ame, and in diffe­<lb/>rent<emph.end type="italics"/> Mediums.</s></p><p type="margin"> <s><margin.target id="marg1059"></margin.target>* Or Pewter.</s></p><p type="main"> <s>SAGR. </s> <s>I have made a great acqui&longs;t in a bu&longs;ine&longs;&longs;e of it &longs;elf cu­<lb/>rious, and in which, but without any benefit, I have many times <lb/>wearied my-thoughts: nor would there any thing be wanting for <lb/>the putting the&longs;e Speculations in practice, &longs;ave onely the way <lb/>how one &longs;hould come to know of what Gravity the Air, is in com­<lb/>pari&longs;on to the Water, and con&longs;equently to other heavy matters.</s></p><p type="main"> <s>SIMP. </s> <s>But in ca&longs;e one &longs;hould finde, that the Air in&longs;tead of <lb/>Gravity had Levity, what ought one to &longs;ay of the foregoing di&longs;­<lb/>cour&longs;es, otherwi&longs;e very ingenuous?</s></p><p type="main"> <s>SALV. </s> <s>It would be nece&longs;&longs;ary to confe&longs;&longs;e that they were truly <lb/>Aerial, Light, and Vain. </s> <s>But will you que&longs;tion whether the Air <lb/>be heavy, having the expre&longs;&longs;e <emph type="italics"/>Text<emph.end type="italics"/> of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> that affirmeth it, <lb/>&longs;aying, That all the Elements have Gravity, even the Air it &longs;elf; <lb/><arrow.to.target n="marg1060"></arrow.to.target><lb/>a &longs;igne of which (&longs;ubjoyns he) we have in that a ^{*} Bladder blown, <lb/>weigheth heavier than un&longs;well'd.</s></p><p type="margin"> <s><margin.target id="marg1060"></margin.target>* Or <emph type="italics"/>Boracho<emph.end type="italics"/>; a <lb/>bottle made of a <lb/>Goat skin, u&longs;ed <lb/>to hold wine and <lb/>other Liquids.</s></p><p type="main"> <s>SIMP. </s> <s>That a <emph type="italics"/>Boracho,<emph.end type="italics"/> or Bladder blown, weigheth more, <lb/>might proceed, as I could &longs;uppo&longs;e, not from the Gravity that is <lb/>in the Air, but in the many gro&longs;&longs;e Vapours intermixed with it in <lb/>the&longs;e our lower Regions; by means whereof I might &longs;ay, that the <lb/>Gravity of the Bladder, or <emph type="italics"/>Boracho<emph.end type="italics"/> encrea&longs;eth.</s></p><p type="main"> <s>SALV. </s> <s>I would not have you &longs;ay it, and much le&longs;&longs;e that you <lb/>&longs;hould make <emph type="italics"/>Aristotle<emph.end type="italics"/> &longs;peak it, for he treating of the Elements, <lb/>and de&longs;iring to per&longs;wade me that the Element of Air is grave, <lb/>making me to &longs;ee it by an Experement: if in comming to the proof <lb/>he &longs;hould &longs;ay: Take a Bladder, and fill it with gro&longs;&longs;e Vapours; <lb/>and ob&longs;erve that its weight will encrea&longs;e; I would tell him that <lb/>it would weigh yet more if one &longs;hould fill it with bran; but would <lb/>afterwards adde; that tho&longs;e Experiments prove, that bran, and <lb/>gro&longs;&longs;e Vapours are grave: but as to the Element of Air, I &longs;hould <lb/>be left in the &longs;ame doubt as before. </s> <s>The Experiment of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/><lb/>therefore is good, and the Propo&longs;ition true. </s> <s>But I will not &longs;ay &longs;o <lb/>much, for a certain other rea&longs;on taken expre&longs;ly out of a Philo&longs;o­<lb/>pher who&longs;e name I do not remember, but am &longs;ure that I have read <lb/>it, who argueth the Air to be more grave than light, becau&longs;e it <lb/>more ea&longs;ily carrieth grave Bodies downwards, than the light up­<lb/>wards.</s></p><p type="main"> <s>SAGR. </s> <s>Good i-faith. </s> <s>By this rea&longs;on then, the Air &longs;hall be <pb xlink:href="040/01/757.jpg" pagenum="65"/>much heavier than the Water, &longs;ince, that all Bodies are carried <lb/>more ea&longs;ily downwards thorow the Air than thorow the Water, <lb/>and all light Bodies more ea&longs;ily upwards in this than in that: nay, <lb/>infinite matters a&longs;cend in the Water, that in the Air de&longs;cend. <lb/></s> <s>But be the Gravity of the Bladder, <emph type="italics"/>Simplicius,<emph.end type="italics"/> either by rea&longs;on of <lb/>the gro&longs;&longs;e Vapours, or pure Air, this nothing concerns our pur­<lb/>po&longs;e, for we &longs;eek that which happeneth to Moveables that move <lb/>in this our Vaporous Region. </s> <s>Therefore, returning to that which <lb/>more concerneth me, I would for a full and ab&longs;olute informati­<lb/>on in the pre&longs;ent bu&longs;ine&longs;&longs;e, not onely be a&longs;&longs;ured that the Air is <lb/>grave, as I hold for certain, but I would, if it be po&longs;&longs;ible, know <lb/>what its Gravity is. </s> <s>Therefore, <emph type="italics"/>Salviatus,<emph.end type="italics"/> if you have wherewith <lb/>to &longs;atisfie me in this al&longs;o, I entreat you to favour me with the <lb/>&longs;ame.</s></p><p type="main"> <s>SALV. </s> <s>That there re&longs;ideth in the Air po&longs;itive Gravity, and <lb/><arrow.to.target n="marg1061"></arrow.to.target><lb/>not, as &longs;ome have thought, Levity, which haply is in no Mat­<lb/>ter to be found, the Experiment of the Blown-Bladder, alledged <lb/>by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> affordeth us a &longs;ufficiently-convincing Argument; for <lb/>if the quality of ab&longs;olute and po&longs;itive Levity were in the Air, <lb/>then the Air being multiplied and compre&longs;&longs;ed, the Levity would <lb/>encrea&longs;e, and con&longs;equently the propen&longs;ion of going upwards: <lb/>but Experience &longs;hews the contrary. </s> <s>As to the other demand, that <lb/><arrow.to.target n="marg1062"></arrow.to.target><lb/>is, of the Method how to inve&longs;tigate its Gravity, I have tried to <lb/>do it in this manner: I have taken a pretty bigge Gla&longs;&longs;e ^{*} Bottle, <lb/><arrow.to.target n="marg1063"></arrow.to.target><lb/>with its neck bended, and a Finger-&longs;tall of Leather fa&longs;t about <lb/>it, having in the top of the &longs;aid Finger-&longs;tall in&longs;erted and fa­<lb/>&longs;tened a Valve of Leather, by which with a Siringe I have made <lb/>pa&longs;&longs;e into the Bottle by force a great quantity of Air, of which, <lb/>becau&longs;e it admits of great Conden&longs;ation, it may take in two or <lb/>three other Bottles-ful over and above that which is naturally con­<lb/>tained therein. </s> <s>Then I have in an exact Ballance very preci&longs;ely <lb/>weighed that Bottle with the Air compre&longs;&longs;ed within it, adju&longs;ting <lb/>the weight with &longs;mall Sands. </s> <s>Afterwards, the Valve being opened, <lb/>and the Air let out, that was violently conteined in the Ve&longs;&longs;el, I <lb/>have put it again into the Scales, and finding it notably aleviated, <lb/>I have by degrees taken &longs;o much Sand from the other Scale, keep­<lb/>ing it by it &longs;elf, that the Ballance hath at la&longs;t &longs;tood <emph type="italics"/>in Equilibrio<emph.end type="italics"/><lb/>with the remaining counter-poi&longs;e, that is with the Bottle. </s> <s>And <lb/>here there is no que&longs;tion, but that the weight of the re&longs;erved Sand <lb/>is that of the Air that was forceably driven into the Bottle, and <lb/>which is at la&longs;t gone out thence. </s> <s>But this Experiment hitherto a&longs;­<lb/>&longs;ureth me of no more but this, that the Air violently deteined in <lb/>the Ve&longs;&longs;el, weigheth as much as the re&longs;erved Sand, but how much <lb/>the Air re&longs;olutely and determinately weigheth in re&longs;pect of the <lb/>Water, or other grave matter, I do not as yet know, nor can <pb xlink:href="040/01/758.jpg" pagenum="66"/>I tell, unle&longs;&longs;e I mea&longs;ure the quantity of the Air compre&longs;&longs;ed: and <lb/>for the di&longs;covering of this a Rule is nece&longs;&longs;ary, which I have <lb/>found may be performed two manner of wayes, one of which <lb/>is to take &longs;uch another Bottle or Flask as the former, and in like <lb/>manner bended, with a Finger-&longs;tall of Leather, the end of which <lb/>may clo&longs;ely imbrace the Volve of the other, and let it be very <lb/>fa&longs;t tied about it. </s> <s>It's requi&longs;ite, that this &longs;econd Bottle be bored in <lb/>the bottom, &longs;o that as by that hole we may thru&longs;t in a Wier, <lb/>wherewith we may, at plea&longs;ure, open the &longs;aid Volve, to let out <lb/>the &longs;uperfluous Air of the other Ve&longs;&longs;el, after it hath been weighed: <lb/>but this &longs;econd Bottle ought to be full of Water. </s> <s>All being pre­<lb/>pared in the manner afore&longs;aid, and with the Wier opening the <lb/>Volve, the Air i&longs;&longs;uing out with impetuo&longs;ity, and pa&longs;&longs;ing into the <lb/>Ve&longs;&longs;el of Water, &longs;hall drive it out by the hole at the Bottom: <lb/>and it is manife&longs;t, that the quantity of Water which &longs;hall be <lb/>thru&longs;t out, is equal to the Ma&longs;&longs;e and quantity of Air that &longs;hall <lb/>have i&longs;&longs;ued from th'other Ve&longs;&longs;el: that Water therefore being <lb/>kept, and returning to weigh the Ve&longs;&longs;el lightned of the Air com­<lb/>pre&longs;&longs;ed (which I &longs;uppo&longs;e to have been weighed likewi&longs;e fir&longs;t with <lb/>the &longs;aid forced Air) and the &longs;uperfluous &longs;and being laid by, as I <lb/>directed before; it is manife&longs;t, that this is the ju&longs;t weight of &longs;o <lb/>much Air in ma&longs;&longs;e, as is the ma&longs;&longs;e of the expul&longs;ed and re&longs;erved <lb/>Water; which we are to weigh, and &longs;ee how many times its <lb/>weight &longs;hall contain the weight of the re&longs;erved &longs;and: and we may <lb/>without errour affirme, that the Water is &longs;o many times heavier <lb/>than Air; which &longs;hall not be ten times, as it &longs;eemeth <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/><lb/>held, but very neer four hundred, as the &longs;aid Experiment &longs;heweth.</s></p><p type="margin"> <s><margin.target id="marg1061"></margin.target><emph type="italics"/>The Air hath Po­<lb/>&longs;itive Gravity.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1062"></margin.target><emph type="italics"/>How that Gravity <lb/>may be computed.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1063"></margin.target>* <emph type="italics"/>Un Fia&longs;co,<emph.end type="italics"/> tho&longs;e <lb/>long-neckt gla&longs;&longs;e <lb/>bottles in which <lb/>we have our <lb/><emph type="italics"/>Florence<emph.end type="italics"/> Wine <lb/>brought to us.</s></p><p type="main"> <s>The other way is more expeditious, and it may be done with <lb/>one Ve&longs;&longs;el onely, that is with the fir&longs;t accomodated after the man­<lb/>ner before directed, into which I will not that any other Air be <lb/>put, more than that which naturally is found therein; but I will, <lb/>that we inject Water without &longs;uffering any Air to come out, <lb/>which being forced to yield to the &longs;upervenient Water mu&longs;t of <lb/>nece&longs;&longs;ity be compre&longs;&longs;ed: having gotten in, therefore, as much <lb/>Water as is po&longs;&longs;ible, (but yet without great violence one cannot get <lb/>in three quarters of what the Bottle will hold) put it into the <lb/>Scales, and very carefully weigh it: which done, holding the <lb/>Ve&longs;&longs;el with the neck upwards, open the Volve, letting out the <lb/>Air, of which there will preci&longs;ely i&longs;&longs;ue forth &longs;o much as there is <lb/>Water in the Bottle. </s> <s>The Air being gone out, put the Ve&longs;&longs;el again <lb/>into the Scales, which by the departure of the Air will be found <lb/>lightened, and abating from the oppo&longs;ite Scale the &longs;uperfluous <lb/>weight, it &longs;hall give us the weight of as much Air as there is <lb/>Water in the Bottle.</s></p><p type="main"> <s>SIMP. </s> <s>The Contrivances you found out cannot but be con­<pb xlink:href="040/01/759.jpg" pagenum="67"/>fe&longs;&longs;ed to be witty and very ingenuous, but whil&longs;t, me thinks, they <lb/>fully &longs;atisfie my under&longs;tanding, they another way occa&longs;ion in <lb/>me much Confu&longs;ion, for it being undoubtedly true that the Ele­<lb/>ments in their proper Region are neither heavy nor light, I can­<lb/>not comprehend, how and which way that portion of Air, which <lb/>&longs;eemeth to have weighed <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> four drams of &longs;and, &longs;hould af­<lb/>terwards have that &longs;ame Gravity in the Air, in which the &longs;and is <lb/>contained that weigheth again&longs;t it: and therefore me thinks that <lb/>the Experiment ought not to be practiced in the Element of Air, <lb/>but in a <emph type="italics"/>Medium<emph.end type="italics"/> in which the Air it &longs;elf might exerci&longs;e its quality <lb/>of Gravitation, if it really be owner thereof.</s></p><p type="main"> <s>SALV. </s> <s>Certainly the Objection of <emph type="italics"/>Simplicius<emph.end type="italics"/> is very acute, <lb/>and therefore its nece&longs;&longs;ary, either that it be unan&longs;werable, or that <lb/>the Solution be no le&longs;&longs;e acute. </s> <s>That that Air, which compre&longs;­<lb/>&longs;ed, appeared to weigh as much as that &longs;and, left at liberty in its <lb/>Element is no longer to weigh any thing as the Sand doth, is a thing <lb/>manife&longs;t: and therefore for making of &longs;uch an Experiment, its <lb/>requi&longs;ite to choo&longs;e a place and <emph type="italics"/>Medium<emph.end type="italics"/> wherein the Air as well as <lb/>the Sand might weigh: for, as hath &longs;everal times been &longs;aid, the <lb/><emph type="italics"/>Medium<emph.end type="italics"/> &longs;ub&longs;tracts from the Weight of every Matter that is im­<lb/>merged therein, &longs;o much, as &longs;uch another quantity of the &longs;aid <lb/><emph type="italics"/>Medium,<emph.end type="italics"/> as is that of the ma&longs;&longs;e immer&longs;ed, weigheth: &longs;o that <lb/>the Air depriveth the Air of all its Gravity. </s> <s>The operation, there­<lb/><arrow.to.target n="marg1064"></arrow.to.target><lb/>fore, to the end it were made exactly, ought to be tried in a <emph type="italics"/>Va­<lb/>cuum,<emph.end type="italics"/> wherein every grave Body would exerci&longs;e its Moment <lb/>without any diminution. </s> <s>In ca&longs;e therefore, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that we <lb/>&longs;hould weigh a portion of Air in a <emph type="italics"/>Vacuum,<emph.end type="italics"/> would you then be <lb/>convinced and a&longs;&longs;ured of the bu&longs;ine&longs;&longs;e?</s></p><p type="margin"> <s><margin.target id="marg1064"></margin.target><emph type="italics"/>The Air compre&longs;­<lb/>&longs;ed and violently <lb/>pent up, weigheth in <lb/>a<emph.end type="italics"/> Vacuum; <emph type="italics"/>and <lb/>how its weight is to <lb/>be e&longs;timated.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>Verily I &longs;hould: but this is to defire, or enjoyn that <lb/>which is impo&longs;&longs;ible.</s></p><p type="main"> <s>SALV. </s> <s>And therefore the obligation mu&longs;t needs be great that <lb/>you owe to me, when ever I &longs;hall for your &longs;ake effect an impo&longs;&longs;ibi­<lb/>lity: but I will not &longs;ell you that which I have already given you: <lb/>for we, in the foregoing Experiment, weigh the Air in a <emph type="italics"/>Vacuum,<emph.end type="italics"/><lb/>and not in the Air, or in any other Replete <emph type="italics"/>Medium.<emph.end type="italics"/> That from <lb/>the Ma&longs;s, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that in the fluid <emph type="italics"/>Medium<emph.end type="italics"/> is immerged certain <lb/>Gravity is &longs;ub&longs;tracted by the &longs;aid <emph type="italics"/>Medium,<emph.end type="italics"/> this commeth to pa&longs;s <lb/>by rea&longs;on that it re&longs;i&longs;teth its being opened, driven back, and in a <lb/>word commoved; a &longs;ign of which is its pronene&longs;s to return in&longs;tant­<lb/>ly to fill the Space up again, that the immer&longs;ed ma&longs;s occupied in it, <lb/>as &longs;oon as ever it departeth thence; for if it &longs;uffered not by that <lb/>immer&longs;ion, it would not operate again&longs;t the &longs;ame. </s> <s>Now tell me, <lb/>when you have in the Air the Bottle before filled with the &longs;ame Air <lb/>naturally contained therein, what divi&longs;ion, repul&longs;e, or, in &longs;hort, <lb/>what mutation doth the external ambient Air receive from the &longs;e­<pb xlink:href="040/01/760.jpg" pagenum="68"/>cond Air that was newly infu&longs;ed with force into the Ve&longs;&longs;el? </s> <s>Doth <lb/>it enlarge the Bottle, whereupon the Ambient ought the more to <lb/>retire it &longs;elf to make room for it? </s> <s>Certainly no: And therefore <lb/>we may &longs;ay, that the &longs;econd Air is not immer&longs;ed in the Ambient, <lb/>not occupying any Space therein; but is as if it was in a <emph type="italics"/>Vacuum,<emph.end type="italics"/><lb/>nay more, is really con&longs;tituted in it, and is placed in Vacuities that <lb/>were not repleted by the former un-conden&longs;ed Air. </s> <s>And, really, I <lb/>know not how to di&longs;cern any difference between the two Con&longs;ti <lb/>tutions of Inclo&longs;ed and <emph type="italics"/>Ambient,<emph.end type="italics"/> whil&longs;t in this the <emph type="italics"/>Ambient<emph.end type="italics"/> doth <lb/>no-ways pre&longs;s the Inclo&longs;ed, and in that the Inclo&longs;ed doth not re­<lb/>repul&longs;e the <emph type="italics"/>Ambient<emph.end type="italics"/>: and &longs;uch is the placing of any matter in a <lb/><emph type="italics"/>Vacuum,<emph.end type="italics"/> and the &longs;econd Air compre&longs;sed in the Flask. </s> <s>The weight <lb/>therefore that is found in that &longs;ame conden&longs;ed Air, is the &longs;ame that <lb/>it would have, were it freely di&longs;tended in a <emph type="italics"/>Vacuum.<emph.end type="italics"/> Tis true in­<lb/>deed, that the weight of the Sand that weigheth again&longs;t it, as ha­<lb/>ving been in the open Air, would in a <emph type="italics"/>Vacuum<emph.end type="italics"/> have been a little <lb/>more than ju&longs;t &longs;o heavy; and therefore it is nece&longs;&longs;ary to &longs;ay, that <lb/>the weighed Air is in reality &longs;omewhat le&longs;&longs;e heavy than the Sand <lb/>that counterpoi&longs;eth it, that is, &longs;o much, by how much the like <lb/>quantity of Air would weigh in a <emph type="italics"/>Vacuum.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>I had thought that there was &longs;omething to have been <lb/>wi&longs;hed for in the Experiments before produced; but now I am <lb/>thorowly &longs;atisfied.<lb/><arrow.to.target n="marg1065"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1065"></margin.target><emph type="italics"/>The difference, <lb/>though very great, <lb/>of the Gravity of <lb/>Moveables hath <lb/>no part in differer­<lb/>cing their Veloci­<lb/>ties.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>The things by me hitherto alledged, and in particular, <lb/>this, That the difference of Gravity, although exceeding great, <lb/>hath no part in diver&longs;ifying the Velocities of Moveables, &longs;o that, <lb/>notwith&longs;tanding any thing depending on that, they would all <lb/>move with equal Celerity, is &longs;o new, and at the fir&longs;t apprehen&longs;i­<lb/>on &longs;o remote from probability, that, were there not a way to de­<lb/>lucidate it, and make it as clear as the Sun, it would be better <lb/>to pa&longs;&longs;e it over in &longs;ilence, than to divulge it: therefore &longs;eeing <lb/>that I have let it e&longs;cape from me, its fit that I omit neither Expe­<lb/>riment nor Rea&longs;on that may corroborate it.</s></p><p type="main"> <s>SAGR. </s> <s>Not onely this, but many other al&longs;o of your A&longs;&longs;erti­<lb/>ons are &longs;o remote from the Opinions and Doctrines commonly <lb/>received, that &longs;ending them abroad, you would &longs;tir up a great <lb/>number of Antagoni&longs;ts: in regard, that the innate Di&longs;po&longs;ition of <lb/>Men doth not &longs;ee with good eyes, when others in their Studies <lb/>di&longs;cover Truths or Fallacies, that were not di&longs;covered by them­<lb/>&longs;elves: and with the title of Innovators of Doctrines, little plea­<lb/>&longs;ing to the ears of many, they &longs;tudy to cut tho&longs;e knots which <lb/>they cannot untie, and with &longs;ub-terranean Mines to blow up <lb/>tho&longs;e Structures, which have been with the ordinary Tools by <lb/>patient Architects erected: but with us here, who are far from <lb/>any &longs;uch thoughts, your Experiments and Arguments are <pb xlink:href="040/01/761.jpg" pagenum="69"/>&longs;ufficient to give full &longs;atisfaction: yet neverthele&longs;&longs;e, if &longs;o be you <lb/>have other more palpable Experiments, and more convincing <lb/>Rea&longs;ons we would very gladly hear them.</s></p><p type="main"> <s>SALV. </s> <s>The Experiment made with two Moveables, as different <lb/>in weight as may be, by letting them de&longs;cend from a place on <lb/>high, thereby to &longs;ee whether their Velocity be equal, meets with <lb/>&longs;ome difficulty: for if the height &longs;hall be great, the <emph type="italics"/>Medium,<emph.end type="italics"/><lb/>which is to be opened and laterally repelled by the <emph type="italics"/>Impetus<emph.end type="italics"/> of the <lb/>cadent Body, &longs;hall be of much greater prejudice to the &longs;mall Mo­<lb/>ment of the light Moveable, than to the violence of the heavy <lb/>one; whereupon in a long way the light one will be left behind: <lb/>and in a little altitude it might be doubted whether there were <lb/>really any difference, or if there were, whether it would be <lb/>&longs;en&longs;ible. </s> <s>Therefore I have oft been thinking to reiterate the de­<lb/>&longs;cent &longs;o many times from &longs;mall heights, and to accumulate toge­<lb/>ther &longs;o many of tho&longs;e minute differences of time, as might inter­<lb/>cede between the arrival or fall of the heavy Body to the ground, <lb/>and the arrival of the light one, which &longs;o conjoyned, would make <lb/>a time not onely ob&longs;ervable, but ob&longs;ervable with much facility <lb/>Moreover, that I might help my &longs;elf with Motions as &longs;low as po&longs;­<lb/>&longs;ible may be, in which the Re&longs;i&longs;tance of the <emph type="italics"/>Medium<emph.end type="italics"/> operates <lb/>le&longs;&longs;e in altering the effect that dependeth on &longs;imple Gravity, I <lb/>have had thoughts to cau&longs;e the Moveable to de&longs;cend upon a de­<lb/>clining Plane, not much rai&longs;ed above the Plane of the Horizon; <lb/>for upon this, no le&longs;&longs;e than in perpendicularity, we may di&longs;cover <lb/>that which is done by Grave Bodies different in weight: and pro­<lb/>ceeding farther, I have de&longs;ired to free my &longs;elf from any what&longs;o­<lb/>ever impediment, that might ari&longs;e from the Contact of the &longs;aid <lb/>Moveables upon the &longs;aid declining Plane: and la&longs;tly, I have ta­<lb/>ken two Balls, one of Lead, and one of Cork, that above an hun­<lb/>dred times more grave than this, and have fa&longs;tened them to two <lb/>&longs;mall threads, each equally four or five yards long, tyed on <lb/>high: and having removed a&longs;wel the one as the other Ball from <lb/>the &longs;tate of Perpendicularity, I have let them both go in the &longs;ame <lb/>Moment, and they de&longs;cending by the Circumferences of Circles <lb/>de&longs;cribed by the equal Strings their Semidiameters, and having <lb/>pa&longs;&longs;ed beyond the Perpendicular, they afterwards by the &longs;ame <lb/>way returned back, and reiterating the&longs;e Vibrations, and re­<lb/>turns of them&longs;elves neer an hundred times, they have &longs;hewn ve­<lb/>ry &longs;en&longs;ibly, that the grave <emph type="italics"/>Pendulum<emph.end type="italics"/> moveth &longs;o exactly under the <lb/>time of the light one, that it doth not in an hundred, no nor in a <lb/>thou&longs;and Vibrations, anticipate the time of one &longs;mall moment, <lb/>but that they keep an equal pa&longs;&longs;e in their Recur&longs;ions. </s> <s>They al&longs;o <lb/>&longs;hew the Operation of the <emph type="italics"/>Medium,<emph.end type="italics"/> which conferring &longs;ome im­<lb/>pediment on the Motion, doth much more dimini&longs;h the Vibrati­<pb xlink:href="040/01/762.jpg" pagenum="70"/>ons of the Cork, than that of the Lead: not that it maketh them <lb/>more or le&longs;&longs;e frequent, nay, when the Arches pa&longs;&longs;ed by the Cork <lb/>were not of above five or &longs;ix degrees, and tho&longs;e of the Lead fif­<lb/>ty, they did pa&longs;s them under the &longs;ame times.</s></p><p type="main"> <s>SIMP. </s> <s>If this be &longs;o, how is it then that the Velocity of the <lb/>Lead is not greater than that of the Cork? </s> <s>that pa&longs;&longs;ing a jour­<lb/>ney of &longs;ixty degrees, in the time that this pa&longs;seth hardly &longs;ix?</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>But what would you &longs;ay, <emph type="italics"/>Simplicius,<emph.end type="italics"/> in ca&longs;e they <lb/>&longs;hould both di&longs;patch their Recur&longs;ions in the &longs;ame time, when the <lb/>Cork being removed thirty degrees from the Perpendicular, <lb/>&longs;hould pa&longs;s an arch of &longs;ixty, and the Lead removed from the <lb/>&longs;ame middle point onely two degrees, &longs;hould run an arch of four? <lb/></s> <s>would not then the Cork be &longs;o much more &longs;wift than the Lead? <lb/></s> <s>and yet Experience &longs;hews that &longs;o it happeneth: therefore ob&longs;erve, <lb/>The <emph type="italics"/>Pendulum<emph.end type="italics"/> of Lead being carried <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> fifty degrees from the <lb/>Perpendicular, and thence let go, &longs;wingeth, and pa&longs;&longs;ing beyond <lb/>the Perpendicular, neer fifty more degrees, de&longs;cribeth an arch <lb/>of well neer an hundred degrees; and returning of its &longs;elf back <lb/>again, it de&longs;cribeth another arch, not much le&longs;&longs;e than the former, <lb/>and continuing its Vibrations, after a great number of them, it <lb/>finally returneth to Re&longs;t: Each of tho&longs;e Vibrations are made un­<lb/>der equal times a&longs;wel tho&longs;e of ninety degrees, as tho&longs;e of fifty, <lb/>twenty, ten, or four; &longs;o that by con&longs;equence, the Velocity of the <lb/>Moveable doth &longs;ucce&longs;&longs;ively langui&longs;h and abate, in regard, that <lb/>under equal times it doth &longs;ucce&longs;&longs;ively pa&longs;&longs;e arches continually <lb/>le&longs;&longs;er and le&longs;&longs;er. </s> <s>The like, yea the &longs;elf &longs;ame effect is performed <lb/>by the Cork, hanging by a &longs;tring of the like length, &longs;ave that <lb/>in a le&longs;&longs;e number of Vibracions it returneth to Re&longs;t, as being le&longs;s <lb/>apt, by means of its Levity, to overcome the ob&longs;tacle of the Air: <lb/>and yet neverthele&longs;s all the Vibrations, both great and &longs;mall, are <lb/>made under times equal to one another, and equal al&longs;o to the <lb/>times of the times of the Vibrations of the Lead. </s> <s>Whereupon it <lb/>is true, that if whil&longs;t the Lead pa&longs;&longs;eth an arch of fifty degrees, <lb/>the Cork pa&longs;seth one but of ten, the Cork is then more &longs;low <lb/>than the Lead: but it will al&longs;o happen on the other &longs;ide, that the <lb/>Cork pa&longs;seth the arch of fifty degrees, when the Lead pa&longs;seth <lb/>but that of ten or &longs;ix; and &longs;o in &longs;everal times the Lead &longs;hall be <lb/>&longs;wifter onewhile, and the Cork another while: but if the &longs;ame <lb/>Moveables &longs;hall al&longs;o under the &longs;ame equal times, pa&longs;s arches that <lb/>are equal, one may then very &longs;afely &longs;ay, that their Velocities are <lb/>equal.</s></p><p type="main"> <s>SIMP. </s> <s>This di&longs;cour&longs;e &longs;eems to me concluding, and not con­<lb/>cluding, and I finde in my thoughts &longs;uch a Confu&longs;ion, ari&longs;ing <lb/>from the one-while &longs;wift, another-while &longs;low, another-while ex­<lb/>treme &longs;low motion of both the one and other Moveable; as that <pb xlink:href="040/01/763.jpg" pagenum="71"/>it permits me not to di&longs;cern clearly, whether it be true, That their <lb/>Velocities are alwaies equal.</s></p><p type="main"> <s>SAGR. </s> <s>Give me leave, I pray you, <emph type="italics"/>Salviatus,<emph.end type="italics"/> to interpo&longs;e two <lb/>words. </s> <s>And tell me, <emph type="italics"/>Simplicius,<emph.end type="italics"/> whether you admit, that it may be <lb/>&longs;aid with ab&longs;olute verity that the Velocities of the Cork and of <lb/>the Lead are equal, in ca&longs;e, that both of them departing at the <lb/>&longs;ame moment from Re&longs;t, and moving by the &longs;ame declivities, they <lb/>&longs;hould alwaies pa&longs;&longs;e equal Spaces in equal times?</s></p><p type="main"> <s>SIMP. </s> <s>This admits of no doubt, nor can it be contradicted.</s></p><p type="main"> <s>SAGR. </s> <s>It hapneth now in the Pendulums that each of them <lb/>pa&longs;&longs;eth now &longs;ixty degrees, now fifty, now thirty, now ten, now <lb/>eight, four, and two; and when each of them pa&longs;&longs;eth the Arch of <lb/>&longs;ixty degrees they pa&longs;&longs;e it in the &longs;ame time; in the Arch of fifty the <lb/>&longs;ame time is &longs;pent by both the one and the other Moveable; &longs;o in <lb/>the Arch of thirty, of ten, and of the re&longs;t: and therefore it is con­<lb/>cluded, that the Velocity of the Lead in the Arch of &longs;ixty degrees, <lb/>is equal to the Velocity of the Cork in the &longs;ame Arch of &longs;ixty de­<lb/>grees: and that the Velocities in the Arch of fifty, are likewi&longs;e <lb/>equal to one the other, and &longs;o in the re&longs;t. </s> <s>But it is not &longs;aid, that the <lb/>Velocity that is exerci&longs;ed in the Arch of &longs;ixty is equal to the Ve­<lb/>locity that is exerci&longs;ed in the Arch of fifty, nor this to that of the <lb/>Arch of thirty. </s> <s>But the Velocities are alwaies le&longs;&longs;er, in the le&longs;&longs;er <lb/>Arches. </s> <s>And this is collected from our &longs;en&longs;ibly &longs;eeing the &longs;ame <lb/>Moveable con&longs;ume as much time in pa&longs;&longs;ing the great Arch of &longs;ixty <lb/>degrees, as in pa&longs;&longs;ing the le&longs;&longs;er of fifty, or the lea&longs;t of ten: and, in a <lb/>word, in their being all pa&longs;&longs;ed alwaies under equal times. </s> <s>It is true <lb/>therefore, that both the Lead and the Cork &longs;ucce&longs;&longs;ively retard the <lb/>Motion, according to the Diminution of the Arches, but yet do <lb/>not alter their harmony in keeping the equality of Velocity in all <lb/>the &longs;ame Arches by them pa&longs;&longs;ed. </s> <s>I de&longs;ired to &longs;ay thus much, more <lb/>to try whether I have rightly apprehended the Conceit of <emph type="italics"/>Salvia­<lb/>tus,<emph.end type="italics"/> than out of any nece&longs;&longs;ity that I thought <emph type="italics"/>Simplicius<emph.end type="italics"/> to &longs;tand in <lb/>of a more plain Explanation than that of <emph type="italics"/>Salviatus,<emph.end type="italics"/> which is, as <lb/>in all other things, extreamly clear, and &longs;uch, that, it being fre­<lb/>quent with him to re&longs;olve Que&longs;tions, in appearance not only ob­<lb/>&longs;cure, but repugnant to Nature, and to the Truth, with Rea&longs;ons, <lb/>or Ob&longs;ervations, or Experiments very trite and familiar to every <lb/>one, it hath (as I have under&longs;tood from divers) given occa&longs;ion to <lb/>one of the mo&longs;t e&longs;teemed Profe&longs;&longs;ors of our Age to put the le&longs;&longs;e <lb/>e&longs;teem upon his Novelties, holding them to have as much of Sor­<lb/>didne&longs;&longs;e, for that they depend on over low and popular Funda­<lb/>mentals: as if the mo&longs;t admirable and mo&longs;t-to-be-prized Proper­<lb/>ty of the Demon&longs;trative Sciences, were not to &longs;pring and ari&longs;e <lb/>from Principles known, under&longs;tood, and granted by every one. <lb/></s> <s>But let us, for all that, continue to banquet our &longs;elves with this diet <pb xlink:href="040/01/764.jpg" pagenum="72"/>that is &longs;o light of dige&longs;tion; and &longs;uppo&longs;ing that <emph type="italics"/>Simplicius<emph.end type="italics"/> is fully <lb/>&longs;atisfied in under&longs;tanding and admitting, That the intern Gravity <lb/>of different Moveables hath no &longs;hare in differencing their Veloci­<lb/>ties, &longs;o that all of them, for ought that dependeth on that, would <lb/>move with the &longs;ame Velocities; tell us, <emph type="italics"/>Salviatus,<emph.end type="italics"/> in what you <lb/>place the &longs;en&longs;ible and apparent inequalities of Motion; and an­<lb/>&longs;wer to that In&longs;tance that <emph type="italics"/>Simplicius<emph.end type="italics"/> produceth, and which I like­<lb/>wi&longs;e confirm, I mean, of &longs;eeing a Cannon Bullet move more &longs;wift­<lb/>ly than a drop of Bird-&longs;hot, for the difference of Velocity &longs;hall be <lb/>but &longs;mall, in re&longs;pect of that which I object again&longs;t you of Movea­<lb/>bles of the &longs;ame matter, of which &longs;ome of the greater will de&longs;cend <lb/>in a <emph type="italics"/>Medium,<emph.end type="italics"/> in le&longs;&longs;e than one beat of the Pul&longs;e, that &longs;pace, that <lb/>others which are le&longs;&longs;er will not pa&longs;&longs;e in an hour, nor in four, nor in <lb/>twenty; &longs;uch are pebbles and minute gravel-&longs;tones, e&longs;pecially, <lb/>that &longs;mall &longs;and which muddieth the Water; in which <emph type="italics"/>Medium<emph.end type="italics"/><lb/>they will not de&longs;cend in many hours &longs;o much as two fathoms, <lb/>which Stones, and tho&longs;e of no great bigne&longs;&longs;e, do pa&longs;&longs;e in one beat <lb/>of the Pul&longs;e.</s></p><p type="main"> <s>SALV. </s> <s>That which the <emph type="italics"/>Medium<emph.end type="italics"/> operates, in retarding Movea­<lb/>bles, the more according as they are compared to one another, le&longs;s <lb/>grave <emph type="italics"/>in &longs;pecie,<emph.end type="italics"/> hath been already declared, &longs;hewing that it pro­<lb/>ceeds from the &longs;ub&longs;traction of weight. </s> <s>But how one and the &longs;ame <lb/><emph type="italics"/>Medium<emph.end type="italics"/> can with &longs;o great difference dimini&longs;h the Velocity in <lb/>Moveables that differ only in Magnitude, although they are of <lb/>the &longs;ame Matter, and of the &longs;ame Figure, requireth for its expli­<lb/>cation a more &longs;ubtil di&longs;cour&longs;e, than that which &longs;ufficeth for under­<lb/>&longs;tanding how the more dilated Figure of the Moveable, or the <lb/>Motion of the <emph type="italics"/>Medium<emph.end type="italics"/> that is made contrary to the Moveable, re­</s></p><p type="main"> <s><arrow.to.target n="marg1066"></arrow.to.target><lb/>tardeth the Velocity of the &longs;aid Moveable. </s> <s>I reduce the cau&longs;e of <lb/>the &longs;aid Problem to the Scabro&longs;ity, and Poro&longs;ity, that is common­<lb/>ly, and, for the mo&longs;t part, nece&longs;&longs;arily found in the Superficies of <lb/>Solid Bodies, the which Scabro&longs;ities, in their Motion, go repul&longs;ing <lb/>and commoving the Air, or other Ambient <emph type="italics"/>Medium<emph.end type="italics"/>: of which we <lb/>have an evident te&longs;timony, in that we hear the Bodies, though made <lb/>as round as is po&longs;&longs;ible for them to be, to hum whil&longs;t they pa&longs;&longs;e ve­<lb/>ry &longs;wiftly thorow the Air; and they are not only heard to hum, but <lb/>to whir and whi&longs;tle, if there be but in them &longs;ome more than ordi­<lb/>nary cavity or prominency. </s> <s>We &longs;ee al&longs;o, that in turning round <lb/>every rotund Solid maketh a little wind: And what need more? <lb/></s> <s>Do we not hear a notable whirring, and in a very &longs;harp Accent, <lb/>made by a Top, while it turneth round on the ground with great <lb/>Celerity? </s> <s>The &longs;hrilne&longs;s of which whizzing groweth flatter accor­<lb/>ding as the Velocity of the <emph type="italics"/>Vertigo<emph.end type="italics"/> doth by degrees more and <lb/>more &longs;lacken: a nece&longs;&longs;ary Argument likewi&longs;e of the commotion <lb/>and percu&longs;&longs;ion of the Air by tho&longs;e (though very &longs;mall) Scabro&longs;i­<pb xlink:href="040/01/765.jpg" pagenum="73"/>ties of their Superficies. </s> <s>It is not to be doubted, but that the&longs;e in the <lb/>de&longs;cent of Moveables, grating upon, and repul&longs;ing the fluid Am­<lb/>bient, procure retardment in the Velocity, and &longs;o much the greater, <lb/>by how much the Superficies &longs;hall be greater, as is that of le&longs;&longs;er <lb/>Solids compared to bigger.</s></p><p type="margin"> <s><margin.target id="marg1066"></margin.target><emph type="italics"/>The greater or le&longs;s <lb/>Scabro&longs;ity and Po­<lb/>ro&longs;ity of the Super­<lb/>ficies of Movea­<lb/>bles, a probable <lb/>cau&longs;e of their grea­<lb/>ter or le&longs;&longs;er Retar­<lb/>dation.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. Stay, I pray you, for here I begin to be at a lo&longs;&longs;e: for <lb/>though I under&longs;tand and admit, that the Confrication of the <emph type="italics"/>Medi­<lb/>um<emph.end type="italics"/> with the Superficies of the Moveable retardeth the Motion, <lb/>and that it more retardeth it where <emph type="italics"/>(ceteris paribus)<emph.end type="italics"/> the Superficies <lb/>is greater, yet do I not comprehend upon what ground you call the <lb/>Superficies of le&longs;&longs;er Solids greater: & farthermore if, as you affirm, the <lb/>greater Superficies ought to cau&longs;e greater retardment, the greater <lb/>Solids ought to be the &longs;lower, which is not &longs;o: but this Objection <lb/>may ea&longs;ily be removed, by &longs;aying, that although the greater hath <lb/>a greater Superficies, it hath al&longs;o a greater Gravity, upon which <lb/>the impediment of the greater Superficies hath not &longs;o much more <lb/>prevalent influence, than the impediment of the le&longs;&longs;er Superficies <lb/>hath upon the le&longs;&longs;er Gravity, as that the Velocity of the greater <lb/>Solid &longs;hould become the le&longs;&longs;er. </s> <s>And therefore I &longs;ee no rea&longs;on why <lb/>one &longs;hould alter the equality of the Velocities, whil&longs;t, that looking <lb/>how much the Moving Gravity dimini&longs;heth, the faculty of the Re­<lb/>tarding Superficies doth dimini&longs;h at the &longs;ame rate.</s></p><p type="main"> <s>SALV. </s> <s>I will re&longs;olve all that which you object in one word. <lb/></s> <s>Therefore, <emph type="italics"/>Simplicius,<emph.end type="italics"/> you will without controver&longs;ie admit, that <lb/>when, of two equal Moveables of the &longs;ame Matter, and alike in Fi­<lb/>gure (which undoubtedly would move with equal &longs;wiftne&longs;&longs;e) as <lb/>well the Gravity, as the Superficies of one of them dimini&longs;heth, <lb/>(yet &longs;till retaining the &longs;imilitude of Figure) the Velocity like­<lb/>wi&longs;e, for the &longs;ame rea&longs;on, would not be dimini&longs;hed in that which <lb/>was le&longs;&longs;ened.</s></p><p type="main"> <s>SIMP. Really, I think, that it ought &longs;o to follow as you &longs;ay, <lb/>granting the pre&longs;ent Doctrine with a <emph type="italics"/>&longs;alvo<emph.end type="italics"/> &longs;till to our Doctrine, <lb/>which teacheth, that the greater or le&longs;&longs;er Gravity hath no operati­<lb/>on in accelerating or retarding Motion.</s></p><p type="main"> <s>SALV. </s> <s>And this I confirm; and grant you likewi&longs;e your Po­<lb/>&longs;ition, from whence, in my opinion, may be inferred, That in ca&longs;e <lb/>the Gravity dimini&longs;heth more than the Superficies, there may be <lb/>introduced in the Moveable, in that manner dimini&longs;hed, &longs;ome re­<lb/>tardment of Motion, and that greater and greater, by how much in <lb/>proportion, the diminution of the Weight was greater than the di­<lb/>minution of the Superficies</s></p><p type="main"> <s>SIMP. </s> <s>I make not the lea&longs;t que&longs;tion of it.<lb/><arrow.to.target n="marg1067"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1067"></margin.target><emph type="italics"/>Solids cannot be <lb/>dimini&longs;hed at the <lb/>&longs;ame rate in Super­<lb/>ficies as in Weight, <lb/>retaining the &longs;imi­<lb/>litude of the Fi­<lb/>gures.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Now know, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that in Solids one cannot di­<lb/>mini&longs;h the Superficies &longs;o much as the Weight keeping the &longs;imili­<lb/>tude of Figure. </s> <s>For it being manife&longs;t, that in dimini&longs;hing of grave <pb xlink:href="040/01/766.jpg" pagenum="74"/>Solids, the Weight le&longs;&longs;eneth as much as the Bulk, when ever the <lb/>Bulk happens to be dimini&longs;hed more than the Superficies, (care <lb/>being had to retain the &longs;imilitude of Figure) the Gravity likewi&longs;e <lb/>would come to be more dimini&longs;hed than the Superficies. </s> <s>But <emph type="italics"/>Geo­<lb/>metry<emph.end type="italics"/> teacheth us, that there is much greater proportion between <lb/>the Bulk and the Bulk in like Solids, than between their Superfi­<lb/>cies. </s> <s>Which for your better under&longs;tanding, I &longs;hall explain in &longs;ome <lb/>particular ca&longs;e. </s> <s>Therefore fancy to your &longs;elf, for example, a Dye, <lb/>one of the Sides of which is <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> two Inches long, &longs;o that one of <lb/>its Surfaces &longs;hall be four Square Inches, and all &longs;ix, that is, all its <lb/>Superficies twenty four Square Inches. </s> <s>Then &longs;uppo&longs;e the &longs;ame <lb/>Dye at three &longs;awings cut into eight &longs;mall Dice, the Side of every <lb/>one of which will be one Inch, and one of its Surfaces an Inch <lb/>Square, and its whole Superficies &longs;ix Square Inches, of which the <lb/>whole Dye contained twenty four in its Superficial content. </s> <s>Now, <lb/>you &longs;ee, that the Superficial content of the little Dye is the fourth <lb/>part of the Superficial content of the great one, (for &longs;ix is the <lb/>fourth part of twenty four) but the Solid content of the &longs;aid Dye <lb/>is only the eighth part: therefore the Bulk, and con&longs;equently the <lb/>Weight, doth much more dimini&longs;h than the Superficies. </s> <s>And if <lb/>you &longs;ubdivide the little Dye into eight others, we &longs;hall have for <lb/>the whole Superficial content of one of the&longs;e, one and an half <lb/>Square Inches, which is the &longs;ixteenth part of the Superficies of the <lb/>fir&longs;t Dye; but its Bulk, or Ma&longs;s, is only the &longs;ixty fourth part of that. <lb/></s> <s>You &longs;ee therefore, how that in only the&longs;e two divi&longs;ions the Bulks <lb/>decrea&longs;e four times fa&longs;ter than their Superficies: and if we &longs;hould <lb/>pro&longs;ecute the Subdivi&longs;ion, untill that we had reduced the fir&longs;t So­<lb/>lid into a &longs;mall powder, we &longs;hould find the Gravity of the minute <lb/>Atomes to be le&longs;&longs;ened an hundred and an hundred times more <lb/>than their Superficies. </s> <s>And this which I have exemplified in <lb/>Cubes, hapneth in all like Solids, the Bulks of which are in Se&longs;­<lb/>quialter proportion of their Superficies. </s> <s>You &longs;ee, therefore, in how <lb/>much greater proportion the Impediment of the Contact of the <lb/>Superficies of the Moveable with the <emph type="italics"/>Medium<emph.end type="italics"/> encrea&longs;eth in &longs;mall <lb/>Moveables, than in greater: and if we &longs;hould add, that the Sca­<lb/>bro&longs;ities in the very &longs;mall Superficies of the minute Atomes are <lb/>not happily le&longs;&longs;er than tho&longs;e of the Superficies of greater Solids, <lb/>that are diligently poli&longs;hed, ob&longs;erve how fluid, and void of all Re­<lb/>&longs;i&longs;tance being opened, the <emph type="italics"/>Medium<emph.end type="italics"/> is required to be, when it is to <lb/>give pa&longs;&longs;age to &longs;o feeble a Virtue. </s> <s>And therefore take notice, <emph type="italics"/>Sim­<lb/>plicius,<emph.end type="italics"/> that I did not equivocate, when even now I &longs;aid, That the <lb/>Superficies of le&longs;&longs;er Solids is greater, in compari&longs;on of that of <lb/>bigger.</s></p><p type="main"> <s>SIMP. </s> <s>I am wholly &longs;atisfied: and I verily believe, that if I were <lb/>to begin my Studies again, I &longs;hould follow the Coun&longs;el of <emph type="italics"/>Plato,<emph.end type="italics"/><pb xlink:href="040/01/767.jpg" pagenum="75"/>and enter my &longs;elf fir&longs;t in the Mathematicks, which I &longs;ee to proceed <lb/>very &longs;crupulou&longs;ly, and refu&longs;e to admit any thing for certain, &longs;ave <lb/>that which they nece&longs;&longs;arily demon&longs;trate.</s></p><p type="main"> <s>SAGR. </s> <s>I have taken great delight in this Di&longs;cour&longs;e; but, be­<lb/>fore we pa&longs;&longs;e any further, I would be glad to be &longs;atisfied in one <lb/>particular, which newly came into my thoughts, when but ju&longs;t <lb/>now you &longs;aid, that Like-Solids are in Se&longs;quialter proportion to <lb/>their Superficies for I have &longs;een, and under&longs;tood the Propo&longs;ition </s></p><p type="main"> <s><arrow.to.target n="marg1068"></arrow.to.target><lb/>with its Demon&longs;tration, in which it is proved, That the Superficies <lb/>of Like-Solids are in duplicate proportion of their Sides; and ano­<lb/>ther that proveth the &longs;ame Solids to be in triple proportion of the <lb/>&longs;ame Sides; but the proportion of Solids to their Superficies, I do <lb/>not remember that I ever &longs;o much as heard it mentioned.</s></p><p type="margin"> <s><margin.target id="marg1068"></margin.target><emph type="italics"/>Solids are to each <lb/>other in Se&longs;quial­<lb/>ter proportion to <lb/>their Superficies.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>You your &longs;elf have an&longs;wered and declared the doubt. <lb/></s> <s>For that which is triple of a thing of which another is double, doth <lb/>it not come to be Se&longs;quialter of this double? </s> <s>Yes doubtle&longs;&longs;e. </s> <s>Now, <lb/>if Superficies are in double proportion of the Lines, of which the <lb/>Solids are in triple proportion, may not we &longs;ay, That the Solids are <lb/>in Se&longs;quialter proportion of their Superficies?</s></p><p type="main"> <s>SAGR. </s> <s>I under&longs;tand you very well. </s> <s>And although other par­<lb/>ticulars, pertaining to the matter of which we have treated, do re­<lb/>main for me to ask, yet if we &longs;hould thus run from one Digre&longs;&longs;ion <lb/>to another, it will be late before we &longs;hould come to the Que&longs;tions <lb/>principally intended, which concern the diver&longs;ities of the Acci­<lb/>dents of the Re&longs;i&longs;tances of Solids again&longs;t Fraction; and therefore, <lb/>if you &longs;o plea&longs;e, we may return to the fir&longs;t Theme, which we pro­<lb/>po&longs;ed in the beginning.</s></p><p type="main"> <s>SALV. </s> <s>You &longs;ay very well; but the &longs;o many, and &longs;o different <lb/>things that have been examined, have &longs;toln &longs;o much of our time, <lb/>that there is but little of it left in this day to &longs;pend in our other <lb/>principal Argument, which is full of Geometrical Demon&longs;trati­<lb/>ons that are to be con&longs;idered with attention: &longs;o that I &longs;hould think <lb/>it were better to adjourn our meeting till to morrow, as well for <lb/>this which I have told you, as al&longs;o becau&longs;e I might bring with me <lb/>&longs;ome Papers, on which I have, in order, &longs;et down the Theorems and <lb/>Problems, in which are propo&longs;ed and demon&longs;trated the different <lb/>Pa&longs;&longs;ions of this Subject, which, it may be, would not otherwi&longs;e <lb/>with requi&longs;ite Method come into my mind.</s></p><p type="main"> <s>SAGR. </s> <s>I very gladly comply with your advice, and &longs;o much the <lb/>more willingly, in regard that, for a Conclu&longs;ion of this daies Con­<lb/>ference, I &longs;hall have time to hear you re&longs;olve &longs;ome doubts that I <lb/>find in my mind concerning the Point la&longs;t handled. </s> <s>Of which one <lb/>is, Whether we are to hold, that the Impediment of the <emph type="italics"/>Medium<emph.end type="italics"/><lb/>may be &longs;ufficient to a&longs;&longs;ign bounds to the Acceleration of Bodies of <lb/>very grave Matter, that are of great Bulk, and of a Spherical Figure: <pb xlink:href="040/01/768.jpg" pagenum="76"/>and I in&longs;tance in the Spherical Figure, that I might take that which <lb/>is contained under the lea&longs;t Superficies, and therefore le&longs;&longs;e &longs;ubject <lb/>to Retardment. </s> <s>Another &longs;hall be, touching the Vibrations of Pen­<lb/>dulums, and this hath many heads: One &longs;hall be, Whether all, <lb/>both Great, Mean, and Little, are made really and preci&longs;ely under <lb/>equal Times: And another, What is the proportion of the Times <lb/>of Moveables, &longs;u&longs;pended at unequal &longs;trings, of the Times of their <lb/>Vibrations I mean.</s></p><p type="main"> <s>SALV. </s> <s>The Que&longs;tions are ingenious, and, like as it is incident <lb/>to all Truths, I &longs;uppo&longs;e, that, which ever of them we handle, it will <lb/>draw after it &longs;o many other Truths, and curious Con&longs;equences, <lb/>that I cannot tell whether the remainder of this day may &longs;uffice <lb/>for the di&longs;cu&longs;&longs;ing of them all.</s></p><p type="main"> <s>SAGR. </s> <s>If they &longs;hall be but as delightful as the precedent, it <lb/>would be more grateful for me to employ as many daies, not to &longs;ay, <lb/>hours, as it is unto night, and I believe that <emph type="italics"/>Simplicius<emph.end type="italics"/> will not be <lb/>cloy'd with &longs;uch Argumentations as the&longs;e.</s></p><p type="main"> <s>SIMP. </s> <s>No certainly: and e&longs;pecially, when the Que&longs;tions trea­<lb/>ted of are Phy&longs;ical, touching which we read not the Opinions or <lb/>Di&longs;cour&longs;es of other Philo&longs;ophers.<lb/><arrow.to.target n="marg1069"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1069"></margin.target><emph type="italics"/>Any Body, of any <lb/>Figure, Greatne&longs;s, <lb/>and Gravity, is <lb/>checked by the Re­<lb/>nitence of the<emph.end type="italics"/> Me­<lb/>dium, <emph type="italics"/>though ne­<lb/>ver &longs;o tenuous, in <lb/>&longs;uch &longs;ort, that the <lb/>Motion continuing, <lb/>it is reduced to <lb/>equability.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>I come therefore to the fir&longs;t, affirming without any <lb/>hæ&longs;itation, that there is not a Sphere &longs;o big, nor of Matter &longs;o grave, <lb/>but that the Renitence of the <emph type="italics"/>Medium,<emph.end type="italics"/> though very tenuous, checks <lb/>its Acceleration, and in the continuation of the Motion reduceth <lb/>it to Equability, of which we may draw a very clear Argument <lb/>from Experience it &longs;elf. </s> <s>For if any falling Moveable were able in <lb/>its continuation of Motion to attain any degree of Velocity, no <lb/>Velocity that &longs;hould be conferred upon it, could be &longs;o great but <lb/>that it would depo&longs;e it, and free it &longs;elf of it by help of the Impe­<lb/>diment of the <emph type="italics"/>Medium.<emph.end type="italics"/> And thus, a Cannon-bullet, that had de <lb/>&longs;cended through the Air, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> four yards, and had, for example, <lb/>acquired ten degrees of Velocity, and that with the&longs;e &longs;hould enter <lb/>into the Water, in ca&longs;e the Impediment of the Water were not <lb/>able to prohibit &longs;uch a certain <emph type="italics"/>Impetus<emph.end type="italics"/> in the Ball, it would en­<lb/>crea&longs;e it, or at lea&longs;t would continue it unto the bottom; which is <lb/>not ob&longs;erved to en&longs;ue: nay, the Water, although it were but a few <lb/>fathoms in depth, would impede and debilitate it in &longs;uch a man­<lb/>ner, that it will make but a &longs;mall impre&longs;&longs;ion in the bottom of the <lb/>River or Lake. </s> <s>It is therefore manife&longs;t, that that Velocity, of <lb/>which the Water had ability to deprive it in a very &longs;hort way, <lb/>would never be permitted to be acquired by it, though in a depth <lb/>of a thou&longs;and Fathoms. </s> <s>And why &longs;hould it be permitted to gain <lb/>it in a thou&longs;and, to be taken from it again in four? </s> <s>What need we <lb/>more? </s> <s>Do we not &longs;ee the immen&longs;e <emph type="italics"/>Impetus<emph.end type="italics"/> of the Ball, &longs;hot from <lb/>the Cannon it &longs;elf, to be in &longs;uch a manner flatted by the interpo­<pb xlink:href="040/01/769.jpg" pagenum="77"/>&longs;ition of a few Fathom of Water, that without any harm to the <lb/>Ship, it but very hardly reacheth to make a dent in it? </s> <s>The Air al­<lb/>&longs;o, though very yielding, doth neverthele&longs;&longs;e repre&longs;&longs;e the Velocity <lb/>of the falling Moveable, although it be very heavy, as we may by <lb/>&longs;uch like Experiments collect; for if from the top of a very high <lb/>Tower we &longs;hould di&longs;charge a Mu&longs;quet downwards, this will make <lb/>a le&longs;&longs;er impre&longs;&longs;ion on the ground, than if we &longs;hould di&longs;charge the <lb/>Mu&longs;quet at the height of four or &longs;ix yards above the Plane: an <lb/>evident &longs;ign, that the <emph type="italics"/>Impetus,<emph.end type="italics"/> wherewith the Bullet i&longs;&longs;ueth from <lb/>the Gun, di&longs;charged on the top of the Tower, doth gradually di­<lb/>mini&longs;h in de&longs;cending thorow the Air: therefore the de&longs;cending <lb/>from any what&longs;oever great height will not &longs;uffice to make it ac­<lb/>quire that <emph type="italics"/>Impetus,<emph.end type="italics"/> of which the Re&longs;i&longs;tance of the Air deprived <lb/>it, when it had in any manner been conferred upon it. </s> <s>The batte­<lb/>ry likewi&longs;e that the force of a Bullet, &longs;hot from a Culverin, &longs;hall <lb/>make in a Wall at the di&longs;tance of twenty Paces, would not, I be­<lb/>lieve, be &longs;o great, if the Bullet was &longs;hot perpendicularly from any <lb/>immen&longs;e Altitude. </s> <s>I believe, therefore, that there is a Bound or <lb/>term belonging to the Acceleration of every Natural Moveable <lb/>that departs from Re&longs;t, and that the Impediment of the <emph type="italics"/>Medium<emph.end type="italics"/> in <lb/>the end reduceth it to ^{*} Equality, in which it afterwards alwaies </s></p><p type="main"> <s><arrow.to.target n="marg1070"></arrow.to.target><lb/>continueth.</s></p><p type="margin"> <s><margin.target id="marg1070"></margin.target>* Or Equability.</s></p><p type="main"> <s>SAGR. </s> <s>The Experiments are really, in my opinion, much to <lb/>the purpo&longs;e: nor doth any thing remain, unle&longs;&longs;e the Adver&longs;ary <lb/>&longs;hould fortifie him&longs;elf, by denying, that they will hold true in great <lb/>and ponderous Ma&longs;&longs;es, and that a Cannon-bullet coming from the <lb/>Concave of the Moon, or from the upper Region of the Air, <lb/>would make a greater percu&longs;&longs;ion than coming from the Cannon.</s></p><p type="main"> <s>SALV. </s> <s>There is no que&longs;tion, but that many things may be <lb/>objected, and that they may not be all &longs;alved by Experiments; ne­<lb/>verthele&longs;&longs;e in this contradiction, me thinks, there is &longs;omething that <lb/>may fall under con&longs;ideration; <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> that it is very probable, <lb/><arrow.to.target n="marg1071"></arrow.to.target><lb/>that the Grave Body, falling from an Altitude, acquireth &longs;o much <lb/><emph type="italics"/>Impetus,<emph.end type="italics"/> at its arrival to the ground, as would &longs;uffice to return it <lb/>to that height, as is plainly &longs;een in a <emph type="italics"/>Pendulum<emph.end type="italics"/> rea&longs;onable weighty, <lb/>that being removed fifty or &longs;ixty degrees from the Perpendicular, <lb/>gaineth that Velocity and Virtue which exactly &longs;ufficeth to force it <lb/>to the like Recur&longs;ion, that little abated, which is taken from it by <lb/>the Impediment of the Air. </s> <s>To con&longs;titute, therefore, the Cannon­<lb/>bullet in &longs;uch an Altitude as may &longs;uffice for the acqui&longs;t of an <emph type="italics"/>Impe­<lb/>tus,<emph.end type="italics"/> as great as that which the Fire giveth it in its i&longs;&longs;uing from the <lb/>Piece, it would &longs;uffice to &longs;hoot it upwards perpendicularly with <lb/>the &longs;aid Cannon, and then ob&longs;erving, whether in its fall it maketh <lb/>an impre&longs;&longs;ion equal to that of the percu&longs;&longs;ion made near at hand in <lb/>its i&longs;&longs;uing forth; but, indeed, I believe, that it would not be any <pb xlink:href="040/01/770.jpg" pagenum="78"/>whit near &longs;o forcible. </s> <s>And therefore I hold that the Velocity, <lb/>which the Bullet hath near to its going out of the Piece, would <lb/>be one of tho&longs;e that the Impediment of the Air would never &longs;uffer <lb/>it to acquire, whil&longs;t it &longs;hould with a natural Motion de&longs;cend, leaving <lb/>the &longs;tate of Re&longs;t, from any great height. </s> <s>I come now to the other <lb/>Que&longs;tions belonging to <emph type="italics"/>Pendulums,<emph.end type="italics"/> matters which to many would <lb/>&longs;eem very frivolous, and more e&longs;pecially to tho&longs;e Philo&longs;ophers that <lb/>are continually bu&longs;ied in the more profound Que&longs;tions of Natural <lb/>Philo&longs;ophy: yet, notwith&longs;tanding, will not I contemn them, being <lb/>encouraged by the Example of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf, in whom I admire <lb/>this above all things; that he hath not, as one may &longs;ay, omitted any <lb/>matter that any waies merited con&longs;ideration, which he hath not <lb/>&longs;poken of: and now upon the Que&longs;tions you propounded, I think <lb/>I can tell you a certain conceit of mine upon &longs;ome Problems con­<lb/>cerning Mu&longs;ick, a noble Subject, of which &longs;o many famous men, <lb/>and <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf, have written; and touching it, he con&longs;ide­<lb/>reth many curious Problems: &longs;o that if I likewi&longs;e &longs;hall from &longs;o fa­<lb/>miliar and &longs;en&longs;ible Experiments, draw Rea&longs;ons of admirable acci­<lb/>dents on the Argument of Sounds, I may hope that my di&longs;cour&longs;es <lb/>will be accepted by you.</s></p><p type="margin"> <s><margin.target id="marg1071"></margin.target><emph type="italics"/>A Grave Body, <lb/>falling from an <lb/>Altitude, acqui­<lb/>reth &longs;o much<emph.end type="italics"/> Im­<lb/>petus <emph type="italics"/>at its arri­<lb/>val to the ground, <lb/>as in all probabili­<lb/>ty, would &longs;uffice to <lb/>recarry it to the <lb/>&longs;ame height from <lb/>whence it fell.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR Not only accepted, but by me, in particular, mo&longs;t pa&longs;­<lb/>&longs;ionately de&longs;ired, in regard that I taking a great delight in all Mu­<lb/>&longs;ical In&longs;truments, and being rea&longs;onably well in&longs;tructed concerning <lb/>Con&longs;onances, have alwaies been ignorant and perplexed with <lb/>endeavouring to know, whence it cometh that one &longs;hould more <lb/>plea&longs;e and delight me than another; and that &longs;ome not only pro­<lb/>cure me no delight, but highly di&longs;plea&longs;e me: the trite Ptoblem al­<lb/>&longs;o of the two Chords &longs;et to an Uni&longs;on, one of which moveth and <lb/>actually &longs;oundeth at the touching of the other, I al&longs;o am unre&longs;ol­<lb/>ved in: nor am I very clearly informed concerning the Forms of <lb/>Con&longs;onances, and other particularities.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>We will &longs;ee, if from the&longs;e our <emph type="italics"/>Peudulums<emph.end type="italics"/> one may ga­<lb/>ther any &longs;atisfaction in all the&longs;e Doubts. </s> <s>And as to the fir&longs;t Que­<lb/>&longs;tion, that is, Whether the &longs;ame <emph type="italics"/>Pendulum<emph.end type="italics"/> doth really and punctu­<lb/>ally perform all its Vibrations, great, le&longs;&longs;er, and lea&longs;t, under Times <lb/>preci&longs;ely equal; I refer my &longs;elf to that which I have heretofore <lb/>learnt from our <emph type="italics"/>Academian,<emph.end type="italics"/> who plainly demon&longs;trateth, that the <lb/><arrow.to.target n="marg1072"></arrow.to.target><lb/>Moveable that &longs;hould de&longs;cend along the Chords, that are Subten­<lb/>&longs;es to any Arch, would nece&longs;&longs;arily pa&longs;&longs;e them all in equal Times, <lb/>as well the Subten&longs;e under an hundred and eighty degrees, (that <lb/>is, the whole Diameter) as the Subten&longs;es of an hundred, &longs;ixty, ten, <lb/>two, or half a degree, or of four minutes: &longs;till &longs;uppo&longs;ing that they <lb/>all determine in the lowe&longs;t Point touching the Horizontal Plane. <lb/></s> <s>Next as to the de&longs;cendents by the Arches of the &longs;ame Chords eli­<lb/>vated above the Horizon, and that are not greater than a Qua­<pb xlink:href="040/01/771.jpg" pagenum="79"/>drant, that is, than ninety degrees, Experience likewi&longs;e &longs;hews, that <lb/><arrow.to.target n="marg1073"></arrow.to.target><lb/>they pa&longs;&longs;e all in Times equal, but yet &longs;horter than the Times of <lb/>the pa&longs;&longs;ages by the Chords: an effect which hath &longs;o much of won­<lb/>der in it, by how much at the fir&longs;t apprehen&longs;ion one would think <lb/>the contrary ought to follow: For the terms of the beginning, <lb/>and the end of the Motion being common, and the Right-Line be­<lb/>ing the &longs;horte&longs;t, that can be comprehended between the &longs;aid <lb/>Terms, it &longs;eemeth rea&longs;onable, that the Motion made by it &longs;hould <lb/>be fini&longs;hed in the &longs;horte&longs;t Time, which yet is not &longs;o: but the &longs;hor­<lb/>te&longs;t Time, and con&longs;equently, the &longs;wifte&longs;t Motion, is that made by <lb/>the Arch of which the &longs;aid Right-Line is Chord. </s> <s>In the next <lb/><arrow.to.target n="marg1074"></arrow.to.target><lb/>place, as to the Times of the Vibrations of Moveables, &longs;u&longs;pended <lb/>by &longs;trings of different lengths, tho&longs;e Times are in Subduple pro­<lb/>portion to the lengths of the &longs;trings, or, if you will, the lengths <lb/>are in duplicate proportion to the Times, that is, are as the Squares <lb/>of the Times: &longs;o that if, for example, the Time of a Vibration <lb/>of one <emph type="italics"/>Pendulum<emph.end type="italics"/> is double to the Time of a Vibration of another, <lb/>it followeth, that the length of the &longs;tring of that is quadruple to <lb/>the length of the &longs;tring of this. </s> <s>And in the Time of one Vibration <lb/>of that, another &longs;hall then make three Vibrations, when the &longs;tring <lb/>of that &longs;hall be nine times as long as the other. </s> <s>From whence doth <lb/>follow, that the length of the &longs;trings have to each other the &longs;ame <lb/>proportion, that the Squares of the Numbers of the Vibrations that <lb/>are made in the &longs;ame Times have.</s></p><p type="margin"> <s><margin.target id="marg1072"></margin.target><emph type="italics"/>Moveables de&longs;cen­<lb/>ding along the <lb/>Chords, that are <lb/>Subten&longs;es to any <lb/>Arch of a Circle, <lb/>pa&longs;&longs;e as well the <lb/>greater as the le&longs;­<lb/>&longs;er Chords in equal <lb/>Times.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1073"></margin.target><emph type="italics"/>Moveables and<emph.end type="italics"/><lb/>Pendula <emph type="italics"/>de&longs;cend­<lb/>ing along the Ar­<lb/>ches of the &longs;ame <lb/>Chords, elivated as <lb/>far as 90 deg. </s> <s>pa&longs;s <lb/>the &longs;aid Arches in <lb/>Times equal, but <lb/>that are &longs;horter <lb/>than the tran&longs;iti­<lb/>ons along the <lb/>Chords.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1074"></margin.target><emph type="italics"/>The Times of the <lb/>Vibrations of Mo­<lb/>vables, hanging at <lb/>alonger or &longs;horter <lb/>thread, are to one <lb/>another in propor­<lb/>tion &longs;ubduple the <lb/>lengths of the <lb/>&longs;trings, at which <lb/>they hang.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. Then, if I have rightly under&longs;tood you, I may ea&longs;ily <lb/><arrow.to.target n="marg1075"></arrow.to.target><lb/>know the length of a &longs;tring, hanging at any never-&longs;o-great height, <lb/>although the &longs;ublime term of the &longs;u&longs;pen&longs;ion were invi&longs;ible to me, <lb/>and I only &longs;aw the other lower extream. </s> <s>For if I &longs;hall fa&longs;ten a <lb/>weight of &longs;ufficient Gravity to the &longs;aid &longs;tring here below, and &longs;et <lb/>it on vibrating to and again, and a friend telling &longs;ome of its Recur­<lb/>&longs;ions, and I at the &longs;ame time tell the Recur&longs;ions of another Movea­<lb/>ble, &longs;u&longs;pended at a &longs;tring that is preci&longs;ely a yard long, by the <lb/>Numbers of the Vibrations of the&longs;e <emph type="italics"/>Pendula,<emph.end type="italics"/> made in the &longs;ame <lb/>Time, I will find the length of the &longs;tring. </s> <s>As for example, &longs;uppo&longs;e <lb/>that in the time that my friend hath counted twenty Recur&longs;ions of <lb/>the long &longs;tring, I had told two hundred and forty of my &longs;tring, <lb/>that is one yard long: &longs;quaring the two numbers twenty and two <lb/>hundred and forty, which are 400, and 57600, I will &longs;ay, that the <lb/>long &longs;tring containeth 57600 of tho&longs;e Mea&longs;ures, of which my <lb/>&longs;tring containeth 400. and becau&longs;e the &longs;tring is one &longs;ole yard, I will <lb/>divide 57600 by 400, and the quotient will be 144, and I will af­<lb/>firm that &longs;tring to be 144 yards long.</s></p><p type="margin"> <s><margin.target id="marg1075"></margin.target><emph type="italics"/>To find the Length <lb/>of any Rope, or <lb/>&longs;tring, at which a <lb/>Moveable hang­<lb/>eth, by the frequen­<lb/>cy of its Vibrations<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Nor will you be mi&longs;taken one Inch; and e&longs;pecially, if <lb/>you take a great Number of Vibrations.</s></p><p type="main"> <s>SAGR. </s> <s>You give me frequent occa&longs;ion to admire the Riches, <pb xlink:href="040/01/772.jpg" pagenum="80"/>and withal the extraordinary bounty of Nature, whil'&longs;t by things <lb/>&longs;o common, and, I might in a certain &longs;ence &longs;ay, vile, you go col­<lb/>lecting of Notions very curious, new, and oftentimes, remote <lb/>from all imagination. </s> <s>I have an hundred times con&longs;idered the Vi­<lb/>brations, in particular, of the Lamps in &longs;ome Churches, hanging <lb/>by very long ropes, when they have been unawares &longs;tirred by <lb/>any one: but the mo&longs;t that I inferred from that &longs;ame Ob&longs;ervati­<lb/>on, was the improbability of the Opinion of tho&longs;e who hold, <lb/>that &longs;uch-like Motions are maintained and continued by the <emph type="italics"/>Medi­<lb/>um,<emph.end type="italics"/> that is by the Air: for it &longs;hould &longs;eem to me, that the Air had <lb/>a great judgment, and withal but little bu&longs;ine&longs;&longs;e to &longs;pend &longs;o ma­<lb/>ny hours time in vibrating an hanging Weight with &longs;o much Regu­<lb/>larity: but that I &longs;hould have learnt, that that &longs;ame Moveable, <lb/>&longs;u&longs;pended at a &longs;tring of an hundred yards long, being removed <lb/>from Perpendicularity one while ninety degrees, and another <lb/>while one degree onely, or half a degree, &longs;hould &longs;pend as much time <lb/>in pa&longs;&longs;ing this little, as in pa&longs;&longs;ing that great Arch, certainly would <lb/>never have come into my head, for I &longs;till think, that it bordereth <lb/>upon Impo&longs;sibility. </s> <s>Now I am in expectation to hear that the&longs;e <lb/>petty Notions will a&longs;sign me &longs;uch Rea&longs;ons of tho&longs;e Mu&longs;ical Pro­<lb/>blems, as may, in part at lea&longs;t, give me &longs;atisfaction.<lb/><arrow.to.target n="marg1076"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1076"></margin.target><emph type="italics"/>Every<emph.end type="italics"/> Pendulum <lb/><emph type="italics"/>hath the Time of <lb/>its Vibration &longs;o li­<lb/>mited; that it is <lb/>not po&longs;&longs;ible to make <lb/>it move under any <lb/>other Period.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Above all things, you are to know, that every <emph type="italics"/>Pendu­<lb/>lum<emph.end type="italics"/> hath the Time of its Vibrations &longs;o limited, and prefixed, that <lb/>it is impo&longs;&longs;ible to make it move under any other Period, than that <lb/>onely one, which is natural unto it. </s> <s>Let any one take the &longs;tring in <lb/>hand, to which the Weight is fa&longs;tened, and trie all the wayes <lb/>he can to encrea&longs;e or decrea&longs;e the frequency of its Vibrations, <lb/>and he &longs;hall finde it labour in vain: but we may, on the contrary, <lb/>on a <emph type="italics"/>Pendulum,<emph.end type="italics"/> though grave and at re&longs;t, by onely blowing up­<lb/>on it, conferre a Motion, and a Motion con&longs;iderably great, by <lb/>reiterating the bla&longs;ts, but under the Time that is properly be­<lb/>longing to its Vibrations: for if at the fir&longs;t bla&longs;t we &longs;hould have re­<lb/>moved it from Perpendicularity half an Inch, adding a &longs;econd, <lb/>after that it being returned towards us, is ready to begin the &longs;e­<lb/>cond Vibration, we &longs;hould conferre new Motion on it, and &longs;o <lb/>&longs;ucce&longs;&longs;ively with other bla&longs;ts, but given in Time, and not when <lb/>the <emph type="italics"/>Pendulum<emph.end type="italics"/> is comming towards us (for &longs;o we &longs;hould impede; <lb/>and not help the Motion) and &longs;o continuing with many Impul­<lb/>&longs;es, we &longs;hould confer upon it &longs;uch an <emph type="italics"/>Impetus,<emph.end type="italics"/> that a greater <lb/>force by much than that of a bla&longs;t of our breath, will be required <lb/>to &longs;tay it.</s></p><p type="main"> <s>SAGR. </s> <s>I have, from my childhood, ob&longs;erved, that one man a­<lb/>lone, by means of the&longs;e Impul&longs;es, given in Time, hath been able <lb/>to towl a very great Bell, and when it was to cea&longs;e, I have &longs;een <lb/>four or &longs;ix men more lay hold on the Bell-rope, and they have all <pb xlink:href="040/01/773.jpg" pagenum="81"/>been rai&longs;ed from the ground: &longs;o many together being unable to <lb/>arre&longs;t that <emph type="italics"/>Impetus,<emph.end type="italics"/> which one alone, with regular Pulls, had con­<lb/>ferred upon the Bell.</s></p><p type="main"> <s>SALV. </s> <s>An example, that declareth my meaning with no le&longs;&longs;e </s></p><p type="main"> <s><arrow.to.target n="marg1077"></arrow.to.target><lb/>propriety than this that I have premi&longs;ed, doth &longs;ute to render the <lb/>rea&longs;on of the admirable Problem of the Chord of the Lute or Viol, <lb/>which moveth, and maketh not onely that really to &longs;ound, which <lb/>is tuned to the Uni&longs;on, but that al&longs;o which is &longs;et to an Eighth <lb/>and a Fifth. </s> <s>The Chord being toucht, its Vibrations begin, and <lb/>continue all the Time that its Sound is heard to endure: the&longs;e <lb/>Vibrations make the Air neer adjacent to vibrate and tremble, <lb/>who&longs;e tremblings and quaverings di&longs;tend them&longs;elves a great way, <lb/>and &longs;trike upon all the Chords of the In&longs;trument, and al&longs;o of o­<lb/><arrow.to.target n="marg1078"></arrow.to.target><lb/>thers neer unto it: the Chord that is &longs;et to an Uni&longs;on, with that <lb/>which is toucht, being di&longs;po&longs;ed to make its Vibrations ^{*} in the <lb/>&longs;ame Time, beginneth at the fir&longs;t impul&longs;e to move a little, and <lb/><arrow.to.target n="marg1079"></arrow.to.target><lb/>a &longs;econd, a third, a twentieth, and many more, overtaking it, all <lb/>in ju&longs;t and Periodick Times, it receiveth at la&longs;t, the &longs;ame Tre­<lb/>mulation, with that fir&longs;t touched, and one may clearly &longs;ee it go, <lb/>dilating its Vibrations exactly according to the Pace of its Mo­<lb/>ver. </s> <s>This Undulation that di&longs;tendeth it &longs;elf thorow the Air, mo­<lb/>veth, and makes to vibrate, not onely the Chords, but likewi&longs;e <lb/>any other Body di&longs;po&longs;ed to trembling, and to vibrate in the very <lb/>Time of the trembling Chord: &longs;o that if we fix in the Sides of <lb/>the In&longs;trument &longs;everal &longs;mall pieces of Bri&longs;tles, or of other flexible <lb/>matters, you &longs;hall &longs;ee upon the &longs;ounding of the Viol, now one, <lb/>now another of tho&longs;e Corpu&longs;cles tremble, according as that <lb/>Chord is toucht, who&longs;e Vibrations return in the &longs;ame Time: the <lb/>others will not move at the &longs;triking of this Chord, nor will that <lb/>Bri&longs;tle tremble at the &longs;triking of another Chord. </s> <s>If with the Bow <lb/>one &longs;martly &longs;trike the Ba&longs;e-Chord of a Viol, and &longs;et a drinking <lb/>Gla&longs;&longs;e, thin and &longs;mooth, neer unto it, if the Tone of the Chord <lb/>be an Uni&longs;on to the Tone of the Gla&longs;&longs;e, the Gla&longs;&longs;e &longs;hall dance, <lb/>and &longs;en&longs;ibly re-&longs;ound. </s> <s>Again, the ample dilating of the Tremor <lb/>or Undulation of the <emph type="italics"/>Medium<emph.end type="italics"/> about the Body re&longs;ounding, is ap­<lb/>parently &longs;een in making the Gla&longs;&longs;e to &longs;ound, by putting a little <lb/>Water in it, and then chafing the brim or edge of it with the tip <lb/>of the finger: for the included Water is ob&longs;erved to undulate in <lb/>a mo&longs;t regular order: and the &longs;ame effect will be yet more clearly <lb/>&longs;een, by &longs;etting the foot of the Gla&longs;&longs;e in the bottom of a rea&longs;o­<lb/>nable large Ve&longs;&longs;el, in which there is Water as high almo&longs;t as to <lb/>the brim of the Gla&longs;&longs;e, for making it to &longs;ound, as before, with <lb/>the Confrication of the finger, we &longs;hall &longs;ee the trembling of the <lb/>Water to diffu&longs;e it &longs;elf mo&longs;t regularly, and with great Velocity, <lb/>to a great di&longs;tance round about the Gla&longs;&longs;e; and it hath many <pb xlink:href="040/01/774.jpg" pagenum="82"/>times been my fortune, in making a rea&longs;onable big Gla&longs;&longs;e, almo&longs;t <lb/>full of Water, to &longs;ound as afore&longs;aid, to &longs;ee the Waves in the <lb/>Water, at fir&longs;t formed with an exact equality; and it hapning <lb/>&longs;ometimes, that the Tone of the Gla&longs;&longs;e ri&longs;eth an Eighth higher, at <lb/>the &longs;ame in&longs;tant, I have &longs;een every one of the &longs;aid Waves to divide <lb/>them&longs;elves in two: an accident that very clearly proveth the <lb/>forme of the Octave to be the double.</s></p><p type="margin"> <s><margin.target id="marg1077"></margin.target><emph type="italics"/>The Chord of a <lb/>Mu&longs;ical In&longs;tru­<lb/>ment touched, mo­<lb/>veth, and maketh <lb/>the Chords &longs;et to an <lb/>Uni&longs;on, Fifth and <lb/>Eighth, with it to <lb/>&longs;ound; and why.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1078"></margin.target><emph type="italics"/>Sundry Problems <lb/>touching Mu&longs;ical <lb/>Proportions, and <lb/>their Solutions.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1079"></margin.target>* Or under.</s></p><p type="main"> <s>SAGR. </s> <s>The &longs;ame hath al&longs;o befaln me more than once, to my <lb/>delight, and al&longs;o benefit: for I &longs;tood a long time perplexed a­<lb/>bout the&longs;e Forms of Con&longs;onants, not conceiving, that the Rea­<lb/>&longs;on, commonly given thereof by the Authours that have hither­<lb/>to written learnedly of Mu&longs;ick, were &longs;ufficiently convincing, <lb/>they tell us, that the Diapa&longs;on, that is the Eighth, is contained <lb/>by the double, the Diapente, which we call the Fifth, by the <lb/>Se&longs;quialter: for a Chord being di&longs;tended on the ^{*} Monochord, <lb/><arrow.to.target n="marg1080"></arrow.to.target><lb/>&longs;triking it all; and afterwards &longs;triking but the half of it, by pla­<lb/>cing a Bridge in the middle, one heareth an Eighth; and if the <lb/>Bridge be placed at a third of the whole Chord, touching the <lb/>whole, and then the two thirds, it &longs;oundeth a Fifth; whereupon <lb/>they infer, that the Eighth is contained between two and one, and <lb/>the Fifth between three and two. </s> <s>This Rea&longs;on, I &longs;ay, &longs;eemed to <lb/>me not nece&longs;&longs;arily concluding for the a&longs;&longs;igning ju&longs;tly the double <lb/>and the Se&longs;quialter, for the natural Forms of the Diapa&longs;on and <lb/>the Diapente. </s> <s>And that which moved me &longs;o to think, was this. <lb/></s> <s>There are three ways, by which we may &longs;harpen the Tone of a <lb/>Chord: one is, by making it &longs;horter, the other is by di&longs;tending; <lb/>or making it more ten&longs;e; and the third is by making it thinner. </s> <s>If, <lb/>retaining the &longs;ame Tention and thickne&longs;&longs;e, we would hear an <lb/>Eighth, it is nece&longs;&longs;ary to &longs;horten it to one half, which is done by <lb/>&longs;triking it all, and then half. </s> <s>But if, retaining the &longs;ame length <lb/>and thickne&longs;&longs;e, we would have it ri&longs;e to an Eighth, by &longs;crewing <lb/>it higher, it will not &longs;uffice to &longs;tretch it double as much, but we <lb/>&longs;hall need the quadruple, &longs;o that, if before it was &longs;tretched by a <lb/>Weight of one pound, it will be needful to fa&longs;ten four pound <lb/>to it to &longs;harpen it to an Eighth. </s> <s>And la&longs;tly, if, keeping the &longs;ame <lb/>length and Tention, we would have a Chord, that by being &longs;mal­<lb/>ler, rendereth an Eighth, it will be nece&longs;&longs;ary, that it retain onely <lb/>a fourth part of the thickne&longs;&longs;e of the other more Grave. </s> <s>And this <lb/>which I &longs;peak of the Eighth, that is, that its form taken from the <lb/>Tention, or from the thickne&longs;&longs;e of the Chord, is in duplicate <lb/>proportion to that which it receiveth from the length, is to be <lb/>under&longs;toood of all other Mu&longs;ical Intervals: for that which the <lb/>length giveth us in a Se&longs;quialter proportion, <emph type="italics"/>i. </s> <s>e.<emph.end type="italics"/> by &longs;triking it all, <lb/>and then the two thirds, if you would have it proceed from the <lb/>Tention, or from the di&longs;gro&longs;&longs;ing, you mu&longs;t double the Se&longs;qui­<pb xlink:href="040/01/775.jpg" pagenum="83"/>alter proportion, taking the double Se&longs;quiquartan: and if the <lb/>Grave Chord were &longs;tretched by four pound weight, fa&longs;ten to the <lb/>Acute not &longs;ix, but nine: and, as to the thickne&longs;&longs;e, make the Grave <lb/>Chord thicker than the Acute, according to the proportion of <lb/>nine to four, to have the Fifth. </s> <s>The&longs;e being mo&longs;t exact Experi­<lb/>ments, I thought, that I &longs;aw no rea&longs;on, why the&longs;e Sage Philo&longs;o­<lb/>phers &longs;hould e&longs;tabli&longs;h the form of the Eighth to be rather the dou­<lb/>ble, than quadruple; and the Form of the Fifth to be rather the <lb/>Se&longs;quialter, than the double Se&longs;quiquartan. </s> <s>But becau&longs;e the <lb/>numbring of the Vibrations of a Chord, which in giving a &longs;ound, <lb/>are extreme frequent, is altogether impo&longs;&longs;ible, I &longs;hould always <lb/>have been in doubt, whether or no it were true, that the more <lb/>Acute Chord of the Eighth, made in the &longs;ame time, double the <lb/>number of the Vibrations of the more Grave, if the Waves, <lb/>which may be continued as long as you plea&longs;e, by making the <lb/>Gla&longs;s to &longs;ound and vibrate, had not &longs;en&longs;ibly &longs;hewn me, that in <lb/>the &longs;elf &longs;ame moment that (&longs;ometimes) the Sound is heard to ri&longs;e <lb/>to an Eighth, there are &longs;een to ari&longs;e other Waves more minute, <lb/>which with infinite &longs;moothne&longs;s cut in the middle each of tho&longs;e <lb/>fir&longs;t.</s></p><p type="margin"> <s><margin.target id="marg1080"></margin.target>* An In&longs;trument <lb/>of but one &longs;tring; <lb/>called by <emph type="italics"/>Mar­<lb/>&longs;ennus la Tromper­<lb/>te Marine.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>An excellent Ob&longs;ervation for di&longs;tingui&longs;hing one by <lb/>one the Undulations ari&longs;ing from the Tremulation of the re­<lb/>&longs;ounding Body: which are tho&longs;e that diffu&longs;ing them&longs;elves tho­<lb/>row the Air, make the titillation upon the Drum of our Ear, that <lb/>in our Soul becommeth a Sound: But whereas beholding and ob­<lb/>&longs;erving them in the Water, endure no longer than the confrica­<lb/>tion of the finger la&longs;teth, and al&longs;o in that time they are not per­<lb/>manent, but are continually made and di&longs;&longs;olved, would it not <lb/>be an ingenious undertaking, if one could make, with much <lb/>exqui&longs;itene&longs;&longs;e, &longs;uch, as would continue a long time; I mean <lb/>Moneths and Years, &longs;o as to give a man opportunity mea&longs;ure, <lb/>and with ea&longs;e to number them?</s></p><p type="main"> <s>SAGR. </s> <s>I a&longs;&longs;ure you I &longs;hould highly value &longs;uch an Invention.</s></p><p type="main"> <s>SALV. </s> <s>The di&longs;covery was accidental, and the Ob&longs;ervation <lb/>and applicative improvement of it onely were mine, and I hold <lb/>it to be a Circum&longs;tance of noble Contemplation, althongh a bu&longs;i­<lb/>ne&longs;&longs;e in its &longs;elf &longs;ufficiently homely. </s> <s>Scraping a Bra&longs;&longs;e Plate with <lb/>an Iron Chizzel to fetch out &longs;ome Spots, in moving the Chizzel to <lb/>and again upon it pretty quick, I heard it (once or twice among&longs;t <lb/>many gratings) to Sibilate and &longs;end forth a whi&longs;tling noi&longs;e, very <lb/>&longs;hrill and audible: and looking upon the Plate, I &longs;aw a long <lb/>row of &longs;mall &longs;treaks, parallel to one another, and di&longs;tant from <lb/>one another by mo&longs;t equal Intervals: returning to my &longs;craping <lb/>again, I perceived by &longs;everal trials, that in tho&longs;e &longs;crapings, and <lb/>tho&longs;e onely that whi&longs;tled, the Chizzel left the &longs;treaks upon the <pb xlink:href="040/01/776.jpg" pagenum="84"/>Plate: but when the Scraping pa&longs;&longs;ed without any Sibilation, <lb/>there was not &longs;o much as the lea&longs;t &longs;ign of any &longs;uch &longs;treaks. </s> <s>Re­<lb/>peating the Experiment &longs;everal times afterwards, &longs;craping now <lb/>with greater, now with le&longs;&longs;e velocity, the Sibilation hapned to <lb/>be of a Tone &longs;ometimes acuter, &longs;ometimes graver; and I ob&longs;erved <lb/>the marks made in the more acute &longs;ounds to be clo&longs;er together, <lb/>and tho&longs;e of the more grave farther a&longs;under: and &longs;ometimes al&longs;o, <lb/>according as the &longs;elf &longs;ame &longs;crape was made towards the end, with <lb/>greater velocity than at the beginning, the &longs;ound was heard to <lb/>grow &longs;harper, and the &longs;treaks were ob&longs;erved to &longs;tand thicker, <lb/>but ever with extream neatne&longs;&longs;e, and marked with exact equidi­<lb/>&longs;tance: and farther-more, in the Sibilating &longs;crapes; I felt the <lb/>Chizzel to &longs;hake or tremulate in my hand, and a certain chilne&longs;&longs;e <lb/>to run along my arm; and in &longs;hort, I &longs;aw the &longs;ame effected upon <lb/>the Toole, which we u&longs;e to ob&longs;erve in whi&longs;pering, and after­<lb/>wards &longs;peaking aloud, for &longs;ending forth the breath without <lb/>forming a &longs;ound, we do not perceive any moving in the throat <lb/>and mouth, in compari&longs;on of that which we di&longs;cern to be in the <lb/>Wind-pipe and Throat of every one, in &longs;ending forth the voice; <lb/>and e&longs;pecially in grave and loud Tones. </s> <s>I have likewi&longs;e &longs;ome­<lb/>times among&longs;t the Chords of the Viols, ob&longs;erved two that were <lb/>Uni&longs;ons to the Sibilations made by &longs;craping after the manner I <lb/>told you, and that were mo&longs;t different in Tone, from which two <lb/>they preci&longs;ely were di&longs;tant a perfect Fifth, and then mea&longs;uring <lb/>the intervals of the &longs;treaks of both the Scrapes, I &longs;aw the di­<lb/>&longs;tance that conteined forty five &longs;paces of the one, conteined <lb/>thirty of the other: which, indeed, is the Form attributed to the <lb/>Diapente. </s> <s>But here, before I proceed any farther, I will tell you, <lb/>that of the three manners of rendring a Sound Acute, that which <lb/>you refer to the &longs;lenderne&longs;&longs;e or finene&longs;&longs;e of the Chord, may <lb/>with more truth be a&longs;cribed to the Weight. </s> <s>For the alteration ta­<lb/>ken from the thickne&longs;&longs;e, an&longs;wereth, when the Chords are of the <lb/>&longs;ame matter; and &longs;o a Gut-&longs;tring to make an Eighth, ought to be <lb/>four times thicker than the other Gut-&longs;tring; and one of Wier four <lb/>times thicker than another of Wier. </s> <s>But if I would make an Eighth <lb/>with one of Wier to one of Gut-&longs;tring, I am not to make it four <lb/>times thicker, but four times graver, &longs;o that, as to thickne&longs;&longs;e, <lb/>this of Wier &longs;hall not be four times thicker, but quadruple in <lb/>Gravity, for &longs;ome times it &longs;hall be more &longs;mall than its re&longs;pon­<lb/>dent to the Acuter Eighth, that is of Gut-&longs;tring. </s> <s>Hence it com­<lb/>meth to pa&longs;&longs;e that, &longs;tringing an In&longs;trument with Chords of Gold, <lb/>and another with Chords of Bra&longs;&longs;e, if they &longs;hall be of the &longs;ame <lb/>length, thickne&longs;&longs;e, and Tention, Gold being almo&longs;t twice as <lb/>heavy, the Strings &longs;hall prove about a Fifth more Grave. </s> <s>And <lb/>here it is to be noted, that the Gravity of the Moveable more re­<pb xlink:href="040/01/777.jpg" pagenum="85"/>&longs;i&longs;teth the Velocity, than the thickne&longs;&longs;e doth; contrary to what <lb/>others at the fir&longs;t would think: for indeed, in appearance, its more <lb/>rea&longs;onable, that the Velocity &longs;hould be retarded by the Re&longs;i&longs;tance <lb/>of the <emph type="italics"/>Medium<emph.end type="italics"/> again&longs;t Opening in a Moveable thick and light, <lb/>than in one grave and &longs;lender: and yet in this ca&longs;e it happeneth <lb/>quite contrary. </s> <s>But pur&longs;uing our fir&longs;t Intent, I &longs;ay, That the <lb/>ncere&longs;t and immediate rea&longs;ons of the Forms of Mu&longs;ical Intervals, <lb/>is neither the length of the Chord, nor the Tention, nor the <lb/>thickne&longs;&longs;e, but the proportion of the numbers of the Vibrations, <lb/>and Percu&longs;&longs;ions of the Undulations of the Air that beat upon the <lb/>Drum of our Ear, which it &longs;elf al&longs;o doth tremulate under the <lb/>&longs;ame mea&longs;ures of Time. </s> <s>Having e&longs;tabli&longs;hed this Point, we may, <lb/>perhaps, a&longs;&longs;ign a very apt rea&longs;on, whence it commeth, that of <lb/>tho&longs;e Sounds that are different in Tone, &longs;ome Couples are re­<lb/>ceived with great delight by our Sence, others with le&longs;s, and <lb/>others occa&longs;ion in us a very great di&longs;turbance; which is to &longs;eek a <lb/>rea&longs;on of the Con&longs;onances more or le&longs;&longs;e perfect, and of Di&longs;lo­<lb/>nances. </s> <s>The mole&longs;tation and har&longs;hne&longs;&longs;e of the&longs;e proceeds, as I <lb/>believe, from the di&longs;cordant Pul&longs;ations of two different Tones, <lb/>which di&longs;proportionally &longs;trike the Drum of our Ear: and the <lb/>Di&longs;&longs;onances &longs;hall be extreme har&longs;h, in ca&longs;e the Times of the Vi­<lb/>brations were incommen&longs;urable. </s> <s>For one of which take that, <lb/>when of two Chords &longs;et to an Uni&longs;on, one is &longs;ounded, and &longs;uch <lb/>a part of another, as is the Side of the Square of its Diameter; <lb/>a Di&longs;&longs;onance like to the ^{*} Tritone, or Semi-diapente. </s> <s>Con&longs;onan­<lb/><arrow.to.target n="marg1081"></arrow.to.target><lb/>ces, and with plea&longs;ure received, &longs;hall tho&longs;e Couples of Sounds <lb/>be, that &longs;hall &longs;trike in &longs;ome order upon the Drum; which order <lb/>requireth, fir&longs;t, that the Pul&longs;ations made in the &longs;ame Time be <lb/>commen&longs;urable in number, to the end, the Cartillage of the Drum, <lb/>may not &longs;tand in the perpetual Torment of a double inflection of <lb/>allowing and obeying the ever di&longs;agreeing Percu&longs;&longs;ions. </s> <s>Therefore <lb/>the fir&longs;t and mo&longs;t grateful Con&longs;onance &longs;hall be the Eighth, being, <lb/>that for every &longs;troke, that the Grave-&longs;tring or Chord giveth upon <lb/>the Drum, the Acute giveth, two; &longs;o that both beat together <lb/>in every &longs;econd Vibration of the Acute Chord; and &longs;o of the <lb/>whole number of &longs;trokes, the one half accord to &longs;trike together, <lb/>but the &longs;trokes of the Chords that are Uni&longs;ons, alwayes joyn <lb/>both together, and therefore they are, as if they were of the <lb/>&longs;ame Chord, nor make they a Con&longs;onance. </s> <s>The Fifth delighteth <lb/>likewi&longs;e, in regard, that for every two &longs;troaks of the Grave <lb/>Chord, the Acute giveth three: from whence it followeth, that <lb/>numbering the Vibrations of the Acute Chord, the third part of <lb/>that number will agree to beat together; that is, two Solitary ones <lb/>interpo&longs;e between every couple of Con&longs;onances; and in the Di­<lb/>ate&longs;&longs;eron there interpo&longs;e three. </s> <s>In the &longs;econd, that is in the <emph type="italics"/>Se&longs;-<emph.end type="italics"/><pb xlink:href="040/01/778.jpg" pagenum="86"/><emph type="italics"/>quioctave<emph.end type="italics"/> Tone for every nine Pul&longs;ations, one onely &longs;trikes in Con­<lb/>&longs;ort with the other of the Graver Chord; all the re&longs;t are Di&longs;cords, <lb/>and received upon the Drum with regret, and are judged Di&longs;&longs;o­<lb/>nances by the Ear.</s></p><p type="margin"> <s><margin.target id="marg1081"></margin.target>* Or a fal&longs;e Fifth.</s></p><p type="main"> <s>SIMP. </s> <s>I could wi&longs;h this Di&longs;cour&longs;e were a little explained.</s></p><p type="main"> <s>SALV. </s> <s>Suppo&longs;e this line A B the Space, and dilating of a Vi­<lb/>bration of the Grave Chord; and the line C D that of the Acute <lb/>Chord, which with the other giveth the Eighth: and let A B be <lb/>divided in the mid&longs;t in E. </s> <s>It is manife&longs;t, that the Chords begin­<lb/>ing to move at the terms A and C, by that time the Acute Vibra­<lb/>tion &longs;hall be come to the term D, the other <lb/><figure id="id.040.01.778.1.jpg" xlink:href="040/01/778/1.jpg"/><lb/>&longs;hall be di&longs;tended onely to the half E, which <lb/>not being the bound or term of the Motion, <lb/>it &longs;trikes not: but yet a &longs;troak is made in D. <lb/></s> <s>The Vibrations afterwards returning from D <lb/>to C, the other pa&longs;&longs;eth from E to B, where­<lb/>upon the two Percu&longs;&longs;ions of B and C &longs;trike <lb/>both together upon the Drum: and &longs;o con­<lb/>tinuing to reiterate the like &longs;ub&longs;equent Vi­<lb/>brations; one &longs;hall &longs;ee, that the union of the <lb/>Percu&longs;&longs;ions of the Vibrations C D with tho&longs;e of A B, happen al­<lb/>ternately every other time: but the Pullations of the terms A B <lb/>are alwayes accompanied with one of C D, and that alwayes the <lb/>&longs;ame: which is manife&longs;t, for &longs;uppo&longs;ing that A and C &longs;trike to­<lb/>gether; in the time that A is pa&longs;&longs;ing to B, C goeth to D, and <lb/>returneth back to C: &longs;o that the &longs;troaks at B and C are al&longs;o <lb/>together. </s> <s>But now let the two Vibrations A B and C D be tho&longs;e <lb/>that produce the Diapente, the times of which are in proportion <lb/>Se&longs;quialter, and divide A B of the Grave Chord, in three equal <lb/>parts in E and O; And &longs;uppo&longs;e the Vibrations to begin at the <lb/>&longs;ame moment from the terms A and C: It is manife&longs;t, that at the <lb/>&longs;troke that &longs;hall be made in D, the Vibration of A B &longs;hall have <lb/>got no farther than O, the Drum therefore receiveth the Pul&longs;a­<lb/>tion D onely: again in the return from D to C, the other Vibra­<lb/>tion pa&longs;&longs;eth from O to B, and returneth to O, making the Pul­<lb/>&longs;ation in B, which likewi&longs;e is &longs;olitary, and in Counter-time, (an <lb/>accident to be con&longs;idered:) for we having &longs;uppo&longs;ed the fir&longs;t <lb/>Pul&longs;ations to be made at the &longs;ame moment in the terms A and C, <lb/>the &longs;econd, which was onely by the term D, was made as long after <lb/>as the time of the tran&longs;ition C D, that is A O, imports; but <lb/>that which followeth, made in B, is di&longs;tant from the other one­<lb/>ly &longs;o much as is the time O B, which is the half: afterwards con­<lb/>tinuing the Recur&longs;ion from O to A, whil&longs;t the other goeth from <lb/>C to D, the two Pul&longs;ations come to be made both at once in A <lb/>and D. </s> <s>There afterwards follow other Periods like to the&longs;e, that <pb xlink:href="040/01/779.jpg" pagenum="87"/>is, with the interpo&longs;ition of two &longs;ingle and &longs;olitary Pul&longs;ations of <lb/>the Acute Chord, and one of the Grave Chord, likewi&longs;e &longs;olita­<lb/>ry, is interpo&longs;ed between the two &longs;olitary &longs;trokes of the Acute. </s> <s>So <lb/>that if we did but &longs;uppo&longs;e the Time divided into Moments, that is, <lb/>into &longs;mall equal Particles: &longs;uppo&longs;ing that in the two fir&longs;t moments, <lb/>I pa&longs;&longs;ed from the Concordant Pul&longs;ations made in A and C to O <lb/>and D, and that in D, I make a Percu&longs;&longs;ion: and that in the third <lb/>and fourth moment I return from D to C, &longs;triking in C, and <lb/>that from O, I pa&longs;t to B, and returned to O, &longs;triking in B; and <lb/>that la&longs;tly in the fifth and &longs;ixth moment from O and C, I pa&longs;t to <lb/>A and D &longs;triking in both: we &longs;hall have the Pul&longs;ations di&longs;tributed <lb/>with &longs;uch order upon the Drum, that &longs;uppo&longs;ing the Pul&longs;ations of <lb/>the two Chords in the &longs;ame in&longs;tant, it &longs;hall two moments after <lb/>receive a &longs;olitary Percu&longs;&longs;ion, in the third moment anothor, &longs;oli­<lb/>tary likewi&longs;e, in the fourth another &longs;ingle one, and two moments <lb/>after, that is, in the &longs;ixth, two together; and here ends the <lb/>Period, and, if I may &longs;o &longs;ay, Anomaly; which Period is oft-times <lb/>afterwards replicated.</s></p><p type="main"> <s>SAGR. </s> <s>I can hold no longer, but mu&longs;t needs expre&longs;&longs;e the con­<lb/>tent I take in hearing rea&longs;ons &longs;o appo&longs;itely a&longs;&longs;igned of effects that <lb/>have &longs;o long time held me in darkne&longs;&longs;e and blindne&longs;&longs;e. </s> <s>Now I <lb/>know why the Uni&longs;on differeth not at all from a &longs;ingle Tone: I <lb/>&longs;ee why the Eighth is the principal Con&longs;onance, but withal &longs;o <lb/>like to an Uni&longs;on, that, as an Uni&longs;on, it is taken and cojoyned <lb/>with others: it re&longs;embleth an Uni&longs;on, for that whereas the Pul­<lb/>&longs;ations of Chords &longs;et to an Uni&longs;on, keep time in &longs;triking, the&longs;e <lb/>of the Grave Chord in an Eighth alwayes keep time with tho&longs;e <lb/>of the Acute, and of the&longs;e one interpo&longs;eth alone, and in equal <lb/>di&longs;tances, and as, one may &longs;ay, without any variety, whereupon <lb/>that Con&longs;onance is over &longs;weet. </s> <s>But the Fifth, with tho&longs;e its <lb/>Counter-times, and with the interpo&longs;ures of two &longs;olitary Pul&longs;a­<lb/>tions of the Acute Chord, and one of the Grave Chord, <lb/>between the Couples of Di&longs;cordant Pul&longs;ations, and tho&longs;e <lb/>three &longs;olitary ones, with an interval of time, as great as the half of <lb/>that which interpo&longs;eth between each Couple, and the &longs;olitary <lb/>Percu&longs;&longs;ions of the Acute Chord, maketh &longs;uch a Titillation and <lb/>Tickling upon the Cartillage of the Drum of the Ear, that al­<lb/>laying the Dulcity with a mixture of Acrimony, it &longs;eemeth at <lb/>one and the &longs;ame time to ki&longs;&longs;e and bite.</s></p><p type="main"> <s>SALV. </s> <s>It is convenient, in regard I &longs;ee, that you take &longs;uch de­<lb/>light in the&longs;e Novelties, that I &longs;hew you the way whereby the Eye <lb/>al&longs;o, and not the Ear alone, may recreate it &longs;elf in beholding <lb/>the &longs;ame &longs;ports that the Ear feeleth. </s> <s>Su&longs;pend Balls of Lead or o­<lb/>ther heavy matter on three &longs;trings of different lengths, but in <lb/>&longs;uch proportion, that while the longer maketh two Vibrations, <pb xlink:href="040/01/780.jpg" pagenum="88"/>the &longs;horter may make four, and the middle one three; which <lb/>will happen, when the longe&longs;t containeth &longs;ixteen feet, or other <lb/>mea&longs;ures, of which the middle one containeth nine, and the <lb/>&longs;horte&longs;t four: and removing them all together from Perpendi­<lb/>cularity, and then letting them go, you &longs;hall &longs;ee a plea&longs;ing In­<lb/>termixtion of the &longs;aid <emph type="italics"/>Pendulums<emph.end type="italics"/> with various encounters, but <lb/>&longs;uch, that, at every fourth Vibration of the longe&longs;t, all the three <lb/>will concurre in one and the &longs;ame term together, and then again <lb/>will depart from it, reiterating anew the &longs;ame Period: the which <lb/>commixture of Vibrations, is the &longs;ame, that being made by the <lb/>Chords, pre&longs;ents to the Ear an Eighth, with a Fifth in the mid&longs;t. <lb/></s> <s>And if you qualifie the length of other &longs;trings in the like di&longs;po­<lb/>&longs;ure, &longs;o that their Vibrations an&longs;wer to tho&longs;e of other Mu&longs;ical, <lb/>but Con&longs;onant Intervals, you &longs;hall &longs;ee other and other Inter­<lb/>weavings, and alwaies &longs;uch, that in determinate times, and after <lb/>determinate numbers of Vibrations, all the &longs;trings (be they three, <lb/>or be they four) will agree to joyn in the &longs;ame moment, in the <lb/>term of their Recur&longs;ions, and from thence to begin &longs;uch another <lb/>Period: but if the Vibrations of two or more &longs;trings are either <lb/>Incommen&longs;urable, &longs;o, that they never return harmoniou&longs;ly to ter­<lb/>minate determinate numbers of Vibrations, or though they be <lb/>not Incommen&longs;urable, yet if they return not till after a long time, <lb/>and after a great number of Vibrations, then the &longs;ight is con­<lb/>founded in the di&longs;orderly order of irregular Intermixtures, and <lb/>the Ear with wearine&longs;&longs;e and regret receiveth the intemperate Im­<lb/>pul&longs;es of the Airs Tremulations, that without Order or Rule, <lb/>&longs;ucce&longs;&longs;ively beat upon its Drum.</s></p><p type="main"> <s>But whither, my Ma&longs;ters, have we been tran&longs;ported for &longs;o <lb/>many hours by various Problems, and unlook't for Di&longs;cour&longs;es? <lb/></s> <s>We have made it Night, and yet we have handled few or none of <lb/>the points propounded; nay we have &longs;o lo&longs;t our way, that I <lb/>&longs;car&longs;e remember our fir&longs;t entrance, and that &longs;mall Introduction, <lb/>which we laid down, as the Hypothe&longs;is and beginning of the fu­<lb/>ture Demon&longs;trations.</s></p><p type="main"> <s>SAGR It will be convenient, therefore, that we break up our <lb/>Conference for this time, giving our Minds leave to compo&longs;e <lb/>them&longs;elves in the Nights Repo&longs;e, that we may to Morrow (if <lb/>you plea&longs;e &longs;o far to favour us) rea&longs;&longs;ume the Di&longs;cour&longs;es de&longs;ired, <lb/>and chiefly intended.</s></p><p type="main"> <s>SALV. </s> <s>I &longs;hall not fail to be here to Morrow at the u&longs;ual <lb/>hour, to &longs;erve and enjoy you.</s></p><p type="head"> <s><emph type="italics"/>The End of the Fir&longs;t Dialogue.<emph.end type="italics"/></s></p></chap><chap><pb xlink:href="040/01/781.jpg" pagenum="89"/><p type="head"> <s>GALILEUS, <lb/>HIS <lb/>DIALOGUES <lb/>OF <lb/>MOTION.</s></p><p type="head"> <s>The Second Dialogue.</s></p><p type="head"> <s><emph type="italics"/>INTERLOCUTORS,<emph.end type="italics"/></s></p><p type="head"> <s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"> <s>SAGREDUS.</s></p><p type="main"> <s><emph type="italics"/>Simplicius,<emph.end type="italics"/> and I, &longs;taid expecting your com­<lb/>ing, and we have been trying to recall to <lb/>memory our la&longs;t Con&longs;ideration, which, as <lb/>the Principle and Suppo&longs;ition, on which <lb/>you ground the Conclu&longs;ions that you in­<lb/>tended to Demon&longs;trate to us, was that <lb/>Re&longs;i&longs;tance, that all Bodies have to <emph type="italics"/>Fracti­<lb/>on,<emph.end type="italics"/> depending on that Cement, that con­<lb/>nects and glutinates the parts, &longs;o, as that <lb/>they do not &longs;eparate and divide without a powerful attraction: <lb/>and our enquiry hath been, what might be the Cau&longs;e of that <lb/>Coherence, which in &longs;ome Solids is very vigorous; propounding <lb/>that of <emph type="italics"/>Vacuum<emph.end type="italics"/> for the principal, which afterwards occa&longs;ioned &longs;o <lb/>many Digre&longs;&longs;ions as held us the whole day, and far from the <pb xlink:href="040/01/782.jpg" pagenum="90"/>matter at fir&longs;t propo&longs;ed, which was the Contemplation of the Re­<lb/>&longs;i&longs;tances of Solids to Fraction.</s></p><p type="main"> <s>SALV. </s> <s>I remember all that hath been &longs;aid, and returning to <lb/>our begun di&longs;cour&longs;e; What ever this Re&longs;i&longs;tance of Solids to brea­<lb/>king by a violent attraction, is &longs;uppo&longs;ed to be, it is &longs;ufficient, that it <lb/>is to be found in them: which, though it be very great again&longs;t the <lb/>&longs;trength of one that draweth them &longs;treight out, it is ob&longs;erved to be <lb/>le&longs;&longs;e in forcing them tran&longs;ver&longs;ely, or &longs;idewaies: and thus we &longs;ee, <lb/>for example, a rod of Steel, or Gla&longs;&longs;e to &longs;u&longs;tain the length-waies a <lb/>weight of a thou&longs;and pounds, which, fa&longs;tned at Right-Angles in­<lb/>to a Wall, will break if you hang upon it but only fifty. </s> <s>And of <lb/>this &longs;econd Re&longs;i&longs;tance we are to &longs;peak, enquiring, according to <lb/>what proportions it is found in Pri&longs;mes, and Cylinders of like and <lb/>unlike figure, length, and thickne&longs;s, and, withal, of the &longs;ame mat­<lb/>ter. </s> <s>In which Speculation, I take for a known Principle, that which <lb/>in the Mechanicks is demon&longs;trated among&longs;t the Pa&longs;&longs;ions of the <lb/>Vectis, which we call the Leaver: namely, That in that u&longs;e of the <lb/>Leaver, the Force is to the Re&longs;i&longs;tance in Reciprocal proportion, <lb/>as the Di&longs;tances from the Fulciment to the &longs;aid Force and the Re­<lb/>&longs;i&longs;tance.</s></p><p type="main"> <s>SIMP. </s> <s>This <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> in his Mechanicks, demon&longs;trated before <lb/>any other man.</s></p><p type="main"> <s>SALV. </s> <s>I am content to grant him the precedency in time, but <lb/>for the firmne&longs;&longs;e o&longs; Demon&longs;tration, I think, that <emph type="italics"/>Archimedes<emph.end type="italics"/><lb/>ought to be preferred far before him, on one &longs;ole Propo&longs;ition of <lb/>whom, by him demon&longs;trated in his Book, <emph type="italics"/>De Equiponderantium,<emph.end type="italics"/><lb/>depend the Rea&longs;ons, not only of the Leaver, but of the greater <lb/>part of the other Mechanick In&longs;truments.</s></p><p type="main"> <s>SAGR. </s> <s>But &longs;ince that this Principle is the foundation of all <lb/>that which you intend to demon&longs;trate to us, it would be very re­<lb/>qui&longs;ite, that you produce us the proof of this &longs;ame Suppo&longs;ition, <lb/>if it be not too long a work, giving us a full and perfect informati­<lb/>on thereof.</s></p><p type="main"> <s>SALV. </s> <s>Though I am to do this, yet it will be better, that I lead <lb/>you into the field of all our future Speculations, by an enterance <lb/>&longs;omewhat different from that of <emph type="italics"/>Archimedes<emph.end type="italics"/>; and that, &longs;uppo­<lb/>&longs;ing no more, but only that equal Weights, put into a Ballance of <lb/>equal Arms, make an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> (a Principle likewi&longs;e &longs;uppo&longs;ed <lb/>by <emph type="italics"/>Archimedes<emph.end type="italics"/> him&longs;elf.) I come, in the next place, to demon­<lb/>&longs;trate to you, that not only it is as true as the other, That unequal <lb/>Weights make an <emph type="italics"/>Equilibrium<emph.end type="italics"/> in a Stiliard of Armes unequal, ac­<lb/>cording to the proportion of tho&longs;e Weights Reciprocally &longs;u&longs;pen­<lb/>ded, but that it is one and the &longs;ame thing to place equal Weights <lb/>at equal di&longs;tances, as to place unequal Weights at di&longs;tances that <lb/>are in Reciprocal Proportion to the Weights. </s> <s>Now for a plain <pb xlink:href="040/01/783.jpg" pagenum="91"/>Demon&longs;tration of what I &longs;ay, de&longs;cribe a Solid Pri&longs;m or Cylinder <lb/>A B, [<emph type="italics"/>as in<emph.end type="italics"/> Figure 1. <emph type="italics"/>at the end of this Dialogue,<emph.end type="italics"/>] &longs;u&longs;pended by <lb/>its ends at the Line H I, and &longs;u&longs;tained by two Cords, H A, and I B. <lb/></s> <s>It is manife&longs;t, that if I &longs;u&longs;pend the whole by the Cord C, placed <lb/>in the middle of the Beam or Ballance H I, the Pri&longs;m A B will be <lb/>equilibrated, one half of its weight, being on one &longs;ide, and the other <lb/>half on the other &longs;ide of the Point of Su&longs;pen&longs;ion C by the Princi­<lb/>ple that we pre&longs;uppo&longs;ed. </s> <s>Now let the Pri&longs;m be divided into un­<lb/>equal parts by the Line D, and let the part D A be grea­<lb/>ter, and D B le&longs;&longs;er; and to the end, that &longs;uch divi&longs;ion being made, <lb/>the Parts of the Pri&longs;m may re&longs;t in the &longs;ame &longs;cituation and con&longs;ti­<lb/>tution, in re&longs;pect of the Line H I, let us help it with a Cord E D, <lb/>which, being fa&longs;tened in the Point E, &longs;u&longs;taineth the parts A D, and <lb/>D B: It is not to be doubted, but that there being no local muta­<lb/>tion in the Pri&longs;m, in re&longs;pect of the Ballance H I, it &longs;hall remain in <lb/>the &longs;ame &longs;tate of Equilibration. </s> <s>But it will re&longs;t in the &longs;ame Con­<lb/>&longs;titution likewi&longs;e, if the Part of the Pri&longs;m, that is now &longs;u&longs;pended at <lb/>the two extreams, or ends with Cords A H and D E, be hanged at <lb/>one &longs;ole Cord G L, placed in the mid&longs;t: and likewi&longs;e the other <lb/>part D B, will not change &longs;tate, if &longs;u&longs;pended by the middle, and <lb/>&longs;u&longs;tained by the Cord F M. </s> <s>So that the Cords H A, E D, and I B <lb/>being untied, and only the two Cords G L, and F M being left, the <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> will &longs;till remain, the Su&longs;pen&longs;ion being &longs;till made at <lb/>the Point C. Now, here let us confider, that we have two Grave <lb/>Bodies A D, and D B, hanging at the terms G and F of a Beam <lb/>G F, in which the <emph type="italics"/>Equilibrium<emph.end type="italics"/> is made at the Point C: in &longs;uch <lb/>manner, that the di&longs;tance of the &longs;u&longs;pen&longs;ion of the Weight A D <lb/>from the Point C, is the Line C G, and the other part C F, is the <lb/>di&longs;tance at which the other Weight D B hangeth. </s> <s>It remaineth, <lb/>therefore, only to be demon&longs;trated, that tho&longs;e Di&longs;tances have the <lb/>&longs;ame proportion to one another, as the Weights them&longs;elves have, <lb/>but reciprocally taken: that is, that the di&longs;tance G C is to the di­<lb/>&longs;tance C F, as the Pri&longs;m D B to the Pri&longs;m D A, which we prove <lb/>thus. </s> <s>The Line G E being the half of E H, and E F the half of <lb/>E I, all G F &longs;hall be equall to all H I, and therefore equal to C I: <lb/>and taking away the common part C F, the remainder G C &longs;hall <lb/>be equal to the remainder F I, that is, to F E: and C E taken in <lb/>common, the two Lines G E and C F &longs;hall be equal: and, there­<lb/>fore, as G E, is to E F, &longs;o is F C, to C G: but as G C is to E F, &longs;o is <lb/>the double to the double; that is H E to E I; that is, the Pri&longs;m <lb/>A D to the Pri&longs;m D B. </s> <s>Therefore by Equality of proportion, <lb/>and by Conver&longs;ion, as the di&longs;tance G C is to the di&longs;tance C F, &longs;o <lb/>is the Weight B D to the Weight D A: which is that that I was to <lb/>demon&longs;trate. </s> <s>If you under&longs;tand this, I believe that you will not <lb/>&longs;cruple to admit, that the two Pri&longs;mes A D, and D B make an <pb xlink:href="040/01/784.jpg" pagenum="92"/><emph type="italics"/>Equilibrium<emph.end type="italics"/> in th Point C, for the half of the whole Solid A B is <lb/>on the right hand of the Su&longs;pen&longs;ion C, and the other half on the <lb/>left; and that in this manner there are repre&longs;ented two equal <lb/>Weights, di&longs;po&longs;ed and di&longs;tended at two equal di&longs;tances. </s> <s>Again, <lb/>that the two Pri&longs;mes A D, and D B, being reduced into two Dice, <lb/>or two Balls, or into any two other Figures, (provided that they <lb/>keep the &longs;ame Su&longs;pen&longs;ions G and F) do continue to make their <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> in the Point C, I believe none can deny, for that it is <lb/>mo&longs;t manife&longs;t, that Figures change not weight, where the &longs;ame <lb/>quantity of matter is retained. </s> <s>From which we may gather the <lb/>general Conclu&longs;ion, That two Weights, whatever they be, make <lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> at Di&longs;tances reciprocally an&longs;wering to their Gra­<lb/>vities. </s> <s>This Principle, therefore, being e&longs;tabli&longs;hed, before we pa&longs;s <lb/>any farther, I am to propo&longs;e to Con&longs;ideration, how the&longs;e Forces, <lb/>Re&longs;i&longs;tances, Moments, Figures, may be con&longs;idered in Ab&longs;tract, <lb/>and &longs;eparate from Matter, as al&longs;o in Concrete and conjoyned <lb/>with Matter; and in this manner tho&longs;e Accidents that agree with <lb/>Figures, con&longs;idered as Immaterial, &longs;hall receive certain Modifica­<lb/>tions, when we &longs;hall come to add Matter to them, and con&longs;equent­<lb/>ly Gravity. </s> <s>As for example, if we take a Leaver, as for in&longs;tance <lb/>B A [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>2.] which, re&longs;ting upon the Fulciment E, we ap­<lb/>ply to rai&longs;e the heavy Stone D: It is manife&longs;t by the Principle de­<lb/>mon&longs;trated, that the Force placed at the end B, &longs;hall &longs;uffice to <lb/>equal the Re&longs;i&longs;tance of the Weight D, if &longs;o be, that its Moment <lb/>have the &longs;ame proportion to the Moment of the &longs;aid D, that the <lb/>Di&longs;tance A C hath to the Di&longs;tance C B: and this is true, if we <lb/>confider no other Moments than tho&longs;e of the &longs;imple Force in B, <lb/>and of the Re&longs;i&longs;tance in D, as if the &longs;aid Leaver were immaterial, <lb/>and void of Gravity. </s> <s>But if we bring to account the Gravity al&longs;o <lb/>of the In&longs;trument or Leaver it &longs;elf, which hapneth &longs;ometimes to be <lb/>of Wood, and &longs;ometimes of Iron; it is manife&longs;t, that the weight <lb/>of the Leaver, being added to the Force in B, it will alter the pro­<lb/>portion, which it will be requi&longs;ite to deliver in other terms. </s> <s>And <lb/>therefore before we pa&longs;&longs;e any farther, it is nece&longs;&longs;ary, that we di­<lb/>&longs;tingui&longs;h between the&longs;e two waies of Con&longs;ideration, calling that a <lb/>taking it ab&longs;olutely, when we &longs;uppo&longs;e the In&longs;trument to be taken <lb/>in Ab&longs;tract, that is, disjunct from the Gravity of its own Matter; <lb/>but conjoyning the Matter, as al&longs;o the Gravity, with &longs;imple and <lb/>ab&longs;olute Figures, we will phra&longs;e the Figures conjoyn'd with the <lb/>Matter, Moment, or Force compounded.</s></p><p type="main"> <s>SAGR I mu&longs;t of nece&longs;&longs;ity break the Re&longs;olution I had taken, <lb/>not to give occa&longs;ion of digre&longs;&longs;ing, for I &longs;hould not be able to &longs;et <lb/>my &longs;elf to hear what remaines with attention, if a certain &longs;cruple <lb/>were not removed that cometh into my head; and it is this, That <lb/>I gue&longs;&longs;e you make compari&longs;on between the Force placed in B, and <pb xlink:href="040/01/785.jpg" pagenum="93"/>the total Gravity of the Stone D, of which Gravity me thinks, that <lb/>one, and that, very probably, the greater part, re&longs;teth upon the <lb/>Plane of the Horizon: &longs;o that----</s></p><p type="main"> <s>SALV. </s> <s>I have rightly apprehended you, &longs;o that you need &longs;ay <lb/>no more, but only take notice, that I named not the total Gravity <lb/>of the Stone, but &longs;pake of the Moment that it hath, and exerci&longs;eth <lb/>at the Point A, the extream term of the Leaver B A, which is ever <lb/>le&longs;s than the entire weight of the Stone; and is variable according <lb/>to the Figure of the Stone, and according as it hapneth to be more <lb/>or le&longs;&longs;e elevated.</s></p><p type="main"> <s>SAGR. </s> <s>I am &longs;atisfied in that particular, but I have one thing <lb/>more to de&longs;ire, namely, that for my perfect information, you would <lb/>demon&longs;trate to me the way, if there be one, how I may find what <lb/>part of the total weight that is, which cometh to be born by the <lb/>&longs;ubjacent Plane, and what that which gravitates upon the Leaver <lb/>at the extream A.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>Becau&longs;e I can give you &longs;atisfaction in few words, I will <lb/>not fail to &longs;erve you: therefore, de&longs;cribing a &longs;light Figure thereof, <lb/>be plea&longs;ed to &longs;uppo&longs;e, that the Weight, who&longs;e Center of Gravity is <lb/>A, [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>3.] re&longs;teth upon the Horizon with the term B, and <lb/>at the other end is born up by the Leaver C G, on the Fulciment <lb/>N, by a Power placed in G: and that from the Center A, and term <lb/>C, Perpendiculars be let fall to the Horizon, A O, and C F. </s> <s>I &longs;ay, <lb/>That the Moment of the whole Weight &longs;hall have to the Moment <lb/>of the whole Power in G, a proportion compounded of the Di­<lb/>&longs;tance G N to the Di&longs;tance N C, and of F B to B O. Now, as the <lb/>Line F B is to B O, &longs;o let N C be to X. </s> <s>And the whole Weight A <lb/>being born by the two Powers placeed in B and C, the Power B is <lb/>to C, as the di&longs;tance F O to O B: and by Compo&longs;ition, the <lb/>two Powers B and C together, that is, the total Moment of <lb/>the whole Weight A, is to the Power in C, as the Line F B is <lb/>to the Line B O; that is, as N C to X: But the Moment of <lb/>the Power in C is to the Moment of the Power in G, as the Di­<lb/>&longs;tance G N is to N C: Therefore, by Perturbation of proportion, <lb/>the whole Weight A is to the Moment of the Power in G, as G N <lb/>to X: But the proportion of G N to X is compounded of the pro­<lb/>portion G N to N C, and of that of N C to X; that is, of F B to <lb/>B O: Therefore the Weight A is to the Power that bears it up in <lb/>G, in a proportion compounded of G N to N C, and of that of <lb/>F B to B O: which is that that was to be demon&longs;trated. </s> <s>Now re­<lb/>turning to our fir&longs;t intended Argument, all things hitherto decla­<lb/>red being under&longs;tood, it will not be hard to know the rea&longs;on, <lb/>whence it cometh to pa&longs;&longs;e that</s></p><pb xlink:href="040/01/786.jpg" pagenum="94"/><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s><emph type="italics"/>A Solid Pri&longs;m or Cylinder of Gla&longs;&longs;e, Steel, Wood, or <lb/>other Frangible Matter, that being &longs;u&longs;pended length­<lb/>waies, will &longs;u&longs;tain a very great Weight hanged <lb/>Thereat, will, Sidewaies, (as we &longs;aid even now) be <lb/>broken in pieces by a far le&longs;&longs;er Weight, according as <lb/>its length &longs;hall exceed its thickne&longs;s.<emph.end type="italics"/></s></p><p type="main"> <s>Wherefore let us de&longs;cribe the Solid Pri&longs;m A B C D, <lb/>fixed into a Wall by the Part A B, and in the <lb/>other extream &longs;uppo&longs;e the Force of the Weight E; <lb/>(alwaies under&longs;tanding the Wall to be erect to the Horizon, <lb/>and the Pri&longs;m or Cylinder fa&longs;tened in the Wall at Right-An­<lb/>gles) it is manife&longs;t, that being to break, it will be broken in the place <lb/>B, where the Mortace in the Wall &longs;erveth for Fulciment, and B C <lb/>for the part of the Leaver in which lieth the force, and the thick­<lb/>ne&longs;&longs;e of the Solid B A is the other part of the Leaver, in which <lb/>lieth the Re&longs;i&longs;tance, which con&longs;i&longs;teth in the unfa&longs;tening, or divi­<lb/>ding, that is to be made of the part of the Solid B D, that is with­<lb/>out the Wall from that which is within: and by what hath been <lb/>declared, the Moment <lb/><figure id="id.040.01.786.1.jpg" xlink:href="040/01/786/1.jpg"/><lb/>of the Force placed in <lb/>C, is to the Moment of <lb/>the Re&longs;i&longs;tance that lieth <lb/>in the thickne&longs;&longs;e of the <lb/>Pri&longs;m, that is, in the <lb/>Connection of the Ba&longs;e <lb/>B A, with the parts con­<lb/>tiguous to it, as the <lb/>length C B is to the half <lb/>of B A: And therefore <lb/>the ab&longs;olute Re&longs;i&longs;tance <lb/>again&longs;t Fraction that is <lb/>in the Pri&longs;m B D, <lb/>(which ab&longs;olute Re&longs;i­<lb/>&longs;tance is that which is <lb/>made by drawing it <lb/>downwards, for at that <lb/>time the motion of the Mover is the &longs;ame with that of the Body <lb/>Moved) again&longs;t the fracture to be made by help of the Leaver <pb xlink:href="040/01/787.jpg" pagenum="95"/>B C, is as the Length B C to the half of A B in the Pri&longs;m, which <lb/>in the Cylinder is the Semidiameter of its Ba&longs;e. </s> <s>And this is our fir&longs;t <lb/>Propo&longs;ition. </s> <s>And ob&longs;erve, that what I have &longs;aid ought to be un­<lb/>der&longs;tood, when the Confideration of the proper Weight of the So­<lb/>lid B D is removed: which Solid I have taken as weighing nothing. <lb/></s> <s>But in ca&longs;e we would bring its Gravity to account, conjoyning it <lb/>with the Weight E, we ought to add to the Weight E the half of <lb/>the Weight of the Solid B D: &longs;o that the Weight B D being <lb/><emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> two pounds, and the Weight of E ten pounds, we are to <lb/>take the Weight E, as if it were eleven pounds.</s></p><p type="main"> <s>SIMP. </s> <s>And why not as if it were twelve?</s></p><p type="main"> <s>SALV. </s> <s>The Weight E, <emph type="italics"/>Simplicius,<emph.end type="italics"/> hanging at the term C, <lb/>gravitates in re&longs;pect of B C, with all its Moment of ten pounds, <lb/>whereas if only B D were pendent, it would weigh with its whole <lb/>Moment of two pounds; but, as you &longs;ee, that Solid is di&longs;tributed <lb/>thorow all the length B C, uniformly, &longs;o that its parts near to the <lb/>extream B, gravitate le&longs;&longs;e than the more remote: &longs;o that, in a word, <lb/>compen&longs;ating tho&longs;e with the&longs;e, the weight of the whole Pri&longs;m is <lb/>brought to operate under the Center of its Gravity, which an&longs;we­<lb/>reth to the middle of the Leaver B C: But a Weight hanging at <lb/>the end C, hath a Moment double to that which it would have <lb/>hanging at the middle: And therefore the half of the Weight of <lb/>the Pri&longs;m ought to be added to the Weight E, when we would u&longs;e <lb/>the Moment of both, as placed in the Term C.</s></p><p type="main"> <s>SIMP. </s> <s>I apprehend you very well, and, if I deceive not my &longs;elf, <lb/>me thinks, that the Power of both the Weights B D and E, &longs;o placed, <lb/>would have the &longs;ame Moment, as if the whole Weight of B D, and <lb/>the double of E were hanged in the mid&longs;t of the Leaver B C.</s></p><p type="main"> <s>SALV. </s> <s>It is exactly &longs;o, and you are to bear it in mind. </s> <s>Here we <lb/>may immediatly under&longs;tand</s></p><p type="head"> <s>PROPOSITION II.</s></p><p type="main"> <s><emph type="italics"/>How, and with what proportion, a Ruler, or Pri&longs;m, <lb/>more broad than thick, re&longs;i&longs;teth Fraction, better if it <lb/>be forced according to its breadth, than according to <lb/>its thickne&longs;&longs;e.<emph.end type="italics"/></s></p><p type="main"> <s>For under&longs;tanding of which, let a Pri&longs;m be &longs;uppo&longs;ed A D: <lb/>[<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>4.] who&longs;e breadth is A C, and its thickne&longs;s much <lb/>le&longs;&longs;er C B: It is demanded, why we would attempt to break <lb/>it edge-waies, as in the fir&longs;t Figure it will re&longs;i&longs;t the great Weight <lb/>T, but placed flat-waies, as in the &longs;econd Figure, it will not re&longs;i&longs;t <pb xlink:href="040/01/788.jpg" pagenum="96"/>X, le&longs;&longs;er than T: Which is manife&longs;ted, &longs;ince we under&longs;tand the <lb/>Fulciment, one while under the Line B C, and another while under <lb/>C A, and the Di&longs;tances of the Forces to be alike in both Ca&longs;es, to <lb/>wit, the length <emph type="italics"/>B<emph.end type="italics"/> D. </s> <s>But in the fir&longs;t Ca&longs;e, the Di&longs;tance of the Re­<lb/>&longs;i&longs;tance from the Fulciment, which is the half of the Line C A, is <lb/>greater than the Di&longs;tance in the other Ca&longs;e, which is the half of B <lb/>C: Therefore the Force of the Weight T, mu&longs;t of nece&longs;&longs;ity be grea­<lb/>ter than X, as much as the half of the breadth C A is greater than <lb/>half the thichne&longs;&longs;e B C, the fir&longs;t &longs;erving for the Counter-Leaver of <lb/>C A, and the &longs;econd of C B to overcome the &longs;ame Re&longs;i&longs;tance, that <lb/>is the quantity of the <emph type="italics"/>Fibres,<emph.end type="italics"/> or &longs;trings of the whole Ba&longs;e A B. <lb/></s> <s>Conclude we therefore, that the &longs;aid Pri&longs;m or Ruler, which is <lb/>broader than it is thick, re&longs;i&longs;teth, bresking more the edge-waies <lb/>than the flat-waies, according to the Proportion of the breadth to <lb/>the thickne&longs;s.</s></p><p type="main"> <s>It is requi&longs;ite that we begin in the next place</s></p><p type="head"> <s>PROPOSITION III.</s></p><p type="main"> <s><emph type="italics"/>To find according to what proportion the encrea&longs;e of the <lb/>Moment of the proper Gravity is made in a Pri&longs;m <lb/>or Cylinder, in relation to the proper Re&longs;i&longs;tance <lb/>again&longs;t Fraction, whil&longs;t that being parallel to the <lb/>Horizon, it is made longer and longer: Which Mo­<lb/>ment I find to encrea&longs;e &longs;ucce&longs;sively in duplicate Pro­<lb/>portion to that of the prolongation.<emph.end type="italics"/></s></p><p type="main"> <s>For demon&longs;tration whereof, de&longs;cribe the Pri&longs;m or Cylin­<lb/>der A D, firmly fa&longs;tned in the Wall at the end A, and let <lb/>it be equidi&longs;tant from the Horizon, and let the &longs;ame be <lb/>under&longs;tood to be prolonged as far as E, adding thereto the part <lb/><emph type="italics"/>B<emph.end type="italics"/> E. </s> <s>It is manife&longs;t, that the prolongation of the Leaver A <emph type="italics"/>B<emph.end type="italics"/><lb/>to C encrea&longs;eth, by it &longs;elf alone, that is taken ab&longs;olutely, the <lb/>Moment of the Force pre&longs;&longs;ing again&longs;t the Re&longs;i&longs;tance of the <lb/>Separation and Rupture to be made in A, according to the pro­<lb/>portion of C A to <emph type="italics"/>B<emph.end type="italics"/> A: but, moreover, the Weight of the Solid <lb/>affixed <emph type="italics"/>B<emph.end type="italics"/> E, encrea&longs;eth the Moment of the pre&longs;&longs;ing Gravity of <lb/>the Weight of the Solid A <emph type="italics"/>B,<emph.end type="italics"/> according to the Proportion of <lb/>the Pri&longs;m A E to the Pri&longs;m A <emph type="italics"/>B<emph.end type="italics"/>; which proportion is the &longs;ame <lb/>as that of the length A C, to the length A <emph type="italics"/>B<emph.end type="italics"/>: Therefore it is clear <pb xlink:href="040/01/789.jpg" pagenum="97"/>that the two augmentations of the Lengths and of the Gravities <lb/>being put together, the Moment compounded of both is in double <lb/><figure id="id.040.01.789.1.jpg" xlink:href="040/01/789/1.jpg"/><lb/>proportion to ei­<lb/>ther of them. </s> <s>We <lb/>conclude there­<lb/>fore, That the Mo­<lb/>ments of the For­<lb/>ces of Pri&longs;mes and <lb/>Cylinders of equal <lb/>thickne&longs;&longs;e, but of <lb/>unequal length, are <lb/>to one another in <lb/>duplicate proporti­<lb/>on to that of their <lb/>Lengths; that is, <lb/>are as the Squares of <lb/>their Lengths.</s></p><p type="main"> <s>We will &longs;hew, in <lb/>the &longs;econd place, <lb/>according to what proportion the Re&longs;i&longs;tance of Fraction in Pri&longs;mes <lb/>and Cylinders encrea&longs;eth, when they continue of the &longs;ame length, <lb/>and encrea&longs;e in thickne&longs;s. </s> <s>And here I &longs;ay, that</s></p><p type="head"> <s>PROPOSITION IV.</s></p><p type="main"> <s><emph type="italics"/>In Pri&longs;mes and Cylinders of equal length, but unequal <lb/>thickne&longs;s, the Re&longs;i&longs;tance again&longs;t Fraction encrea&longs;eth <lb/>in a proportion iriple to the Diameters of their <lb/>Thickne&longs;&longs;es, that is, of their Ba&longs;es.<emph.end type="italics"/></s></p><p type="main"> <s>Let the two Cylinders be the&longs;e A and <emph type="italics"/>B, [as in<emph.end type="italics"/> Fig. </s> <s>5.] <lb/>who&longs;e equal lengths are D G, and F H, the unequal <emph type="italics"/>B<emph.end type="italics"/>a&longs;es <lb/>the Circles, who&longs;e Diameters are C D, and E F. </s> <s>I &longs;ay, <lb/>that the Re&longs;i&longs;tance of the Cylinder <emph type="italics"/>B<emph.end type="italics"/> is to the Re&longs;i&longs;tance of the <lb/>Cylinder A again&longs;t Fraction, in a proportion triple to that which <lb/>the Diameter F E hath to the Diameter D C. </s> <s>For if we con&longs;ider <lb/>the ab&longs;olute and &longs;imple Re&longs;i&longs;tance that re&longs;ides in the <emph type="italics"/>B<emph.end type="italics"/>a&longs;es, that <lb/>is, in the Circles E F, and D C to breaking, offering them vio­<lb/>lence by pulling them end-waies, without all doubt, the Re&longs;i&longs;tance <lb/>of the Cylinder <emph type="italics"/>B,<emph.end type="italics"/> is &longs;o much greater than that of the Cylinder A, <lb/>by how much the Circle E F is greater than C D; for the Fibres, <lb/>Filaments, or tenacious parts, which hold together the Parts of the <lb/>Solid, are &longs;o many the more. <emph type="italics"/>B<emph.end type="italics"/>ut if we con&longs;ider, that in offering <pb xlink:href="040/01/790.jpg" pagenum="98"/>them violence tran&longs;ver&longs;ly we make u&longs;e of two Leavers; of which <lb/>the Parts or Di&longs;tances, at which the Forces are applied are the Lines <lb/>D G, and F H, the Fulciments are in the Points D and F; but the <lb/>other Parts or Di&longs;tances, at which the Re&longs;i&longs;tances are placed, are <lb/>the Semidiameters of the Circles D C and E F, becau&longs;e the Fila­<lb/>ments di&longs;per&longs;ed thorow the whole Superficies of the Circles are as <lb/>if they were all reduced into the Centers: con&longs;idering, I &longs;ay, tho&longs;e <lb/>Leavers, we would be under&longs;tood to intend, that the Re&longs;i&longs;tance in <lb/>the Center of the Ba&longs;e E F again&longs;t the Force of H, is &longs;o much grea­<lb/>ter than the Re&longs;i&longs;tance of the Ba&longs;e C D, again&longs;t the Force placed <lb/>in G, (and the Forces in G and H are of equal Leavers D G, and <lb/>F H) as the Semidiameter F E is greater than the Semidiameter <lb/>D C, the Re&longs;i&longs;tance again&longs;t Fraction, therefore, in the Cylinder <lb/>B, encrea&longs;eth above the Re&longs;i&longs;tance of the Cylinder A, according <lb/>to both the proportions of the Circles E F and D C, and of their <lb/>Semidiameters, or, if you will, Diameters: <emph type="italics"/>B<emph.end type="italics"/>ut the proportion of <lb/>the Circles is double of that of the Diameters; Therefore the pro­<lb/>portion of the Re&longs;i&longs;tances, which is compounded of them, is in <lb/>triplicate proportion of the &longs;aid Diameters: Which is that which <lb/>I was to prove. <emph type="italics"/>B<emph.end type="italics"/>ut becau&longs;e al&longs;o the Cubes are in triplicate pro­<lb/>portion to their Sides, we may likewi&longs;e conclude, <emph type="italics"/>That the Re&longs;i­<lb/>&longs;tances of Cylinders of equal Length, are to one another as the Cubes <lb/>of their Diameters.<emph.end type="italics"/></s></p><p type="main"> <s>From that which we have Demon&longs;trated we may likewi&longs;e con­<lb/>clude, that</s></p><p type="head"> <s>COROLARY.</s></p><p type="main"> <s><emph type="italics"/>The Re&longs;i&longs;tances of Pri&longs;ms, and Cylinders of equal length are in <lb/>Se&longs;quialter proportion to that of the &longs;aid Cylinders.<emph.end type="italics"/></s></p><p type="main"> <s>The which is manife&longs;t, becau&longs;e the Pri&longs;ms and Cylinders, <lb/>equal in height, are to one another, in the &longs;ame proportion as <lb/>their <emph type="italics"/>B<emph.end type="italics"/>a&longs;es; that is, the double of the Sides or Diameters of the <lb/>&longs;aid <emph type="italics"/>B<emph.end type="italics"/>a&longs;es: <emph type="italics"/>B<emph.end type="italics"/>ut the Re&longs;i&longs;tances (as hath been demon&longs;trated) are <lb/>in triplicate proportion to the &longs;aid Sides or Diameters: Therefore <lb/>the proportion of the Re&longs;i&longs;tances is Se&longs;quialter to the proportion <lb/>of the &longs;aid Solids, and, con&longs;equently, to the Weights of the &longs;aid <lb/>Solids.</s></p><p type="main"> <s>SIMP. </s> <s>It is convenient, that, before we proceed any farther, I <lb/>be re&longs;olved of a certain Doubt, and this it is, That I have not hi­<lb/>therto heard propo&longs;ed to Con&longs;ideration another certain kind of <lb/>Re&longs;i&longs;tance, that, in my opinion, is &longs;ucce&longs;&longs;ively dimini&longs;hed in So­<lb/>lids, according as they are more and more prolonged, and not on­<lb/>ly in u&longs;ing them &longs;idelongs, but al&longs;o leng thwaies, in the &longs;elf &longs;ame <pb xlink:href="040/01/791.jpg" pagenum="99"/>manner ju&longs;t as we &longs;ee a very long Cord to be much le&longs;&longs;e apt to <lb/>&longs;u&longs;tain a great weight, than if it were &longs;hort: &longs;o that I believe, that <lb/>a Ruler of Wood or Iron will &longs;u&longs;tain a much greater weight, if it <lb/>&longs;hall be &longs;hort, than if it &longs;hall be very long; under&longs;tanding it al­<lb/>waies to be u&longs;ed lengthwaies, and not tran&longs;ver&longs;ly; and al&longs;o <lb/>its own weight being accounted for, which in the longer is <lb/>greater.</s></p><p type="main"> <s>SALV. </s> <s>I fear, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that in this Point you, with many <lb/>others, are deceived, if &longs;o be, that I have rightly apprehended your <lb/>meaning, &longs;o that you would &longs;ay, that a Cord <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> forty yards <lb/>long cannot &longs;u&longs;tain &longs;o much, as if u&longs;e were made but of one or two <lb/>yards of the &longs;ame Rope.</s></p><p type="main"> <s>SIMP. </s> <s>That is it, which I would have &longs;aid, and as yet it &longs;eemeth <lb/>a very probable Propo&longs;ition.</s></p><p type="main"> <s>SALV. </s> <s>But I hold it not only improbable, but fal&longs;e: and think <lb/>that I can very ea&longs;ily reclaim you from your Errour. </s> <s>Therefore <lb/>let us &longs;uppo&longs;e this Rope A B, [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>6.] fa&longs;tned on high by <lb/>the end A, and by the other end let there hang the Weight C, <lb/>by the force of which, the &longs;aid Rope is to be broken. </s> <s>Do you <lb/>a&longs;&longs;ign me the particular place, <emph type="italics"/>Simplicius,<emph.end type="italics"/> where the Rupture is <lb/>to happen.</s></p><p type="main"> <s>SIMP. </s> <s>Let it be in the place D.</s></p><p type="main"> <s>SALV. </s> <s>I ask what is the cau&longs;e why it &longs;hould break in D.</s></p><p type="main"> <s>SIMP. </s> <s>The rea&longs;on thereof is, becau&longs;e the Rope was not &longs;trong <lb/>enough in that part, to &longs;u&longs;tain <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> an hundred pounds of weight, <lb/>for &longs;o much is the Rope D B with the Stone C.</s></p><p type="main"> <s>SALV. </s> <s>Therefore when ever &longs;uch a Rope &longs;hall come to be vio­<lb/>lently &longs;tretched by tho&longs;e hundred pounds of weight, it &longs;hall break <lb/>in that place.</s></p><p type="main"> <s>SIMP So I think.</s></p><p type="main"> <s>SALV. </s> <s>But tell me now; if one did hang the &longs;ame Weight, not <lb/>at the end of the Rope <emph type="italics"/>B,<emph.end type="italics"/> but near to the point D, as for in&longs;tance, <lb/>in E, or el&longs;e did tye the Rope not at the height A, but very near, <lb/>and almo&longs;t at the Point D it &longs;elf, as in F, tell me, I &longs;ay, whether <lb/>the Point D would feel the &longs;ame weight of an hundred pounds.</s></p><p type="main"> <s>SIMP. </s> <s>It would &longs;o, &longs;till joyning the piece of Rope E <emph type="italics"/>B<emph.end type="italics"/> to the <lb/>Stone C.</s></p><p type="main"> <s>SALV. </s> <s>If then the Rope in the Point D commeth to be drawn <lb/>by the &longs;aid hundred pounds of weight, it will break by your con­<lb/>ce&longs;&longs;ion. </s> <s>And yet F E, is a &longs;mall piece of the length A <emph type="italics"/>B<emph.end type="italics"/>: why do <lb/>you &longs;ay then, that the long Rope is weaker than the &longs;hort one? <lb/><emph type="italics"/>B<emph.end type="italics"/>e content, therefore, to &longs;uffer your &longs;elf to be reclaimed from an <lb/>Errour, in which you have had many Companions, and tho&longs;e in <lb/>other things very knowing. </s> <s>And let us go on: and having demon­<lb/>&longs;trated, that Pri&longs;ms and Cylinders encrea&longs;e their Moments above <pb xlink:href="040/01/792.jpg" pagenum="100"/>their Re&longs;i&longs;tances, according to the Squares of their Lengths (alwaies <lb/>provided, that they retain the &longs;ame thickne&longs;&longs;e) and that likewi&longs;e, <lb/>the&longs;e that are equally long, but different in thickne&longs;&longs;e, encrea&longs;e <lb/>their Re&longs;i&longs;tances according to the proportion of the Cubes of the <lb/>Sides or Diameters of their Ba&longs;es, we may enquire what befal­<lb/>leth to tho&longs;e Solids, being different in length and thickne&longs;s, in which <lb/>I ob&longs;erve, that</s></p><p type="head"> <s>PROPOSITION V.</s></p><p type="main"> <s><emph type="italics"/>Pri&longs;ms and Cylinders, of different length and thickne&longs;s, <lb/>have their Re&longs;i&longs;tances again&longs;t Fraction, in a propor­<lb/>tion compounded of the proportion of the Cubes of the <lb/>Diameters of their Ba&longs;es, and of the proportion of <lb/>their lengths reciprocally taken.<emph.end type="italics"/></s></p><p type="main"> <s>Let the&longs;e two A B C, and D E F, [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>7.] be &longs;uch Cy­<lb/>linders. </s> <s>I &longs;ay, the Re&longs;i&longs;tance of the Cylinder A C &longs;hall be to <lb/>the Re&longs;i&longs;tance of the Cylinder D F, in a proportion com­<lb/>pounded of the proportion of the Cube of the Diameter A B, to <lb/>the Gube of the Diameter D E, and of the proportion of the <lb/>Length E F to the Length B C. </s> <s>Suppo&longs;e E G equal to B C, and to <lb/>the Lines A B, and D E, let C H be a third proportional, and I, <lb/>a fourth; and as E F is to B C, &longs;o let I be to S. </s> <s>And becau&longs;e the <lb/>Re&longs;i&longs;tance of the Cylinder A C is to the Re&longs;i&longs;tance of the Cylin­<lb/>der D G, as the Cube A B to the Cube D E; that is, as the Line <lb/>A B to the Line I: and the Re&longs;i&longs;tance of the Cylinder G D is to <lb/>the Re&longs;i&longs;tance of the Cylinder D F, as the Length F E is to the <lb/>Length E G; that is, as the Line I is to S: Therefore by Equali­<lb/>ty of proportion, as the Re&longs;i&longs;tance of the Cylinder A C is to the <lb/>Re&longs;i&longs;tance of the Cylinder D F, &longs;o is the Line A B to S: But the <lb/>Line A B is to S, in a proportion compounded of A B to I, and of <lb/>I to S: Therefore the Re&longs;i&longs;tance of the Cylinder A C is to the Re­<lb/>&longs;i&longs;tance of the Cylinder D F, in a proportion compounded of A B <lb/>to I, that is, as the Cube of A B to the Cube of D E, and of the <lb/>proportion of the Line I to S; that is, of the Length E F to the <lb/>Length B C: Which was to be demon&longs;trated.</s></p><p type="main"> <s>After the Propo&longs;ition la&longs;t demon&longs;trated, we will con&longs;ider what <lb/>hapneth between like Cylinders and Pri&longs;ms, of which we will de­<lb/>mon&longs;trate, how that</s></p><pb xlink:href="040/01/793.jpg" pagenum="101"/><p type="head"> <s>PROPOSITION VI.</s></p><p type="main"> <s><emph type="italics"/>Of like Cylinders and Pri&longs;ms the Moments compoun­<lb/>ded, that is to &longs;ay, re&longs;ulting from their Gravities, <lb/>and from their Lengths, which are, as it were, Lea­<lb/>vers, have to one another a proportion Se&longs;quialter to <lb/>that which is between the Re&longs;i&longs;tances of their &longs;ame <lb/>Ba&longs;es.<emph.end type="italics"/></s></p><p type="main"> <s>For demon&longs;tration of which let us de&longs;cribe the two like Cy­<lb/>linders A B, and C D, [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>8.] I &longs;ay, that the Mo­<lb/>ment of the Cylinder A B, to overcome the Re&longs;i&longs;tance of its <lb/>Ba&longs;e B, hath to the Moment of C D, to overcome the Re&longs;i&longs;tance <lb/>of its Ba&longs;e C, a proportion Se&longs;quialter to that which the &longs;ame Re­<lb/>&longs;i&longs;tance of the Ba&longs;e B, hath to the Re&longs;i&longs;tance of the Ba&longs;e D: <lb/>And becau&longs;e the Moments of the Solids A B, and C D, to over­<lb/>come the Re&longs;i&longs;tances of their Ba&longs;es B and D, are compounded of <lb/>their Gravities, and of the Forces of their Leavers, and the Force <lb/>of the Leaver A B is equal to the Force of the Leaver C D, and <lb/>that becau&longs;e the length A B hath the &longs;ame proportion to the Semi­<lb/>diameter of the Ba&longs;e B, (by the &longs;imilitude of the Cylinders) that <lb/>the Length C D hath to the Semidiameter of the Ba&longs;e D; it re­<lb/>maineth, that the total Moment of the Cylinder A B, be to the <lb/>total Moment of C D, as the &longs;ole Gravity of the Cylinder A B is <lb/>to the &longs;ole Gravity of the Cylinder C D; that is, as the &longs;aid Cy­<lb/>linder A B is to the &longs;aid C D: But the&longs;e are in triplicate propor­<lb/>tion to the Diameters of their Ba&longs;es <emph type="italics"/>B<emph.end type="italics"/> and D; and the Re&longs;i&longs;tances <lb/>of the &longs;ame <emph type="italics"/>B<emph.end type="italics"/>a&longs;es, being to one another as the &longs;aid <emph type="italics"/>B<emph.end type="italics"/>a&longs;es, they are <lb/>con&longs;equently in duplicate proportion to their &longs;ame <emph type="italics"/>B<emph.end type="italics"/>a&longs;es: There­<lb/>fore the Moments of Cylinders are in Se&longs;quialter proportion to <lb/>the Re&longs;i&longs;tances of their <emph type="italics"/>B<emph.end type="italics"/>a&longs;es.</s></p><p type="main"> <s>SIMP. </s> <s>This Propo&longs;ition, indeed, is not only new, but unexpe­<lb/>cted to me, and at fir&longs;t &longs;ight, very remote from the judgment that <lb/>I &longs;hould have conjecturally pa&longs;t upon it: for in regard, that the&longs;e <lb/>Figures are in all other re&longs;pects alike, I &longs;hould have thought that <lb/>their Moments likewi&longs;e &longs;hould have retained the &longs;ame proportion <lb/>towards their proper Re&longs;i&longs;tances.</s></p><p type="main"> <s>SAGR. </s> <s>This is the Demon&longs;tration of that Propo&longs;ition, that in <lb/>the beginning of our Di&longs;cour&longs;es, I &longs;aid, I thought------I had &longs;ome <lb/>glimps of.</s></p><p type="main"> <s>SALV. </s> <s>That which now befalleth, <emph type="italics"/>Simplicius,<emph.end type="italics"/> hapned for &longs;ome <pb xlink:href="040/01/794.jpg" pagenum="102"/>time to my &longs;elf, believing, that the Re&longs;i&longs;tances of like Solids were <lb/>alike, till that a certain, and that no very fixed or accurate Ob&longs;er­<lb/>vation &longs;eemed to repre&longs;ent unto me, that Solids do not contain <lb/>an equal tenure in their Toughne&longs;s, but that the bigger are le&longs;&longs;e <lb/>apt to &longs;uffer violent accidents, as lu&longs;ty men are more damnified by <lb/>their falls than little children; and, as in the begining we &longs;aid, we <lb/>&longs;ee a great <emph type="italics"/>B<emph.end type="italics"/>eam or Column break to pieces falling from the &longs;ame <lb/>height, and not a &longs;mall Pri&longs;in or little Cylinder of Marble. </s> <s>This <lb/>&longs;ame Ob&longs;ervation gave me the hint for finding of that which I am <lb/>now about to demon&longs;trate; a Quality truly admirable, for that <lb/>among&longs;t the infinite Solid-like Figures, there are not &longs;o much <lb/>as two, who&longs;e Moments retain the &longs;ame proportion towards their <lb/>proper Re&longs;i&longs;tances.</s></p><p type="main"> <s>SIMP. </s> <s>Now you put me in mind of &longs;omething in&longs;erted by <emph type="italics"/>Ari­<lb/>&longs;totle<emph.end type="italics"/> among&longs;t his Mechanical Que&longs;tions, where he would give a <lb/>Rea&longs;on, whence it is, that <emph type="italics"/>B<emph.end type="italics"/>eams the longer they are, they are by &longs;o <lb/>much the more weak, and bend more and more, although the &longs;hort <lb/>ones be the &longs;lendere&longs;t, and the long ones thicke&longs;t: and, if I well re­<lb/>member, he reduceth the Rea&longs;on to the &longs;imple Leaver.</s></p><p type="main"> <s>SALV. </s> <s>It is very true, and becau&longs;e the Solution &longs;eemeth not <lb/>wholly to remove the cau&longs;e of doubting <emph type="italics"/>Mon&longs;ignore di Guevara,<emph.end type="italics"/><lb/>who, the truth is, with his mo&longs;t learned <emph type="italics"/>Commentaries<emph.end type="italics"/> hath highly <lb/>enobled and illu&longs;trated that Work, enlargeth him&longs;elf with other <lb/>accute Speculations for the obviating all difficulties, yet him&longs;elf <lb/>al&longs;o remaining perplexed in this point, whether, the lengths and <lb/>thickne&longs;&longs;es of &longs;uch Solid Figures, encrea&longs;ing with the &longs;elf &longs;ame <lb/>proportion, they ought to retain the &longs;ame tenure in their Tough­<lb/>ne&longs;&longs;es and Re&longs;i&longs;tances again&longs;t their breaking, and likewi&longs;e again&longs;t <lb/>their bending. </s> <s>After I had long con&longs;idered thereon, I have, in <lb/>this manner found, that which I am about to tell you. </s> <s>And fir&longs;t <lb/>I will demon&longs;trate that</s></p><pb xlink:href="040/01/795.jpg" pagenum="103"/><p type="head"> <s>PROPOSITION VII.</s></p><p type="main"> <s><emph type="italics"/>Of like and heavy Pri&longs;ms or Cylinders there is one only, <lb/>and no more, that is reduced (being charged with its <lb/>own weight) to the ultimate &longs;tate between breaking <lb/>and holding it &longs;elf together: &longs;othat every greater, as <lb/>being unable to re&longs;i&longs;t its own weight, will break, <lb/>and every le&longs;&longs;er re&longs;i&longs;teth &longs;ome Force that is employed <lb/>again&longs;t it to break, it.<emph.end type="italics"/></s></p><p type="main"> <s>Let the heavy Pri&longs;m be A B [<emph type="italics"/>as in<emph.end type="italics"/> Fig 9.] reduced to the <lb/>utmo&longs;t length of its Con&longs;i&longs;tance, &longs;o that being lengthned <lb/>never &longs;o little more it will break: I &longs;ay, that this is the only <lb/>one among&longs;t all tho&longs;e that are like unto it, (which yet are infinite) <lb/>that is capable of being reduced to that dubious and tickli&longs;h &longs;tate; <lb/>&longs;o that every greater being oppre&longs;&longs;ed with its own weight will <lb/>break, and every le&longs;&longs;er not, nay, will be able to re&longs;i&longs;t &longs;ome additi­<lb/>on of a new violence, over and above that of its own weight. <lb/></s> <s>Fir&longs;t, take the Pri&longs;m C E, like to, and greater than A B. </s> <s>I &longs;ay, that <lb/>this cannot con&longs;i&longs;t, but will break, being overcome by its own <lb/>Gravity. </s> <s>Suppo&longs;e the part C D as long as A B. </s> <s>And becau&longs;e the <lb/>Re&longs;i&longs;tance C D is to that of A B, as the Cube of the thickne&longs;&longs;e of <lb/>C D to the Cube of the thickne&longs;s of A B; that is, as the Pri&longs;m <lb/>C E to the Pri&longs;m A B (being alike:) Therefore the Weight of <lb/>C E is the greate&longs;t that can be &longs;u&longs;tained at the length of the Pri&longs;m <lb/>C D: But the Length C E is greater: Therefore the Pri&longs;m C E <lb/>will break. </s> <s>But let F G be le&longs;&longs;et: it &longs;hall be demon&longs;trated like­<lb/>wi&longs;e (&longs;uppo&longs;ing F H equal to B A) that the Re&longs;i&longs;tance of F G is <lb/>to that of A B, as the Pri&longs;m F G is to the Pri&longs;m A B, in ca&longs;e that the <lb/>Di&longs;tance A B, that is F H, were equal to F G, but it is greater: <lb/>Therefore the Moment of the Pri&longs;m F G, placed in G, doth not <lb/>&longs;uffice to break the Pri&longs;m F G.</s></p><p type="main"> <s>SAGR. </s> <s>A mo&longs;t manife&longs;t and brief Demon&longs;tration, inferring the <lb/>truth and nece&longs;&longs;ity of a Propo&longs;ition that at fir&longs;t &longs;ight &longs;eemeth far <lb/>from probability. </s> <s>It would be requi&longs;ite, therefore, to alter much <lb/>the proportion betwixt the Length and Thickne&longs;&longs;e of the greater <lb/>Pri&longs;m by making it thicker or &longs;horter, to the end it might be re­<lb/>duced to that nice &longs;tate of indifferency between holding and brea­<lb/>king; and the Inve&longs;tigation of that &longs;ame State, as I think, would <lb/>be no le&longs;&longs;e ingenuous.</s></p><p type="main"> <s>SALV. Nay, rather more, as it is al&longs;o more laborious: and I am <pb xlink:href="040/01/796.jpg" pagenum="104"/>&longs;ure I have &longs;pent no &longs;mall time to find it; and I will now impart it <lb/>to you: Therefore</s></p><p type="head"> <s>PROP. VIII. PROBL. I.</s></p><p type="main"> <s><emph type="italics"/>A Cylinder or Pri&longs;m of the utmo&longs;t length not to be bro­<lb/>ken by its own weight, and al&longs;o a greaver length, be­<lb/>ing given, to find the thickne&longs;&longs;e of another Cylinder <lb/>or Pri&longs;m that under-given length is the only one, and <lb/>bigge&longs;t, that can re&longs;i&longs;t its own weight.<emph.end type="italics"/></s></p><p type="main"> <s>Let the Cylinder B C [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>10.] be the bigge&longs;t that <lb/>can re&longs;i&longs;t its own weight, and let D E be a Length greater <lb/>than A C; it is required to find the Thickne&longs;&longs;e of the Cylin­<lb/>der, that under the Length D E is the greate&longs;t re&longs;i&longs;ting its own <lb/>weight. </s> <s>Let I be a third proportional to the Lengths D E, and <lb/>A C; and as D E is to I, &longs;o let the Diameter F D be to the Dia­<lb/>meter B A: and make the Cylinder F E. </s> <s>I &longs;ay, that this is the big­<lb/>ge&longs;t, and only one among&longs;t all that are like to it that re&longs;i&longs;teth its <lb/>own weight. </s> <s>To the Lines D C and I let M be a third propor­<lb/>tional, and O a fourth. </s> <s>And &longs;uppo&longs;e F G equal to A C. </s> <s>And be­<lb/>cau&longs;e the Diameter F D is to the Diameter A B, as the Line D E <lb/>to I, and O is a fourth proportional to D E and I, the Cube of <lb/>F D &longs;hall be to the Cube of B A as D E is to O: But as the Cube of <lb/>F D is to the Cube of B A, &longs;o is the Re&longs;i&longs;tance of the Cylinder <lb/>D G to the Re&longs;i&longs;tance of the Cylinder B C: Therefore the Re&longs;i­<lb/>&longs;tance of the Cylinder D G is to that of the Cylinder B C, as the <lb/>Line D F is to O. </s> <s>And becau&longs;e the Moment of the Cylinder B C <lb/>is equal to its Re&longs;i&longs;tance, if we &longs;hew that the Moment of the Cylin­<lb/>der F E is to the Moment of the Cylinder B C, as the Re&longs;i&longs;tance <lb/>D F to the Re&longs;i&longs;tance B A; that is, as the Cube of F D to the Cube <lb/>of B A; that is, as the Line D E to O, we &longs;hall have our intent: <lb/>that is, that the Moment of the Cylinder F E is equal to the Re&longs;i­<lb/>&longs;tance placed in F D. </s> <s>The Moment of the Cylinder F E is to the <lb/>Moment of the Cylinder D G, as the Square of D E is to the <lb/>Square of A C; that is, as the Line D E to I: But the Moment of <lb/>the Cylinder D G is to the Moment of the Cylinder B C, as the <lb/>Square D F to the Square B A; that is, as the Square of D E to the <lb/>Square of I; that is, as the Square of I to the Square of M; that <lb/>is, as I to O: Therefore, by Equality of proportion, as the Mo­<lb/>ment of the Cylinder F E is to the Moment of the Cylinder B C, <lb/>&longs;o is the Line D E to O; that is, the Cube D F to the Cube <lb/>B A; that is, the Re&longs;i&longs;tance of the Ba&longs;e D F to the Re&longs;i&longs;tance <pb xlink:href="040/01/797.jpg" pagenum="105"/>of the Ba&longs;e B A: Which is that that was &longs;ought.</s></p><p type="main"> <s>SAGR This, <emph type="italics"/>Salviatus,<emph.end type="italics"/> is a long Demon&longs;tration, and very hard <lb/>to be born in mind at the fir&longs;t hearing, therefore I could wi&longs;h, that <lb/>you would plea&longs;e to repeat it.</s></p><p type="main"> <s>SALV. </s> <s>I will do what you &longs;hall command; but haply it would <lb/>be better to produce one more conci&longs;e and &longs;hort: but then it will <lb/>be requi&longs;ite to de&longs;cribe a Figure &longs;omewhat different.</s></p><p type="main"> <s>SAGR. </s> <s>The favour will then be the greater: and be&longs;tow upon <lb/>me the draught of that already explained, that I may at my lea&longs;ure <lb/>con&longs;ider it again.</s></p><p type="main"> <s>SALV. </s> <s>I will not fail to &longs;erve you. </s> <s>Now, &longs;uppo&longs;e a Cylinder A, <lb/><arrow.to.target n="marg1082"></arrow.to.target><lb/>[<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>11.] the Diameter of who&longs;e Ba&longs;e let be the Line D C, <lb/>and let this A be the greate&longs;t that can &longs;u&longs;tain it &longs;elf and not break, <lb/>than which we will find a bigger, which likewi&longs;e &longs;hall be the big­<lb/>ge&longs;t al&longs;o, and the only one that &longs;u&longs;taineth it &longs;elf. </s> <s>Let us de&longs;ire one <lb/>like to the &longs;aid A, and as long as the a&longs;&longs;igned Line, and let this be <lb/><emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> E, the Diameter of who&longs;e Ba&longs;e let be K L; and to the two <lb/>Lines D C, and K L let M N be a third proportional; which let be <lb/>the Diameter of the Ba&longs;e of the Cylinder X, in length equal to E. <lb/></s> <s>I &longs;ay, that this X is that which we &longs;eek. </s> <s>And becau&longs;e the Re&longs;i­<lb/>&longs;tance D C is to the Re&longs;i&longs;tance K L, as the Square D C to the <lb/><emph type="italics"/>S<emph.end type="italics"/>quare K L; that is, as the Square K L to the Square M N; that <lb/>is, as the Cylinder E to the Cylinder X; that is, as the Moment E <lb/>to the Moment X: But the Re&longs;i&longs;tance K L is to M N, as the Cube <lb/>of K L is to the Cube of M N; that is, as the Cube B C to the <lb/>Cube K L; that is, as the Cylinder A to the Cylinder E; that is, <lb/>as the Moment A to the Moment E: Therefore, by Perturbation <lb/>of proportion, as the Re&longs;i&longs;tance D C is to M N, &longs;o is the Moment <lb/>A to the Moment X: Therefore the Pri&longs;m X, is in the &longs;ame Con&longs;ti­<lb/>tution of Moment and Re&longs;i&longs;tance as the Pri&longs;m A.</s></p><p type="margin"> <s><margin.target id="marg1082"></margin.target><emph type="italics"/>The la&longs;t Problem <lb/>performed another <lb/>way.<emph.end type="italics"/></s></p><p type="main"> <s>But let us make the Problem more general, and let the Propo­<lb/>&longs;ition be this:</s></p><p type="main"> <s><emph type="italics"/>The Cylinder<emph.end type="italics"/> A C <emph type="italics"/>being given, and its Moment to-<emph.end type="italics"/><lb/><arrow.to.target n="marg1083"></arrow.to.target><lb/><emph type="italics"/>wards its Re&longs;i&longs;tance being &longs;uppo&longs;ed at plea&longs;ure, and <lb/>any Length<emph.end type="italics"/> D E <emph type="italics"/>being a&longs;signed, to find the Thick­<lb/>ne&longs;&longs;e af the Cylinder who&longs;e Length is<emph.end type="italics"/> D E, <emph type="italics"/>and who&longs;e <lb/>Moment towards its Re&longs;i&longs;tance retaineth the &longs;ame <lb/>proportion, that the Moment of the Cylinder<emph.end type="italics"/> A C <lb/><emph type="italics"/>doth to its Re&longs;i&longs;tance.<emph.end type="italics"/></s></p><pb xlink:href="040/01/798.jpg" pagenum="106"/><p type="margin"> <s><margin.target id="marg1083"></margin.target><emph type="italics"/>The la&longs;t Propo&longs;i­<lb/>tion made more ge­<lb/>neral.<emph.end type="italics"/></s></p><p type="main"> <s>Rea&longs;&longs;uming the above &longs;aid Figure and almo&longs;t the &longs;ame Me­<lb/>thod, we will &longs;ay: Becau&longs;e the Moment of the Cylinder <lb/>F E hath the &longs;ame proportion to the Moment of the part <lb/>D G, that the Square E D hath to the Square F G; that is that <lb/>the Line D E hath to I: and becau&longs;e the Moment of the Cylinder <lb/>F G is to the Moment of the Cylinder A C, as the Square F D to <lb/>the Square A B; that is, as the Square D E to the Square I; that <lb/>is, as the Square I to the Square M; that is, as the Line I to O: <lb/>Therefore, <emph type="italics"/>ex æquali,<emph.end type="italics"/> the Moment of the Cylinder F E hath the <lb/>&longs;ame proportion to the Moment of the Cylinder A C, that the <lb/>Line D E hath to the Line O; that is, that the Cube D E hath <lb/>to the Cube of I; that is, that the Cube of F D hath to the <lb/>Cube of A B; that is, that the Re&longs;i&longs;tance of the Ba&longs;e F D hath to <lb/>the Re&longs;i&longs;tance of the Ba&longs;e A B: Which was to be performed.</s></p><p type="main"> <s>Now, let it be ob&longs;erved, that from the things hitherto demon&longs;tra­<lb/>ted, we may plainly gather, how Impo&longs;&longs;ible it is, not only for Art, but <lb/><arrow.to.target n="marg1084"></arrow.to.target><lb/>for Nature her &longs;elf to encrea&longs;e her Machines to an immen&longs;e Va&longs;t­<lb/>ne&longs;&longs;e: &longs;o that it would be impo&longs;&longs;ible by Art to build extraordina­<lb/>ry va&longs;t Ships, Palaces, or Temples, who&longs;e ^{*} Oars, Sail-yards, Beams, <lb/>Iron Bolts, and, in a word, their other parts &longs;hould con&longs;i&longs;t or hold <lb/>together: neither again could Nature make Trees of unmea&longs;ura­<lb/><arrow.to.target n="marg1085"></arrow.to.target><lb/>ble greatne&longs;&longs;e, for that their Arms or Bows being oppre&longs;&longs;ed with <lb/>their own weight would at la&longs;t break: and likewi&longs;e it would be <lb/>impo&longs;&longs;ible for her to make &longs;tructures of Bones for men, Hor&longs;es, or <lb/>other Animals, that might &longs;ub&longs;i&longs;t, and proportionatly perform <lb/>their Offices, when tho&longs;e Animals &longs;hould be augmented to im­<lb/>men&longs;e heights, unle&longs;&longs;e &longs;he &longs;hould take Matter much more hard and <lb/>Refi&longs;ting than that which &longs;he commonly u&longs;eth, or el&longs;e &longs;hould de­<lb/>form tho&longs;e Bones by augmenting them beyond their due Symetry, <lb/>and making the Figure or &longs;hape of the Animal to become mon­<lb/>&longs;trou&longs;ly big: Which haply was hinted by my mo&longs;t Witty Poet, <lb/>where de&longs;cribing an huge Giant, he &longs;aith,</s></p><p type="margin"> <s><margin.target id="marg1084"></margin.target>* Oares are u&longs;ed <lb/>in the Ships or <lb/>Gallies of the <lb/>Mediterrane, up­<lb/>on which our <lb/>Author was a <lb/>Coa&longs;ter.</s></p><p type="margin"> <s><margin.target id="marg1085"></margin.target><emph type="italics"/>Bones of Animals <lb/>magnified beyond <lb/>their ratural &longs;ize, <lb/>would not &longs;ub&longs;i&longs;t, if <lb/>it be required to <lb/>retain the &longs;ame <lb/>proportion of thick­<lb/>ne&longs;s and hardne&longs;s <lb/>in them that is in <lb/>tho&longs;e of Natural <lb/>Animals.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Non &longs;i puo compartir quanto &longs;ia lungo,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Si &longs;mi&longs;uratamente è tutto gro&longs;&longs;o.<emph.end type="italics"/><lb/><arrow.to.target n="marg1086"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1086"></margin.target><emph type="italics"/>Example of the <lb/>Bone of an Animal <lb/>enlarged to thrice <lb/>the Natural pro­<lb/>portion, how much <lb/>thicker it ought to <lb/>be to perform its <lb/>office.<emph.end type="italics"/></s></p><p type="main"> <s>And for a &longs;hort example of this that I &longs;ay, [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>12.] I <lb/>have heretofore drawn the Figure of a Bone only trebled in <lb/>Length, and augmented in Thickne&longs;&longs;e in &longs;uch proportion, as that <lb/>it may in its great Animal perform the office proportionate to that <lb/>of the le&longs;&longs;er Bone in a &longs;maller Animal, and the Figures are the&longs;e: <lb/>whereby you &longs;ee what a di&longs;proportionate Figure that of the aug­<lb/>mented Bone becometh. </s> <s>Whence it is manife&longs;t, that he that would <lb/>in an huge Giant keep the proportions that the Members have in <pb xlink:href="040/01/799.jpg" pagenum="107"/>an ordinary Man, mu&longs;t either find Matter much more hard and re­<lb/>&longs;i&longs;ting to make Bone of, or el&longs;e mu&longs;t admit that its Strength is in <lb/>proportion much more weak than in Men of middle Stature: other­<lb/>wi&longs;e, encrea&longs;ing the Giant to an immea&longs;urable height he would be <lb/>oppre&longs;&longs;ed, and fall under his own weight. </s> <s>Whereas on the con­<lb/>trary, in dimini&longs;hing of Bodies we do not &longs;ee the Strength and <lb/>Forces to dimini&longs;h in the &longs;ame proportion, nay, in the le&longs;&longs;er the <lb/>Robu&longs;tiou&longs;ne&longs;&longs;e encrea&longs;eth with a great proportion. </s> <s>So that I <lb/>believe, that a little Dog could carry on his back two or three Dogs <lb/>equal to him&longs;elf, but I do not think that an Hor&longs;e could carry &longs;o <lb/>much as one &longs;ingle Hor&longs;e of his own &longs;ize.</s></p><p type="main"> <s>SIMP. </s> <s>But if it be &longs;o, I have great rea&longs;on to doubt the Im­<lb/>men&longs;e bulks that we &longs;ee in Fi&longs;hes, for (if I rightly under&longs;tand <lb/>you) a Whale &longs;hall be as big as ten Elephants, and yet they &longs;u­<lb/>&longs;tain them&longs;elves.</s></p><p type="main"> <s>SALV. </s> <s>Your doubt, <emph type="italics"/>Simplicius,<emph.end type="italics"/> prompts me with another Con­<lb/>dition which I perceived not before, which is al&longs;o able to make <lb/>Giants and other very big Animals to con&longs;i&longs;t, and act them&longs;elves <lb/>no le&longs;&longs;e than &longs;maller, and this will happen when not only Strength <lb/>is added to the Bones and other Parts, who&longs;e office it is to &longs;u&longs;tain <lb/>their own and the &longs;upervenient weight; but the &longs;tructure of the <lb/>Bones being left with the &longs;ame proportions, the &longs;ame Fabricks <lb/>would ju&longs;t in the &longs;ame manner, yea, with much more ea&longs;e, con­<lb/>&longs;i&longs;t, when the Gravity of the matter of tho&longs;e Bones, or that of <lb/>the Fle&longs;h, or whatever el&longs;e is to re&longs;t it &longs;elf upon the Bones is dimini­<lb/>&longs;hed in that proportion: and of this &longs;econd Artifice, Nature hath <lb/>made u&longs;e in the framing of Fi&longs;hes, making their Bones, and Pulps, <lb/>not only very light, but without any Gravity.</s></p><p type="main"> <s>SIMP. </s> <s>I &longs;ee very well, <emph type="italics"/>Salviatus,<emph.end type="italics"/> whither your Di&longs;cour&longs;e ten­<lb/>deth: you will &longs;ay, that becau&longs;e the Element of Water is the Ha­<lb/>bitation of Fi&longs;hes, which by its Corpulence, or, as others will, by <lb/>its Gravity dimini&longs;heth the weight of Bodies demerged in it, for <lb/>that rea&longs;on the Matter of Fi&longs;hes, not weighing any thing, may be <lb/>&longs;u&longs;tained without &longs;urcharging their Bones: but this doth not &longs;uf­<lb/>fice, for although the re&longs;t of the &longs;ub&longs;tance of the Fi&longs;h weigh not, <lb/>yet without doubt the matter of their Bones hath its weight: <lb/>and who will &longs;ay, that the Rib of a Whale that is as big as a <lb/>Beam doth not weigh very much, and in Water &longs;inketh to the Bot­<lb/>tom? </s> <s>The&longs;e therefore &longs;hould not be able to &longs;ub&longs;i&longs;t in &longs;o va&longs;t a <lb/>Bulk.</s></p><p type="main"> <s>SALV. </s> <s>You argue very cunningly; and for an an&longs;wer to your <lb/>Doubt, tell me, whether you have ob&longs;erved Fi&longs;hes to &longs;tand im­<lb/>moveable under water at their plea&longs;ures, and not to de&longs;cend to­<lb/>wards the Bottom, or rai&longs;e them&longs;elves towards the top without <lb/>making &longs;ome motion with their Fins?</s></p><pb xlink:href="040/01/800.jpg" pagenum="108"/><p type="main"> <s>SIMP. </s> <s>This is a very manife&longs;t Ob&longs;ervation.</s></p><p type="main"> <s><arrow.to.target n="marg1087"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1087"></margin.target><emph type="italics"/>The Cau&longs;e why <lb/>Fi&longs;hes do equili­<lb/>brate them&longs;elves <lb/>in the Water.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>This power therefore that the Fi&longs;hes have to &longs;tay them­<lb/>&longs;elves, as if they were immoveable in the mid&longs;t of the Water, is a <lb/>mo&longs;t infallible argument, that the Compofition of their Corporeal <lb/>Ma&longs;&longs;e equalleth the Specifick Gravity of the Water, &longs;o that if <lb/>there be found in them &longs;ome parts that are more grave than the <lb/>Water, it is nece&longs;&longs;arily requi&longs;ite that they have others &longs;o much <lb/>le&longs;&longs;e grave, &longs;o that the <emph type="italics"/>Equilibrium<emph.end type="italics"/> may be ballanced. </s> <s>If therefore <lb/>the Bones be more grave, it is nece&longs;&longs;ary that the Pulps, or other <lb/>Matters that are in them, be more light; and the&longs;e will with their <lb/>lightne&longs;&longs;e counterpoi&longs;e and compen&longs;ate the weight of the Bones. <lb/></s> <s>So that in Aquatick Animals the quite contrary hapneth to that <lb/>which befals the Terre&longs;trial, namely, that in the latter it is the of­<lb/>fice of the Bones to &longs;u&longs;tain their own weight, and the weight of <lb/>the Fle&longs;h; and in the former, the <emph type="italics"/>Fle&longs;h [if one may &longs;o call it]<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1088"></arrow.to.target><lb/>beareth up its own weight, and that of the Bones. </s> <s>And therefore <lb/>cea&longs;e to wonder how there may be mo&longs;t va&longs;t Animals in the Wa­<lb/>ter, but not on the Earth, that is, in the Air.</s></p><p type="margin"> <s><margin.target id="marg1088"></margin.target><emph type="italics"/>Aquatick Animals <lb/>greater than the <lb/>Terre&longs;trial, and for <lb/>what Rea&longs;on.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>I am &longs;atisfied, and moreover ob&longs;erve, that the&longs;e which <lb/>we call Terre&longs;trial Animals, ought with more rea&longs;on to be called <lb/>Aerial; becau&longs;e in the Air they really live, and by the Air they are <lb/>environ'd, and of the Air they breath.</s></p><p type="main"> <s>SAGR. </s> <s>The Di&longs;cour&longs;e of <emph type="italics"/>Simplicius<emph.end type="italics"/> plea&longs;eth me, as al&longs;o his <lb/>Doubt and its Solution. </s> <s>And farthermore I comprehend very ea­<lb/>&longs;ily, that one of the&longs;e huge Fi&longs;hes being haul'd on &longs;hore, could not <lb/>perchance be able to &longs;u&longs;tain it &longs;elf for any time; but that the Con­<lb/>nections of the Bones being relaxed, its Ma&longs;&longs;e would be cru&longs;h'd un­<lb/>der its own weight.</s></p><p type="main"> <s>SALV. </s> <s>For the pre&longs;ent, I encline to the &longs;ame Opinion: nor am <lb/>I far from thinking that the &longs;ame would happen to that huge Ship, <lb/>which floating in the Sea is not di&longs;&longs;olved by its weight, and the bur­<lb/>den of its Lading and Artilery, but on dry ground, and environed <lb/>with Air, it perhaps would fall in pieces. </s> <s>But let us pur&longs;ue our bu­<lb/>&longs;ine&longs;&longs;e, and demon&longs;trate, that</s></p><pb xlink:href="040/01/801.jpg" pagenum="109"/><p type="head"> <s>PROP. IX. PROBL. II.</s></p><p type="main"> <s><emph type="italics"/>A Pri&longs;me or Cylinder with its weight, and the great­<lb/>e&longs;t Weight &longs;u&longs;tained by it being given, to find the <lb/>greate&longs;t Length, beyond which being prolonged. </s> <s>it <lb/>would break under its own Weight.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be given the Pri&longs;me A C (<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>13.) with its <lb/>weight, and likewi&longs;e let the Weight D be given, the great­<lb/>e&longs;t that can be &longs;u&longs;tained by the extreme C: it is required to <lb/>finde the greate&longs;t Length unto which the &longs;aid Pri&longs;me may be pro­<lb/>longed, without breaking. </s> <s>As the weight of the Pri&longs;me A C is to <lb/>the Compound of the weights A C, with the double of the <lb/>Weight D, &longs;o let the length C A be to C A H: between which <lb/>let A G be a Mean-Proportional. </s> <s>I &longs;ay that A G is the Length <lb/>&longs;ought. </s> <s>For the depre&longs;&longs;ing Moment of the Weight D in C, is <lb/>equal to the Moment of the double weight D, if it be placed in <lb/>the middle of A C, where is al&longs;o the Center of the Moment of <lb/>the Pri&longs;me A C: The Moment, therefore, of the Re&longs;i&longs;tance of <lb/>the Pri&longs;me A C, which re&longs;ides in A, is equivalent to the gravi­<lb/>tation of the double of the Weight D with the weight A C, but <lb/>hanged in the mid&longs;t of A C. </s> <s>And becau&longs;e it hath been made, <lb/>that as the Moment of the &longs;aid Weights &longs;o &longs;ituated, that is, of <lb/>the double of D, with A C, is to the Moment of A C, &longs;o is H A <lb/>to A C, between which A G is a Mean Proportional: There­<lb/>fore the Moment of D doubled with the Moment of A C, is to <lb/>the Moment A C, as the Square G A to the Square A C: But the <lb/>pre&longs;&longs;ing Moment of the Pri&longs;me G A, is to the Moment of A C, <lb/>as the Square G A to the Square A C: Therefore the Length <lb/>A G is the greate&longs;t that was &longs;ought, namely, that unto which the <lb/>Pri&longs;me A G being prolonged, it would &longs;u&longs;tain it &longs;elf, but beyond <lb/>it would break.</s></p><p type="main"> <s>Hitherto we have con&longs;idered the Moments and Re&longs;i&longs;tances of <lb/>&longs;olid Pri&longs;mes and Cylinders, one end of which is &longs;uppo&longs;ed im­<lb/>moveable, and to the other onely the Force of a pre&longs;&longs;ing weight <lb/>is applyed, con&longs;idering it by it &longs;elf alone, or joyned with the <lb/>Gravity of the &longs;ame Solid, or el&longs;e the &longs;ole Gravity of the &longs;aid <lb/>Solid. </s> <s>Now I de&longs;ire that we may &longs;peak &longs;omething of tho&longs;e &longs;ame <lb/>Pri&longs;mes or Cylinders, in ca&longs;e they were &longs;u&longs;tained at both ends, or <lb/>did re&longs;t upon one &longs;ole point taken between the ends. </s> <s>And fir&longs;t, <lb/>I &longs;ay that,</s></p><pb xlink:href="040/01/802.jpg" pagenum="110"/><p type="head"> <s>PROPOSITION X.</s></p><p type="main"> <s><emph type="italics"/>The Cylinder that being charged with its own Weight <lb/>&longs;hall be reduced to its greate&longs;t Length, beyond which <lb/>it would not &longs;u&longs;tain it &longs;elf, whether it be born up in <lb/>the middle by one &longs;ole Fulciment, or el&longs;e by two at <lb/>the ends, may be double in length to that which <lb/>&longs;hould be fa&longs;tned in the Wall, that is &longs;u&longs;tained at but <lb/>one end.<emph.end type="italics"/></s></p><p type="main"> <s>Which of it &longs;elt is very obvious; for if we &longs;hall &longs;up­<lb/>po&longs;e of the Cylinder which I de&longs;cribe A B C, its <lb/>half A B to be the utmo&longs;t Length that is able to be <lb/>&longs;u&longs;tained, being fa&longs;tened at the end B, it &longs;hall be &longs;u&longs;tained in the <lb/>&longs;ame manner, if being laid upon the Fulciment G, it &longs;hall be <lb/>counterpoi&longs;ed by its other half B C. </s> <s>And likewi&longs;e, if of the Cy­<lb/>linder D E F, the Length &longs;hall be &longs;uch that onely one half of it <lb/>can be &longs;u&longs;tained, being fa&longs;tened at the end D, and con&longs;equent­<lb/>ly the other E F, fixed at the end F; it is manife&longs;t, that placing <lb/>the Fulciments H and I under the ends D and F, every Moment <lb/>of Force or of Weight that is added in E, will there make the <lb/>Fracture.</s></p><p type="main"> <s>That which requireth a more &longs;ubtil Speculation is, when &longs;ub­<lb/>&longs;tracting from the proper Gravity of &longs;uch Solids, it were pro­<lb/>pounded to us</s></p><p type="head"> <s>PROP. XI. PROBL. III.</s></p><p type="main"> <s><emph type="italics"/>To find whether that Force or weight, that being ap­<lb/>plied to the middle of a Cylinder &longs;u&longs;tained at the <lb/>ends, would &longs;uffice to break it, could do the &longs;ame, <lb/>applied in any other place, neerer to one end than to <lb/>the other.<emph.end type="italics"/></s></p><p type="main"> <s>As for Example, whether we de&longs;iring to break a Staffe <lb/>and took it with the ends in our hands, and &longs;etting our <lb/>knee, to the mid&longs;t of it, the &longs;ame Force that &longs;hould &longs;uf­<lb/>fice to break it in that manner, would al&longs;o &longs;uffice in ca&longs;e the knee <pb xlink:href="040/01/803.jpg" pagenum="111"/>were &longs;et, not in the mid&longs;t, but neerer to one of the ends.</s></p><p type="main"> <s>SAGR. </s> <s>I think the Problem is toucht upon by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in his <lb/><emph type="italics"/>Mechanical Que&longs;tions.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>The Que&longs;tion of <emph type="italics"/>Aristotle<emph.end type="italics"/> is not preci&longs;ely the &longs;ame, <lb/>for he &longs;eeks no more, but to render a rea&longs;on why le&longs;&longs;e labour is <lb/>required to break the Staffe, holding the hands at the ends of it, <lb/>that is, far di&longs;tant from the Knee, than if we held them neerer: <lb/>and he giveth a general Rea&longs;on of the &longs;ame, reducing the cau&longs;e <lb/>of it to the Leavers, which are longer when the Arms are ex­<lb/>tended, gra&longs;ping the ends. </s> <s>Our Que&longs;tion addeth &longs;omething <lb/>more, &longs;eeking whether, &longs;etting the Knee in the mid&longs;t, or in ano­<lb/>ther place, but alwayes keeping the hands at the ends, the &longs;ame <lb/>Force &longs;erveth in all &longs;ituations.</s></p><p type="main"> <s>SAGR. </s> <s>At fir&longs;t apprehen&longs;ion it &longs;hould &longs;eem that it doth, for <lb/>that the two Leavers retain in a certain fa&longs;hion the &longs;ame Moment, <lb/>&longs;eeing that as the one is &longs;hortned, the other is lengthened.</s></p><p type="main"> <s>SALV. </s> <s>Now you &longs;ee, how ea&longs;ie it is to make Equivocations, <lb/>and with what caution and circum&longs;pection we are to walk, lea&longs;t <lb/>we run into them. </s> <s>This that you &longs;ay, and which indeed at the <lb/>fir&longs;t &longs;ight carrieth with it &longs;o much of probability, is in the &longs;trict­<lb/>ne&longs;&longs;e of it &longs;o fal&longs;e, that whether the Knee, which is the Fulci­<lb/>ment of the two Leavers, be placed or not placed in the mid&longs;t, <lb/>it maketh &longs;uch alteration, that of that Force which would &longs;uffice <lb/>to make the Fracture in the mid&longs;t, it being to be made in &longs;ome <lb/>other place, it will not &longs;uffice to apply four times &longs;o much, nor <lb/>ten, nor an hundred, no nor a thou&longs;and. </s> <s>Upon this we will <lb/>make &longs;ome general Con&longs;ideration, and then we will come to the <lb/>Specifick Determination of the Propo&longs;ition, according to which, <lb/>the Forces for making of Fractures gradually vary more in one <lb/>point than in another.</s></p><p type="main"> <s>Let us fir&longs;t de&longs;igne this Truncheon A B to be broken in the <lb/>mid&longs;t upon the Fulciment C, and neer unto that let us de&longs;igne <lb/>it again, but under the Characters D E, to be broken on the <lb/>Fulciment F, remote from the middle. </s> <s>Fir&longs;t it is manife&longs;t, that <lb/>the Di&longs;tances A C and C B being equal, the Force &longs;hall be &longs;ha­<lb/>red equally in the ends B and A. Again, according as the Di­<lb/>&longs;tance D F groweth le&longs;&longs;e than the Di&longs;tance A C, the Moment <lb/>of the Force placed in D groweth le&longs;&longs;e than the Moment in A, <lb/>that is placed at the Di&longs;tance C A, and le&longs;&longs;eneth according to <lb/>the proportion of the Line D F to A C; and con&longs;equently, it is <lb/>requi&longs;ite to encrea&longs;e it to equalize or exceed the Re&longs;i&longs;tance of F: <lb/>But the Di&longs;tance D F may dimini&longs;h <emph type="italics"/>in infinitum,<emph.end type="italics"/> in relation to <lb/>the Di&longs;tance A C: Therefore it is requi&longs;ite, that it be po&longs;&longs;ible for <lb/>the Force to be applyed in D, to encrea&longs;e <emph type="italics"/>in infinitum,<emph.end type="italics"/> that it <lb/>may countervail the Re&longs;i&longs;tance in F. But, on the contrary, ac­<pb xlink:href="040/01/804.jpg" pagenum="112"/>cording as the Di&longs;tance F E encrea&longs;eth above C B, it is requi&longs;ite <lb/>to dimini&longs;h the Force in E, that it may compen&longs;ate the Re&longs;i­<lb/>&longs;tance in F: But the Di&longs;tance F E in relation to C B, cannot en­<lb/>crea&longs;e <emph type="italics"/>in infinitum,<emph.end type="italics"/> by drawing the Fulciment F towards the end <lb/>D, no nor yet to the double: Therefore, the Force in E, that it <lb/>may compen&longs;ate the Re&longs;i&longs;tance in F, &longs;hall be alwayes more than <lb/>half of the Force in B. </s> <s>We may comprehend, therefore, the ne­<lb/>ce&longs;&longs;ity of augmenting the Moments of the Collected Forces in E <lb/>and D infinitely to equalize or exceed the Re&longs;i&longs;tance placed in F, <lb/>according as the Fulciment F &longs;hall approach neerer and neerer <lb/>to the end D.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>AGR. </s> <s>What will <emph type="italics"/>Simplicius<emph.end type="italics"/> &longs;ay to this? </s> <s>Mu&longs;t he not con­<lb/>fe&longs;&longs;e the Virtue of Geometry to be a more powerful in&longs;trument <lb/>than all others, to &longs;harpen the Wit, and di&longs;po&longs;e it to di&longs;cour&longs;e <lb/>and &longs;peculate well? </s> <s>and that <emph type="italics"/>Plato<emph.end type="italics"/> had great rea&longs;on to de&longs;ire that <lb/>his Scholars &longs;hould be well grounded in the Mathematicks? </s> <s>I <lb/>have very well under&longs;tood the nature of the Leaver, and how <lb/>that its Length encrea&longs;ing or decrea&longs;ing, the Moment of the <lb/>Force and of the Re&longs;i&longs;tance augmented or dimini&longs;hed, and yet in <lb/>the determination of the pre&longs;ent Problem I deceived my &longs;elf, and <lb/>that not a little, but infinitely much.</s></p><p type="main"> <s>SIMP. </s> <s>The truth is, I begin to &longs;ee that Logick, although it <lb/>be a mo&longs;t appo&longs;ite In&longs;trument to regulate our Di&longs;cour&longs;e, doth <lb/>not attain, as to the prompting of the Mind with Invention, <lb/>unto the acutene&longs;&longs;e of Geometry.</s></p><p type="main"> <s>SAGR. </s> <s>In my conceit, Logick giveth us to under&longs;tand, whe­<lb/>ther the Di&longs;courfes and Demon&longs;trations already made and found <lb/>are concluding, but that it teacheth us how to finde concluding <lb/>Di&longs;cour&longs;es and Demon&longs;trations; the truth is, I do not believe: <lb/>But it will be better, that <emph type="italics"/>Salviatus<emph.end type="italics"/> &longs;hew us according to what pro­<lb/>portion the Moments of the Forces do go increa&longs;ing, to overcome <lb/>the Re&longs;i&longs;tance of the &longs;ame Piece of Wood, according to the &longs;e­<lb/>veral places of the Fracture.</s></p><p type="main"> <s>SALV. </s> <s>The proportion that you &longs;eek, proceedeth after &longs;uch <lb/>a manner, that</s></p><pb xlink:href="040/01/805.jpg" pagenum="113"/><p type="head"> <s>PROPOSITION XII.</s></p><p type="main"> <s><emph type="italics"/>If in the length of a Cylinder we &longs;hall marke two places, <lb/>upon which we would make the Fracture of the &longs;aid <lb/>Cylinder, the Re&longs;i&longs;tances of tho&longs;e two places have <lb/>the &longs;ame proportion to each other, as have the Re­<lb/>ctangles made by the Di&longs;tances of tho&longs;e places <lb/>reciprocally taken.<emph.end type="italics"/></s></p><p type="main"> <s>Let the two Forces (<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>16.) be A and B the lea&longs;t, to <lb/>break in C, and E and F likewi&longs;e the lea&longs;t, to break in D. <lb/></s> <s>I &longs;ay the Forces A and B have the &longs;ame proportion to the <lb/>Forces E and F, that the Rectangle A D B hath to the Rectan­<lb/>gle A C B. </s> <s>For the Forces A and B, have to the Forces E and F, a <lb/>proportion compounded of the Forces A and B, to the Force <lb/>B, of B to F, and of F to E and E: But as the Forces A and <lb/>B are to the Force B, &longs;o is the Length B A to A C; and as the <lb/>Force B is to F, &longs;o is the Line D B to B C; and as the Force F is <lb/>to F and E, &longs;o is the Line D A to A B: Therefore the Forces A <lb/>and B have to the Forces E and F a proportion compounded of <lb/>the&longs;e three, namely, of B A to A C, of D B to B C, and of D A <lb/>A B. </s> <s>But of the two proportions D A to A B, and A B to A C, <lb/>is compounded the proportion of D A to A C: Therefore the <lb/>Forces A and B have to the Forces E and F, the proportion com­<lb/>pounded of this D A to A C, and of the other D B to D C. <lb/></s> <s>But the Rectangle A D B hath to the Rectangle A C B, a pro­<lb/>portion compounded of the &longs;ame D A to A C, and of D B to <lb/>B C: Therefore the Forces A and B are to the Forces E and F, <lb/>as the Rectangle A D B is to the Rectangle A C B; which is as <lb/>much as to &longs;ay, the Re&longs;i&longs;tance again&longs;t Fraction in C, hath the <lb/>&longs;ame proportion to the Re&longs;i&longs;tance again&longs;t Fraction in D, that <lb/>the Rectangle A D B hath to the Rectangle A C B: Which was <lb/>to be demon&longs;trated.</s></p><p type="main"> <s>In con&longs;equence of this Theorem we may re&longs;olve a Problem of <lb/>great Curio&longs;ity; and it is this:</s></p><pb xlink:href="040/01/806.jpg" pagenum="114"/><p type="head"> <s>PROP. XIII. PROBL. IV.</s></p><p type="main"> <s><emph type="italics"/>There being given the greate&longs;t Weight that can be &longs;up­<lb/>ported at the middle of a Cylinder or Pri&longs;me, where <lb/>the Re&longs;i&longs;tance is leafl; and there being given a <lb/>Weight greater than that, to find in the &longs;aid Cylin­<lb/>der, the point at which the given greater Weight may <lb/>be &longs;upporited as the greate&longs;t Weight.<emph.end type="italics"/></s></p><p type="main"> <s>Let the given weight greater than the greate&longs;t weight that <lb/>can be &longs;upported at the middle of the Cylinder A B, have <lb/>unto the &longs;aid greate&longs;t weight, the proportion of the line E <lb/>to F: it is required to find the point in the Cylinder at which the <lb/>&longs;aid given weight commeth to be &longs;upported as the bigge&longs;t. </s> <s>Be­<lb/>tween E and F let G be a Mean-Proportional; and as E is to G, <lb/>&longs;o let A D be to S, S &longs;hall be le&longs;&longs;er than A D. </s> <s>Let A D be the <lb/>Diameter of the Semicircle A H D: in which &longs;uppo&longs;e A H equal <lb/>to S; and joyn together H and D, and take D R equal to it. <lb/></s> <s>I &longs;ay that R is the point &longs;ought, at which the given weight, <lb/>greater than the greate&longs;t that can be &longs;upported at the middle of the <lb/>Cylinder D, would become as the greate&longs;t weight. </s> <s>On the length <lb/><emph type="italics"/>B<emph.end type="italics"/>A de&longs;cribe the Semicircle A N B, and rai&longs;e the Perpendicular <lb/>RN, and conjoyn N and <lb/>D: And becau&longs;e the two <lb/><figure id="id.040.01.806.1.jpg" xlink:href="040/01/806/1.jpg"/><lb/>Squares N R and R D are <lb/>equal to the Square N D; <lb/>that is, to the Square A D; <lb/>that is, to the two A H and <lb/>and H D; and H D is equal <lb/>to the Square D R: There­<lb/>fore the Square N R, that <lb/>is, the Rectangle A R B <lb/>&longs;hall be equal to the Square A H; that is, to the Square S: But <lb/>the Square S is to the Square A D, as F to E; that is, as the <lb/>greate&longs;t &longs;upportable Weight at D to the given greater Weight: <lb/>Therefore this greater &longs;hall be &longs;upported at R, as the greate&longs;t <lb/>that can be there &longs;u&longs;tained. </s> <s>Which is that that we &longs;ought.</s></p><p type="main"> <s>SAGR. </s> <s>I under&longs;tand you very well, and am con&longs;idering that <lb/>the Pri&longs;me A B having alwayes more &longs;trength and re&longs;i&longs;tance a­<lb/>gain&longs;t Pre&longs;&longs;ion in the parts that more and more recede from the <lb/>middle, whether in very great and heavy Beams one may take <pb xlink:href="040/01/807.jpg" pagenum="115"/>away a pretty big part towards the end with a notable alleviation <lb/>of the weight; which in Beams of great Rooms would be commo­<lb/>dious, and of no &longs;mall pro&longs;it. </s> <s>And it would be pretty, to find what <lb/>Figure that Solid ought to have, that it might have equal Re&longs;i­<lb/>&longs;tance in all its parts; &longs;o as that it were not with more ea&longs;e to be <lb/>broken by a weight that &longs;hould pre&longs;&longs;e it in the mid&longs;t, than in any <lb/>other place.</s></p><p type="main"> <s>SALV. </s> <s>I was ju&longs;t about to tell you a thing very notable and <lb/>plea&longs;ant to this purpo&longs;e. </s> <s>I will a&longs;&longs;ume a brief Scheme for the bet­<lb/>ter explanation of my meaning. </s> <s>This Figure D B is a Pri&longs;m, who&longs;e <lb/>Re&longs;i&longs;tance again&longs;t Fraction in the term A D by a Force pre&longs;&longs;ing <lb/>at the term B, is le&longs;&longs;e than the Re&longs;i&longs;tance that would be found in <lb/>the place C I, by how much the length C B is le&longs;&longs;er than B A; as <lb/>hath already been demon­<lb/>&longs;trated. </s> <s>Now &longs;uppo&longs;e the <lb/><figure id="id.040.01.807.1.jpg" xlink:href="040/01/807/1.jpg"/><lb/>&longs;aid Pri&longs;me to be &longs;awed <lb/>Diagonally according to the <lb/>Line FB, &longs;o that the oppo­<lb/>&longs;ite Surfaces may be two <lb/>Triangles, one of which to­<lb/>wards us is F A B. </s> <s>This So­<lb/>lid obtains a quality contrary to the Pri&longs;me, to wit, that it le&longs;&longs;e re­<lb/>&longs;i&longs;teth Fraction by the Force placed in B at the term C than at A, <lb/>by as much the Length C <emph type="italics"/>B<emph.end type="italics"/> is le&longs;&longs;e than <emph type="italics"/>B<emph.end type="italics"/> A; Which we will ea <lb/>&longs;ily prove: For imagining the Section C N O parallel to the other <lb/>A F D, the Line <emph type="italics"/>F<emph.end type="italics"/> A &longs;hall be to C N in the Triangle F A <emph type="italics"/>B<emph.end type="italics"/> in the <lb/>&longs;ame proportion, as the Line A <emph type="italics"/>B<emph.end type="italics"/> is to <emph type="italics"/>B<emph.end type="italics"/> C: and therefore if we <lb/>&longs;uppo&longs;e the Fulciment of the two Leavers to be in the Points A <lb/>and C, who&longs;e Di&longs;tances are <emph type="italics"/>B<emph.end type="italics"/> A, A F, <emph type="italics"/>B<emph.end type="italics"/> C, and C N, the&longs;e, I &longs;ay, <lb/>&longs;hall be like: and therefore that Moment which the <emph type="italics"/>F<emph.end type="italics"/>orce placed <lb/>at <emph type="italics"/>B<emph.end type="italics"/> hath at the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> A above the Re&longs;i&longs;tance placed at the <lb/>Di&longs;tance A <emph type="italics"/>F<emph.end type="italics"/>, the &longs;aid <emph type="italics"/>F<emph.end type="italics"/>orce at <emph type="italics"/>B<emph.end type="italics"/> &longs;hall have at the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/>C <lb/>above the &longs;ame Re&longs;i&longs;tance, were it placed at the Di&longs;tance C N: <lb/><emph type="italics"/>B<emph.end type="italics"/>ut the Re&longs;i&longs;tance to be overcome at the <emph type="italics"/>F<emph.end type="italics"/>ulciment C, being pla­<lb/>ced at the Di&longs;tance C N, from the <emph type="italics"/>F<emph.end type="italics"/>orce in <emph type="italics"/>B<emph.end type="italics"/> is le&longs;&longs;er than the <lb/>Re&longs;i&longs;tance in A &longs;o much as the Rectangle C O is le&longs;&longs;e than the <lb/>Rectangle A D; that is, &longs;o much as the Line C N is le&longs;s than A <emph type="italics"/>F<emph.end type="italics"/>; <lb/>that is, C <emph type="italics"/>B<emph.end type="italics"/> than B A: Therefore the Re&longs;i&longs;tance of the part O C B <lb/>again&longs;t <emph type="italics"/>F<emph.end type="italics"/>raction in C is &longs;o much le&longs;s than the Re&longs;i&longs;tance of the <lb/>whole D A O again&longs;t <emph type="italics"/>F<emph.end type="italics"/>racture in O, as the Length C B is le&longs;s than <lb/>A B. </s> <s>We have therefore from the Beam or Pri&longs;me D B, taken <lb/>away a part, that is half, cutting it Diagonally, and left the Wedge <lb/>or triangular Pri&longs;m <emph type="italics"/>F<emph.end type="italics"/> B A; and they are two Solids of contrary <lb/>Qualities, namely, that more re&longs;i&longs;ts the more it is &longs;hortned, and this <lb/>in &longs;hortning lo&longs;eth its toughne&longs;s as fa&longs;t. </s> <s>Now this being granted, <pb xlink:href="040/01/808.jpg" pagenum="116"/>it &longs;eemeth very rea&longs;onable, nay, nece&longs;&longs;ary, that one may give it <lb/>a cut, by which taking away that which is &longs;uperfluous, there remai­<lb/>neth a Solid of &longs;uch a <emph type="italics"/>F<emph.end type="italics"/>igure, as in all its parts hath equal Re&longs;i­<lb/>&longs;tance.</s></p><p type="main"> <s>SIMP. </s> <s>It mu&longs;t needs be &longs;o; for where there is a tran&longs;ition from <lb/>the greater to the le&longs;&longs;er, one meeteth al&longs;o with the equal.</s></p><p type="main"> <s>SAGR. </s> <s>But the bu&longs;ine&longs;&longs;e is to find how we are to guide the <lb/>Saw for making of this Section.</s></p><p type="main"> <s>SIMP. </s> <s>This &longs;eemeth to me as if it were a very ea&longs;ie bu&longs;ine&longs;&longs;e; <lb/>for if in &longs;awing the Pri&longs;m diagonally, taking away half of it, the <lb/>Figure that remains retaineth a contrary quality to that of the <lb/>whole Pri&longs;m, &longs;o as that in all places wherein this acquireth &longs;trength, <lb/>that as fa&longs;t lo&longs;eth it, me thinks, that keeping the middle way, that <lb/>is, taking only the half of that half, which is the fourth part of the <lb/>whole, the remaining Figure will not gain or lo&longs;e &longs;trength in any <lb/>of all tho&longs;e places wherein the lo&longs;&longs;e and the gain of the other two <lb/>Figures were alwaies equal.</s></p><p type="main"> <s>SALV. </s> <s>You have not hit the mark, <emph type="italics"/>Simplicius<emph.end type="italics"/>; and as I &longs;hall <lb/>&longs;hew you, it will appear in reality, that that which may be cut off <lb/>from the Pri&longs;m, and taken away without weakening it is not its <lb/>fourth part, but the third. </s> <s>Now it remaineth (which is that that <lb/>was hinted by <emph type="italics"/>Sagredus<emph.end type="italics"/>)</s></p><p type="head"> <s>PROP. XIV. PROBL. V.</s></p><p type="main"> <s><emph type="italics"/>To find according to what Line the Section is to be <lb/>made; Which I will prove to be a Parabolical <lb/>Line.<emph.end type="italics"/></s></p><p type="main"> <s>But fir&longs;t it is nece&longs;&longs;ary to demon&longs;trate a certain Lemma, which <lb/>is this:</s></p><p type="head"> <s>LEMMA I.</s></p><p type="main"> <s><emph type="italics"/>If there &longs;hall be two Ballances or Leavers divided by their Fulci­<lb/>ments in &longs;uch &longs;ort that the two Distances where at the Forces <lb/>are to be placed, have to each other double the proportion of <lb/>the Di&longs;tances at which the Re&longs;i&longs;tances &longs;ball be, which Re&longs;i­<lb/>&longs;tances are to each other as their Di&longs;tances, the &longs;u&longs;taining <lb/>Powers &longs;hall be equal.<emph.end type="italics"/></s></p><p type="main"> <s>Let A B and C D be two Leavers divided upon their Fulciments <lb/>E and F, in &longs;uch &longs;ort that the Di&longs;tance E B hath to F D a pro­<lb/>portion double to that which the Di&longs;tance E A hath to F C. </s> <s>I &longs;ay, <pb xlink:href="040/01/809.jpg" pagenum="117"/>the Powers that in BD &longs;hall &longs;u&longs;tain the Re&longs;i&longs;tances A and C &longs;hall <lb/>be equal to each other. </s> <s>Let E G be &longs;uppo&longs;ed a Mean-Proporti­<lb/>onal between E B and F D; therefore as B E is to E G, &longs;o &longs;hall <lb/>G E be to F D, and A E to C <emph type="italics"/>F<emph.end type="italics"/>; and &longs;o is &longs;uppo&longs;ed the Re&longs;i&longs;tance <lb/>of A to the Re&longs;i&longs;tance of C. </s> <s>And becau&longs;e that as E G is to <emph type="italics"/>F<emph.end type="italics"/> D, <lb/>&longs;o is A E to C <emph type="italics"/>F<emph.end type="italics"/>; by Permutation as G E is to E A, &longs;o &longs;hall D <emph type="italics"/>F<emph.end type="italics"/><lb/>be to <emph type="italics"/>F<emph.end type="italics"/> C: And therefore (in <lb/>regard that the two Leavers <lb/><figure id="id.040.01.809.1.jpg" xlink:href="040/01/809/1.jpg"/><lb/>D C and G A are divided pro­<lb/>portionally in the Points <emph type="italics"/>F<emph.end type="italics"/> and <lb/>E) in ca&longs;e the Power that being <lb/>placed at D compen&longs;ates the <lb/>Re&longs;i&longs;tance of C were at G, it <lb/>would countervail the &longs;ame Re&longs;i&longs;tance of C placed in A: But by <lb/>what hath been granted, the Re&longs;i&longs;tance of A hath the &longs;ame propor­<lb/>tion to the Re&longs;i&longs;tance of C, that AE hath to C <emph type="italics"/>F<emph.end type="italics"/>; that is, B E <lb/>hath to E G: Therefore the Power G, or if you will D, placed at <lb/>B will &longs;u&longs;tain the Re&longs;i&longs;tance placed at A: Which was to be de­<lb/>mon&longs;trated.</s></p><p type="main"> <s>This being under&longs;tood: in the Surface <emph type="italics"/>F<emph.end type="italics"/> B of the Pri&longs;me D B, <lb/>let the Parabolical Line <emph type="italics"/>F<emph.end type="italics"/> N B be drawn, who&longs;e Vertex is B, ac­<lb/>cording to which let the &longs;aid Pri&longs;me be &longs;uppo&longs;ed to be &longs;awed, the <lb/>Solid compri&longs;ed between the Ba&longs;e A D, the Rectangular Plane <lb/>A G, the Bight Line B G, and the Superficies D G B <emph type="italics"/>F<emph.end type="italics"/> being le&longs;t <lb/>incurvated according to the Curvity of the Parabolical Line <lb/><emph type="italics"/>F<emph.end type="italics"/> N B. </s> <s>I &longs;ay, that <lb/>that Solid is through­<lb/><figure id="id.040.01.809.2.jpg" xlink:href="040/01/809/2.jpg"/><lb/>out of equal Re&longs;i­<lb/>&longs;tance. </s> <s>Let it be cut <lb/>by the Plane C O pa­<lb/>rallel to A D; and <lb/>imagine two Leavers <lb/>divided and &longs;uppor­<lb/>ted upon the Fulciments A and C; and let the Di&longs;tances of one <lb/>be B A and A F, and of the other B C, and C N. </s> <s>And becau&longs;e in <lb/>the Parabola <emph type="italics"/>F B<emph.end type="italics"/> A, A <emph type="italics"/>B<emph.end type="italics"/> is to <emph type="italics"/>B<emph.end type="italics"/> C, as the Square of <emph type="italics"/>F<emph.end type="italics"/> A to the <lb/>Square of C N, it is manife&longs;t, that the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> A of one Leaver, <lb/>hath to the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> C of the other a proportion double to that <lb/>which the other Di&longs;tance A <emph type="italics"/>F<emph.end type="italics"/> hath to the other C N, And be­<lb/>cau&longs;e the Re&longs;i&longs;tance that is to be equal by help of the Leaver <lb/><emph type="italics"/>B<emph.end type="italics"/> A hath the &longs;ame proportion to the Re&longs;i&longs;tance that is to be <lb/>equal by help of the Leaver <emph type="italics"/>B<emph.end type="italics"/> C, that the Rectangle D A hath to <lb/>the Rectangle O C; which is the &longs;ame that the Line A <emph type="italics"/>F<emph.end type="italics"/> hath to <lb/>N C, which are the other two Di&longs;tances of the Leavers; it is ma­<lb/>nife&longs;t by the fore going Lemma, that the &longs;ame Force that being <pb xlink:href="040/01/810.jpg" pagenum="118"/>applyed to the Line <emph type="italics"/>B<emph.end type="italics"/> G will equal the Re&longs;i&longs;tance D A, will like­<lb/>wi&longs;e equal the Re&longs;i&longs;tance C O. </s> <s>And the &longs;ame may be demon&longs;tra­<lb/>ted, if one cut the Solid in any other place: therefore that Parabo­<lb/>lical Solid is throughout of equal Re&longs;i&longs;tance. </s> <s>In the next place, <lb/>that cutting the Pri&longs;me according to the Parabolical Line F N B, <lb/>the third part of it is taken away, appeareth, For that the Semi­<lb/>Parabola F N <emph type="italics"/>B<emph.end type="italics"/> A and the Rectangle F <emph type="italics"/>B<emph.end type="italics"/> are Ba&longs;es of two Solids <lb/>contained between two parallel Planes, that is, between the Rect­<lb/>angles F B and D G, whereby they retain the &longs;ame Proportion, as <lb/>tho&longs;e their Ba&longs;es: But the Rectangle F <emph type="italics"/>B<emph.end type="italics"/> is Se&longs;quialter to the Se­<lb/>miparabola F N <emph type="italics"/>B<emph.end type="italics"/> A: Therefore cutting the Pri&longs;ine according to <lb/>the Parabolick Line, we take away the third part of it. </s> <s>Hence we <lb/>&longs;ee, that <emph type="italics"/>B<emph.end type="italics"/>eams may be made with the diminution of their Weight <lb/>more than thirty three in the hundred, without dimini&longs;hing their <lb/>Strength in the lea&longs;t; which in great Ships, in particular, for bea­<lb/>ring the Decks may be of no &longs;mall benefit; for that in &longs;uch kind <lb/>of Fabricks Lightne&longs;&longs;e is of infinite importance.</s></p><p type="main"> <s>SAGR. </s> <s>The Commodities are &longs;o many, that it would be tedi­<lb/>ous, if not impo&longs;&longs;ible, to mention them all. <emph type="italics"/>B<emph.end type="italics"/>ut I, laying a&longs;ide <lb/>the&longs;e, would more gladly under&longs;tand that the alleviation is made <lb/>according to the a&longs;&longs;igned proportions. </s> <s>That the Section, according <lb/>to the Diagonal Line, cuts away half of the weight I very well <lb/>know: but that the other Section according to the Parabolical Line <lb/>takes away the third part of the Pri&longs;me I can believe upon the <lb/>word of <emph type="italics"/>Salviatus,<emph.end type="italics"/> who evermore &longs;peaks the truth, but in this <lb/>Ca&longs;e Science would better plea&longs;e me than Faith.</s></p><p type="main"> <s>SALV. </s> <s>I &longs;ee then that you would have the Demon&longs;tration, <lb/>whether or no it be true, that the exce&longs;&longs;e of the Pri&longs;me over and <lb/>above this, which for this time we will call a Parabolical Solid, is <lb/>the third part of the whole Pri&longs;me. </s> <s>I am certain that I have for­<lb/>merly demo&longs;trated it; I will try now whether I can put the <lb/>Demon&longs;tration together again: to which purpo&longs;e I do remember <lb/>that I made u&longs;e of a Certain Lemma of <emph type="italics"/>Archimedes,<emph.end type="italics"/> in&longs;erted by <lb/>him in his <emph type="italics"/>B<emph.end type="italics"/>ook <emph type="italics"/>de Spiralibus,<emph.end type="italics"/> and it is this:</s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"/>If any number of Lines at plea&longs;ure &longs;hall exceed one another equal­<lb/>ly, and the exce&longs;&longs;es be equal to the lea&longs;t of them, and there be as <lb/>many more, each of them equal to the greate&longs;t; the Squares of all <lb/>the&longs;e &longs;hall be le&longs;&longs;e than the triple of the Squares of tho&longs;e that <lb/>exceed one another: but they &longs;hall be more than triple to tho&longs;e <lb/>others that remain, the Square of the greate&longs;t being &longs;ub­<lb/>&longs;tracted.<emph.end type="italics"/></s></p><pb xlink:href="040/01/811.jpg" pagenum="119"/><p type="main"> <s>This being granted: Let the Parabolick Line A <emph type="italics"/>B<emph.end type="italics"/> be in&longs;cribed <lb/>in this Rectangle A C <emph type="italics"/>B<emph.end type="italics"/> P: we are to prove the Mixt Triangle <lb/><emph type="italics"/>B<emph.end type="italics"/> A P, who&longs;e &longs;ides are <emph type="italics"/>B<emph.end type="italics"/> P and P A, and <emph type="italics"/>B<emph.end type="italics"/>a&longs;e the Parabolical Line <lb/><emph type="italics"/>B<emph.end type="italics"/> A, to be the third part of the whole Rectangle C P. </s> <s>For if it be <lb/>not &longs;o, it will be either more than the third part, or le&longs;&longs;e. </s> <s>Let it be <lb/>&longs;uppo&longs;ed that it may be <lb/>le&longs;&longs;e, and to that which is <lb/><figure id="id.040.01.811.1.jpg" xlink:href="040/01/811/1.jpg"/><lb/>wanting &longs;uppo&longs;e the Space <lb/>X to be equal. </s> <s>Then di­<lb/>viding the Rectangle con­<lb/>tinually into equal parts <lb/>with Lines parallel to the <lb/>Sides <emph type="italics"/>B<emph.end type="italics"/> P and C A, we <lb/>&longs;hall in the end arrive at <lb/>&longs;uch parts, as that one of them &longs;hall be le&longs;&longs;e than the Space X. <lb/></s> <s>Now let one of them be the Rectangle O <emph type="italics"/>B,<emph.end type="italics"/> and by the Points <lb/>where the other Parallels inter&longs;ect the Parabolick Line, let the Pa­<lb/>rallels to A P pa&longs;&longs;e: and here I will &longs;uppo&longs;e a Figure to be cir­<lb/>cum&longs;cribed about our Mixt-Triangle, compo&longs;ed of Rectangles, <lb/>which are <emph type="italics"/>B<emph.end type="italics"/> O, I N, H M, F L, E K, G A; which Figure &longs;hall al&longs;o <lb/>yet be le&longs;s than the third part of the Rectangle C P, in regard that <lb/>the exce&longs;&longs;e of that Figure over and above the Mixed Triangle is <lb/>much le&longs;&longs;e than the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O, which yet again is le&longs;&longs;e than <lb/>the Space X.</s></p><p type="main"> <s>SAGR. Softly, I pray you, for I do not &longs;ee how the exce&longs;&longs;e of <lb/>this circum&longs;cribed Figure above the Mixt Triangle is con&longs;iderably <lb/>le&longs;&longs;er than the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O.</s></p><p type="main"> <s>SALV. </s> <s>Is not the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O equal to all the&longs;e &longs;mall Rect­<lb/>angles by which our Parabolical Line pa&longs;&longs;eth; I mean the&longs;e, <emph type="italics"/>B<emph.end type="italics"/> I, <lb/>I H, H F, F E, E G, and G A, of which one part only lyeth with­<lb/>out the Mixt Triangle? </s> <s>And the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O, is it not al&longs;o &longs;up­<lb/>po&longs;ed to be le&longs;&longs;e than the Space X? </s> <s>Therefore if the Triangle to­<lb/>gether with X did, as the Adver&longs;ary &longs;uppo&longs;eth, equalize the third <lb/>part of the Rectangle C P the circum&longs;cribed Figure that adjoyns <lb/>to the Triangle &longs;o much le&longs;&longs;e than the Space X, will remain even <lb/>yet le&longs;&longs;e than the third part of the &longs;aid Rectangle C P. <emph type="italics"/>B<emph.end type="italics"/>ut this <lb/>cannot be, for it is more than a third part, therefore it is not true <lb/>that our Mixt Triangle is le&longs;&longs;e than one third of the Rectangle.</s></p><p type="main"> <s>SAGR. </s> <s>I under&longs;tand the Solution of my Doubt. <emph type="italics"/>B<emph.end type="italics"/>ut it is <lb/>requi&longs;ite now to prove unto us, that the Circum&longs;cribed Figure is <lb/>more than a third part of the Rectangle C P; which, I believe, will <lb/>be harder to do.</s></p><p type="main"> <s>SALV. </s> <s>Not at all. </s> <s>For in the Parabola the Square of the Line <lb/><arrow.to.target n="marg1089"></arrow.to.target><lb/>D E hath the &longs;ame proportion to the Square of Z G, that the Line <pb xlink:href="040/01/812.jpg" pagenum="120"/>D A hath to A Z; which is the &longs;ame that the Rectangle K E hath to <lb/>the Rectangle A G, their heights A K and K L being equal. </s> <s>There­<lb/>fore the proportion that the Square E D hath to the Square Z G; <lb/>that is, the Square L A hath to the Square A K, the Rectangle K E <lb/>hath likewi&longs;e to the Rectangle K Z. </s> <s>And in the &longs;elf-&longs;ame manner <lb/>we might prove that the other Rectangles L F, M H, N I, O B are <lb/>to one another as the Squares of the Lines M A, N A, O A, P A. <lb/></s> <s>Con&longs;ider we in the next place, how the Circum&longs;cribed Figure is <lb/>compounded of certain Spaces that are to one another as the <lb/>Squares of the Lines that exceed with Exce&longs;&longs;es equal to the lea&longs;t, <lb/>and how the Rectangle C P is compounded of &longs;o many other Spa­<lb/>ces each of them equal to the Greate&longs;t, which are all the Rectan­<lb/>gles equal to O B. Therefore, by the Lemma of <emph type="italics"/>Archimedes,<emph.end type="italics"/> the <lb/>Circum&longs;cribed Figure is more than the third part of the Rectangle <lb/>C P: But it was al&longs;o le&longs;&longs;e, which is impo&longs;&longs;ible: Therefore the <lb/>Mixt-Triangle is not le&longs;&longs;e than one third of the Rectangle C P. <lb/></s> <s>I &longs;ay likewi&longs;e, that it is not more: For if it be more than one <lb/>third of the Rectangle C P, &longs;uppo&longs;e the Space X equal to the ex­<lb/>ce&longs;&longs;e of the Triangle above the third part of the &longs;aid Rectangle <lb/>C P, and the divi&longs;ion and &longs;ubdivi&longs;ion of the Rectangle into Rect­<lb/>angolets, but alwaies equal, being made, we &longs;hall meet with &longs;uch as <lb/>that one of them is le&longs;&longs;er than the Space X; which let be done: <lb/>and let the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O be le&longs;&longs;er than X; and, having de&longs;cribed <lb/>the Figure as before, we &longs;hall have in&longs;cribed in the Mixt-Triangle <lb/>a Figure compounded of the Rectangles V O, T N, S M, N L, Q K, <lb/>which yet &longs;hall not be le&longs;s <lb/><figure id="id.040.01.812.1.jpg" xlink:href="040/01/812/1.jpg"/><lb/>than the third part of the <lb/>great Rectangle C P, for <lb/>the Mixt Triangle doth <lb/>much le&longs;&longs;e exceed the In­<lb/>&longs;cribed Figure than it doth <lb/>exceed the third part of <lb/>the Rectangle C P; Be­<lb/>cau&longs;e the exce&longs;&longs;e of the <lb/>Triangle above the third part of the Rectangle C P is equal to <lb/>the Space X which is greater than the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O, and this al­<lb/>&longs;o is con&longs;iderably greater than the exce&longs;&longs;e of the Triangle above <lb/>the In&longs;cribed Figure: For to the Rectangle <emph type="italics"/>B<emph.end type="italics"/> O, all the Rectan­<lb/>golets A G, G E, E <emph type="italics"/>F,<emph.end type="italics"/> F H, H I, I <emph type="italics"/>B<emph.end type="italics"/> are equal, of which the Ex­<lb/>ce&longs;&longs;es of the Triangle above the In&longs;cribed <emph type="italics"/>F<emph.end type="italics"/>igure are le&longs;&longs;e than <lb/>half: And therefore the Triangle exceeding the third part of the <lb/>Rectangle C P, by much more (exceeding it by the Space X) <lb/>than it exceedeth its in&longs;cribed <emph type="italics"/>F<emph.end type="italics"/>igure, that &longs;ame <emph type="italics"/>F<emph.end type="italics"/>igure &longs;hall al&longs;o <lb/>be greater than the third part of the Rectangle C P: <emph type="italics"/>B<emph.end type="italics"/>ut it is le&longs;&longs;er, <lb/>by the Lemma pre&longs;uppo&longs;ed: <emph type="italics"/>F<emph.end type="italics"/>or that the Rectangle C P, as being <pb xlink:href="040/01/813.jpg" pagenum="127"/>the Aggregate of all the bigge&longs;t Rectangles, hath the &longs;ame pro­<lb/>portion to the Rectangles compounding the In&longs;cribed <emph type="italics"/>F<emph.end type="italics"/>igure, that <lb/>the Aggregate of of all the Squares of the Lines equal to the big­<lb/>ge&longs;t, hath to the Squares of the Lines that exceed equally, &longs;ub&longs;tra­<lb/>cting the Square of the bigge&longs;t: And therefore (as it hapneth in <lb/>Squares) the whole Aggregate of the bigge&longs;t (that is the Rectan­<lb/>gle C P) is more than triple the Aggregate of the exceeding <lb/>ones, the bigge&longs;t deducted, that compound the In&longs;cribed <emph type="italics"/>F<emph.end type="italics"/>i­<lb/>gure. </s> <s>Therefore the Mixt-Triangle is neither greater nor le&longs;&longs;er <lb/>than the third part of the Rectangle C P: It is therefore equal.</s></p><p type="margin"> <s><margin.target id="marg1089"></margin.target><emph type="italics"/>The Quadrature of <lb/>the Parabola &longs;hewn <lb/>by one &longs;ingle De­<lb/>mon&longs;tration.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>A pretty and ingenuous Demon&longs;tration: and &longs;o much <lb/>the more, in that it giveth us the Quadrature of the Parabola, &longs;hew­<lb/>ing it to be <emph type="italics"/>Se&longs;quitertial<emph.end type="italics"/> of the Triangle in&longs;cribed in the &longs;ame; <lb/>proving that which <emph type="italics"/>Archimedes<emph.end type="italics"/> demon&longs;trateth by two very diffe­<lb/>rent, but both very admirable, methods of a great number of Pro­<lb/>po&longs;itions. </s> <s>As hath likewi&longs;e been demon&longs;trated lately by <emph type="italics"/>Lucas <lb/>Valerius,<emph.end type="italics"/> another &longs;econd <emph type="italics"/>Archimedes<emph.end type="italics"/> of our Age, which Demon­<lb/>&longs;tration is &longs;et down in the Book that he writ of the Center of the <lb/>Gravity of Solids.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>A Treati&longs;e which verily is not to come behind any one <lb/>that hath been written by the mo&longs;t <emph type="italics"/>F<emph.end type="italics"/>amous Geometricians of the <lb/>pre&longs;ent and all pa&longs;t Ages: which when it was read by our <emph type="italics"/>Acade­<lb/>mick,<emph.end type="italics"/> it made him de&longs;i&longs;t from pro&longs;ecuting his Di&longs;coveries that he <lb/>was then proceeding to write on the &longs;ame Subject: in regard he <lb/>&longs;aw the whole bu&longs;ine&longs;s &longs;o happily found and demon&longs;trated by the <lb/>&longs;aid <emph type="italics"/>Valerius.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>I was informed of all the&longs;e things by our <emph type="italics"/>Academick<emph.end type="italics"/>; <lb/>and have be&longs;ought him withall that he would one day let me &longs;ee <lb/>his Demon&longs;trations that he had &longs;ound at the time when he met <lb/>with the <emph type="italics"/>B<emph.end type="italics"/>ook of <emph type="italics"/>Valerius:<emph.end type="italics"/> but I never was &longs;o happy as to &longs;ee them.</s></p><p type="main"> <s>SALV. </s> <s>I have a Copy of them, and will impart them to you, <lb/>for you will be much plea&longs;ed to &longs;ee the variety of Methods, which <lb/>the&longs;e two Authors take to inve&longs;tigate the &longs;ame Conclu&longs;ions, and <lb/>their Demon&longs;trations: wherein al&longs;o &longs;ome of the Conclu&longs;ions have <lb/>different Explanations, howbeit in effect equally true.</s></p><p type="main"> <s>SAGR. </s> <s>I &longs;hall be very glad to &longs;ee them, therefore when you re­<lb/>turn to our wonted Conferences you may do me the favour to <lb/>bring them with you. <emph type="italics"/>B<emph.end type="italics"/>ut in the mean time, this &longs;ame of the Re­<lb/>fi&longs;tance of the Solid taken from the Pri&longs;me by a Parabolick Secti­<lb/>on, being an Operation no le&longs;&longs;e ingenuous than beneficial in many <lb/>Mechanical Works, it would be good that Artificers had &longs;ome ea­<lb/>&longs;ie and expedite Rule how they may draw the &longs;aid Parabolick <lb/>Line upon the Plane of the Pri&longs;me.</s></p><p type="main"> <s>SALV. </s> <s>There are &longs;everal waies to draw tho&longs;e Lines, but two <lb/><arrow.to.target n="marg1090"></arrow.to.target><lb/>that are more expedite than all the re&longs;t, I will de&longs;cribe unto you. <pb xlink:href="040/01/814.jpg" pagenum="122"/>One of which is truly admirable, &longs;ince that thereby, in le&longs;&longs;e time <lb/>than another can with Compa&longs;&longs;es &longs;lightly draw upon a paper <lb/>four or &longs;ix Circles of different &longs;izes, I can de&longs;ign thirty or forty <lb/>Parabolick Lines no le&longs;&longs;e exact, &longs;mall, and &longs;mooth than the Cir­<lb/>cumferences of tho&longs;e Circles. </s> <s>I have a <emph type="italics"/>B<emph.end type="italics"/>all of <emph type="italics"/>B<emph.end type="italics"/>ra&longs;&longs;e exqui&longs;itely <lb/>round, no bigger than a Nut, this thrown upon a Steel Mirrour <lb/>held, not erect to the Horizon, but &longs;omewhat inclined, &longs;o that the <lb/><emph type="italics"/>B<emph.end type="italics"/>all in its motion may run along pre&longs;&longs;ing lightly upon it, leaveth <lb/>a Parabolical Line finely and &longs;moothly de&longs;cribed, and wider or <lb/>narrower according as the Projection &longs;hall be more or le&longs;s elevated. <lb/></s> <s>Whereby al&longs;o we have a clear and &longs;en&longs;ible Experiment that the <lb/>Motion of Projects is made by Parabolick Lines: an Effect ob&longs;er­<lb/>ved by none before our <emph type="italics"/>Academick,<emph.end type="italics"/> who al&longs;o layeth down the <lb/>Demon&longs;tration of it in his <emph type="italics"/>B<emph.end type="italics"/>ook of Motion, which we will joynt­<lb/>ly peru&longs;e at our next meeting. </s> <s>Now the <emph type="italics"/>B<emph.end type="italics"/>all, that it may de&longs;cribe <lb/>by its motion tho&longs;e Parabola's, mu&longs;t be rouled a little in the hands <lb/>that it may be warmed, and &longs;omewhat moy&longs;tned, for by this <lb/>means it will leave its track more apparent upon the Mirrour. </s> <s>The <lb/>other way to draw the Line that we de&longs;ire upon the Pri&longs;me is after <lb/>this manner. </s> <s>Let two Nailes be fa&longs;tned on high in a Wall, at an <lb/>equal di&longs;tance from the Horizon, and remote from one another <lb/>twice the breadth of the Rectangle upon which we would trace the <lb/>Semiparabola, and to the&longs;e two Nails tye a &longs;mall thread of &longs;uch a <lb/>length that its doubling may reach as far as the length of the <lb/>Pri&longs;me; this &longs;tring will hang in a Parabolick <emph type="italics"/>F<emph.end type="italics"/>igure: &longs;o that tra­<lb/>cing out upon the Wall the way that the &longs;aid String maketh on it, <lb/>we &longs;hall have a whole Parabola de&longs;cribed: which a Perpendicular <lb/>that hangeth in the mid&longs;t between the&longs;e two Nailes will divide <lb/>into two equal parts. </s> <s>And for the transferring or &longs;etting off of <lb/>that Line afterwards upon the oppo&longs;ite Surfaces of the Pri&longs;me it is <lb/>not difficult at all, &longs;o that every indifferent Arti&longs;t will know how <lb/>to do it. </s> <s>The &longs;ame Line might be drawn upon the &longs;aid Sur­<lb/>face of the Pri&longs;me by help of the Geometrical Lines delineated up­<lb/>on the <emph type="italics"/>Compa&longs;&longs;e<emph.end type="italics"/> of our <emph type="italics"/>Friend,<emph.end type="italics"/> without any more ado.</s></p><p type="margin"> <s><margin.target id="marg1090"></margin.target><emph type="italics"/>Several waies to <lb/>de&longs;cribe a Para­<lb/>bola.<emph.end type="italics"/></s></p><p type="main"> <s>We have hitherto demon&longs;trated &longs;o many Conclu&longs;ions touching <lb/>the Contemplation of the&longs;e Re&longs;i&longs;tances of Solids again&longs;t Fraction <lb/>by having fir&longs;t opened the way unto the Science with &longs;uppo&longs;ing the <lb/>direct Re&longs;i&longs;tance for known, that we may in pur&longs;uance of them <lb/>proceed forwards to the finding of other, and other Conclu&longs;ions, <lb/>with their Demon&longs;trations of tho&longs;e which in Nature are infinite. <lb/></s> <s>Only at pre&longs;ent, for a final conclu&longs;ion of this daies Conferences, <lb/>I will add the Speculation of the Re&longs;i&longs;tances of the Hollow Solids <lb/>which Art, and chiefly Nature, u&longs;eth in an hundred Operations, <lb/>when without encrea&longs;ing the weight &longs;he greatly augmenteth the <lb/>&longs;trength: as is &longs;een in the Bones of Birds, and in many Canes that <pb xlink:href="040/01/815.jpg" pagenum="123"/>are light and of great Re&longs;i&longs;tance again&longs;t bending and breaking. <lb/></s> <s>For if a Wheat Straw that &longs;upports an Ear that is heavier than the <lb/>whole Stalk, were made of the &longs;ame quantity of matter but were <lb/>ma&longs;&longs;ie or &longs;olid, it would be much le&longs;&longs;e repugnant to Fraction or <lb/>Flection. </s> <s>And with the &longs;ame Rea&longs;on Art hath ob&longs;erved, and Ex­<lb/>perience confirmed, that an hollow Cane, or a Trunk of Wood <lb/>or Metal, is much more firm and tough than if being of the &longs;ame <lb/>weight and length it were &longs;olid, which con&longs;equently would be <lb/>more flender, and therefore Art hath contrived to make Lances hol­<lb/>low within when they are de&longs;ired to be &longs;trong and light. </s> <s>We will <lb/>&longs;hew therefore, that</s></p><p type="head"> <s>PROPOSITION XV.</s></p><p type="main"> <s><emph type="italics"/>The Re&longs;i&longs;tances of two Cylinders, equall, and equally <lb/>long, one of which is Hollow, and the other Ma&longs;sie, <lb/>have to each other the &longs;ame proportion, as their Dia­<lb/>meters.<emph.end type="italics"/></s></p><p type="main"> <s>Let the Cane or Hollow Cylinder be A E, [<emph type="italics"/>as in<emph.end type="italics"/> Fig. </s> <s>17.] <lb/>and the Cylinder I N Ma&longs;&longs;ie, and equall in weight and length. <lb/></s> <s>I &longs;ay, the Re&longs;i&longs;tance of the Cane A E hath the &longs;ame propor­<lb/>tion to the Re&longs;i&longs;tance of the &longs;olid Cylinder, as the Diameter <lb/>A B hath to the Diameter I L. </s> <s>Which is very manife&longs;t; For the <lb/>Cane and the Cylinder I N being equal, and of equal lengths, the <lb/>Circle I L that is Ba&longs;e of the Cylinder &longs;hall be equal to the Ring <lb/>A B that is Ba&longs;e of the Cane A E, (I call the Superficies that re­<lb/>maineth when a le&longs;&longs;er Circle is taken out of a greater that is Con­<lb/>centrick with it a Ring:) and therefore their Ab&longs;olute Re&longs;i&longs;tan­<lb/>ces &longs;hall be equal: but becau&longs;e in breaking cro&longs;&longs;e-waies we make <lb/>u&longs;e in the Cylinder I N of the length L N for a Leaver, and of the <lb/>point L for a Fulciment, and of the Semidiameter or Diameter L I <lb/>for a Counter-Leaver; and in the Cane the part of the Leaver, <lb/>that is the Line B E is equal to L N; but the Counter-Leaver at <lb/>the Fulciment B is the Diameter or Semidiameter A B: It is mani­<lb/>fe&longs;t therefore that the Re&longs;i&longs;tance of the Cane exceedeth that of <lb/>the Solid Cylinder as much as the Diameter A B exceeds the Dia­<lb/>meter I L; Which is that that we &longs;ought. </s> <s>Toughne&longs;s therefore is ac­<lb/>quired in the hollow Cane above the Toughne&longs;s of the &longs;olid Cylin­<lb/>der according to the proportion of the Diameters: provided al­<lb/>waies that they be both of the &longs;ame matter, weight, and length.</s></p><p type="main"> <s>It would be well, that in con&longs;equence of this we try to inve&longs;tigate <lb/>that which hapneth in other Ca&longs;es indifferently between all Canes <lb/>and &longs;olid Cylinders of equal length, although unequal in quantity <lb/>of weight, and more or le&longs;s evacuated. </s> <s>And fir&longs;t we will demon­<lb/>&longs;trate, that</s></p><pb xlink:href="040/01/816.jpg"/><figure id="id.040.01.816.1.jpg" xlink:href="040/01/816/1.jpg"/><p type="caption"> <s><emph type="italics"/>Place this at the end of the &longs;econd Dialogue pag:<emph.end type="italics"/> 124,</s></p><pb xlink:href="040/01/817.jpg" pagenum="124"/><p type="head"> <s>PROP. XVI. PROBL. VI.</s></p><p type="main"> <s><emph type="italics"/>A Trunk or Hollow Cane being given, a Solid Cylinder <lb/>may be found equal to it.<emph.end type="italics"/></s></p><p type="main"> <s>This Operation is very ea&longs;ie. </s> <s>For let the Line A B, be the Dia­<lb/>meter of the Cane, and C D the Diameter of the Hollow or <lb/>Cavity. </s> <s>Let the Line A E be &longs;et off upon the greater Circle <lb/>equal to the Diameter C D, and conjoyn E B. </s> <s>And becau&longs;e in <lb/><figure id="id.040.01.817.1.jpg" xlink:href="040/01/817/1.jpg"/><lb/>the Semicircle A E B the Angle E is Right­<lb/>Angle, the Circle who&longs;e Diameter is A B <lb/>&longs;hall be equall to the two Circles of the Di­<lb/>ameters A E and E B: But A E is the Dia­<lb/>meter of the Hollow of the Cane: Therefore <lb/>the Circle who&longs;e Diameter is E B, &longs;hall be <lb/>equal to the Ring A C B D: And therefore <lb/>the &longs;olid Cylinder, the Circle of who&longs;e Ba&longs;e <lb/>hath the Diameter E B &longs;hall be equal to the <lb/>Cane, they being of the &longs;ame length. </s> <s>This demon&longs;trated, we may <lb/>pre&longs;ently be able</s></p><p type="head"> <s>PROP. XVII. PROBL. VII.</s></p><p type="main"> <s><emph type="italics"/>To find what proportion is betwixt the Re&longs;i&longs;tances of <lb/>any what&longs;oever Cane and Cylinder, their lengths be­<lb/>ing equal.<emph.end type="italics"/></s></p><p type="main"> <s>LET the Cane A B E, and the Cylinder R S M, be of equal <lb/>length: it is required to find what proportion the Re&longs;i&longs;tances <lb/>have to each other. </s> <s>By the precedent let the Cylinder I L N <lb/>be found equal to the Cane, and of the &longs;ame length; and to the <lb/>Lines I L and R S (Diameters of the Ba&longs;es of the Cylinders I N and <lb/><figure id="id.040.01.817.2.jpg" xlink:href="040/01/817/2.jpg"/><lb/>R M) let the Line V be a fourth <lb/>Proportional. </s> <s>I &longs;ay, the Re&longs;i&longs;tance <lb/>of the Cane A E is to the Re&longs;i­<lb/>&longs;tance of the Cylinder R M, as the <lb/>Line A B is to V. </s> <s>For the Cane <lb/>A E being equal to, and of the <lb/>&longs;ame length with the Cylinder <lb/>I N, the Re&longs;i&longs;tance of the Cane <lb/>&longs;hall be to the Re&longs;i&longs;tance of the <lb/>Cylinder, as the Line A B is to I L: <lb/>But the Re&longs;i&longs;tance of the Cylinder I N is to the Re&longs;i&longs;tance of the <lb/>Cylinder R M, as the Cube I L is to the Cube R S; that is, as the <lb/>Line I L to V: Therefore, <emph type="italics"/>ex æquali,<emph.end type="italics"/> the Re&longs;i&longs;tance of the Cane <lb/>A E hath the &longs;ame proportion to the Re&longs;i&longs;tance of the Cylinder <lb/>R M, that the Line A B hath to V: Which is that that was &longs;ought.</s></p><p type="head"> <s><emph type="italics"/>The End of the Second Dialogue.<emph.end type="italics"/></s></p></chap><chap><pb xlink:href="040/01/818.jpg" pagenum="125"/><p type="head"> <s>GALILEUS, <lb/>HIS <lb/>DIALOGUES <lb/>OF <lb/>MOTION.</s></p><p type="head"> <s>The Third Dialogue.</s></p><p type="head"> <s><emph type="italics"/>INTERLOCUTORS,<emph.end type="italics"/></s></p><p type="head"> <s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="head"> <s>OF LOCAL MOTION.</s></p><p type="main"> <s><emph type="italics"/>We promote a very new Science, but of a very <lb/>old Subject. </s> <s>There is nothing in Nature more <lb/>antient than<emph.end type="italics"/> MOTION, <emph type="italics"/>of which <lb/>many and great Volumns have been written <lb/>by Philo&longs;ophers: But yet there are &longs;undry <lb/>Symptomes and Properties in it worthy of <lb/>our Notice, which I find not to have been hi­<lb/>therto ob&longs;erved, much le&longs;&longs;e demon&longs;trated by <lb/>any. </s> <s>Some &longs;light particulars have been no­<lb/>ted: as that the Natural Motion of Grave Bodies continually accelle-<emph.end type="italics"/><pb xlink:href="040/01/819.jpg" pagenum="126"/><emph type="italics"/>rateth, as they de&longs;cend towards their Center: but it hath not been as yet <lb/>declared in what proportion that Acceleration is made. </s> <s>For no man, <lb/>that I know, hath ever demon&longs;trated, That there is the &longs;ame proportion <lb/>between the Spaces, thorow which a thing moveth in equal Times, as <lb/>there is between the Odde Numbers which follow in order after a Vnite. <lb/></s> <s>It hath been ob&longs;erved that Projects [or things thrown or darted with vi­<lb/>olence] make a Line that is &longs;omewhat curved; but that this line is a Pa­<lb/>rabola, none have hinted: Yet the&longs;e, and &longs;undry other things, no <lb/>le&longs;&longs;e worthy of our knowledg, will I here demon&longs;trate: And which <lb/>is more, I will open a way to a mo&longs;t ample and excellent Science, <lb/>of which the&longs;e our Labours &longs;hall be the Elements: into which more <lb/>&longs;ubtil and piercing Wits than mine will be better able to dive.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>We divide this Treati&longs;e into three parts. </s> <s>In the fir&longs;t part we con&longs;ider <lb/>&longs;uch things as re&longs;pect Equable or Vniforme Motion. </s> <s>In the &longs;econd we <lb/>write of Motion naturally accelerate. </s> <s>In the third we treat of Violent <lb/>Motion, or<emph.end type="italics"/> De Projectis.</s></p><p type="head"> <s>OF EQVABLE MOTION.</s></p><p type="main"> <s><emph type="italics"/>Concerning Equable or Vniform Motion we have need of onely one <lb/>Definition, which I thus deliver.<emph.end type="italics"/></s></p><p type="head"> <s>DEFINITION.</s></p><p type="main"> <s>By an Equable or Uniform Motion, I under&longs;tand that by which a <lb/>Moveable in all equal Times pa&longs;&longs;eth thorow equal Spaces.</s></p><p type="head"> <s>ADVERTISEMENT.</s></p><p type="main"> <s><emph type="italics"/>I thought good to add to the old Definition (which &longs;imply termeth <lb/>that an Equable Motion, whereby equal Spaces are pa&longs;t in equal <lb/>Times) this Particle<emph.end type="italics"/> All, <emph type="italics"/>that is, any what&longs;oever Times that are equal: <lb/>for it may happen, that a Moveable may pa&longs;&longs;e thorow equal Spaces in cer­<lb/>tain equal Times, though the Spaces be not equal which it hath gone in <lb/>le&longs;&longs;er, though equal parts of the &longs;ame Time. </s> <s>From this our Definition <lb/>follow the&longs;e four Axiomes:<emph.end type="italics"/> &longs;cilicet,</s></p><p type="head"> <s>AXIOMEL</s></p><p type="main"> <s>In the &longs;ame Equable Motion that Space is greater which is pa&longs;&longs;ed <lb/>in a longer Time, and that le&longs;&longs;er which is pa&longs;t in a &longs;horter.</s></p><pb xlink:href="040/01/820.jpg" pagenum="127"/><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s>In the &longs;ame Equable Motion, the greater the Space is that hath <lb/>been gone thorow, the longer was the Time in which the Move­<lb/>able was going it.</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s>The Space which a greater Velocity pa&longs;&longs;eth in any Time, is great­<lb/>er than the Space which a le&longs;&longs;er Velocity pa&longs;&longs;eth in the &longs;ame <lb/>Time.</s></p><p type="head"> <s>AXIOME IV.</s></p><p type="main"> <s>The Velocity which pa&longs;&longs;eth a greater Space, is greater than the <lb/>Velocity which pa&longs;&longs;eth a le&longs;&longs;er Space in the &longs;ame Time.</s></p><p type="head"> <s>THEOR. I. PROP. I.</s></p><p type="main"> <s>If a Moveable moving with an Equable Motion, <lb/>and with the &longs;ame Velocity pa&longs;&longs;e two &longs;everal <lb/>Spaces, the Times of the Motion &longs;hall be to <lb/>one another as the &longs;aid Spaces.</s></p><p type="main"> <s><emph type="italics"/>Let the Moveable by an Equable Motion with the &longs;ame Velocity paß <lb/>the two Spaces A B and B C: and let D E be the Time of the Moti­<lb/>on thorow A B; and let the Time of the Motion thorow B C be E F <lb/>I &longs;ay that the Time D E to the Time E F, is as the Space A B to the <lb/>Space B C. </s> <s>Protract the Spaces and Times on both &longs;ides, towards <lb/>G H and I K, and in A G take any number of Spaces equal to A B,<emph.end type="italics"/><lb/><figure id="id.040.01.820.1.jpg" xlink:href="040/01/820/1.jpg"/><lb/><emph type="italics"/>and in D I the like number of Times equal to D E. Again, in C H take <lb/>any number of Spaces equal to B C, and in F K take the &longs;ame number <lb/>of Times equal to the Time E F. </s> <s>This done, the Space B G will con­<lb/>tain ju&longs;t as many Spaces equal to B A, as the Time E I containeth <lb/>Times equal to E D, equimultiplied according to what ever Rate; And <lb/>likewi&longs;e the Space B H will contain as many Spaces equal to B C, as<emph.end type="italics"/><pb xlink:href="040/01/821.jpg" pagenum="128"/><emph type="italics"/>the Time K E containeth Times equal to F E, at what ever rate equi­<lb/>multiplied. </s> <s>And fora&longs;much as D E is the Time of the Motion thorow <lb/>A B, the whole Time E I, &longs;hall be the Time of the whole Space of the <lb/>Motion thorow B G, by rea&longs;on that the Motion is Equable, and that the <lb/>number of the Times in E I equal to D E, is the &longs;ame with the number <lb/>of Spaces in B G, equal to B A: For the &longs;ame rea&longs;on E K is the Time <lb/>of the Motion thorow H B. </s> <s>Now in regard the Motion is Equable, if the <lb/>Space G B were equal to H B, the Time I E would be equal to E K: <lb/>and if G B be greater than B H, I E &longs;hall likewi&longs;e be greater than E K: <lb/>and if le&longs;&longs;er, le&longs;&longs;er. </s> <s>They are therefore four Magnitudes; A B the fir&longs;t, <lb/>B C the &longs;econd, D E the third, and E F the Fourth; and the fir&longs;t <lb/>and third, to wit, the Space A B, and Time D E, there were taken the <lb/>Time I E, and the Space G B equimultiple, according to any multi­<lb/>plication; and it hath been demon&longs;trated that the&longs;e do at once either <lb/>equal, or fall &longs;hort of, or el&longs;e exceed the Time E K, and Space B H, <lb/>which are equimultiple of the &longs;econd and fourth: Therefore the fir&longs;t <lb/>bath to the &longs;econd, to wit the Space A B to the Space B C, the &longs;ame <lb/>proportion that the third hath to the fourth, to wit, the Time D E to <lb/>the Time E F. </s> <s>Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. II. PROP. II.</s></p><p type="main"> <s>If a Moveable in equal Times pa&longs;&longs;e thorow two <lb/>Spaces, the &longs;aid Spaces will be to each other, <lb/>as the Velocities. </s> <s>And if the Spaces are to each <lb/>other as the Velocities, the Times will be <lb/>equal.</s></p><p type="main"> <s><emph type="italics"/>Let us &longs;uppo&longs;e A B and B C in the former Figure, to be two <lb/>Spaces pa&longs;t, by the Moveable in equal times; the Space A B with <lb/>the Velocity D E, and the Space B C with the Velocity E F. </s> <s>I <lb/>&longs;ay, that the Space A B is to the Space B C, as the Velocity D E is to <lb/>the Velocity E F: and thus I prove it. </s> <s>Take as before, of the Spaces <lb/>and Velocities equi-multiples, accordieg to any what ever Rate, &longs;ci­<lb/>licet G B and I E, of A B and D E, and likewi&longs;e H B and K E, of <lb/>B C and E F: It may be concluded as above, that G B and I E are <lb/>both at once either equal to, or fall &longs;hort of, or el&longs;e exceed the equi-mul­<lb/>tiples of D H and E K. </s> <s>Therefore the Propo&longs;ition is proved.<emph.end type="italics"/></s></p><pb xlink:href="040/01/822.jpg" pagenum="129"/><p type="head"> <s>THEOR. III. PROP. III.</s></p><p type="main"> <s>The Times in which the &longs;ame Space is pa&longs;t tho­<lb/>row by unequal Velocities, have the &longs;ame pro­<lb/>portion to each other as their Velocities contra­<lb/>rily taken.</s></p><p type="main"> <s><emph type="italics"/>Let the two unequal Velocities be A the greater, and B the le&longs;&longs;e: <lb/>and according to both the&longs;e let a Motion be made thorow the &longs;ame <lb/>Space C D. </s> <s>I &longs;ay the Time in which the Velocity A pa&longs;&longs;eth the <lb/>Space C D, &longs;hall be to the Time in which the Velocity B pa&longs;&longs;eth the <lb/>&longs;aid Space, as the Velocity B to the Velocity A. </s> <s>As A is to B, &longs;o let <lb/>C D be to C E: Then, by the <lb/>former Propo&longs;ition, the Time in<emph.end type="italics"/><lb/><figure id="id.040.01.822.1.jpg" xlink:href="040/01/822/1.jpg"/><lb/><emph type="italics"/>which the Velocity A pa&longs;&longs;eth <lb/>C D, &longs;hall be the &longs;ame with <lb/>the Time in which B pa&longs;&longs;eth <lb/>C E. </s> <s>But the Time in which <lb/>the Velocity B pa&longs;&longs;eth C E, is <lb/>to the Time in which it pa&longs;&longs;eth C D, as C E is to C D: Therefore <lb/>the Time in which the Velocity A pa&longs;&longs;eth C D, is to the Time in which <lb/>the Velocity B pa&longs;&longs;eth the &longs;ame C D, as C E is to C D; that is, the Ve­<lb/>locity B is to the Velocity A: Which was to be proved.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. IV. PROP. IV.</s></p><p type="main"> <s>If two Moveables move with an Equable Mo­<lb/>tion, but with unequal Velocities, the Spaces <lb/>which they pa&longs;&longs;e in unequal Times, are to each <lb/>other in a proportion compounded of the pro­<lb/>portion of the Velocities, and of the propor­<lb/>tion of the Times.</s></p><p type="main"> <s><emph type="italics"/>Let the two Moveables moving with an Equable Motion, be E and <lb/>F: And let the proportion of the Velocity of the Moveable E be <lb/>to the Velocity of the Moveable F, as A is to B: And let the Time <lb/>in which E is moved, be unto the Time in which F is moved, as C is <lb/>to D. </s> <s>I &longs;ay the Space pa&longs;&longs;ed by E, with the Velocity A in the Time C, is to <lb/>the Space pa&longs;&longs;ed by F, with the Velocity B in the Time D, in a proportion <lb/>compounded of the proportion of the Velocity A to the Velocity B, and of<emph.end type="italics"/><pb xlink:href="040/01/823.jpg" pagenum="130"/><emph type="italics"/>the proportion of the Time C to the Time D. </s> <s>Let the Space pa&longs;&longs;ed by the <lb/>Moveable E, with the Velocity A in the Time C, be G: And as the <lb/>Velocity A is to the Velocity B, <lb/><figure id="id.040.01.823.1.jpg" xlink:href="040/01/823/1.jpg"/><lb/>&longs;o let G be to I: And as the <lb/>Time C is to the Time D, &longs;o <lb/>let I be to L: It is manife&longs;t, <lb/>that I is the Space pa&longs;&longs;ed by F <lb/>in the &longs;ame Time in which E <lb/>pa&longs;&longs;eth thorow G; &longs;eeing that <lb/>the Spaces G and I are as the <lb/>Velocities A and B; and &longs;eeing that as the Time C is to the Time D, &longs;o <lb/>is I unto L; and &longs;ince that I is the Space pa&longs;&longs;ed by the Moveable F in the <lb/>Time C: Therefore L &longs;hall be the Space that F pa&longs;&longs;eth in the Time D, <lb/>with the Velocity B: But the proportion of G to L, is compounded of the <lb/>proportions of G to I, and of I to L; that is, of the proportions of the <lb/>Velocity A to the Velocity B, and of the Time C to the Time D: <lb/>Therefore the Propo&longs;ition is demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. V. PROP. V.</s></p><p type="main"> <s>If two Moveables move with an Equable Motion, <lb/>but with unequal Velocities, and if the Spaces <lb/>pa&longs;&longs;ed be al&longs;o unequal, the Times &longs;hall be to <lb/>each other in a proportion compounded of the <lb/>proportion of the Spaces, and of the proporti­<lb/>on of the Velocities contrarily taken.</s></p><p type="main"> <s><emph type="italics"/>Let A and B be the two Moveables, and let the Velocity of A be to <lb/>the Velocity of B, as V to T, and let the Spaces pa&longs;&longs;ed, be as S to <lb/>R. </s> <s>I &longs;ay the proportion of the Time in which A is moved to the <lb/>Time in which B is moved, &longs;hall be compounded of the proportions of the <lb/>Velocity T to the Velocity V, and of the Space S to the Space R. </s> <s>Let C be <lb/>the Time of the Motion A;<emph.end type="italics"/><lb/><figure id="id.040.01.823.2.jpg" xlink:href="040/01/823/2.jpg"/><lb/><emph type="italics"/>and as the Velocity T is to <lb/>the Velocity V, &longs;o let the <lb/>Time C be to the Time E: <lb/>And for a&longs;much as C is the <lb/>Time in which A with <lb/>the Velocity V pa&longs;&longs;eth the <lb/>Space S; and that the <lb/>Time C is to the Time E, as the Velocity T of the Moveable B is to the <lb/>Velocity V, E &longs;hall be the Time in which the Moveable B would pa&longs;&longs;e<emph.end type="italics"/><pb xlink:href="040/01/824.jpg" pagenum="131"/><emph type="italics"/>the &longs;ame Space S. </s> <s>Again as the Space S is to the Space R, &longs;o let the <lb/>Time E be to the Time G: Therefore G is the Time in which B would <lb/>pa&longs;&longs;e the Space R. </s> <s>And becau&longs;e the proportion of C to G is compounded <lb/>of the proportions of C to E, and of E to G; And &longs;ince the proportion <lb/>of C to E is the &longs;ame with that of the Velocities of the Moveables A and <lb/>B contrarily taken; that is, with that of T and V; And the proportion <lb/>of E to G is the &longs;ame with the proportion of the Spaces S and R: There­<lb/>fore the Propo&longs;ition is demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. VI. PROP. VI.</s></p><p type="main"> <s>If two Moveables move with an Equable Motion, <lb/>the proportion of their Velocities &longs;hall be com­<lb/>pounded of the proportion of the Spaces pa&longs;­<lb/>&longs;ed, and of the proportion of the Times con­<lb/>trarily taken.</s></p><p type="main"> <s><emph type="italics"/>Let A and B be the two Moveables moving with an Equable <lb/>Motion; and let the Spaces by them pa&longs;&longs;ed, be as V to T; and <lb/>let the Times be as S to R. </s> <s>I &longs;ay that the proportion of the Ve­<lb/>locity of the Moveable A, to that of the Velocity of B, &longs;hall be <lb/>compounded of the proportions of the Space V to the Space T, and <lb/>of the Time R to the Time S. </s> <s>Let C be the Velocity with which the <lb/>Moveable A pa&longs;&longs;eth the Space V in the Time S: And let the Velocity C <lb/>be to the Velo-<emph.end type="italics"/><lb/><figure id="id.040.01.824.1.jpg" xlink:href="040/01/824/1.jpg"/><lb/><emph type="italics"/>city E, as the <lb/>Space V is to <lb/>the Space T; <lb/>And E &longs;hall <lb/>be the Veloci­<lb/>ty with which <lb/>the Moveable <lb/>B pa&longs;&longs;eth the Space T in the Time S: Again, let the Velocity E be to the <lb/>other Velocity G, as the Time R is to the Time S; And G &longs;hall be the <lb/>Velocity with which the Moveable B pa&longs;&longs;eth the Space T in the Time R. <lb/></s> <s>We have therefore the Velocity C, wherewith the Moveable A pa&longs;&longs;eth <lb/>the Space V in the Time S; and the Velocity G, wherewith the Move­<lb/>able B pa&longs;&longs;eth the Space T in the Time R: And the proportion of C to <lb/>G is compounded of the proportions of C to E and of E to G: But the <lb/>proportion of C to E, is &longs;uppo&longs;ed the &longs;ame with that of the Space V to <lb/>the Space T; and the proportion of E to G, is the &longs;ame with that of R <lb/>to S: Therefore the Propo&longs;ition is manifest.<emph.end type="italics"/><pb xlink:href="040/01/825.jpg" pagenum="132"/><arrow.to.target n="marg1091"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1091"></margin.target>* That is the A­<lb/>cademick, <emph type="italics"/>i. </s> <s>e. <lb/></s> <s>Galileus.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>This that we have read, is what our ^{*} <emph type="italics"/>Author<emph.end type="italics"/> hath written <lb/>of the Equable Motion. </s> <s>We will pa&longs;s therefore to a more &longs;ubtil and <lb/>new Contemplation touching the Motion Naturally Accelerate: <lb/>and behold here the Title and Introduction.</s></p><p type="head"> <s>OF MOTION <lb/>NATVRALLY ACCELERATE.</s></p><p type="main"> <s><emph type="italics"/>In the former Book we have con&longs;idered the Accidents which ac­<lb/>company Equable Motion; we are now to treat of another kind of <lb/>Motion which we call Accelerate. </s> <s>And fir&longs;t it will be expedient to <lb/>find out and explain a Definition be&longs;t agreeing to that which Nature <lb/>makes u&longs;e of. </s> <s>For though it be not nconvenient to feign a Motion at plea­<lb/>&longs;ure, and then to con&longs;ider the Accidents that attend it (as tho&longs;e have <lb/>done, who having framed in their imagination Helixes and Conchoi­<lb/>des, which are Lines ari&longs;ing from certain Motions, although not u&longs;ed <lb/>by Nature, and upon that Suppo&longs;ition have laudably demon&longs;trated the <lb/>Symptomes thereof) yet in regard that Nature maketh u&longs;e of a certain <lb/>kind of Acceleration in the de&longs;cent of Grave Bodies, we are re&longs;olved to <lb/>&longs;earch out and contemplate the pa&longs;&longs;ions thereof, and &longs;ee whether the <lb/>Definition that we are about to produce of this our Accelerate Motion, <lb/>doth aptly and congruou&longs;ly &longs;ute with the E&longs;&longs;ence of Motion Naturally <lb/>Accelerate. </s> <s>After many long and laborious Studies we have found out <lb/>a Definition which &longs;eemeth to expre&longs;&longs;e the true nature of this Accelerate <lb/>Motion, in regard that all the Natural Experiments that fall under <lb/>the Ob&longs;ervation of our Sen&longs;es, do agree with tho&longs;e its properties that <lb/>we intend anon to demon&longs;trate. </s> <s>In this Di&longs;qui&longs;ition we have been a&longs;&longs;i­<lb/>&longs;ted, and as it were led by the hand by that ob&longs;ervation of the u&longs;ual <lb/>Method and common procedure of Nature her &longs;elf in her other Operati­<lb/>ons, wherein &longs;he con&longs;tantly makes u&longs;e of the Fir&longs;t, Simple&longs;t, and Ea­<lb/>&longs;ie&longs;t Means that are: for I believe that no man can think that Swim­<lb/>ming or flying can be performed in a more &longs;imple or ea&longs;ie way, than that <lb/>which Fi&longs;hes and Birds do u&longs;e out of a Natural In&longs;tinct. </s> <s>Why there­<lb/>fore &longs;hall not I be per&longs;waded, that, when I &longs;ee a Stone to acquire conti­<lb/>nually new additions of Velocity in its de&longs;cending from its Re&longs;t out of &longs;ome <lb/>high place, this encrea&longs;e made in the &longs;imple&longs;t ea&longs;ie&longs;t and mo&longs;t obvious <lb/>manner that we can imagine? </s> <s>Now if we &longs;eriou&longs;ly examine all the ways <lb/>that can be devi&longs;ed, we &longs;hall find no encrea&longs;es, no acqui&longs;itions <lb/>le&longs;&longs;e intricate or more intelligible than that which ever encrea&longs;eth or <lb/>makes its additions after the &longs;ame manner. </s> <s>This appeareth by the great<emph.end type="italics"/><lb/>Affinity <emph type="italics"/>that is between Time and Motion. </s> <s>For as the Equability or <lb/>Vniformity of Motion is defined and expre&longs;&longs;ed by the Equability of the<emph.end type="italics"/><pb xlink:href="040/01/826.jpg" pagenum="133"/><emph type="italics"/>Times and Spaces, (for we call that Motion or Lation Equable, by which <lb/>equal Spaces are pa&longs;t in equal Times) &longs;o by the &longs;ame Equability of the <lb/>parts of Time, we may perceive, that the encrea&longs;e of Celerity in the Natu­<lb/>ral Motion of Grave Bodies, is made after a Simple and plain manner; <lb/>conceiving in our Mind that their Motion is continually accelerated uni­<lb/>formly and at the &longs;ame Rate, whil&longs;t equal additions of Celerity are <lb/>conferred upon them in all equal Times. </s> <s>So that taking any equal par­<lb/>ticles of Time beginning from the fir&longs;t In&longs;tant in which the Moveable <lb/>departeth from Re&longs;t, and entereth upon its De&longs;cent, the Degree of <lb/>Velocity acquired in the fir&longs;t and &longs;econd Particles of Time, is double the <lb/>degree of Velocity that the Moveable acquired in the fir&longs;t Particle: and <lb/>the degree of Velocity that it acquireth in three Particles, is triple, and <lb/>that in four quadruple to the &longs;ame Degree of the fir&longs;t Time: As, for <lb/>our better under&longs;tanding, if a Moveable &longs;hould continue its Motion <lb/>according to the degree or moment of Velocity acquired in the fir&longs;t Parti­<lb/>cle of Time, and &longs;hould extend its cour&longs;e equably with that &longs;ame De­<lb/>gree; this Motion would be twice as &longs;low as that which it would obtain <lb/>according to the degree of Velocity acquired in two Particles of Time: <lb/>So that it will not be improper if we under&longs;tand the Intention of the Ve­<lb/>locity, to proceed according to the Exten&longs;ion of the Time. </s> <s>From whence <lb/>we may frame this Definition of the Motion of which we are about to <lb/>treat.<emph.end type="italics"/></s></p><p type="head"> <s>DEFINITION.</s></p><p type="main"> <s>Motion Accelerate in an Equable or Vniform <lb/>Proportion, I call that which departing from <lb/>Re&longs;t, &longs;uperaddeth equal moments of Velocity <lb/>in equal Times.</s></p><p type="main"> <s>SAGR. </s> <s>Though it were Irrational for me to oppo&longs;e this or any <lb/>other Definition a&longs;&longs;igned by any what&longs;oever Author, they being all <lb/>Arbitrary, yet I may very well, without any offence, que&longs;tion whe­<lb/>ther this Definition, which is under&longs;tood and admitted in Ab&longs;tract, <lb/>doth &longs;ute, agree, and hold true in that &longs;ort of Accelerate Motion, <lb/>which Grave Bodies de&longs;cending naturally do exerci&longs;e. </s> <s>And becau&longs;e <lb/>the Authour &longs;eemeth to promi&longs;e us, that the Natural Motion of <lb/>Grave Bodies is &longs;uch as he hath defined it, I could wi&longs;h that &longs;ome <lb/>Scruples were removed that trouble my mind; that &longs;o I might apply <lb/>my &longs;elf afterwards with greater attention to the Proportions and <lb/>Demon&longs;trations which are expected.</s></p><p type="main"> <s>SALV. </s> <s>I like well, that you and <emph type="italics"/>Simplicius<emph.end type="italics"/> do propound <lb/>Doubts as they come in the way: which I do imagine will be the <pb xlink:href="040/01/827.jpg" pagenum="134"/>&longs;ame that I my &longs;elf did meet with when I fir&longs;t read this Treati&longs;e, <lb/>and that, either were re&longs;olved by conferring with the Author, or <lb/>removed by my own con&longs;idering of them.</s></p><p type="main"> <s>SAGR. </s> <s>Whil&longs;t I am fancying to my &longs;elf a Grave De&longs;cending <lb/>Moveable to depart from Re&longs;t, that is from the privation of all <lb/>Velocity, and to enter into Motion, and in that to go encrea­<lb/>&longs;ing, according to the proportion after which the Time encrea&longs;eth <lb/>from the fir&longs;t in&longs;tant of the Motion; and to have <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> in eight <lb/>Pul&longs;ations, acquired eight degrees of Velocity, of which in the <lb/>fourth Pul&longs;ation it had gained four, in the &longs;econd two, in the <lb/>fir&longs;t one, Time being &longs;ubdivi&longs;ible <emph type="italics"/>in infinitum,<emph.end type="italics"/> it followeth, that <lb/>the Antecedent Velocity alwayes dimini&longs;hing at that Rate, there <lb/>will bt no degree of Velocity &longs;o &longs;mall, or, if you will, of Tardity <lb/>&longs;o great, in which the &longs;aid Moveable is not found to be con&longs;ti­<lb/>tuted, after its departure from infinite Tardity, that is, from <lb/>Re&longs;t. </s> <s>So that if that degree of Velocity which it had at four Pul­<lb/>&longs;ations of Time, was &longs;uch, that maintaining it Equable, it would <lb/>have run two Miles in an hour, and with the degree of Velocity <lb/>that it had in the &longs;econd Pul&longs;ation, it would have gone one mile <lb/>an hour, it mu&longs;t be granted, that in the In&longs;tants of Time neeter <lb/>and neerer to its fir&longs;t In&longs;tant of moving from Re&longs;t, it is &longs;o &longs;low, <lb/>as that (continuing to move with that Tardity) it would not have <lb/>pa&longs;&longs;ed a Mile in an hour, nor in a day, nor in a year, nor in a <lb/>thou&longs;and; nay, nor have gone one &longs;ole foot in a greater time: <lb/>An accident to which me thinks the Imagination but very unea­<lb/>&longs;ily accords, &longs;eeing that Sen&longs;e &longs;heweth us, that a Grave Falling <lb/>Body commeth down &longs;uddenly, and with great Velocity.</s></p><p type="main"> <s>SALV. </s> <s>This is one of tho&longs;e Doubts that al&longs;o fell in my way <lb/>upon my fir&longs;t thinking on this affair, but not long after I remo­<lb/>ved it: and that removal was the effect of the &longs;elf &longs;ame Expe­<lb/>riment which at pre&longs;ent &longs;tarts it to you. </s> <s>You &longs;ay, that in your <lb/>opinion, Experience &longs;heweth that the Moveable hath no &longs;ooner <lb/>departed from Re&longs;t, but it entereth into a very notable Velocity: <lb/>and I &longs;ay, that this very Experiment proves it to us, that the fir&longs;t <lb/>Impetus's of the Cadent Body, although it be very heavy, are <lb/>mo&longs;t &longs;lack and &longs;low. </s> <s>Lay a Grave Body upon &longs;ome yielding mat­<lb/>ter, and let it continue upon it till it hath pre&longs;&longs;ed into it as far as <lb/>it can with its &longs;imple Gravity; it is manife&longs;t, that rai&longs;ing it a yard <lb/>or two, and then letting it fall upon the &longs;ame matter, it &longs;hall <lb/>with its percu&longs;&longs;ion make a new pre&longs;&longs;ure, and greater than that <lb/>made at fir&longs;t by its meer weight: and the effect &longs;hall be cau&longs;ed <lb/>by the falling Moveable conjoyned with the Velocity acquired in <lb/>the Fall: which impre&longs;&longs;ion &longs;hall be greater and greater, accord­<lb/>ing as the Percu&longs;&longs;ion &longs;hall come from a greater height; that is, <lb/>according as the Velocity of the Percutient &longs;hall be greater. </s> <s>We <pb xlink:href="040/01/828.jpg" pagenum="135"/>may therefore without mi&longs;take conjecture the quantity of the Ve­<lb/>locity of a falling heavy Body; by the quality and quantity of <lb/>the Percu&longs;&longs;ion. </s> <s>But tell me Sirs, that Beetle which being let fall <lb/>upon a Stake from an height of four yards, driveth it into the <lb/>ground, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> four inches, comming from an height of two yards, <lb/>&longs;hall drive it much le&longs;&longs;e, and le&longs;&longs;e from an height of one, and <lb/>le&longs;&longs;e from a foot; and la&longs;tly lifting it up an inch, what will it do <lb/>more than if without any blow it were laid upon it? </s> <s>Certainly <lb/>but very little, and the operation would be wholly impercep­<lb/>tible, if it were rai&longs;ed the thickne&longs;&longs;e of a leaf. </s> <s>And becau&longs;e the <lb/>effect of the Percu&longs;&longs;ion is regulated by the Velocity of the Percu­<lb/>tient, who will que&longs;tion but that the Motion is very &longs;low, and <lb/>the Velocity extreme &longs;mall, where its operation is impercep­<lb/>tible? </s> <s>See now of what power Truth is, &longs;ince the &longs;ame Experi­<lb/>ment that &longs;eemed at the fir&longs;t blu&longs;h to hold forth one thing, be­<lb/>ing better con&longs;idered, a&longs;certains us of the contrary. </s> <s>But without <lb/>having recour&longs;e to that Experiment (which without doubt is mo&longs;t <lb/>per&longs;wa&longs;ive) me-thinks that it is not hard to penetrate &longs;uch a <lb/>Truth as this by meer Di&longs;cour&longs;e. </s> <s>We have an heavy &longs;tone &longs;u­<lb/>&longs;tained in the Air at Re&longs;t: let it be di&longs;engaged from its uphol­<lb/>der, and &longs;et at liberty; and, as being more grave than the Air, it <lb/>goeth de&longs;cending downwards, and that not with a Motion Equa­<lb/>ble, but &longs;low in the beginning, and continually afterwards ac­<lb/>celerate: and &longs;eeing that the Velocity is Augmentable and Di­<lb/>mini&longs;hable <emph type="italics"/>in infinitum,<emph.end type="italics"/> what Rea&longs;on &longs;hall per&longs;wade me, that that <lb/>Moveable departing from an infinite Tardity (for &longs;uch is Re&longs;t) <lb/>entereth immediately into ten degrees of Velocity, rather than in <lb/>one of four, or in this more than in one of two, of one, of half <lb/>one, or of the hundredth part of one; and to be &longs;hort, in all <lb/>the infinite le&longs;&longs;er? </s> <s>Pray you hear me. </s> <s>I do not think that you <lb/>would &longs;cruple to grant me, that the acqui&longs;t of the Degrees of Ve­<lb/>locity of the falling Stone may be made with the &longs;ame Order as <lb/>is the Diminution and lo&longs;&longs;e of the &longs;ame degrees, when with an <lb/>impellent Virtue it is driven upwards to the &longs;ame height: But if <lb/>that be &longs;o, I do not &longs;ee how it can be &longs;uppo&longs;ed that in the diminu­<lb/>tion of the Velocity of the a&longs;cendent Stone, &longs;pending it all, it <lb/>can come to the &longs;tate of Re&longs;t before it hath pa&longs;&longs;ed thorow all the <lb/>degrees of Tardity.</s></p><p type="main"> <s>SIMP. </s> <s>But if the greater and greater degrees of Tardity are <lb/>infinite, it &longs;hall never &longs;pend them all; &longs;o that the a&longs;cendent <lb/>Grave will never attain to Re&longs;t, but will move <emph type="italics"/>ad infinitum,<emph.end type="italics"/> &longs;till <lb/>retarding: a thing which we &longs;ee not to happen.</s></p><p type="main"> <s>SALV. </s> <s>This would happen, <emph type="italics"/>Simplicius,<emph.end type="italics"/> in ca&longs;e the Moveable <lb/>&longs;hould &longs;tay for &longs;ome time in each degree: but it pa&longs;&longs;eth thorow <lb/>them, without &longs;taying longer than an in&longs;tant in any of them. <pb xlink:href="040/01/829.jpg" pagenum="136"/>And becau&longs;e in every quantitative Time, though never &longs;o &longs;mall, <lb/>there are infinite In&longs;tants, therefore they are &longs;ufficient to an&longs;wer <lb/>to the infinite degrees of Velocity dimini&longs;hed. </s> <s>And that the <lb/>a&longs;cendent Grave Body per&longs;i&longs;ts not for any quantitative Time in <lb/>one and the &longs;ame degree of Velocity, may thus be made out: <lb/>Becau&longs;e, a certain quantitative Time being a&longs;&longs;igned it in the fir&longs;t <lb/>in&longs;tant of that Time, and likewi&longs;e in the la&longs;t, the Moveable <lb/>&longs;hould be found to have one and the &longs;ame degree of Velocity, it <lb/>might by this &longs;econd degree be likewi&longs;e driven upwards &longs;uch an­<lb/>other Space, like as from the fir&longs;t it was tran&longs;ported to the &longs;e­<lb/>cond; and by the &longs;ame rea&longs;on it would pa&longs;&longs;e from the &longs;econd to <lb/>the third, and, in &longs;hort, would continue its Motion Uniform <emph type="italics"/>ad <lb/>infinitum.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>From this Di&longs;cour&longs;e, as I conceive, one might derive a <lb/>very appo&longs;ite Rea&longs;on of the Que&longs;tion controverted among&longs;t Philo. <lb/></s> <s>&longs;ophers, Touching what &longs;hould be the Cau&longs;e of the acceleration <lb/>of the Natural Motion of Grave Moveables. </s> <s>For when I confider <lb/>in the Grave Body driven upwards, its continual Diminution of <lb/>that Virtue impre&longs;&longs;ed upon it by the Projicient, which &longs;o long as <lb/>it was &longs;uperiour to that other contrary one of Gravity, forced it <lb/>upwards, this and that being come to an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> the Move­<lb/>able cea&longs;eth to ri&longs;e any higher, and pa&longs;&longs;eth thorow the &longs;tate of <lb/>Re&longs;t, in which the <emph type="italics"/>Impetus<emph.end type="italics"/> impre&longs;&longs;ed is not annihilated, but one­<lb/>ly that exce&longs;&longs;e is &longs;pent, which it before had above the Gravity of <lb/>the Moveable, whereby prevailing over the &longs;ame, it did drive <lb/>it upwards. </s> <s>And the Diminution of this forrein <emph type="italics"/>Impetus<emph.end type="italics"/> continu­<lb/>ing, and con&longs;equently the advantage beginning to be on the part <lb/>of the Gravity, the De&longs;cent al&longs;o beginneth but &longs;low, in regard <lb/>of the oppo&longs;ition of the Virtue impre&longs;&longs;ed, a con&longs;iderable part of <lb/>which &longs;till remaineth in the Moveable: but becau&longs;e it doth go <lb/>continually dimini&longs;hing, and is &longs;till with a greater and greater <lb/>proportion overcome by the Gravity, hence ari&longs;eth the continual <lb/>Acceleration of the Motion.</s></p><p type="main"> <s>SIMP. </s> <s>The conceit is witty, but more &longs;ubtil than &longs;olid: for in <lb/>ca&longs;e it were concludent, it &longs;alveth onely tho&longs;e Natural Motions <lb/>to which a Violent Motion preceded, in which part of the extern <lb/>Virtue &longs;till remains in force: but where there is no &longs;uch remaining <lb/>impul&longs;e, as where the Moveable departeth from a long Quie&longs;­<lb/>cence, the &longs;trength of your whole Di&longs;cour&longs;e vani&longs;heth.</s></p><p type="main"> <s>SAGR. </s> <s>I believe that you are in an Errour, and that this Di­<lb/>&longs;tinction of Ca&longs;es which you make, is needle&longs;&longs;e, or, to &longs;ay bet­<lb/>ter, <emph type="italics"/>Null.<emph.end type="italics"/> Therefore tell me, whether may there be impre&longs;&longs;ed <lb/>on the Project by the Projicient &longs;ometimes much, and &longs;ometimes <lb/>little Vertue; &longs;o as that it may be &longs;tricken upwards an hundred <lb/>yards, and al&longs;o twenty, or four, or one?</s></p><pb xlink:href="040/01/830.jpg" pagenum="137"/><p type="main"> <s>SIMP. </s> <s>No doubt but there may.</s></p><p type="main"> <s>SAGR. </s> <s>And no le&longs;&longs;e po&longs;&longs;ible is it, that the &longs;aid Virtue impre&longs;&longs;ed <lb/>&longs;hall &longs;o little &longs;eperate the Re&longs;i&longs;tance of the Gravity, as not to <lb/>rai&longs;e the Project above an inch: and finally the Virtue of the <lb/>Projicient may be onely &longs;o much, as ju&longs;t to equalize and com­<lb/>pen&longs;ate the Re&longs;i&longs;tance of the Gravity, &longs;o as that the Moveable <lb/>is not driven upwards, but onely &longs;u&longs;tained. </s> <s>So that when you <lb/>hold a Stone in your hand, what el&longs;e do you, but impre&longs;&longs;e on it <lb/>&longs;o much Virtue impelling upwards, as is the faculty of its Gra­<lb/>vity drawing downwards? </s> <s>And this your Virtue, do you not <lb/>continue to keep it impre&longs;&longs;ed on the Stone all the time that you <lb/>hold it in your hand? </s> <s>What &longs;ay you, is it dimini&longs;hed by your <lb/>long holding it? </s> <s>And this &longs;u&longs;tention which impedeth the Stones <lb/>de&longs;cent, what doth it import, whether it be made by your hand, <lb/>or by a Table, or by a Rope, that &longs;u&longs;pends it? </s> <s>Doubtle&longs;&longs;e no <lb/>thing at all. </s> <s>Conclude with your &longs;elf therefore, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that <lb/>the precedence of a long, a &longs;hort, or a Momentary Re&longs;t to the <lb/>Fall of the Stone, makes no alteration at all, &longs;o that the Stone <lb/>&longs;hould not alwaies depart affected with &longs;o much Virtue contrary <lb/>to Gravity, as did exactly &longs;uffice to have kept it in Re&longs;t.</s></p><p type="main"> <s>SALV. </s> <s>I do not think it a &longs;ea&longs;onable time at pre&longs;ent to enter <lb/>upon the Di&longs;qui&longs;ition of the Cau&longs;e of the Acceleration of Natu­<lb/>ral Motion: touching which &longs;undry Philo&longs;ophers have produced <lb/>&longs;undry opinions: &longs;ome reducing it to the approximation unto <lb/>the Center others to the le&longs;&longs;e parts of the <emph type="italics"/>Medium<emph.end type="italics"/> &longs;ucce&longs;&longs;ively re­<lb/>maining to be perforated; others to a certain Extru&longs;ion of the <lb/>Ambient <emph type="italics"/>Medium,<emph.end type="italics"/> which in reuniting upon the back of the <lb/>Moveable, goeth driving and continually thru&longs;ting it; which <lb/>Fancies, and others of the like nature, it would be nece&longs;&longs;ary to <lb/>examine, and with &longs;mall benefit to an&longs;wer. </s> <s>It &longs;erveth our Au­<lb/>thours turn at the pre&longs;ent, that we under&longs;tand that he will de­<lb/>clare and demon&longs;trate to us &longs;ome Pa&longs;&longs;ions of an Accelerate Mo­<lb/>tion (be the Cau&longs;e of its Acceleration what it will) &longs;o as that the <lb/>Moments of its Velocity do go encrea&longs;ing, after its departure from <lb/>Re&longs;t with that mo&longs;t &longs;imple proportion wherewith the Continua­<lb/>tion of the Time doth encrea&longs;e: which is as much as to &longs;ay, that <lb/>in equal Times there are made equal additaments of Velocity. <lb/></s> <s>And if it &longs;hall be found, that the Accidents that &longs;hall hereafter <lb/>be demon&longs;trated, do hold true in the Motion of Naturally De­<lb/>&longs;cendent and Accelerate Grave Moveables, we may account, <lb/>that the a&longs;&longs;umed Definition taketh in that Motion of Grave Bo­<lb/>dies, and that it is true, that their Acceleration doth encrea&longs;e ac­<lb/>cording as the Time and Duration of the Motion encrea&longs;eth.</s></p><p type="main"> <s>SAGR. </s> <s>By what as yet is &longs;et before my Intellectuals, it appears <lb/>to me that one might with (haply) more plainne&longs;&longs;e define, and yet <pb xlink:href="040/01/831.jpg" pagenum="138"/>never alter the Conceit; &longs;aying that, A Motion uniformly accele­<lb/>rate is that in which the Velocity goeth encrea&longs;ing according as <lb/>the Space encrea&longs;eth that is pa&longs;&longs;ed thorow: So that, for example, <lb/>the degree of Velocity acquired by the Moveable in a de&longs;cent of <lb/>four yards &longs;hould be double to that that it would have after it had <lb/>de&longs;cended a Space of two, and this double to that acquired in the <lb/>Space of the fir&longs;t Yard. </s> <s>For I do not think that it can be doubted, <lb/>but that that Grave Moveable which falleth from an height of &longs;ix <lb/>yards hath, and percu&longs;&longs;eth with an <emph type="italics"/>Impetus<emph.end type="italics"/> double to that which <lb/>it had when it had de&longs;cended three yards, and triple to that which <lb/>it had at two, and &longs;extuple to that had in the Space of one.</s></p><p type="main"> <s>SALV. </s> <s>I comfort my &longs;elf in that I have had &longs;uch a Companion <lb/>in my Errour: and I will tell you farther, that your Di&longs;cour&longs;e hath <lb/>&longs;o much of likelihood and probability in it, that our Author him&longs;elf <lb/>did not deny unto me, when I propo&longs;ed it to him, that he likewi&longs;e <lb/>had been for &longs;ome time in the &longs;ame mi&longs;take. <emph type="italics"/>B<emph.end type="italics"/>ut that which I af­<lb/>terwards extreamly wondred at, was to &longs;ee in four plain words, <lb/>di&longs;covered, not only the falfity, but impo&longs;&longs;ibility of two Propo&longs;i­<lb/>tions that carry with them &longs;o much of &longs;eeming truth, that having <lb/>propounded them to many, I never met with any one but did freely <lb/>admit them to be &longs;o.</s></p><p type="main"> <s>SIMP. </s> <s>Certainly I &longs;hould be of the number, and that the De­<lb/>&longs;cendent Grave Moveable <emph type="italics"/>vires acquir at eundo,<emph.end type="italics"/> encrea&longs;ing its Ve­<lb/>locity at the rate of the Space, and that the Moment of the &longs;ame <lb/>Percutient is double, coming from a double height, &longs;eem to me Pro­<lb/>po&longs;itions to be granted without any hæ&longs;itation or controver&longs;ie.</s></p><p type="main"> <s>SALV. </s> <s>And yet they are as fal&longs;e and impo&longs;&longs;ible, as that Moti­<lb/>on is made in an in&longs;tant. </s> <s>And hear a clear proof of the &longs;ame. </s> <s>In <lb/>ca&longs;e the Velocities have the &longs;ame proportion as the Spaces pa&longs;&longs;ed, <lb/>or to be pa&longs;&longs;ed, tho&longs;e Spaces &longs;hall be pa&longs;&longs;ed in equal Times: if <lb/>therefore the Velocities with which the falling Moveable pa&longs;&longs;eth <lb/>the Space of four yards, were double to the Velocities with which it <lb/>pa&longs;&longs;eth the two fir&longs;t yards (like as the Space is double to the Space) <lb/>then the Times of tho&longs;e Tran&longs;itions are equal: but the &longs;ame Move­<lb/>able's pa&longs;&longs;ing the four yards, and the two in one and the &longs;ame Time, <lb/>hath place only in In&longs;tantaneous Motion. <emph type="italics"/>B<emph.end type="italics"/>ut we &longs;ee, that the <lb/>falling grave <emph type="italics"/>B<emph.end type="italics"/>ody maketh its Motion in Time, and pa&longs;&longs;eth the two <lb/>yards in a le&longs;&longs;er than it doth the four. </s> <s>Therefore it is fal&longs;e that its <lb/>Velocity encrea&longs;eth as its Space. </s> <s>The other Propo&longs;ition is demon­<lb/>&longs;trated to be fal&longs;e with the &longs;ame per&longs;picuity. </s> <s>For that which per­<lb/>cu&longs;&longs;eth being the &longs;ame, the difference and Moment of the Percu&longs;&longs;ton <lb/>cannot be determined but by the difference of Velocity; If there­<lb/>fore the percutient, coming from a double height, make a Percu&longs;&longs;i­<lb/>on with a double Moment, it is nece&longs;&longs;ary that it &longs;trike with a dou­<lb/>ble Velocity: <emph type="italics"/>B<emph.end type="italics"/>ut the double Velocity pa&longs;&longs;eth the double Space in <pb xlink:href="040/01/832.jpg" pagenum="139"/>the &longs;ame Time; and we &longs;ee the Time of the De&longs;cent from the grea­<lb/>ter altitude to be longer.</s></p><p type="main"> <s>SAGR. </s> <s>This is too great an Evidence, too great a Facility <lb/>wherewith you manife&longs;t ab&longs;truce Conclu&longs;ions: this extream ea&longs;i­<lb/>ne&longs;s rendreth them of le&longs;&longs;e value than they were whil&longs;t they lay hid <lb/>under contrary appearances. </s> <s>I believe that the Generality of men <lb/>little pre&longs;&longs;e tho&longs;e Notions which are ea&longs;ily obtained, in compari­<lb/>&longs;on of tho&longs;e about which men make &longs;o long and inexplicable alter­<lb/>cations.</s></p><p type="main"> <s>SALV. </s> <s>To tho&longs;e which with great brevity and clarity &longs;hew the <lb/>fallacies of Propo&longs;itions that have been commonly received for <lb/>true by the generality of people, it would be a very tolerable in­<lb/>jury to return them only &longs;lighting in&longs;tead of thanks: but there is <lb/>much di&longs;plea&longs;ure and mole&longs;tation in another certain affection <lb/>&longs;ometimes found in &longs;ome men, that pretending in the &longs;ame Studies <lb/>at lea&longs;t Parity with any whom&longs;oever, do &longs;ee that they have let <lb/>pa&longs;s &longs;uch and &longs;uch for true Conclu&longs;ions, which afterwards by <lb/>another, with a &longs;hort and ea&longs;ie di&longs;qui&longs;ition, have been detected and <lb/>convicted for fal&longs;e. </s> <s>I will not call that affection Envy, that is ac­<lb/>cu&longs;tomed to convert in time to hatred and de&longs;pite again&longs;t the di&longs;­<lb/>coverers of &longs;uch Fallacies, but I will call it an itch, and a de&longs;ire to <lb/>be able rather to maintain their inveterate Errours, than to per­<lb/>mit the reception of new-di&longs;covered Truths. </s> <s>Which humour &longs;ome­<lb/>times induceth them to write in contradiction of tho&longs;e truths <lb/>which are but too perfectly known unto them&longs;elves only to keep <lb/>the Reputation of others low in the opinion of the numerous and <lb/>ill-informed Vulgar. </s> <s>Of &longs;uch fal&longs;e Conclu&longs;ions received for true, <lb/>and very ea&longs;ie to be confuted, I have heard no &longs;mall number from <lb/>our <emph type="italics"/>Academick,<emph.end type="italics"/> of &longs;ome of which I have kept account.</s></p><p type="main"> <s>SAGR. </s> <s>And you mu&longs;t not deprive us of them; but in due time <lb/>impart them to us, when a particular Meeting &longs;hall be appointed <lb/>for them. </s> <s>For the pre&longs;ent, continuing the di&longs;cour&longs;e we are about, <lb/>I think that by this time we have e&longs;tabli&longs;hed the Definition of Mo­<lb/>tion uniformly Accelerate, treated of in the en&longs;uing di&longs;cour&longs;es, <lb/>and it is this;</s></p><p type="main"> <s><emph type="italics"/>A Motion Equable, or Vniformly Accelerate, we call that which <lb/>departing from Re&longs;t &longs;uperadds equal Moments of Velocity in <lb/>equal Times.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>That Definition being confirmed, the Author asketh <lb/>and &longs;uppo&longs;eth but one only Principle to be true, namely:</s></p><pb xlink:href="040/01/833.jpg" pagenum="140"/><p type="head"> <s>SVPPOSITION.</s></p><p type="main"> <s><emph type="italics"/>I &longs;uppo&longs;e that the degrees of Velocity acquired by the <lb/>&longs;ame Moveable upon Planes of different inclinations <lb/>are equal then, when the Elevations of the &longs;aid <lb/>Planes are equal.<emph.end type="italics"/></s></p><p type="main"> <s>By the Elevation of an inclined Plane he meaneth the Per­<lb/>pendicular, which from the higher term of the &longs;aid Plane <lb/>falleth upon the Horizontal Line produced along by the <lb/>lower term of the &longs;aid Plane inclined: as for better under&longs;tanding; <lb/>the Line A B being parallel to the Horizon, upon which let the two <lb/><figure id="id.040.01.833.1.jpg" xlink:href="040/01/833/1.jpg"/><lb/>Planes C A, and C D be inclined: <lb/>the Perpendicular C B falling up­<lb/>on the Horizontal Line B A the <lb/>Author calleth the Elevation <lb/>of the Planes C A and C D; <lb/>and &longs;uppo&longs;eth that the degrees of <lb/>Velocity of the &longs;ame Moveable <lb/>de&longs;cending along the inclined Planes C A and C D, acqui­<lb/>red in the Terms A and D are equal, for that their Elevation is <lb/>the &longs;ame C B. </s> <s>And &longs;o great al&longs;o ought the degree of Velocity be <lb/>under&longs;tood to be which the &longs;ame Moveable falling from the Point <lb/>C would acquire in the term B.</s></p><p type="main"> <s>SAGR. </s> <s>The truth is, this Suppo&longs;ition hath in it &longs;o much of pro­<lb/>bability, that it de&longs;erveth to be granted without di&longs;pute, alwaies <lb/>pre&longs;uppo&longs;ing that all accidental and extern Impediments are re­<lb/>moved, and that the Planes be very Solid and Ter&longs;e, and the Move­<lb/>able in Figure mo&longs;t perfectly Rotund, &longs;o that neither the Plane, <lb/>nor the Moveable have any unevenne&longs;s. </s> <s>All Contra&longs;ts and Im­<lb/>pediments, I &longs;ay, being removed, the light of Nature dictates to <lb/>me without any difficulty, that a Ball heavy and perfectly round <lb/>de&longs;cending by the Lines C A, C D, and C B would come to the <lb/>terms A D, and B with equal <emph type="italics"/>Impetus's.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>You argue very probably; but over and above the pro­<lb/>bability, I will by an Experiment &longs;o increa&longs;e the likelihood, as that <lb/>it wants but little of being equal to a very nece&longs;&longs;ary Demon&longs;trati­<lb/>on. </s> <s>Imagine this leafe of Paper to be a Wall erect at Right-angles <lb/>to the Horizon, and at a Nail, fa&longs;tned in the &longs;ame, hang a Ball or <lb/>Plummet of Lead, weighing an ounce or two, &longs;u&longs;pended by the <lb/>&longs;mall thread A B, two or three yards long, perpendicular to the <lb/>Horizon: and on the Wall draw an Horizontal Line D C, cutting <pb xlink:href="040/01/834.jpg" pagenum="141"/>the Perpendicular A B at Right angles, which A B mu&longs;t hang two <lb/>Inches, or thereabouts, from the Wall: Then transferring the <lb/>&longs;tring A B with the Ball into C, let go the &longs;aid Ball; which you will <lb/><figure id="id.040.01.834.1.jpg" xlink:href="040/01/834/1.jpg"/><lb/>&longs;ee fir&longs;t to de&longs;cend <lb/>de&longs;cribing C B D, and <lb/>to pa&longs;s &longs;o far beyond <lb/>the Term B, that run­<lb/>ning along the Arch <lb/>B D it will ri&longs;e almo&longs;t <lb/>as high as the de&longs;igned <lb/>Parallel C D, wanting <lb/>but a very &longs;mall mat­<lb/>ter of reaching to it, <lb/>the preci&longs;e arrival thi­<lb/>ther being denied it by <lb/>the Impediment of the Air, and of the Thread. </s> <s>From which we <lb/>may truly conclude, that the <emph type="italics"/>Impetus<emph.end type="italics"/> acquired in the point B by <lb/>the Ball in its de&longs;cent along the Arch C B, was &longs;o much as &longs;ufficed <lb/>to carry it upwards along &longs;uch another Arch B D unto the &longs;ame <lb/>height: having made, and often reiterated this Experiment, let <lb/>us drive into the Wall, along which the Perpendicular A B pa&longs;&longs;eth, <lb/>another Nail, as in E or in F, which is to &longs;tand out five or &longs;ix In­<lb/>ches; and this to the end that the thread A B, returning as before <lb/>to carry back the Ball C along the Arch C B, when it is come to <lb/>B, the Thread &longs;topping at the Nail E may be con&longs;trained to move <lb/>along the Circumference B G, de&longs;cribed about the Center E: by <lb/>which we &longs;hall &longs;ee what that &longs;ame <emph type="italics"/>Impetus<emph.end type="italics"/> is able to do, which be­<lb/>fore, being conceived in the &longs;ame term B, carried the &longs;ame Move­<lb/>able along the Arch B D unto the height of the Horizontal Line <lb/>C D. Now, Sirs, you &longs;hall with delight &longs;ee the Ball carried unto <lb/>the Horizontal Line in the Point G; and the &longs;ame will happen if <lb/>the &longs;top be placed lower, as in F, where the Ball would de&longs;cribe <lb/>the Arch B I, evermore terminating its a&longs;cent exactly in the Line <lb/>C D: and in ca&longs;e the Check were &longs;o low that the overplus of the <lb/>thread beneath it cannot reach to the height of C D, (which would <lb/>happen if it were nearer to the point B than to the inter&longs;ection of <lb/>A B with the Horizontal Line C D) then the thread would <lb/>whirle and twine about the Nail. </s> <s>This experiment leaveth no <lb/>place for our doubting of the truth of the Suppo&longs;ition: for the <lb/>two Arches C B and D B being equall, and &longs;cituate alike, the <lb/>acqui&longs;t of Moment made along the De&longs;cent in the Arch C B, is <lb/>the &longs;ame with that made along the De&longs;cent in the Arch D B. </s> <s>But <lb/>the Moment acquired in <emph type="italics"/>B,<emph.end type="italics"/> along the Arch C <emph type="italics"/>B,<emph.end type="italics"/> is able to carry the <lb/>&longs;ame Moveable upwards along the Arch <emph type="italics"/>B<emph.end type="italics"/> D: Therefore the Mo­<lb/>ment acquired in the De&longs;cent D <emph type="italics"/>B<emph.end type="italics"/> is equall to that which driveth <pb xlink:href="040/01/835.jpg" pagenum="142"/>the &longs;ame Moveable along the &longs;ame Arch from <emph type="italics"/>B<emph.end type="italics"/> to D: So that ge­<lb/>nerally every Moment acquired along the De&longs;cent of an Arch is <lb/>equall to that which hath power to make the &longs;ame Moveable re­<lb/>a&longs;cend along the &longs;ame Arch: <emph type="italics"/>B<emph.end type="italics"/>ut all the Moments that make the <lb/>Moveable a&longs;cend along all the Arches <emph type="italics"/>B<emph.end type="italics"/> D, <emph type="italics"/>B<emph.end type="italics"/> G, <emph type="italics"/>B<emph.end type="italics"/> I are equal, <lb/>&longs;ince they are made by one and the &longs;ame Moment acquired along <lb/>the De&longs;cent C <emph type="italics"/>B,<emph.end type="italics"/> as Experience &longs;hews: Therefore all the Moments <lb/>that are acquired by the De&longs;cents along the Arches D <emph type="italics"/>B,<emph.end type="italics"/> G <emph type="italics"/>B,<emph.end type="italics"/> and <lb/>I <emph type="italics"/>B<emph.end type="italics"/> are equal.</s></p><p type="main"> <s>SAGR. </s> <s>Your Di&longs;cour&longs;e is in my Judgment very Rational, and <lb/>the Experiment &longs;o appo&longs;ite and pertinent to verifie the <emph type="italics"/>Po&longs;tulatum,<emph.end type="italics"/><lb/>that it very well de&longs;erveth to be admitted as if it were Demon­<lb/>&longs;trated.</s></p><p type="main"> <s>SALV. </s> <s>I will not con&longs;ent, <emph type="italics"/>Sagredus,<emph.end type="italics"/> that we take more to our <lb/>&longs;elves than we ought; and the rather for that we are chiefly to <lb/>make u&longs;e of this A&longs;&longs;umption in Motions made upon &longs;treight and <lb/>not curved Superficies; in which the Acceleration proceedeth with <lb/>degrees very different from tho&longs;e wherewith we &longs;uppo&longs;e it to pro­<lb/>ceed in &longs;treight Planes. </s> <s>In&longs;omuch, that although the Experiment <lb/>alledged &longs;hews us, that the de&longs;cent along the Arch C <emph type="italics"/>B<emph.end type="italics"/> conferreth <lb/>on the Moveable &longs;uch a Moment, as that it is able to re-carry it <lb/>to the &longs;ame height along any other Arch <emph type="italics"/>B<emph.end type="italics"/> C, <emph type="italics"/>B<emph.end type="italics"/> G, and <emph type="italics"/>B<emph.end type="italics"/> I, yet <lb/>we cannot with the like evidence &longs;hew, that the &longs;ame would hap­<lb/>pen in ca&longs;e a mo&longs;t exact <emph type="italics"/>B<emph.end type="italics"/>all were to de&longs;cend by &longs;treight Planes in­<lb/>clined according to the inclinations of the Chords of the&longs;e &longs;ame <lb/>Arches: yea, it is credible, that Angles being formed by the &longs;aid <lb/>Right Planes in the term <emph type="italics"/>B,<emph.end type="italics"/> the <emph type="italics"/>B<emph.end type="italics"/>all de&longs;cended along the Declivi­<lb/>ty according to the Chord C <emph type="italics"/>B,<emph.end type="italics"/> finding a &longs;top in the Planes a&longs;cend­<lb/>ing according to the Chords <emph type="italics"/>B<emph.end type="italics"/> D, <emph type="italics"/>B<emph.end type="italics"/> G, and <emph type="italics"/>B<emph.end type="italics"/> I, in ju&longs;tling again&longs;t <lb/>them, would lo&longs;e of its <emph type="italics"/>Impetus,<emph.end type="italics"/> and could not be able in ri&longs;ing to <lb/>attain the height of the Line C D. <emph type="italics"/>B<emph.end type="italics"/>ut the Ob&longs;tacle being remo­<lb/>ved, which prejudiceth the Experiment, I do believe, that the un­<lb/>der&longs;tanding may conceive, that the <emph type="italics"/>Impetus<emph.end type="italics"/> (which in effect de­<lb/>riveth vigour from the quantity of the De&longs;cent) would be able to <lb/>remount the Moveable to the &longs;ame height. </s> <s>Let us therefore take <lb/>this at pre&longs;ent for a <emph type="italics"/>Po&longs;tulatum<emph.end type="italics"/> or Petition, the ab&longs;olute truth of <lb/>which will come to be e&longs;tabli&longs;hed hereafter by &longs;eeing other Con­<lb/>clu&longs;ions rai&longs;ed upon this Hypothe&longs;is to an&longs;wer, and exactly jump <lb/>with the Experiment. </s> <s>The Author having &longs;uppo&longs;ed this only Prin­<lb/>ciple, he pa&longs;&longs;eth to the Propo&longs;itions, demon&longs;tratively proving them; <lb/>of which the fir&longs;t is this;</s></p><pb xlink:href="040/01/836.jpg" pagenum="143"/><p type="head"> <s>THEOR. I. PROP. I.</s></p><p type="main"> <s>The time in which a Space is pa&longs;&longs;ed by a Movea­<lb/>ble with a Motion Vniformly Accelerate, out of <lb/>Re&longs;t, is equal to the Time in which the &longs;ame <lb/>Space would be pa&longs;t by the &longs;ame Moveable <lb/>with an Equable Motion, the degree of who&longs;e <lb/>Velocity is &longs;ubduple to the greate&longs;t and ulti <lb/>mate degree of the Velocity of the former Vni­<lb/>formly Accelerate Motion.</s></p><p type="main"> <s><emph type="italics"/>Let us by the exten&longs;ion A B repre&longs;ent the Time, in which the <lb/>Space<emph.end type="italics"/> C D <emph type="italics"/>is pa&longs;&longs;ed by a Moveable with a Motion Vniformly <lb/>Accelerate, out of Re&longs;t in C: and let the greate&longs;t and la&longs;t de-<emph.end type="italics"/><lb/><figure id="id.040.01.836.1.jpg" xlink:href="040/01/836/1.jpg"/><lb/><emph type="italics"/>gree of Velocity acquired in the In&longs;tants of the Time<emph.end type="italics"/><lb/>A B <emph type="italics"/>be repre&longs;ented by<emph.end type="italics"/> E B; <emph type="italics"/>and con&longs;titute at plea­<lb/>&longs;ure upon<emph.end type="italics"/> A B <emph type="italics"/>any number of parts, and thorow the <lb/>points of divi&longs;ion draw as many Lines, continued <lb/>out unto the Line<emph.end type="italics"/> A E, <emph type="italics"/>and equidi&longs;tant to<emph.end type="italics"/> B E, <lb/><emph type="italics"/>which will repre&longs;ent the encrea&longs;e of the degrees of <lb/>Velocity after the fir&longs;t In&longs;tant A. </s> <s>Then divide<emph.end type="italics"/> B E <lb/><emph type="italics"/>into two equall parts in<emph.end type="italics"/> F, <emph type="italics"/>and draw<emph.end type="italics"/> F G <emph type="italics"/>and<emph.end type="italics"/> A G <lb/><emph type="italics"/>parallel to B A and<emph.end type="italics"/> B F<emph type="italics"/>: The Parallelogram<emph.end type="italics"/> A G <lb/>F B <emph type="italics"/>&longs;hall be equall to the Triangle<emph.end type="italics"/> A E B, <emph type="italics"/>its Side<emph.end type="italics"/><lb/>G F <emph type="italics"/>dividing<emph.end type="italics"/> A E <emph type="italics"/>into two equall parts in I: For <lb/>if the Parallels of the Triangle<emph.end type="italics"/> A E <emph type="italics"/>B be continued <lb/>out unto<emph.end type="italics"/> I G F, <emph type="italics"/>we &longs;hall have the Aggregate of all <lb/>the Parallels contained in the Quadrilatural Figure <lb/>equal to the Aggregate of all the Parallels compre­<lb/>hended in the Triangle<emph.end type="italics"/> A E <emph type="italics"/>B; For tho&longs;e in the Triangle<emph.end type="italics"/> I E F <emph type="italics"/>are equal <lb/>to tho&longs;e contained in the Triangle<emph.end type="italics"/> G I A, <emph type="italics"/>and tho&longs;e that are in the<emph.end type="italics"/> Tra­<lb/>pezium <emph type="italics"/>are in common. </s> <s>Now &longs;ince all and &longs;ingular the In&longs;tants of Time <lb/>do an&longs;wer to all and &longs;ingular the Points of the Line A B; and &longs;ince the <lb/>Parallels contained in the Triangle<emph.end type="italics"/> A E <emph type="italics"/>B do repre&longs;ent the degrees of Ac­<lb/>celeration or encrea&longs;ing Velocity, and the Parallels contained in the Pa­<lb/>rallelogram do likewi&longs;e repre&longs;ent as many degrees of Equable Motion or <lb/>unencrea&longs;ing Velocity: It appeareth, that as many Moments of Velocity <lb/>pa&longs;&longs;ed in the Accelerate Motion according to the encrea&longs;ing Parallels of the <lb/>Triangle A E B, as in the Equable Motion according to the Parallels of <lb/>the Parallelogram G B: Becau&longs;e what is wanting in the fir&longs;t half of the<emph.end type="italics"/><pb xlink:href="040/01/837.jpg" pagenum="144"/><emph type="italics"/>Accelerate Motion of the Velocity of the Equable Motion (which defi­<lb/>cient Moments are repre&longs;ented by the Parallels of the Triangle A<emph.end type="italics"/> G I) <lb/><emph type="italics"/>is made up by the moments repre&longs;ented by the Parallels of the Triangle<emph.end type="italics"/><lb/>I E F. <emph type="italics"/>It is manife&longs;t, therefore, that tho&longs;e Spaces are equal which are <lb/>in the &longs;ame Time by two Moveables, one whereof is moved with a Mo­<lb/>tion uniformly Accelerated from Re&longs;t, the other with a Motion Equable <lb/>according to the Moment &longs;ubduple of that of the greate&longs;t Velocity of the <lb/>Accelerated Motion: Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. II. PROP. II.</s></p><p type="main"> <s>If a <emph type="italics"/>M<emph.end type="italics"/>oveable de&longs;cend out of Re&longs;t with a <emph type="italics"/>M<emph.end type="italics"/>oti­<lb/>on uniformly Accelerate, the Spaces which it <lb/>pa&longs;&longs;eth in any what&longs;oever Times are to each <lb/>other in a proportion Duplicate of the &longs;ame <lb/>Times; that is, they are as the Squares of <lb/>them.</s></p><p type="main"> <s><emph type="italics"/>Let<emph.end type="italics"/> A B <emph type="italics"/>repre&longs;ent a length of Time beginning at the fir&longs;t In&longs;tant A; <lb/>and let<emph.end type="italics"/> A D <emph type="italics"/>and<emph.end type="italics"/> A E <emph type="italics"/>repre&longs;ent any two parts of the &longs;aid Time; <lb/>and let<emph.end type="italics"/> H I <emph type="italics"/>be a Line in which the Moveable out of H, (as the fir&longs;t <lb/>beginning of the Motion) de&longs;cendeth uniformly accelerating; and let the<emph.end type="italics"/><lb/><figure id="id.040.01.837.1.jpg" xlink:href="040/01/837/1.jpg"/><lb/><emph type="italics"/>Space<emph.end type="italics"/> H L <emph type="italics"/>be pa&longs;&longs;ed in the fir&longs;t Time<emph.end type="italics"/> A D; <emph type="italics"/>and let<emph.end type="italics"/> H M <lb/><emph type="italics"/>be the Space that it &longs;hall de&longs;cend in the Time<emph.end type="italics"/> A E. <emph type="italics"/>I &longs;ay, <lb/>the Space<emph.end type="italics"/> M H <emph type="italics"/>is to the Space<emph.end type="italics"/> H L <emph type="italics"/>in duplicate propor­<lb/>tion of that which the Time<emph.end type="italics"/> E A <emph type="italics"/>hath to the Time<emph.end type="italics"/> A D<emph type="italics"/>: <lb/>Or, if you will, that the Spaces<emph.end type="italics"/> M H <emph type="italics"/>and<emph.end type="italics"/> H L <emph type="italics"/>are to one <lb/>another in the &longs;ame proportion as the Squares<emph.end type="italics"/> E A <emph type="italics"/>and<emph.end type="italics"/><lb/>A D. <emph type="italics"/>Draw the Line<emph.end type="italics"/> A C <emph type="italics"/>at any Angle with<emph.end type="italics"/> A B, <emph type="italics"/>and <lb/>from the points D and E draw the Parallels<emph.end type="italics"/> D O <emph type="italics"/>and<emph.end type="italics"/><lb/>P E<emph type="italics"/>: of which<emph.end type="italics"/> D O <emph type="italics"/>will repre&longs;ent the greate&longs;t degree <lb/>of Velocity acquired in the In&longs;tant D of the Time<emph.end type="italics"/> A D; <lb/><emph type="italics"/>and<emph.end type="italics"/> P <emph type="italics"/>the greate&longs;t degree of Velocity acquired in the In­<lb/>&longs;tant E of the Time<emph.end type="italics"/> A E. <emph type="italics"/>And becau&longs;e we have de­<lb/>mon&longs;trated in the la&longs;t Propo&longs;ition concerning Spaces, that <lb/>tho&longs;e are equal to one another, of which two Moveables <lb/>have pa&longs;t in the &longs;ame Time, the one by a Moveable out <lb/>of Re&longs;t with a Motion uniformly Accelerate, and the <lb/>other by the &longs;ame Moveable with an Equable Motion, <lb/>who&longs;e Velocity is &longs;ubduple to the greate&longs;t acquired by the <lb/>Accelerate Motion: Therefore<emph.end type="italics"/> M H <emph type="italics"/>and<emph.end type="italics"/> H L <emph type="italics"/>are the Spaces that two <lb/>Lquable Motions, who&longs;e Velocities &longs;hould be as the half of<emph.end type="italics"/> P E, <emph type="italics"/>and<emph.end type="italics"/><pb xlink:href="040/01/838.jpg" pagenum="145"/><emph type="italics"/>half of<emph.end type="italics"/> O D, <emph type="italics"/>would pa&longs;&longs;e in the Times<emph.end type="italics"/> E A <emph type="italics"/>and<emph.end type="italics"/> D A. <emph type="italics"/>If it be proved <lb/>therefore that the&longs;e Spaces<emph.end type="italics"/> M H <emph type="italics"/>and<emph.end type="italics"/> L H <emph type="italics"/>are in duplicate proportion to <lb/>the Times<emph.end type="italics"/> E A <emph type="italics"/>and<emph.end type="italics"/> D A; <emph type="italics"/>We &longs;hall have done that which was intended. <lb/></s> <s>But in the fourth Propo&longs;ition of the Fir&longs;t Book we have demon&longs;trated: <lb/>That the Spaces pa&longs;t by two Moveables with an Equable Motion are <lb/>to each other in a proportion compounded of the proportion of the Velo­<lb/>cities and of the proportion of the Times: But in this ca&longs;e the propor­<lb/>tion of the Velocities and the proportion of the Times is the &longs;ame<emph.end type="italics"/> (<emph type="italics"/>for <lb/>as the half of<emph.end type="italics"/> P E <emph type="italics"/>is to the half of<emph.end type="italics"/> O D, <emph type="italics"/>or the whole<emph.end type="italics"/> P E <emph type="italics"/>to the whole<emph.end type="italics"/><lb/>O D, <emph type="italics"/>&longs;o is<emph.end type="italics"/> A E <emph type="italics"/>to<emph.end type="italics"/> A D<emph type="italics"/>: Therefore the proportion of the Spaces pa&longs;­<lb/>&longs;ed is double to the proportion of the Times. </s> <s>Which was to be demon­<lb/>&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Hence likewi&longs;e it is manife&longs;t, that the proportion of the &longs;ame Spaces <lb/>is double to the proportions of the greate&longs;t degrees of Velocity: that is, <lb/>of the Lines<emph.end type="italics"/> P E <emph type="italics"/>and<emph.end type="italics"/> O D<emph type="italics"/>: becau&longs;e<emph.end type="italics"/> P E <emph type="italics"/>is to<emph.end type="italics"/> O D, <emph type="italics"/>as<emph.end type="italics"/> E A <emph type="italics"/>to<emph.end type="italics"/> D A.</s></p><p type="head"> <s>COROLARY I.</s></p><p type="main"> <s><emph type="italics"/>Hence it is manife&longs;t, that if there were many equal Times taken in or­<lb/>der from the fir&longs;t In&longs;tant or beginniug of the Motion, as &longs;uppo&longs;e<emph.end type="italics"/><lb/>A D, D E, E F, F G, <emph type="italics"/>in which the Spaces<emph.end type="italics"/> H L, L M, M N, N I <lb/><emph type="italics"/>are pa&longs;&longs;ed, tho&longs;e Spaces &longs;hall be to one another as the odd numbers <lb/>from an Vnite:<emph.end type="italics"/> &longs;cilicet, <emph type="italics"/>as 1, 3, 5, 7. For this is the Rate or pro­<lb/>portion of the exce&longs;&longs;es of the Squares of Lines that equally exceed <lb/>one another, and the exce&longs;&longs;e of which is equal to the least of them, <lb/>or, if you will, of Squares that follow one another, beginning<emph.end type="italics"/> ab <lb/>Unitate. <emph type="italics"/>Whil&longs;t therefore the degree of Velocity is encrea&longs;ed ac­<lb/>cording to the &longs;imple Series of Numbers in equal Times, the Spaces <lb/>pa&longs;t in tho&longs;e Times make their encrea&longs;e according to the Series of <lb/>odd Numbers from an Vnite.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>Be plea&longs;ed to &longs;tay your Reading, whil&longs;t I do paraphra&longs;e <lb/>touching a certain Conjecture that came into my mind <lb/>but even now; for the explanation of which, unto your under­<lb/>&longs;tanding and my own, I will de&longs;cribe a &longs;hort Scheme: in which I <lb/>fan&longs;ie by the Line A I the continuation of the Time after the fir&longs;t <lb/>In&longs;tant, applying the Right Line A F unto A according to any <lb/>Angle: and joyning together the Terms I F, I divide the Time A I <lb/>in half at C, and then draw C B parallel to I F. <emph type="italics"/>A<emph.end type="italics"/>nd then con&longs;ide­<lb/>ring B C, as the greate&longs;t degree of Velocity which beginning from <lb/>Re&longs;t in the fir&longs;t In&longs;tant of the Time <emph type="italics"/>A<emph.end type="italics"/> goeth augmenting accord­<lb/>ing to the encrea&longs;e of the Parallels to B C, drawn in the Triangle <lb/><emph type="italics"/>A<emph.end type="italics"/> B C, (which is all one as to encrea&longs;e according to the encrea&longs;e <lb/>of the Time) I admit without di&longs;pute, upon what hath been &longs;aid <lb/>already, That the Space pa&longs;t by the falling Moveable with the <pb xlink:href="040/01/839.jpg" pagenum="146"/>Velocity encrea&longs;ed in the manner afore&longs;aid would be equal to the <lb/>Space that the &longs;aid Moveable would pa&longs;&longs;e, in ca&longs;e it were in the <lb/>&longs;ame Time <emph type="italics"/>A<emph.end type="italics"/> C, moved with an Uniform Motion, who&longs;e degree of <lb/>Velocity &longs;hould be equal to E C, the half of B C. </s> <s>I now proceed <lb/>farther, and imagine the Moveable; having de&longs;cended with an <lb/><emph type="italics"/>A<emph.end type="italics"/>ccelerate Motion, to have in the In&longs;tant <lb/>C the degree of Velocity B C: It is ma­<lb/><figure id="id.040.01.839.1.jpg" xlink:href="040/01/839/1.jpg"/><lb/>nife&longs;t, that if it did continue to move <lb/>with the &longs;ame degree of Velocity B C, <lb/>without farther <emph type="italics"/>A<emph.end type="italics"/>cceleration, it would <lb/>pa&longs;&longs;e in the following Time C I, a Space <lb/>double to that which it pa&longs;&longs;ed in the equal <lb/>Time <emph type="italics"/>A<emph.end type="italics"/> C, with the degree of Uniform <lb/>Velocity E C, the half of the Degree B C. <lb/></s> <s>But becau&longs;e the Moveable de&longs;cendeth <lb/>with a Velocity encrea&longs;ed alwaies Uni­<lb/>formly in all equal Times; it will add to <lb/>the degree C B in the following Time <lb/>C I, tho&longs;e Tame Moments of Velocity <lb/>that encrea&longs;e according to the Parallels of <lb/>the Triangle B F G, equal to the Triangle <lb/><emph type="italics"/>A<emph.end type="italics"/> B C. </s> <s>So that adding to the degree of <lb/>Velocity G I, the half of the degree F G, the greate&longs;t of tho&longs;e ac­<lb/>quired in the <emph type="italics"/>A<emph.end type="italics"/>ccelerate Motion, and regulated by the Parallels of <lb/>the Triangle B F G, we &longs;hall have the degree of Velocity I N, with <lb/>which, with an Uniform Motion, it would have moved in the <lb/>Time C I: Which degree I N, being triple the degree E C, pro­<lb/>veth that the Space pa&longs;&longs;ed in the &longs;econd Time C I ought to be tri­<lb/>ple to that of the fir&longs;t Time C <emph type="italics"/>A. A<emph.end type="italics"/>nd if we &longs;hould &longs;uppo&longs;e to be <lb/>added to <emph type="italics"/>A<emph.end type="italics"/> I another equal part of Time I O, and the Triangle to <lb/>be enlarged unto <emph type="italics"/>A<emph.end type="italics"/> P O; it is manife&longs;t, that if the Motion &longs;hould <lb/>continue for all the Time I O with the degree of Velocity I F, <lb/>acquired in the <emph type="italics"/>A<emph.end type="italics"/>ccelerate Motion in the Time <emph type="italics"/>A<emph.end type="italics"/> I, that degree <lb/>I F being Quadruple to E C, the Space pa&longs;&longs;ed would be Quadruple <lb/>to that pa&longs;&longs;ed in the equal fir&longs;t Time <emph type="italics"/>A<emph.end type="italics"/> C: But continuing the <lb/>encrea&longs;e of the Uniform <emph type="italics"/>A<emph.end type="italics"/>cceleration in the Triangle F P Q like <lb/>to that of the Triangle <emph type="italics"/>A<emph.end type="italics"/> B C, which being reduced to equable <lb/>Motion addeth the degree equal to E C, Q R being added, equal <lb/>to E C, we &longs;hall have the whole Equable Velocity exerci&longs;ed in the <lb/>Time I O, quintuple to the Equable Velocity of the fir&longs;t Time <emph type="italics"/>A<emph.end type="italics"/> C, <lb/>and therefore the Space pa&longs;&longs;ed quintuple to that pa&longs;t in the fir&longs;t <lb/>Time <emph type="italics"/>A<emph.end type="italics"/> C. </s> <s>We &longs;ee therefore, even by this familiar computation, <lb/>That the Spaces pa&longs;&longs;ed in equal Times by a Moveable which <lb/>departing from Re&longs;t goeth acquiring Velocity, according to the <lb/>encrea&longs;e of the Time, are to one another as the odd Numbers <emph type="italics"/>ab<emph.end type="italics"/><pb xlink:href="040/01/840.jpg" pagenum="147"/><emph type="italics"/>unitate 1, 3, 5: A<emph.end type="italics"/>nd that the Spaces pa&longs;&longs;ed being conjunctly taken, <lb/>that pa&longs;&longs;ed in the double Time is quadruple to that pa&longs;&longs;ed in the <lb/>&longs;ubduple, that pa&longs;&longs;ed in the triple Time is nonuple; and, in a word, <lb/>that the Spaces pa&longs;&longs;ed are in duplicate proportion to their Times; <lb/>that is, as the Squares of the &longs;aid Times.</s></p><p type="main"> <s>SIMP. </s> <s>I mu&longs;t confe&longs;&longs;e that I have taken more plea&longs;ure in this <lb/>plain and clear di&longs;cour&longs;e of <emph type="italics"/>Sagredus,<emph.end type="italics"/> than in the to-me-more <lb/>ob&longs;cure Demon&longs;tration of the <emph type="italics"/>A<emph.end type="italics"/>uthor: &longs;o that I am very well <lb/>&longs;atisfied, that the bu&longs;ine&longs;&longs;e is to &longs;ucceed as hath been &longs;aid, the <lb/>Definition of Uniformly <emph type="italics"/>A<emph.end type="italics"/>ccelerate Motion being &longs;uppo&longs;ed, and <lb/>granted. </s> <s>But whether this be the <emph type="italics"/>A<emph.end type="italics"/>cceleration of which Nature <lb/>maketh u&longs;e in the Motion of its de&longs;cending Grave Bodies, I yet <lb/>make a que&longs;tion: and therefore for information of me, and of <lb/>others like unto me, me thinks it would be &longs;ea&longs;onable in this place <lb/>to produce &longs;ome Experiment among&longs;t tho&longs;e which were &longs;aid to be <lb/>many, which in &longs;undry Ca&longs;es agree with the Conclu&longs;ions demon­<lb/>&longs;trated.</s></p><p type="main"> <s>SALV. You, like a true <emph type="italics"/>A<emph.end type="italics"/>rti&longs;t, make a very rea&longs;onable demand, <lb/>and &longs;o it is u&longs;ual and convenient to do in Sciences that apply <lb/>Mathematical Demon&longs;trations to Phy&longs;ical Conclu&longs;ions, as we &longs;ee <lb/>in the Profe&longs;&longs;ors of Per&longs;pection, <emph type="italics"/>A<emph.end type="italics"/>&longs;tronomy, Mechanicks, Mu&longs;ick, <lb/>and others, who with Sen&longs;ible Experiments confirm tho&longs;e their <lb/>Principles that are as the foundations of all the following Structure: <lb/>and therefore I de&longs;ire that it may not be thought &longs;uperfluous, that <lb/>we di&longs;cour&longs;e with &longs;ome prolixity upon this fir&longs;t and grand funda­<lb/>mental on which we lay the weight of the Immen&longs;e Machine of <lb/>infinite Conclu&longs;ions, of which we have but a very &longs;mall part &longs;et <lb/>down in this Book by our <emph type="italics"/>A<emph.end type="italics"/>uthor, who hath done enough to open <lb/>the way and door that hath been hitherto &longs;hut unto all Specula­<lb/>tive Wits. </s> <s>Touching Experiments, therefore, the <emph type="italics"/>A<emph.end type="italics"/>uthor hath <lb/>not omitted to make &longs;everal; and to a&longs;&longs;ure us, that the <emph type="italics"/>A<emph.end type="italics"/>ccelerati­<lb/>on of natural-de&longs;cending Graves hapneth in the afore&longs;aid propor­<lb/>tion, I have many times in his company &longs;et my &longs;elf to make a triall <lb/>thereof in the following Method.</s></p><p type="main"> <s>In a pri&longs;me or Piece of Wood, about twelve yards long, and <lb/>half a yard broad one way, and three Inches the other, we made, <lb/>upon the narrow Side or edge a Groove of little more than an Inch <lb/>wide; we &longs;hot it with the Grooving Plane very &longs;traight, and to <lb/>make it very &longs;mooth and &longs;leek, we glued upon it a piece of Vellum, <lb/>poli&longs;hed and &longs;moothed as exactly as can be po&longs;&longs;ible: and in it we <lb/>have let a brazen Ball, very hard, round, and &longs;mooth, de&longs;cend. <lb/></s> <s>Having placed the &longs;aid Pri&longs;me Pendent, rai&longs;ing one of its ends <lb/>above the Horizontal Plane a yard or two at plea&longs;ure, we have let <lb/>the Ball (as I &longs;aid) de&longs;cend along the Grove, ob&longs;erving, in the <lb/>manner that I &longs;hall tell you pre&longs;ently, the Time which it &longs;pent in <pb xlink:href="040/01/841.jpg" pagenum="148"/>runing it all; repeating the &longs;ame ob&longs;ervation again and again to <lb/>a&longs;&longs;ure our &longs;elves of the Time, in which we never found any diffe­<lb/>rence, no not &longs;o much as the tenth part of one beat of the Pul&longs;e. <lb/></s> <s>Having done, and preci&longs;ely ordered this bu&longs;ine&longs;&longs;e, we made the <lb/>&longs;ame Ball to de&longs;cend only the fourth part of the length of that <lb/>Grove: and having mea&longs;ured the time of its de&longs;cent, we alwaies <lb/>found it to be punctually half the other. </s> <s>And then making trial of <lb/>other parts, examining one while the Time of the whole Length <lb/>with the Time of half the Length, or with that of 2/3, or of 3/4, or, in <lb/>brief, with any whatever other Divi&longs;ion, by Experiments repeated <lb/>near an hundred Times, we alwaies found the Spaces to be to one <lb/>another as the Squares of the Times. </s> <s>And this in all Inclinations <lb/>of the Plane, that is, of the Grove in which the Ball was made to <lb/>de&longs;cend. </s> <s>In which we ob&longs;erved moreover, that the Times of the <lb/>De&longs;cents along &longs;undry Inclinations did retain the &longs;ame proportion <lb/>to one another, exactly, which anon you will &longs;ee a&longs;&longs;igned to them, <lb/>and demon&longs;trated by the Author. </s> <s>And as to the mea&longs;uring of the <lb/>Time; we had a good big Bucket full of Water hanged on high, <lb/>which by a very &longs;mall hole, pierced in the bottom, &longs;pirted, or, as <lb/>we &longs;ay, &longs;pin'd forth a &longs;mall thread of Water, which we received <lb/>with a &longs;mall cup all the while that the Ball was de&longs;cending in the <lb/>Grove, and in its parts; and then weighing from time to time the <lb/>&longs;mall parcels of Water, in that manner gathered, in an exact pair <lb/>of &longs;cales, the differences and proportions of their Weights gave <lb/>ju&longs;tly the differences and proportions of the Times; and this with <lb/>&longs;uch exactne&longs;&longs;e, that, as I &longs;aid before, the trials being many <lb/>and many times repeated, they never differed any con&longs;iderable <lb/>matter.</s></p><p type="main"> <s>SIMP. </s> <s>I &longs;hould have received great &longs;atisfaction by being pre&longs;ent <lb/>at tho&longs;e Experiments: but being confident of your diligence in <lb/>making them, and veracity in relating them, I content my &longs;elf, and <lb/>admit them for true and certain.</s></p><p type="main"> <s>SALV. </s> <s>We may, then, rea&longs;&longs;ume our Reading, and go on.</s></p><p type="head"> <s>COROLLARY II.</s></p><p type="main"> <s>It is collected in the &longs;econd place, that if any two Spaces are ta­<lb/>ken from the beginning of the Motion, pa&longs;&longs;ed in any Times, <lb/>tho&longs;e Times &longs;hall be unto each other as one of them is to a <lb/>Space that is the Mean proportional between them.</s></p><p type="main"> <s><emph type="italics"/>For taking two Spaces S T, and S V from the beginning of the Mo­<lb/>tion S, to which S X is a Mean-proportional, the Time of the de&longs;cent <lb/>along S T, &longs;hall be to the Time of the de&longs;cent along S V, as S T to S X; <lb/>or, if you will, the Time along S V &longs;hall be to the Time along S T,<emph.end type="italics"/><pb xlink:href="040/01/842.jpg" pagenum="149"/><figure id="id.040.01.842.1.jpg" xlink:href="040/01/842/1.jpg"/><lb/><emph type="italics"/>as VS is to SX. </s> <s>For it is demon&longs;trated, that Spaces <lb/>pa&longs;&longs;ed are in duplicate proportion to the Times, or, (which <lb/>is the &longs;ame) are as the Squares of the Times: But the pro­<lb/>portion of the Space VS to the Space ST is double to the <lb/>proportion of V S to SX, or is the &longs;ame that V S, and S X <lb/>&longs;quared have to one another: Therefore, the proportion of <lb/>the Times of the Motion by V S, and ST, is as the Spaces or <lb/>Lines V S to S X.<emph.end type="italics"/></s></p><p type="head"> <s>SCHOLIUM.</s></p><p type="main"> <s><emph type="italics"/>That which is demon&longs;trated in Motions that are made Perpendicu­<lb/>larly, may be under&longs;tood al&longs;o to hold true in the Motions made along <lb/>Planes of any whatever Inclination; for it is &longs;uppo&longs;ed, that in them <lb/>the degree of Acceleration encrea&longs;eth in the &longs;ame proportion; that <lb/>is, according to the encrea&longs;e of the Time; or, if you will, according <lb/>to the &longs;imple and primary Series of Numbers.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Here I de&longs;ire <emph type="italics"/>Sagredus,<emph.end type="italics"/> that I al&longs;o may be allowed, al­<lb/>beit perhaps with too much tediou&longs;ne&longs;&longs;e in the opinion of <emph type="italics"/>Simplici­<lb/>us,<emph.end type="italics"/> to defer for a little time the pre&longs;ent Reading, untill I may have <lb/>explained what from that which hath been already &longs;aid and de­<lb/>mon&longs;trated, and al&longs;o from the knowledge of certain Mechanical <lb/>Conclu&longs;ions heretofore learnt of our <emph type="italics"/>Academick,<emph.end type="italics"/> I now remember <lb/>to adjoyn for the greater confirmation of the truth of the Princi­<lb/>ple, which hath been examined by us even now with probable <lb/>Rea&longs;ons and Experiments: and, which is of more importance, for <lb/>the Geometrical proof of it, let me fir&longs;t demon&longs;trate one &longs;ole Ele­<lb/>mental <emph type="italics"/>Lemma<emph.end type="italics"/> in the Contemplation of <emph type="italics"/>Impetus's.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>If our advantage &longs;hall be &longs;uch as you promi&longs;eus, there <lb/>is no time that I would not mo&longs;t willingly &longs;pend in di&longs;cour&longs;ing <lb/>about the confirmation and thorow e&longs;tabli&longs;hing the&longs;e Sciences of <lb/>Motion: and as to my own particular, I not only grant you liber­<lb/>ty to &longs;atisfie your &longs;elf in this particular, but moreover entreat you <lb/>to gratifie, as &longs;oon as you can, the Curio&longs;ity which you have begot <lb/>in me touching the &longs;ame: and I believe that <emph type="italics"/>Simplicius<emph.end type="italics"/> al&longs;o is of the <lb/>&longs;ame mind.</s></p><p type="main"> <s>SIMP. </s> <s>I cannot deny what you &longs;ay.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>Seeing then that I have your permi&longs;&longs;ion, I will in the <lb/>fir&longs;t place con&longs;ider, as an Effect well known, That</s></p><pb xlink:href="040/01/843.jpg" pagenum="150"/><p type="head"> <s>LEMMA.</s></p><p type="main"> <s><emph type="italics"/>That the Moments or Velocities of the &longs;ame Moveable are different <lb/>upon different Inclinations of Planes, and the greate&longs;t is by the <lb/>Line elevated perpendicularly above the Horizon, and by the <lb/>others inclined, the &longs;aid Velocity dimini&longs;heth according as they <lb/>more and more depart from Perpendicularity, that is, as they in­<lb/>cline more obliquely: &longs;o that the Impetus, Talent, Energy, or, we <lb/>may &longs;ay, Moment of de&longs;cending is dimini&longs;hed in the Moveable by <lb/>the &longs;ubjected Plane, upon which the &longs;aid Moveable lyeth and <lb/>de&longs;cendeth.<emph.end type="italics"/></s></p><p type="main"> <s>And the better to expre&longs;s my &longs;elf, let the Line A B be perpen­<lb/>dicularly erected upon the Horizon A C: then &longs;uppo&longs;e the <lb/>&longs;ame to be declined in &longs;undry Inclinations towards the Horizon, as <lb/>in A D, A E, A F, <emph type="italics"/>&c.<emph.end type="italics"/> I &longs;ay, that the greate&longs;t and total <emph type="italics"/>Impetus<emph.end type="italics"/><lb/>of the Grave Body in de&longs;cending is along the Perpendicular B A, <lb/>and le&longs;s than that along D A, <lb/><figure id="id.040.01.843.1.jpg" xlink:href="040/01/843/1.jpg"/><lb/>and yet le&longs;s along E A; and <lb/>&longs;ucce&longs;&longs;ively dimini&longs;hing along <lb/>the more inclined F <emph type="italics"/>A,<emph.end type="italics"/> and fi­<lb/>nally is wholly extinct in the <lb/>Horizontal C <emph type="italics"/>A,<emph.end type="italics"/> where the <lb/>Moveable is indifferent either <lb/>to Motion or Re&longs;t, and hath not <lb/>of it &longs;elf any Inclination to <lb/>move one way or other, nor yet <lb/>any Re&longs;i&longs;tance to its being mo­<lb/>ved: for as it is impo&longs;&longs;i­<lb/>ble that a Grave Body, or a <lb/>Compound thereof &longs;hould move naturally upwards, receding from <lb/>the Common Center, towards which all Grave Matters con&longs;pire <lb/>to go, &longs;o it is impo&longs;&longs;ible that it do &longs;pontaneou&longs;ly move, unle&longs;s <lb/>with that Motion its particular Center of Gravity do acquire Proxi­<lb/>mity to the &longs;aid Common Center: &longs;o that upon the Horizontal <lb/>which here is under&longs;tood to be a Superficies equidi&longs;tant from the <lb/>&longs;aid Center, and therefore altogether void of Inclination, the <emph type="italics"/>Im­<lb/>petus<emph.end type="italics"/> or Moment of that &longs;ame Moveable &longs;hall be nothing at all. <lb/></s> <s>Having under&longs;tood this mutation of <emph type="italics"/>Impetus,<emph.end type="italics"/> I am to explain that <lb/>which, in an old Treati&longs;e of the Mechanicks, written heretofore <lb/>in <emph type="italics"/>Padona<emph.end type="italics"/> by our <emph type="italics"/>Academick,<emph.end type="italics"/> only for the u&longs;e of his Scholars, was <lb/>diffu&longs;ely and demon&longs;tratively proved, upon the occa&longs;ion of con­<lb/>&longs;idering the Original and Nature of the admirable In&longs;trument cal­<lb/>led the Screw, and it is, With what proportion that mutation of <pb xlink:href="040/01/844.jpg" pagenum="151"/><emph type="italics"/>Impetus<emph.end type="italics"/> is made along &longs;everal Inclinations or Declivities of <lb/>Planes.</s></p><p type="main"> <s>As, for example, in the inclined Plane A F, drawing its Eleva­<lb/>tion above the Horizontal, that is, the Line F C, along the which <lb/>the <emph type="italics"/>Impetus<emph.end type="italics"/> of a Grave Body, and the Moment of De&longs;cent is the <lb/>greate&longs;t; it is &longs;ought what proportion this Moment hath to the <lb/>Moment of the &longs;ame Moveable along the Declivity F A: Which <lb/>Proportion, I &longs;ay, is Reciprocal to the &longs;aid Lengths. </s> <s>And this is <lb/>the <emph type="italics"/>Lemma<emph.end type="italics"/> that was to go before the Theorem, which I hope to be <lb/>able anon to Demon&longs;trate. </s> <s>Hence it is manife&longs;t, That the <emph type="italics"/>Impetus<emph.end type="italics"/><lb/>of De&longs;cent of a Grave Body is as much as the Re&longs;i&longs;tance or lea&longs;t <lb/>force that &longs;ufficeth to arre&longs;t and &longs;tay it. </s> <s>For this Force or Re&longs;i­<lb/>&longs;tance, and its mea&longs;ure, I will make u&longs;e of the Gravity of another <lb/>Moveable. </s> <s>Let us now upon the Plane F A put the Moveable G <lb/>tyed to a thread which &longs;liding over F hath fa&longs;tned at its other end <lb/>the Weight H: and let us con&longs;ider that the Space of the De&longs;cent <lb/>or A&longs;cent of the Weight H along the Perpendicular, is alwaies <lb/>equal to the whole A&longs;cent or De&longs;cent of the other Moveable G <lb/>along the ^{*} Declivity A F, but yet not to the A&longs;cent or De&longs;cent </s></p><p type="main"> <s><arrow.to.target n="marg1092"></arrow.to.target><lb/>along the Perpendicular, in which only the &longs;aid Moveable G (like <lb/>as every other Moveable) exerci&longs;eth its Re&longs;i&longs;tance. </s> <s>Which is <lb/>manife&longs;t: for con&longs;idering in the Triangle AFC the Motion of <lb/>the Moveable G, as for example, upwards from A to F, to be com­<lb/>po&longs;ed of the tran&longs;ver&longs;e Horizontal Line A C, and of the Perpendi­<lb/>cular C F: <emph type="italics"/>A<emph.end type="italics"/>nd in regard, that as to the Horizontal Plane along <lb/>which the Moveable, as hath been &longs;aid, hath no Re&longs;i&longs;tance to mo­<lb/>ving (it not making by that Motion any lo&longs;s, nor yet acqui&longs;t in <lb/>regard of its particular di&longs;tance from the Common Center of Grave <lb/>Matters, which in the Horizon continueth &longs;till the &longs;ame) it remai­<lb/>neth that the Re&longs;i&longs;tance be only in re&longs;pect of the <emph type="italics"/>A<emph.end type="italics"/>&longs;cent that it is to <lb/>make along the Perpendicular C F. </s> <s>Whil&longs;t therefore the Grave <lb/>Moveable G, moving from <emph type="italics"/>A<emph.end type="italics"/> to F, hath only the Perpendicular <lb/>Space C F to re&longs;i&longs;t in its <emph type="italics"/>A<emph.end type="italics"/>&longs;cent, and whil&longs;t the other Grave Move­<lb/>able H de&longs;cendeth along the Perpendicular of nece&longs;&longs;ity as far as <lb/>the whole Space F <emph type="italics"/>A,<emph.end type="italics"/> and that the &longs;aid proportion of <emph type="italics"/>A<emph.end type="italics"/>&longs;cent and <lb/>De&longs;cent maintains it &longs;elf alwaies the &longs;ame, be the Motion of the <lb/>&longs;aid Moveables little or much (by rea&longs;on they are tyed toge­<lb/>ther) we may confidently affirm, that in ca&longs;e there were an <emph type="italics"/>Equi­<lb/>librium,<emph.end type="italics"/> that is Re&longs;t, to en&longs;ue betwixt the &longs;aid Moveables, the Mo­<lb/>ments, the Velocities, or their Propen&longs;ions to Motion, that is the <lb/>Spaces which they would pa&longs;s in the &longs;ame Time &longs;hould an&longs;wer re­<lb/>ciprocally to their Gravities, according to that which is demon&longs;tra­<lb/>ted in all ca&longs;es of Mechanick Motions: &longs;o that it &longs;hall &longs;uffice to <lb/>impede the de&longs;cent of G, if H be but &longs;o much le&longs;s grave than it, as <lb/>in proportion the Space C F is le&longs;&longs;er than the Space F <emph type="italics"/>A.<emph.end type="italics"/> Therefore <pb xlink:href="040/01/845.jpg" pagenum="152"/>&longs;uppo&longs;e that the Moveable G is to the Moveable H, as F <emph type="italics"/>A<emph.end type="italics"/> is to <lb/>F C; and then the <emph type="italics"/>Equilibrium<emph.end type="italics"/> &longs;hall follow, that is, the Moveables <lb/>H and G &longs;hall have equal Moments, and the Motion of the &longs;aid <lb/>Moveables &longs;hall cea&longs;e. <emph type="italics"/>A<emph.end type="italics"/>nd becau&longs;e we &longs;ee that the <emph type="italics"/>Impetus,<emph.end type="italics"/><lb/>Energy, Moment, or Propen&longs;ion of a Moveable to Motion is the <lb/>&longs;ame as is the Force or &longs;malle&longs;t Re&longs;i&longs;tance that &longs;ufficeth to &longs;top it; <lb/>and becau&longs;e it hath been concluded, that the Grave Body H is &longs;uf. <lb/></s> <s>ficient to arre&longs;t the Motion of <lb/><figure id="id.040.01.845.1.jpg" xlink:href="040/01/845/1.jpg"/><lb/>the Grave Body G: Therefore <lb/>the le&longs;&longs;er Weight H, which in <lb/>the Perpendicular F C imploy­<lb/>eth its total Moment, &longs;hall be <lb/>the preci&longs;e mea&longs;ure of the par­<lb/>tial Moment that the greater <lb/>Weight G exerci&longs;eth along the <lb/>inclined Plane F <emph type="italics"/>A<emph.end type="italics"/>: But the <lb/>mea&longs;ure of the total Moment of <lb/>the &longs;aid Grave Body G, is the <lb/>&longs;elf &longs;ame, (&longs;ince that to impede <lb/>the Perpendicular De&longs;cent of a <lb/>Grave Body there is required the oppo&longs;ition of &longs;uch another Grave <lb/>Body, which likewi&longs;e is at liberty to move Perpendicularly:) <lb/>Therefore the partial <emph type="italics"/>Impetus<emph.end type="italics"/> or Moment of G along the inclined <lb/>Plane F A &longs;hall be to the grand and total <emph type="italics"/>Impetus<emph.end type="italics"/> of the &longs;ame G <lb/>along the Perpendicular F C, as the Weight H to the Weight G: <lb/>that is, by Con&longs;truction, as the &longs;aid Perpendicular F C, the Eleva­<lb/>tion of the inclined Plane, is to the &longs;ame inclined Plane F A: <lb/>Which is that that by the <emph type="italics"/>Lemma<emph.end type="italics"/> was propo&longs;ed to be demon­<lb/>&longs;trated, and which by our Author, as we &longs;hall &longs;ee, is &longs;uppo&longs;ed as <lb/>known in the &longs;econd part of the Sixth Propo&longs;ition of the pre&longs;ent <lb/>Treati&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1092"></margin.target>* Or inclined <lb/>Plane.</s></p><p type="main"> <s>SAGR. </s> <s>From this that you have already concluded I conceive <lb/>one may ea&longs;ily deduce, arguing <emph type="italics"/>ex æquali<emph.end type="italics"/> by perturbed Proportion, <lb/>that the Moments of the &longs;ame Moveable, along Planes variou&longs;ly <lb/>inclined (as F A and F I) that have the &longs;ame Elevation, are to each <lb/>other in Reciprocal proportion to the &longs;ame Planes.</s></p><p type="main"> <s>SALV. <emph type="italics"/>A<emph.end type="italics"/> mo&longs;t certain Conclu&longs;ion. </s> <s>This being agreed on, we <lb/>will pa&longs;s in the next place to demon&longs;trate the <emph type="italics"/>Theoreme,<emph.end type="italics"/> namely, <lb/>that</s></p><pb xlink:href="040/01/846.jpg" pagenum="153"/><p type="head"> <s>THEOREM.</s></p><p type="main"> <s><emph type="italics"/>The degrees of Velocity of a Moveable de&longs;cending with a Natural <lb/>Motion from the &longs;ame height along Planes in any manner inclined <lb/>at the arrival to the Horizon are alwaies equal, Impediments be­<lb/>ing removed.<emph.end type="italics"/></s></p><p type="main"> <s>Here we are in the fir&longs;t place to adverti&longs;e you, that it having <lb/>been proved, that in any Inclination of the Plane the Move­<lb/>able from its rece&longs;&longs;ion from Quie&longs;&longs;ence goeth encrea&longs;ing its Ve­<lb/>locity, or quantity of its <emph type="italics"/>Impetus,<emph.end type="italics"/> with the proportion of the <lb/>Time (according to the Definition which the Author giveth of <lb/>Motion naturally Accelerate) whereupon, as he hath by the pre­<lb/>cedent Propo&longs;ition demon&longs;trated, the Spaces pa&longs;&longs;ed are in dupli­<lb/>cate proportion to the Times, and, con&longs;equently, to the degrees <lb/>of Velocity: look what the <emph type="italics"/>Impetus's<emph.end type="italics"/> were in that which was fir&longs;t <lb/>moved, &longs;uch proportionally &longs;hall be the degrees of Velocity gai­<lb/>ned in the &longs;ame Time; &longs;eeing that both the&longs;e and tho&longs;e encrea&longs;e <lb/>with the &longs;ame proportion in the &longs;ame Time.</s></p><p type="main"> <s>Now let the inclined Plane be A B, its elevation above the Ho <lb/>rizon the Perpendicular A C, and the Horizontal Plane C B: and <lb/>becau&longs;e, as was even now concluded, the <emph type="italics"/>Impetus<emph.end type="italics"/> of a Moveable <lb/>along the Perpendicular A C is to the <emph type="italics"/>Impetus<emph.end type="italics"/> of the &longs;ame along <lb/>the inclined Plane A B, as A B is to A C, let there be taken in the <lb/>inclined Plane A B, A D a third proportional to A B and A C: <lb/>The <emph type="italics"/>Impetus,<emph.end type="italics"/> therefore, along A C is to the <emph type="italics"/>Impetus<emph.end type="italics"/> along A B, <lb/>that is along A D, as A C is to <lb/><figure id="id.040.01.846.1.jpg" xlink:href="040/01/846/1.jpg"/><lb/>A D: And therefore the Move­<lb/>able in the &longs;ame Time that it <lb/>would pa&longs;s the Perpendicular <lb/>Space AC, &longs;hall likewi&longs;e pa&longs;s the <lb/>Space A D, in the inclined Plane <lb/>A B, (the Moments being as <lb/>the Spaces:) And the degree of Velocity in C &longs;hall have the &longs;ame <lb/>proportion to the degree of Velocity in D, as A C hath to A D: <lb/>But the degree of Velocity in B is to the &longs;ame degree in D, as the <lb/>Time along A B is to the Time along AD, by the definition of <lb/>Accelerate Motion; And the Time along AB is to the Time along <lb/>A D, as the &longs;ame A C, the Mean Proportional between B A and <lb/>A D, is to A D, by the la&longs;t Corollary of the &longs;econd Propo&longs;ition: <lb/>Therefore the degrees of Velocity in B and in C have to the de­<lb/>gree in D, the &longs;ame Proportion as A C hath to A D; and therefore <lb/>are equal: Which is the <emph type="italics"/>Theorem<emph.end type="italics"/> intended to be demon&longs;trated.</s></p><p type="main"> <s>By this we may more concludingly prove the en&longs;uing third <pb xlink:href="040/01/847.jpg" pagenum="154"/>Propo&longs;ition of the Author, in which he makes u&longs;e of this Princi­<lb/>ple; and it is, That the Time along the inclined Plane, hath to the <lb/>Time along the Perpendicular, the &longs;ame proportion as the &longs;aid In­<lb/>clined Plane and Perpendicular. </s> <s>For if we put the ca&longs;e that BA <lb/>be the Time along A B, the Time along A D &longs;hall be the Mean <lb/>between them, that is A C, by the &longs;econd Corollary of the &longs;econd <lb/>Propo&longs;ition: But if C A be the Time along A D, it &longs;hall likewi&longs;e <lb/>be the Time along <emph type="italics"/>A<emph.end type="italics"/> C, by rea&longs;on that <emph type="italics"/>A<emph.end type="italics"/> D and <emph type="italics"/>A<emph.end type="italics"/> C are pa&longs;t in <lb/>equal Times: And therefore in ca&longs;e B <emph type="italics"/>A<emph.end type="italics"/> be the Time along A B, <lb/><emph type="italics"/>A<emph.end type="italics"/> C &longs;hall be the Time along <emph type="italics"/>A<emph.end type="italics"/> C: Therefore, as <emph type="italics"/>A<emph.end type="italics"/> B is to A C, &longs;o <lb/>is the Time along <emph type="italics"/>A<emph.end type="italics"/> B to the Time along <emph type="italics"/>A<emph.end type="italics"/> C.</s></p><p type="main"> <s>By the &longs;ame di&longs;cour&longs;e one &longs;hall prove, that the Time along <emph type="italics"/>A<emph.end type="italics"/> C <lb/>is to the Time along the inclined Plane <emph type="italics"/>A<emph.end type="italics"/> E, as <emph type="italics"/>A<emph.end type="italics"/> C is to <emph type="italics"/>A<emph.end type="italics"/> E: <lb/>Therefore, <emph type="italics"/>ex æquali,<emph.end type="italics"/> the Time along the inclined Plane <emph type="italics"/>A B<emph.end type="italics"/> is, <lb/>Directly, to the Time along the inclined Plane <emph type="italics"/>A<emph.end type="italics"/> E as <emph type="italics"/>A B<emph.end type="italics"/> to <lb/><emph type="italics"/>A E, &c.<emph.end type="italics"/></s></p><p type="main"> <s>One might al&longs;o by the &longs;ame application of the <emph type="italics"/>Theorem,<emph.end type="italics"/> as <emph type="italics"/>Sa­<lb/>gredus<emph.end type="italics"/> &longs;hall very evidently &longs;ee anon, immediately demon&longs;trate the <lb/>&longs;ixth Propo&longs;ition of the <emph type="italics"/>A<emph.end type="italics"/>uthor: <emph type="italics"/>B<emph.end type="italics"/>ut let this Digre&longs;&longs;ion &longs;uffice <lb/>for the pre&longs;ent, which he perhaps thinketh too tedious, though in­<lb/>deed it is of &longs;ome importance in the&longs;e matters of Motion.</s></p><p type="main"> <s>SAGR. </s> <s>You may &longs;ay extreamly delightful, and mo&longs;t nece&longs;&longs;ary <lb/>to the perfect under&longs;tanding of that Principle.</s></p><p type="main"> <s>SALV. </s> <s>I will go on, then, in my Reading of the Text.</s></p><p type="head"> <s>THEOR. III. PROP. III.</s></p><p type="main"> <s>If a Moveable departing from Re&longs;t do move along <lb/>an Inclined Plane, and al&longs;o along the Perpendi­<lb/>cular who&longs;e heights are the &longs;ame, the Times of <lb/>their Motions &longs;hall be to one another as the <lb/>Lengths of the &longs;aid Plane and Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Let the inclined Plane be A C, and the Perpendicular A B, <lb/>who&longs;e heights are the &longs;ame above the Horizon C B, to wit, <lb/>the &longs;elf &longs;ame Line B A. </s> <s>I &longs;ay, that the Time of the De&longs;cent <lb/>of the &longs;ame Moveable upon the Plane A C, hath the &longs;ame Proporti­<lb/>on to the Time of the De&longs;cent along the Perpendicular A B, as the <lb/>Length of the Plane A C hath to the Length of the &longs;aid Perpendi­<lb/>cular. </s> <s>For let any number of Lines D G, E I, F L, be drawn, Paral­<lb/>lel to the Horizon C B: It is manife&longs;t from the A&longs;&longs;umption fore­<lb/>going, that the degrees of Velocity of the Moveable, departing from <lb/>A the beginning of Motion, acquired in the Points G and D are<emph.end type="italics"/><pb xlink:href="040/01/848.jpg" pagenum="155"/><emph type="italics"/>equal, their exce&longs;&longs;e or elevation above the Horizon being equal; <lb/>and &longs;o the degrees in the Points I and E; as al&longs;o the degrees in L <lb/>and F. </s> <s>And if not only the&longs;e Parallels, but many more were &longs;up­<lb/>po&longs;ed to be drawn from all the points imagined to be in the Line <lb/>A B, untill they meet the Line A C, the Mo-<emph.end type="italics"/><lb/><figure id="id.040.01.848.1.jpg" xlink:href="040/01/848/1.jpg"/><lb/><emph type="italics"/>ments, or degrees of the Velocities along the <lb/>extreams [or ends] of every one of tho&longs;e <lb/>Parallels, &longs;hall be alwaies equal to one ano­<lb/>ther: Therefore the two Spaces A C and A B <lb/>are pa&longs;t with the &longs;ame degree of Velocity: <lb/>But it hath been demon&longs;trated, that if two <lb/>Spaces be pa&longs;&longs;ed by a Moveable with one <lb/>and the &longs;ame degree of Velocity, the Times <lb/>of the Motions have the &longs;ame proportion as <lb/>tho&longs;e Spaces: Therefore the Time of the Motion along A C is to the <lb/>Time along A B, as the Length of the Plane A C to the length of the <lb/>Perdendicular A B. </s> <s>Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>It &longs;eemeth to me, that the &longs;ame might very clearly and <lb/>conci&longs;ely be concluded, it having fir&longs;t been proved that the &longs;um of <lb/>the Accelerate Motion of the Tran&longs;itions along A C and A B, is <lb/>as much as the Equable Motion, who&longs;e degree of Velocity is &longs;ub­<lb/>duple to the greate&longs;t degree C B: Therefore the two Spaces AC <lb/>and A B being pa&longs;&longs;ed with the &longs;ame Equable Motion, it hath been <lb/>&longs;hewn, by the Fir&longs;t Propo&longs;ition of the fir&longs;t, that the Times of the <lb/>Tran&longs;itions &longs;hall be as the &longs;aid Spaces.</s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence is collected, that the Times of the De&longs;cents along Planes <lb/>of different Inclination, but of the &longs;ame Elevation, are to <lb/>one another according to their Lengths.</s></p><p type="main"> <s><emph type="italics"/>For if we &longs;uppo&longs;e another Plane A M, coming from A, and ter­<lb/>minated by the &longs;ame Horizontal C B; it &longs;hall in like manner be <lb/>demon&longs;trated, that the Time of the De&longs;cent along A M, is to the <lb/>Time along A B, as the Line A M to A B: But as the Time A B is <lb/>to the Time along A C, &longs;o is the Line A B to A C: Therefore,<emph.end type="italics"/> ex <lb/>æquali, <emph type="italics"/>as A M is to A C, &longs;o is the Time along A M to the Time <lb/>along A C.<emph.end type="italics"/></s></p><pb xlink:href="040/01/849.jpg" pagenum="156"/><p type="head"> <s>THEOR. IV. PROP. IV.</s></p><p type="main"> <s>The Times of the Motions along equal Planes, <lb/>but unequally inclined, are to each other in <lb/>&longs;ubduple proportion of the Elevations of tho&longs;e <lb/>Planes Reciprocally taken.</s></p><p type="main"> <s><emph type="italics"/>Let there proceed from the term B two equal Planes, but une­<lb/>qually inclined, B A and B C, and let A E and C D be Hori­<lb/>zontal Lines, drawn as far as the Perpendicular B D: Let the <lb/>Elevation of the Plane B A be B E; and let the Elevation of the <lb/>Plane B C be B D: And let B I be a Mean Proportional between the <lb/>Elevations D B and B E: It is manife&longs;t<emph.end type="italics"/><lb/><figure id="id.040.01.849.1.jpg" xlink:href="040/01/849/1.jpg"/><lb/><emph type="italics"/>that the proportion of D B to B I, is &longs;ub­<lb/>duple the proportion of D B to B E. </s> <s>Now <lb/>I &longs;ay, that the proportion of the Times <lb/>of the De&longs;cents or Motions along the <lb/>Planes B A and B C, are the &longs;ame with <lb/>the proportion of D B to B I Reciprocal­<lb/>ly taken: So that to the Time B A the <lb/>Elevation of the other Plane B C, that is <lb/>B D be Homologal; and to the Time along <lb/>B C, B I be Homologal: Therefore it is <lb/>to be demon&longs;trated, That the Time along B A is to the Time along <lb/>B C, as D B is to B I. </s> <s>Let I S be drawn equidi&longs;tant from D C. </s> <s>And <lb/>becau&longs;e it hath been demon&longs;trated that the Time of the De&longs;cent <lb/>along B A, is to the Time of the De&longs;cent along the Perpendicular <lb/>B E, as the &longs;aid B A is to B E; and the Time along B E is to the <lb/>Time along B D, as B E is to B I; and the Time along B D is to the <lb/>Time along B C, as B D to B C, or as B I to B S: Therefore,<emph.end type="italics"/> ex æqua­<lb/>li, <emph type="italics"/>the Time along B A &longs;hall be to the Time along B C as B A to B S, <lb/>or as C B to BS: But C B is to B S, as D B to B I: Therefore the <lb/>Propo&longs;ition is manife&longs;t:<emph.end type="italics"/></s></p><pb xlink:href="040/01/850.jpg" pagenum="157"/><p type="head"> <s>THEOR. V. PROP. V.</s></p><p type="main"> <s>The proportion of the Times of the De&longs;cents <lb/>along Planes that have different Inclinations <lb/>and Lengths, and the Elivations unequal, is <lb/>compounded of the proportion of the Lengths <lb/>of tho&longs;e Planes, and of the &longs;ubduple proporti­<lb/>on of their Elevations Reciprocally taken.</s></p><p type="main"> <s><emph type="italics"/>Let A B and A C be Planes inclined after different manners, <lb/>who&longs;e Lengths are unequal, as al&longs;o their Elevations. </s> <s>I &longs;ay, <lb/>the proportion of the Time of the De&longs;cent along A C to the <lb/>Time along A B, is compounded of the proportion of the &longs;aid A C <lb/>to A B, and of the &longs;ubduple proportion of their Elevation Recipro­<lb/>cally taken. </s> <s>For let the Perpendicular A D be drawn, with which <lb/>let the Horizontal Lines B G and C D inter&longs;ect, and let A L be a <lb/>Mean-proportional between C A and A E; and from the point L let <lb/>a Parallel be drawn to the Horizon inter&longs;ecting<emph.end type="italics"/><lb/><figure id="id.040.01.850.1.jpg" xlink:href="040/01/850/1.jpg"/><lb/><emph type="italics"/>the Plane A C in F; and A F &longs;hall be a Mean <lb/>proportional between C A and A E. </s> <s>And becau&longs;e <lb/>the Time along A C is to the Time along A E, as <lb/>the Line F A to A E; and the Time along A E is <lb/>to the Time along A B, as the &longs;aid A E to the &longs;aid <lb/>A B: It is manife&longs;t that the Time along A C is to <lb/>the Time along A B, as A F to A B. </s> <s>It remaineth, <lb/>therefore, to be demon&longs;trated, that the proportion <lb/>of A F to A B is compounded of the proportion of <lb/>C A to A B, and of the proportion of G A to A L; <lb/>which is the &longs;ubduple proportion of the Elevati­<lb/>ons D A and A G Reciprocally taken. </s> <s>But that is manife&longs;t, C A <lb/>being put between F A and A B: For the proportion of F A to A C <lb/>is the &longs;ame as that of L A to A D, or of G A to A L; which is &longs;ub­<lb/>duple of the proportion of the Elevations G A and A D; and the <lb/>proportion of C A to A B is the proportion of the Lengths: Therefore <lb/>the Propo&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><pb xlink:href="040/01/851.jpg" pagenum="158"/><p type="head"> <s>THEOR. VI. PROP. VI.</s></p><p type="main"> <s>If from the highe&longs;t or lowe&longs;t part of a Circle, <lb/>erect upon the Horizon, certain Planes be <lb/>drawn inclined towards the Circumference, <lb/>the Times of the De&longs;cents along the &longs;ame <lb/>&longs;hall be equal.</s></p><p type="main"> <s><emph type="italics"/>Let the Circle be erect upon the Horizon G H, who&longs;e Diameter <lb/>recited upon the lowe&longs;t point, that is upon the contact with the <lb/>Horizon, let be F A, and from the highe&longs;t point A let certain <lb/>Planes A B and A C incline towards the Circumference: I &longs;ay that the <lb/>Times of the De&longs;cents along the &longs;ame are equal. </s> <s>Let B D and C E be <lb/>two Perpendiculars let fall unto the Diameter; and let A I be a Mean­<lb/>Proportional between the Altitudes<emph.end type="italics"/><lb/><figure id="id.040.01.851.1.jpg" xlink:href="040/01/851/1.jpg"/><lb/><emph type="italics"/>of the Planes E A and A D. </s> <s>And <lb/>becau&longs;e the Rectangles F A E and <lb/>F A D are equal to the Squares of <lb/>A C and A B; And al&longs;o becau&longs;e <lb/>that as the Rectangle F A E, is to <lb/>the Rectangle F A D, &longs;o is E A to <lb/>A D. </s> <s>Therefore as the Square of <lb/>C A is to the Square of B A, <lb/>&longs;o is the Line E A to the Line <lb/>A D. </s> <s>But as the Line E A is to <lb/>D A, &longs;o is the Square of I A to the Square of A D: Therefore <lb/>the Squares of the Lines C A and A B are to each other as the Squares <lb/>of the Lines I A and A D: And therefore as the Line C A is to A B, <lb/>&longs;o is I A to A D: But in the precedent Propo&longs;ition it hath been demon­<lb/>&longs;trated that the proportion of the Time of the De&longs;cent along A C to the <lb/>Time of the De&longs;cent by A B, is compounded of the proportions of C A <lb/>to A B, and of D A to A I, which is the &longs;ame with the proportion of <lb/>B A to A C: Therefore the proportion of the Time of the De&longs;cent along <lb/>A C, to the Time of the De&longs;cent along A B, is compounded of the pro­<lb/>portions of C A to A B, and of B A to A C: Therefore the proporti­<lb/>on of tho&longs;e Times is a proportion of equality: Therefore the Propo&longs;ition <lb/>is evident.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The &longs;ame is another way demon&longs;trated from the Mechanicks: Name­<lb/>ly that in the en&longs;uing Figure the Moveable pa&longs;&longs;eth in equal Times along <lb/>C A and D A. </s> <s>For let B A be equal to the &longs;aid D A, ond let fall the <lb/>Perpendiculars B E and D F: It is manife&longs;t by the Elements of the<emph.end type="italics"/><pb xlink:href="040/01/852.jpg" pagenum="159"/><emph type="italics"/>Mechanicks: That the Moment of the Weight elevated upon the Plane <lb/>according to the Line A B C, is <lb/>to its total Moment, as B E to B A;<emph.end type="italics"/><lb/><figure id="id.040.01.852.1.jpg" xlink:href="040/01/852/1.jpg"/><lb/><emph type="italics"/>And that the Moment of the &longs;ame <lb/>Weight upon the Elevation A D, <lb/>is to its total Moment, as D F to <lb/>D A or B A: Therefore the Mo­<lb/>ment of the &longs;aid Weight upon the <lb/>Plane inclined according to D A, <lb/>is to the Moment upon the Plane <lb/>inclined according to A B C, as <lb/>the Line D F to the Line B E: <lb/>Therefore the Spaces which the <lb/>&longs;aid Weight &longs;hall pa&longs;&longs;e in equal <lb/>Times along the Inclined Planes C A and D A, &longs;hall be to each other as <lb/>the Line B E to D F; by the &longs;econd Propo&longs;ition of the Fir&longs;t Book: <lb/>But as B E is to D F, &longs;o A C is demon&longs;trated to be to D A: <lb/>Therefore the &longs;ame Moveable will in equal Times pa&longs;&longs;e the Lines <lb/>C A and D A.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And that C A is to D A as B E is to D F, is thus demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Draw a Line from C to D; and by D and B draw the Lines <lb/>D G L, (cutting C A in the point I) and B H, Parallels to A F: <lb/>And the Angle A D I &longs;hall be equal to the Angle D C A, for that <lb/>the parts L A and A D of the Circumference &longs;ubtending them, are <lb/>equal, and the Angle D A C common to them both: Therefore of <lb/>the equiangled Triangles C A D and D A I, the &longs;ides about the <lb/>equal Angles &longs;hall be proportional: And as C A is to A D, &longs;o is <lb/>D A to A I, that is B A to A I, or H A to A G; that is, B E to <lb/>D F: Which was to be proved.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Or el&longs;e the &longs;ame &longs;hall be demon&longs;trated more &longs;peedily thus.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Vnto the Horizon A B, let a Circle be erect, who&longs;e Diameter is <lb/>perpendicular to the Horizon: and <lb/>from the highe&longs;t Term D let a Plane<emph.end type="italics"/><lb/><figure id="id.040.01.852.2.jpg" xlink:href="040/01/852/2.jpg"/><lb/><emph type="italics"/>at plea&longs;ure D F, be inclined to the <lb/>Circumference. </s> <s>I &longs;ay that the De­<lb/>&longs;cent along the Plane D F, and the <lb/>Fall along the Diameter B C, will <lb/>be pa&longs;&longs;ed by the &longs;ame Moveable in <lb/>equal Times. </s> <s>For let F G be drawn <lb/>parallel to the Horizon A B, which <lb/>&longs;hall be perpendicular to the Diameter <lb/>D C, and let a Line conjoyn F and <lb/>C: and becau&longs;e the Time of the Fall <lb/>along D C, is to the Time of the Fall along D G, as the Mean <lb/>Proportional between C D and D G, is to the &longs;aid D G; and the<emph.end type="italics"/><pb xlink:href="040/01/853.jpg" pagenum="160"/><emph type="italics"/>Mean between C D and D G being D F, (for that the Angle D F C <lb/>in the Semicircle, is a Right Angle, and F G perpendicular to D C:) <lb/>Therefore the Time of the Fall along D C is to the Time of the Fall <lb/>along D G, as the Line F D to D G: But it hath been demon&longs;trated <lb/>that the Time of the De&longs;cent along D F, is to the Time of the Fall <lb/>along D G, as the &longs;ame Line D F is to D G: The Times, therefore, <lb/>of the De&longs;cent along D F and Fall along D C, are to the Time of the <lb/>Fall along the &longs;aid D G in the &longs;ame proportion: Therefore they are <lb/>equal. </s> <s>It will likewi&longs;e be demon&longs;trated, if from the lowe&longs;t Term C, <lb/>one &longs;hould rai&longs;e the Chord C E, and draw E H parallel to the Hori­<lb/>zon, and conjoyn E and D, that the Time of the De&longs;cent along E C <lb/>equals the Time of the Fall along the Diameter D C.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARY I.</s></p><p type="main"> <s>Hence is collected that the Times of the De&longs;cents along all the <lb/>Chords drawn from the Terms C or D are equal to one <lb/>another.</s></p><p type="head"> <s>COROLLARY II.</s></p><p type="main"> <s>It is al&longs;o collected that if the Perpendicular and inclined Plane <lb/>de&longs;cend from the &longs;ame point along which the De&longs;cents are <lb/>made in equal Times, they are in a Semicircle who&longs;e Dia­<lb/>meter is the &longs;aid Perpendicular.</s></p><p type="head"> <s>COROLLARY III.</s></p><p type="main"> <s>Hence it is collected that the Times of the Motions along inclined <lb/>Planes, are then equal, where the Elevations of equal parts of <lb/>tho&longs;e Planes &longs;hall be to one another as their Longitudes.</s></p><p type="main"> <s><emph type="italics"/>For it hath been &longs;hewn that the Times C A and D A in the la&longs;t Fi­<lb/>gure &longs;ave one are equal, the Elevation of the part A B being equal <lb/>to A D, that is, that B E &longs;hall be to the Elevation D F, as C A <lb/>to D A.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>Pray you Sir be plea&longs;ed to &longs;tay your Reading of what <lb/>followeth until that I have &longs;atisfied my &longs;elf in a Contemplation <lb/>that ju&longs;t now cometh into my mind, which if it be not a delu&longs;i­<lb/>on, is not far from being a plea&longs;ing diverti&longs;ement: as are all &longs;uch <lb/>that proceed from Nature or nece&longs;&longs;ity.</s></p><p type="main"> <s>It is manife&longs;t, that if from a point a&longs;&longs;igned in an Horizontal <lb/>Plane, one &longs;hall produce along the &longs;ame Plane infinite right Lines <lb/>every way, upon each of which a point is under&longs;tood to move with <lb/>an Equable Motion, all beginning to move in the &longs;ame in&longs;tant <pb xlink:href="040/01/854.jpg" pagenum="161"/>of Time from the a&longs;&longs;igned point, and the Velocities of them all <lb/>being equal, there &longs;hall con&longs;equently be de&longs;cribed by tho&longs;e move­<lb/>able points Circumferences of Circles alwayes bigger and bigger, <lb/>all concentrick about the fir&longs;t point a&longs;&longs;igned: ju&longs;t in the &longs;ame <lb/>manner as we &longs;ee it done in the Undulations of &longs;tanding Water, <lb/>when a &longs;tone is dropt into it; the percu&longs;&longs;ion of which &longs;erveth to <lb/>give the beginning to the Motion on every &longs;ide, and remaineth <lb/>as the Center of all the Circles that happen to be de&longs;igned &longs;ucce&longs;­<lb/>&longs;ively bigger and bigger by the &longs;aid Undulations. </s> <s>But if we ima­<lb/>gine a Plane erect unto the Horizon, and a point be noted in the <lb/>&longs;ame on high, from which infinite Lines are drawn inclined, ac­<lb/>cording to all inclinations, along which we fancy grave Movea­<lb/>bles to de&longs;cend, each with a Motion naturally Accelerate <lb/>with tho&longs;e Velocities that agree with the &longs;everal Inclinations; <lb/>&longs;uppo&longs;ing that tho&longs;e de&longs;cending Moveables were continually vi&longs;i­<lb/>ble, in what kind of Lines &longs;hould we &longs;ee them continually di&longs;po&longs;ed? <lb/></s> <s>Hence my wonder ari&longs;eth, &longs;ince that the precedent Demon&longs;trati­<lb/>ons a&longs;&longs;ure me, that they &longs;hall all be alwayes &longs;een in one and the <lb/>&longs;ame Circumference of Circles &longs;ucce&longs;&longs;ively encrea&longs;ing, according <lb/>as the Moveables in de&longs;cending go more and more &longs;ucce&longs;&longs;ively re­<lb/>ceding from the highe&longs;t point in which their Fall began: And the <lb/>better to declare my &longs;elf, let the chiefe&longs;t point A be marked, from <lb/>which Lines de&longs;cend according to any Inclinations A F, A H, and <lb/>the Perpendicular A B, in which taking the points C and D, de­<lb/>&longs;cribe Circles about them that pa&longs;s by <lb/><figure id="id.040.01.854.1.jpg" xlink:href="040/01/854/1.jpg"/><lb/>the point A, inter&longs;ecting the inclined <lb/>Lines in the points F, H, B, and E, G, <lb/>I. </s> <s>It is manife&longs;t, by the fore-going <lb/>Demon&longs;trations, that Moveables de­<lb/>&longs;cendent along tho&longs;e Lines departing <lb/>at the &longs;ame Time from the term A, <lb/>one &longs;hall be in E, the other &longs;hall be in <lb/>G, and the other in I; and &longs;o con­<lb/>tinuing to de&longs;cend they &longs;hall arrive <lb/>in the &longs;ame moment of Time at F, H, <lb/>and B: and the&longs;e and infinite others continuing to move along the <lb/>infinite differing Inclinations, they &longs;hall alwayes &longs;ucce&longs;&longs;ively arrive <lb/>at the &longs;elf-&longs;ame Circumferences made bigger & bigger <emph type="italics"/>in infinitum.<emph.end type="italics"/><lb/>From the two Species, therefore, of Motion of which Nature makes <lb/>u&longs;e, ari&longs;eth, with admirable harmonious variety, the generation of in­<lb/>&longs;inite Circles. </s> <s>She placeth the one as in her Seat, and original be­<lb/>ginning, in the Center of infinite concentrick Circles; the other <lb/>is con&longs;tituted in the &longs;ublime or highe&longs;t Contact of infinite Circum­<lb/>ferences of Circles, all excentrick to one another: Tho&longs;e proceed <lb/>from Motions all equal and Equable; The&longs;e from Motions all al­<pb xlink:href="040/01/855.jpg" pagenum="162"/>wayes Inequable to them&longs;elves, and all unequal to one another, <lb/>that de&longs;cend along the infinite different Inclinations. </s> <s>But we fur­<lb/>ther adde, that if from the two points a&longs;&longs;igned for the Emanations, <lb/>we &longs;hall &longs;uppo&longs;e Lines to proceed, not onely along two Superfi­<lb/>cies Horizontal and Upright [or erect] but along all every ways <lb/>like as from tho&longs;e, beginning at one &longs;ole point, we pa&longs;&longs;ed to the <lb/>production of Circles from the lea&longs;t to the greate&longs;t, &longs;o beginning <lb/>from one &longs;ole point we &longs;hall &longs;ucce&longs;&longs;ively produce in&longs;inite Spheres, <lb/>or we may &longs;ay one Sphere, that &longs;hall <emph type="italics"/>gradatim<emph.end type="italics"/> increa&longs;e to infinite <lb/>bigne&longs;&longs;es: And this in two fa&longs;hions; that is, either with placing <lb/>the original in the Center, or el&longs;e in the Circumference of tho&longs;e <lb/>Spheres.</s></p><p type="main"> <s>SALV. </s> <s>The Contemplation is really ingenuous, and adequate <lb/>to the Wit of <emph type="italics"/>Sagredus.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>Though I am at lea&longs;t capable of the Speculation, ac­<lb/>cording to the two manners of the production of Circles and <lb/>Spheres, with the two different Natural Motions, howbeit I do <lb/>not perfectly under&longs;tand the production depending on the Acce­<lb/>lerate Motion and its Demon&longs;tration, yet notwith&longs;tanding that <lb/>licence of a&longs;&longs;igning for the place of that Emanation as well the <lb/>lowe&longs;t Center, as the highe&longs;t Spherical Superficies, maketh me to <lb/>think that its po&longs;&longs;ible that &longs;ome great Mi&longs;tery may be contained <lb/>in the&longs;e true and admirable Conclu&longs;ions: &longs;ome Mi&longs;tery I &longs;ay <lb/>touching the Creation of the Univer&longs;e, which is held to be of <lb/>Spherical form, and concerning the Re&longs;idence of the Fir&longs;t <lb/>Cau&longs;e.</s></p><p type="main"> <s>SALV. </s> <s>I am not unwilling to think the &longs;ame: but &longs;uch pro­<lb/>found Speculations are to be expected from Sharper Wits than <lb/>ours. </s> <s>And it &longs;hould &longs;uffice us, that if we be but tho&longs;e le&longs;&longs;e noble <lb/>Workmen that di&longs;cover and draw forth of the Quarry the <lb/>Marbles, in which the Indu&longs;trious Statuaries afterwards make <lb/>wonderful Images appear, that lay hid under rude and mi&longs;haped <lb/>Cru&longs;ts. </s> <s>Now, if you plea&longs;e, we will go on.</s></p><p type="head"> <s>THEOR. VII. PROP. VII.</s></p><p type="main"> <s>If the Elevations of two Planes &longs;hall have a pro­<lb/>portion double to that of their Lengths, the <lb/>Motions in them from Re&longs;t &longs;hall be fini&longs;hed in <lb/>equal Times.</s></p><p type="main"> <s><emph type="italics"/>Let A E and A B be two unequal Planes, and unequally inclined, <lb/>and let their Elevations be F A and D A, and let F A have the <lb/>&longs;ame proportion to D A, as A E hath to A B. </s> <s>I &longs;ay that the Times <lb/>of the Motions along the Planes A E and A B, out of Re&longs;t in A are<emph.end type="italics"/><pb xlink:href="040/01/856.jpg" pagenum="163"/><emph type="italics"/>equal. </s> <s>Draw Horizontal Parallels to the Line of Elevation E F and <lb/>B D, which cutteth A E in G. </s> <s>And be-<emph.end type="italics"/><lb/><figure id="id.040.01.856.1.jpg" xlink:href="040/01/856/1.jpg"/><lb/><emph type="italics"/>cau&longs;e the proportion of F A to A D, is <lb/>double the proportion of E A to A B; and <lb/>as F A to A D, &longs;o is E A to A G: There­<lb/>fore the proportion of E A to A G, is dou­<lb/>ble the proportion of E A to A B: There­<lb/>fore A B is a Mean-Proportional between <lb/>E A and A G: And becau&longs;e the Time of the <lb/>De&longs;cent along A B, is to the Time of the De­<lb/>&longs;cent along A G, as A B to A G; and the <lb/>Time of the De&longs;cent along AG, is to the Time of the De&longs;cent along A E, as <lb/>A G is to the Mean-proportional between A G and A E, which is A B: <lb/>Therefore<emph.end type="italics"/> ex equali, <emph type="italics"/>the Time along A B is to the Time along A E, as A B <lb/>unto it &longs;elf: Therefore the Times are equal: Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. VIII. PROP. VIII.</s></p><p type="main"> <s>In Planes cut by the &longs;ame Circle, erect to the <lb/>Horizon, in tho&longs;e which meet with the end of <lb/>the erect Diameter, whether upper or lower, <lb/>the Times of the Motions are equal to the <lb/>Time of the Fall along the Diameter: and in <lb/>tho&longs;e which fall &longs;hort of the Diameter, the <lb/>Times are &longs;horter; and in tho&longs;e which inter­<lb/>&longs;ect the Diameter, they are longer.</s></p><p type="main"> <s><emph type="italics"/>Let A B be the Perpendicular Diameter of the Circle erect to the <lb/>Horizon. </s> <s>That the Times of the Motions along the Planes pro­<lb/>duced out of the Terms A and B unto the Circumference are equal, <lb/>hath already been demon&longs;trated: That the Time of the De&longs;cent along <lb/>the Plane D F, not reaching to the<emph.end type="italics"/><lb/><figure id="id.040.01.856.2.jpg" xlink:href="040/01/856/2.jpg"/><lb/><emph type="italics"/>Diameter is &longs;borter, is demon&longs;trated <lb/>by drawing the Plane D B, which <lb/>&longs;hall be both longer and le&longs;&longs;e decli­<lb/>ning than D F. </s> <s>Therefore the Time <lb/>along D F is &longs;horter than the Time <lb/>along D B, that is, along A B. </s> <s>And <lb/>that the Time of the De&longs;cent along <lb/>the Plane that inter&longs;ecteth the Dia­<lb/>meter, as C O is longer, doth in the <lb/>&longs;ame manner appear, for that it is <lb/>longer and le&longs;&longs;e declining than C B: Therefore the Propo&longs;ition is de­<lb/>mon&longs;trated.<emph.end type="italics"/></s></p><pb xlink:href="040/01/857.jpg" pagenum="164"/><p type="head"> <s>THEOR. IX. PROP. IX.</s></p><p type="main"> <s>If two Planes be inclined at plea&longs;ure from a point <lb/>in a Line parallel to the Horizon, and be inter­<lb/>&longs;ected by a Line which may make Angles Al­<lb/>ternately equal to the Angles contained be­<lb/>tween the &longs;aid Planes and Horizontal Parallel, <lb/>the Motion along the parts cut off by the &longs;aid <lb/>Line, &longs;hall be performed in equal Times.</s></p><p type="main"> <s><emph type="italics"/>From off the point C of the Horizontal Line X, let any two Planes <lb/>be inclined at plea&longs;ure C D and C E, and in any point of the <lb/>Line C D make the Angle C D F equal to the Angle X C E: <lb/>and let the Line D F cut the Plane C E in F, in &longs;uch a manner that <lb/>the Angles C D F and C F D may be equal to the Angles X C E, L C D <lb/>Alternately taken. </s> <s>I &longs;ay, that<emph.end type="italics"/><lb/><figure id="id.040.01.857.1.jpg" xlink:href="040/01/857/1.jpg"/><lb/><emph type="italics"/>the Times of the De&longs;cents along <lb/>C D and C F are equal. </s> <s>And <lb/>that (the Angle C D F being <lb/>&longs;uppo&longs;ed equal to the Angle <lb/>X C E) the Angle C F D is <lb/>equal to the Angle D C L, is <lb/>manife&longs;t. </s> <s>For the Common An­<lb/>gle D C F being taken from the <lb/>three Angles of the Triangle <lb/>C D F equal to two Right An­<lb/>gles, to which are equal all the Angles made with to the Line L X <lb/>at the point C, there remains in the Triangle two Angles C D F and <lb/>C F D, equal to the two Angles X C E and L C D: But it was &longs;up­<lb/>po&longs;ed that C D F is equal to the Angle X C E: Therefore the remaining <lb/>Angle C F D is equal to the remaining angle D C L. </s> <s>Let the Plane <lb/>C E be &longs;uppo&longs;ed equal to the Plane C D, and from the points D and <lb/>E rai&longs;e the Perpendiculars D A and E B, unto the Horizontal Paral­<lb/>lel X L; and from C unto D F let fall the Perpendicular C G. </s> <s>And <lb/>becau&longs;e the Angle C D G is equal to the Angle E C B; and becau&longs;e <lb/>D G C and C B E are Right Angles; The Triangles C D G and <lb/>C B E &longs;hall be equiangled: And as D C is to C G, &longs;o let C E be <lb/>to E B: But D C is equal to C E: Therefore C G &longs;hall be equal to <lb/>E B. </s> <s>And inregard that of the Triangles D A C and C G F, the An­<lb/>gles C and A are equal to the Angles F and G: Therefore as C D is to <lb/>D A, &longs;o &longs;hall F C be to C G; and Alternately, as D C is to C F, &longs;o<emph.end type="italics"/><pb xlink:href="040/01/858.jpg" pagenum="165"/><emph type="italics"/>is D A to C G, or B E. </s> <s>The proportion therefore of the Elevations <lb/>of the Planes equal to C D and C E, is the &longs;ame with the proportion <lb/>of the Longitudes D C and C E: Therefore, by the fir&longs;t Corollary of <lb/>the precedent Sixth Propo&longs;ition, the Times of the Dc&longs;cent along the <lb/>&longs;ame &longs;hall be equal: Which mas to be proved.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Take the &longs;ame another way: Draw F S perpendicular to the <lb/>Horizontal Parallel A S. </s> <s>Becau&longs;e the Triangle C S F is like to <lb/>the Triangle D G C, it &longs;hall be, that as S F is to F C, &longs;o is G C <lb/>to C D. </s> <s>And becau&longs;e the Triangle C F G is like to the Triangle <lb/>D C A, it &longs;hall be, that as F C is to C G, &longs;o is C D to D A: <lb/>Therefore,<emph.end type="italics"/> ex æquali, <emph type="italics"/>as <lb/>S F is to C G, &longs;o is C G to <lb/>D A: Thorefore C G is a<emph.end type="italics"/><lb/><figure id="id.040.01.858.1.jpg" xlink:href="040/01/858/1.jpg"/><lb/><emph type="italics"/>Mean-proportional between <lb/>S F and D A: And as DA <lb/>is to S F, &longs;o is the Square <lb/>D A unto the Square C G <lb/>Again, the Triangle A C D <lb/>being like to the Triangle <lb/>C G F, it &longs;hall be, that as <lb/>D A is to D C, &longs;o is G C <lb/>to C F: and, Alternately, <lb/>as D A is to G C, &longs;o is D C to C F; and as the Square of D A <lb/>is to the Square of C G, &longs;o is the Square of D C to the Square of <lb/>C F. </s> <s>But it hath been proved that the Square D A is to the <lb/>Square C G as the Line D A is to the Line F S: Therefore, as the <lb/>Square D C is to the Square C F, &longs;o is the Line D E to F S: There­<lb/>fore, by the &longs;eventh fore-going, in regard that the Elevations D A <lb/>and F S, of the Planes C D, and C F are in double proportion to <lb/>their Planes; the Times of the Motions along the &longs;ame &longs;hall be <lb/>equal.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. X. PROP. X.</s></p><p type="main"> <s>The Times of the Motions along &longs;everal Inclina­<lb/>tions of Planes who&longs;e Elevations are equal, <lb/>are unto one another as the Lengths of tho&longs;e <lb/>Planes, whether the Motions be made from <lb/>Re&longs;t, or there hath proceeded a Motion from <lb/>the &longs;ame height.</s></p><p type="main"> <s><emph type="italics"/>Let the Motions be made along A B C, and along A B D, until <lb/>they come to the Horizon D C, in &longs;uch &longs;ort as that the Motion <lb/>along A B precedeth the Motions along B D and B C. </s> <s>I &longs;ay, <lb/>that the Time of the Motion along B D, is to the Time along B C, as<emph.end type="italics"/><pb xlink:href="040/01/859.jpg" pagenum="166"/><emph type="italics"/>the Length B D is to B C. </s> <s>Let A F be drawn parallel to the Ho­<lb/>rizon, to which continue out D B, meeting it in F; and let F E be <lb/>a Mean-proportional between D F and F B; and draw E O parallel <lb/>to D C, and A O &longs;hall be a Mean-proportional between C A and <lb/>A B: But if we &longs;uppo&longs;e the Time <lb/>along A B, to be as A B, the Time a-<emph.end type="italics"/><lb/><figure id="id.040.01.859.1.jpg" xlink:href="040/01/859/1.jpg"/><lb/><emph type="italics"/>long F B &longs;hall be as F B. </s> <s>And the <lb/>Time along all A C, &longs;hall be as the <lb/>Mean-proportional A O; and along <lb/>all F D &longs;hall be F E: Wherefore the <lb/>Time along the remainder B C &longs;hall <lb/>be B O; and along the remainder <lb/>B D &longs;hall be B E. </s> <s>But as B E is to <lb/>B O, &longs;o is B D to B C: Therefore <lb/>the Times along B D and B C, after the De&longs;cent along A B and <lb/>F B, or which is the &longs;ame, along the Common part A B, &longs;hall be to <lb/>one another as the Lengths B D and B C: But that the Time along <lb/>B D, is to the Time along B C, out of Re&longs;t in B, as the Length <lb/>B D to B C, hath already been demon&longs;trated. </s> <s>Therefore the Times <lb/>of the Motions along different Planes who&longs;e Elevations are equal, are <lb/>to one another as the Lengths of the &longs;aid Planes, whether the Motion <lb/>be made along the &longs;ame out of Re&longs;t, or whether another Motion of <lb/>the &longs;ame Altitude do precede tho&longs;e Motions: Which was to be de­<lb/>mon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. XI. PROP. XI.</s></p><p type="main"> <s>If a Plane, along which a Motion is made out of <lb/>Re&longs;t, be divided at plea&longs;ure, the Time of <lb/>the Motion along the fir&longs;t part, is to the Time <lb/>of the Motion along the &longs;econd, as the &longs;aid <lb/>fir&longs;t part is to the exce&longs;&longs;e whereby the &longs;ame <lb/>part &longs;hall be exceeded by the Mean-Propor­<lb/>tional between the whole Plane and the &longs;ame <lb/>fir&longs;t part.</s></p><p type="main"> <s><emph type="italics"/>Let the Motion be along the whole Plane A B, ex quiete in A, <lb/>which let be divided at plea&longs;ure in C; and let A F be a Mean <lb/>proportional between the whole B A and the fir&longs;t part A C; <lb/>C F &longs;hall be the exce&longs;&longs;e of the Mean proportional F A above the part <lb/>A C. </s> <s>I &longs;ay the Time of the Motion along A C is to the Time of the <lb/>following Motion along C B, as A C to C F. </s> <s>Which is manife&longs;t;<emph.end type="italics"/><pb xlink:href="040/01/860.jpg" pagenum="167"/><emph type="italics"/>For the Time along A C is to the Time along all <lb/>A B, as A C to the Mean-proportional A F: There-<emph.end type="italics"/><lb/><figure id="id.040.01.860.1.jpg" xlink:href="040/01/860/1.jpg"/><lb/><emph type="italics"/>fore, by Divi&longs;ion, the Time along A C, &longs;hall be to <lb/>the Time along the remainder C B as A C to C F: <lb/>If therefore the Time along A C be &longs;uppo&longs;ed to be <lb/>the &longs;aid A C, the Time along C B &longs;hall be C F: <lb/>Which was the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>But if the Motion be not made along the continu­<lb/>ate Plane A C B, but by the inflected Plane A C D <lb/>until it come to the Horizon B D, to which from F a Parallel is <lb/>drawn F E. </s> <s>It &longs;hall in like manner be<emph.end type="italics"/><lb/><figure id="id.040.01.860.2.jpg" xlink:href="040/01/860/2.jpg"/><lb/><emph type="italics"/>demon&longs;trated, that the Time along <lb/>A C is to the Time along the reflected <lb/>Plane C D, as A C is to C E. </s> <s>For <lb/>the Time along A C is to the Time a­<lb/>long C B, as A C is to C F: But the <lb/>Time along C B, after A C hath been <lb/>demon&longs;trated to be to the Time along <lb/>C D, after the &longs;aid De&longs;oent along <lb/>A C, as C B is to C D; that is, as <lb/>C F to C E: Therefore,<emph.end type="italics"/> ex æquali, <emph type="italics"/>the Time along A C &longs;hall be to <lb/>the Time along C D, as the Line A C to C E.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. XII. PROP. XII.</s></p><p type="main"> <s>If the Perpendicular and Plane Inclined at plea­<lb/>&longs;ure, be cut between the &longs;ame Horizontal <lb/>Lines, and Mean-Proportionals between <lb/>them and the parts of them contained betwixt <lb/>the common Section and upper Horizontal <lb/>Line be given; the Time of the Motion a­<lb/>long the Perpendicular &longs;hall have the &longs;ame <lb/>proportion to the Time of the Motion along <lb/>the upper part of the Perpendicular, and af­<lb/>terwards along the lower part of the inter&longs;e­<lb/>cted Plane, as the Length of the whole Per­<lb/>pendicular hath to the Line compounded of <lb/>the Mean-Proportional given upon the Per­<lb/>pendicular, and of the exce&longs;&longs;e by which the <lb/>whole Plane exceeds its Mean-Proporttonal.</s></p><pb xlink:href="040/01/861.jpg" pagenum="168"/><p type="main"> <s><emph type="italics"/>Let the Horizontal Lines be A F the upper, and C D the low­<lb/>er; between which let the Perpendicular A C, and inclined <lb/>Plane D F, be cut in B; and let A R be a Mean-Proportional <lb/>between the whole Perpendicular C A, and the upper part A B; and <lb/>let F S be a Mean-proportional between the whole Inclined Plane D F, <lb/>and the upper part B F. </s> <s>I &longs;ay, that the Time of the Fall along the <lb/>whole Perpendicular A C hath the &longs;ame proportion to the Time along <lb/>its upper part A B, with the lower of the Plane, that is, with B D, <lb/>as A C hath to the Mean-proporti­<lb/>onal of the Perpendicular, that is<emph.end type="italics"/><lb/><figure id="id.040.01.861.1.jpg" xlink:href="040/01/861/1.jpg"/><lb/><emph type="italics"/>A R, with S D, which is the ex­<lb/>ce&longs;&longs;e of the whole Plane D F above <lb/>its Mean-proportional F S. </s> <s>Let a <lb/>Line be drawn from R to S, which <lb/>&longs;hall be parallel to the two Horizon­<lb/>tal Lines. </s> <s>And becau&longs;e the Time of <lb/>the Fall along all A C, is to the <lb/>Time along the part A B, as C A is <lb/>to the Mean proportional A R, if we &longs;uppo&longs;e A C to be the Time of <lb/>the Fall along A C, A R &longs;hall be the Time of the Fall along A B, <lb/>and R C that along the remainder B C. </s> <s>For if the Time along A C <lb/>be &longs;uppo&longs;ed, as was done, to be A C it &longs;elf the Time along F D &longs;hall <lb/>be F D; and in like manner D S may be concluded to be the Time a­<lb/>long B D, after F B, or after A B. </s> <s>The Time therefore along the <lb/>whole A C, is A R, with R C; And the Time along the inflected <lb/>Plane A B D, &longs;hall be A R, with S D: Which was to be proved.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The &longs;ame happeneth, if in&longs;tead of the Perpendicular, another <lb/>Plane were taken, as &longs;uppo&longs;e N O; and the Demonstration is the <lb/>&longs;ame.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL I. PROP. XIII.</s></p><p type="main"> <s>A Perpendicular being given, to Inflect a Plane <lb/>unto it, along which, when it hath the &longs;ame <lb/>Elevation with the &longs;aid Perpendicular, it may <lb/>make a Motion after its Fall along the Per­<lb/>pendicular in the &longs;ame Time, as along the <lb/>&longs;ame Perpendicular <emph type="italics"/>ex quiete.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular given be A B, to which extended to C, <lb/>let the part B C be equal; and draw the Horizontal Lines <lb/>C E and A G. </s> <s>It is required from B to inflect a Plane reach­<lb/>ing to the Horizon C E, along which a Motion, after the Fall out<emph.end type="italics"/><pb xlink:href="040/01/862.jpg" pagenum="169"/><emph type="italics"/>of A, &longs;hall be made in the &longs;ame Time, as along A B from Re&longs;t in A. </s> <s>Let <lb/>C D be equal to C B, and drawing B D, let B E be applied equal to both <lb/>B D and D C. </s> <s>I &longs;ay B E is the Plane required. </s> <s>Continue out E B to <lb/>meet the Horizontal Line A G in G;<emph.end type="italics"/><lb/><figure id="id.040.01.862.1.jpg" xlink:href="040/01/862/1.jpg"/><lb/><emph type="italics"/>and let G F be a Mean-Proportional be­<lb/>tween the &longs;aid E G and G B. </s> <s>E F &longs;hall <lb/>be to F B, as E G is to G F; and the <lb/>Square E F &longs;hall be to the Square F B, as <lb/>the Square E G is to the Square G F; <lb/>that is as the Line E G to G B: But <lb/>E G is double to G B: Therefore the <lb/>Square of E F is double to the Square of F B: But al&longs;o the Square of <lb/>D B is double to the Square of B C: Therefore, as the Line E F is to <lb/>F B, &longs;o is D B to B C: And by Compo&longs;ition and Permutation, as E B is <lb/>to the two D B and B C, &longs;o is B F to B C: But B E is equal to the two <lb/>D B and B C: Therefore B F is equal to the &longs;aid B C, or B A. </s> <s>If there­<lb/>fore A B be under&longs;tood to be the Time of the Fall along A B, G B &longs;hall <lb/>be the Time along G B, and G F the Time along the whole G E: There­<lb/>fore B F &longs;hall be the Time along the remainder B E, after the Fall from <lb/>G, or from A, which was the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. II. PROP. XIV.</s></p><p type="main"> <s>A <emph type="italics"/>P<emph.end type="italics"/>erpendicular and a <emph type="italics"/>P<emph.end type="italics"/>lane inclined to it being <lb/>given, to find a part in the upper <emph type="italics"/>P<emph.end type="italics"/>erpendicu­<lb/>lar which &longs;hall be pa&longs;t <emph type="italics"/>ex quiete<emph.end type="italics"/> in a Time <lb/>equal to that in which the inclined <emph type="italics"/>P<emph.end type="italics"/>lane is <lb/>pa&longs;t after the Fall along the part found in the <lb/>Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular be D B, and the Plane inclined to it A C. </s> <s>It is <lb/>required in the Perpendicular A D to find a part which &longs;hall be <lb/>pa&longs;t<emph.end type="italics"/> ex quiete <emph type="italics"/>in a Time equal to that in which the Plane A C is <lb/>pa&longs;t after the Fall along the &longs;aid part. </s> <s>Draw the Horizontal Line C B; <lb/>and as B A more twice A C is to A C, &longs;o let E A be to A R; And from <lb/>R let fall the Perpendicular R X unto D B. </s> <s>I &longs;ay X is the point requi­<lb/>red. </s> <s>And becau&longs;e as B A more twice A C is to A C, &longs;o is C A to A E, <lb/>by Divi&longs;ion it &longs;hall be that as B A more A C is to A C, &longs;o is C E to E A: <lb/>And becau&longs;e as B A is to A C, &longs;o is E A to A R, by Compo&longs;ition it &longs;hall <lb/>be that as B A more A C is to A C, &longs;o is E R to R A: But as B A more <lb/>A C is to A C, &longs;o is C E to E A: Therefore, as C E is to E A, &longs;o is E R, <lb/>to R A, and both the Antecedents to both the Con&longs;equents, that is, C R<emph.end type="italics"/><pb xlink:href="040/01/863.jpg" pagenum="170"/><emph type="italics"/>to R E: Therefore C R, R E, and R A are Proportionals. </s> <s>Farther­<lb/>more, becau&longs;e as B A is to A C, &longs;o E A is &longs;uppo&longs;ed to be to A R, and,<emph.end type="italics"/><lb/><figure id="id.040.01.863.1.jpg" xlink:href="040/01/863/1.jpg"/><lb/><emph type="italics"/>in regard of the likene&longs;&longs;e of the Triangles, <lb/>as B A is to A C, &longs;o is X A to A R: There­<lb/>fore, as E A is to A R, &longs;o is X A to A R: <lb/>Therefore E A and X A are equal. </s> <s>Now if <lb/>we under&longs;tand the Time along R A to be as <lb/>R A, the Time along R C &longs;hall be R E, the <lb/>Mean-Proportional between C R and R A: <lb/>And A E &longs;hall be the Time along A C after <lb/>R A or after X A: But the Time along X A <lb/>is X A, &longs;o long as R A is the Time along R <lb/>A: But it hath been proved that X A and <lb/>A E are equal: Therefore the Propo&longs;ition is proved.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. III. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> XV.</s></p><p type="main"> <s>A <emph type="italics"/>P<emph.end type="italics"/>erpendicular and a <emph type="italics"/>P<emph.end type="italics"/>lane inflected to it being <lb/>given, to find a part in the <emph type="italics"/>P<emph.end type="italics"/>erpendicular ex­<lb/>tended downwards which &longs;hall be pa&longs;&longs;ed in the <lb/>&longs;ame. </s> <s>Time as the inflected <emph type="italics"/>P<emph.end type="italics"/>lane after the Fall <lb/>along the given Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular be A B, and the Plane In&longs;lected to it B C. </s> <s>It <lb/>is required in the Perpendicular extended downwards to find a <lb/>part which from the Fall out of A &longs;hall be pa&longs;t in the &longs;ame Time as <lb/>B C is pa&longs;&longs;ed from the &longs;ame Fall out of A. </s> <s>Draw the Horizontal Line <lb/>A D, with which let C B meet extended to D; and let D E be a Mean­<lb/>proportional between C D and D B;<emph.end type="italics"/><lb/><figure id="id.040.01.863.2.jpg" xlink:href="040/01/863/2.jpg"/><lb/><emph type="italics"/>and let B F be equal to B E; and let <lb/>A G be a third Proportional to B A and <lb/>A F. </s> <s>I &longs;ay, B G is the Space that after <lb/>the Fall A B &longs;hall be pa&longs;t in the &longs;ame <lb/>Time, as the Plane B C &longs;hall be pa&longs;t af­<lb/>ter the &longs;ame Fall. </s> <s>For if we &longs;uppo&longs;e <lb/>the Time along A B to be as A B, the <lb/>Time along D B &longs;hall be as D B: And <lb/>becau&longs;e D E is the Mean-proportional <lb/>between B D and D C, the &longs;ame D E <lb/>&longs;hall be the Time along the whole D C, and B E the Time along the Part <lb/>or Remainder B C<emph.end type="italics"/> ex quiete, <emph type="italics"/>in D, or<emph.end type="italics"/> ^{*} ex ca&longs;u <emph type="italics"/>A B: And it may in<emph.end type="italics"/><lb/><arrow.to.target n="marg1093"></arrow.to.target><lb/><emph type="italics"/>like manner be proved, that B F is the Time along B G, after the &longs;ame <lb/>Fall: But B F is equal to B E: Which was the Propo&longs;ition to be proved.<emph.end type="italics"/></s></p><pb xlink:href="040/01/864.jpg" pagenum="171"/><p type="margin"> <s><margin.target id="marg1093"></margin.target>* From or after <lb/>the Fall A B.</s></p><p type="head"> <s>THEOR. XIII. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> XVI.</s></p><p type="main"> <s>If the parts of an inclined <emph type="italics"/>P<emph.end type="italics"/>lane and <emph type="italics"/>P<emph.end type="italics"/>erpendicu­<lb/>lar, the Times of who&longs;e Motions <emph type="italics"/>ex quiete<emph.end type="italics"/> are <lb/>equal, be joyned together at the &longs;ame point, a <lb/>Moveable coming out of any &longs;ublimer Height <lb/>&longs;hall &longs;ooner pa&longs;&longs;e the &longs;aid part of the inclined <lb/><emph type="italics"/>P<emph.end type="italics"/>lane, than that part of the Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular be E B, and the Inclined Plane C E, joyned <lb/>at the &longs;ame Point E, the Times of who&longs;e Motions from off Re&longs;t in <lb/>E are equal, and in the Perpendicular continued out, let a &longs;ublime <lb/>point A be taken at plea&longs;ure, out of which the Moveables may be let <lb/>fall. </s> <s>I &longs;ay, that the Inclined Plane E C &longs;hall be pa&longs;&longs;ed in a le&longs;&longs;e Time <lb/>than the Perpendicular E B, after the Fall A E. </s> <s>Draw a Line from C <lb/>to B, and having drawn the Horizontal Line A D continue out C E till <lb/>it meet the &longs;ame in D; and let D F be a Mean-Proportional between <lb/>C D and D E; and let A G be a<emph.end type="italics"/><lb/><figure id="id.040.01.864.1.jpg" xlink:href="040/01/864/1.jpg"/><lb/><emph type="italics"/>Mean-Proportional between B A and <lb/>A E; and draw F G and D G. </s> <s>And <lb/>becau&longs;e the Time of the Motion along <lb/>E C and E B out of Re&longs;t in E are <lb/>equal, the Angle C &longs;hall be a Right <lb/>Angle, by the &longs;econd Corollary of the <lb/>Sixth Propo&longs;ition; and A is a Right <lb/>Angle, and the Vertical Angles <lb/>at E are equal: Therefore the Tri­<lb/>angles A E D and C E B are equian­<lb/>gled, and the Sides about equal An­<lb/>gles are Proportionals: Therefore as <lb/>B E is to E C, &longs;o is D E to E A. <lb/></s> <s>Therefore the Rectangle B E A is <lb/>equal to the Rectangle C E D: And <lb/>becau&longs;e the Rectangle C D E ex­<lb/>ceedeth the Rectangle C E D, by the Square E D, and the Rectangle <lb/>B A E doth exceed the Rectangle B E A, by the Square E A: The <lb/>exce&longs;&longs;e of the Rectangle C D E above the Rectangle B A E, that is of <lb/>the Square F D above the Square A G &longs;hall be the &longs;ame as the exce&longs;&longs;e <lb/>of the Square D E above the Square A E; which exce&longs;s is the <lb/>Square D A: Therefore the Square F D is equal to the two Squares <lb/>G A and A D, to which the Square G D is al&longs;o equal: Therefore the<emph.end type="italics"/><pb xlink:href="040/01/865.jpg" pagenum="172"/><emph type="italics"/>Line D F is equal to D G, and the Angle D G F is equal to the An­<lb/>gle D F G, and the Angle E G F is le&longs;&longs;c than the Angle E F G, and <lb/>the oppo&longs;ite Side E F le&longs;&longs;e than the Side E G. </s> <s>Now if we &longs;uppo&longs;e <lb/>the Time of the Fall along A E to be as A E, the Time by D E &longs;hall <lb/>be as D E; and A G being a Mean-Proportional between B A and A E, <lb/>A G &longs;hall be the Time along the whole A B, and the part E G &longs;hall be <lb/>the Time along the Part E B<emph.end type="italics"/> ex quiete <emph type="italics"/>in A. </s> <s>And it may in like man­<lb/>ner be proved that E F is the Time along E C after the De&longs;cent D E, or <lb/>after the Fall A E: But E F is proved to be le&longs;&longs;er than E G: Therefore <lb/>the Propo&longs;ition is proved.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>By this and the precedent it appears, that the Space that is pa&longs;­<lb/>&longs;ed along the Perpendicular after the Fall from above in the <lb/>&longs;ame Time in which the Inclined Plane is pa&longs;t, is le&longs;&longs;e than <lb/>that which is pa&longs;t in the &longs;ame Time as in the Inclined, no fall <lb/>from above preceding, yet greater than the &longs;aid Inclined <lb/>Plane.</s></p><p type="main"> <s><emph type="italics"/>For it having been proved, but now, that of the Moveables coming <lb/>from the &longs;ublime Term A the Time of the Conver&longs;ion along E C is <lb/>&longs;horter than the Time of the Progre&longs;&longs;ion along E B; It is manife&longs;t that <lb/>the Space that is pa&longs;t along E B in a Time equal to the Time along E C <lb/>is le&longs;s than the whole Space E B. </s> <s>And that the &longs;ame Space along the <lb/>Perpendicular is greater than E C is mani­<lb/>fe&longs;ted by rea&longs;&longs;uming the Figure of the pre-<emph.end type="italics"/><lb/><figure id="id.040.01.865.1.jpg" xlink:href="040/01/865/1.jpg"/><lb/><emph type="italics"/>cedent Propo&longs;ition, in which the part of the <lb/>Perpendicular B G hath been demon&longs;trated <lb/>to be pa&longs;&longs;ed in the &longs;ame Time as B C after <lb/>the Fall A B: But that B G is greater than <lb/>B C is thus collected. </s> <s>Becau&longs;e B E and F B <lb/>are equal, and B A le&longs;&longs;er than B D, F B, <lb/>hath greater proportion to B A, than E B <lb/>hath to B D: And, by Compo&longs;ition, F A <lb/>hath greater proportion to A B, than E D <lb/>to D B: But as F A is to A B, &longs;o is G F <lb/>to F B, (for A F is the Mean-Proportional <lb/>between B A and A G:) And in like man­<lb/>ner, as E D is to B D, &longs;o is C E to E B: Therefore G B hath greater <lb/>proportion to B F, than C B hath to B E: Therefore G B is greater <lb/>than B C.<emph.end type="italics"/></s></p><pb xlink:href="040/01/866.jpg" pagenum="173"/><p type="head"> <s>PROBL. IV. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> XVII.</s></p><p type="main"> <s>A <emph type="italics"/>P<emph.end type="italics"/>erpendicular and <emph type="italics"/>P<emph.end type="italics"/>lane Inflected to it being <lb/>given, to a&longs;&longs;ign a part in the given <emph type="italics"/>P<emph.end type="italics"/>lane, in <lb/>which after the Fall along the <emph type="italics"/>P<emph.end type="italics"/>erpendicular <lb/>the Motion may be made in a Time equal to <lb/>that in which the Moveable <emph type="italics"/>ex quiete<emph.end type="italics"/> pa&longs;&longs;eth <lb/>the <emph type="italics"/>P<emph.end type="italics"/>erpendicular given.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular be A B, and a Plane Inflected to it B E: It is <lb/>required in B E to a&longs;&longs;ign a Space along which the Moveable af­<lb/>ter the Fall along A B may move in a Time equal to that in which <lb/>the &longs;aid Perpendicular A B is pa&longs;&longs;ed<emph.end type="italics"/> ex quiete. <emph type="italics"/>Let the Line A D be <lb/>parallel to the Horizon, with which let the Plane prolonged meet in D; <lb/>and &longs;uppo&longs;e F B equal to B A; and as B D <lb/>is to D F, &longs;o let F D be to D E. </s> <s>I &longs;ay, that<emph.end type="italics"/><lb/><figure id="id.040.01.866.1.jpg" xlink:href="040/01/866/1.jpg"/><lb/><emph type="italics"/>the Time along B E after the Fall along A B <lb/>equalleth the Time along A B, out of Re&longs;t <lb/>in A. </s> <s>For if we &longs;uppo&longs;e A B to be the Time <lb/>along A B, D B &longs;hall be the Time along <lb/>D B. </s> <s>And becau&longs;e, as B D is to D F, &longs;o is <lb/>F D to D E, D F &longs;hall be the Time along <lb/>the whole Plane D E, and B F along the <lb/>part B E out of D: But the Time along <lb/>B E after D B, is the &longs;ame as after A B: Therefore the Time along B E <lb/>after A B &longs;hall be B F, that is, equal to the Time<emph.end type="italics"/> ex quiete <emph type="italics"/>in A: <lb/>Which was the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>P<emph.end type="italics"/>ROBL. V. PROP. XVIII.</s></p><p type="main"> <s>Any Space in the Perpendicular being given from <lb/>the a&longs;&longs;igned beginning of Motion that is <lb/>pa&longs;&longs;ed in a Time given, and any other le&longs;&longs;er <lb/>Time being al&longs;o given, to find another Space in <lb/>the &longs;aid Perpendicular that may be pa&longs;&longs;ed in <lb/>the given le&longs;&longs;er Time.</s></p><pb xlink:href="040/01/867.jpg" pagenum="174"/><p type="main"> <s><emph type="italics"/>Let the Perpendicular be A D, in which let the Space a&longs;&longs;igned be <lb/>A B, who&longs;e Time from the beginning A let be A B: and let the <lb/>Horizon be C B E, and let a Time be given le&longs;s than A B, to <lb/>which let B C be noted equal in the Horizon: It is required in the <lb/>&longs;aid Perpendicular to find a Space equal to the &longs;ame A B that &longs;hall be <lb/>pa&longs;&longs;ed in the Time B C. </s> <s>Draw a Line from A to<emph.end type="italics"/><lb/><figure id="id.040.01.867.1.jpg" xlink:href="040/01/867/1.jpg"/><lb/><emph type="italics"/>C. </s> <s>And becau&longs;e B C is le&longs;&longs;e than B A, the Angle <lb/>B A C &longs;hall be le&longs;&longs;e than the Angle B C A. </s> <s>Let <lb/>C A E be made equal to it, and the Line A E meet <lb/>with the Horizon in the Point E, to which &longs;up­<lb/>po&longs;e E D a Perpendicular, cutting the Perpendi­<lb/>cular in D, and let D F be cut equal to B A. </s> <s>I <lb/>&longs;ay, that the &longs;aid F D is a part of the Perpendi­<lb/>cular along which the Lation from the beginning <lb/>of Motion in A, the Time B C given will be &longs;pent. <lb/></s> <s>For if in the Right-angled Triangle A E D, a <lb/>Perpendicular to the oppo&longs;ite Side A D, be drawn <lb/>E B, A E &longs;hall be a Mean-Proportional betwixt <lb/>D A and A B, and B E a Mean-Proportional betwixt D B and B A, <lb/>or betwixt F A and A B (for F A is equal to D B.) And in regard <lb/>A B hath been &longs;uppo&longs;ed to be the Time along A B, A E, or E C &longs;hall be <lb/>the Time along the whole A D, and E B the Time along A F: There­<lb/>fore the part B C &longs;hall be the Time along the part F D: Which was <lb/>intended.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. VI. PROP. XIX.</s></p><p type="main"> <s>Any Space in the Perpendicular pa&longs;&longs;ed from the <lb/>beginning of the Motion being given, and the <lb/>Time of the Fall being a&longs;&longs;igned, to find the <lb/>Time in which another Space. </s> <s>equal to the gi­<lb/>ven one, and taken in any part of the &longs;aid Per­<lb/>pendicular, &longs;hall be afterwards pa&longs;t by the <lb/>&longs;ame Moveable.</s></p><p type="main"> <s><emph type="italics"/>In the Perpendicular A B let A C be any Space taken from the be­<lb/>ginning of the Motion in A, to which let D B be another equal Space <lb/>taken any where at plea&longs;ure, and let the Time of the Motion along <lb/>A C be given, and let it be A C. </s> <s>It is required to &longs;ind the Time of the<emph.end type="italics"/><pb xlink:href="040/01/868.jpg" pagenum="175"/><emph type="italics"/>Motion along D B after the Fall from A. </s> <s>About the whole A B de­<lb/>&longs;cribe a Semicircle A E B, and from<emph.end type="italics"/><lb/><figure id="id.040.01.868.1.jpg" xlink:href="040/01/868/1.jpg"/><lb/><emph type="italics"/>C let fall C E, a Perpendicular to A <lb/>B, and draw a Line from A to E; <lb/>which &longs;hall be greater than E C. <lb/></s> <s>Let E F be out equall to E C: I &longs;ay, <lb/>that the remainder F A is the Time <lb/>of the Motion along D B. </s> <s>For be­<lb/>cau&longs;e A E is a Mean-proportional be­<lb/>twixt B A and and A C, and A C <lb/>is the Time of the Fall along A C; <lb/>A E &longs;hall be the Time along the <lb/>Whole A B. </s> <s>And becau&longs;e C E is a <lb/>Mean-proportional betwixt D A and <lb/>A C, (for D A is equal to B C) <lb/>C E, that is E F &longs;hall be the Time <lb/>along A D: Therefore the Remainder A F &longs;hall be the Time along the <lb/>Remainder B B: Which is the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence is gathered, that if the Time of any Space <emph type="italics"/>ex quiete<emph.end type="italics"/> be <lb/>as the &longs;aid Spaec, the Time thereof after another Space is ad­<lb/>ded &longs;hall be the exce&longs;&longs;e of the Mean-proportional betwixt <lb/>the Addition and Space taken together, and the &longs;aid Space <lb/>above the Mean-proportional betwixt the fir&longs;t Space and the <lb/>Addition.</s></p><p type="main"> <s><emph type="italics"/>As for example, it being &longs;uppo&longs;ed that the Time along<emph.end type="italics"/><lb/><figure id="id.040.01.868.2.jpg" xlink:href="040/01/868/2.jpg"/><lb/><emph type="italics"/>A B, out of Re&longs;t in A, be A B; A S being another Space <lb/>added, The Time along A B after S A &longs;hall be the exce&longs;&longs;e of <lb/>the Mean-proportional betwixt S B and B A above the <lb/>Mean-proportional betwixt B A and A S.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL VII. PROP. XX.</s></p><p type="main"> <s>Any Space and a part therein after the begining <lb/>of the Motion being given, to find another <lb/>part towards the end that &longs;hall be pa&longs;t in the <lb/>&longs;ame Time as the fir&longs;t part given.</s></p><p type="main"> <s><emph type="italics"/>Let the Space be C B, and let the part in it given after the begin­<lb/>ing of the Motion in C be C D. </s> <s>It is required to find another <lb/>part towards the end B, which &longs;hall be pa&longs;t in the &longs;ame Time as<emph.end type="italics"/><pb xlink:href="040/01/869.jpg" pagenum="176"/><emph type="italics"/>the given part C D. </s> <s>Take a Mean-proportional betwixt B C and C D, <lb/>to which &longs;uppo&longs;e B A equal; and let C E be a third proportional be-<emph.end type="italics"/><lb/><figure id="id.040.01.869.1.jpg" xlink:href="040/01/869/1.jpg"/><lb/><emph type="italics"/>tween B C and C A. </s> <s>I &longs;ay, that E B is the Space that after <lb/>the Fall out of C &longs;hall be past in the &longs;ame Time as the &longs;aid <lb/>C D is pa&longs;&longs;ed. </s> <s>For if we &longs;uppo&longs;e the Time along C B <lb/>to be as C B; B A (that is the Mean-proportional betwixt <lb/>B C and C D) &longs;hall be the Time along C D. </s> <s>And becau&longs;e <lb/>C A is the Mean proportional betwixt B C and C E, C A <lb/>&longs;hall be the Time along C E: But the whole B C is the <lb/>Time along the Whole C B: Therefore the part B A &longs;hall be <lb/>the Time along the part E B, after the Fall out of C: But <lb/>the &longs;aid B A was the Time along C D: Therefore C D and <lb/>E B &longs;hall be pa&longs;t in equal Times out of Re&longs;t in C: Which <lb/>was to be done.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. XIV. PROP. XXI.</s></p><p type="main"> <s>If along the Perpendicular a Fall be made <emph type="italics"/>ex quie­<lb/>te,<emph.end type="italics"/> in which from the begining of the Motion <lb/>a part is taken at plea&longs;ure, pa&longs;&longs;ed in any Time, <lb/>after which an Inflex Motion followeth along <lb/>any Plane however Inclined, the Space which <lb/>along that Plane is pa&longs;&longs;ed in a Time equal to <lb/>the Time of the Fall already made along the <lb/>Perpendicular &longs;hall be to the Space then pa&longs;­<lb/>&longs;ed along the Perpendicular more than double, <lb/>and le&longs;&longs;e than triple.</s></p><p type="main"> <s><emph type="italics"/>From the Horizon A E let fall a Perpendicular A B, along which <lb/>from the begining A let a Fall be made, of which let a part A C <lb/>be taken at plea&longs;ure; then out of C let any Plane G be inclined at <lb/>plea&longs;ure: along which after the Fall along A C let the Motion be con­<lb/>tinued. </s> <s>I &longs;ay, the Space pa&longs;&longs;ed by that Motion along C G in a Time <lb/>equall to the Time of the Fall along A C, is more than double, and le&longs;s <lb/>than triple that &longs;ame Space A C. </s> <s>For &longs;uppo&longs;e C F equal to A C, and <lb/>extending out the Plane G C as far as the Horizon in E, and as C E <lb/>is to E F, &longs;o let F E be to E G. </s> <s>If therefore we &longs;uppo&longs;e the Time of<emph.end type="italics"/><pb xlink:href="040/01/870.jpg" pagenum="177"/><emph type="italics"/>the Fall along A C to be as the Line A C; C E &longs;hall be the Time along <lb/>E C, and C F or C A the Time of the Motion along C G. </s> <s>Therefore <lb/>it is to be proved that the<emph.end type="italics"/><lb/><figure id="id.040.01.870.1.jpg" xlink:href="040/01/870/1.jpg"/><lb/><emph type="italics"/>Space C G is more than <lb/>double, and le&longs;&longs;e than <lb/>triple the &longs;aid C A. </s> <s>For <lb/>in regard that as C E is <lb/>to E F, &longs;o is F E to E G; <lb/>therefore al&longs;o &longs;o is C F to <lb/>F G. </s> <s>But E C is le&longs;&longs;e <lb/>than E F: Therefore C F <lb/>&longs;hall be le&longs;&longs;e than F G, and <lb/>G C more than double to <lb/>F C or A C. </s> <s>And moreover, in regard that F E is le&longs;&longs;e than double to <lb/>E C, (for E C is greater than C A or C F) G F &longs;hall al&longs;o be le&longs;&longs;e <lb/>than double to F C, and G C le&longs;&longs;e than triple to C F or C A: Which <lb/>was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And the &longs;ame may be more generally propounded: for that which <lb/>hapneth in the Perpendicular and Inclined Plane, holdeth true al&longs;o if <lb/>after the Motion a Plane &longs;omewhat inclined it be inflected along a more <lb/>inclining Plane, as is &longs;een in the other Figure: And the Demon&longs;tration <lb/>is the &longs;ame.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>P<emph.end type="italics"/>ROBL. VIII. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> XXII.</s></p><p type="main"> <s>Two unequall Times being given, and a Space <lb/>that is pa&longs;t <emph type="italics"/>ex quiete<emph.end type="italics"/> along the Perpendicular <lb/>in the &longs;horte&longs;t of tho&longs;e given Times, to inflect <lb/>a Plane from the highe&longs;t point of the Perpen­<lb/>dicular unto the Horizon, along which the <lb/>Moveable may de&longs;cend in a Time equal to the <lb/>longe&longs;t of tho&longs;e Times given.</s></p><p type="main"> <s><emph type="italics"/>Let the unsqual Times be A the greater, and B the le&longs;&longs;er; and let <lb/>the Space that is pa&longs;t<emph.end type="italics"/> ex quiete <emph type="italics"/>along the Perpendicular in the <lb/>Time B, be C D. </s> <s>It is required from the Term C to inflect<emph.end type="italics"/> [or <lb/><figure id="id.040.01.870.2.jpg" xlink:href="040/01/870/2.jpg"/><lb/>bend] <emph type="italics"/>a Plane untill it reach the Horizon that may be pa&longs;&longs;ed in the<emph.end type="italics"/><pb xlink:href="040/01/871.jpg" pagenum="178"/><emph type="italics"/>Time A. </s> <s>As B is to A, &longs;o let C D be to another Line, to which let C X <lb/>be equal that de&longs;cendeth from C unto the Horizon: It is manife&longs;t that <lb/>the Plane C X is that along which the Moveable de&longs;cendeth in the Gi­<lb/>ven Time A. </s> <s>For it hath been demon&longs;trated, that the Time along the <lb/>inclined Plane hath the &longs;ame proportion to the Time along its ^{*} Eleva-<emph.end type="italics"/><lb/><arrow.to.target n="marg1094"></arrow.to.target><lb/><emph type="italics"/>tion, as the Length of the Plane hath to the Length of its Elevation,. <lb/>The Time, therefore, along C X is to the Time along C D, as C X is to <lb/>C D, that is, as the Time A is to the Time B: But the Time B is that <lb/>in which the Perpendicular is pa&longs;t<emph.end type="italics"/> ex quiete: <emph type="italics"/>Therefore the Time A is <lb/>that in which the Plane C X is pa&longs;&longs;ed.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1094"></margin.target>* Or Perpendi­<lb/>cular.</s></p><p type="head"> <s><emph type="italics"/>P<emph.end type="italics"/>ROBL. IX. PROP. XXIII.</s></p><p type="main"> <s>A Space pa&longs;t <emph type="italics"/>ex quiete<emph.end type="italics"/> along the Perpendicular in <lb/>any Time being given, to inflect a Plane from <lb/>the lowe&longs;t term of that Space, along which, <lb/>after the Fall along the Perpendicular, a Space <lb/>equal to any Space given may be pa&longs;&longs;ed in the <lb/>&longs;ame Time: which neverthele&longs;&longs;e is more than <lb/>double, and le&longs;&longs;e than triple the Space pa&longs;&longs;ed <lb/>along the Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Along the Perpendicular A S, in the Time A C, let the Space <lb/>A C be pa&longs;t<emph.end type="italics"/> ex quiete <emph type="italics"/>in A; to which let I R be more than <lb/>double, and le&longs;&longs;e than triple. </s> <s>It is required from the Terme C <lb/>to inflect a Plane, along which a Moveable after the Fall along A C <lb/>may in the &longs;ame Time A C pa&longs;&longs;e a Space equal to the &longs;aid I R. </s> <s>Let <lb/>R N, and N M be equal to A C: And look what proportion the part <lb/>I M hath to M N, the &longs;ame &longs;hall the Line A C have to another, equal <lb/>to which draw C E from C to<emph.end type="italics"/><lb/><figure id="id.040.01.871.1.jpg" xlink:href="040/01/871/1.jpg"/><lb/><emph type="italics"/>the Horizon A E, which con­<lb/>tinue out towards O, and take <lb/>C F, F G, and G O, equal to <lb/>the &longs;aid R N, N M, and M I. <lb/></s> <s>I &longs;ay, that the Time along the <lb/>inflected Plane C O, after the <lb/>Fall A G, is equal to the Time <lb/>A C out of Re&longs;t in A. </s> <s>For in <lb/>regard that as O G is to G F, <lb/>&longs;o is F C to C E by Compo&longs;ition it &longs;hall be that as O F is to F G or F C, <lb/>&longs;o is F E to E C; and as one of the Antecedents is to one of the Con­<lb/>&longs;equents, &longs;o are all to all; that is, the whole O E is to E F as F E to <lb/>E C: Therefore O E, E F, and E C are Continual Proportionals:<emph.end type="italics"/><pb xlink:href="040/01/872.jpg" pagenum="179"/><emph type="italics"/>And &longs;ince it was &longs;uppo&longs;ed that the Time along A C is as A C, C E &longs;hall <lb/>be the Time along E C; and E F the Time along the whole E O; and <lb/>the part C F that along the part C O: But C F is equal to the &longs;aid C A: <lb/>Therefore that is done which was required: For the Time C A is the <lb/>Time of the Fall along A C<emph.end type="italics"/> ex quiete <emph type="italics"/>in A; and C F (which is equal <lb/>to C A) is the Time along C O, after the De&longs;cent along E C, or after <lb/>the Fall along A C: Which was the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And here it is to be noted, that the &longs;ame may happen if the preceding <lb/>Motion be not made along the Perpendicular, but along an Inclined Plane: <lb/>As in the following Figure, in which let the preceding Lation be made <lb/>along the inclined Plane A S beneath the Horizon A E: And the Demon­<lb/>&longs;tration is the very &longs;ame.<emph.end type="italics"/></s></p><p type="head"> <s>SCHOLIUM.</s></p><p type="main"> <s>If one ob&longs;erve well, it &longs;hall be manife&longs;t, that the le&longs;&longs;e the given <lb/>Line I R wanteth of being triple to the &longs;aid A C, the nearer <lb/>&longs;hall the Inflected Plane, along which the &longs;econd Motion is <lb/>to be made, which &longs;uppo&longs;e to be C O, come to the Perpen­<lb/>dicular, along which in a Time equal to A C a Space &longs;hall <lb/>be pa&longs;&longs;ed triple to A C.</s></p><p type="main"> <s><emph type="italics"/>For in ca&longs;e I R were very near the triple of A C, I M &longs;hould be well­<lb/>near equal to M N: And if, as I M is to M N by Con&longs;truction, &longs;o <lb/>A C is to C E, then it is evident that the &longs;aid C E will be found but <lb/>little bigger than C A, and, which followeth of con&longs;equence, the point E <lb/>&longs;hall be found very near the point A, and C O to containe a very acute<emph.end type="italics"/><lb/><figure id="id.040.01.872.1.jpg" xlink:href="040/01/872/1.jpg"/><lb/><emph type="italics"/>Angle with C S, and <lb/>almo&longs;t to concur both in <lb/>one Line. </s> <s>And on the <lb/>contrary, if the &longs;aid I R <lb/>were but a very little <lb/>more than double the <lb/>&longs;aid A C, I M &longs;hould <lb/>be a very &longs;hort Line. <lb/></s> <s>Hence it may happen <lb/>al&longs;o that A C may come <lb/>to be very &longs;hort in re&longs;pect of C E which &longs;hall be very long, and &longs;hall ap­<lb/>proach very near the Horizontal Parallel drawn from C. </s> <s>And from <lb/>hence we may collect, that if in the pre&longs;ent Figure after the De&longs;cent along <lb/>the inclined Plane A C, a Reflexion be made along the Horizontal Line, <lb/>as<emph.end type="italics"/> v. </s> <s>gr. <emph type="italics"/>C T, the Space along which the Moveable afterwards moved <lb/>in a Time equal to the Time of the De&longs;cent along A C would be exactly <lb/>double to the Space A C. </s> <s>And it appears that the like Di&longs;cour&longs;e may be <lb/>here applied: For it is apparent by what hath been &longs;aid, that &longs;ince O E<emph.end type="italics"/><pb xlink:href="040/01/873.jpg" pagenum="180"/><emph type="italics"/>is to E F, as F E is to E C, that F C determineth the Time along C O: <lb/>And if a part of the Horizontal Line T C double to C A be divided in <lb/>two equal parts in V, the exten&longs;ion towards X &longs;hall be prolonged<emph.end type="italics"/> in in­<lb/>finitum, <emph type="italics"/>whil&longs;t it &longs;eeks to meet with the prolonged Line A E: And the <lb/>proportion of the Infinite Line T X to the Infinite Line V X, &longs;hall be <lb/>no other than the proportion of the Infinite Line V X to the Infinite <lb/>Line X C.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>We may conclude the &longs;elf-&longs;ame thing another way by rea&longs;&longs;uming the <lb/>&longs;ame Rea&longs;oning that we u&longs;ed in the Demon&longs;tration of the fir&longs;t Propo&longs;i­<lb/>tion. </s> <s>For re&longs;uming the Triangle A B C, repre&longs;enting to us by its Pa­<lb/>rallels to the Ba&longs;e B C the Degrees of Velocity continually encrea&longs;ed ac­<lb/>cording to the encrea&longs;es of the Time; from which, &longs;ince they are infi­<lb/>nite, like as the Points are infinite in the Line A C, and the In&longs;tants <lb/>in any Time, &longs;hall re&longs;ult the Superficies of that &longs;ame Triangle, if we <lb/>under&longs;tand the Motion to continue for &longs;uch another Time, but no far­<lb/>ther with an Accelerate, but with an Equable Motion, according to the <lb/>greate&longs;t degree of Velocity acquired, which degree is repre&longs;ented <lb/>by the Line B C. </s> <s>Of &longs;uch degrees &longs;hall be made up an Aggregate like to <lb/>a Parallelogram A D B C, which is the double of<emph.end type="italics"/><lb/><figure id="id.040.01.873.1.jpg" xlink:href="040/01/873/1.jpg"/><lb/><emph type="italics"/>the Triangle A B C. </s> <s>Wherefore the Space which <lb/>with degrees like to tho&longs;e &longs;hall be pa&longs;&longs;ed in the &longs;ame <lb/>Time, &longs;hall be double to the Space pa&longs;t with the de­<lb/>grees of Velocity repre&longs;ented by the Triangle A B C: <lb/>But along the Horizontal Plane the Motion is Equa­<lb/>ble, for that there is no cau&longs;e of Acceleration, or Re­<lb/>tardation: Therefore it may be concluded that the <lb/>Space C D, pa&longs;&longs;ed in a Time equall to the Time A C is double to the <lb/>Space A C: For this Motion is made<emph.end type="italics"/> ex quiete <emph type="italics"/>Accelerate according <lb/>to the Parallels of the Triangle; and that according to the Parallels <lb/>of the Parallelogram, which, becau&longs;e they are infinite, are donble to <lb/>the infinite Parallels of the Triangle.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Moreover it may farther be ob&longs;erved, that what ever degree of <lb/>&longs;wiftne&longs;s is to be found in the Moveable, is indelibly impre&longs;&longs;ed upon it <lb/>of its own nature, all external cau&longs;es of Acceleration or Retardation <lb/>being removed; which hapneth only in Horizontal Planes: for in de­<lb/>clining Planes there is cau&longs;e of greater Acceleration, and in the ri&longs;ing <lb/>Planes of greater Retardation. </s> <s>From whence in like manner it fol­<lb/>loweth that the Motion along the Horizontal Plane is al&longs;o Perpetual: <lb/>for if it be Equable, it can neither be weakned nor retarded, nor much <lb/>le&longs;&longs;e de&longs;troyed. </s> <s>Farthermore, the degree of Celerity acquired by the <lb/>Moveable in a Natural De&longs;cent, being of its own Nature Indelible and <lb/>Penpetual, it is worthy con&longs;ideration, that if after the De&longs;cent along a <lb/>declining Plane a Reflexion be made along another Plane that is ri&longs;ing, <lb/>in this latter there is cau&longs;e of Retardation, for in the&longs;e kind of Planes<emph.end type="italics"/><pb xlink:href="040/01/874.jpg" pagenum="181"/><emph type="italics"/>the &longs;aid Moveable doth naturally de&longs;cend; whereupon there re&longs;ults a <lb/>mixture of certain contrary Affections, to wit, that degree of Celerity <lb/>acquired in the precedent De&longs;cent, which would of it &longs;elf carry the Move­<lb/>able uniformly<emph.end type="italics"/> in infinitum, <emph type="italics"/>and of Natural Propen&longs;ion to the Motion of <lb/>De&longs;cent according to that &longs;ame proportion of Acceleration wherewith it <lb/>alwaies moveth. </s> <s>So that it will be but rea&longs;onable, if, enquiring what <lb/>accidents happen when the Moveable after the De&longs;cent along any incli­<lb/>ned Plane is Reflected along &longs;ome ri&longs;ing Plane, we take that greate&longs;t de­<lb/>gree acquired in the De&longs;cent to keep it &longs;elf perpetually the &longs;ame in the <lb/>A&longs;cending Plane; But that there is &longs;uperadded to it in the A&longs;cent the <lb/>Natural Inclination downwards, that is the Motion from Re&longs;t Accelerate <lb/>according to the received proportion: And le&longs;t this &longs;hould, perchance, be <lb/>&longs;omewhat intricate to be under&longs;tood, it &longs;hall be more clearly explained by a <lb/>Scheme.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Let the De&longs;cent therefore be &longs;uppo&longs;ed to be made along the Declining <lb/>Plane A B, from which let the Reflex Motion be continued along another <lb/>Ri&longs;ing Plane B C: And in the fir&longs;t place let the Planes be equal, and <lb/>elevated at equal Angles to the Horizon G H. </s> <s>Now it is manife&longs;t, that <lb/>the Moveable<emph.end type="italics"/> ex quiete <emph type="italics"/>in A de&longs;cending along A B acquireth degrees of <lb/>Velocity according to the increa&longs;e of its Time, and that the degree in B <lb/>is the greate&longs;t of tho&longs;e acquired and by Nature immutably impre&longs;&longs;ed, I <lb/>mean the Cau&longs;es of new Acceleration or Retardation being removed: <lb/>of Acceleration, I &longs;ay, if it &longs;hould pa&longs;&longs;e any farther along the extended <lb/>Plane; and of Retardation, whil&longs;t the Reflection is making along the <lb/>Acclivity B C: But along the Horizontal Plane G H the Equable Mo­<lb/>tion according to the de-<emph.end type="italics"/><lb/><figure id="id.040.01.874.1.jpg" xlink:href="040/01/874/1.jpg"/><lb/><emph type="italics"/>gree of Velocity acquired <lb/>from A unto B would ex­<lb/>tend<emph.end type="italics"/> in infinitum. <emph type="italics"/>And <lb/>&longs;uch a Velocity would <lb/>that be which in a Time <lb/>equal to the Time of the <lb/>De&longs;cent along A B would pa&longs;&longs;e a Space in double the Horizon to the &longs;aid <lb/>A B. </s> <s>Now let us &longs;uppo&longs;e the &longs;ame Moveable to be Equably moved with <lb/>the &longs;ame degree of Swiftne&longs;&longs;e along the Plane B C, in &longs;uch &longs;ort that al&longs;o <lb/>in this Time equal to the Time of the De&longs;cent along A B a Space may be <lb/>pa&longs;&longs;ed a long B C extended double to the &longs;aid A B. </s> <s>And let us under­<lb/>&longs;tand that as &longs;oon as it beginneth to a&longs;cend there naturally befalleth the <lb/>&longs;ame that hapneth to it from A along the Plane A B, to wit, a certain <lb/>De&longs;cent<emph.end type="italics"/> ex quiete <emph type="italics"/>according to tho&longs;e degrees of Acceleration, by vertue <lb/>of which, as it befalleth in A B, it may de&longs;cend as much in the &longs;ame <lb/>Time along the Reflected Plane as it doth along A B: It is manife&longs;t, that <lb/>by this &longs;ame Mixture of the Equable Motion of A&longs;cent, and the Acce­<lb/>lerate of De&longs;cent the Moveable may be carried up to the Term C along <lb/>the Plane B C according to tho&longs;e degrees of Velocity, which &longs;hall be<emph.end type="italics"/><pb xlink:href="040/01/875.jpg" pagenum="182"/><emph type="italics"/>equal. </s> <s>And that two points at plea&longs;ure D and E being taken, equally <lb/>remote from the Angle B, the Tran&longs;ition along D B is made in a Time <lb/>equal to the Time of the Reflection along B E, we may collect from hence: <lb/>Draw D F, which &longs;hall be Parallel to B C; for it is manife&longs;t that the <lb/>De&longs;cent along A D is reflected along D F: And if after D the Move­<lb/>able pa&longs;&longs;e along the Horizontal Plane D E, the<emph.end type="italics"/> Impetus <emph type="italics"/>in E &longs;hall be <lb/>the &longs;ame as the<emph.end type="italics"/> Impetus <emph type="italics"/>in D: Therefore it will a&longs;cend from E to C: <lb/>And therefore the degree of Velocity in D is equal to the degree in E. <lb/></s> <s>From the&longs;e things, therefore, we may rationally affirm, that, if a de­<lb/>&longs;cent be made along any inclined Plane, after which a Reflection may <lb/>follow along an elevated Plane, the Moveable may by the conceived<emph.end type="italics"/><lb/>Impetus <emph type="italics"/>a&longs;cend untill it attain the &longs;ame beight, or Elevation from the <lb/>Horizon. </s> <s>As if a De&longs;cent be made along A B, the Moveable would <lb/>pa&longs;&longs;e along the Reflected Plane B C, untill it arrive at the Horizon <lb/>A C D; and that not only when the Inclinations of the Planes are <lb/>equal, but al&longs;o when they are unequal, as is the Plane B D: For it was <lb/>first &longs;uppo&longs;ed, that the degrees of Velocity are equal, which are acqui­<lb/>red upon Planes unequally inclined, &longs;o long as the Elevation of tho&longs;e <lb/>Planes above the Horizon was the &longs;ame: But, if there being the &longs;ame <lb/>Inclination of the Planes E B and B D, the De&longs;cent along E B &longs;ufficeth <lb/>to drive the Moveable along the Plane BD as far as D, &longs;eeing this Impul&longs;e<emph.end type="italics"/><lb/><figure id="id.040.01.875.1.jpg" xlink:href="040/01/875/1.jpg"/><lb/><emph type="italics"/>is made by the<emph.end type="italics"/> Impe­<lb/>tus <emph type="italics"/>of Velocity in the <lb/>point B; and if the<emph.end type="italics"/><lb/>Impetus <emph type="italics"/>be the &longs;ame <lb/>in B, whether the <lb/>Moveable de&longs;cend a­<lb/>long A B, or along E B: It is manife&longs;t, that the Moveable &longs;hall be in <lb/>the &longs;ame manner driven along B D, after the De&longs;cent along A B, and <lb/>after that along E B: But it will happen that the Time of the A&longs;cent <lb/>along B D &longs;hall be longer than along B C, like as the De&longs;cent along <lb/>E B is made in a longer time than along A B: But the Proportion of <lb/>tho&longs;e Times was before demon&longs;trated to be the &longs;ame as the Lengths of <lb/>tho&longs;e Planes. </s> <s>Now it follows, that we &longs;eek the proportion of the Spaces <lb/>pa&longs;t in equal Times along Planes, who&longs;e Inclinations are different, but <lb/>their Elevations the &longs;ame; that is, which are comprehended between <lb/>the &longs;ame Horizontal Parallels. </s> <s>And this hapneth according to the fol­<lb/>lowing Propo&longs;ition.<emph.end type="italics"/></s></p><pb xlink:href="040/01/876.jpg" pagenum="183"/><p type="head"> <s>THEOR. XV. PROP. XXIV.</s></p><p type="main"> <s>There being given between the &longs;ame Horizontal <lb/>Parallels a Perpendicular and a <emph type="italics"/>P<emph.end type="italics"/>lane eleva­<lb/>ted from its lowe&longs;t term, the Space that a <lb/>Moveable after the Fall along the <emph type="italics"/>P<emph.end type="italics"/>erpendi­<lb/>cular pa&longs;&longs;eth along the Elevated <emph type="italics"/>P<emph.end type="italics"/>lane in a <lb/>Time equal to the Time of the Fall, is greater <lb/>than that <emph type="italics"/>P<emph.end type="italics"/>erpendicular, but le&longs;&longs;e than double <lb/>the &longs;ame.</s></p><p type="main"> <s><emph type="italics"/>Between the &longs;ame Horizontal Parallels B C and H G let there <lb/>be the Perpendicular A E; and let the Elevated Plane be E B, <lb/>along which after the Fall along the Perpendicular A E out of <lb/>the Term E let a Reflexion be made towards B. </s> <s>I &longs;ay, that the Space, <lb/>along which the Moveable a&longs;cendeth in a Time equal to the Time of the <lb/>De&longs;cent A E, is greater than A E, but le&longs;&longs;e than double the &longs;ame A E. <lb/></s> <s>Let E D be equal to A E, and as E B is to B D, &longs;o let D B be to B F. </s> <s>It <lb/>&longs;hall be proved, fir&longs;t that the point F is the Term at which the Moveable <lb/>with a Reflex Motion along E B arriveth in a Time equal to the Time <lb/>A E: And then, that E F is greater than E A, but le&longs;&longs;e than double the <lb/>&longs;ame. </s> <s>If we &longs;uppo&longs;e the Time of the De&longs;cent along A E to be as A E, <lb/>the Time of the De&longs;cent along B E, or A&longs;cent along E B &longs;hall be as the <lb/>&longs;ame Line B E: And D B being a Mean-Proportional betwixt E B <lb/>and B F, and B E being the Time of De&longs;cent along the whole B E, B D <lb/>&longs;hall be the Time of the De&longs;cent along B F, and the Remaining part <lb/>D E the Time of the<emph.end type="italics"/><lb/><figure id="id.040.01.876.1.jpg" xlink:href="040/01/876/1.jpg"/><lb/><emph type="italics"/>De&longs;cent along the Re­<lb/>maining part F E: But <lb/>the Time along F E<emph.end type="italics"/> ex <lb/>quiete <emph type="italics"/>in B, and the <lb/>Time of the A&longs;cent a­<lb/>long E F is the &longs;ame, &longs;ince that the Degree of Velocity in E was acqui­<lb/>red along the De&longs;cent B E, or A E: Therefore the &longs;ame Time D E &longs;hall <lb/>be that in which the Moveable after the Fall out of A along A E, <lb/>with a Reflex Motion along E B &longs;hall reach to the Mark F: But it hath <lb/>been &longs;uppo&longs;ed that E D is equal to the &longs;aid A E: Which was fir&longs;t to be <lb/>proved. </s> <s>And becau&longs;e that as the whole E B is to the whole B D, &longs;o is the <lb/>part taken away D B to the part taken away B F, therefore, as the whole <lb/>E B is to the whole B D, &longs;o &longs;hall the Remainder E D be to D F: <lb/>But E B is greater than B D: Therefore E D is greater than D F, and <lb/>E F le&longs;&longs;e than double to D E or A E: Which was to be proved.<emph.end type="italics"/></s></p><pb xlink:href="040/01/877.jpg" pagenum="184"/><p type="main"> <s><emph type="italics"/>And the &longs;ame al&longs;o hapneth if the precedent Motion be not made <lb/>along the Perpendicular, but along an Inclined Plane; and the Demon­<lb/>&longs;tration is the &longs;ame, provided that the Reflex Plane be le&longs;&longs;e ri&longs;ing, that is, <lb/>longer than the declining Plane.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. XVI. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> XXV.</s></p><p type="main"> <s>If after the De&longs;cent along any Inclined Plane a <lb/>Motion follow along the Plane of the Hori­<lb/>zon, the Time of the De&longs;cent along the Incli­<lb/>ned Plane &longs;hall be to the Time of the Motion <lb/>along any Horizontal Line; as the double <lb/>Length of the Inclined Plane is to the Line ta­<lb/>ken in the Horizon.</s></p><p type="main"> <s><emph type="italics"/>Let the Horizontal Line be C B, the inclined Plane A B, and after <lb/>the De&longs;cent along A B let a Motion follow along the Horizon, in <lb/>which take any Space B D. </s> <s>I &longs;ay, that the Time of the De&longs;cent <lb/>along A B to the Time of the Motion along B D is as the double of A B <lb/>to B D. </s> <s>For B C being &longs;uppo&longs;ed <lb/>the double of A B, it is manife&longs;t by<emph.end type="italics"/><lb/><figure id="id.040.01.877.1.jpg" xlink:href="040/01/877/1.jpg"/><lb/><emph type="italics"/>what hath already been demon&longs;tra­<lb/>ted that the Time of the De&longs;cent <lb/>along A B is equal to the Time of <lb/>the Motion along B C: But the <lb/>Time of the Motion along B C is to <lb/>the Time of the Motion along B D, as the Line C B is to the Line B D: <lb/>Therefore the Time of the Motion along A B is the Time along B D, as <lb/>the Double of A B is to B D: Which was to be proved.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL X. PROP. XXVI.</s></p><p type="main"> <s>A Perpendicular between two Horizontal <emph type="italics"/>P<emph.end type="italics"/>aral­<lb/>lel Lines, as al&longs;o a Space greater than the &longs;aid <lb/><emph type="italics"/>P<emph.end type="italics"/>erpendicular, but le&longs;&longs;e than double the &longs;ame, <lb/>being given, to rai&longs;e a <emph type="italics"/>P<emph.end type="italics"/>lane between the &longs;aid <lb/><emph type="italics"/>P<emph.end type="italics"/>arallels from the lowe&longs;t Term of the <emph type="italics"/>P<emph.end type="italics"/>er­<lb/>pendicular, along which the Moveable may <lb/>with a Reflex Motion after the Fall along the <lb/><emph type="italics"/>P<emph.end type="italics"/>erpendicular pa&longs;&longs;e a Space equal to the Space <lb/>given, and in a Time equal to the Time of the <lb/>Fall along the <emph type="italics"/>P<emph.end type="italics"/>erpendicular.</s></p><pb xlink:href="040/01/878.jpg" pagenum="185"/><p type="main"> <s><emph type="italics"/>Let A B be a Perpendicular between the Horizontal Parallels A O <lb/>and B C; and let F E be greater than B A, but le&longs;&longs;e than double <lb/>the &longs;ame. </s> <s>It is required between the &longs;aid Parallels from the point <lb/>B to rai&longs;e a Plane, along which the Moveable after the Fall from A to <lb/>B may with a Reflex Motion in a Time equal to the Time of the Fall <lb/>along A B pa&longs;&longs;e a Space a&longs;cending equal to the &longs;aid E F. </s> <s>Suppo&longs;e E D <lb/>equall to A B, the Remaining Part D F &longs;hall be le&longs;&longs;e, for that the whole <lb/>E F is le&longs;&longs;e than double to A B: Let D I be equal to D F, and as E I is <lb/>to I D, &longs;o let D F be to another Space F X, and out of B let the Right-<emph.end type="italics"/><lb/><figure id="id.040.01.878.1.jpg" xlink:href="040/01/878/1.jpg"/><lb/><emph type="italics"/>Line B O be reflected, equal to E X. </s> <s>I &longs;ay, that the Plane along B O <lb/>is that along which after the Fall A B a Moveable in a Time equal <lb/>to the Time of the Fall along A B pa&longs;&longs;eth a&longs;cending a Space equal to <lb/>the given Space E F. </s> <s>Suppo&longs;e B R and R S equal to the &longs;aid E D and <lb/>D F. </s> <s>And becau&longs;e that as E I is to I D, &longs;o is D F to F X; therefore, <lb/>by Compo&longs;ition, as E D is to D I, &longs;o &longs;hall D X be to X F; that is, as <lb/>E D is to D F, &longs;o &longs;hall D X be to X F, and E X to X D; that is, as <lb/>B O is to O R, &longs;o &longs;hall R O be to O S: And if we &longs;uppo&longs;e the Time <lb/>along A B to be A B, the Time along O B &longs;hall be the &longs;ame O B, and <lb/>R O the Time along O S, and the Remaining Part B R the Time along <lb/>the Remaining Part S B, de&longs;cending from O to B: But the Time of <lb/>the De&longs;cent along S B from Rest in O, is equal to the Time of the <lb/>A&longs;cent from B to S after the Fall A B: Therefore B O is the Plane ele­<lb/>vated from B, along which after the Fall along A B the Space B S <lb/>equal to the given Space E F is pa&longs;&longs;ed in the Time B R or B A: Which <lb/>was required to be done.<emph.end type="italics"/></s></p><pb xlink:href="040/01/879.jpg" pagenum="186"/><p type="head"> <s>THEOR. XVII. PROP. XXVII.</s></p><p type="main"> <s>If a Moveable de&longs;cend along unequal <emph type="italics"/>P<emph.end type="italics"/>lanes, <lb/>who&longs;e Elevation is the &longs;ame, the Space that <lb/>&longs;hall be pa&longs;t along the lower part of the longe&longs;t <lb/>in a Time equal to that in which the whole <lb/>&longs;horter <emph type="italics"/>P<emph.end type="italics"/>lane is pa&longs;&longs;ed, is equal to the Space <lb/>that is compounded of the &longs;aid &longs;horter <emph type="italics"/>P<emph.end type="italics"/>lane <lb/>and of the part to which that &longs;horter <emph type="italics"/>P<emph.end type="italics"/>lane <lb/>hath the &longs;ame <emph type="italics"/>P<emph.end type="italics"/>roportion that the longer <lb/><emph type="italics"/>P<emph.end type="italics"/>lane hath to the Exce&longs;&longs;e by which the longe&longs;t <lb/>exceedeth the &longs;horte&longs;t.</s></p><p type="main"> <s><emph type="italics"/>Let A C be the longer Plane, and A B the &longs;horter, who&longs;e Elevation <lb/>A D is the &longs;ame; and in the lower part of A C take the Space <lb/>C E, equal to the &longs;aid A B; and as C A is to A E, (that is to <lb/>the exce&longs;&longs;e of the Plane C A above A B) &longs;o let C E be to E F. </s> <s>I &longs;ay, <lb/>that the Space F C is that which is pa&longs;t after the De&longs;cent out of A in <lb/>a Time equal to the Time of<emph.end type="italics"/><lb/><figure id="id.040.01.879.1.jpg" xlink:href="040/01/879/1.jpg"/><lb/><emph type="italics"/>the De&longs;cent along A B. </s> <s>For <lb/>the whole C A, being to the <lb/>whole A E, as the part taken <lb/>away C E is to the part taken <lb/>away E F, therefore the re­<lb/>maining part E A &longs;hall be to <lb/>the remaining part A F, as the <lb/>whole C A is to the whole A E: Therefore the three Spaces C A, <lb/>A E, and A F are three Continual proportionals. </s> <s>And if the Time <lb/>along A B be &longs;uppo&longs;ed to be as A B, the Time along A C &longs;hall be as <lb/>A C, and the Time along A F &longs;hall be as A E, and along the remain­<lb/>ing part F C &longs;hall be as E C: But E C is equal to the &longs;aid A B: There­<lb/>fore the Propo&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. XVIII. PROP. XXVIII.</s></p><p type="main"> <s><emph type="italics"/>Let the Horizontal Line A G be Tangent to a Circle, and from the <lb/>point of Contact let A B be the Diameter, and A E B two Chords <lb/>at plea&longs;ure: We are to a&longs;&longs;ign the proportion of the Time of the <lb/>Fall along A B to the Time of the De&longs;cent along both the Chords <lb/>A E B. </s> <s>Let B E be continued out till it meet the Tangent in G, and<emph.end type="italics"/><pb xlink:href="040/01/880.jpg" pagenum="187"/><emph type="italics"/>let the Angle B A E be cut in two equal parts, and draw A F. </s> <s>I &longs;ay, <lb/>that the Time along A B is to the Time along A E B, as A E is to A E F. <lb/></s> <s>For in regard the Angle F A B is equal to the Angle F A E, and the An­<lb/>gle E A G to the Angle A B F, the whole Angle G A F &longs;hall be equal to <lb/>the two Angles F A B, and A B F; <lb/>to which al&longs;o the Angle G F A<emph.end type="italics"/><lb/><figure id="id.040.01.880.1.jpg" xlink:href="040/01/880/1.jpg"/><lb/><emph type="italics"/>is equal: Therefore the Line G F <lb/>is equal to G A. </s> <s>And becau&longs;e the <lb/>Rectangle B G E is equal to the <lb/>Square of G A, it &longs;hall likewi&longs;e <lb/>be equal to the Square of G F, and <lb/>the three Lines B G, G F, and <lb/>G E &longs;hall be proportionals. </s> <s>And <lb/>if we &longs;uppo&longs;e A E to be the Time <lb/>along A E, G E &longs;hall be the Time <lb/>along G E, and G F the Time along the whole G B, and E F the Time <lb/>along E B, after the De&longs;cent out of G, or out of A, along A E: The Time, <lb/>therefore, along A E, or along A B &longs;hall be to the Time along A E B, as <lb/>A E is to A E F: Which was to be determined.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>More briefly thus. </s> <s>Let G F be cut equal to G A: It is manife&longs;t <lb/>that G F is the Mean-proportional between B G, and G E. </s> <s>The re&longs;t as <lb/>before.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. <emph type="italics"/>XI. P<emph.end type="italics"/>RO<emph type="italics"/>P. XXIX.<emph.end type="italics"/></s></p><p type="main"> <s>Any Horizontal Space being given upon the <lb/>end of which a Perpendicular is erected, <lb/>in which a part is taken equal to half of the <lb/>Space given in the Horizontal a Moveable fal­<lb/>ling from that height, and turned along the <lb/>Horizon, &longs;hall pa&longs;&longs;e the Horizontal Space to­<lb/>gether with the Perpendicular in a &longs;horter <lb/>Time than any other Space of the <emph type="italics"/>P<emph.end type="italics"/>erpendi­<lb/>cular with the &longs;ame Horizontal Space.</s></p><p type="main"> <s><emph type="italics"/>Let there be an Horizontal Space in which let any Space be given <lb/>B C, and on B let there be a Perpendicular erected, in which let <lb/>B A be the half of the fore&longs;aid B C. </s> <s>I &longs;ay, that the Time in which <lb/>a Moveable let fall out of A pa&longs;&longs;eth both the Spaces A B and B C is the <lb/>&longs;horte&longs;t of all Times in which the &longs;aid Space B C with a part of the <lb/>Perpendicular, whether greater or le&longs;&longs;er than the part A B, &longs;hall be pa&longs;­<lb/>&longs;ed. </s> <s>Let a greater be taken, as in the &longs;ir&longs;t Figure, or le&longs;&longs;er, as in the<emph.end type="italics"/><pb xlink:href="040/01/881.jpg" pagenum="188"/><emph type="italics"/>&longs;econd, which let be E B. </s> <s>It is to be proved that the Time in which the <lb/>Spaces E B and B C are pa&longs;&longs;ed is longer than the Time in which A B <lb/>and B C are pa&longs;&longs;ed. </s> <s>Let the Time along A B be as A B; the &longs;ame &longs;hall <lb/>be the Time of the Motion along the Horizontal Space B G; becau&longs;e <lb/>B C is double to A B, and the Time along both the Spaces A B C &longs;hall <lb/>be double of O B A. </s> <s>Let B O<emph.end type="italics"/><lb/><figure id="id.040.01.881.1.jpg" xlink:href="040/01/881/1.jpg"/><lb/><emph type="italics"/>be a Mean-proportional between <lb/>E B and B A. </s> <s>B O &longs;hall be the <lb/>Time of the Fall along E B. <lb/>Again, let the Horizontal Space <lb/>B D be double to the &longs;aid B E: <lb/>It is manife&longs;t that the Time of it <lb/>after the Fall E B is the &longs;ame <lb/>B O. </s> <s>As D B is to B C, or as <lb/>E B is to B A, &longs;o let O B be to <lb/>B N: and in regard the Motion <lb/>along the Horizontal Plane is Equable, and O B being the Time along <lb/>B D after the Fall out of E, therefore N B &longs;hall be the Time along B C <lb/>after the Fall from the &longs;ame Altitude E. </s> <s>Hence it is manife&longs;t, that O B, <lb/>together with B N is the Time along E B C; and becau&longs;e the double of <lb/>B A is the Time along A B C; it remains to be proved, that O B, to­<lb/>gether with B N is more than double B A. </s> <s>Now becau&longs;e O B is a Mean <lb/>between E B and B A, the proportion of E B to B A is double the pro­<lb/>portion of O B to B A: and, in regard that E B is to B A, as O B is to <lb/>B N, the proportion of O B to B N &longs;hall al&longs;o be double the proportion of <lb/>O B to B A: But that proportion of O B to B N is compounded of the <lb/>proportions of O B to B A, and of A B to B N: therefore the proportion <lb/>of A B to B N is the &longs;ame with that of O B to B A. </s> <s>Therefore B O, <lb/>B A, and B N are three continual Proportionals, and O B, together with <lb/>B N, are greater than double B A: Whereupon the Propo&longs;ition is ma­<lb/>nife&longs;t.<emph.end type="italics"/></s></p><pb xlink:href="040/01/882.jpg" pagenum="189"/><p type="head"> <s>THEOR. <emph type="italics"/>XIX.<emph.end type="italics"/> PROP. <emph type="italics"/>XXX.<emph.end type="italics"/></s></p><p type="main"> <s>If a Perpendicular be let fall from any point of the <lb/>Horizontal Line, and out of another point in <lb/>the &longs;ame Horizontal Line a Plane be drawn <lb/>forth untill it meet the Perpendicular, along <lb/>which a Moveable de&longs;cendeth in the &longs;horte&longs;t <lb/>time unto the &longs;aid Perpendicular, this Plane <lb/>&longs;hall be that which cutteth off a part equall to <lb/>the di&longs;tance of the a&longs;&longs;igned point from the end <lb/>of the Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular B D be let fall from the point B of the Ho­<lb/>rizontal Line A C, in which let there be any point C, and in the <lb/>Perpendicular let the Di&longs;tance B E be &longs;uppo&longs;ed equal to the Di­<lb/>&longs;tance B C, and draw C E. </s> <s>I &longs;ay, that of all Planes inclined out of <lb/>the point C till they meet the Perpendicular C E is that, along which <lb/>in the &longs;horte&longs;t of all Times the De&longs;cent<emph.end type="italics"/><lb/><figure id="id.040.01.882.1.jpg" xlink:href="040/01/882/1.jpg"/><lb/><emph type="italics"/>is made unto the Perpendicular. </s> <s>For <lb/>let the Planes C F and C G be inclined <lb/>above and below, and draw I K a Tan­<lb/>gent unto the Semidiameter B C of the <lb/>de&longs;cribed Circle in C, which &longs;hall be <lb/>equidi&longs;tant from the Perpendicular; <lb/>and unto the &longs;aid C F let E K be Paral­<lb/>lel cutting the Circumference of the Cir­<lb/>cle in L: It is manife&longs;t that the Time of <lb/>the De&longs;cent along L E is equal to the <lb/>Time of the De&longs;cent along C E: But <lb/>the Time along K E is longer than along <lb/>L E: Therefore the Time along K E is <lb/>longer than that along C E: But the <lb/>Time along K E is equal to the Time a­<lb/>long C F, they being equal, and drawn <lb/>according to the &longs;ame Inclination: Likewi&longs;e &longs;ince C G, and I E are <lb/>equal, and inclined according to the &longs;ame Inclination, the Times of the <lb/>Motions along them &longs;hall be equal: But H E being &longs;horter than I E, the <lb/>Time along it is al&longs;o &longs;horter than I E: Therefore the Time al&longs;o along <lb/>C E, (which is equal to the Time along H E) &longs;hall be &longs;horter than the <lb/>Time along I E: The Propo&longs;ition, therefore, is manife&longs;t.<emph.end type="italics"/></s></p><pb xlink:href="040/01/883.jpg" pagenum="190"/><p type="head"> <s>THEOR. <emph type="italics"/>XX.<emph.end type="italics"/> PROP. <emph type="italics"/>XXXI.<emph.end type="italics"/></s></p><p type="main"> <s>If a Right-Line &longs;hall be in any manner inclined <lb/>upon the Horizontal Line, the Plane produced <lb/>from a given point in the Horizon untill it <lb/>meet with the Inclined Plane, along which <lb/>the De&longs;cent is made in the &longs;horte&longs;t of all <lb/>Times, is that which &longs;hall divide the Angle <lb/>contained between the two <emph type="italics"/>P<emph.end type="italics"/>erpendiculars <lb/>drawn from the given <emph type="italics"/>P<emph.end type="italics"/>oint, the one unto the <lb/>Horizontal Line, the other to the Inclined <lb/>Line, into two equal parts.</s></p><p type="main"> <s><emph type="italics"/>Let C D be a Line inclined in any manner upon the Hori­<lb/>zontal Line A B, and let any point A be given in the Hori­<lb/>zon, and from it let A C be drawn Perpendicular to A B, <lb/>and A E Perpendicular to C D, and let the Line F A divide the <lb/>Angle C A E into two equal parts. </s> <s>I &longs;ay, that of all Planes incli­<lb/>ned out of any point of the Line C D to the point A that &longs;ame pro­<lb/>duced along F A is it along<emph.end type="italics"/><lb/><figure id="id.040.01.883.1.jpg" xlink:href="040/01/883/1.jpg"/><lb/><emph type="italics"/>which the De&longs;cent is made in <lb/>the &longs;horte&longs;t of all Times. </s> <s>Let <lb/>F G be drawn Parallel to AE; <lb/>the alternate Angles G F A <lb/>and F A E &longs;hall be equal: But <lb/>E A F is equal to that other <lb/>F A G: Therefore of the Tri­<lb/>angle the Sides F G and G A <lb/>&longs;hall be equal. </s> <s>If therefore <lb/>about the Center G, at the di­<lb/>&longs;tance G A, a Circle be de&longs;cri­<lb/>bed it &longs;hall pa&longs;&longs;e by F, and &longs;hall <lb/>touch the Horizontal, and the Inclined Lines in the points A and F: <lb/>For the Angle G F C is a Right Angle, and likewi&longs;e G F is equidi&longs;tant <lb/>to A E: Whence it is manife&longs;t that all Lines produced from the point <lb/>A unto the inclined Plane do extend beyond the Circumference, and, <lb/>which followeth of con&longs;equence, that the Motions along the &longs;ame do <lb/>take up more Time than along F A. </s> <s>Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><pb xlink:href="040/01/884.jpg" pagenum="191"/><p type="head"> <s>LEMMA.</s></p><p type="main"> <s>If two Circles touch one another within, the innermo&longs;t of which <lb/>toucheth &longs;ome Right Line, and the exteriour one cutteth it, <lb/>three Lines produced from the Contact of the Circles unto <lb/>three points of the Tangent Right-Line, that is, to the Con­<lb/>tact of the interiour Circle, and to the Sections of the exte­<lb/>riour &longs;hall contain equall Angles in the Contact of the <lb/>Circles.</s></p><p type="main"> <s><emph type="italics"/>Let two Circles touch one another in the point A, of which let the <lb/>Centers be B, that of the le&longs;&longs;er, and C that of the greater; and let <lb/>the interiour Circle touch any Line F G in the point H, and let the grea­<lb/>ter cut it in the points F and G, and connect the three Lines A F, A H, <lb/>and A G. </s> <s>I &longs;ay, that the Angles by<emph.end type="italics"/><lb/><figure id="id.040.01.884.1.jpg" xlink:href="040/01/884/1.jpg"/><lb/><emph type="italics"/>them contained F A H and G A H are <lb/>equal. </s> <s>Produce A H untill it meeteth <lb/>the Circumference in I, and from the <lb/>Centers draw B H and C I, and thorow <lb/>the &longs;aid Centers let B C be drawn, <lb/>which continued forth &longs;hall meet with <lb/>the Contact A, and with the Circum­<lb/>ferences of the Circles in O and N. <lb/></s> <s>And becau&longs;e the Angles I C N and <lb/>H O B are equal, for as much as either <lb/>of them is double to the Angle I A N, <lb/>the Lines B H and C I &longs;hall be Parallels: And becau&longs;e B H drawn <lb/>from the Center to the Contact is Perpendicular to F G; C I &longs;hall al&longs;o be <lb/>Perpendicular to the &longs;ame, and the Arch F I equal to the Arch I G, and, <lb/>which followeth of con&longs;equence, the Angle F A I to the Angle I A G: <lb/>Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><pb xlink:href="040/01/885.jpg" pagenum="192"/><p type="head"> <s>THEOR. <emph type="italics"/>XXI.<emph.end type="italics"/> PROP. <emph type="italics"/>XXXII.<emph.end type="italics"/></s></p><p type="main"> <s>If two points be taken in the Horizon, and any <lb/>Line &longs;hould be inclined from one of them to­<lb/>wards the other, out of which a Right-Line is <lb/>drawn unto the Inclined Line, cutting off a <lb/>part thereof equal to that which is included <lb/>between the points of the Horizon, the De­<lb/>&longs;cent along this la&longs;t drawn &longs;hall be &longs;ooner per­<lb/>formed, than along any other Right Lines pro­<lb/>duced from the &longs;ame point unto the &longs;aid Incli­<lb/>ned Line. </s> <s>And along other Lines which are <lb/>on each hand of this by equal Angles a De­<lb/>&longs;cent &longs;hall be made in equal Times.</s></p><p type="main"> <s><emph type="italics"/>In the Horizon let there be two points A and B, and from B incline <lb/>the Right Line B C, in which from the Term B take B D equal to <lb/>the &longs;aid B A, and draw a Line from A to D. </s> <s>I &longs;ay, that the De­<lb/>&longs;cent along A D is more &longs;wiftly made, than along any other what&longs;oever <lb/>drawn from the point A unto the inclined Line B C. </s> <s>For out of the <lb/>points A and D unto B A and<emph.end type="italics"/><lb/><figure id="id.040.01.885.1.jpg" xlink:href="040/01/885/1.jpg"/><lb/><emph type="italics"/>B D draw the Perpendiculars <lb/>A E and D E, inter&longs;ecting one <lb/>another in E: and fora&longs;much as <lb/>in the equicrural Triangle A B D <lb/>the Angles B A D and B D A <lb/>are equal, the remainders to the <lb/>Right-Angles D A E and E D A <lb/>&longs;hall be equal. </s> <s>Therefore a Circle <lb/>de&longs;cribed about the Center E at <lb/>the di&longs;tance A E &longs;hall al&longs;o pa&longs;&longs;e <lb/>by D; and the Lines B A and <lb/>B D will touch it in the points A <lb/>and D. </s> <s>And &longs;ince A is the end of the Perpendicular A E, the De&longs;cent <lb/>along A D &longs;hall be &longs;ooner performed, than along any other produced from <lb/>the &longs;ame Term A unto the Line B C beyond the Circumference of the <lb/>Circle: Which was fir&longs;t to be proved.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>But if in the Perpendicular A E being prolonged any Center be taken as <lb/>F, and at the di&longs;tance F A the Circle A G C be de&longs;cribed cutting the <lb/>Tangent Line in the points G and C; drawing A G and A C they &longs;hall <lb/>make equal Angles with the middle Line A D by what hath been afore<emph.end type="italics"/><pb xlink:href="040/01/886.jpg" pagenum="193"/><emph type="italics"/>demon&longs;trated, and the Motions thorow them &longs;hall be performed in equal <lb/>Times &longs;eeing that they terminate in A unto the Circumference of the <lb/>Circle A G O from the highe&longs;t point of it A.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. XII. PROP. <emph type="italics"/>XXXIII.<emph.end type="italics"/></s></p><p type="main"> <s>A Perpendicular and Plane inclined to it being <lb/>given, who&longs;e height is one and the &longs;ame, as al­<lb/>&longs;o the highe&longs;t term, to find a point in the Per­<lb/>pendicular above the common term, out of <lb/>which if a Moveable be demitted that &longs;hall <lb/>afterwards turn along the inclined Plane, the <lb/>&longs;aid Plane may be pa&longs;t in the &longs;ame Time in <lb/>which the <emph type="italics"/>P<emph.end type="italics"/>erpendicular <emph type="italics"/>ex quiete<emph.end type="italics"/> would be <lb/>pa&longs;&longs;ed.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular and inclined Plane, who&longs;e Altitude is the <lb/>&longs;ame, be A B and A C. </s> <s>It is required in the Perpendicular B A, <lb/>continued out from the point A to find a Point out of which a <lb/>Moveable de&longs;cending may pa&longs;&longs;e the Space A C in the &longs;ame Time in <lb/>which it will pa&longs;&longs;e the &longs;aid Perpendicular A B out of Re&longs;t in A. </s> <s>Draw <lb/>D C E at Right-Angles to A C, and let C D be cut equal to A B, and <lb/>draw a Line from A to D: The Angle A D C &longs;hall be greater than the <lb/>Angles C A D: (for C A is greater than A B or C D:) Let the <lb/>Angle D A E be equal to the Angle A D E; and to A E let E F an in­<lb/>clined Plane be Perpen-<emph.end type="italics"/><lb/><figure id="id.040.01.886.1.jpg" xlink:href="040/01/886/1.jpg"/><lb/><emph type="italics"/>dicular, and let both be­<lb/>ing prolonged meet in F, <lb/>and unto both A I and <lb/>A G &longs;uppo&longs;e C F to be <lb/>equal, and by G draw <lb/>G H equidi&longs;tant to the <lb/>Horizon. </s> <s>I &longs;ay, that H <lb/>is the point which is <lb/>&longs;ought. </s> <s>For &longs;uppo&longs;ing the <lb/>Time of the Fall along <lb/>the Perpendicular A B <lb/>to be A B, the Time along <lb/>A C ex quiete in A &longs;hall be the &longs;ame A C. </s> <s>And becau&longs;e in the Right­<lb/>angled Triangle A E F, from the Right Angle E unto the Ba&longs;e A F, <lb/>E C is a Perpendicular, A E &longs;hall be a Mean-Proportional betwixt F A <lb/>and A C, and C E a Mean betwixt A C and C F, that is, betwixt C A <lb/>and A I: and fora&longs;much as the Time of A C out of A is A C, A E<emph.end type="italics"/><pb xlink:href="040/01/887.jpg" pagenum="194"/><emph type="italics"/>&longs;hall be the Time of the whole A F, and E C the Time of A I: And be­<lb/>cau&longs;e in the Equicrural Triangle A E D the Side A E is equal to the <lb/>Side E D, E D &longs;hall be the Time along A F, and E C is the Time along <lb/>A I: Therefore C D, that is A B &longs;hall be the Time along A F<emph.end type="italics"/> ex qui­<lb/>ete <emph type="italics"/>in A; which is the &longs;ame as if we &longs;aid, that A B is the Time along <lb/>A G out of G, or out of H: Which was to be done.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. <emph type="italics"/>XIII. P<emph.end type="italics"/>RO<emph type="italics"/>P. XXXIV.<emph.end type="italics"/></s></p><p type="main"> <s>An inclined <emph type="italics"/>P<emph.end type="italics"/>lane and Perpendicular who&longs;e &longs;ub­<lb/>lime term is the &longs;ame being given, to find a <lb/>more &longs;ublime point in the Perpendicular pro­<lb/>longed out of which a Moveable falling, and <lb/>being turned along the inclined <emph type="italics"/>P<emph.end type="italics"/>lane, may <lb/>pa&longs;&longs;e them both in the &longs;ame Time, as it doth <lb/>the &longs;ole inclined <emph type="italics"/>P<emph.end type="italics"/>lane <emph type="italics"/>ex quiete<emph.end type="italics"/> in its &longs;uperi­<lb/>our Term.</s></p><p type="main"> <s><emph type="italics"/>Let the inclined Plane and Perpendicular be A B and A C, who&longs;e <lb/>Term A is the &longs;ame. </s> <s>It is required in the Perpendicular prolonged <lb/>from A to find a &longs;ublime point, out of which the Moveable de&longs;cen­<lb/>ding, and being turned along the Plane A B, may pa&longs;&longs;e the a&longs;&longs;igned part <lb/>of the Perpendicular and the Plane A B in the &longs;ame Time, as it would the <lb/>&longs;ole Plane A B out of Re&longs;t in A.<emph.end type="italics"/></s></p><figure id="id.040.01.887.1.jpg" xlink:href="040/01/887/1.jpg"/><p type="main"> <s><emph type="italics"/>Let the Ho­<lb/>rizontal Line <lb/>be B C, and <lb/>let A N be <lb/>cut equal to <lb/>A C; and as <lb/>A B is to B N, <lb/>&longs;o let A L be <lb/>to L C: and <lb/>unto A L let <lb/>A I be equal, <lb/>and unto A C <lb/>and B I let C <lb/>E be a third <lb/>proportional, <lb/>marked in the <lb/>Perpendicular A C produced. </s> <s>I &longs;ay, that C E is the Space acquired; <lb/>&longs;o that the Perpendicular being extended above A, and the part A X <lb/>equal to C E being taken, a Moveable out of X will pa&longs;&longs;e both the<emph.end type="italics"/><pb xlink:href="040/01/888.jpg" pagenum="195"/><emph type="italics"/>Spaces X A B in the &longs;ame Time as it would the &longs;ole Space A B out of A. <lb/></s> <s>Draw the Horizontal Line X R Parallel to B C, with which let B A <lb/>being prolonged meet in R, and then A B being continued out unto D <lb/>draw E D Parallel to C B, and upon A D de&longs;cribe a Semicircle, and <lb/>from B, and Perpendicular to D A, erect B F till it meet with the Cir­<lb/>cumference. </s> <s>It is manife&longs;t that F B is a Mean-proportional betwixt <lb/>A B and B D, and that the Line drawn from F to A is a Mean-propor­<lb/>tional betwixt D A and A B. </s> <s>Suppo&longs;e B S equal to B I, and F H equal <lb/>to F B: And becau&longs;e, as A B is to B D, &longs;o is A C to C E, and becau&longs;e <lb/>B F is a Mean-proportional betwixt A B and B D, and becau&longs;e B I is a <lb/>Mean-proportional betwixt A C and C E; therefore as B A is to A C, <lb/>&longs;o is F B to B S. </s> <s>And becau&longs;e as B A is to A C, or A N, &longs;o is F B to <lb/>B S, therefore, by Conver&longs;ion of the proportion, B F is to F S, as A B is <lb/>to B N, that is, A L to L C; therefore the Rectangle under F B and <lb/>C L, is equal to the Rectangle under A L, and S F: But this Rectangle <lb/>A L, and S F, is the exce&longs;&longs;e of the Rectangle under A L and F B, or A I <lb/>and B F, over and above the Triangle A I and B S, or A I B; and the <lb/>Rectangle F B and L C is the exce&longs;&longs;e of the Rectangle A C and B F <lb/>over and above the Rectangle A L and B F: But the Rectangle A C and <lb/>B F is equal to the Rectangle A B I; (for as B A is to A C, &longs;o is F B to <lb/>B I:) The exce&longs;&longs;e, therefore, of the Rectangle A B I above the Rectan­<lb/>gle A I and B F, or A I and F H, is equal to the exce&longs;&longs;e of the Rectangle <lb/>A I and F H above the Rectangle A I B: Therefore twice the Rectan­<lb/>gle A I and F H is equal to the two Rectangles A B I and A I B; that <lb/>is twice A I B with the Square of B I. </s> <s>Let the Square A I be common <lb/>to both, and twice the Rectangle A I B with the two Squares A I, and <lb/>I B, (that is, the Square A B) &longs;hall be equal to twice the Rectangle <lb/>A I and F H, with the Square A I: Again, taking in commonly the <lb/>Square B F; the two Squares A B and B F, that is the &longs;ole Square A F <lb/>&longs;hall be equal to twice the Rectangle A I and F H, with the two Squares <lb/>A I and F B, that is A I and F H: But the &longs;ame Square A F is equal <lb/>to twice the Rectangle A H F, with the two Squares A H and H F: <lb/>Therefore twice the Rectangle A I and F H, with the Squares A I and <lb/>F H, are equal to twice the Rectangle A H F, with the Squares A H <lb/>and H F: And, the Common Square H F being taken away, twice the <lb/>Rectangle A I and F H, with the Square A I, &longs;hall be equal to twice the <lb/>Rectangle A H F, with the Square A H. </s> <s>And becau&longs;e that in all the <lb/>Rectangles F H is the Common Side, the Line A H &longs;hall be equal to A I: <lb/>For if it &longs;hould be greater or le&longs;&longs;er, then the Rectangles F H A and the <lb/>Square H A would al&longs;o be greater or le&longs;&longs;er than the Rectangles F H and <lb/>I A, and the Square I A: Contrary to what hath been demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Now if we &longs;uppo&longs;e the Time of the De&longs;cent along A B to be as A B, <lb/>the Time along A C &longs;hall be as A C, and I B the Mean-proportional be­<lb/>twixt A C and C E &longs;hall be the Time along C E, or along X A from <lb/>Re&longs;t in X: And becau&longs;e betwixt D A and A B, or R B and B A the<emph.end type="italics"/><pb xlink:href="040/01/889.jpg" pagenum="196"/><emph type="italics"/>Mean-proportional is A F, and between A B and B D, that is, R A and <lb/>A B the Mean is B F, to which F H is equal; Therefore,<emph.end type="italics"/> exprædemon­<lb/>&longs;tratis, <emph type="italics"/>the exce&longs;&longs;e A H &longs;hall be the Time along A B<emph.end type="italics"/> ex quiete <emph type="italics"/>in R, or <lb/>after the Fall out of X; &longs;ince the Time along the &longs;aid A B<emph.end type="italics"/> ex quiete <emph type="italics"/>in <lb/>A, &longs;hall be A B. </s> <s>Therefore the Time along X A is I B; and along A B <lb/>after R A, or after X A, is A I: Therefore the Time along X A B &longs;hall <lb/>be as A B, namely the &longs;elf-&longs;ame with the Time along the &longs;ole A B<emph.end type="italics"/> ex qui­<lb/>ete <emph type="italics"/>in A. </s> <s>Which was the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. XIV. PROP. XXXV.</s></p><p type="main"> <s>An Inflected Line unto a given <emph type="italics"/>P<emph.end type="italics"/>erpendicular be­<lb/>ing a&longs;&longs;igned, to take part in the Inflected Line, <lb/>along which alone <emph type="italics"/>ex quiete<emph.end type="italics"/> a Motion may be <lb/>made in the &longs;ame Time, as it would be along <lb/>the &longs;ame together with the Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>Let the Perpendicular be A B, and a Line inflected to it B C. </s> <s>It is <lb/>required in B C to take a part, along which alone out of Re&longs;t a <lb/>Motion may be made in the &longs;ame Time as it would along the &longs;ame <lb/>together with the Perpendicular A B. </s> <s>Draw the Horizon A D, with <lb/>which let the Inclined Line C B prolonged meet in E; and &longs;uppo&longs;e B F <lb/>equal to B A, and on the Center E at the di&longs;tance E F de&longs;cribe the Circle <lb/>F I G; and continue out F E unto the Circumference in G; and as G B <lb/>is to B F, &longs;o let B H be to H F; and let H I touch the Circle in I. </s> <s>Then <lb/>out of B erect B K<emph.end type="italics"/><lb/><figure id="id.040.01.889.1.jpg" xlink:href="040/01/889/1.jpg"/><lb/><emph type="italics"/>Perpendicular to <lb/>F C, with which <lb/>let the Line E I L <lb/>meet in L; and la&longs;t <lb/>of all let fall L M <lb/>Perpendicular to E <lb/>L, meeting B C in <lb/>M. </s> <s>I &longs;ay, that along <lb/>the Line B M from <lb/>Rest in B a Motion <lb/>may be made in the <lb/>&longs;ame Time, as it <lb/>would be<emph.end type="italics"/> ex quiete <emph type="italics"/>in A along both A B and B M. </s> <s>Let E N be made <lb/>equal to E L. </s> <s>And becau&longs;e as G B is to B F, &longs;o is B H to H F; there­<lb/>fore, by Permutation as G B is to B H, &longs;o will B F be to F H; and, by <lb/>Divi&longs;ion, G H &longs;hall be to H B, as B H is to H F: Wherefore the Rect­<lb/>angle G H F &longs;hall be equal to the Square H B: But the &longs;aid Rectangle <lb/>is al&longs;o equal to the Square H I: Therefore B H is equal to the &longs;ame H I.<emph.end type="italics"/><pb xlink:href="040/01/890.jpg" pagenum="197"/><emph type="italics"/>And becau&longs;e in the Quadrilateral Figure I L B H the Sides H B and <lb/>H I are equal, and the Angles B and I Right Angles, the Side B L &longs;hall <lb/>likewi&longs;e be equal to the Side L I: But E I is equal to E F: Therefore the <lb/>whole Line L E, or N E is equal to the two Lines L B and E F: Let <lb/>the Common Line E F be taken away, and the remainder F N &longs;hall be <lb/>equal to L B: And F B was &longs;uppo&longs;ed equal to B A: Therefore L B &longs;hall <lb/>be equal to the two Lines A B and B N. Again, if we &longs;uppo&longs;e the <lb/>Time along A B to be the &longs;aid A B, the Time along E B &longs;hall be equal to <lb/>E B; and the Time along the whole E M &longs;hall be E N, namely, the <lb/>Mean-proportional betwixt M E and E B: I berefore the Time of the <lb/>De&longs;cent of the remaining part B M after E B, or after A B, &longs;hall be the <lb/>&longs;aid B N: But it hath been &longs;uppo&longs;ed, that the Time along A B is A B: <lb/>Therefore the Time of the Fall along both A B and B M is A B N: <lb/>And becau&longs;e the Time along E B<emph.end type="italics"/> ex quiete <emph type="italics"/>in E is E B, the Time along <lb/>B M<emph.end type="italics"/> ex quiete <emph type="italics"/>in B &longs;hall be the Mean-proportional between B E and <lb/>B M; and this is B L: The Time, therefore, along both A B M<emph.end type="italics"/> ex quiete <lb/><emph type="italics"/>in A is A B N: And the Time along B M only<emph.end type="italics"/> ex quiete <emph type="italics"/>in B is B L: <lb/>But it was proved that B L is equal to the two A B and B N: Therefore <lb/>the Propo&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Otherwi&longs;e with more expedition.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Let B C be the Inclined Plane, and B A the Perpendicular. </s> <s>Continue <lb/>out C B to E, and unto E C erect a Perpendicular at B, which being <lb/>prolonged &longs;uppo&longs;e B H equal to the exce&longs;&longs;e of B E above B A; and to the <lb/>Angle B H E let the Angle H E L be equal; and let E L continued out <lb/>meet with B K in L; and from L erect the Perpendicular L M unto E L <lb/>meeting B C in M. </s> <s>I &longs;ay, that<emph.end type="italics"/><lb/><figure id="id.040.01.890.1.jpg" xlink:href="040/01/890/1.jpg"/><lb/><emph type="italics"/>B M is the Space acquired in <lb/>the Plane B C. </s> <s>For becau&longs;e <lb/>the Angle M L E is a Right­<lb/>Angle, therefore B L &longs;hall be <lb/>a Mean-proportional betwixt <lb/>M B and B E; and L E a <lb/>Mean proportional betwixt M <lb/>E and E B; to which E L let <lb/>E N be cut equal: And the <lb/>three Lines N E, E L, and <lb/>L H &longs;hall be equal; and H B &longs;hall be the exce&longs;&longs;e of N E above B L: But <lb/>the &longs;aid H B is al&longs;o the exce&longs;&longs;e of N E above N B and B A: Therefore <lb/>the two Lines N B and B A are equal to B L. </s> <s>And if we &longs;uppo&longs;e E B <lb/>to be the Time along E B, B L &longs;hall be the Time along B M<emph.end type="italics"/> ex quiete <emph type="italics"/>in <lb/>B; and B N &longs;hall be the Time of the &longs;ame B M after E B or after A B; <lb/>and A B &longs;hall be the Time along A B: Therefore the Times along A B M, <lb/>namely, A B N, are equal to the Times along the &longs;ole Line B M<emph.end type="italics"/> ex quiete <lb/><emph type="italics"/>in B: Which was intended.<emph.end type="italics"/></s></p><pb xlink:href="040/01/891.jpg" pagenum="198"/><p type="head"> <s>LEMMAI.</s></p><p type="main"> <s><emph type="italics"/>Let D C be Perpendicular to the Diameter B A; and from the Term <lb/>B continue forth B E D at plea&longs;ure, and draw a Line from F to B. </s> <s>I <lb/>&longs;ay, that F B is a Mean-proportional be-<emph.end type="italics"/><lb/><figure id="id.040.01.891.1.jpg" xlink:href="040/01/891/1.jpg"/><lb/><emph type="italics"/>twixt D B and B E. </s> <s>Draw a Line from E <lb/>to F, and by B draw the Tangent B G; <lb/>which &longs;hall be Parallel to the former C D: <lb/>Wherefore the Angle D B G &longs;hall be equal <lb/>to the Angle F D B, like as the &longs;ame G B D <lb/>is equal al&longs;o to the Angle E F B in the al­<lb/>tern Portion or Segment: Therefore the <lb/>Triangles F B D and F E B are alike: And, <lb/>as B D is to B F, &longs;o is F B to B E.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"/>Let the Line A C be greater than D F; and let A B have greater <lb/>proportion to B C, than D E hath to E F. </s> <s>I &longs;ay, that A B is greater <lb/>than D E. </s> <s>For becau&longs;e A B hath to B C<emph.end type="italics"/><lb/><figure id="id.040.01.891.2.jpg" xlink:href="040/01/891/2.jpg"/><lb/><emph type="italics"/>greater proportion than D E hath to D F, <lb/>therefore look what proportion A B hath to <lb/>B C, the &longs;ame &longs;hall D E have to a Line le&longs;­<lb/>&longs;er than E F; let it have it to E G: And <lb/>becau&longs;e A B to B C, is as D E, to E G, there­<lb/>fore, by Compo&longs;ition, and by converting the Proportion, as C A is to A B, <lb/>&longs;o is G D to D E: But C A is greater than G D: Therefore B A &longs;hall <lb/>be greater than D E.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA III.</s></p><figure id="id.040.01.891.3.jpg" xlink:href="040/01/891/3.jpg"/><p type="main"> <s><emph type="italics"/>Let A C I B be the Quadrant of a Circle: <lb/>and to A C let B E be drawn from B Pa­<lb/>rallel: And out of any Center taken in the <lb/>&longs;ame de&longs;cribe the Circle B O E S, touching <lb/>A B in B, and cutting the Circumference of <lb/>the Quadrant in I; and draw a Line from <lb/>C to B, and another from C to I continued <lb/>out to S. </s> <s>I &longs;ay, that the Line C I is alwaies <lb/>le&longs;&longs;e than C O. </s> <s>Draw a Line from A to I; <lb/>which toucheth the Circle B O E. </s> <s>And if <lb/>D I be drawn it &longs;hall be equal to D B: And <lb/>becau&longs;é D B toucheth the Quadrant, the &longs;aid <lb/>D I &longs;hall likewi&longs;e touch it; and &longs;hall be Per-<emph.end type="italics"/><pb xlink:href="040/01/892.jpg" pagenum="199"/><emph type="italics"/>pendicular to the Diameter A I: Wherefore al&longs;o A I toucheth the Cir­<lb/>cle B O E in I. And, becau&longs;e the Angle A I C is greater than the An­<lb/>gle A B C, as in&longs;i&longs;ting on a larger Periphery: Therefore the Angle <lb/>S I N &longs;hall be al&longs;o greater than the &longs;ame A B C: Therefore the Portion <lb/>I E S is greater than the Portion B O; and the Line C S, nearer to the <lb/>Center, greater than C B: Therefore al&longs;o C O is greater than C I; <lb/>for that S C is to C B, as O C is to C I.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And the &longs;ame al&longs;o would happen to be greater, if (as in the other <lb/>Figure) the Quadrant B I C were<emph.end type="italics"/><lb/><figure id="id.040.01.892.1.jpg" xlink:href="040/01/892/1.jpg"/><lb/><emph type="italics"/>le&longs;&longs;er: For the Perpendicular D B <lb/>will cut the Circle C I B: Wherefore <lb/>D I al&longs;o is equal to the &longs;aid D B; and <lb/>the Angle D I A &longs;hall be Obtu&longs;e, and <lb/>therefore A I N will al&longs;o cut B I N: <lb/>And becau&longs;e the Angle A B C is le&longs;&longs;e <lb/>than the Angle A I C, which is equal <lb/>to S I N; and this now is le&longs;&longs;e than that <lb/>which would be made at the Contact in <lb/>I by the Line S I: Therefore the Porti­<lb/>on S E I is much greater than the Por­<lb/>tion B O: Wherefore,<emph.end type="italics"/> &c. <emph type="italics"/>Which was <lb/>to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. <emph type="italics"/>XXII.<emph.end type="italics"/> PROP. <emph type="italics"/>XXXVI.<emph.end type="italics"/></s></p><p type="main"> <s>If from the lowe&longs;t point of a Circle erect unto <lb/>the Horizon a Plane &longs;hould be elevated &longs;ub­<lb/>tending a Circumference not greater than a <lb/>Quadrant, from who&longs;e Terms two other <lb/>Planes are Inflected to any point of the Cir­<lb/>cumference, the De&longs;cent along both the Infle­<lb/>cted Planes would be performed in a &longs;horter <lb/>Time than along the former elevated Plane <lb/>alone, or than along but one of the other two, <lb/>namely, along the lower.</s></p><p type="main"> <s><emph type="italics"/>Let C B D be the Circumference not greater than a Quadrant of a <lb/>Circle erect unto the Horizon on the lower point C, in which let <lb/>C D be an elevated Plane; and let two Planes be inflected from the <lb/>Terms D and C to any point in the Circumference taken at plea&longs;ure, <lb/>as B. </s> <s>I &longs;ay, that the Time of the De&longs;cent along both tho&longs;e Planes D B C <lb/>is &longs;horter than the Time of the De&longs;cent along the &longs;ole Plane D C, or <lb/>along the other only B C<emph.end type="italics"/> ex quiete <emph type="italics"/>in B. </s> <s>Let the Horizontal Line M D A<emph.end type="italics"/><pb xlink:href="040/01/893.jpg" pagenum="200"/><emph type="italics"/>be drawn by D, with which let C B prolonged meet in A; and let fall <lb/>the Perpendiculars D N and M C to M D, and B N to B D; and about <lb/>the Right-angled Triangle D B N de&longs;cribe the Semicircle D F B N, <lb/>cutting D C in F; and let D O be a Mean-proportional betwixt C D <lb/>and D F; and A V a Mean-proportional betwixt C A and A B: And <lb/>let P S be the time in which the whole D C, or B C, &longs;hall be pa&longs;&longs;ed; <lb/>(for it is manife&longs;t that they &longs;hall be both pa&longs;t in the &longs;ame Time;) And <lb/>look what proportion C D hath to D O, the &longs;ame &longs;hall the Time S P <lb/>have to the Time P R: the Time P R &longs;hall be that in which a Movea­<lb/>ble out of D will pa&longs;&longs;e D F; and R S that in which it &longs;hall pa&longs;&longs;e the re­<lb/>mainder F C. </s> <s>And becau&longs;e P S is al&longs;o the Time in which the Movea­<lb/>ble out of B &longs;hall pa&longs;&longs;e B C; if it be &longs;uppo&longs;ed that as B C is to C D, &longs;o is <lb/>S P to P T, P T &longs;hall be the Time of the De&longs;cent out of A to C: by <lb/>rea&longs;on D C is a Mean-proportional betwixt A C and C B, by what was <lb/>before demon&longs;trated: La&longs;t of all, as C A is to A V, &longs;o let T P be to<emph.end type="italics"/><lb/><figure id="id.040.01.893.1.jpg" xlink:href="040/01/893/1.jpg"/><lb/><emph type="italics"/>P G: P G &longs;hall be the Time, <lb/>in which thé Moveable out <lb/>of A de&longs;cendeth to B. </s> <s>And <lb/>becau&longs;e of the Circle D F N <lb/>the Diameter erect to the <lb/>Horizon is D N, the Lines <lb/>D F and D B &longs;hall be pa&longs;­<lb/>&longs;ed in equal Times. </s> <s>So that <lb/>if it &longs;hould be demon&longs;tra­<lb/>ted that the Moveable would <lb/>&longs;ooner pa&longs;&longs;e B C after the <lb/>De&longs;cent D B, than F C after the Lation D F; we &longs;hould have our in­<lb/>tent. </s> <s>But the Moveable will with the &longs;ame Celerity of Time pa&longs;&longs;e B C <lb/>coming out of D along D B, as if it came out of A along A B: for that <lb/>in both the De&longs;cents D B and A B it acquireth equal Moments of Velo­<lb/>city: Therefore it &longs;hall re&longs;t to be demon&longs;trated that the Time is &longs;horter <lb/>in which B C is pa&longs;&longs;ed after A B, than that in which F C is pa&longs;t after <lb/>D F. </s> <s>But it hath been demon&longs;trated, that the Time in which B C is <lb/>pa&longs;&longs;ed after A B is G T; and the Time of F C after D F is R S. </s> <s>It is <lb/>to be proved therefore, that R S is greater than G T: Which is thus <lb/>done. </s> <s>Becau&longs;e as S P is to P R, &longs;o is C D to D O, therefore, by Conver­<lb/>&longs;ion of proportion, and by Inver&longs;ion, as R S is to S P, &longs;o is O C to C D: <lb/>and as S P is to P T, &longs;o is D C to C A: And, becau&longs;e as T P is to PG, <lb/>&longs;o is C A to A V: Therefore al&longs;o, by Conver&longs;ion of the proportion, as <lb/>P T is to T G, &longs;o is A C to C V: therefore, ex equali, as R S is to G T, <lb/>&longs;o is O C to C V. </s> <s>But O C is greater than C V, as &longs;hall anon be de­<lb/>mon&longs;trated: Therefore the Time R S is greater than the Time G T: <lb/>Which it was required to demon&longs;trate. </s> <s>And becau&longs;e C F is greater than <lb/>C B, and F D le&longs;&longs;e than B A, therefore C D &longs;hall have greater propor­<lb/>tion to D F than C A to A B: And as C D is to D F, &longs;o is the Square<emph.end type="italics"/><pb xlink:href="040/01/894.jpg" pagenum="201"/><emph type="italics"/>C O to the Square O F; fora&longs;much as C D, D O, and O F are Propor­<lb/>tionals: And as C A is to A B, &longs;o is the Square C V to the Square <lb/>V B: Therefore C O hath greater proportion to O F, than C V to V B: <lb/>Therefore, by the foregoing Lemma, C O is greater than C V. </s> <s>It is <lb/>manife&longs;t moreover, that the Time along D C is to the Time along <lb/>D B C, as D O C is to D O together with C V.<emph.end type="italics"/></s></p><p type="head"> <s>SCHOLIUM.</s></p><p type="main"> <s>From the&longs;e things that have been demon&longs;trated may evidently <lb/>be gathered, that the &longs;wifte&longs;t of all Motions betwixt Term <lb/>and Term is not made along the &longs;horte&longs;t Line, that is by the <lb/>Right, but along a portion of a Circle.</s></p><p type="main"> <s><emph type="italics"/>For in the Quadrat B A E C, who&longs;e Side B C is erect to the Hori­<lb/>zon, let the Arch A C be divided into any number of equal parts, <lb/>A D, D E, E F, F G, G C; and let Right-lines be drawn from C to <lb/>the Points A, D, E, F, G, H; and al&longs;o by Lines joyn A D, D E, E F, <lb/>F G. and G C. </s> <s>It is manifest, that the Motion along the two Lines <lb/>A D C is &longs;ooner performed than along the<emph.end type="italics"/><lb/><figure id="id.040.01.894.1.jpg" xlink:href="040/01/894/1.jpg"/><lb/><emph type="italics"/>&longs;ole Line A C, or D C out of Re&longs;t in D: <lb/>But out of Re&longs;t in A, D C is &longs;ooner pa&longs;t <lb/>than the two A D C: But along the two <lb/>D E C out of Re&longs;t in A the De&longs;cent is <lb/>likewi&longs;e &longs;ooner made than along the &longs;ole <lb/>C D: Therefore the De&longs;cent along the <lb/>three Lines A D E C &longs;hall be performed <lb/>&longs;ooner than along the two A D C. </s> <s>And <lb/>in like manner the De&longs;cent along A D E <lb/>preceding, the Motion is more &longs;peedily con­<lb/>&longs;ummated along the two EFC than along the &longs;ole FC: Therfore along the <lb/>four A D E F C the Motion is quicklier accompli&longs;hed than along the <lb/>three A D E C: And &longs;o, in the la&longs;t place, along the two F G C after the <lb/>precedent De&longs;cent along A D E F the Motion will be &longs;ooner con&longs;umma­<lb/>ted than along the &longs;ole F C: Therefore along the five A D E F G C <lb/>the De&longs;cent &longs;hall be effected in a yet &longs;horter Time than along the four <lb/>A D E F C: Whereupon the nearer by in&longs;cribed Poligons we approach <lb/>the Circumference, the &longs;ooner will the Motion be performed between the <lb/>two a&longs;&longs;igned points A C.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And that which is explained in a Quadrant, holdeth true likewi&longs;e <lb/>in a Circumference le&longs;&longs;e than the Quadrant: and the Ratiocination is <lb/>the &longs;ame.<emph.end type="italics"/></s></p><pb xlink:href="040/01/895.jpg" pagenum="202"/><p type="head"> <s>PROBL.XV. PROP. XXXVII.</s></p><p type="main"> <s>A Perpendicular and Inclined Plane of the &longs;ame <lb/>Elevation being given, to find a part in the In­<lb/>clined Plane that is equal to the Perpendicu­<lb/>lar, and pa&longs;&longs;ed in the &longs;ame Time as the &longs;aid <lb/>Perpendicular.</s></p><p type="main"> <s><emph type="italics"/>LET A B be the Perpendicular, and A C the Inclined Plane. </s> <s>It is <lb/>required in the Inclined to find a part equal to the Perpendicular <lb/>A B, that after Re&longs;t in A may be pa&longs;&longs;ed in a Time equal to the <lb/>Time in which the Perpendicular is pa&longs;&longs;ed. </s> <s>Let A D be equal to A B, <lb/>and cut the Remainder B C in two equal parts in I; and as A C is to<emph.end type="italics"/><lb/><figure id="id.040.01.895.1.jpg" xlink:href="040/01/895/1.jpg"/><lb/><emph type="italics"/>C I, &longs;o let C I be to another Line <lb/>A E; to which let D G be equal: It <lb/>is manife&longs;t that E G is equal to A D <lb/>and to A B. </s> <s>I &longs;ay moreover, that <lb/>this &longs;ame E G is the &longs;ame that is <lb/>pa&longs;&longs;ed by the Moveable coming out <lb/>of Re&longs;t in A in a Time equal to the <lb/>Time in which the Moveable fall eth along A B. </s> <s>For becau&longs;e that as <lb/>A C is to C I, &longs;o is C I to A E, or I D to D G; Therefore by Conver&longs;ion <lb/>of the proportion, as C A is to A I, &longs;o is D I to I G. </s> <s>And becau&longs;e as the <lb/>whole C A is to the whole A I, &longs;o is the part taken away C I to the part <lb/>I G; therefore the Remaining part I A &longs;hall be to the Remainder A G, <lb/>as the whole C A is to the whole A I: Therefore A I is a Mean-propor­<lb/>tional betwixt C A and A G; and C I a Mean-proportional betwixt <lb/>C A and A E: If therefore we &longs;uppo&longs;e the Time along A B to be as A B; <lb/>A C &longs;hall be the Time along A C, and C I or I D the Time along A E: <lb/>And becau&longs;e A I is a Mean-proportional betwixt C A and A G; and <lb/>C A is the Time along the whole A C: Therefore A I &longs;hall be the Time <lb/>along. </s> <s>A G; and the Remainder I C that along the Remainder G C: But <lb/>D I was the Time along A E: Therefore D I and I C are the Times <lb/>along both the Spaces A E and C G: Therefore the Remainder D A &longs;hall <lb/>be the Time along E G, to wit, equal to the Time along A B. </s> <s>Which was <lb/>to be done.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARIE.</s></p><p type="main"> <s>Hence it is manife&longs;t, that the Space required is an intermedial be­<lb/>tween the upper and lower parts that are pa&longs;t in equal <lb/>Times.</s></p><pb xlink:href="040/01/896.jpg" pagenum="203"/><p type="head"> <s><emph type="italics"/>P<emph.end type="italics"/>ROBL. XVI. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> XXXVIII.</s></p><p type="main"> <s>Two Horizontal Planes cut by the Perpendicular <lb/>being given, to find a &longs;ublime point in the <emph type="italics"/>P<emph.end type="italics"/>er­<lb/>pendicular, out of which Moveables falling <lb/>and being reflected along the Horizontal <lb/><emph type="italics"/>P<emph.end type="italics"/>lanes may in Times equal to the Times of <lb/>the De&longs;cents along the &longs;aid Horizontal <emph type="italics"/>P<emph.end type="italics"/>lanes, <lb/>namely, along the upper and along the lower, <lb/>pa&longs;&longs;e Spaces that have to each other any given <lb/>proportion of the le&longs;&longs;er to the greater.</s></p><p type="main"> <s><emph type="italics"/>LET the Planes C D and B E be inter&longs;ected by the Perpendicular <lb/>A C B, and let the given proportion of the le&longs;&longs;e to the greater be <lb/>N to F G. </s> <s>It is required in the Perpendicular A B to find a point <lb/>on high, out of which a Moveable falling, and reflected along C D may <lb/>in a Time equal to the Time of its Fall, pa&longs;&longs;e a Space, that &longs;hall have <lb/>unto the Space pa&longs;&longs;ed by the other Moveable coming out of the &longs;ame &longs;ub­<lb/>lime point in a Time equal to the Time of its Fall with a Reflex Motion <lb/>along the Plane B E the &longs;ame proportion as the given Line N batb to<emph.end type="italics"/><lb/><figure id="id.040.01.896.1.jpg" xlink:href="040/01/896/1.jpg"/><lb/><emph type="italics"/>F G. </s> <s>Let G H be <lb/>made equal to the <lb/>&longs;aid N; and as F H <lb/>is to H G, &longs;o let <lb/>B C be to C L. </s> <s>I &longs;ay, <lb/>L is the &longs;ublime <lb/>point required. </s> <s>For <lb/>taking C M double <lb/>to C L, draw L M <lb/>meeting the Plane <lb/>B E in O; B O <lb/>&longs;hall be double to <lb/>B L: And becau&longs;e, <lb/>as F H is to H G, &longs;o is B C to C L; therefore, by Compo&longs;ition and In­<lb/>ver&longs;ion, as H G, that is, N is to G F, &longs;o is C L to L B, that is, C M to <lb/>B O: But becau&longs;e C M is double to L C; let the Space C M be that <lb/>which by the Moveable coming from L after the Fall L C is pa&longs;&longs;ed along <lb/>the Plane C D; and by the &longs;ame rea&longs;on B O is that which is pa&longs;&longs;ed after <lb/>the Fall L B in a Time equal to the Time of the Fall along L B; fora&longs;­<lb/>much as B O is double to B L: Therefore the Propo&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><pb xlink:href="040/01/897.jpg" pagenum="204"/><p type="main"> <s>SAGR. </s> <s>Really me thinks that we may ju&longs;tly grant our <emph type="italics"/>Acade­<lb/>mian<emph.end type="italics"/> what he without arrogance a&longs;&longs;umed to him&longs;elf in the begining <lb/>of this his Treati&longs;e of &longs;hewing us a <emph type="italics"/>New Science<emph.end type="italics"/> about <emph type="italics"/>a very old <lb/>Subject.<emph.end type="italics"/> And to &longs;ee with what Facility and Per&longs;picuity he deduceth <lb/>from one &longs;ole Principle the Demon&longs;trations of &longs;o many Propo&longs;iti­<lb/>ons, maketh me not a little to wonder how this bu&longs;ine&longs;s e&longs;caped <lb/>unhandled by <emph type="italics"/>Archimedes, Apollonius, Euclid,<emph.end type="italics"/> and &longs;o many other <lb/><emph type="italics"/>I<emph.end type="italics"/>llu&longs;trious Mathematicians and Phylo&longs;ophers: e&longs;pecially &longs;ince <lb/>there are found many great Volumns of <emph type="italics"/>Motion.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>There is extant a &longs;mall Fragment of <emph type="italics"/>Euclid<emph.end type="italics"/> touching <lb/><emph type="italics"/>Motion,<emph.end type="italics"/> but there are no marks to be &longs;een therein of any &longs;teps that he <lb/>took towards the di&longs;covery of the Proportion of <emph type="italics"/>Acceleration,<emph.end type="italics"/> and <lb/>of its Varieties along different <emph type="italics"/>I<emph.end type="italics"/>nclinations. </s> <s>So that indeed one <lb/>may &longs;ay, that never till now was the door opened to a new Con­<lb/>templation fraught with infinite and admirable Conclu&longs;ions, which <lb/>in times to come may bu&longs;ie other Wits.</s></p><p type="main"> <s>SAGR. <emph type="italics"/>I<emph.end type="italics"/> verily believe, that as tho&longs;e few Pa&longs;&longs;ions (<emph type="italics"/>I<emph.end type="italics"/> will &longs;ay <lb/>for example) of the Circle demon&longs;trated by <emph type="italics"/>Euclid<emph.end type="italics"/> in the third of <lb/>his <emph type="italics"/>Elements<emph.end type="italics"/> are an introduction to innumerable others more ab­<lb/>&longs;truce, &longs;o tho&longs;e produced and demon&longs;trated in this &longs;hort Tractate, <lb/>when they &longs;hall come to the hands of other Speculative Wits, &longs;hall <lb/>be a manuduction unto infinite others mote admirable: and it is to <lb/>be believed that thus it will happen by rea&longs;on of the Nobility of <lb/>the Argument above all others Phy&longs;ical.</s></p><p type="main"> <s>This daies Conference hath been very long and laborious; in <lb/>which <emph type="italics"/>I<emph.end type="italics"/> have ta&longs;ted more of the &longs;imple Propo&longs;itions than of their <lb/>Demon&longs;trations; many of which, <emph type="italics"/>I<emph.end type="italics"/> believe, will co&longs;t me more than <lb/>an hour a piece well to comprehend them: a task that <emph type="italics"/>I<emph.end type="italics"/> re&longs;erve to <lb/>my &longs;elf to perform at lea&longs;ure, you leaving the Book in my hands &longs;o <lb/>&longs;oon as we &longs;hall have heard this part that remains about the Moti­<lb/>on of Projects: which &longs;hall, if you &longs;o plea&longs;e, be to morrow.</s></p><p type="main"> <s>SALV. <emph type="italics"/>I<emph.end type="italics"/> &longs;hall not fail to be with you.</s></p><p type="head"> <s><emph type="italics"/>The End of the Third Dialogue.<emph.end type="italics"/></s></p></chap><chap><pb xlink:href="040/01/898.jpg" pagenum="205"/><p type="head"> <s>GALILEUS, <lb/>HIS <lb/>DIALOGUES <lb/>OF <lb/>MOTION.</s></p><p type="head"> <s>The Fourth Dialogue.</s></p><p type="head"> <s><emph type="italics"/>INTERLOCUTORS,<emph.end type="italics"/></s></p><p type="head"> <s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"> <s>SALVIATUS.</s></p><p type="main"> <s><emph type="italics"/>Simplicius<emph.end type="italics"/> likewi&longs;e cometh in the nick of time, therefore <lb/>without interpo&longs;ing any <emph type="italics"/>Re&longs;t<emph.end type="italics"/> let us proceed to <emph type="italics"/>Motion<emph.end type="italics"/>; <lb/>and &longs;ee here the <emph type="italics"/>Text<emph.end type="italics"/> of our <emph type="italics"/>Author.<emph.end type="italics"/></s></p><p type="head"> <s>OF THE MOTION OF <lb/>PROJECTS.</s></p><p type="main"> <s><emph type="italics"/>What accidents belong to<emph.end type="italics"/> Equable Motion, <emph type="italics"/>as al&longs;o to the<emph.end type="italics"/> Na­<lb/>turally Accelerate <emph type="italics"/>along all whatever Inclinations of Planes, <lb/>we have con&longs;idered above. </s> <s>In this Contemplation which we are now <lb/>entering upon, I will attempt to declare, and with &longs;olid Demon&longs;trations<emph.end type="italics"/><pb xlink:href="040/01/899.jpg" pagenum="206"/><emph type="italics"/>to e&longs;tabli&longs;h &longs;ome of the principal Symptomes, and tho&longs;e worthy of know­<lb/>ledge, which befall a Moveable whil&longs;t it is moved with a Motion com­<lb/>pounded of a twofold Lation, to wit, of the Equable and Naturally­<lb/>Accelerate: and this is that Motion, which we call the Motion of Pro­<lb/>jects: who&longs;e Generation I constitute to be in this manner.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>I fancy in my mind a certain Moveable projected or thrown along <lb/>an Horizontal Plane, all impediment &longs;ecluded: Now it is manife&longs;t by <lb/>what we have el&longs;ewhere &longs;poken at large, that that Motion will be Equa­<lb/>ble and Perpetual along the &longs;aid Plane, if the Plane be extended<emph.end type="italics"/> in in­<lb/>finitum<emph type="italics"/>: but if we &longs;uppo&longs;e it terminate, and placed on high, the Move­<lb/>able, which I conceive to be endued with Gravity, being come to the end <lb/>of the Plane, proceeding forward, it addeth to the Equable and Indeli­<lb/>ble fir&longs;t Lation that propen&longs;ion downwards which it receiveth from its <lb/>Gravity, and from thence a certain Motion doth re&longs;ult compounded of <lb/>the Equable Horizontal, and of the De&longs;cending naturally. </s> <s>Accellerate <lb/>Lations: which I call<emph.end type="italics"/> Projection. <emph type="italics"/>Some of who&longs;e Accidents we will de­<lb/>mon&longs;trate; the fir&longs;t of which &longs;hall be this.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR.I. PROP.I.</s></p><p type="main"> <s><emph type="italics"/>A Project, when it is moved with a Motion compounded <lb/>of the Horizontal Equable, and of the Naturally­<lb/>Accelerate downwards, &longs;hall de&longs;cribe a Semipara­<lb/>bolical Line in its Lation.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>It is requi&longs;ite, <emph type="italics"/>Salviatus,<emph.end type="italics"/> in favour of my &longs;elf, and, as I <lb/>believe, al&longs;o of <emph type="italics"/>Simplicius,<emph.end type="italics"/> here to make a pau&longs;e; for I <lb/>am not &longs;o far gone in Geometry as to have &longs;tudied <emph type="italics"/>Apol­<lb/>lonius,<emph.end type="italics"/> &longs;ave only &longs;o far as to know that he treateth of the&longs;e Para­<lb/>bola's, and of the other Conick Sections, without the knowledge <lb/>of which, and of their Pa&longs;&longs;ions, I do not think that one can under­<lb/>&longs;tand the Demon&longs;trations of other Propo&longs;itions depending on <lb/>them. </s> <s>And becau&longs;e already in the very fir&longs;t Propo&longs;ition it is pro­<lb/>po&longs;ed by the Author to prove the Line de&longs;cribed by the Project to <lb/>be Parabolical, I imagine to my &longs;elf, that being to treat of none <lb/>but &longs;uch Lines, it is ab&longs;olutely nece&longs;&longs;ary to have a perfect know­<lb/>ledge, if not of all the Pa&longs;&longs;ions of tho&longs;e Figures that are demon­<lb/>&longs;trated by <emph type="italics"/>Apollonius,<emph.end type="italics"/> at lea&longs;t of tho&longs;e that are nece&longs;&longs;ary for the Sci­<lb/>ence in hand.</s></p><p type="main"> <s>SALV. </s> <s>You undervalue your &longs;elf very much, to make &longs;trange <lb/>of tho&longs;e Notions, which but even now you admitted as very well <lb/>under&longs;tood: I told you heretofore, that in the Treati&longs;e of Re&longs;i­<lb/>&longs;tances we had need of the knowledge of certain Propo&longs;itions of <pb xlink:href="040/01/900.jpg" pagenum="207"/><emph type="italics"/>Apollonius,<emph.end type="italics"/> at which you made no &longs;eruple.</s></p><p type="main"> <s>SAGR. </s> <s>It may be either that I knew them by chance, or that I <lb/>might for once gue&longs;&longs;e at, and take for granted &longs;o much as &longs;erved my <lb/>turn in that Tractate: but here where I imagine that we are to <lb/>hear all the Demon&longs;trations that concern tho&longs;e Lines, it is not con­<lb/>venient, as we &longs;ay, to &longs;wallow things whole, lo&longs;ing our time and <lb/>pains.</s></p><p type="main"> <s>SIMP. </s> <s>But as to what concerns me, although <emph type="italics"/>Sagredus<emph.end type="italics"/> were, <lb/>as I believe he is, well provided for his occa&longs;ions, the very fir&longs;t <lb/>Terms already are new to me: for though our Philo&longs;ophers have <lb/>handled this Argument of the Motion of Projects, I do not remem­<lb/>ber that they have confined them&longs;elves to de&longs;ine what the Lines <lb/>are which they de&longs;cribe, &longs;ave only in general that they are alwaies <lb/>Curved Lines, except it be in Projections Perpendicularly upwards. <lb/></s> <s>Therefore in ca&longs;e that little Geometry that I have learnt from <emph type="italics"/>Eu­<lb/>clid<emph.end type="italics"/> &longs;ince the Time that we have had other Conferences, be not &longs;uf­<lb/>ficient to render me capable of the Notions requi&longs;ite for the under­<lb/>&longs;tanding of the following Demon&longs;trations, I mu&longs;t content my &longs;elf <lb/>with bare Propo&longs;itions believed, but not under&longs;tood.</s></p><p type="main"> <s>SALV. </s> <s>But I will have you to know them by help of the Au­<lb/>thor of this Book him&longs;elf, who when he heretofore granted me a <lb/>&longs;ight of this his Work, becau&longs;e I al&longs;o at that time was not perfect <lb/>in the Books of <emph type="italics"/>Apollonius,<emph.end type="italics"/> took the pains to demon&longs;trate to me <lb/>two mo&longs;t principal Pa&longs;&longs;ions of the Parabola without any other Pre­<lb/>cognition, of which two, and no more, we &longs;hall &longs;tand in need in <lb/>the pre&longs;ent Treati&longs;e; which are both likewi&longs;e proved by <emph type="italics"/>Apollonius,<emph.end type="italics"/><lb/>but after many others, which it would take up a long time to look <lb/>over, and I am de&longs;irous that we may much &longs;horten the Journey, ta­<lb/>king the fir&longs;t immediately from the pure and &longs;imple generation of <lb/>the &longs;aid Parabola, and from this al&longs;o immediately &longs;hall be deduced <lb/>the Demon&longs;tration of the &longs;econd. </s> <s>Coming therefore to the fir&longs;t;</s></p><p type="main"> <s>De&longs;cribe the Right Cone, who&longs;e Ba&longs;e let be the Circle I B K C, <lb/>and Vertex the point L, in which, cut by a Plane parallel to the <lb/><figure id="id.040.01.900.1.jpg" xlink:href="040/01/900/1.jpg"/><lb/>Side L K, ari&longs;eth the Section B A C <lb/>called a Parabola; and let its Ba&longs;e <lb/>B C cut the Diameter I K of the <lb/>Circle I B K C at Right-Angles; <lb/>and let the Axis of the Parabola <lb/>A D be Parallel to the &longs;ide L K; <lb/>and taking any point F in the Line <lb/>B F A, draw the Right-Line F E <lb/>parallel to B D. </s> <s>I &longs;ay, that the Square <lb/>of B D hath to the Square of F E <lb/>the &longs;ame proportion that the Axis <lb/>D A hath to the part A E. </s> <s>Let a Plane parallel to the Circle I B K C <pb xlink:href="040/01/901.jpg" pagenum="208"/>be &longs;uppo&longs;ed to pa&longs;&longs;e by the Point E, which &longs;hall make in the Cone <lb/>a Circular Section, who&longs;e Diameter is G E H. </s> <s>And becau&longs;e upon <lb/>the Diameter I K of the Circle I B K, B D is a Perpendicular, the <lb/>Square of B D &longs;hall be equal to the Rectangle made by the parts <lb/>I D and D K: And likewi&longs;e in the upper Circle which is under&longs;tood <lb/>to pa&longs;&longs;e by the points G F H, the Square of the Line F E is equal <lb/>to the Rectangle of the parts G E H: Therefore the Square of B D <lb/>hath the &longs;ame proportion to the Square of F E, that the Rectangle <lb/>I D K hath to the Rectangle G E H. </s> <s>And becau&longs;e the Line E D is <lb/>Parallel to H K, E H &longs;hall be equal to D K, which al&longs;o are Parallels: <lb/>And therefore the Rectangle I D K &longs;hall have the &longs;ame proportion <lb/>to the Rectangle G E H, as I D hath to G E; that is, that D A hath <lb/>to A E: Therefore the Rectangle I D K to the Rectangle G E H, <lb/>that is, the Square B D to the Square F E, hath the &longs;ame proportion <lb/>that the Axis D A hath to the part A E: Which was to be de­<lb/>mon&longs;trated.</s></p><p type="main"> <s>The other Propo&longs;ition, likewi&longs;e nece&longs;&longs;ary to the pre&longs;ent Tract, <lb/>we will thus make out. </s> <s>Let us de&longs;cribe the Parabola, of which let the <lb/>Axis C A be prolonged out unto D; and taking any point B, let the <lb/>Line B C be &longs;uppo&longs;ed to be continued out by the &longs;ame Parallel un­<lb/><figure id="id.040.01.901.1.jpg" xlink:href="040/01/901/1.jpg"/><lb/>to the Ba&longs;e of the &longs;aid Parabola; <lb/>and let D A be &longs;uppo&longs;ed equal <lb/>to the part of the Axis C A. </s> <s>I &longs;ay, <lb/>that the Right-Line drawn by <lb/>the points D and B, falleth not <lb/>within the Parabola, but without, <lb/>&longs;o as that it only toucheth the <lb/>&longs;ame in the &longs;aid point B: For, if <lb/>it be po&longs;&longs;ible for it to fall within, <lb/>it cutteth it above, or being pro­<lb/>longed, it cutteth it below. </s> <s>And <lb/>in that Line let any point G be <lb/>taken, by which pa&longs;&longs;eth the Right <lb/>Line F G E. </s> <s>And becau&longs;e the <lb/>Square F E is greater than the <lb/>Square G E, the &longs;aid Square F E <lb/>&longs;hall have greater proportion to <lb/>the Square B C, than the &longs;aid Square G E hath to the &longs;aid B C. </s> <s>And <lb/>becau&longs;e, by the precedent, the Square F E is to the Square B C as <lb/>E A is to A C; therefore E A hath greater proportion to A C, than <lb/>the Square G E hath to the Square B C; that is, than the Square <lb/>E D hath to the Square D C: (becau&longs;e in the Triangle D G E as <lb/>G E is to the Parallel B C, &longs;o is E <emph type="italics"/>D<emph.end type="italics"/> to <emph type="italics"/>D<emph.end type="italics"/> C:) But the Line E A to <lb/>A C, that is, to A <emph type="italics"/>D<emph.end type="italics"/> hath the &longs;ame proportion that four Rectangles <lb/>E A <emph type="italics"/>D<emph.end type="italics"/> hath to four Squares of A <emph type="italics"/>D,<emph.end type="italics"/> that is, to the Square C <emph type="italics"/>D,<emph.end type="italics"/><pb xlink:href="040/01/902.jpg" pagenum="209"/>(which is equal to four Squares of A D:) Therefore four Rectan­<lb/>gles E A D &longs;hall have greater proportion to the Square C D, than <lb/>the Square E D hath to the Square D C: Therefore four Rectan­<lb/>gles E A D &longs;hall be greater than the Square E D: which is fal&longs;e, <lb/>for they are le&longs;&longs;e; becau&longs;e the parts E A and A D of the Line E D <lb/>are not equal: Therefore the Line D B toucheth the Parabola in B, <lb/>and doth not cut it: Which was to be demon&longs;trated.</s></p><p type="main"> <s>SIMP. </s> <s>You proceed in your Demon&longs;trations too &longs;ublimely, <lb/>and &longs;till, as far as I can perceive, &longs;uppo&longs;e that the Propo&longs;itions of <lb/><emph type="italics"/>Euclid<emph.end type="italics"/> are as familiar and ready with me, as the fir&longs;t Axioms them­<lb/>&longs;elves, which is not &longs;o. </s> <s>And the impo&longs;ing upon me, ju&longs;t now, that <lb/>four Rectangles E A <emph type="italics"/>D<emph.end type="italics"/> are le&longs;s than the Square <emph type="italics"/>D<emph.end type="italics"/> E becau&longs;e the <lb/>parts E A and A <emph type="italics"/>D<emph.end type="italics"/> of the Line E <emph type="italics"/>D<emph.end type="italics"/> are not equal, doth not &longs;atis&longs;ie <lb/>me, but leaveth me in doubt.</s></p><p type="main"> <s>SALV. </s> <s>The truth is, all the Mathematicians that are not vulgar <lb/>&longs;uppo&longs;e that the Reader hath ready by heart the Elements of <lb/><emph type="italics"/>Euclid<emph.end type="italics"/>: And here to &longs;upply your want, it &longs;hall &longs;u&longs;fice to remember <lb/>you of a Propo&longs;ition in the &longs;econd Book, in which it is demon&longs;trated <lb/>that when a Line is cut into equal parts, and into unequal, the <lb/>Rectangle of the unequal parts is le&longs;s than the Rectangle of the <lb/>equal, (that is, than the Square of the half) by &longs;o much as is the <lb/>Square of the Line comprized between the Sections. </s> <s>Whence it is <lb/>manife&longs;t, that the Square of the whole, which continueth four <lb/>Squares of the Half, is greater than four Rectangles of the unequal <lb/>parts. </s> <s>Now it is nece&longs;&longs;ary that we bear in mind the&longs;e two Propo&longs;i­<lb/>tions which have been demon&longs;trated, taken from the Conick Ele­<lb/>ments, for the better under&longs;tanding the things that follow in the <lb/>pre&longs;ent Treati&longs;e: for of the&longs;e two, and no more, the Author <lb/>makes u&longs;e. </s> <s>Now we may rea&longs;&longs;ume the Text to &longs;ee in what manner <lb/>he doth demon&longs;trate his fir&longs;t Propo&longs;ition, in which he intendeth to <lb/>prove unto us, That the Line de&longs;cribed by the Grave Moveable, <lb/>when it de&longs;cends with a Motion compounded of the Equable <lb/>Horizontal, and of the Natural <emph type="italics"/>D<emph.end type="italics"/>e&longs;cending is a Semiparabola.</s></p><p type="main"> <s><emph type="italics"/>Suppo&longs;e the Horizontal Line or Plane A B placed on high; upon<emph.end type="italics"/><lb/>[or along] <emph type="italics"/>which let the Moveable pa&longs;&longs;e with an Equable Motion out <lb/>of A unto B: and the &longs;upport of the Plane failing in B let there be <lb/>derived upon the Moveable from its own Gravity a Motion naturally <lb/>downwards according to the Perpendicular B N. </s> <s>Let the Line B E be <lb/>&longs;uppo&longs;ed applyed unto the Plane A B right out, as if it were the Efflux <lb/>or mea&longs;ure of the Time, on which at plea&longs;ure note any equal parts of <lb/>Time, B C, C D, D E: And out of the points B C D E &longs;uppo&longs;e Per­<lb/>pendicular Lines to be let fall equidi&longs;tant or parallel to B N: In the fir&longs;t <lb/>of which take any part C I, who&longs;e quadruple take in the following one <lb/>D F, nonuple E H, and &longs;o in the re&longs;t that follow according to the propor-<emph.end type="italics"/><pb xlink:href="040/01/903.jpg" pagenum="210"/><emph type="italics"/>tion of the Squares of C B, D B, E B, or, if you will, in the doubled <lb/>proportion of the Lines. </s> <s>And if unto the Moveable moved beyond B <lb/>towards C with the Equable Lation we &longs;uppo&longs;e the Perpendicular <lb/>De&longs;cent to be &longs;uperadded according to the quantity C I, in the Time <lb/>B C it &longs;hall be found con&longs;tituted in the Term I. </s> <s>And proceeding farther,<emph.end type="italics"/><lb/><figure id="id.040.01.903.1.jpg" xlink:href="040/01/903/1.jpg"/><lb/><emph type="italics"/>in the Time D B, namely, <lb/>in the double of B C, the <lb/>Space of the De&longs;cent down­<lb/>wards &longs;hall be quadruple to <lb/>the fir&longs;t Space C I: For <lb/>it hath beendemon&longs;trated in <lb/>the fir&longs;t Trastate, that the <lb/>Spaces pa&longs;&longs;ed by GraveBo­<lb/>dies with a Motion Natu­<lb/>rally Accelerate are in du­<lb/>plicate proportion of their Times. </s> <s>And it likewi&longs;e followeth, that the <lb/>Space E H pa&longs;&longs;ed in the Time B E, &longs;hall be as G. </s> <s>So that it is manife&longs;tly <lb/>proved, that the Spaces E H, D F, C I, are to one another as the Squares <lb/>of the Lines E B, D B, C B. </s> <s>Now from the points I, F, and H draw <lb/>the Right Lines I O, F G, H L, Parallel to the &longs;aid E B; and each of <lb/>the Lines H L, F G, and I O &longs;hall be equal to each of the other Lines <lb/>E B, D B, and C B; as al&longs;o each of tho&longs;e B O, B G, and B L, &longs;hall be <lb/>equal to each of tho&longs;e C I, D F, and E H: And the Square H L &longs;hall <lb/>be to the Square F G, as the Line L B to B G: And the Square F G <lb/>&longs;hall be to the Square I O, as G B to B O: Therefore the Points I, F, <lb/>and H are in one and the &longs;ame Parabolical Line. </s> <s>And in like manner <lb/>it &longs;hall be demon&longs;trated, any equalparticles of Time of what&longs;oever Mag­<lb/>nitude being taken, that the place of the Moveable who&longs;e Motion is <lb/>compounded of the like Lations, is in the &longs;ame Times to be found in the <lb/>&longs;ame Parabolick Line: Therefore the Propo&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>This Conclu&longs;ion is gathered from the Conver&longs;ion of the <lb/>fir&longs;t of tho&longs;e two Propo&longs;itions that went before, for the Parabola <lb/>being, for example, de&longs;cribed by the points B H, if either of the <lb/>two F or I were not in the de&longs;cribed Parabolick Line, it would be <lb/>within, or without; and by con&longs;equence the Line F G would be <lb/>either greater or le&longs;&longs;er than that which &longs;hould determine in the Pa­<lb/>rabolick Line; Wherefore the Square of HL would have, not to <lb/>the Square of F G, but to another greater or le&longs;&longs;er, the &longs;ame pro­<lb/>portion that the Line L B hath to BG, but it hath the &longs;ame propor­<lb/>tion to the Square of F G: Therefore the point F is in the Parabo­<lb/>lick Line: And &longs;o all the re&longs;t, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>It cannot be denied but that the Di&longs;cour&longs;e is new, in­<lb/>genious and concludent, arguing <emph type="italics"/>ex &longs;uppo&longs;itione,<emph.end type="italics"/> that is, &longs;uppo&longs;ing <lb/>that the Tran&longs;ver&longs;e Motion doth continue alwaies Equable, and <pb xlink:href="040/01/904.jpg" pagenum="211"/>that the Natural <emph type="italics"/>Dcor&longs;um<emph.end type="italics"/> do likewi&longs;e keep its tenour of continu­<lb/>ally Accelerating according to a proportion double to the Times; <lb/>and that tho&longs;e Motions and their Velocities in mingling be not al­<lb/>tered, di&longs;turbed, and impeded, &longs;o that finally the Line of the Pro­<lb/>ject do not in the continuation of the Motion degenerate into an­<lb/>other kind; a thing which &longs;eemeth to me to be impo&longs;&longs;ible. </s> <s>For, in <lb/>regard that the Axis of our Parabola, according to which we &longs;up­<lb/>po&longs;e the Natural Motion of Graves to be made, being Perpendicu­<lb/>lar to the Horizon, doth terminate in the Center of the Earth; and <lb/>in regard that the Parabolical Line doth &longs;ucce&longs;&longs;ively enlarge from <lb/>its Axis, no Project would ever come to terminate in the Center, or <lb/>if it &longs;hould come thitherwards, as it &longs;eemeth nece&longs;&longs;ary that it mu&longs;t, <lb/>the Line of the Project &longs;hould de&longs;cribe another mo&longs;t different from <lb/>that of the Parabola.</s></p><p type="main"> <s>SIMP. </s> <s>I add to the&longs;e difficulties &longs;everal others; one of which is <lb/>that we &longs;uppo&longs;e, that the Horizontal Plane which hath neither accli­<lb/>vity or declivity is a Right Line; as if that &longs;uch a Line were in all <lb/>its parts equidi&longs;tant from the Center, which is not true: for depart­<lb/>ing from its middle it goeth towards the extreams, alwaies more and <lb/>more receding from the Center, and therefore alwaies a&longs;cending: <lb/>which of con&longs;equence rendereth it Impo&longs;&longs;ible that its Motion <lb/>&longs;hould be perpetual, or that it &longs;hould for any time continue Equa­<lb/>ble, and nece&longs;&longs;itates it to grow continually more and more weak. <lb/></s> <s>Moreover, it is, in my Opinion, impo&longs;&longs;ible to avoid the Impedi­<lb/>ment of the <emph type="italics"/>Medium,<emph.end type="italics"/> but that it will take away the Equability of <lb/>the Tran&longs;ver&longs;e Motion, and the Rule of the Acceleration in falling <lb/>Grave Bodies. </s> <s>By all which difficulties it is rendred very improba­<lb/>ble that the things demon&longs;trated with &longs;uch incon&longs;tant Suppo&longs;i­<lb/>tions &longs;hould afterwards hold true in the practical Experiments.</s></p><p type="main"> <s>SALV. </s> <s>All the Objections and Difficulties alledged are &longs;o <lb/>well grounded, that I e&longs;teem it impo&longs;&longs;ible to remove them; and <lb/>for my own part I admit them all, as al&longs;o I believe the Author <lb/>him&longs;elf would do. </s> <s>And I grant that the Conclu&longs;ions thus demon­<lb/>&longs;trated in Ab&longs;tract, do alter and prove fal&longs;e, and that &longs;o egregiou&longs;­<lb/>ly, in Concrete, that neither is the Tran&longs;ver&longs;e Motion Equable, <lb/>nor is the Acceleration of the Natural in the proportion &longs;uppo&longs;e, <lb/>nor is the Line of the Project Parabolical, <emph type="italics"/>&c. </s> <s>B<emph.end type="italics"/>ut yet on the <lb/>contrary, I de&longs;ire that you would not &longs;cruple to grant to this our <lb/>Author that which other famous Men have &longs;uppo&longs;ed, although <lb/>fal&longs;e. </s> <s>And the &longs;ingle Authority of <emph type="italics"/>Archimedes<emph.end type="italics"/> may &longs;atisfie every <lb/>one: who in his Mechanicks, and in the fir&longs;t Quadrature of the <lb/>Parabola, taketh it as a true Principle, that the <emph type="italics"/>B<emph.end type="italics"/>eam of the <emph type="italics"/>B<emph.end type="italics"/>allance <lb/>or Stilliard is a Right Line in all its points equidi&longs;tant from the <lb/>Common Center of Grave <emph type="italics"/>B<emph.end type="italics"/>odies, and that the Scale-ropes, to <lb/>which the Weights are hanged, are parallel to one another. </s> <s>Which <pb xlink:href="040/01/905.jpg" pagenum="212"/>Liberty of his hath been excu&longs;ed by &longs;ome, for that in our practices <lb/>the In&longs;truments we u&longs;e, and the Di&longs;tances which we take are &longs;o <lb/>&longs;mall in compari&longs;on of our great remotene&longs;s from the Center of <lb/>the Terre&longs;trial Globe, that we may very well take a Minute of a <lb/>degree of the great Circle as if it were a Right Line, and two Per­<lb/>pendiculars that &longs;hould hang at its extreams as if they were Paral­<lb/>lels. </s> <s>For if we were in practical Operations to keep account of <lb/>&longs;uch like Minutes, we &longs;hould begin to reprove the Architects, who <lb/>with the Plumb Line &longs;uppo&longs;e that they rai&longs;e very high Towers <lb/>between Lines equidi&longs;tant. </s> <s>And I here add, that we may &longs;ay that <lb/><emph type="italics"/>Archimedes,<emph.end type="italics"/> and others &longs;uppo&longs;e in their Contemplations that they <lb/>were con&longs;tituted remote at an infinite di&longs;tance from the Center; <lb/>in which ca&longs;e their A&longs;&longs;umptions were not fal&longs;e: And that therefore <lb/>they did conclude by Ab&longs;olute Demon&longs;tration. </s> <s>Again, if we will <lb/>practice the demon&longs;trated Conclu&longs;ions in terminate Di&longs;tances, by <lb/>&longs;uppo&longs;ing an immen&longs;e Di&longs;tance, we ought to defalk from the <lb/>truth demon&longs;trated that which our Di&longs;tance from the Center doth <lb/>import, not being really infinite, but yet &longs;uch as that it may be <lb/>termed Immen&longs;e in compari&longs;on of the Artifices that we make u&longs;e <lb/>of, the greate&longs;t of which will be the Ranges of Projects, and among&longs;t <lb/>the&longs;e that only of Canon &longs;hot; which though it be great, yet &longs;hall <lb/>it not exceed four of tho&longs;e Miles of which we are remote from the <lb/>Center well-nigh &longs;o many thou&longs;ands: and the&longs;e coming to deter­<lb/>mine in the Surface of the Terre&longs;trial Globe may very well only in­<lb/>&longs;en&longs;ibly alter that Parabolick Figure, which we grant would be <lb/>extreamly transformed in going to determine in the Center. </s> <s>In <lb/>the next place as to the perturbation proceeding from the Impedi­<lb/>ment of the <emph type="italics"/>Medium,<emph.end type="italics"/> this is more con&longs;iderable, and, by rea&longs;on of <lb/>its &longs;o great multiplicity of Varieties, incapable of being brought <lb/>under any certain Rules, and reduced to a Science: for if we <lb/>&longs;hould propo&longs;e to con&longs;ideration no more but the Impediment which <lb/>the Air procureth to the Motions con&longs;idered by us, this alone &longs;hall <lb/>be found to di&longs;turb all, and that infinite waies, according as we <lb/>infinite waies vary the Figures, Gravities, and Velocities of the <lb/>Moveables. </s> <s>For as to the Velocity, according as this &longs;hall be grea­<lb/>ter, the greater &longs;hall the oppo&longs;ition be that the Air makes again&longs;t <lb/>them, which &longs;hall yet more impede the &longs;aid Moveable according as <lb/>they are le&longs;s Grave: &longs;o that although the de&longs;cending Grave Body <lb/>ought to go Accelerating in a duplicate proportion to the Duration <lb/>of its Motion, yet neverthele&longs;s, albeit the Moveable were very <lb/>Grave, in coming from very great heights, the Impediment of the <lb/>Air &longs;hall be &longs;o great, as that it will take from it all power of far­<lb/>ther encrea&longs;ing its Velocity, and will reduce it to an Uniform and <lb/>Equable Motion: And this Adequation &longs;hall be &longs;o much the &longs;ooner <lb/>obtained, and in &longs;o much le&longs;&longs;er heights, by how much the Moveable <pb xlink:href="040/01/906.jpg" pagenum="213"/>&longs;hall be le&longs;s Grave. </s> <s>That Motion al&longs;o which along the Horizontal <lb/>Plane, all other Ob&longs;tacles being removed, ought to be Equable <lb/>and perpetual, &longs;hall come to be altered, and in the end arre&longs;ted by <lb/>the Impediment of the Air: and here likewi&longs;e &longs;o much the &longs;ooner, <lb/>by how much the Moveable &longs;hall be Lighter. </s> <s>Of which Accidents <lb/>of Gravity, of Velocity, and al&longs;o of Figure, as being varied &longs;eve­<lb/>ral waies, there can no fixed Science be given. </s> <s>And therefore that <lb/>we may be able Scientifically to treat of this Matter it is requi&longs;ite <lb/>that we ab&longs;tract from them; and, having found and demon&longs;trated <lb/>the Conclu&longs;ions ab&longs;tracted from the Impediments, that we make <lb/>u&longs;e of them in practice with tho&longs;e Limitations that Experience &longs;hall <lb/>from time to time &longs;hew us. </s> <s>And yet neverthele&longs;s the benefit &longs;hall <lb/>not be &longs;mall, becau&longs;e &longs;uch Matters, and their Figures &longs;hall be made <lb/>choice of as are le&longs;s &longs;ubject to the Impediments of the <emph type="italics"/>Medium<emph.end type="italics"/>; <lb/>&longs;uch are the very Grave, the Rotund: and the Spaces, and the <lb/>Velocities for the mo&longs;t part will not be &longs;o great, but that their ex­<lb/>orbitances may with ea&longs;ie ^{*} Allowance be reduced to a certainty. <lb/><arrow.to.target n="marg1095"></arrow.to.target><lb/>Yea more, in Projects practicable by us, that are of Grave Matters, <lb/>and of Round Figure, and al&longs;o that are of Matters le&longs;&longs;e Grave, <lb/>and of Cylindrical Figure, as Arrows, &longs;hot from Slings or Bows, <lb/>the variation of their Motion from the exact Parabolical Figure <lb/>&longs;hall be altogether in&longs;en&longs;ible. </s> <s>Nay, (and I will a&longs;&longs;ume to my &longs;elf <lb/>a little more freedom) that in ^{*} In&longs;truments that are practicable by <lb/><arrow.to.target n="marg1096"></arrow.to.target><lb/>us, their &longs;malne&longs;s rendreth the extern and accidental Impediments, <lb/>of which that of the <emph type="italics"/>Medium<emph.end type="italics"/> is mo&longs;t con&longs;iderable, to be but of <lb/>very &longs;mall note, I am able by two experiments to make manife&longs;t. <lb/></s> <s>I will con&longs;ider the Motions made thorow the Air, for &longs;uch are tho&longs;e <lb/>chiefly of which we &longs;peak: again&longs;t which the &longs;aid Air in two man­<lb/>ners exerci&longs;eth its power. </s> <s>The one is by more impeding the Movea­<lb/>bles le&longs;s Grave, than tho&longs;e very Grave. </s> <s>The other is in more oppo­<lb/>&longs;ing the greater than the le&longs;s Velocity of the &longs;ame Moveable. </s> <s>As <lb/>to the fir&longs;t; Experience &longs;hewing us that two Balls of equal <lb/>bigne&longs;s, but in weight one ten or twelve times more Grave than the <lb/>other, as, for example, one of Lead and another of Oak would <lb/>be, de&longs;cending from an height of 150, or 200 Yards, arrive to the <lb/>Earth with Velocity very little different, it a&longs;&longs;ureth us that the Im­<lb/>pediment or Retardment of the Air in both is very &longs;mall: for if <lb/>the <emph type="italics"/>B<emph.end type="italics"/>all of Lead departing from on high in the &longs;ame Moment with <lb/>that of Wood, were but little retarded, and this much, the Lead at <lb/>its coming to the ground &longs;hould leave the Wood a very con&longs;idera­<lb/>ble Space behind, &longs;ince it is ten times more Grave; which never­<lb/>thele&longs;s doth not happen: nay, its Anticipation &longs;hall not be &longs;o <lb/>much as the hundredth part of the whole height. </s> <s>And between a <lb/><emph type="italics"/>B<emph.end type="italics"/>all of Lead, and another of Stone which weighs a third part, or <lb/>half &longs;o much as it, the difference of the Times of their coming to <pb xlink:href="040/01/907.jpg" pagenum="214"/>the ground would be hardly ob&longs;ervable. </s> <s>Now becau&longs;e the <emph type="italics"/>Impe­<lb/>tus<emph.end type="italics"/> that a <emph type="italics"/>B<emph.end type="italics"/>all of Lead acquireth in falling from an height of 200 <lb/>Yards (which is &longs;o much that continuing it in an Equable Moti­<lb/>on it would in a like Time run 400 Yards) is very con&longs;iderable in <lb/>compari&longs;on of the Velocity that we confer with <emph type="italics"/>B<emph.end type="italics"/>ows or other Ma­<lb/>chines, upon our Projects (excepting the <emph type="italics"/>Impetus's<emph.end type="italics"/> that depend <lb/>on the Fire) we may without any notable Errour conclude and <lb/>account the Propo&longs;itions to be ab&longs;olutely true that are demon&longs;tra­<lb/>ted without any regard had to the alteration of the <emph type="italics"/>Medium.<emph.end type="italics"/> In <lb/>the next place as touching the other part, that is to &longs;hew, that the <lb/>Impediment that the &longs;aid Moveable receiveth from the Air whil&longs;t <lb/>it moveth with great Velocity is not much greater than that which <lb/>oppo&longs;eth it in moving &longs;lowly, the en&longs;uing Experiment giveth us <lb/>full a&longs;&longs;urance of it. </s> <s>Su&longs;pend by two threads both of the &longs;ame <lb/>length, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> four or five Yards, two equal <emph type="italics"/>B<emph.end type="italics"/>alls of Lead: and <lb/>having fa&longs;tned the &longs;aid threads on high, let both the <emph type="italics"/>B<emph.end type="italics"/>alls be re­<lb/>moved from the &longs;tate of Perpendicularity; but let the one be re­<lb/>moved 80. or more degrees, and the other not above 4 or 5: &longs;o <lb/>that one of them being left at liberty de&longs;cendeth, and pa&longs;&longs;ing be­<lb/>yond the Perpendicular, de&longs;cribeth very great Arches of 160, 150, <lb/>140, <emph type="italics"/>&c.<emph.end type="italics"/> degrees, dimini&longs;hing them by little and little: but the <lb/>other &longs;winging freely pa&longs;&longs;eth little Arches of 10, 8, 6, <emph type="italics"/>&c.<emph.end type="italics"/> this <lb/>al&longs;o dimini&longs;hing them in like manner by little and little. </s> <s>Here I <lb/>&longs;ay, in the fir&longs;t place, that the fir&longs;t <emph type="italics"/>B<emph.end type="italics"/>all &longs;hall pa&longs;s its 180, 160, <emph type="italics"/>&c.<emph.end type="italics"/><lb/>degrees in as much Time as the other doth its 10, 8, <emph type="italics"/>&c.<emph.end type="italics"/> From <lb/>whence it is manife&longs;t, that the Velocity of the fir&longs;t <emph type="italics"/>B<emph.end type="italics"/>all &longs;hall be 16 <lb/>and 18 times greater than the Velocity of the &longs;econd: &longs;o that in <lb/>ca&longs;e the greater Velocity were to be more impeded by the Air than <lb/><arrow.to.target n="marg1097"></arrow.to.target><lb/>the le&longs;&longs;er, the Vibrations &longs;hould be more ^{*} rare in the greate&longs;t <lb/>Arches of 180, or 160 degrees, <emph type="italics"/>&c.<emph.end type="italics"/> than in the lea&longs;t of 10, 8, 4, <lb/>and al&longs;o of 2, and of 1; but this is contradicted by Experience: <lb/>for if two A&longs;&longs;i&longs;tants &longs;hall &longs;et them&longs;elves to count the Vibrations, <lb/>one the greate&longs;t, the other the lea&longs;t, they will find that they &longs;hall <lb/>number not only tens, but hundreds al&longs;o, without di&longs;agreeing one <lb/>&longs;ingle Vibration, yea, or one &longs;ole point. </s> <s>And this ob&longs;ervati­<lb/>on joyntly a&longs;&longs;ureth us of the two Propo&longs;itions, namely, that the <lb/>greate&longs;t and lea&longs;t Vibrations are all made one after another under <lb/>equal Times, and that the Impediment and Retardment of the Air <lb/>operates no more in the &longs;wifte&longs;t Motion, than in the &longs;lowe&longs;t: <lb/>contrary to that which before it &longs;eemed that we our &longs;elves al&longs;o <lb/>would have judged for company.</s></p><p type="margin"> <s><margin.target id="marg1095"></margin.target>* Tarra.</s></p><p type="margin"> <s><margin.target id="marg1096"></margin.target>* Artifizii.</s></p><p type="margin"> <s><margin.target id="marg1097"></margin.target>Or &longs;ewer.</s></p><p type="main"> <s>SAGR. Rather, becau&longs;e it cannot be denied but that the Air <lb/>impedeth both tho&longs;e and the&longs;e, &longs;ince they both continually grow <lb/>more languid, and at la&longs;t cea&longs;e, it is requi&longs;ite to &longs;ay that tho&longs;e Re­<lb/>tardations are made with the &longs;ame proportion in the one and in the <pb xlink:href="040/01/908.jpg" pagenum="215"/>other Operation. </s> <s>And then, the being to make greater Re&longs;i&longs;tance <lb/>at one time than at another, from what other doth it proceed, but <lb/>only from its being a&longs;&longs;ailed at one time with a greater <emph type="italics"/>Impetus<emph.end type="italics"/> and <lb/>Velocity, and at another time with le&longs;&longs;er? </s> <s>And if this be &longs;o then the <lb/>&longs;ame quantity of the Velocity of the Moveable is at once the Cau&longs;e <lb/>and the Mealure of the quantity of the Re&longs;i&longs;tance. </s> <s>Therefore all <lb/>Motions, whether they be &longs;low or &longs;wift, are retarded and impe­<lb/>ded in the &longs;ame proportion: a Notion in my judgment not con­<lb/>temptible.</s></p><p type="main"> <s>SALV. </s> <s>We may al&longs;o in this &longs;econd ca&longs;e conclude, That the <lb/>Fallacies in the Conclu&longs;ions, which are demon&longs;trated, ab&longs;tracting <lb/>from the extern Accidents, are in our In&longs;truments of very &longs;mall <lb/>con&longs;ideration, in re&longs;pect of the Motions of great Velocities of <lb/>which for the mo&longs;t part we &longs;peak, and of the Di&longs;tances which are <lb/>but very &longs;mall in relation to the Semidiameter and great Circles of <lb/>the Terre&longs;trial Globe.</s></p><p type="main"> <s>SIMP. </s> <s>I would gladly hear the rea&longs;on why you &longs;eque&longs;trate <lb/>the Projects from the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Fire, that is, as I conceive from <lb/>the force of the Powder, from the other Projects made by Slings, <lb/>Bows, or Cro&longs;s-bows, touching their not being in the &longs;ame manner <lb/>&longs;ubject to the Acceleration and Impediment of the Air.</s></p><p type="main"> <s>SALV. </s> <s>I am induced thereto by the exce&longs;&longs;ive, and, as I may &longs;ay, <lb/>Supernatural Fury or Impetuou&longs;ne&longs;s with which tho&longs;e Projects are <lb/>driven out: For indeed I think that the Velocity with which a <emph type="italics"/>B<emph.end type="italics"/>ul­<lb/>let is &longs;hot out of a Musket or Piece of Ordinance may without any <lb/>Hyperbole be called Supernatural. </s> <s>For one of tho&longs;e <emph type="italics"/>B<emph.end type="italics"/>ullets de­<lb/>&longs;cending naturally thorow the Air from &longs;ome immen&longs;e height, its <lb/>Velocity, by rea&longs;on of the Re&longs;i&longs;tance of the Air will not go in­<lb/>crea&longs;ing perpetually: but that which in Cadent <emph type="italics"/>B<emph.end type="italics"/>odies of &longs;mall <lb/>Gravity is &longs;een to happen in no very great ^{*} Space, I mean their <lb/><arrow.to.target n="marg1098"></arrow.to.target><lb/>being reduced in the end to an Equable Motion, &longs;hall al&longs;o happen <lb/>after a De&longs;cent of thou&longs;ands of yards, in a <emph type="italics"/>B<emph.end type="italics"/>all of Iron or Lead: <lb/>and this determinate and ultimate Velocity may be &longs;aid to be the <lb/>greate&longs;t that &longs;uch a <emph type="italics"/>B<emph.end type="italics"/>ody can obtain or acquire thorow the Air: <lb/>which Velocity I account to be much le&longs;&longs;er than that which cometh <lb/>to be impre&longs;&longs;ed on the &longs;ame <emph type="italics"/>B<emph.end type="italics"/>all by the fired Powder. </s> <s>And of this <lb/>a very appo&longs;ite Experiment may adverti&longs;e us. </s> <s>At an height of an <lb/>hundred or more yards let off a Musket charged with a Leaden <lb/><emph type="italics"/>B<emph.end type="italics"/>ullet perpendicularly downwards upon a Pavement of Stone; and <lb/>with the &longs;ame Musket &longs;hoot again&longs;t &longs;uch another Stone at the Di­<lb/>&longs;tance of a yard or two, and then &longs;ee which of the two <emph type="italics"/>B<emph.end type="italics"/>ullets is <lb/>more flatted: for if that coming from on high be le&longs;s ^{*} dented than <lb/><arrow.to.target n="marg1099"></arrow.to.target><lb/>the other, it &longs;hall be a &longs;ign that the Air hath impeded it, and dimi­<lb/>ni&longs;hed the Velocity conferred upon it by the Fire in the beginning <lb/>of the Motion: and that, con&longs;equently, &longs;o great a Velocity the Air <pb xlink:href="040/01/909.jpg" pagenum="216"/>would not &longs;uffer it to gain coming from never &longs;o great an height: <lb/>for in ca&longs;e the Velocity impre&longs;&longs;ed upon it by the Fire &longs;hould not <lb/>exceed that which it might acquire of its &longs;elf de&longs;cending naturally, <lb/>the battery downwards ought rather to be more valid than le&longs;s. <lb/></s> <s>I have not made &longs;uch an Experiment, but incline to think that a <lb/>Musket or Cannon Bullet falling from never &longs;o great an height, <lb/>will not make that percu&longs;&longs;ion which it maketh in a Wall at a Di­<lb/>&longs;tance of a few yards, that is of &longs;o few that the &longs;hort perforation, <lb/>or, if you will, Sci&longs;&longs;ure to be made in the Air &longs;ufficeth not to ob­<lb/>viate the exce&longs;s of the &longs;upernatural impetuo&longs;ity impre&longs;&longs;ed on it by <lb/>the Fire. </s> <s>This exce&longs;&longs;ive <emph type="italics"/>Impetus<emph.end type="italics"/> of &longs;uch like forced &longs;hots may <lb/>cau&longs;e &longs;ome deformity in the Line of the Projection; making <lb/>the beginning of the Parabola le&longs;s inclined or curved than the end. <lb/><emph type="italics"/>B<emph.end type="italics"/>ut this can be but of little or no prejudice to our Author in <lb/>practical Operations: among&longs;t the which the principal is the com­<lb/>po&longs;ition of a Table for the Ranges, or Flights, which containeth <lb/>the di&longs;tances of the Falls of <emph type="italics"/>B<emph.end type="italics"/>alls &longs;hot according to all Elevations. <lb/></s> <s>And becau&longs;e the&longs;e kinds of Projections are made with Mortar­<lb/>Pieces, and with no great charge; in the&longs;e the <emph type="italics"/>Impetus<emph.end type="italics"/> not being <lb/>&longs;upernatural, the Ranges de&longs;cribe their Lines very exactly.</s></p><p type="margin"> <s><margin.target id="marg1098"></margin.target>* Or Way.</s></p><p type="margin"> <s><margin.target id="marg1099"></margin.target>* Or battered.</s></p><p type="main"> <s><emph type="italics"/>B<emph.end type="italics"/>ut for the pre&longs;ent let us proceed forwards in the Treati&longs;e, <lb/>where the Author de&longs;ireth to lead us to the Contemplation and <lb/>Inve&longs;tigation of the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Moveable whil&longs;t it moveth <lb/>with a Motion compounded of two. </s> <s>And fir&longs;t of that compoun­<lb/>ded of two Equable Motions; the one Horizontal, and the other <lb/>Perpendicular.</s></p><p type="head"> <s>THEOR. II. PROP. II.</s></p><p type="main"> <s>If any Moveable be moved with a twofold Equa­<lb/>ble Motion, that is, Horizontal and Perpen­<lb/>dicular, the <emph type="italics"/>Impetus<emph.end type="italics"/> or Moment of the Lation <lb/>compounded of both the Motions &longs;hall be <emph type="italics"/>po­<lb/>tentia<emph.end type="italics"/> equal to both the Moments of the fir&longs;t <lb/>Motions.</s></p><p type="main"> <s><emph type="italics"/>For let any Moveable be moved Equably with a double Lation, <lb/>and let the Mutations of the Perpendicular an&longs;wer to the Space <lb/>A B, and let B C an&longs;wer to the Horizontal Lation pa&longs;&longs;ed in <lb/>the &longs;ame Time. </s> <s>Fora&longs;much therefore as the Spa-<emph.end type="italics"/><lb/><figure id="id.040.01.909.1.jpg" xlink:href="040/01/909/1.jpg"/><lb/><emph type="italics"/>ces A B, and B C are pa&longs;&longs;ed by the Equable Mo­<lb/>tion in the &longs;ame Time, their Moments &longs;hall be to <lb/>cach other as the &longs;aid A B and B C. </s> <s>But the <lb/>Moveable which is moved according to the&longs;e two Mutations &longs;hall de-<emph.end type="italics"/><pb xlink:href="040/01/910.jpg" pagenum="217"/><emph type="italics"/>&longs;cribe the Diagonal A C, and its Moment &longs;hall be as A C. </s> <s>But A C is<emph.end type="italics"/><lb/>potentia <emph type="italics"/>equal to the &longs;aid A B and B C: therefore the Moment com­<lb/>pounded of both the Moments A B and B C, is<emph.end type="italics"/> potentia <emph type="italics"/>equal to them <lb/>both taken together: Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s>SIMP. </s> <s>It is nece&longs;&longs;ary that you ea&longs;e me of one Scruple that <lb/>cometh into my mind, it &longs;eemeth to me that this which is now con­<lb/>cluded oppugneth another Propo&longs;ition of the former Tractate: in <lb/>which it is affirmed, That the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Moveable coming <lb/>from A into B is equal to that coming from A into C; and now it is <lb/>concluded, that the <emph type="italics"/>Impetus<emph.end type="italics"/> in C is greater than that in B.</s></p><p type="main"> <s>SALV. </s> <s>The Propo&longs;itions, <emph type="italics"/>Simplicius,<emph.end type="italics"/> are both true, but very <lb/>different from one another. </s> <s>Here the Author &longs;peaks of one &longs;ole <lb/>Moveable moved with one &longs;ole Motion, but compounded of two, <lb/>both Equable; and there he &longs;peaks of two Moveables moved <lb/>with Motions Naturally Accelerated, one along the Perpendicular <lb/>A B, and the other along the Inclined Plane A C: and moreover, <lb/>the Times there are not &longs;uppo&longs;ed equal, but the Time along <lb/>the Inclined Plane A C is greater than the Time along the Perpen­<lb/>dicular A B: but in the Motion &longs;poken of at pre&longs;ent, the Motions <lb/>along A B, B C and A C are under&longs;tood to be Equable, and made <lb/>in the &longs;ame Time.</s></p><p type="main"> <s>SIMP. </s> <s>Excu&longs;e me, and go on, for I am &longs;atisfied.</s></p><p type="main"> <s>SALV. </s> <s>The Author proceeds to &longs;hew us that which hapneth <lb/>concerning the <emph type="italics"/>Impetus<emph.end type="italics"/> of a Moveable moved in like manner with <lb/>one Motion compounded of two, that is to &longs;ay, the one Horizon­<lb/>tal and Equable, and the other Perpendicular but Naturally-Acce­<lb/>lerate, of which in fine the Motion of the Project is compounded, <lb/>and by which the Parabolick Line is de&longs;cribed; in each point of <lb/>which the Author endeavours to determine what the <emph type="italics"/>Impetus<emph.end type="italics"/> of the <lb/>Project is; for under&longs;tanding of which he &longs;heweth us the manner, <lb/>or, if you will, Method of regulating and mea&longs;uring that &longs;ame <emph type="italics"/>Im­<lb/>petus<emph.end type="italics"/> upon the &longs;aid Line, along which the Motion of the Grave <lb/>Moveable de&longs;cending with a Natural-Accelerate Motion departing <lb/>from Re&longs;t is made, &longs;aying:</s></p><p type="head"> <s>THEOR. III. PROP. III.</s></p><p type="main"> <s><emph type="italics"/>Let a Motion be made along the Line A B out of Re&longs;t in A, and <lb/>take in &longs;ome point C; and &longs;uppo&longs;e the &longs;aid A C to be the Time or <lb/>Mea&longs;ure of the Time of the &longs;aid Fall along the Space A C, as al&longs;o <lb/>the Mea&longs;ure of the<emph.end type="italics"/> Impetus <emph type="italics"/>or Moment in the Point C acquired by <lb/>the De&longs;cent along A C. </s> <s>Now let there be taken in the &longs;aid Line <lb/>A B any other Point, as &longs;uppo&longs;e B, in which we are to determine of the<emph.end type="italics"/><lb/>Impetus <emph type="italics"/>acquired by the Moveable along the Fall A B, in proportion to<emph.end type="italics"/><pb xlink:href="040/01/911.jpg" pagenum="218"/><emph type="italics"/>the<emph.end type="italics"/> Impetus, <emph type="italics"/>which it obtaineth in C, who&longs;e Mea&longs;ure is &longs;uppo&longs;ed to be <lb/>A C, Let A S be a Mean-proportional betwixt B A and A C. </s> <s>We will <lb/>demon&longs;trate that the<emph.end type="italics"/> Impetus <emph type="italics"/>in B is to the<emph.end type="italics"/> Impetus <emph type="italics"/>in C, as S A is to <lb/>A C. </s> <s>Let the Horizontal Line C D be double to the &longs;aid A C; and B E <lb/>double to B A. </s> <s>It appeareth by what hath been demon&longs;trated, That the <lb/>Cadent along A C being turned along the Horizon C D, and according <lb/>to the<emph.end type="italics"/> Impetus <emph type="italics"/>acquired in C, with an Equable Motion, &longs;hall pa&longs;s the <lb/>Space C D in a Time equal to that <lb/>in which the &longs;aid A C is pa&longs;&longs;ed<emph.end type="italics"/><lb/><figure id="id.040.01.911.1.jpg" xlink:href="040/01/911/1.jpg"/><lb/><emph type="italics"/>with an Accelerate Motion; and <lb/>likewi&longs;e that B E is pa&longs;&longs;ed in the <lb/>&longs;ame time as A B: But the Time of <lb/>the De&longs;cent along A B is A S: There­<lb/>fore the Horizontal Line B E is <lb/>pa&longs;&longs;ed in A S. </s> <s>As the Time S A is <lb/>to the Time A C, &longs;o let E B be to <lb/>B L. </s> <s>And becau&longs;e the Motion by <lb/>B E is Equable, the Space B L &longs;hall be pa&longs;&longs;ed in the Time A C ac­<lb/>cording to the Moment of Celerity in B: But in the &longs;ame Time A C <lb/>the Space C D is pa&longs;&longs;ed, according to the Moment of Velocity in C: <lb/>the Moments of Velocity therefore are to one another as the Spaces <lb/>which according to the &longs;ame Moments are pa&longs;&longs;ed in the &longs;ame Time: <lb/>Therefore the Moment of Velocity in C is to the Moment of Celerity in <lb/>B, as D C is to B L. </s> <s>And becau&longs;e as D C is to B E, &longs;o are their halfs, <lb/>to wit, C A to A B: but as E B is to B L, &longs;o is B A to A S: Therefore,<emph.end type="italics"/><lb/>exæquali, <emph type="italics"/>as D C is to B L, &longs;o is C A to A S: that is, as the Moment <lb/>of Velocity in C is to the Moment of Velocity in B, &longs;o is C A to A S; that <lb/>is, the Time along C A to the Time along A B. </s> <s>I he manner of Mea&longs;u­<lb/>ring the<emph.end type="italics"/> Impetus, <emph type="italics"/>or the Moment of Velocity upon a Line along which it <lb/>makes a Motion of De&longs;cent is therefore manife&longs;t; which<emph.end type="italics"/> Impetus <lb/><emph type="italics"/>is indeed &longs;uppo&longs;ed to encrea&longs;e according to the Proportion of the <lb/>Time.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>But this, before we proceed any farther, is to be premoni&longs;hed, that in <lb/>regard we are to &longs;peak for the future of the Motion compounded of the <lb/>Equable Horizontal, and of the Naturally Accelerate downwards, (for <lb/>from this Mixtion re&longs;ults, and by it is de&longs;igned the Line of the Project, <lb/>that is a Parabola;) it is nece&longs;&longs;ary that we define &longs;ome common mea&longs;ure <lb/>according to which we may mea&longs;ure the Velocity,<emph.end type="italics"/> Impetus, <emph type="italics"/>or Moment <lb/>of both the Motions. </s> <s>And &longs;eeing that of the Equable Motion the de­<lb/>grees of Velocity are innumerable, of which you may not take any <lb/>promi&longs;cuou&longs;ly, but one certain one which may be be compared and con­<lb/>joyned with the Degree of Velocity naturally Accelerate. </s> <s>I can think of <lb/>no more ea&longs;ie way for the electing and determining of that, than by a&longs;­<lb/>&longs;uming another of the &longs;ame kind. </s> <s>And that I may the better expre&longs;s <lb/>my meaning; Let A C be Perpendicular to the Horizon C B; and A C<emph.end type="italics"/><pb xlink:href="040/01/912.jpg" pagenum="219"/><emph type="italics"/>to be the Altitude, and C B the Amplitude of the Semiparabola A B; <lb/>which is de&longs;cribed by the Compo&longs;ition of two Lations; of which one is <lb/>that of the Moveable de&longs;cending along A C with a Motion Naturally <lb/>Acceler ate<emph.end type="italics"/> ex quiete <emph type="italics"/>in A; the other is the Equable Tran&longs;ver&longs;al Moti­<lb/>on according to the Horizontal Line A D. The<emph.end type="italics"/> Impetus <emph type="italics"/>acquired in C <lb/>along the De&longs;cent A C is determined by the quantity of the &longs;aid height <lb/>A C; for the<emph.end type="italics"/> Impetus <emph type="italics"/>of a Moveable<emph.end type="italics"/><lb/><figure id="id.040.01.912.1.jpg" xlink:href="040/01/912/1.jpg"/><lb/><emph type="italics"/>falling from the &longs;ame height is alwaies <lb/>one and the &longs;ame: but in the Horizontal <lb/>Line one may a&longs;&longs;ign not one, but innume­<lb/>rable Degrees of Velocities of Equable <lb/>Motions: out of which multitude that I <lb/>may &longs;ingle out, and as it were point with <lb/>the finger to that which I make choice of, <lb/>I extend or prolong the Altitude C A<emph.end type="italics"/> in <lb/>&longs;ublimi, <emph type="italics"/>in which, as was done before, I <lb/>will pitch upon A E; from which if I <lb/>conceive in my mind a Moveable to fall<emph.end type="italics"/><lb/>ex quiete <emph type="italics"/>in E, it appeareth that its<emph.end type="italics"/> Im­<lb/>petus <emph type="italics"/>acquired in the Time A, is one with which I conceive the &longs;ame <lb/>Moveable being turned along A D to be moved; and its degree of <lb/>Vclocity to be that, which in the Time of the De&longs;cent along E A pa&longs;&longs;eth <lb/>a Space in the Horizon double to the &longs;aid E A. </s> <s>This Præmonition I <lb/>judged nece&longs;&longs;ary.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>It is moreover to be advertized that the Amplitude of the Semi­<lb/>parabola A B &longs;hall be called by me the Horizontal Line<emph.end type="italics"/> [or Plane] <lb/><emph type="italics"/>C B.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The Altitude, to with A C, the Axis of the &longs;aid Parabola.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And the Line E A, by who&longs;e De&longs;cent the Horizontal<emph.end type="italics"/> Impetus <emph type="italics"/>is de­<lb/>termined, I call the Sublimity, or height.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The&longs;e things being declared and defined, I proceed to Demon&longs;tra­<lb/>tion.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. Stay, I pray you, for here me thinks it is convenient to <lb/>adorn this Opinion of our Author with the conformity of it to <lb/>the Conceit of <emph type="italics"/>Plato<emph.end type="italics"/> about the determining the different Veloci­<lb/>ties of the Equable Motions of the Revolutions of the Cœle&longs;tial <lb/>Bodies; who, having perhaps had a conjecture that no Moveable <lb/>could pa&longs;&longs;e from Re&longs;t into any determinate degree of Velocity in <lb/>which it ought afterwards to be perpetuated, unle&longs;s by pa&longs;&longs;ing <lb/>thorow all the other le&longs;&longs;er degrees of Velocity, or, if you will, <lb/>greater degrees of Tardity, which interpo&longs;e between the a&longs;&longs;igned <lb/>degree, and the highe&longs;t degree of Tardity, that is of Re&longs;t, &longs;aid that <lb/>God after he had created the Moveable Cœle&longs;tial <emph type="italics"/>B<emph.end type="italics"/>odies that he <lb/>might a&longs;&longs;ign them tho&longs;e Velocities wherewith they were afterwards <pb xlink:href="040/01/913.jpg" pagenum="220"/>to be perpetually moved with an Equable Circular Motion, made <lb/>them, they departing from Re&longs;t, to move along determinate Spaces <lb/>with that Natural Motion in a Right Line, according to which we <lb/>&longs;en&longs;ibly &longs;ee our Moveables to move from the &longs;tate of Re&longs;t &longs;ucce&longs;­<lb/>&longs;ively Accelerating. </s> <s>And he addeth, that having made them to <lb/>acquire that degree in which it plea&longs;ed him that they &longs;hould after­<lb/>wards be perpetually con&longs;erved, he converted their Right or direct <lb/>Motion into Circular; which only is apt to con&longs;erve it &longs;elf Equa­<lb/>ble, alwaies revolving without receding from, or approaching to <lb/>any prefixed term by them de&longs;ired. </s> <s>The Conceit is truly worthy <lb/>of <emph type="italics"/>Plato<emph.end type="italics"/>; and is the more to be e&longs;teemed in that the grounds there­<lb/>of pa&longs;&longs;ed over in &longs;ilence by him, and di&longs;covered by our Author by <lb/>taking off the Mask or Poetick Repre&longs;entation, do &longs;hew it to be <lb/>in its native a&longs;pect a true Hi&longs;tory. </s> <s>And I think it very credible that <lb/>we having by the Doctrine of A&longs;tronomy &longs;ufficiently competent <lb/>Knowledge of the Magnitudes of the Orbes of the Planets, and of <lb/>their Di&longs;tances from the Center about which they move, as al&longs;o <lb/>of their Velocities, our Author (to whom <emph type="italics"/>Plato's<emph.end type="italics"/> Conjecture was <lb/>not unknown) may &longs;ometime for his curio&longs;ity have had &longs;ome <lb/>thought of attempting to inve&longs;tigate whether one might a&longs;&longs;ign a <lb/>determinate Sublimity from which the <emph type="italics"/>B<emph.end type="italics"/>odies of the Planets depar­<lb/>ting, as from a &longs;tate of Re&longs;t, and moved for certain Spaces with a <lb/>Right and Naturally Accelerate Motion, afterwards converting <lb/>the Acquired Velocity into Equable Motions, they might be found <lb/>to corre&longs;pond with the greatne&longs;s of their Orbes, and with the Times <lb/>of their Revolutions.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>I think I do remember that he hath heretofore told me, <lb/>that he had once made the Computation, and al&longs;o that he found <lb/>it exactly to an&longs;wer the Ob&longs;ervations; but that he had no mind to <lb/>&longs;peak of them, doubting le&longs;t the two many Novelties by him di&longs;­<lb/>covered, which had provoked the di&longs;plea&longs;ure of many again&longs;t him, <lb/>might blow up new &longs;parks. <emph type="italics"/>B<emph.end type="italics"/>ut if any one &longs;hall have the like de­<lb/>&longs;ire he may of him&longs;elf by the Doctrine of the pre&longs;ent Tract give <lb/>him&longs;elf content. <emph type="italics"/>B<emph.end type="italics"/>ut let us pur&longs;ue our bu&longs;ine&longs;s, which is to <lb/>&longs;hew;</s></p><p type="head"> <s>PROBL. I. PROP. IV.</s></p><p type="main"> <s>How in a Parabola given, de&longs;cribed by the Pro­<lb/>ject, the <emph type="italics"/>Impetus<emph.end type="italics"/> of each &longs;everal point may be <lb/>determined.</s></p><p type="main"> <s><emph type="italics"/>Let the Semiparabola be B E C, who&longs;e Amplitude is C D and Al­<lb/>titude D B, with which continued out on high the Tangent of the <lb/>Parabola C A meeteth in A; and along the<emph.end type="italics"/> Vertex <emph type="italics"/>B let B I be<emph.end type="italics"/><pb xlink:href="040/01/914.jpg" pagenum="221"/><emph type="italics"/>an Horizontal Line, and parallel to C D. </s> <s>And if the Amplitude C D <lb/>be equal to the whole Altitude D A, B I &longs;hall be equal to B A and B D. <lb/></s> <s>And if the Time of the Fall along A B, and the Moment of Velocity <lb/>acquired in B along the De&longs;cent A B<emph.end type="italics"/> ex quiete <emph type="italics"/>in A be &longs;uppo&longs;ed to be <lb/>mea&longs;ured by the &longs;aid A B, then D C (that is twice B I) &longs;hall be the <lb/>Space which &longs;hall be pa&longs;&longs;ed by the<emph.end type="italics"/> Impetus A <emph type="italics"/>B turned along the Hori­<lb/>zontal Line in the &longs;ame Time: But in the &longs;ame Time falling along B D <lb/>out of Re&longs;t in B, it &longs;hall pa&longs;s the Altitude B D: Therefore the Movea­<lb/>ble falling out of Re&longs;t in A along A B, <lb/>being converted with the<emph.end type="italics"/> Impetus <emph type="italics"/>A B<emph.end type="italics"/><lb/><figure id="id.040.01.914.1.jpg" xlink:href="040/01/914/1.jpg"/><lb/><emph type="italics"/>along the Horizontal Parallel &longs;hall <lb/>pa&longs;s a Space equal to D C. </s> <s>And the <lb/>Fall along B D &longs;upervening, it pa&longs;&longs;eth <lb/>the Altitude B D, and de&longs;cribes the <lb/>Parabola B C; who&longs;e<emph.end type="italics"/> Impetus <emph type="italics"/>in the <lb/>Term C is compounded of the Equable <lb/>Tran&longs;ver&longs;al who&longs;e Moment is as A B, <lb/>and of another Moment acquired in the <lb/>Fall B D in the Term D or C; which <lb/>Moments are Equal. </s> <s>If therefore we <lb/>&longs;uppo&longs;e A B to be the Mea&longs;ure of one of them, as &longs;uppo&longs;e of the Equa­<lb/>ble Tran&longs;ver&longs;al; and B I, which is equal to B D, to be the Mea&longs;ure of <lb/>the<emph.end type="italics"/> Impetus <emph type="italics"/>acquired in D or C; then the Subten&longs;e I A &longs;hall be the <lb/>quantity of the Moment compound of them both: Therefore it &longs;hall be <lb/>the quantity or Mea&longs;ure of the whole Moment which the Project de&longs;cend­<lb/>ing along the Parabola B C &longs;hall acquire of<emph.end type="italics"/> Impetus <emph type="italics"/>in C. </s> <s>This pre­<lb/>mi&longs;ed, take in the Parabola any point E, in which we are to determine <lb/>of the<emph.end type="italics"/> Impetus <emph type="italics"/>of the Project. </s> <s>Draw the Horizontal Parallel E F, <lb/>and let B G be a Mean-proportional between B D and B F. </s> <s>And fora&longs;­<lb/>much as A B or B D is &longs;uppo&longs;ed to be the Mea&longs;ure of the Time, and of <lb/>the Moment of the Velocity in the Fall B D<emph.end type="italics"/> ex quiete <emph type="italics"/>in B: B G &longs;hall <lb/>be the Time, or the Mea&longs;ure of the Time, and of the<emph.end type="italics"/> Impetus <emph type="italics"/>in F, coming <lb/>out of B. </s> <s>If therefore B O be &longs;uppo&longs;ed equal to B G, the Diagonal <lb/>drawn from A to O &longs;hall be the quantity of the<emph.end type="italics"/> Impetus <emph type="italics"/>in E; for <lb/>A B hath been &longs;uppo&longs;ed the determinator of the Time, and of the<emph.end type="italics"/> Impe­<lb/>tus <emph type="italics"/>in B, which turned along the Horizontal Parallel doth alwaies <lb/>continue the &longs;ame: And B O determineth the<emph.end type="italics"/> Impetus <emph type="italics"/>in F or in E <lb/>along the De&longs;cent<emph.end type="italics"/> ex quiete <emph type="italics"/>in B in the Altitude B F: But the&longs;e two <lb/>A B and B O are<emph.end type="italics"/> potentia <emph type="italics"/>equal to the Power A O. </s> <s>Therefore that is <lb/>manife&longs;t which was &longs;ought.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>The Contemplation of the Compo&longs;ition of the&longs;e diffe­<lb/>rent <emph type="italics"/>Impetus's,<emph.end type="italics"/> and of the quantity of that <emph type="italics"/>Impetus<emph.end type="italics"/> which re&longs;ults <lb/>from this mixture, is &longs;o new to me, that it leaveth my mind in no <lb/>&longs;mall confu&longs;ion. </s> <s>I do not &longs;peak of the mixtion of two Motions <pb xlink:href="040/01/915.jpg" pagenum="222"/>Equable, though unequal to one another, made the one along the <lb/>Horizontal Line, and the other along the Perpendicular, for I very <lb/>well comprehend that there is made a Motion of the&longs;e two <emph type="italics"/>poten­<lb/>tia<emph.end type="italics"/> equal to both the Compounding Motions, but my confu&longs;ion <lb/>ari&longs;eth upon the mixing of the Equable-Horizontal and Perpendi­<lb/>cular-Naturally-Accelerate Motion. </s> <s>Therefore I could wi&longs;h we <lb/>might toge ther a little better con&longs;ider this bu&longs;ine&longs;s.</s></p><p type="main"> <s>SIMP. </s> <s>And I &longs;tand the more in need thereof in that I am not <lb/>yet &longs;o well &longs;atisfied in Mind as I &longs;hould be, in the Propo&longs;itions that <lb/>are the fir&longs;t foundations of the others that follow upon them. </s> <s>I <lb/>will add, that al&longs;o in the Mixtion of the two Motions Equable <lb/>Horizontal, and Perpendicular, I would better under&longs;tand that <lb/><emph type="italics"/>Potentia<emph.end type="italics"/> of their Compound. </s> <s>Now, <emph type="italics"/>Salviatus,<emph.end type="italics"/> you &longs;ee what we <lb/>want and de&longs;ire.</s></p><p type="main"> <s>SALV. </s> <s>Your de&longs;ire is very rea&longs;onable: and I will e&longs;&longs;ay whe­<lb/>ther my having had a longer time to think thereon may facilitate <lb/>your &longs;atisfaction. </s> <s>But you mu&longs;t bear with and excu&longs;e me if in di&longs;­<lb/>cour&longs;ing I &longs;hall repeat a great part of the things hitherto delivered <lb/>by our Author.</s></p><p type="main"> <s>It is not po&longs;&longs;ible for us to &longs;peak po&longs;itively touching Motions and <lb/>their Velocities or <emph type="italics"/>Impetus's,<emph.end type="italics"/> be they Equable, or be they Naturally <lb/>Accelerate, unle&longs;s we fir&longs;t agree upon the Mea&longs;ure that we are to <lb/>u&longs;e in the commen&longs;uration of tho&longs;e Velocities, as al&longs;o of the Time. <lb/></s> <s>As to the Mea&longs;ure of the Time, we have already that which is <lb/>commonly received by all of Hours, Prime-Minutes, and Se­<lb/>conds, <emph type="italics"/>&c.<emph.end type="italics"/> and as for the mea&longs;uring of Time we have that com­<lb/>mon Mea&longs;ure received by all, &longs;o it is requi&longs;ite to a&longs;&longs;ign another <lb/>Mea&longs;ure for the Velocities that is commonly under&longs;tood and re­<lb/>ceived by every one; that is, which every where is the &longs;ame. </s> <s>The <lb/>Author, as hath been declared, adjudged the Velocity of Naturally <lb/>de&longs;cending Grave-Bodies to be fit for this purpo&longs;e; the encrea&longs;ing <lb/>Velocities of which are the &longs;ame in all parts of the World. </s> <s>So that <lb/>that &longs;ame degree of Velocity which (for example) a Ball of Lead of <lb/>a pound acquireth in having, departing from Re&longs;t, de&longs;cended Per­<lb/>pendicularly as much as the height of a Pike, is alwaies, and in all <lb/>places the &longs;ame, and therefore mo&longs;t commodious for explicating <lb/>the quantity of the <emph type="italics"/>Impetus<emph.end type="italics"/> that is derived from the Natural De­<lb/>&longs;cent. </s> <s>Now it remains to find a way to determine likewi&longs;e the <lb/>Quantity of the <emph type="italics"/>Impetus<emph.end type="italics"/> in an Equable Motion in &longs;uch a manner, <lb/>that all tho&longs;e which di&longs;cour&longs;e about it may form the &longs;ame conceit <lb/>of its greatne&longs;s and Velocity; &longs;o that one may not imagine it more <lb/>&longs;wift, and another le&longs;s; whereupon afterwards in conjoyning and <lb/>mingling this Equable Motion imagined by them with the e&longs;tabli­<lb/>&longs;hed Accelerate Motion &longs;everal men may form &longs;everal Conceits of <lb/>&longs;everal greatne&longs;&longs;es of <emph type="italics"/>Impetus's.<emph.end type="italics"/> To determine and repre&longs;ent this <pb xlink:href="040/01/916.jpg" pagenum="223"/><emph type="italics"/>Impetus,<emph.end type="italics"/> and particular Velocity our Author hath not found any <lb/>way more commodious, than the making u&longs;e of the <emph type="italics"/>Impetus<emph.end type="italics"/> which <lb/>the Moveable from time to time acquires in the Naturally-Accele­<lb/>rate Motion, any acquired Moment of which being reduced into <lb/>an Equable Motion retaineth its Velocity preci&longs;ely limited, and <lb/>&longs;uch, that in &longs;uch another Time as that wherein it did De&longs;cend, it <lb/>pa&longs;&longs;eth double the Space of the Height from whence it fell. </s> <s>But <lb/>becau&longs;e this is the principal point in the bu&longs;ine&longs;s that we are upon, <lb/>it is good to make it to be perfectly under&longs;tood by &longs;ome particular <lb/>Example. </s> <s>Rea&longs;&longs;uming therefore the Velocity and <emph type="italics"/>Impetus<emph.end type="italics"/> acqui­<lb/>red by the Cadent Moveable, as we &longs;aid before, from the height <lb/>of a Pike, of which Velocity we will make u&longs;e for a Mea&longs;ure of <lb/>other Velocities and <emph type="italics"/>Impetu&longs;&longs;es<emph.end type="italics"/> upon other occa&longs;ions, and &longs;uppo­<lb/>&longs;ing, for example, that the Time of that Fall be four &longs;econd Mi­<lb/>nutes of an hour, to find by this &longs;ame Mea&longs;ure how great the <emph type="italics"/>Im­<lb/>petus<emph.end type="italics"/> of the Moveable would be falling from any other height <lb/>greater, or le&longs;&longs;er, we ought not from the proportion that this other <lb/>height hath to the height of a Pike to argue and conclude the quan­<lb/>tity of the <emph type="italics"/>Impetus<emph.end type="italics"/> acquired in this &longs;econd height, thinking, for <lb/>example, that the Moveable falling from quadruple the height <lb/>hath acquired quadruple Velocity, for that it is fal&longs;e: for that the <lb/>Velocity of the Naturally-Accelerate Motion doth not increa&longs;e or <lb/>decrea&longs;e according to the proportion of the Spaces, but according <lb/>to that of the Times, than which that of the Spaces is greater in a <lb/>duplicate proportion, as was heretofore demon&longs;trated. </s> <s>Therefore <lb/>when in a Right Line we have a&longs;&longs;igned a part for the Mea&longs;ure of <lb/>the Velocity, and al&longs;o of the Time, and of the Space in that Time <lb/>pa&longs;&longs;ed (for that for brevity &longs;ake all the&longs;e three Magnitudes are <lb/>often repre&longs;ented by one &longs;ole Line,) to find the quantity of the <lb/>Time, and the degree of Velocity that the &longs;ame Moveable would <lb/>have acquired in another Di&longs;tance we &longs;hall obtain the &longs;ame, not <lb/>immediataly by this &longs;econd Di&longs;tance, but by the Line which &longs;hall <lb/>be a Mean-proportional betwixt the two Di&longs;tances. </s> <s>But I will <lb/>better declare my &longs;elf by an Example. </s> <s>In the Line A C Perpendi­<lb/>cular to the Horizon let the part A B be under&longs;tood to <lb/>be a Space pa&longs;&longs;ed by a Moveable naturally de&longs;cending <lb/><figure id="id.040.01.916.1.jpg" xlink:href="040/01/916/1.jpg"/><lb/>with an Accelerate Motion: the Time of which pa&longs;­<lb/>&longs;age, in regard I may repre&longs;ent it by any Line, I will, for <lb/>brevity, imagine it to be as much as the &longs;ame Line A B <lb/>and likewi&longs;e for a Mea&longs;ure of the <emph type="italics"/>Impetus<emph.end type="italics"/> and Velocity <lb/>acquired by that Motion, I again take the &longs;ame Line <lb/>A B; &longs;o that of all the Spaces that are in the progre&longs;s of <lb/>the Di&longs;cour&longs;e to be con&longs;idered the part A B may be the <lb/>Mea&longs;ure. </s> <s>Having all our plea&longs;ure e&longs;tabli&longs;hed under one <lb/>&longs;ole Magnitude A B the&longs;e three Mea&longs;ures of different kinds of <pb xlink:href="040/01/917.jpg" pagenum="224"/>Quantities, that is to &longs;ay, of Spaces, of Times, and of <emph type="italics"/>Impetus's,<emph.end type="italics"/> let <lb/>it be required to determine in the a&longs;&longs;igned Space, and at the height <lb/>A C, how much the Time of the Fall of the Moveable from A to <lb/>C is to be, and what the <emph type="italics"/>Impetus<emph.end type="italics"/> is that &longs;hall be found to have been <lb/>acquired in the &longs;aid Term C, in relation to the Time and to the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> mea&longs;ured by A B. </s> <s>Both the&longs;e que&longs;tions &longs;hall be re&longs;olved <lb/>taking A D the Mean-proportional betwixt the two Lines A C <lb/>and A B; affirming the Time of the Fall along the whole Space <lb/>A C to be as the Time A D is in relation to A B, a&longs;&longs;igned in the <lb/>beginning for the Quantity of the Time in the Fall A B. </s> <s>And like­<lb/>wi&longs;e we will &longs;ay that the <emph type="italics"/>Impetus,<emph.end type="italics"/> or degree of Velocity that the <lb/>Cadent Moveable &longs;hall obtain in the Term C, in relation to the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> that it had in B, is as the &longs;ame Line A D is in relation to <lb/>A B, being that the Velocity encrea&longs;eth with the &longs;ame proportion <lb/>as the Time doth: Which Conclu&longs;ion although it was a&longs;&longs;umed as <lb/>a <emph type="italics"/>Po&longs;tulatum,<emph.end type="italics"/> yet the Author was plea&longs;ed to explain the Applicati­<lb/>on thereof above in the third Propo&longs;ition.</s></p><p type="main"> <s>This point being well under&longs;tood and proved, we come to the <lb/>Con&longs;ideration of the <emph type="italics"/>Impetus<emph.end type="italics"/> derived from two compound Moti­<lb/>ons: whereof let one be compounded of the Horizontal and alwaies <lb/>Equable, and of the Perpendicular unto the Horizon, and it al&longs;o <lb/>Equable: but let the other be compounded of the Horizontal like­<lb/>wi&longs;e alwaies Equable, and of the Perpendicular Naturally-Accele­<lb/>rate. </s> <s>If both &longs;hall be Equable, it hath been &longs;een already that the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> emerging from the compo&longs;ition of both is <emph type="italics"/>potentia<emph.end type="italics"/> equal to <lb/>both, as for more plainne&longs;s we will thus Exemplifie. </s> <s>Let the Move­<lb/>able de&longs;cending along the Perpendicular A B be &longs;uppo&longs;ed to have, <lb/>for example, three degrees of Equable <emph type="italics"/>Impetus,<emph.end type="italics"/> but being tran&longs;­<lb/>ported along A B towards C, let the &longs;aid Velocity and <emph type="italics"/>Impetus<emph.end type="italics"/> be <lb/>&longs;uppo&longs;ed four degrees, &longs;o that in the &longs;ame Time that falling it would <lb/>pa&longs;s along the Perpendicular, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> three yards, <lb/><figure id="id.040.01.917.1.jpg" xlink:href="040/01/917/1.jpg"/><lb/>it would in the Horizontal pa&longs;s four, but in <lb/>that compounded of both the Velocities it <lb/>cometh in the &longs;ame Timefrom the point A un­<lb/>to the Term C, de&longs;cending all the way along the Diagonal Line <lb/>A C, which is not &longs;even yards long, as that &longs;hould be which is com­<lb/>pounded of the two Lines A B, 3, and B C, 4, but is 5; which 5 is <lb/><emph type="italics"/>potentia<emph.end type="italics"/> equal to the two others, 3 and 4: For having found the <lb/>Squares of 3 and 4, which are 9 and 16, and joyning the&longs;e together, <lb/>they make 25 for the Square of A C, which is equal to the two <lb/>Squares of A B and B C: whereupon A C &longs;hall be as much as is the <lb/>Side, or, if you will, Root of the Square 25, which is 5. For a con&longs;tant <lb/>and certain Rule therefore, when it is required to a&longs;&longs;ign the <lb/>Quantity of the <emph type="italics"/>Impetus<emph.end type="italics"/> re&longs;ulting from two <emph type="italics"/>Impetus's<emph.end type="italics"/> given, the <lb/>one Horizontal, and the other Perpendicular, and both Equable, <pb xlink:href="040/01/918.jpg" pagenum="225"/>they are each of them to be &longs;quared, and their Squares being put <lb/>together the Root of the Aggregate is to be extracted, which &longs;hall <lb/>give us the quantity of the <emph type="italics"/>Impetus<emph.end type="italics"/> compounded of them both. <lb/></s> <s>And thus in the foregoing example, that Moveable that by vertue <lb/>of the Perpendicular Motion would have percu&longs;&longs;ed upon the Hori­<lb/>zon with three degrees of Force, and with only the Horizontal Mo­<lb/>tion would have percu&longs;&longs;ed in C with four degrees, percu&longs;&longs;ing with <lb/>both the <emph type="italics"/>Impetus's<emph.end type="italics"/> conjoyned, the blow &longs;hall be like to that of the <lb/>Percutient moved with five degrees of Velocity and Force. </s> <s>And <lb/>this &longs;ame Percu&longs;&longs;ion would be of the &longs;ame Impetuo&longs;ity in all the <lb/>points of the Diagonal A C, for that the compounded <emph type="italics"/>Impetus's<emph.end type="italics"/><lb/>are alwaies the &longs;ame, never encrea&longs;ing or dimini&longs;hing.</s></p><p type="main"> <s>Let us now &longs;ee what befalls in compounding the Equable Hori­<lb/>zontal Motion with another Perpendicular to the Horizon which <lb/>beginning from Re&longs;t goeth Naturally Accelerating. </s> <s>It is already <lb/>manife&longs;t, that the Diagonal, which is the Line of the Motion com­<lb/>pounded of the&longs;e two, is not a Right Line, but Semiparabolical, <lb/>as hath been demon&longs;trated; ^{*} in which the <emph type="italics"/>Impetus<emph.end type="italics"/> doth go con­<lb/><arrow.to.target n="marg1100"></arrow.to.target><lb/>tinually encrea&longs;ing by means of the continual encrea&longs;e of the Ve­<lb/>locity of the Perpendicular Motion: Wherefore, to determine what <lb/>the <emph type="italics"/>Impetus<emph.end type="italics"/> is in an a&longs;&longs;igned point of that Parabolical Diagonal, it <lb/>is requi&longs;ite fir&longs;t to a&longs;&longs;ign the Quantity of the Uniform Horizontal <lb/><emph type="italics"/>Impetus,<emph.end type="italics"/> and then to find what is the <emph type="italics"/>Impetus<emph.end type="italics"/> of the falling Movea­<lb/>ble in the point a&longs;&longs;igned: the which cannot be determined without <lb/>the con&longs;ideration of the Time &longs;pent from the beginning of the <lb/>Compo&longs;ition of the two Motions: which Con&longs;ideration of the <lb/>Time is not required in the Compo&longs;ition of Equable Motions, the <lb/>Velocities and <emph type="italics"/>Impetus's<emph.end type="italics"/> of which are alwaies the &longs;ame: but here <lb/>where there is in&longs;erted into the mixture a Motion which beginning <lb/>from extream Tardity goeth encrea&longs;ing in Velocity according to <lb/>the continuation of the Time, it is nece&longs;&longs;ary that the quantity of <lb/>the Time do &longs;hew us the quantity of the degree of Velocity in the <lb/>a&longs;&longs;igned point: for, as to the re&longs;t, the <emph type="italics"/>Impetus<emph.end type="italics"/> compounded of the&longs;e <lb/>two (as in Uniform Motions) is <emph type="italics"/>potentia<emph.end type="italics"/> equal to both the others <lb/>compounding. </s> <s>But here again I will better explain my meaning by <lb/>an example. </s> <s>In A C the Perpendicular to the Horizon let any part <lb/>be taken A B; the which I will &longs;uppo&longs;e to &longs;tand for the Mea&longs;ure <lb/>of the Space of the Natural Motion made along the &longs;aid Perpen­<lb/>dicular, and likewi&longs;e let it be the Mea&longs;ure of the Time, and al&longs;o of <lb/>the degree of Velocity, or, if you will, of the <emph type="italics"/>Impetus's.<emph.end type="italics"/> It is ma­<lb/>nife&longs;t in the fir&longs;t place, that if the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Moveable in B <lb/><emph type="italics"/>ex quiete<emph.end type="italics"/> in A &longs;hall be turned along B D parallel to the Horizon in <lb/>an Equable Motion, the quantity of its Velocity &longs;hall be &longs;uch that <lb/>in the Time A B it &longs;hall pa&longs;s a Space double to the Space A B, which <lb/>let be the Line B D. </s> <s>Then let B C be &longs;uppo&longs;ed equal to B A, and <pb xlink:href="040/01/919.jpg" pagenum="226"/>let C E be drawn parallel and equal to B D, and thus by the Points <lb/>B and E we &longs;hall de&longs;cribe the Parabolick Line B E I. </s> <s>And becau&longs;e <lb/>that in the Time A B with the <emph type="italics"/>Impetus<emph.end type="italics"/> A B the Horizontal Line B D <lb/>or C E is pa&longs;&longs;ed, double to A B, and in &longs;uch another Time the Per­<lb/>pendicular B C is pa&longs;&longs;ed with an acqui&longs;t of <emph type="italics"/>Impetus<emph.end type="italics"/> in C equal to <lb/>the &longs;aid Horizontal Line; therefore the Moveable in &longs;uch another <lb/>Time as A B &longs;hall be found to have pa&longs;&longs;ed from B to E along the <lb/>Parabola B E with an <emph type="italics"/>Impetus<emph.end type="italics"/> compounded of two, each equal to <lb/>the <emph type="italics"/>Impetus<emph.end type="italics"/> A B. </s> <s>And becau&longs;e one of them is Horizontal, and the <lb/>other Perpendicular, the <emph type="italics"/>Impetus<emph.end type="italics"/> compound of them &longs;hall be equal <lb/>in Power to them both, that is <lb/><figure id="id.040.01.919.1.jpg" xlink:href="040/01/919/1.jpg"/><lb/>double to one of them. </s> <s>So that <lb/>&longs;uppo&longs;ing B F equal to B A, and <lb/>drawing the Diagonal A F, the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> or the Percu&longs;&longs;ion in E <lb/>&longs;hall be greater than the Percu&longs;­<lb/>&longs;ion in B of the Moveable fal­<lb/>ling from the Height A, or than <lb/>the Percu&longs;&longs;ion of the Horizon­<lb/>tal <emph type="italics"/>Impetus<emph.end type="italics"/> along B D, according <lb/>to the proportion of A F to <lb/>A B. </s> <s>But in ca&longs;e, &longs;till retaining <lb/>B A for the Mea&longs;ure of the <lb/>Space of the Fall from Re&longs;t in <lb/>A unto B, and for the Mea&longs;ure of the Time and of the <emph type="italics"/>Impetus<emph.end type="italics"/> of <lb/>the falling Moveable acquired in B, the Altitude B O &longs;hould not be <lb/>equal to, but greater than A B, taking B G to be a Mean-propor­<lb/>tional betwixt the &longs;aid A B and B O, the &longs;aid B G would be the <lb/>Mea&longs;ure of the Time and of the <emph type="italics"/>Impetus<emph.end type="italics"/> in O, acquired in O by the <lb/>Fall from the height B O; and the Space along the Horizontal <lb/>Line, which being pa&longs;&longs;ed with the <emph type="italics"/>Impetus<emph.end type="italics"/> A B in the Time A B <lb/>would be double to A B, &longs;hall, in the whole duration of the Time <lb/>B G, be &longs;o much the greater, by how much in proportion B G is <lb/>greater than B A. </s> <s>Suppo&longs;ing therefore L B equal to B G, and draw­<lb/>ing the Diagonal A L, it &longs;hall give us the quantity compounded of <lb/>the two <emph type="italics"/>Impetus's<emph.end type="italics"/> Horizontal and Perpendicular, by which the <lb/>Parabola is de&longs;cribed; and of which the Horizontal and Equable is <lb/>that acquired in B by the fall of A B, and the other is that acquired <lb/>in O, or, if you will, in I by the De&longs;cent B O, who&longs;e Time, as al&longs;o <lb/>the quantity of its Moment was B G. </s> <s>And in this Method we &longs;hall <lb/>inve&longs;tigate the <emph type="italics"/>Impetus<emph.end type="italics"/> in the extream term of the Parabola, in ca&longs;e <lb/>its Altitude were le&longs;&longs;er than the Sublimity A B, taking the Mean­<lb/>proportional betwixt them both: which being &longs;et off upon the Ho­<lb/>rizontal Line in the place of B F, and the Diagonal drawn, as A F, <lb/>we &longs;hall hereby have the quantity of the <emph type="italics"/>Impetus<emph.end type="italics"/> in the extream <lb/>term of the Parabola.</s></p><pb xlink:href="040/01/920.jpg" pagenum="227"/><p type="margin"> <s><margin.target id="marg1100"></margin.target>* Or along <lb/>which.</s></p><p type="main"> <s>And to what hath hitherto been propo&longs;ed touching <emph type="italics"/>Impetus's,<emph.end type="italics"/><lb/>Blows, or if you plea&longs;e, Percu&longs;&longs;ions of &longs;uch like Projects, it is ne­<lb/>ce&longs;&longs;ary to add another very nece&longs;&longs;ary Con&longs;ideration; and this it is: <lb/>That it doth not &longs;uffice to have regard to the Velocity only of the <lb/>Project for the determining rightly of the Force and Violence of the <lb/>Percu&longs;&longs;ion, but it is requi&longs;ite likewi&longs;e to examine apart the State <lb/>and Condition of that which receiveth the Percu&longs;&longs;ion, in the effica­<lb/>cy of which it hath for many re&longs;pects a great &longs;hare and intere&longs;t. <lb/></s> <s>And fir&longs;t there is no man but knows that the thing &longs;mitten doth &longs;o <lb/>much &longs;uffer violence from the Velocity of the Percutient by how <lb/>much it oppo&longs;eth it, and either totally or partially checketh its <lb/>Motion: For if the Blow &longs;hall light upon &longs;uch an one as yieldeth to <lb/>the Velocity of the Percutient without any Re&longs;i&longs;tance, that Blow <lb/>&longs;hall be nullified: And he that runneth to hit his Enemy with his <lb/>Launce, if at the overtaking of him it &longs;hall fall out that he moveth, <lb/>giving back with the like Velocity, he &longs;hall make no thru&longs;t, and the <lb/>Action &longs;hall be a meer touch without doing any harm.</s></p><p type="main"> <s>But if the Percu&longs;&longs;ion &longs;hall happen to be received upon an Object <lb/>which doth not wholly yield to the Percutient, but only partially, <lb/>the Percu&longs;&longs;ion &longs;hall do hurt, though not with its whole <emph type="italics"/>Impetus,<emph.end type="italics"/> but <lb/>only with the exce&longs;s of the Velocity of the &longs;aid Percutient above <lb/>the Velocity of the recoile and rece&longs;&longs;ion of the Object percu&longs;&longs;ed: <lb/>&longs;o that, if <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> the Percutient &longs;hall come with 10 degrees of Velo­<lb/>city upon the Percu&longs;&longs;ed Body, which giving back in part retireth <lb/>with 4 degrees, the <emph type="italics"/>Impetus<emph.end type="italics"/> and Percu&longs;&longs;ion &longs;hall be as if it were of <lb/>6 degrees. </s> <s>And la&longs;tly, the Percu&longs;&longs;ion &longs;hall be entire and perfect on <lb/>the part of the Percutient when the thing percu&longs;&longs;ed yieldeth not, <lb/>but wholly oppo&longs;eth and &longs;toppeth the whole Motion of the Percu­<lb/>tient; if haply there can be &longs;uch a ca&longs;e. </s> <s>And I &longs;ay on the part of <lb/>the Percutient, for when the Body percu&longs;&longs;ed moveth with a contra­<lb/>ry Motion towards the Percutient, the Blow and Shock &longs;hall be <lb/>&longs;o much the more Impetuous by how much the two Velocities uni­<lb/>ted are greater than the &longs;ole Velocity of the Percutient. </s> <s>More­<lb/>over, you are likewi&longs;e to take notice, that the more or le&longs;s yielding <lb/>may proceed not only from the quality of the Matter more or le&longs;s <lb/>hard, as if it be of Iron, of Lead, or of Wooll, <emph type="italics"/>&c.<emph.end type="italics"/> but al&longs;o from <lb/>the Po&longs;ition of the Body that receiveth the Percu&longs;&longs;ion. </s> <s>Which Po­<lb/>&longs;ition if it &longs;hall be &longs;uch as that the Motion of the Percutient hap­<lb/>neth to hit it at Right-Angles, the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Percu&longs;&longs;ion &longs;hall <lb/>be the greate&longs;t: but if the Motion &longs;hall proceed obliquely, and, as <lb/>we &longs;ay, a&longs;lant, the Percu&longs;&longs;ion &longs;hall be weaker; and that more, and <lb/>more according to its greater and greater Obliquity: for an Ob­<lb/>ject in that manner &longs;cituate, albeit of very &longs;olid matter, doth not <lb/>damp or arre&longs;t the whole <emph type="italics"/>Impetus<emph.end type="italics"/> and Motion of the Percutient, <lb/>which &longs;lanting pa&longs;&longs;eth farther, continuing at lea&longs;t in &longs;ome part to <pb xlink:href="040/01/921.jpg" pagenum="228"/>move along the Surface of the oppo&longs;ed Body Re&longs;i&longs;ting. </s> <s>When <lb/>therefore we have even now determined of the greatne&longs;s of the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> of the Project in the end of the Parabolicall Line, it ought <lb/>to be under&longs;tood to be meant of the Percu&longs;&longs;ion received upon a <lb/>Line at Right Angles with the &longs;ame Parabolick Line, or with the <lb/>Line that is Tangent to the Parabola in the fore&longs;aid point: for <lb/>although that &longs;ame Motion be compounded of an Horizontal and <lb/>a Perpendicular Motion, the <emph type="italics"/>Impetus<emph.end type="italics"/> is not at the greate&longs;t either <lb/>upon the Horizontal Plane, or upon that erect to the Horizon, be­<lb/>ing received upon them both obliquely.</s></p><p type="main"> <s>SAGR. </s> <s>Your &longs;peaking of the&longs;e Blows, and the&longs;e Percu&longs;&longs;ions <lb/>hath brought into my mind a Problem, or, if you will, Que&longs;tion <lb/>in the Mechanicks, the &longs;olution whereof I could never find in any <lb/>Author, nor any thing that doth dimini&longs;h my admiration, or &longs;o <lb/>much as in the lea&longs;t afford my judgment &longs;atisfaction. </s> <s>And my <lb/>doubt and wonder lyeth in my not being able to comprehend <lb/>whence that Immen&longs;e Force and Violence &longs;hould proceed, and on <lb/>what Principle it &longs;hould depend, which we &longs;ee to con&longs;i&longs;t in Per­<lb/>cu&longs;&longs;ion, in that with the &longs;imple &longs;troke of an Hammer, that doth <lb/>not weigh above eight or ten pounds, we &longs;ee &longs;uch Re&longs;i&longs;tances to be <lb/>overcome as would not yield to the weight of a Grave Body that <lb/>without Percu&longs;&longs;ion hath an <emph type="italics"/>Impetus<emph.end type="italics"/> only by pre&longs;&longs;ing and bearing <lb/>upon it, albeit the weight of this be many hundreds of pounds <lb/>more. </s> <s>I would likewi&longs;e find out a way to mea&longs;ure the Force of this <lb/>Percu&longs;&longs;ion, which I do not think to be infinite, but rather hold <lb/>that it hath its Term in which it may be compared, and in the end <lb/>Regulated with other Forces of pre&longs;&longs;ing Gravities, either of Lea­<lb/>vers, or of Screws, or of other Mechanick In&longs;truments, of who&longs;e <lb/>multiplication of Force I am thorowly &longs;atisfied.</s></p><p type="main"> <s>SALV. </s> <s>You are not alone in the admirablene&longs;s of the effect, <lb/>and the ob&longs;curity of the cau&longs;e of &longs;o &longs;tupendious an Accident. </s> <s>I <lb/>ruminated a long time upon it in vain, my &longs;tupifaction &longs;till encrea­<lb/>&longs;ing; till in the end meeting with our <emph type="italics"/>Academian,<emph.end type="italics"/> I received from <lb/>him a double &longs;atisfaction: fir&longs;t in hearing that he al&longs;o had been a <lb/>long time at the &longs;ame lo&longs;s; and next in under&longs;tanding that after he <lb/>had at times &longs;pent many thou&longs;ands of hours in &longs;tudying and con­<lb/>templating thereon, he had light upon certain Notions far from <lb/>our fir&longs;t conceptions, and therefore new, and for their Novelty to <lb/>be admired. </s> <s>And becau&longs;e that I already &longs;ee that your Curio&longs;ity <lb/>would gladly hear tho&longs;e Conceits which are Remote from common <lb/>Conjecture, I &longs;hall not &longs;tay for your entreaty, but I give you my <lb/>word that &longs;o &longs;oon as we &longs;hall have fini&longs;hed the Reading of this <lb/>Treati&longs;e of Projects, I will &longs;et before you all tho&longs;e Fancies, or, I <lb/>might &longs;ay, Extravagancies that are yet left in my memory of the <lb/>Di&longs;cour&longs;es of the Academick. </s> <s>In the mean time let us pro&longs;ecute <lb/>the Propo&longs;itions of our Author.</s></p><pb xlink:href="040/01/922.jpg" pagenum="229"/><p type="head"> <s>PROBL. II. PROP. V.</s></p><p type="main"> <s>In the Axis of a given Parabola prolonged to find <lb/>a &longs;ublime point out of which the Moveable <lb/>falling &longs;hall de&longs;cribe the &longs;aid Parabola.</s></p><p type="main"> <s><emph type="italics"/>Let the Parabola be A B, its Amplitude H B, and its prolonged <lb/>Axis H E; in which a Sublimity is to be found, out of which the <lb/>Moveable falling, and converting the<emph.end type="italics"/> Impetus <emph type="italics"/>conceived in A <lb/>along the Horizontal Line, de&longs;cribeth the Parabola A B. </s> <s>Draw the <lb/>Horizontal Line A G, which &longs;hall be Parallel to B H, and &longs;uppo&longs;ing A F <lb/>equal to A H draw the Right Line F B, which toucheth the Parabola in <lb/>B, and cutteth the Horizontal Line A G in G; and unto F A and A G <lb/>let A E be a third Proportional. </s> <s>I &longs;ay, that E is the &longs;ublime Point re­<lb/>quired, out of which the Moveable falling<emph.end type="italics"/> ex quiete <emph type="italics"/>in E, and the<emph.end type="italics"/> Im­<lb/>petus <emph type="italics"/>conceived in A being converted along the Horizontal Line over­<lb/>taking the<emph.end type="italics"/> Impetus <emph type="italics"/>of the De&longs;cent<emph.end type="italics"/><lb/><figure id="id.040.01.922.1.jpg" xlink:href="040/01/922/1.jpg"/><lb/><emph type="italics"/>in H<emph.end type="italics"/> ex quiete <emph type="italics"/>in A, de&longs;cribeth the <lb/>Parabola A B. </s> <s>For if we &longs;uppo&longs;e <lb/>E A to be the Mea&longs;ure of the Time <lb/>of the Fall from E to A, and of <lb/>the<emph.end type="italics"/> Impetus <emph type="italics"/>acquired in A, A G <lb/>(that is a Mean-proportional be­<lb/>tween E A and A F) &longs;hall be the <lb/>Time and the<emph.end type="italics"/> Impetus <emph type="italics"/>coming <lb/>from F to A, or from A to H. </s> <s>And <lb/>becau&longs;e the Moveable coming out of <lb/>E in the Time E A with the<emph.end type="italics"/> Impetus <emph type="italics"/>acquired in A pa&longs;&longs;eth in the Ho­<lb/>rizontal Lation with an Equable Motion the double of E A; There­<lb/>fore likewi&longs;e moving with the &longs;ame<emph.end type="italics"/> Impetus <emph type="italics"/>it &longs;hall in the Time A G <lb/>pa&longs;s the double of G A, to wit, the Mean-proportional B H (for the <lb/>Spaces pa&longs;&longs;ed with the &longs;ame Equable Motion are to one another as the <lb/>Times of the &longs;aid Motions:) And along the Perpendicular A H &longs;hall <lb/>be pa&longs;&longs;ed with a Motion<emph.end type="italics"/> ex quiete <emph type="italics"/>in the &longs;ame Time G A: Therefore <lb/>the Amplitude H B, and Altitude A H are pa&longs;&longs;ed by the Moveable in the <lb/>&longs;ame Time: Therefore the Parabola A B &longs;hall be de&longs;cribed by the <lb/>De&longs;cent of the Project coming from the Sublimity E: Which was re­<lb/>quired.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it appeareth that the half of the <emph type="italics"/>B<emph.end type="italics"/>a&longs;e or Amplitude of the <lb/>Semiparabola (which is the fourth part of the Amplitude of <lb/>the whole Parabola) is a Mean-proportional betwixt its Al­<lb/>titude and the Sublimity out of which the Moveable falling <lb/>de&longs;cribeth it.</s></p><pb xlink:href="040/01/923.jpg" pagenum="230"/><p type="head"> <s>PROBL. III. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> VI.</s></p><p type="main"> <s>The Sublimity and Altitude of a Semiparabola <lb/>being given to find its Amplitude.</s></p><p type="main"> <s><emph type="italics"/>Let A C be perpendicular to the<emph.end type="italics"/><lb/><figure id="id.040.01.923.1.jpg" xlink:href="040/01/923/1.jpg"/><lb/><emph type="italics"/>Horizontal Line D C, in <lb/>which let the Altitude C B and <lb/>the Sublimity B A be given: It is <lb/>required in the Horizontal Line <lb/>D C to find the Amplitude of the <lb/>Semiparabola that is de&longs;cribed out of <lb/>the Sublimity B A with the Alti­<lb/>tude B C. </s> <s>Take a Mean proportional <lb/>between C B and B A, to which let <lb/>C D be double, I &longs;ay, that C D is <lb/>the Amplitude required. </s> <s>The which <lb/>is manife&longs;t by the precedent Propo&longs;ition.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. IV. PROP. VII.</s></p><p type="main"> <s>In Projects which de&longs;cribe Semiparabola's of the <lb/>&longs;ame Amplitude, there is le&longs;s <emph type="italics"/>Impetus<emph.end type="italics"/> required <lb/>in that which de&longs;cribeth that who&longs;e Ampli­<lb/>tude is double to its Altitude, than in any <lb/>other.</s></p><p type="main"> <s><emph type="italics"/>For let the Semiparabola be B D, who&longs;e Amplitude C D is dou­<lb/>ble to its Altitude C B; and in its Axis extended on high let B A <lb/>be &longs;uppo&longs;ed equal to the Altitude B C; and draw a Line from <lb/>A to D which toucheth the Semiparabola in D, and &longs;hall cut the Hori­<lb/>zontal Line B E in E; and B E &longs;hall be equal to B C or to B A: It is <lb/>manife&longs;t that it is de&longs;cribed by the Project who&longs;e Equable Horizontal<emph.end type="italics"/><lb/>Impetus <emph type="italics"/>is &longs;uch as is that gained in B of a thing falling from Re&longs;t in A, <lb/>and the<emph.end type="italics"/> Impetus <emph type="italics"/>of the Natural Motion downwards, &longs;uch as is that of <lb/>a thing coming to C<emph.end type="italics"/> ex quiete <emph type="italics"/>in B. </s> <s>Whence it is manife&longs;t, that the<emph.end type="italics"/><lb/>Impetus <emph type="italics"/>compounded of them, and that &longs;triketh in the Term D is as the <lb/>Diagonal A E, that is<emph.end type="italics"/> potentia <emph type="italics"/>equal to them both. </s> <s>Now let there be <lb/>another Semiparabola G D, who&longs;e Amplitude is the &longs;ame C D, and the <lb/>Altitude C G le&longs;s, or greater than the Altitude B C, and let H D touch <lb/>the &longs;ame, cutting the Horizontal Line drawn by G in the point K; and <lb/>as H G is to G K, &longs;o let K G be to G L: by what hath been demon&longs;trated <lb/>G L &longs;hall be the Altitude from which the Project falling de&longs;cribeth the<emph.end type="italics"/><pb xlink:href="040/01/924.jpg" pagenum="231"/><emph type="italics"/>Parabola G D. </s> <s>Let G M be a Mean-proportional betwixt A B and <lb/>G L; G M &longs;hall be the Time, and the Moment or<emph.end type="italics"/> Impetus <emph type="italics"/>in G of the <lb/>Project falling from L, (for it hath been &longs;uppo&longs;ed that A B is the Mea­<lb/>&longs;ure of the Time and<emph.end type="italics"/> Impetus.) <emph type="italics"/>Again, let G N be a Mean-propor­<lb/>tional betwixt B C and C G: this G N &longs;hall be the Mea&longs;ure of the <lb/>Time and the<emph.end type="italics"/><lb/>Impetus <emph type="italics"/>of the<emph.end type="italics"/><lb/><figure id="id.040.01.924.1.jpg" xlink:href="040/01/924/1.jpg"/><lb/><emph type="italics"/>Project falling <lb/>from G to C. <lb/></s> <s>If therefore a <lb/>Line be drawn <lb/>from M to N <lb/>it &longs;hall be the <lb/>the Mea&longs;ure of <lb/>the<emph.end type="italics"/> Impetus <emph type="italics"/>of <lb/>the Project a­<lb/>long the Para­<lb/>bola B D, &longs;cri­<lb/>king in the <lb/>term D. Which<emph.end type="italics"/><lb/>Impetus, <emph type="italics"/>I &longs;ay, <lb/>is greater than the<emph.end type="italics"/> Impetus <emph type="italics"/>of the Project along the Parabola B D, <lb/>who&longs;e quantity was A E. </s> <s>For becau&longs;e G N is &longs;uppo&longs;ed the Mean-pro­<lb/>portional betwixt B C and C G, and B C is equal to B E, that is to H G; <lb/>(for they are each of them &longs;ubduple to D C:) Therefore as C G is to <lb/>G N, &longs;o &longs;hall N G be to G K: and, as C G or H G is to G K, &longs;o &longs;hall the <lb/>Square N G be to the Square of G K: But as H G is to G K, &longs;o was <lb/>K G &longs;uppo&longs;ed to be to G L: Therefore as N G is to the Square G K, &longs;o <lb/>is K G to G L: But as K G is to G L, &longs;o is the Square K G unto the <lb/>Square G M, (for G M is the Mean between K G and G L:) Therefore <lb/>the three Squares N G, K G, and G M are continual proportionals: And <lb/>the two extream ones N G and G M taken together, that is the Square <lb/>M N is greater than double the Square K G, to which the Square A E <lb/>is double: Therefore the Square M N is greater than the Square A E: <lb/>and the Line M N greater than the Line A E: Which was to be de­<lb/>mon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>CORROLLARY I.</s></p><p type="main"> <s>Hence it appeareth, that on the contrary, in the Project out of D <lb/>along the Semiparabola D B, le&longs;s <emph type="italics"/>Impetus<emph.end type="italics"/> is required than <lb/>along any other according to the greater or le&longs;&longs;er Elevation <lb/>of the Semiparabola B D, which is according to the Tan­<lb/>gent A D, containing half a Right-Angle upon the Hori­<lb/>zon.</s></p><pb xlink:href="040/01/925.jpg" pagenum="232"/><p type="head"> <s>COROLLARRY II.</s></p><p type="main"> <s>And that being &longs;o, it followeth, that if Projections be made with <lb/>the &longs;ame <emph type="italics"/>Impetus<emph.end type="italics"/> out of the Term D, according to &longs;everal <lb/>Elevations, that &longs;hall be the greate&longs;t Projection or Amplitude <lb/>of the Semiparabola or whole Parabola which followeth at <lb/>the Elevation of a ^{*} Semi-Right-Angle; and the re&longs;t, made <lb/><arrow.to.target n="marg1101"></arrow.to.target><lb/>according to greater or le&longs;&longs;er Angles, &longs;hall be greater or <lb/>le&longs;&longs;er.</s></p><p type="margin"> <s><margin.target id="marg1101"></margin.target>* Or, at the Ele­<lb/>vation of 45 de­<lb/>grees.</s></p><p type="main"> <s>SAGR. </s> <s>The &longs;trength of Nece&longs;&longs;ary Demon&longs;trations are full of <lb/>plea&longs;ure and wonder; and &longs;uch are only the Mathematical. </s> <s>I un­<lb/>der&longs;tood before upon tru&longs;t from the Relations of &longs;undry Gunners, <lb/>that of all the Ranges of a Cannon, or of a Mortar-piece, the grea­<lb/>te&longs;t, <emph type="italics"/>&longs;cilicet<emph.end type="italics"/> that which carryeth the Ball farthe&longs;t was that made at <lb/>the Elevation of a Semi-Right-Angle, which they call, of the Sixth <lb/>point of the Square: but the knowledge of the Cau&longs;e whence it <lb/>hapneth infinitely &longs;urpa&longs;&longs;eth the bare Notion that I received upon <lb/>their atte&longs;tation, and al&longs;o from many repeated Experiments.</s></p><p type="main"> <s>SALV. </s> <s>You &longs;ay very right: and the knowledge of one &longs;ingle <lb/>Effect acquired by its Cau&longs;es openeth the Intellect to under&longs;tand <lb/>and a&longs;certain our &longs;elves of other effects, without need of repairing <lb/>unto Experiments, ju&longs;t as it hapneth in the pre&longs;ent Ca&longs;e; in which <lb/>having found by demon&longs;trative Di&longs;cour&longs;e the certainty of this, <lb/>That the greate&longs;t of all Ranges is that of the Elevation of a Semi­<lb/>Right-Angle, the Author demon&longs;trates unto us that which po&longs;&longs;ibly <lb/>hath not been ob&longs;erved by Experience: and that is, that of the <lb/>other Ranges tho&longs;e are equal to one another who&longs;e Elevations ex­<lb/>ceed or fall &longs;hort by equal Angles of the Semi-right: &longs;o that the <lb/>Balls &longs;hot from the Horizon, one according to the Elevation of &longs;e­<lb/>ven Points, and the other of 5, &longs;hall light upon the Horizon at <lb/>equal Di&longs;tances: and &longs;o the Ranges of 8 and of 4 points, of 9 and <lb/>of 3, <emph type="italics"/>&c.<emph.end type="italics"/> &longs;hall be equal. </s> <s>Now hear the Demon&longs;tration of it.</s></p><p type="head"> <s>THEOR. V. PROP. VIII.</s></p><p type="main"> <s>The Amplitudes of Parabola's de&longs;cribed by Pro­<lb/>jects expul&longs;ed with the &longs;ame <emph type="italics"/>Impetus<emph.end type="italics"/> according <lb/>to the Elevations by Angles equidi&longs;tant above, <lb/><arrow.to.target n="marg1102"></arrow.to.target><lb/>and beneath from the ^{*} Semi-right, are equal to <lb/>each other.</s></p><pb xlink:href="040/01/926.jpg" pagenum="233"/><p type="margin"> <s><margin.target id="marg1102"></margin.target>* Or Angle of <lb/>45.</s></p><p type="main"> <s><emph type="italics"/>Of the Triangle M C B, about the Right-Angle C, let the Ho­<lb/>rizontal Line B C and the Perpendicular C M be equal; for <lb/>&longs;o the Angle M B C &longs;hall be Semi-right; and prolonging C M <lb/>to D, let there be con&longs;tituted in B two equal Angles above and below <lb/>the Diagonal M B,<emph.end type="italics"/> viz. <emph type="italics"/>M B E, and M B D. </s> <s>It is to be demon&longs;trated <lb/>that the Amplitudes of the Parabola's de&longs;cribed by the Projects be­<lb/>ing emitted<emph.end type="italics"/> [or &longs;hot off] <emph type="italics"/>with the &longs;ame<emph.end type="italics"/> Impetus <emph type="italics"/>out of the Term B, <lb/>according to the Elevations of the Angles E B C and D B C, are equal. <lb/></s> <s>For in regard that the extern Angle B M C, is equal to the two intern <lb/>M D B and M B D, the Angle M B C &longs;hall al&longs;o be equal to them. </s> <s>And if <lb/>we &longs;uppo&longs;e M B E in&longs;tead of the Angle M B D, <lb/>the &longs;aid Angle M B C &longs;hall be equal to the two<emph.end type="italics"/><lb/><figure id="id.040.01.926.1.jpg" xlink:href="040/01/926/1.jpg"/><lb/><emph type="italics"/>Angles M B E and B D C: And taking away <lb/>the common Angle M B E, the remaining An­<lb/>gle B D C &longs;hall be equal to the remaining An­<lb/>gle E B C: Therefore the Triangles D C B <lb/>and B C E are alike. </s> <s>Let the Right Lines <lb/>D C and E C be divided in the mid&longs;t in H and <lb/>F; and draw H I and F G parallel to the Ho­<lb/>rizontal Line C B; and as D H is to H I, &longs;o <lb/>let I H be to H L: the Triangle I H L &longs;hall be <lb/>like to the Triangle I H D, like to which al&longs;o is E G F. </s> <s>And &longs;eeing <lb/>that I H and G F are equal (to wit, halves of the &longs;ame B C:) There­<lb/>fore F E, that is F C, &longs;hall be equal to H L: And, adding the common <lb/>Line F H, C H &longs;hall be equal to F L. </s> <s>If therefore we under&longs;tand the Se­<lb/>miparabola to be de&longs;cribed along by H and B, who&longs;e Altitude &longs;hall be <lb/>H C, and Sublimity H L, its Amplitude &longs;hall be C B, which is double <lb/>to HI, that is, the Mean betwixt D H, or C H, and HL: And D B <lb/>&longs;hall be a Tangent to it, the Lines C H and H D being equal. </s> <s>And if, <lb/>again, we conceive the Parabola to be de&longs;cribed along by F and B from <lb/>the Sublimity FL, with the Altitude F C, betwixt which the Mean­<lb/>proportional is F G, who&longs;e double is the Horizontal Line C B: C B, as <lb/>before, &longs;hall be its Amplitude; and E B a Tangent to it, &longs;ince E F and <lb/>F C are equal: But the Angles D B C and E B C<emph.end type="italics"/> (&longs;cilicet, <emph type="italics"/>their Eleva­<lb/>tions) &longs;hall be equidi&longs;tant from the Semi-Right Angle: Therefore the <lb/>Propo&longs;ition is demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>THEOR. VI. <emph type="italics"/>P<emph.end type="italics"/>RO<emph type="italics"/>P.<emph.end type="italics"/> IX.</s></p><p type="main"> <s>The Amplitudes of Parabola's, who&longs;e Altitudes <lb/>and Sublimities an&longs;wer to each other <emph type="italics"/>è contra­<lb/>rio,<emph.end type="italics"/> are equall.</s></p><pb xlink:href="040/01/927.jpg" pagenum="234"/><p type="main"> <s><emph type="italics"/>Let the Altitude G F of the Parabola F H have the &longs;ame proporti­<lb/>on to the Altitude C B of the Parabola B D, as the Sublimity B A <lb/>hath to the Sublimity F E. </s> <s>I &longs;ay, that the Amplitude H G is equal <lb/>to the Amplitude D C. </s> <s>For &longs;ince the fir&longs;t G F hath the &longs;ame propor­<lb/>tion to the &longs;econd C B, as the third B A hath to the fourth F E; There­<lb/>fore, the Rectangle<emph.end type="italics"/><lb/><figure id="id.040.01.927.1.jpg" xlink:href="040/01/927/1.jpg"/><lb/><emph type="italics"/>G F E of the fir&longs;t and <lb/>fourth, &longs;hall be equal to <lb/>the Rectangle C B A <lb/>of the &longs;econd and <lb/>third: Therefore the <lb/>Squares that are equal <lb/>to the&longs;e Rectangles &longs;hall <lb/>be equal to one another: <lb/>But the Square of half of G H is equal to the Rectangle G F E; and <lb/>the Square of half of C D is equal to the Rectangle C B A: There­<lb/>fore the&longs;e Squares, and their Sides, and the doubles of their Sides &longs;hall <lb/>be equal: But the&longs;e are the Amplitudes G H and C D: Therefore the <lb/>Propo&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA <emph type="italics"/>pro &longs;equenti.<emph.end type="italics"/></s></p><p type="main"> <s>If a Right Line be cut according to any proportion, the Squares <lb/>of the Mean-proportionals between the whole and the two <lb/>parts are equal to the Square of the whole.</s></p><p type="main"> <s><emph type="italics"/>Let A B be cut according to any proportion in C. </s> <s>I &longs;ay, that the <lb/>Squares of the Mean-proportional Lines between the whole A B and <lb/>the parts A C and C B, being taken together are equal to the Square of <lb/>the whole A B. </s> <s>And this appeareth, a Semi-<emph.end type="italics"/><lb/><figure id="id.040.01.927.2.jpg" xlink:href="040/01/927/2.jpg"/><lb/><emph type="italics"/>circle being de&longs;cribed upon the whole Line <lb/>B A, and from C a Perpendicular being ere­<lb/>cted C D, and Lines being drawn from D to <lb/>A, and from D to B. </s> <s>For D A is the Mean­<lb/>proportional betwixt A B and A C; and D B is the Mean-proporti­<lb/>onal between A B and B C: And the Squares of the Lines D A and <lb/>D B taken together are equal to the Square of the whole Line A B, <lb/>the Angle A D B in the Semicircle being a Right-Angle: Therefore <lb/>the Propo&longs;ition is manifest.<emph.end type="italics"/></s></p><pb xlink:href="040/01/928.jpg" pagenum="235"/><p type="head"> <s>THEOR. VII. PROP. X.</s></p><p type="main"> <s>The <emph type="italics"/>Impetus<emph.end type="italics"/> or Moment of any Semiparabola is <lb/>equal to the Moment of any Moveable falling <lb/>naturally along the Perpendicular to the Ho­<lb/>rizon that is equal to the Line compounded of <lb/>the Sublimity and of the Altitude of the Se­<lb/>miparabola.</s></p><p type="main"> <s><emph type="italics"/>Let the Semiparabola be A B, its Sublimity D A, and Altitude <lb/>A C, of which the Perpendicular D C is compounded. </s> <s>I &longs;ay, that <lb/>the<emph.end type="italics"/> Impetus <emph type="italics"/>of the Semiparabola in B is equal to the Moment of <lb/>the Moveable Naturally falling from D to C. </s> <s>Suppo&longs;e D C it &longs;elf to be <lb/>the Mea&longs;ure of the Time and of the<emph.end type="italics"/> Impetus; <emph type="italics"/>and take a Mean-pro­<lb/>portional betwixt C D and D A, to which let<emph.end type="italics"/><lb/><figure id="id.040.01.928.1.jpg" xlink:href="040/01/928/1.jpg"/><lb/><emph type="italics"/>C F be equal; and withal let C E be a Mean­<lb/>proportional between D C and C A: Now C F <lb/>&longs;hall be the Mea&longs;ure of the Time and of the Mo­<lb/>ment of the Moveable &longs;alling along D A out of <lb/>Re&longs;t in D; and C E &longs;hall be the Time and Mo­<lb/>ment of the Moveable falling along A C, out of <lb/>Re&longs;t in A, and the Moment of the Diagonal E F <lb/>&longs;hall be that compounded of both the others,<emph.end type="italics"/> &longs;cil. <lb/><emph type="italics"/>that of the Semiparabola in B. </s> <s>And becau&longs;e <lb/>D C is cut according to any proportion in A, and becau&longs;e C F and C E <lb/>are Mean-Proportionals between C D and the parts D A and A C; the <lb/>Squares of them taken together &longs;hall be equal to the Square of the <lb/>whole; by the Lemma aforegoing: But the Squares of them are al&longs;o <lb/>equal to the Square of E F: Therefore D F is equal al&longs;o to the Line D C: <lb/>Whence it is manife&longs;t that the Moments along D C, and along the Se­<lb/>miparabola A B, are equal in C and B: Which was required.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it is manife&longs;t, that of all Parabola's who&longs;e Altitudes and <lb/>Sublimities being joyned together are equal, the <emph type="italics"/>Impetus's<emph.end type="italics"/> are <lb/>al&longs;o equal.</s></p><pb xlink:href="040/01/929.jpg" pagenum="236"/><p type="head"> <s>PROBL. IV. PROP. XI.</s></p><p type="main"> <s>The <emph type="italics"/>Impetus<emph.end type="italics"/> and Amplitude of a Semiparabola be­<lb/>ing given, to find its Altitude, and con&longs;equently <lb/>its Sublimity.</s></p><p type="main"> <s><emph type="italics"/>Let the<emph.end type="italics"/> Impetus <emph type="italics"/>given be defined by the Perpendicular to the Ho­<lb/>rizon A B; and let the Amplitude along the Horizontal Line be <lb/>B C. </s> <s>It is required to find the Altitude and Sublimity of the <lb/>Parabola who&longs;e<emph.end type="italics"/> Impetus <emph type="italics"/>is A B, and Amplitude B C. </s> <s>It is manife&longs;t, <lb/>from what hath been already demon&longs;trated, that half the Amplitude B C <lb/>will be a Mean-proportional betwixt the Altitude and the Sublimity of <lb/>the &longs;aid Semiparabola, who&longs;e<emph.end type="italics"/> Impetus, <emph type="italics"/>by the precedent Propo&longs;ition, is <lb/>the &longs;ame with the<emph.end type="italics"/> Impetus <emph type="italics"/>of the Moveable falling from Re&longs;t in A along <lb/>the whole Perpendicular A B: Wherefore B A is &longs;o to be cut that the <lb/>Rectangle contained by its parts may be equal to the Square of half of <lb/>B C, which let be B D. </s> <s>Hence it appeareth <lb/>to be nece&longs;&longs;ary that D B do not exceed the<emph.end type="italics"/><lb/><figure id="id.040.01.929.1.jpg" xlink:href="040/01/929/1.jpg"/><lb/><emph type="italics"/>half of B A; for of Rectangles contained by <lb/>the parts the greate&longs;t is when the whole <lb/>Line is cut into two equal parts. </s> <s>Therefore <lb/>let B A be divided into two equal parts in E. <lb/></s> <s>And if B D be equal to B E the work is <lb/>done; and the Altitude of the Semipara­<lb/>bola &longs;hall be B E, and its Sublimity E A: <lb/>(and &longs;ee here by the way that the Amplitude <lb/>of the Parabola of a Semi-right Elevation, <lb/>as was demon&longs;trated above, is the greate&longs;t of <lb/>all tho&longs;e de&longs;cribed with the &longs;ame<emph.end type="italics"/> Impetus.) <lb/><emph type="italics"/>But let B D be le&longs;s than the half of B A, <lb/>which is &longs;o to be cut that the Rectangle under the parts may be equal to <lb/>the Square B D. </s> <s>Upon E A de&longs;cribe a Semicircle, upon which out of A <lb/>&longs;et off A F equal to B D, and draw a Line from F to E, to which cut <lb/>a part equal E G. </s> <s>Now the Rectangle B G A, together with the Square <lb/>E G, &longs;hall be equal to the Square E A; to which the two Squares A F <lb/>and F E are al&longs;o equal: Therefore the equal Squares G E and F E be­<lb/>ing &longs;ub&longs;tracted, there remaineth the Rectangle B G A equal to the <lb/>Square A F,<emph.end type="italics"/> &longs;cilicet, <emph type="italics"/>to B D; and the Line B D is a Mean-proportional <lb/>betwixt B G and G A. </s> <s>Whence it appeareth, that of the Semipa­<lb/>rabola who&longs;e Amplitude is B C, and<emph.end type="italics"/> Impetus <emph type="italics"/>A B, the Altitude is <lb/>B G, and the Sublimity G A. </s> <s>And if we &longs;et off B I below equal to G A, <lb/>this &longs;hall be the Altitude, and I A the Sublimity of the Semiparabola <lb/>I C. </s> <s>From what hath been already demon&longs;trated we are able,<emph.end type="italics"/></s></p><pb xlink:href="040/01/930.jpg" pagenum="237"/><p type="head"> <s>PROBL. V. PROP. XII.</s></p><p type="main"> <s>To collect by Calculation of the Amplitudes of all <lb/>Semiparabola's that are de&longs;cribed by Projects <lb/>expul&longs;ed with the &longs;ame <emph type="italics"/>Impetus,<emph.end type="italics"/> and to make <lb/>Tables thereof.</s></p><p type="main"> <s><emph type="italics"/>It is obvious, from the things demon&longs;trated, that Parabola's are de­<lb/>&longs;cribed by Projects of the &longs;ame<emph.end type="italics"/> Impetus <emph type="italics"/>then, when their Subli­<lb/>mities together with their Altitudes do make up equal Perpendicu­<lb/>lars upon the Horizon. </s> <s>The&longs;e Perpendiculars therefore are to be com­<lb/>prehended between the &longs;ame Horizontal Parallels. </s> <s>Therefore let the <lb/>Horizontal Line C B be &longs;uppo&longs;ed equal to the Perpendicular B A, and <lb/>draw the Diagonal from A to C. </s> <s>The Angle A C B &longs;hall be Semi­<lb/>right, or 45 Degrees. </s> <s>And the Perpendicular B A being divided into <lb/>two equal parts in D, the Semiparabola D C &longs;hall be that which is de­<lb/>&longs;cribed from the Sublimity A D together with the Altitude D B: and <lb/>its<emph.end type="italics"/> Impetus <emph type="italics"/>in C &longs;hall be as great as that of the Moveable coming out of <lb/>Re&longs;t in A along the Perpendicular A B is in B. </s> <s>And if A G be drawn <lb/>parallel to B C, the united Altitudes and Sublimities of all other re­<lb/>maining Semiparabola's who&longs;e future<emph.end type="italics"/> Impetus's <emph type="italics"/>are the &longs;ame with tho&longs;e <lb/>now mentioned mu&longs;t be bounded by the Space between the Parallels<emph.end type="italics"/><lb/><figure id="id.040.01.930.1.jpg" xlink:href="040/01/930/1.jpg"/><lb/><emph type="italics"/>A G and B C. Farthermore, it having <lb/>been but now demon&longs;trated, that the Am­<lb/>plitudes of the Semiparabola's who&longs;e <lb/>Tangents are equidi&longs;tant either above or <lb/>below from the Semi right Elevation are <lb/>equal, the Calculations that we frame <lb/>for the greater Elevations will likewi&longs;e <lb/>&longs;erve for the le&longs;&longs;er. </s> <s>We choo&longs;e moreover <lb/>a number of ten thou&longs;and parts for the <lb/>greate&longs;t Amplitude of the Projection of <lb/>the Semiparabola made at the Elevation <lb/>of 45 degrees: &longs;o much therefore the Line <lb/>B A, and the Amplitude of the Semipa­<lb/>rabola B C, are to be &longs;uppo&longs;ed. </s> <s>And we <lb/>make choice of the number 10000, becau&longs;e we in our Calculation u&longs;e <lb/>the Table of Tangents, in which this number agreeth with the Tangent <lb/>of 45 degrees. </s> <s>Now, to come to the bu&longs;ine&longs;s, let C E be drawn, contain­<lb/>ing the Angle E C B greater (Acute neverthele&longs;s,) than the Angle <lb/>A C B; and let the Semiparabola be de&longs;cribed which is touched by the <lb/>Line E C, and who&longs;e Sublimity united with its Altitude is equal to <lb/>B A. </s> <s>In the Table of Tangents take the &longs;aid B E for the Tangent at the<emph.end type="italics"/><pb xlink:href="040/01/931.jpg" pagenum="238"/><emph type="italics"/>given Angle B C E, which divide into two equal parts at F. </s> <s>Then <lb/>find a third Proportional to B F and B C, (or to the half of B C,) <lb/>which &longs;hall of nece&longs;&longs;ity be greater than F A; therefore let it be F O: <lb/>Of the Semiparabola, therefore, in&longs;cribed in the Triangle E C B, ac­<lb/>cording to the Tangent C E, who&longs;e Amplitude is C B, the Altitude B F, <lb/>and the Sublimity F O is found: But the whole Line B O ri&longs;eth above <lb/>the Parallels A G and C B, whereas our work was to bound it between <lb/>them: For &longs;o both it and the Semiparabola D C &longs;hall be de&longs;cribed by <lb/>the Projects out of C expelled with the &longs;ame<emph.end type="italics"/> Impetus. <emph type="italics"/>Therefore we <lb/>are to &longs;eek another like to this, (for innumerable greater and &longs;maller, <lb/>like to one another, may be de&longs;cribed within the Angle B C E) to who&longs;e <lb/>united Sublimity and Altitude B A &longs;hall be equal. </s> <s>Therefore as O B is <lb/>to B A, &longs;o let the Amplitude B C be to C R: and C R &longs;hall be found,<emph.end type="italics"/><lb/>&longs;cilicet <emph type="italics"/>the Amplitude of the Semiparabola according to the Elevation <lb/>of the Angle B C E, who&longs;e conjoyned Sublimity and Altitude is equal <lb/>to the Space contained between the Parallels G A and C B: Which <lb/>was required. </s> <s>The work, therefore, &longs;hall be after this manner.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Take the Tangent of the given Angle B C E, to the half of which <lb/>add the third Proportional of it, and half of B C, which let be F O: <lb/>Then as O B is to B A, &longs;o let B C be to another, which let be C R, to wit, <lb/>the Amplitude &longs;ought. </s> <s>Let us give an Example.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Let the Angle E C B be 50 degrees, its Tangent &longs;hall be 11918, <lb/>who&longs;e half, to wit, B F, is 5959, and the half of B C is 5000, the third <lb/>proportional of the&longs;e halves is 4195, which added to the &longs;aid B F <lb/>maketh 10154: for the &longs;aid B O. Again, as O B is to B A, that is as <lb/>10154 is to 10000, &longs;o is B E, that is 10000 (for each of them is the <lb/>Tangent of 45 degrees) to another: and that &longs;hall give us the required <lb/>Altitude R C 9848, of &longs;uch as B C (the greate&longs;t Amplitude) is <lb/>10000. To the&longs;e the Amplitudes of the whole Parabola's are double,<emph.end type="italics"/><lb/>&longs;cilicet <emph type="italics"/>19696 and 20000. And &longs;o much likewi&longs;e is the Amplitude of <lb/>the Parabola according to the Elevation of 40 degrees, &longs;ince it is equal­<lb/>ly di&longs;tant from 45 degrees.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>For the perfect under&longs;tanding of this Demon&longs;tration I <lb/>mu&longs;t be informed how true it is, that the Third Proportional to <lb/>B F and B I, is (as the Author &longs;aith) nece&longs;&longs;arily greater than <lb/>F A.</s></p><p type="main"> <s>SALV. </s> <s>That inference, as I conceive, may be deduced thus. <lb/></s> <s>The Square of the Mean of three proportional Lines is equal to <lb/>the Rectangle of the other two: whence the Square of B I, or of <lb/>B D equal to it, ought to be equal to the Rectangle of the fir&longs;t F B <lb/>multiplied into the third to be found: which third is of nece&longs;&longs;ity to <lb/>be greater than F A, becau&longs;e the Rectangle of B F multiplied into <lb/>F A is le&longs;s than the Square B D: and the Defect is as much as the <lb/>Square of D F, as <emph type="italics"/>Euclid<emph.end type="italics"/> demon&longs;trates in a Propo&longs;ition of his <pb xlink:href="040/01/932.jpg" pagenum="239"/>Second Book. </s> <s>You mu&longs;t al&longs;o know, that the point F which divi­<lb/>deth the Tangent E B in the middle, will many other times fall <lb/>above the point A, and once al&longs;o in the &longs;aid A: In which ca&longs;es it is <lb/>evident of it &longs;elf, that the third proportional to the half of the Tan­<lb/>gent, and to B I (which giveth the Sublimity) is all above A. </s> <s>But <lb/>the Author hath taken a Ca&longs;e in which it was not manife&longs;t that the <lb/>&longs;aid third Proportional is alwaies greater than F A: and which <lb/>therefore being &longs;et off above the point F pa&longs;&longs;eth beyond the Paral­<lb/>lel A G. </s> <s>Now let us proceed.</s></p><p type="main"> <s><emph type="italics"/>It will not be unprofitable if by help of this Table we compo&longs;e ano­<lb/>ther, &longs;hewing the Altitudes of the &longs;ame Semiparabola's of Projects of <lb/>the &longs;ame<emph.end type="italics"/> Impetus. <emph type="italics"/>And the Con&longs;truction of it is in this manner.<emph.end type="italics"/></s></p><p type="head"> <s>PROBL. VI. PROP. XIII.</s></p><p type="main"> <s>From the given Amplitudes of Semiparabola's in <lb/>the following Table &longs;et down, keeping the <lb/>common <emph type="italics"/>Impeius<emph.end type="italics"/> with which every one of <lb/>them is de&longs;cribed, to compute the Altitudes of <lb/>each &longs;everal Semiparabola.</s></p><p type="main"> <s><emph type="italics"/>Let the Amplitude given be B C, and of the<emph.end type="italics"/> Impetus, <emph type="italics"/>which is <lb/>&longs;uppo&longs;ed to be alwaies the &longs;ame, let the Mea&longs;ure be O B, to wit, <lb/>the Aggregate of the Altitude and Sublimity. </s> <s>The &longs;aid Altitude <lb/>is required to be found and di&longs;tingui&longs;hed. </s> <s>Which &longs;hall then be done when <lb/>B O is &longs;o divided as that the Rectangle contained under its parts is <lb/>equal to the Square of half the Amplitude B C. </s> <s>Let that &longs;ame divi­<lb/>&longs;ion fall in F; and let both O B and B C be cut in the mid&longs;t at D and I.<emph.end type="italics"/><lb/><figure id="id.040.01.932.1.jpg" xlink:href="040/01/932/1.jpg"/><lb/><emph type="italics"/>The Square I B, therefore, is equal to the <lb/>Rectangle B F O: And the Square D O is <lb/>equal to the &longs;ame Rectangle together with the <lb/>Square F D. </s> <s>If therefore from the Square <lb/>D O we deduct the Square B I, which is equal <lb/>to the Rectangle B F O, there &longs;hall remain <lb/>the Square F D; to who&longs;e Side D F, B D be­<lb/>ing added it &longs;hall give the de&longs;ired Altitude <lb/>Altitude B F. </s> <s>And it is thus compounded<emph.end type="italics"/><lb/>ex datis. <emph type="italics"/>From half of the Square B O known <lb/>&longs;ub&longs;tract the Square B I al&longs;o known, of the remainder take the Square <lb/>Root, to which add D B known; and you &longs;hall have the Altitude &longs;ought <lb/>B F. </s> <s>For example. </s> <s>The Altitude of the Parabola de&longs;cribed at the <lb/>Elevation of 55 degrees is to be found. </s> <s>The Amplitude, by the follow­<lb/>ing Table is 9396, its half is 4698, the Square of that is 22071204,<emph.end type="italics"/><pb xlink:href="040/01/933.jpg" pagenum="240"/><emph type="italics"/>this &longs;ub&longs;tracted from the Square of the half B O, which is alwaies <lb/>the &longs;ame, to wit, 2500000, the remainder is 2928796, who&longs;e Square <lb/>Root is 1710 very near, this added to the half of B O, to wit, 5000, <lb/>gives 67101, and &longs;o much is the Altitude B F. </s> <s>It will not be unprofi­<lb/>table, to give the Third Table, containing the Altitudes and Sublimi­<lb/>ties of Semiparabola's, who&longs;e Amplitude &longs;hall be alwaies the &longs;ame.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>This I would very gladly &longs;ee &longs;ince by it I may come to <lb/>know the Difference of the <emph type="italics"/>Impetus's,<emph.end type="italics"/> and of the Forces that are <lb/>required for carrying the Project to the &longs;ame Di&longs;tance with Ranges <lb/>which are called at Random: which Difference I believe is very <lb/>great according to the different Elevations [<emph type="italics"/>or Mountures:<emph.end type="italics"/>] &longs;o that <lb/>if, for example, one would at the Elevation of 3 or 4 degrees, or of <lb/>87 or 88 make the Ball to fall where it did, being &longs;hot at the Ele­<lb/>vation of <emph type="italics"/>gr.<emph.end type="italics"/> 45. (where, as hath been &longs;hewn, the lea&longs;t <emph type="italics"/>Impetus<emph.end type="italics"/> is <lb/>required) I believe that it would require a very much greater <lb/>Force.</s></p><p type="main"> <s>SALV. </s> <s>You are in the right: and you will find that to do the <lb/>full execution in all the Elevations it is requi&longs;ite to make great Pro­<lb/>gre&longs;&longs;ions towards an infinite <emph type="italics"/>Impetus.<emph.end type="italics"/> Now let us &longs;ee the Con&longs;tru­<lb/>ction of the Table.<pb xlink:href="040/01/934.jpg" pagenum="241"/><arrow.to.target n="table75"></arrow.to.target><lb/><arrow.to.target n="table76"></arrow.to.target><lb/><arrow.to.target n="table77"></arrow.to.target></s></p><pb xlink:href="040/01/935.jpg" pagenum="242"/><table><table.target id="table75"></table.target><row><cell>Degrees of Elevation.</cell><cell></cell><cell></cell></row><row><cell>The Amplitudes of the Semipara-bola's, de&longs;cribed with the &longs;ame <emph type="italics"/>Impetus.<emph.end type="italics"/></cell><cell></cell><cell></cell></row><row><cell>Gr.</cell><cell></cell><cell>Gr.</cell></row><row><cell>45</cell><cell>10000</cell><cell></cell></row><row><cell>46</cell><cell>9994</cell><cell>44</cell></row><row><cell>47</cell><cell>9976</cell><cell>43</cell></row><row><cell>48</cell><cell>9945</cell><cell>42</cell></row><row><cell>49</cell><cell>9902</cell><cell>41</cell></row><row><cell>50</cell><cell>9848</cell><cell>40</cell></row><row><cell>51</cell><cell>9782</cell><cell>39</cell></row><row><cell>52</cell><cell>9704</cell><cell>38</cell></row><row><cell>53</cell><cell>9612</cell><cell>37</cell></row><row><cell>54</cell><cell>9511</cell><cell>36</cell></row><row><cell>55</cell><cell>9396</cell><cell>35</cell></row><row><cell>56</cell><cell>9272</cell><cell>34</cell></row><row><cell>57</cell><cell>9136</cell><cell>33</cell></row><row><cell>58</cell><cell>8989</cell><cell>32</cell></row><row><cell>59</cell><cell>8829</cell><cell>31</cell></row><row><cell>60</cell><cell>8659</cell><cell>30</cell></row><row><cell>61</cell><cell>8481</cell><cell>29</cell></row><row><cell>62</cell><cell>8290</cell><cell>28</cell></row><row><cell>63</cell><cell>8090</cell><cell>27</cell></row><row><cell>64</cell><cell>7880</cell><cell>26</cell></row><row><cell>65</cell><cell>7660</cell><cell>25</cell></row><row><cell>66</cell><cell>7431</cell><cell>24</cell></row><row><cell>67</cell><cell>7191</cell><cell>23</cell></row><row><cell>68</cell><cell>6944</cell><cell>22</cell></row><row><cell>69</cell><cell>6692</cell><cell>21</cell></row><row><cell>70</cell><cell>6428</cell><cell>20</cell></row><row><cell>71</cell><cell>6157</cell><cell>19</cell></row><row><cell>72</cell><cell>5878</cell><cell>18</cell></row><row><cell>73</cell><cell>5592</cell><cell>17</cell></row><row><cell>74</cell><cell>5300</cell><cell>16</cell></row><row><cell>75</cell><cell>5000</cell><cell>15</cell></row><row><cell>76</cell><cell>4694</cell><cell>14</cell></row><row><cell>77</cell><cell>4383</cell><cell>13</cell></row><row><cell>78</cell><cell>4067</cell><cell>12</cell></row><row><cell>79</cell><cell>3746</cell><cell>11</cell></row><row><cell>80</cell><cell>3420</cell><cell>10</cell></row><row><cell>81</cell><cell>3090</cell><cell>9</cell></row><row><cell>82</cell><cell>2756</cell><cell>8</cell></row><row><cell>83</cell><cell>2419</cell><cell>7</cell></row><row><cell>84</cell><cell>2079</cell><cell>6</cell></row><row><cell>85</cell><cell>1736</cell><cell>5</cell></row><row><cell>86</cell><cell>1391</cell><cell>4</cell></row><row><cell>87</cell><cell>1044</cell><cell>3</cell></row><row><cell>88</cell><cell>698</cell><cell>2</cell></row><row><cell>89</cell><cell>349</cell><cell>1</cell></row></table><table><table.target id="table76"></table.target><row><cell>Degrees of Elevation.</cell><cell></cell><cell></cell><cell></cell></row><row><cell>The Altitudes of the Se-miparabola's, who&longs;e <emph type="italics"/>Impetus<emph.end type="italics"/> is the &longs;ame.</cell><cell></cell><cell></cell><cell></cell></row><row><cell>Gr.</cell><cell></cell><cell>Gr.</cell><cell></cell></row><row><cell>1</cell><cell>3</cell><cell>46</cell><cell>5173</cell></row><row><cell>2</cell><cell>13</cell><cell>47</cell><cell>5346</cell></row><row><cell>3</cell><cell>28</cell><cell>48</cell><cell>5523</cell></row><row><cell>4</cell><cell>50</cell><cell>49</cell><cell>5698</cell></row><row><cell>5</cell><cell>76</cell><cell>50</cell><cell>5868</cell></row><row><cell>6</cell><cell>108</cell><cell>51</cell><cell>6038</cell></row><row><cell>7</cell><cell>150</cell><cell>52</cell><cell>6207</cell></row><row><cell>8</cell><cell>194</cell><cell>53</cell><cell>6379</cell></row><row><cell>9</cell><cell>245</cell><cell>54</cell><cell>6546</cell></row><row><cell>10</cell><cell>302</cell><cell>55</cell><cell>6710</cell></row><row><cell>17</cell><cell>365</cell><cell>56</cell><cell>6873</cell></row><row><cell>12</cell><cell>432</cell><cell>57</cell><cell>7033</cell></row><row><cell>13</cell><cell>506</cell><cell>58</cell><cell>7190</cell></row><row><cell>14</cell><cell>585</cell><cell>59</cell><cell>7348</cell></row><row><cell>15</cell><cell>670</cell><cell>60</cell><cell>7502</cell></row><row><cell>16</cell><cell>760</cell><cell>61</cell><cell>7649</cell></row><row><cell>17</cell><cell>855</cell><cell>62</cell><cell>7796</cell></row><row><cell>18</cell><cell>955</cell><cell>63</cell><cell>7939</cell></row><row><cell>19</cell><cell>1060</cell><cell>64</cell><cell>8078</cell></row><row><cell>20</cell><cell>1170</cell><cell>65</cell><cell>8214</cell></row><row><cell>21</cell><cell>1285</cell><cell>66</cell><cell>8346</cell></row><row><cell>22</cell><cell>1402</cell><cell>67</cell><cell>8474</cell></row><row><cell>23</cell><cell>1527</cell><cell>68</cell><cell>8597</cell></row><row><cell>24</cell><cell>1685</cell><cell>69</cell><cell>8715</cell></row><row><cell>25</cell><cell>1786</cell><cell>70</cell><cell>8830</cell></row><row><cell>26</cell><cell>1922</cell><cell>71</cell><cell>8940</cell></row><row><cell>27</cell><cell>2061</cell><cell>72</cell><cell>9045</cell></row><row><cell>28</cell><cell>2204</cell><cell>73</cell><cell>9144</cell></row><row><cell>29</cell><cell>2351</cell><cell>74</cell><cell>9240</cell></row><row><cell>30</cell><cell>2499</cell><cell>75</cell><cell>9330</cell></row><row><cell>31</cell><cell>2653</cell><cell>76</cell><cell>9415</cell></row><row><cell>32</cell><cell>2810</cell><cell>77</cell><cell>9493</cell></row><row><cell>33</cell><cell>2967</cell><cell>78</cell><cell>9567</cell></row><row><cell>34</cell><cell>3128</cell><cell>79</cell><cell>9636</cell></row><row><cell>35</cell><cell>3289</cell><cell>80</cell><cell>9698</cell></row><row><cell>36</cell><cell>3456</cell><cell>81</cell><cell>9755</cell></row><row><cell>37</cell><cell>3621</cell><cell>82</cell><cell>9806</cell></row><row><cell>38</cell><cell>3793</cell><cell>83</cell><cell>9851</cell></row><row><cell>39</cell><cell>3962</cell><cell>84</cell><cell>9890</cell></row><row><cell>40</cell><cell>4132</cell><cell>85</cell><cell>9924</cell></row><row><cell>41</cell><cell>4302</cell><cell>86</cell><cell>9951</cell></row><row><cell>42</cell><cell>4477</cell><cell>87</cell><cell>9972</cell></row><row><cell>43</cell><cell>4654</cell><cell>88</cell><cell>9987</cell></row><row><cell>44</cell><cell>4827</cell><cell>89</cell><cell>9998</cell></row><row><cell>45</cell><cell>5000</cell><cell>90</cell><cell>10000</cell></row></table><table><table.target id="table77"></table.target><row><cell>A Table containing the Altitudes and Subli-mities of the Semiparabola's, who&longs;e Am-plitudes are the &longs;ame, that is to &longs;ay, of 10000 parts, calculated to each Deg. of Elevation.</cell><cell></cell><cell></cell><cell></cell><cell></cell><cell></cell></row><row><cell>Gr.</cell><cell>Altit.</cell><cell>Sublim.</cell><cell>Gr.</cell><cell>Altit.</cell><cell>Sublim.</cell></row><row><cell>1</cell><cell>87</cell><cell>286533</cell><cell>46</cell><cell>5177</cell><cell>4828</cell></row><row><cell>2</cell><cell>175</cell><cell>142450</cell><cell>47</cell><cell>5363</cell><cell>4662</cell></row><row><cell>3</cell><cell>262</cell><cell>95802</cell><cell>48</cell><cell>5553</cell><cell>4502</cell></row><row><cell>4</cell><cell>349</cell><cell>71531</cell><cell>49</cell><cell>5752</cell><cell>4345</cell></row><row><cell>5</cell><cell>437</cell><cell>57142</cell><cell>50</cell><cell>5959</cell><cell>4106</cell></row><row><cell>6</cell><cell>525</cell><cell>47573</cell><cell>51</cell><cell>6174</cell><cell>4048</cell></row><row><cell>7</cell><cell>614</cell><cell>40716</cell><cell>52</cell><cell>6399</cell><cell>3006</cell></row><row><cell>8</cell><cell>702</cell><cell>35587</cell><cell>53</cell><cell>6635</cell><cell>3765</cell></row><row><cell>9</cell><cell>792</cell><cell>31565</cell><cell>54</cell><cell>6882</cell><cell>3632</cell></row><row><cell>10</cell><cell>881</cell><cell>28367</cell><cell>55</cell><cell>7141</cell><cell>3500</cell></row><row><cell>11</cell><cell>972</cell><cell>25720</cell><cell>56</cell><cell>7413</cell><cell>3372</cell></row><row><cell>12</cell><cell>1063</cell><cell>23518</cell><cell>57</cell><cell>7699</cell><cell>3247</cell></row><row><cell>13</cell><cell>1154</cell><cell>21701</cell><cell>58</cell><cell>8002</cell><cell>3123</cell></row><row><cell>14</cell><cell>1246</cell><cell>20056</cell><cell>59</cell><cell>8332</cell><cell>3004</cell></row><row><cell>11</cell><cell>1339</cell><cell>18663</cell><cell>60</cell><cell>8600</cell><cell>2887</cell></row><row><cell>16</cell><cell>1434</cell><cell>17405</cell><cell>61</cell><cell>9020</cell><cell>2771</cell></row><row><cell>17</cell><cell>1529</cell><cell>16355</cell><cell>62</cell><cell>9403</cell><cell>2658</cell></row><row><cell>18</cell><cell>1624</cell><cell>15389</cell><cell>63</cell><cell>9813</cell><cell>2547</cell></row><row><cell>19</cell><cell>1722</cell><cell>14522</cell><cell>64</cell><cell>10251</cell><cell>2438</cell></row><row><cell>20</cell><cell>1820</cell><cell>13736</cell><cell>65</cell><cell>10722</cell><cell>2331</cell></row><row><cell>21</cell><cell>1919</cell><cell>13024</cell><cell>66</cell><cell>11220</cell><cell>2226</cell></row><row><cell>22</cell><cell>2020</cell><cell>12376</cell><cell>67</cell><cell>11779</cell><cell>2122</cell></row><row><cell>23</cell><cell>2123</cell><cell>11778</cell><cell>68</cell><cell>12375</cell><cell>2020</cell></row><row><cell>24</cell><cell>2226</cell><cell>11230</cell><cell>69</cell><cell>13025</cell><cell>1919</cell></row><row><cell>25</cell><cell>2332</cell><cell>10722</cell><cell>70</cell><cell>13237</cell><cell>1819</cell></row><row><cell>26</cell><cell>2439</cell><cell>10253</cell><cell>71</cell><cell>14521</cell><cell>1721</cell></row><row><cell>27</cell><cell>2547</cell><cell>9814</cell><cell>72</cell><cell>15388</cell><cell>1624</cell></row><row><cell>28</cell><cell>2658</cell><cell>9404</cell><cell>73</cell><cell>16354</cell><cell>1528</cell></row><row><cell>29</cell><cell>2772</cell><cell>9020</cell><cell>74</cell><cell>17437</cell><cell>1413</cell></row><row><cell>30</cell><cell>2887</cell><cell>8659</cell><cell>75</cell><cell>18660</cell><cell>1339</cell></row><row><cell>31</cell><cell>3008</cell><cell>8336</cell><cell>76</cell><cell>20054</cell><cell>1246</cell></row><row><cell>32</cell><cell>3124</cell><cell>8001</cell><cell>77</cell><cell>21657</cell><cell>1154</cell></row><row><cell>33</cell><cell>3247</cell><cell>7699</cell><cell>78</cell><cell>23523</cell><cell>1062</cell></row><row><cell>34</cell><cell>3373</cell><cell>7413</cell><cell>79</cell><cell>25723</cell><cell>972</cell></row><row><cell>35</cell><cell>3501</cell><cell>7141</cell><cell>80</cell><cell>28356</cell><cell>881</cell></row><row><cell>36</cell><cell>3633</cell><cell>6882</cell><cell>81</cell><cell>31560</cell><cell>792</cell></row><row><cell>37</cell><cell>3768</cell><cell>6635</cell><cell>82</cell><cell>35577</cell><cell>702</cell></row><row><cell>38</cell><cell>3906</cell><cell>6395</cell><cell>83</cell><cell>40222</cell><cell>613</cell></row><row><cell>39</cell><cell>4049</cell><cell>6174</cell><cell>84</cell><cell>47572</cell><cell>525</cell></row><row><cell>40</cell><cell>4196</cell><cell>5959</cell><cell>85</cell><cell>57150</cell><cell>437</cell></row><row><cell>41</cell><cell>4246</cell><cell>5752</cell><cell>86</cell><cell>71503</cell><cell>349</cell></row><row><cell>42</cell><cell>4502</cell><cell>5553</cell><cell>87</cell><cell>95405</cell><cell>262</cell></row><row><cell>43</cell><cell>4662</cell><cell>5362</cell><cell>88</cell><cell>143181</cell><cell>174</cell></row><row><cell>44</cell><cell>4828</cell><cell>5177</cell><cell>89</cell><cell>286499</cell><cell>87</cell></row><row><cell>45</cell><cell>5000</cell><cell>5000</cell><cell>90</cell><cell>Infinite</cell><cell></cell></row></table><p type="head"> <s>PROBL. VII. PROP. XIV.</s></p><p type="main"> <s>To find the Altitudes and Sublimities of Semipa­<lb/>rabola's who&longs;e Amplitudes &longs;hall be equal for <lb/>each degree of Elevation.</s></p><p type="main"> <s><emph type="italics"/>This we &longs;hall ea&longs;ily do. </s> <s>For &longs;uppo&longs;ing the Amplitude of the Semi­<lb/>par abola to be of 10000 parts, the half of the Tangent of each <lb/>degree of Elevation &longs;hews the Altitude. </s> <s>As for example, of the <lb/>Semiparabola who&longs;e Elevation is 30 degrees, and Amplitude, as is <lb/>&longs;uppo&longs;ed, 10000 parts, the Altitude &longs;hall be 2887, for &longs;o much, very <lb/>near, is the half of the Tangent. </s> <s>And having found the Altitude the <lb/>Sublimity is to be known in this manner. </s> <s>For a&longs;much as it hath been <lb/>demon&longs;trated that the half of the Amplitude of a Semiparabola is the <lb/>Mean proportional betwixt the Altitude and Sublimity, and the Alti­<lb/>tude being already found, and the half of the Amplitude being alwaies <lb/>the &longs;ame, to wit, 5000 parts, if we &longs;hall divide the Square thereof by <lb/>the Altitude found, the de&longs;ired Sublimity &longs;hall come forth. </s> <s>As in the <lb/>Example: The Altitude found was 2887; The Square of the 5000 <lb/>parts is 25000000; which being divided by 2887, giveth 8659, ve­<lb/>ry near, for the Sublimity &longs;ought.<emph.end type="italics"/></s></p><p type="main"> <s>SALV. </s> <s>Now here we &longs;ee, in the &longs;ir&longs;t place, that the Conje­<lb/>cture is very true which was mentioned afore, that in different <lb/>Elevations the farther one goeth from the middlemo&longs;t, whether it <lb/>be in the Higher, or in the Lower, &longs;o much greater <emph type="italics"/>Impetus<emph.end type="italics"/> and Vio­<lb/>lence is required to carry the Project to the &longs;ame Di&longs;tance. </s> <s>For the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> lying in the mixture of the two Motions, Equable, Hori­<lb/>zontal, and Perpendicular Naturally-Accelerate, of which <emph type="italics"/>Impetus<emph.end type="italics"/><lb/>the Aggregate of the Altitude and Sublimity is the Mea&longs;ure, we do <lb/>&longs;ee in the propounded Table that that &longs;ame Aggregate is lea&longs;t in <lb/>the Elevation of <emph type="italics"/>gr.<emph.end type="italics"/> 45, in which the Altitude and Sublimity are <lb/>equal, <emph type="italics"/>&longs;cilicet<emph.end type="italics"/> each 5000, and their Aggregate 10000. But if we <lb/>&longs;hould look on any greater Elevation, as, for example, of <emph type="italics"/>gr.<emph.end type="italics"/> 50, we <lb/>&longs;hould &longs;ind the Altitude to be 5959, and the Sublimity 4196, which <lb/>added together make 10155. And &longs;o much al&longs;o we &longs;hould find the <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> of <emph type="italics"/>gr.<emph.end type="italics"/> 40 to be, this and that Elevation being equally re­<lb/>mote from the middlemo&longs;t. </s> <s>Where we are to note, in the &longs;econd <lb/>place, that it is true, That equal <emph type="italics"/>Impetus's<emph.end type="italics"/> are &longs;ought by two, and <lb/>two in the Elevations equidi&longs;tant from the middlemo&longs;t, with this <lb/>pretty variation over and above that the Altitudes and the Subli­<lb/>mities of the ^{*} &longs;uperiour Elevations an&longs;wer alternally to the Sub­<lb/><arrow.to.target n="marg1103"></arrow.to.target><lb/>limities and Altitudes of the Inferiour: &longs;o that whereas in the <pb xlink:href="040/01/936.jpg" pagenum="243"/>example propo&longs;ed, in the Elevation of <emph type="italics"/>gr.<emph.end type="italics"/> 50. the Altitude is 5959 <lb/>and the Sublimity 4196, in the Elevation of <emph type="italics"/>gr.<emph.end type="italics"/> 40. it falls out on <lb/>the contrary that the Altitude is 4196, and the Sublimity 5959: <lb/>And the &longs;ame happens in all others without any difference; &longs;ave <lb/>only that for the avoyding of tediou&longs;ne&longs;s in Calculations we have <lb/>kept no account of &longs;ome fractions, which in &longs;o great &longs;ums are of no <lb/>value, but may without any prejudice be omitted.</s></p><p type="margin"> <s><margin.target id="marg1103"></margin.target>* <emph type="italics"/>i.e.<emph.end type="italics"/> Tho&longs;e above <lb/>45 deg.</s></p><p type="main"> <s>SAGR. </s> <s>I am ob&longs;erving that of the two <emph type="italics"/>Impetus's<emph.end type="italics"/> Horizontal and <lb/>Perpendicular in Projections, the more Sublime they are, they need <lb/>&longs;o much the le&longs;s of the Horizontal, and the more of the Perpendi­<lb/>cular. </s> <s>Moreover in tho&longs;e of &longs;mall Elevation, great mu&longs;t be the <lb/>Force of the Horizontal <emph type="italics"/>Impetus,<emph.end type="italics"/> which is to carry the Project in a <lb/>little Altitude. </s> <s>But although I comprehend very well that in the <lb/>Total Elevation of <emph type="italics"/>gr.<emph.end type="italics"/> 90, all the force in the world &longs;ufficeth not <lb/>to drive the Project one &longs;ingle Inch from the Perpendicular, but <lb/>that it mu&longs;t of nece&longs;&longs;ity fall in the &longs;ame place whence it was expel­<lb/>led; yet dare I not with the like certainty affirm that likewi&longs;e in the <lb/>nullity of Elevation, that is in the Horizontal Line, the Project <lb/>cannot by any Force le&longs;s than infinite, be driven to any di­<lb/>&longs;tance: So, as that, for example, a Culverin it &longs;elf &longs;hould not be <lb/>able to carry a Ball of Iron Horizontally, or, as they &longs;ay, at Point <lb/>blank, that is at no point, which is when it hath no Elevation. </s> <s>I <lb/>&longs;ay, in this ca&longs;e I &longs;tand in &longs;ome doubt; and that I do not re&longs;olute­<lb/>ly deny the thing, the rea&longs;on depends on another Accident which <lb/>&longs;eems no le&longs;s &longs;trange, and yet I have a very nece&longs;&longs;ary Demon&longs;trati­<lb/>on for it. </s> <s>And the Accident is this, the Impo&longs;&longs;ibility of di&longs;tending <lb/>a Rope, &longs;o, as that it may be &longs;tretched right out, and parallel to the <lb/>Horizon, but that it alwaies &longs;wayes and bendeth, nor is there any <lb/>Force that can &longs;tretch it otherwi&longs;e.</s></p><p type="main"> <s>SALV. </s> <s>So then, <emph type="italics"/>Sagredus,<emph.end type="italics"/> your wonder cea&longs;eth in this ca&longs;e of <lb/>the Rope becau&longs;e you have the Demon&longs;tration of it. </s> <s>But if we <lb/>&longs;hall well con&longs;ider the matter, it may be we &longs;hall find &longs;ome corre­<lb/>&longs;pondence between the Accident of the Project and this of the <lb/>Rope. </s> <s>The Curvity of the Line of the Horizontal Projection &longs;eem­<lb/>eth to be derived from two Forces, of which one, (which is that of <lb/>the Projicient) driveth it Horizontally, and the other, (which <lb/>is the Gravity of the Project) draweth it downwards Perpendicu­<lb/>larly. </s> <s>Now &longs;o in the &longs;tretching of the Rope, there are the Forces <lb/>of tho&longs;e that pull it Horizontally, and there is al&longs;o the weight of <lb/>the Rope it &longs;elf, which naturally inclineth it downwards. </s> <s>The&longs;e <lb/>two effects are very much alike in the generation of them. </s> <s>And if <lb/>you allow the weight of the Rope &longs;o much &longs;trength and power as to <lb/>be able to oppo&longs;e and overcome any whatever Immen&longs;e Force, that <lb/>would di&longs;tend it right out, why will you deny the like to the weight <lb/>of the Bullet? </s> <s>But be&longs;ides, I &longs;hall tell you, and at once procure your <pb xlink:href="040/01/937.jpg" pagenum="244"/>wonder, and delight, that the Rope thus tentered, and &longs;tretcht little <lb/>or much, doth &longs;hape it &longs;elf into Lines that come very near to Para­<lb/>bolical, and the re&longs;emblance is &longs;o great, that if you draw a Para­<lb/>bolical Line upon a plain Superficies that is erect unto the Horizon, <lb/>and holding it rever&longs;ed, that is with the Vertex downwards and <lb/>with the Ba&longs;e Parallel to the Horizon, you cau&longs;e a Chain to be held <lb/>pendent, and &longs;u&longs;tained at the extreams of the Ba&longs;e of the De&longs;cribed <lb/>Parabola, you &longs;hall &longs;ee the &longs;aid Chain, as you &longs;laken it more or le&longs;s, <lb/>to incurvate and apply it &longs;elf to the &longs;ame Parabola, and this &longs;ame <lb/>Application &longs;hall be &longs;o much the more exact, when the de&longs;cribed <lb/>Parabola is le&longs;s curved, that is more di&longs;tended: So that in Parabola's <lb/>de&longs;cribed with Elevations under <emph type="italics"/>gr.<emph.end type="italics"/> 45, the Chain an&longs;wereth the <lb/>Parabola almo&longs;t to an hair.</s></p><p type="main"> <s>SAGR. </s> <s>It &longs;eems then that with &longs;uch a Chain wrought into &longs;mall <lb/>Links one might in an in&longs;tant trace out many Parabolick Lines up­<lb/>on a plain Superficies.</s></p><p type="main"> <s>SALV. </s> <s>One might, and that al&longs;o with no &longs;mall commodity, as I <lb/>&longs;hall tell you anon.</s></p><p type="main"> <s>SIMP. </s> <s>But before you pa&longs;s any farther, I al&longs;o would gladly be <lb/>a&longs;certained at lea&longs;t in that Propo&longs;ition of which you &longs;ay there is a <lb/>very nece&longs;&longs;ary Demon&longs;tration, I mean that of the Impo&longs;&longs;ibility of <lb/>di&longs;tending a Rope, by any whatever immen&longs;e Force, right out and <lb/>equidi&longs;tant from the Horizon.</s></p><p type="main"> <s>SAGR. </s> <s>I will &longs;ee if I remember the Demon&longs;tration, for under­<lb/>&longs;tanding of which it is nece&longs;&longs;ary, <emph type="italics"/>Simplicius,<emph.end type="italics"/> that you &longs;uppo&longs;e for <lb/>true, that which in all Mechanick In&longs;truments is confirmed, not on­<lb/>ly by Experience, but al&longs;o by Demon&longs;tration: and this it is, That <lb/>the Velocity of the Mover, though its Force be very &longs;mall, may <lb/>overcome the Re&longs;i&longs;tance, though very great, of a Re&longs;i&longs;ter, which <lb/>mu&longs;t be moved &longs;lowly when ever the Velocity of the Mover hath <lb/>greater proportion to the Tardity of the Re&longs;i&longs;ter, than the Re&longs;i­<lb/>&longs;tance of that which is to be moved hath to the Force of the Mo­<lb/>ver.</s></p><p type="main"> <s>SIMP. </s> <s>This I know very well, and it is demon&longs;trated by <emph type="italics"/>Ari­<lb/>&longs;totle<emph.end type="italics"/> in his Mechanical Que&longs;tions, and is manife&longs;tly &longs;een in the Lea­<lb/>ver and in the Stiliard, in which the Roman which weigheth not <lb/>above 4 pounds, will lift up a weight of 400 in ca&longs;e the di&longs;tance of <lb/>the &longs;aid Roman from the Center on which the Beam turneth be <lb/>more than an hundred times greater than the di&longs;tance of that point <lb/>at which the great weight hangeth from the &longs;ame Center: and this <lb/>cometh to pa&longs;s becau&longs;e in the de&longs;cent which the Roman maketh <lb/>pa&longs;&longs;eth a Space above an hundred times greater than the Space <lb/>which the great weight mounteth in the &longs;ame Time: Which is all <lb/>one as to &longs;ay, that the little Roman moveth with a Velocity above <lb/>an hundred times greater than the Velocity of the great Weight.</s></p><pb xlink:href="040/01/938.jpg" pagenum="245"/><p type="main"> <s>SAGR. </s> <s>You argue very well, and make no &longs;eruple at all of <lb/>granting, that be the Force of the Mover never &longs;o &longs;mall it &longs;hall &longs;u­<lb/>perate any what ever great Re&longs;i&longs;tance at all times when that &longs;hall <lb/>more exceed in Velocity than this doth in Force and Gravity. <lb/></s> <s>Now come we to the ca&longs;e of the Rope. </s> <s>And drawing a &longs;mall <lb/>Scheme be plea&longs;ed to under&longs;tand for once that this Line A B, re&longs;t­<lb/>ing upon the two fixed and &longs;tanding points A and B, to have hang­<lb/>ing at its ends, as you &longs;ee, two immen&longs;e Weights C and D, which <lb/>drawing it with great Force make it to &longs;tand directly di&longs;tended, it <lb/>being a &longs;imple Line without any gravity. </s> <s>And here I proceed, and <lb/>tell you, that if at the mid&longs;t of that which is the point E, you &longs;hould <lb/>hang any never &longs;o little a Weight, as is this H, the Line A B would <lb/>yield, and inclining towards the point F, and by con&longs;equence <lb/>lengthening, will con&longs;train the two great Weights C and D to <lb/>a&longs;cend upwards: which I demon&longs;trate to you in this manner: <lb/>About the two points A and B as Centers I de&longs;cribe two Quadrants <lb/>E F G, and E L M, and in regard that the two Semidiameters AI <lb/>and B L are equal to the two Semidiameters A E and E B, the exce&longs;­<lb/>&longs;es F I and F L &longs;hall be the quantity of the prolongations of the <lb/>parts A F and F B, above A E and E B; and of con&longs;equence &longs;hall <lb/><figure id="id.040.01.938.1.jpg" xlink:href="040/01/938/1.jpg"/><lb/>determine the A&longs;cents <lb/>of the Weights C and <lb/>D, in ca&longs;e that the <lb/>Weight H had had a <lb/>power to de&longs;cend to F: <lb/>which might then be <lb/>in ca&longs;e the Line E F, <lb/>which is the quantity <lb/>of the De&longs;cent of the <lb/>&longs;aid Weight H, had <lb/>greater proportion to <lb/>the Line F I which de­<lb/>termineth the A&longs;cent of <lb/>the two Weights C & <lb/>D, than the pondero­<lb/>&longs;ity of both tho&longs;e Weights hath to the pondero&longs;ity of the Weight <lb/>H. </s> <s>But this will nece&longs;&longs;arily happen, be the pondero&longs;ity of the <lb/>Weights C and D never &longs;o great, and that of H never &longs;o &longs;mall; for <lb/>the exce&longs;s of the Weights C and D above the Weight His not &longs;o <lb/>great, but that the exce&longs;s of the Tangent E F above the part of the <lb/>Secant F I may bear a greater proportion. </s> <s>Which we will prove <lb/>thus: Let there be a Circle who&longs;e Diameter is G A I; and look <lb/>what proportion the pondero&longs;ity of the Weights C and D have to <lb/>the pondero&longs;ity of H, let the Line B O have the &longs;ame proportion to <lb/>another, which let be C, than which let D be le&longs;&longs;er: So that B O <pb xlink:href="040/01/939.jpg" pagenum="246"/>&longs;hall have greater proportion to D, than to C. </s> <s>Unto O B and D <lb/>take a third proportional B E; and as O E is to E B, &longs;o let the Dia­<lb/>meter G I (prolonging it) be to I F: and from the Term F <lb/>draw the Tangent F N. </s> <s>And becau&longs;e it hath been pre&longs;uppo&longs;ed, <lb/>that as O E is to E B, &longs;o is G I to I F: therefore, by Compo&longs;ition, as <lb/>O B is to B E, &longs;o is G F to F I: But betwixt O B and B E the Mean­<lb/>proportional is D; and betwixt G F and F I the Mean-proporti­<lb/>onal is N F: Therefore N F hath the &longs;ame proportion to F I that <lb/>O B hath to D: which proportion is greater than that of the <lb/>Weights C and D to the Weight H. Therefore, the De&longs;cent or <lb/>Velocity of the Weight H having greater proportion to the A&longs;cent <lb/>or Velocity of the Weights C and D, than the pondero&longs;ity of the <lb/>&longs;aid Weights C and D hath to the pondero&longs;ity of the Weight H: <lb/>It is manife&longs;t, that the Weight H &longs;hall de&longs;cend, that is, that the <lb/>Line A B &longs;hall depart from Horizontal Rectitude. </s> <s>And that which <lb/>befalleth the right Line A B deprived of Gravity in ca&longs;e any &longs;mall <lb/>Weight H cometh to be hanged at the &longs;ame in E, happens al&longs;o to <lb/>the &longs;aid Rope A B, &longs;uppo&longs;ed to be of ponderous Matter, without <lb/>the addition of any other Grave Body; for that the Weight of <lb/>the Matter it &longs;elf compounding the &longs;aid Rope AB is &longs;u&longs;pended <lb/>thereat.</s></p><p type="main"> <s>SIMP. </s> <s>You have fully &longs;atisfied me; therefore <emph type="italics"/>Salviatus<emph.end type="italics"/> may ac­<lb/>cording to his promi&longs;e declare unto us, what the Commodity is that <lb/>may be drawn from &longs;uch like Chains, and after that relate unto us <lb/>tho&longs;e Speculations which have been made by our <emph type="italics"/>Accademian<emph.end type="italics"/><lb/>touching the Force of Percu&longs;&longs;ion.</s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>ALV. </s> <s>We are for this day &longs;ufficiently employed in the Con­<lb/>templations already delivered, and the Time, which is pretty late, <lb/>would not be enough to carry us through the matters you mention; <lb/>therefore we &longs;hall defer our Conference till &longs;ome more convenient <lb/>time.</s></p><p type="main"> <s>SAGR. </s> <s>I concur with you in opinion, for that by &longs;undry di&longs;­<lb/>cour&longs;es that I have had with the Friends of our <emph type="italics"/>Academick<emph.end type="italics"/> I have <lb/>learnt that this Argument of the Force of Percu&longs;&longs;ion is very ob­<lb/>&longs;cure, nor hath hitherto any one that hath treated thereof penetra­<lb/>ted its intricacies, full of darkne&longs;s, and altogether remote from <lb/>mans fir&longs;t imaginations: and among&longs;t the Conclu&longs;ions that I have <lb/>heard of, one runs in my mind that is very extravagant and odde, <lb/>namely, That the Force of Percu&longs;&longs;ion is Interminate, if not Infi­<lb/>nite. </s> <s>We will therefore attend the lea&longs;ure of <emph type="italics"/>Salviatus.<emph.end type="italics"/> But for <lb/>the pre&longs;ent, tell me what things are tho&longs;e which are written at the <lb/>end of the Treati&longs;e of Projects?</s></p><p type="main"> <s>SALV. </s> <s>The&longs;e are certain Propo&longs;itions touching the Center of <lb/>Gravity of Solids, which our <emph type="italics"/>Academick<emph.end type="italics"/> found out in his youth, <lb/><arrow.to.target n="marg1104"></arrow.to.target><lb/>conceiving that what ^{*} <emph type="italics"/>Frederico Comandino<emph.end type="italics"/> had writ touching the <pb xlink:href="040/01/940.jpg" pagenum="247"/>&longs;ame was not altogether without Imper&longs;ection. </s> <s>He therefore <lb/>thought that with the&longs;e Propo&longs;itions, which here you &longs;ee written, <lb/>he might &longs;upply that which is wanting in the Book of <emph type="italics"/>Comandine<emph.end type="italics"/>; <lb/>and he applyed him&longs;elf to the &longs;ame at the In&longs;tance of the mo&longs;t <lb/>Illu&longs;trious Lord Marque&longs;s <emph type="italics"/>Guid' Vbaldo dal Monte,<emph.end type="italics"/> the mo&longs;t ex­<lb/>cellent Mathematician of his Time, as his &longs;everal Printed Works <lb/>do &longs;peak him; and gave a Copy thereof to that Noble Lord with <lb/>thoughts to have pur&longs;ued the &longs;ame Argument in other Solids not <lb/>mentioned by <emph type="italics"/>Comandine:<emph.end type="italics"/> But he chanced after &longs;ome Time to <lb/>meet with the ^{*} Book of <emph type="italics"/>Signore Luca Valerio,<emph.end type="italics"/> a mo&longs;t famous <lb/><arrow.to.target n="marg1105"></arrow.to.target><lb/>Geometrician, and &longs;aw that he re&longs;olveth all the&longs;e matters with­<lb/>out omi&longs;&longs;ion of any thing, he proceeded no farther, although his <lb/>Agre&longs;&longs;ions were by methods very different from the&longs;e of <emph type="italics"/>Signore <lb/>Valerio.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1104"></margin.target>* <emph type="italics"/>Fredericus Co­<lb/>mandinus.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1105"></margin.target>* <emph type="italics"/>De.<emph.end type="italics"/></s></p><p type="main"> <s>SAGR. </s> <s>It would be a favour, therefore, if, for this time, which <lb/>interpo&longs;eth between this and our next Meeting, you would plea&longs;e <lb/>to leave the Book in my hands: for I &longs;hall all the while be read­<lb/>ing and &longs;tudying the Propo&longs;itions that are con&longs;equently therein <lb/>writ.</s></p><p type="main"> <s>SALV. </s> <s>I &longs;hall very willingly obey your Command; and hope <lb/>that you will take plea&longs;ure in the&longs;e Propo&longs;itions.</s></p></chap><chap><pb xlink:href="040/01/941.jpg" pagenum="248"/><p type="head"> <s>AN <lb/>APPENDIX, <lb/>In which is contained certain <lb/>THE OREMS and their DEMONSTRATIONS: <lb/>Formerly written by the &longs;ame Author, touching the <lb/><emph type="italics"/>CENTER<emph.end type="italics"/> of <emph type="italics"/>GRAVITY,<emph.end type="italics"/> of <lb/>SOLIDS.</s></p><p type="head"> <s>POSTVLATVM.</s></p><p type="main"> <s><emph type="italics"/>We pre&longs;uppo&longs;e equall Weights to be alike di&longs;po­<lb/>&longs;ed in &longs;ever all Ballances, if the Center of Gra­<lb/>vity of &longs;ome of tho&longs;e Compounds &longs;hall divide the Ballance <lb/>according to &longs;ome proportion, and the Ballance &longs;hall <lb/>al&longs;o divide their Center of Gravity according to the <lb/>&longs;ame proportion.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA.</s></p><p type="main"> <s><emph type="italics"/>Let the line A B be cut in two equall parts in C, <lb/>who&longs;e half A C let be divided in E, &longs;o that as B E is to <lb/>E A, &longs;o may A E be to E C. </s> <s>I &longs;ay that B E is double<emph.end type="italics"/><lb/><figure id="id.040.01.941.1.jpg" xlink:href="040/01/941/1.jpg"/><lb/><emph type="italics"/>to E A. </s> <s>For as B E is to E <lb/>A, &longs;o is E A to E C: there­<lb/>fore by Compo&longs;ition and by Permutation of Proportion, as <lb/>B A is to A C, &longs;o is A E to E C: But as A E is to E C, <lb/>that is, B A to A C, &longs;o is B E to E A: Wherefore B <lb/>E is double to E A.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>This &longs;uppo&longs;ed, we will Demon&longs;trate, That,<emph.end type="italics"/></s></p><pb xlink:href="040/01/942.jpg" pagenum="249"/><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If certain Magnitudes at any Rate equally exceed­<lb/>ing one another, and who&longs;e exce&longs;s is equal to <lb/>the lea&longs;t of them, be &longs;o di&longs;po&longs;ed in the Balance, <lb/>as that they hang at equal di&longs;tances, to divide <lb/>the Center of Gravity of the whole Balance <lb/>&longs;o, that the part towards the le&longs;&longs;er Magnitudes <lb/>be double to the remainder.</s></p><p type="main"> <s><emph type="italics"/>In the ^{*} Ballance A B, therefore, let there be &longs;u&longs;pended at equal di-<emph.end type="italics"/><lb/><arrow.to.target n="marg1106"></arrow.to.target><lb/><emph type="italics"/>&longs;tances any number of Magnitudes, as hath been &longs;aid, F, G, H, K, <lb/>N; of which let the lea&longs;t be N, and let the points of the Su&longs;pen&longs;ions <lb/>be A, C, D, E, B, and let the Center of Gravity of all the Magnitudes <lb/>&longs;o di&longs;po&longs;ed be X. </s> <s>It is to be proved that the part of the Ballance B X <lb/>towards the le&longs;&longs;er Magnitudes is double to the remaining part X A.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1106"></margin.target>* Or Beam.</s></p><p type="main"> <s><emph type="italics"/>Let the Ballance be divided in two equal parts in D, for it mu&longs;t ei­<lb/>ther fall in &longs;ome point of the Su&longs;pen&longs;ions, or el&longs;e in the middle point be­<lb/>tween two of the points of the Su&longs;pen&longs;ions: and let the remaining di­<lb/>&longs;tances of the Su&longs;pen&longs;ions which fall between A and D, be all divided <lb/>into halves by the Points M and I; and let all the Magnitudes be divi-<emph.end type="italics"/><lb/><figure id="id.040.01.942.1.jpg" xlink:href="040/01/942/1.jpg"/><lb/><emph type="italics"/>ded into parts equal to <lb/>N: Now the parts of F <lb/>&longs;hall be &longs;o many in num­<lb/>ber, as tho&longs;e Magnitudes <lb/>be which are &longs;u&longs;pended <lb/>at the Ballance, and the <lb/>parts of G one fewer, <lb/>and &longs;o of the re&longs;t. </s> <s>Let <lb/>the parts of F therefore be N, O, R, S, T, and let tho&longs;e of G be N, O, <lb/>R, S, tho&longs;e of H al&longs;o N, O, R, then let tho&longs;e of K be N, O: and all the <lb/>Magnitudes in which are N &longs;hall be equal to F; and all the Magnitudes <lb/>in which are O &longs;hall be equal to G; and all the Magnitudes in which <lb/>are R &longs;hall be equal to H; and tho&longs;e in which S &longs;hall be equal to K; and <lb/>the Magnitude T is equal to N. </s> <s>Becau&longs;e therefore all the Magnitudes <lb/>in which are N are equal to one another, they &longs;hall equiponderate in <lb/>the point D, which divideth the Ballance into two equal parts; and for <lb/>the &longs;ame cau&longs;e all the Magnitudes in which are O do equiponderate in <lb/>I; and tho&longs;e in which are R in C; and in which are S in M do equi­<lb/>ponderate; and T is &longs;u&longs;pended in A. </s> <s>Therefore in the Ballance A D at <lb/>the equal di&longs;tances D, I, C, M, A, there are Magnitudes &longs;u&longs;pended ex­<lb/>ceeding one another equally, and who&longs;e exce&longs;s is equal to the lea&longs;t: and <lb/>the greate&longs;t, which is compounded of all the N N hangeth at D, the<emph.end type="italics"/><pb xlink:href="040/01/943.jpg" pagenum="250"/><emph type="italics"/>lea&longs;t which is T hangeth at A; and the re&longs;t are ordinately di&longs;po&longs;ed. <lb/></s> <s>And again there is another Ballance A B in which other Magnitudes <lb/>equal in number and Magnitude to the former are di&longs;po&longs;ed in the &longs;ame <lb/>order. </s> <s>Wherefore the Ballances A B and A D are divided by the Cen­<lb/>ter of all the Magnitudes according to the &longs;ame proportion: But the <lb/>Center of Gravity of the afore&longs;aid Magnitudes is X: Wherefore X <lb/>divideth the Ballances B A and A D according to the &longs;ame proportion; <lb/>&longs;o that as B X is to X A, &longs;o is X A to X D: Wherefore B X is double <lb/>to X A, by the Lemma aforegoing: Which was to be proved.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If in a Parabolical Conoid Figure be de&longs;cribed, <lb/>and another circum&longs;cribed by Cylinders of <lb/>equal Altitude; and the Axis of the &longs;aid Co­<lb/>noid be divided in &longs;uch proportion that the <lb/>part towards the Vertex be double to that to­<lb/>wards the Ba&longs;e; the Center of Gravity of the <lb/>in&longs;cribed Figure of the Ba&longs;e portion &longs;hall be <lb/>neare&longs;t to the &longs;aid point of divi&longs;ion; and the <lb/>Center of Gravity of the circum&longs;cribed from <lb/>the Ba&longs;e of the Conoid &longs;hall be more remote: <lb/>and the di&longs;tance of either of tho&longs;e Centers <lb/>from that &longs;ame point &longs;hall be equal to the Line <lb/>that is the &longs;ixth part of the Altitude of one of <lb/>the Cylinders of which the Figures are com­<lb/>po&longs;ed.</s></p><p type="main"> <s><emph type="italics"/>Take therefore a Parabolical Conoid, and the Figures that have <lb/>been mentioned: let one of them be in&longs;cribed, the other circum­<lb/>&longs;cribed; and let the Axis of the Conoid, which let be A E, be di­<lb/>vided in N, in &longs;uch proportion as that A N be double to N E. </s> <s>It is to <lb/>be proved that the Center of Gravity of the in&longs;cribed Figure is in the <lb/>Line N E, but the Center of the circum&longs;cribed in the Line A N. </s> <s>Let <lb/>the Plane of the Figures &longs;o di&longs;po&longs;ed be cut through the Axis, and let <lb/>the Section be that of the Parabola B A C: and let the Section of the <lb/>cutting Plane, and of the Ba&longs;e of the Conoid be the Line B C; and <lb/>let the Sections of the Cylinders be the Rectangular Figures; as ap­<lb/>peareth in the de&longs;cription. </s> <s>Fir&longs;t, therefore, the Cylinder of the in&longs;cri­<lb/>bed who&longs;e Axis is D E, hath the &longs;ame proportion to the Cylinder who&longs;e <lb/>Axis is D Y, as the Quadrate I D hath to the Quadrate S Y; that is, <lb/>as D A hath to A Y: and the Cylinder who&longs;e Axis is D Y is<emph.end type="italics"/> potentia <pb xlink:href="040/01/944.jpg" pagenum="251"/><emph type="italics"/>to the Cylinder Y Z as S Y to R Z, that is, as Y A to A Z: and, by the <lb/>&longs;ame rea&longs;on, the Cylinder who&longs;e Axis is Z Y is to that who&longs;e Axis is <lb/>Z V, as Z A is to A V. </s> <s>The &longs;aid Cylinders, therefore, are to one ano­<lb/>ther as the Lines D A, A Y; Z A, A V: But the&longs;e are equally exceed­<lb/>ing to one another, and the exce&longs;s is equal to the lea&longs;t, &longs;o that A Z is <lb/>double to A V; and A Y is triple the<emph.end type="italics"/><lb/><figure id="id.040.01.944.1.jpg" xlink:href="040/01/944/1.jpg"/><lb/><emph type="italics"/>&longs;ame; and D A Quadruple. </s> <s>Tho&longs;e <lb/>Cylinders, therefore, are certain Mag­<lb/>nitudes in order equally exceeding one <lb/>another, who&longs;e exce&longs;s is equal to the <lb/>lea&longs;t of them, and is the Line X M, <lb/>in which they are &longs;u&longs;pended at equal <lb/>di&longs;tances (for that each of the Cy­<lb/>linders hath its Center of Gravity in <lb/>the mia&longs;t of the Axis.) Wherefore, <lb/>by what hath been above demon&longs;tra­<lb/>ted, the Center of Gravity of the Mag­<lb/>nitude compounded of them all divi­<lb/>deth the Line X M &longs;o, that the part <lb/>towards X is double to the re&longs;t. </s> <s>Divide it, therefore, and, let X<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>be <lb/>double<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M: therefore is<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>the Center of Gravity of the in&longs;cribed Fi­<lb/>gure. </s> <s>Divide A V in two equal parts in<emph.end type="italics"/> <foreign lang="greek">e</foreign>: <foreign lang="greek">e</foreign> <emph type="italics"/>X &longs;hall be double to <lb/>M E: But X<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>is double to<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M: Wherefore<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>E &longs;hall be triple E<emph.end type="italics"/> <foreign lang="greek">a.</foreign> <emph type="italics"/>But<emph.end type="italics"/><lb/><foreign lang="greek">a</foreign> <emph type="italics"/>E is triple E N: It is manife&longs;t, therefore, that E N is greater than <lb/>E X; and for that cau&longs;e<emph.end type="italics"/> <foreign lang="greek">a,</foreign> <emph type="italics"/>which is the Center of Gravity of the in­<lb/>&longs;cribed Figure, cometh nearer to the Ba&longs;e of the Conoid than N. </s> <s>And <lb/>becau&longs;e that as A E is to E N, &longs;o is the part taken away<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>E to the part <lb/>taken away E<emph.end type="italics"/> <foreign lang="greek">a</foreign>: <emph type="italics"/>and the remaining part &longs;hall be to the remaming part, <lb/>that is, A<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>to N<emph.end type="italics"/> <foreign lang="greek">a,</foreign> <emph type="italics"/>as A E to E N. Therefore<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>N is the third part of <lb/>A<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>and the &longs;ixt part of A V. </s> <s>And in the &longs;ame manner the Cylinders of <lb/>the circum&longs;cribed Figure may be demon&longs;trated to be equally exceeding <lb/>one another, and the exce&longs;s to me equal to the least; and that they have <lb/>their Centers of Gravity at equal di&longs;tances in the Line<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>M. </s> <s>If therefore<emph.end type="italics"/><lb/><foreign lang="greek">e</foreign> <emph type="italics"/>M be divided in<emph.end type="italics"/> <foreign lang="greek">p,</foreign> <emph type="italics"/>&longs;o as that<emph.end type="italics"/> <foreign lang="greek">e p</foreign> <emph type="italics"/>be double to the remaining part<emph.end type="italics"/> <foreign lang="greek">p</foreign> <emph type="italics"/>M;<emph.end type="italics"/><lb/><foreign lang="greek">p</foreign> <emph type="italics"/>&longs;hall be the Center of Gravity of the whole circum&longs;cribed Magnitude. <lb/></s> <s>And &longs;ince<emph.end type="italics"/> <foreign lang="greek">e p</foreign> <emph type="italics"/>is double to<emph.end type="italics"/> <foreign lang="greek">p</foreign> <emph type="italics"/>M; and A<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>le&longs;s than double EM: (for <lb/>that they are equal:) the whole A E &longs;hall be le&longs;s than triple E<emph.end type="italics"/> <foreign lang="greek">p</foreign><emph type="italics"/>: Where­<lb/>fore E<emph.end type="italics"/> <foreign lang="greek">p</foreign> <emph type="italics"/>&longs;hall be greater than E N. And, &longs;ince<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>M is triple to M<emph.end type="italics"/> <foreign lang="greek">p,</foreign><lb/><emph type="italics"/>and M E with twice<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>A is likewi&longs;e triple to M E: the whole A E with <lb/>A<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>&longs;hall be triple to E<emph.end type="italics"/> <foreign lang="greek">p</foreign><emph type="italics"/>: But A E is triple to E N: Wherefore the <lb/>remaining part A<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>&longs;hall be triple to the remaining part<emph.end type="italics"/> <foreign lang="greek">p</foreign> <emph type="italics"/>N. </s> <s>Therefore <lb/>N<emph.end type="italics"/> <foreign lang="greek">p</foreign> <emph type="italics"/>is the &longs;ixth part of A V. </s> <s>And the&longs;e are the things that were to be <lb/>demon&longs;trated.<emph.end type="italics"/></s></p><pb xlink:href="040/01/945.jpg" pagenum="252"/><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it is manife&longs;t, that a Conoid may be in&longs;cribed in a Para­<lb/>bolical Figure, and another circum&longs;cribed, &longs;o, as that the <lb/>Centers of their Gravities may be di&longs;tant from the point N <lb/>le&longs;s than any Line given.</s></p><p type="main"> <s><emph type="italics"/>For if we a&longs;&longs;ume a Line &longs;excuple of the propo&longs;ed Line, and make the <lb/>Axis of the Cylinders, of which the Figures are compounded given <lb/>le&longs;&longs;er than this a&longs;&longs;umed Line, there &longs;hall fall Lines between the Centers <lb/>of Gravities of the&longs;e Figures and the mark N that are le&longs;s than the <lb/>Line propo&longs;ed.<emph.end type="italics"/></s></p><p type="main"> <s>The former Propo&longs;ition another way.</s></p><p type="main"> <s><emph type="italics"/>Let the Axis of the Conoid (which let be C D) be divided in <lb/>O, &longs;o, as that C O be double to O D. </s> <s>It is to be proved that the <lb/>Center of Gravity of the in&longs;cribed Figure is in the Line O D; <lb/>and the Center of the circum&longs;cribed in C O. </s> <s>Let the Plane of the Fi­<lb/>gures be cut through the Axis and C, as hath been &longs;aid. </s> <s>Becau&longs;e there­<lb/>fore the Cylinders S N, T M, V I,<emph.end type="italics"/><lb/><figure id="id.040.01.945.1.jpg" xlink:href="040/01/945/1.jpg"/><lb/><emph type="italics"/>X E are to one another as the Squares <lb/>of the Lines S D, T N, V M, X I; <lb/>and the&longs;e are to one another as the <lb/>Lines N C, C M, C I, C E: but <lb/>the&longs;e do exceed one another equally; <lb/>and the exce&longs;s is equal to the lea&longs;t, to <lb/>wit, C E: And the Cylinder T M is <lb/>equal to the Cylinder Q N; and the <lb/>Cylinder V I equal to P N; and X E <lb/>is equal to L N: Therefore the Cylin­<lb/>ders S N, Q N, P N, and L N do <lb/>equally exceed one another, and the <lb/>exce&longs;s is equal to the lea&longs;t of them, <lb/>namely, to the Cylinder L N. </s> <s>But <lb/>the exce&longs;s of the Cylinder S N, above <lb/>the Cylinder Q N is a Ring who&longs;e <lb/>height is Q T; that is, N D; and <lb/>its breadth S <expan abbr="q.">que</expan> And the exce&longs;s of the Cylinder Q N above P N, is a <lb/>Ring, who&longs;e breadth is Q P. </s> <s>And the exce&longs;s of the Cylinder P N above <lb/>L N is a Ring, who&longs;e breadth is P L. </s> <s>Wherefore the &longs;aid Rings S Q, <lb/>Q P, P L, are equal to another, and to the Cylinder L N. </s> <s>Therefore the <lb/>Ring S T equalleth the Cylinder X E: the Ring Q V, which is double <lb/>to S T, equalleth the Cylinder V I; which likewi&longs;e is double to the<emph.end type="italics"/><pb xlink:href="040/01/946.jpg" pagenum="253"/><emph type="italics"/>Cylinder X E: and for the &longs;ame cau&longs;e the Ring P X is equal to the <lb/>Cylinder T M; and the Cylinder L E &longs;hall be equal to the Cylinder S N. <lb/></s> <s>In the Beam or Ballance, therefore, K F connecting the middle points of <lb/>the Right-lines E I and D N, and cut into equal parts in the points H <lb/>and G, are certain Magnitudes &longs;u&longs;pended, to wit the Cylinders S N, <lb/>T M, V I, X E; and the Center of Gravity of the fir&longs;t Cylinder is K; <lb/>and of the &longs;econd H; of the third G; of the fourth F. </s> <s>And we have <lb/>another Ballance M K, which is the half of the &longs;aid F K, and a like <lb/>number of points di&longs;tributed into equal parts, to wit, M H, H N, N K, <lb/>and on it other Magnitudes, equal in number and bigne&longs;s to tho&longs;e which <lb/>are on the Beam F K, and having the Centers of Gravity in the points <lb/>M, H, N, and K, and di&longs;po&longs;ed in the &longs;ame order. </s> <s>For the Cylinder L E <lb/>hath its Center of Gravity in M; and is equal to the Cylinder S N that <lb/>hath its Center in K: And the Ring P X hath the Center H; and is <lb/>equal to the Cylinder T M, who&longs;e Center is H: And the Ring Q V ha­<lb/>ving the Center N is equal to the V I who&longs;e Center is G: And la&longs;tly, <lb/>the Ring S T having the Center K, is equal to the Cylinder X E who&longs;e <lb/>Center is F. </s> <s>Therefore the Center of Gravity of the &longs;aid Magnitudes <lb/>divideth the Beam in the &longs;ame proportion: But the Center of them is <lb/>one, and therefore &longs;ome point common to both the Beams or Ballance, <lb/>which let be Y. </s> <s>Therefore F Y and Y K &longs;hall be as K Y and Y M. </s> <s>F Y <lb/>therefore is double to Y K: and C E being divided into two equal parts <lb/>in Z, Z F, &longs;hall be double to K D: and for that cau&longs;e Z D triple to D Y: <lb/>But to the Right Line D O C D is triple: Therefore the Right Line <lb/>D O is greater than D Y: And for the like cau&longs;e Y the Center of the <lb/>in&longs;cribed Figure approacheth nearer the Ba&longs;e than the point O. </s> <s>And <lb/>becau&longs;e as C D is to D O, &longs;o is the part taken away Z D to the part ta­<lb/>ken away D Y; the remaining part C Z &longs;hall be to the remaining part <lb/>Y O, as C D is to D O; that is Y O &longs;hall be the third part of C Z; <lb/>that is, the &longs;ixth part of C E. </s> <s>Again we will, by the &longs;ame rea&longs;on, de­<lb/>mon&longs;trate the Cylinders of the circum&longs;cribed Figure to exceed one ano­<lb/>ther equally, and that the exce&longs;s is equal to the lea&longs;t, and that their <lb/>Centers of Gravity are con&longs;tituted in equal di&longs;tances upon the Beam <lb/>K Z: and likewi&longs;e that the Rings equal to tho&longs;e &longs;ame Cylinders are in <lb/>like manner di&longs;po&longs;ed on another Beam K G, the half of the &longs;aid K Z, <lb/>and that therefore the Center of Gravity of the circum&longs;cribed Figure, <lb/>which let be R, &longs;o divideth the Beam, as that Z R is to R K, as K R is to <lb/>R G. </s> <s>Therefore Z R &longs;hall be double to R K: But C Z is equal to the <lb/>Right Line K D, and not double to it. </s> <s>The whole C D &longs;hall be le&longs;&longs;er <lb/>than triple to D R: Wherefore the Right Line D R is greater than D O; <lb/>that is to &longs;ay, the Center of the circum&longs;cribed Figure recedeth from the <lb/>Ba&longs;e more than the point O. </s> <s>And becau&longs;e Z K is triple to K R; and <lb/>K D with twice Z C is triple to K D; the whole C D with C Z &longs;hall be <lb/>triple to D R: But C D is triple to D O: Wherefore the remaining <lb/>part C Z &longs;hall be triple to the remaining part R O; that is, O R<emph.end type="italics"/><pb xlink:href="040/01/947.jpg" pagenum="254"/><emph type="italics"/>is the &longs;ixth part of E C: Which was the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>This being pre-demon&longs;trated, we will prove that<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity of the Parabolick <lb/>Conoid doth &longs;o divide the Axis, as that the <lb/>part towards the Vertex is double to the re­<lb/>maining part towards the Ba&longs;e.</s></p><p type="main"> <s><emph type="italics"/>Let there be a Parabolick Conoid who&longs;e Axis let be A B divided in <lb/>N &longs;o as that A N be double to N B. </s> <s>It is to be proved that the Cen­<lb/>ter of Gravity of the Conoid is the point N. </s> <s>For if it be not N, it <lb/>&longs;hall be either above or below it. </s> <s>Fir&longs;t let it be below; and let it be X: <lb/>And &longs;et off upon &longs;ome place by it &longs;elf the Line L O equal to N X; and let <lb/>L O be divided at plea&longs;ure in S: and look what proportion B X and <lb/>O S both together have to O S, and the &longs;ame &longs;hall the Conoid have to <lb/>the Solid R. </s> <s>And in the Conoid let Figures be de&longs;cribed by Cylinders <lb/>having equal Altitudes, &longs;o, as that that which lyeth between the Center <lb/>of Gravity and the point N be le&longs;s than L S: and let the exce&longs;s of the <lb/>Conoid above it be le&longs;s than the Solid R: and that this may be done is <lb/>clear. </s> <s>Take therefore the in&longs;cribed, who&longs;e Center of Gravity let be I: <lb/>now I X &longs;hall be greater than S O: And becau&longs;e that as X B with S O <lb/>is to S O, &longs;o is the Conoid to the Solid R: (and R is greater than the <lb/>exce&longs;s by which the Conoid exceeds the in&longs;cribed Figure:) the proporti­<lb/>on of the Conoid to the &longs;aid exce&longs;s &longs;hall be greater than both B X and <lb/>O S unto S O: And, by Divi&longs;ion, the in&longs;cribed Figure &longs;hall have grea­<lb/>ter proportion to the &longs;aid exce&longs;s than B X to S O: But B X hath to <lb/>X I a proportion yet le&longs;s than to S O: Therefore the in&longs;cribed Figure <lb/>&longs;hall have much greater proportion to the re&longs;t of the proportions than <lb/>B X to X I: Therefore what proportion the in&longs;cribed Figure hath to <lb/>there&longs;t of the portions, the &longs;ame &longs;hall a certain other Line have to X I: <lb/>which &longs;hall nece&longs;&longs;arily be greater than B X: Let it, therefore, be M X. <lb/></s> <s>We have therefore the Center of Gravity of the Conoid X: But the <lb/>Center of Gravity of the Figure in&longs;cribed in it is I: of the re&longs;t of the <lb/>portions by which the Conoid exceeds the in&longs;cribed Figure the Center of <lb/>Gravity &longs;hall be in the Line X M, and in it that point in which it &longs;hall <lb/>be &longs;o terminated, that look what proportion the in&longs;cribed Figure hath <lb/>to the exce&longs;s by which the Conoid exceeds it, the &longs;ame it &longs;hall have to <lb/>X I: But it hath been proved, that this proportion is that which M X <lb/>hath to X I: Therefore M &longs;hall be the Center of Gravity of tho&longs;e pro­<lb/>portions by which the Conoid exceeds the in&longs;cribed Figure: Which <lb/>certainly cannot be. </s> <s>For if along by M a Plane be drawn equidi&longs;tant to <lb/>the Ba&longs;e of the Conoid, all tho&longs;e proportions &longs;hall be towards one and<emph.end type="italics"/><pb xlink:href="040/01/948.jpg" pagenum="255"/><emph type="italics"/>the &longs;ame part, and not by it divided. </s> <s>Therefore the Center of Gravity <lb/>of the &longs;aid Conoid is not below the point N: Neither is it above. </s> <s>For, <lb/>if it may, let it be H: and again, as before, &longs;et the Line L O by it &longs;elf <lb/>equalto the &longs;aid H N, and divided at plea&longs;ure in S: and the &longs;ame pro­<lb/>portion that B N and S O both together have to S L, let the Conoid <lb/>have to R: and about the Conoid let a Figure be circum&longs;cribed con&longs;i­<lb/>&longs;ting of Cylinders, as hath been &longs;aid: by which let it be exceeded a le&longs;s <lb/>quantity than that of the Solid R: and let the Line betwixt the Center <lb/>of Gravity of the circum&longs;cribed Figure and the point N be le&longs;&longs;er than <lb/>S O: the remainder V H &longs;hall be greater than S L. </s> <s>And becau&longs;e that as <lb/>both B N and O S is to SL, &longs;o is the<emph.end type="italics"/><lb/><figure id="id.040.01.948.1.jpg" xlink:href="040/01/948/1.jpg"/><lb/><emph type="italics"/>Conoid to R: (and R is greater <lb/>than the exce&longs;s by which the circum­<lb/>&longs;cribed Figure exceeds the Conoid:) <lb/>Therefore B N and S O hath le&longs;s pro­<lb/>portion to S L than the Conoid to the <lb/>&longs;aid exce&longs;s. </s> <s>And B V is le&longs;&longs;er than <lb/>both B N and S O; and V H is grea­<lb/>ter than S L: much greater proporti­<lb/>on, therefore, hath the Conoid to the <lb/>&longs;aid proportions, than B V hath to <lb/>V H. </s> <s>Therefore whatever proporti­<lb/>on the Conoid hath to the &longs;aid pro­<lb/>portions, the &longs;ame &longs;hall a Line greater <lb/>than B V have to V H. </s> <s>Let the &longs;ame be M V: And becau&longs;e the Center <lb/>of Gravity of the circum&longs;cribed Figure is V, and the Center of the <lb/>Conoid is H. and &longs;ince that as the Conoid to the re&longs;t of the proportions, <lb/>&longs;ois M V to V H, M &longs;hall be the Center of Gravity of the remaining <lb/>proportions: which likewi&longs;e is impo&longs;&longs;ible: Therefore the Center of <lb/>Gravity of the Conoid is not above the point N: But it hath been de­<lb/>mon&longs;trated that neither is it beneath: It remains, therefore, that it ne­<lb/>ce&longs;&longs;arily be in the point N it &longs;elf. </s> <s>And the &longs;ame might be demon&longs;trated <lb/>of Conoidal Plane cut upon an Axis not erect. </s> <s>The &longs;ame in other terms, <lb/>as appears by what followeth:<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity of the Parabolick Co­<lb/>noid falleth betwixt the Center of the cir­<lb/>cum&longs;cribed Figure and the Center of the in­<lb/>&longs;cribed.</s></p><pb xlink:href="040/01/949.jpg" pagenum="256"/><p type="main"> <s><emph type="italics"/>Let there be a Conoid who&longs;e Axis is A B, and the Center of the <lb/>circum&longs;cribed Figure C, and the Center of the in&longs;cribed O. </s> <s>I &longs;ay <lb/>the Center of the Conoid is betwixt the points C and O. </s> <s>For if <lb/>not, it &longs;hall be either above them, or below them, or in one of them. </s> <s>Let <lb/>it be below, as in R. </s> <s>And becau&longs;e R is the Center of Gravity of the <lb/>whole Conoid; and the Center of Gravity of the in&longs;cribed Figure is O: <lb/>Therefore of the remaining proportions by which the Conoid exceeds <lb/>the in&longs;cribed Figure the Center of Gravity &longs;hall be in the Line O R ex­<lb/>tended towards R, and in that point in which it is &longs;o determined, that, <lb/>what proportion the &longs;aid proportions have to the in&longs;cribed Figure, the <lb/>&longs;ame &longs;hall O R have to the Line falling betwixt R and that falling point. <lb/></s> <s>Let this proportion be that of O R to R X. </s> <s>Therefore X falleth either <lb/>without the Conoid or within, or in its<emph.end type="italics"/><lb/><figure id="id.040.01.949.1.jpg" xlink:href="040/01/949/1.jpg"/><lb/><emph type="italics"/>Ba&longs;e. </s> <s>That it falleth without, or in its <lb/>Ba&longs;e it is already manife&longs;t to be an ab&longs;ur­<lb/>dity. </s> <s>Let it fall within: and becau&longs;e X R <lb/>is to R O, as the in&longs;cribed Figure is to <lb/>the exce&longs;s by which the Conoid exceeds <lb/>it; the &longs;ame proportion that B R hath to <lb/>R O, the &longs;ame let the in&longs;cribed Figure <lb/>have to the Solid K: Which nece&longs;&longs;arily <lb/>&longs;hall be le&longs;&longs;er than the &longs;aid exce&longs;s. </s> <s>And let <lb/>another Figure be in&longs;cribed which may be <lb/>exceeded by the Conoid a le&longs;s quantity <lb/>than is K, who&longs;e Center of Gravity falleth betwixt O and C. </s> <s>Let it <lb/>be V. And, becau&longs;e the fir&longs;t Figure is to K as B R to R O, and the &longs;e­<lb/>cond Figure, who&longs;e Center V is greater than the fir&longs;t, and exceeded <lb/>by the Conoid a le&longs;s quantity than is K; what proportion the &longs;econd <lb/>Figure hath to the exce&longs;s by which the Conoid exceeds it, the &longs;ame <lb/>&longs;hall a Line greater than B R have to R V. </s> <s>But R is the Center of Gra­<lb/>vity of the Conoid; and the Center of the &longs;econd in&longs;cribed Figure V: <lb/>The Center therefore of the remaining proportions &longs;hall be without <lb/>the Conoid beneath B: Which is impo&longs;&longs;ible. </s> <s>And by the &longs;ame means <lb/>we might demon&longs;trate the Center of Gravity of the &longs;aid Conoid not to <lb/>be in the Line C A. </s> <s>And that it is none of the points betwixt C and <lb/>O is manife&longs;t. </s> <s>For &longs;ay, that there other Figures de&longs;cribed, greater <lb/>&longs;omething than the in&longs;cribed Figure who&longs;e Center is O, and le&longs;s than <lb/>that circum&longs;cribed Figure who&longs;e Center is C, the Center of the Conoid <lb/>would fall without the Center of the&longs;e Figures: Which but now was <lb/>concluded to be impo&longs;&longs;ible: It re&longs;ts therefore that it be betwixt the Cen­<lb/>ter of the circum&longs;cribed and in&longs;cribed Figure. </s> <s>And if &longs;o, it &longs;hall ne­<lb/>ce&longs;&longs;arily be in that point which divideth the Axis, &longs;o as that the part <lb/>towards the Vertex is double to the remainder; &longs;ince N may circum­<lb/>&longs;cribe and in&longs;cribe Figures, &longs;o, that tho&longs;e Lines which fall between<emph.end type="italics"/><pb xlink:href="040/01/950.jpg" pagenum="257"/><emph type="italics"/>their Centers and the &longs;aid points, may be le&longs;&longs;er than any other Lines. <lb/></s> <s>To expre&longs;s the &longs;ame in other terms, we have reduced it to an impo&longs;&longs;ibi­<lb/>lity, that the Center of the Conoid &longs;hould not fall betwixt the Centers of <lb/>the in&longs;cribed and circum&longs;cribed Figures.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>Suppo&longs;ing three proportional Lines, and that <lb/>what proportion the lea&longs;t hath to the exce&longs;s <lb/>by which the greate&longs;t exceeds the lea&longs;t, the <lb/>&longs;ame &longs;hould a Line given have to two thirds of <lb/>the exce&longs;s by which the greate&longs;t exceeds the <lb/>middlemo&longs;t: and moreover, that what pro­<lb/>portion that compounded of the greate&longs;t, and <lb/>of double the middlemo&longs;t, hath unto that com­<lb/>pounded of the triple of the greate&longs;t and mid­<lb/>dlemo&longs;t, the &longs;ame hath another Line given, to <lb/>the exce&longs;s by which the greate&longs;t exceeds the <lb/>middle one; both the given Lines taken toge­<lb/>ther &longs;hall be a third part of the greate&longs;t of the <lb/>proportional Lines.</s></p><p type="main"> <s><emph type="italics"/>Let A B, B C, and B F, be three proportional Lines; and what <lb/>proportion B F hath to F A, the &longs;ame let M S have to two thirds <lb/>of C A. </s> <s>And what proportion that compounded of A B and the <lb/>double of B C hath to that compounded of the triple of both A B and <lb/>B C, the &longs;ame let another, to wit S N, have to A C. </s> <s>Becau&longs;e therefore <lb/>that A B, B C, and C F,<emph.end type="italics"/><lb/><figure id="id.040.01.950.1.jpg" xlink:href="040/01/950/1.jpg"/><lb/><emph type="italics"/>are proportionals, A G <lb/>and C F &longs;hall, for the &longs;ame <lb/>rea&longs;on, be likewi&longs;e &longs;o. <lb/></s> <s>Therefore, as A B is to <lb/>B C, &longs;o is A C to C F: <lb/>and as the triple of A B is to the triple of B C, &longs;o is A C to C F: <lb/>Therefore, what proportion the triple of A B with the triple of B C <lb/>hath to the triple of C B, the &longs;ame &longs;hall A C have to a Line le&longs;s than <lb/>C F. </s> <s>Let it be C O. </s> <s>Wherefore by Compo&longs;ition and by Conver&longs;ion of <lb/>proportion, O A &longs;hall have to A C, the &longs;ame proportion, as triple A B <lb/>with Sextuple B C, hath to triple A B with triple B C. </s> <s>But A C hath <lb/>to S N the &longs;ame proportion, that triple A B with triple B C hath to A B <lb/>with double B C: Therefore,<emph.end type="italics"/> ex equali, <emph type="italics"/>O A to NS &longs;hall have the <lb/>&longs;ame proportion, as triple A B with Sexcuple B C hath to A B with<emph.end type="italics"/><pb xlink:href="040/01/951.jpg" pagenum="258"/><emph type="italics"/>double B C: But triple A B with &longs;excuple B C, are triple to A B with <lb/>double B C. </s> <s>Therefore A O is triple to S N.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Again, becau&longs;e O C is to C A as triple C B is to triple A B with tri­<lb/>ple C B: and becau&longs;e as C A is to A F, &longs;o is triple A B to triple B C: <lb/>Therefore,<emph.end type="italics"/> ex equali, <emph type="italics"/>by perturbed proportion, as O C is to C F, &longs;o &longs;hall <lb/>triple A B be to triple A B with treble B C: And, by Conver&longs;ion of <lb/>proportion, as O F is to F C, &longs;o is triple B C to triple A B with triple <lb/>B C: And as C F is to F B, &longs;o is A C to C B, and triple A C to triple <lb/>C B: Therefore,<emph.end type="italics"/> ex equali, <emph type="italics"/>by Perturbation of proportion, as O F is <lb/>to F B, &longs;o is triple A C to the triple of both A B and A C together. <lb/></s> <s>And becau&longs;e F C and C A are in the &longs;ame proportion as C B and B A; <lb/>it &longs;hall be that as F C is to C A, &longs;o &longs;hall B C be to B A. And, by Com­<lb/>po&longs;ition, as F A is to A C, &longs;o are both B A and B C to B A: and &longs;o the <lb/>triple to the triple: Therefore as F A is to A C, &longs;o the compound of tri­<lb/>ple B A and triple B C is to triple A B. Wherefore, as F A is to two <lb/>thirds of A C, &longs;o is the compound of triple B A and triple B C to two <lb/>thirds of triple B A; that is, to double B A: But as F A is to two thirds <lb/>of A C, &longs;o is F B to M S: Therefore, as F B is to M S, &longs;o is the compound <lb/>of triple B A and triple B C to double B A: But as O B is to F B, &longs;o <lb/>was Sexcuple A B to triple of both A B and B C: Therefore,<emph.end type="italics"/> ex equa­<lb/>li, <emph type="italics"/>O B &longs;hall have to M S the &longs;ame proportion as Sexcuple A B hath to <lb/>double B A. </s> <s>Wherefore M S &longs;hall be the third part of O B: And it <lb/>hath been demon&longs;trated, that S N is the third part of A O: It is mani­<lb/>fe&longs;t therefore, that MN is a third part likewi&longs;e of A B: And this is <lb/>that which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>Of any <emph type="italics"/>Fru&longs;tum<emph.end type="italics"/> or Segment cut off from a Para­<lb/>bolick Conoid the Center of Gravity is in the <lb/>Right Line that is Axis of the <emph type="italics"/>Fru&longs;tum<emph.end type="italics"/>; which <lb/>being divided into three equal parts the Cen­<lb/>ter of Gravity is in the middlemo&longs;t and &longs;o di­<lb/>vides it, as that the part towards the le&longs;&longs;er Ba&longs;e <lb/>hath to the part towards the greater Ba&longs;e, the <lb/>&longs;ame proportion that the greater Ba&longs;e hath to <lb/>the le&longs;&longs;er.</s></p><p type="main"> <s><emph type="italics"/>From the Conoid who&longs;e Axis is R B let there be cut off the Solid <lb/>who&longs;e Axis is B E; and let the cutting Plane be equidi&longs;taut to <lb/>the Ba&longs;e: and let it be cut in another Plane along the Axis erect <lb/>upon the Ba&longs;e, and let it be the Section of the Parabola V R C: R B <lb/>&longs;hall be the Diameter of the proportion, or the equidi&longs;tant Diameter<emph.end type="italics"/><pb xlink:href="040/01/952.jpg" pagenum="259"/><emph type="italics"/>L M, V C: they &longs;hall be ordinately applyed. </s> <s>Divide therefore E B in­<lb/>to three equal parts, of which let the middlemo&longs;t be Q Y: and divide <lb/>this &longs;o in the point I that Q I may have the &longs;ame proportion to I Y, as <lb/>the Ba&longs;e who&longs;e Diameter is V C hath to the Ba&longs;e who&longs;e Diameter is <lb/>L M; that is, that the Square V C hath to Square L M. </s> <s>It is to be de­<lb/>mon&longs;trated that I is the Center of Gravity of the Fru&longs;trum L M C. <lb/></s> <s>Draw the Line N S, by the by, equall to B R: and let S X be equal to <lb/>E R: and unto N S and S X a&longs;&longs;ume a third proportional S G: and as <lb/>N G is to G S, &longs;o let B Q be to I O. </s> <s>And it nothing matters whether <lb/>the point O fall above or below L M. </s> <s>And becau&longs;e in the Section V R C <lb/>the Lines L M and V C are ordinately<emph.end type="italics"/><lb/><figure id="id.040.01.952.1.jpg" xlink:href="040/01/952/1.jpg"/><lb/><emph type="italics"/>applyed, it &longs;hall be that as the Square <lb/>V C is to the Square L M, &longs;o is the Line <lb/>B R to R E: And as the Square V C is <lb/>to the Square L M, &longs;o is Q I to I Y: and <lb/>as B R is to R E, &longs;o is N S to S X: There­<lb/>fore Q I is to I Y, as R S is to S X. </s> <s>Where­<lb/>fore as G Y is to Y I, &longs;o &longs;hall both N S and <lb/>S X be to S X: and as E B is to Y I, &longs;o <lb/>&longs;hall the compound of triple N S and tri­<lb/>ple S X be to S X: But as E B is to B Y, <lb/>&longs;o is the compound of triple N S and S X <lb/>both together to the compound of N S and S X: Therefore, as E B is to <lb/>B I, &longs;o is the compound of triple N S and triple S X to the compound of <lb/>N S and double S X. </s> <s>Therefore N S, S X, and S G are three proporti­<lb/>onal Lines: And as S G is to G N, &longs;o is the a&longs;&longs;umed O I to two thirds <lb/>of E B; that is, to N X: And as the compound of N S and double <lb/>S X is to the compound of triple N S and triple S X, &longs;o is another a&longs;&longs;u­<lb/>med Line I B to B E; that is, to N X. </s> <s>By what therefore hath been <lb/>above demon&longs;trated, tho&longs;e Lines taken together are a third part of N S; <lb/>that is, of R B: Therefore R B is triple to B O: Wherefore O &longs;hall <lb/>be the Center of Gravity of the Conoid v R C. </s> <s>And let it be the Cen­<lb/>ter of Gravity of the<emph.end type="italics"/> Fru&longs;trum <emph type="italics"/>L R M of the Conoid: Therefore the <lb/>Center of Gravity of V L M C is in the Line O B, and in that point <lb/>which &longs;o terminates it, that as V L M C of the<emph.end type="italics"/> Fru&longs;trum <emph type="italics"/>is to the <lb/>proportion L R M, &longs;o is the Line A O to that which intervenes betwixt <lb/>O and the &longs;aid point. </s> <s>And becau&longs;e R O is two thirds of R B; and <lb/>R A two thirds of R E; the remaining part A O &longs;hall be two thirds <lb/>of the remaining part E B. </s> <s>And becau&longs;e that as the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>V L M C <lb/>is to the proportion L R M, &longs;o is N G to G S: and as N G to G S, &longs;o is <lb/>two thirds of E B to O I: and two thirds of E B is equal to the Line <lb/>A O: it &longs;hall be that as the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>V L M O is to the proportion <lb/>L R M, &longs;o is A O to O I. </s> <s>It is manife&longs;t therefore that of the<emph.end type="italics"/> Fru&longs;tum <lb/><emph type="italics"/>V L M C the Center of Gravity is the point I, and &longs;o divideth the Axis, <lb/>[as?] that the part towards the le&longs;&longs;er Ba&longs;e is to the part towards the grea-<emph.end type="italics"/><pb xlink:href="040/01/953.jpg" pagenum="260"/><emph type="italics"/>ter, as the double of the greater Ba&longs;e together with the Le&longs;&longs;er is to the <lb/>double of the le&longs;&longs;er together with the greater. </s> <s>Which is the Propo&longs;ition <lb/>more elegantly expre&longs;&longs;ed.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If any number of Magnitudes &longs;o di&longs;po&longs;ed to one <lb/>another, as that the &longs;econd addeth unto the fir&longs;t <lb/>the double of the fir&longs;t, the third addeth unto <lb/>the &longs;econd the triple of the fir&longs;t, the fourth <lb/>addeth unto the third the quadruple of the <lb/>fir&longs;t, and &longs;o every one of the following ones <lb/>addeth unto the next unto it the magnitude of <lb/>the fir&longs;t multiplyed according to the number <lb/>which it &longs;hall hold in order; if, I &longs;ay, the&longs;e <lb/>Magnitudes be &longs;u&longs;pended ordinarily on the <lb/>Ballance at equal di&longs;tances; the Center of the <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> of all the compounding Magni­<lb/>tudes &longs;hall &longs;o divide the Beam, as that the part <lb/>towards the le&longs;&longs;er Magnitudes is triple to the <lb/>remainder.</s></p><p type="main"> <s><emph type="italics"/>Let the Beam be L T, and let &longs;uch Magnitudes as were &longs;poken of <lb/>hang upon it; and let them be A, F, G, H, K; of which A is in <lb/>the fir&longs;t place &longs;u&longs;pended at T. </s> <s>I &longs;ay, that the Center of the<emph.end type="italics"/> Equi­<lb/>librium <emph type="italics"/>&longs;o cuts the Beam T L as that the part towards T is triple to the <lb/>re&longs;t. </s> <s>Let T L be triple to L I; and S L triple to L P: and Q L to L N,<emph.end type="italics"/><lb/><figure id="id.040.01.953.1.jpg" xlink:href="040/01/953/1.jpg"/><lb/><emph type="italics"/>and L P to L O: I P, <lb/>P N, N O, and O L <lb/>&longs;hall be equal. </s> <s>And <lb/>in F let a Magnitude <lb/>be placed double to A; <lb/>in G another trebble to <lb/>the &longs;ame; in H ano­<lb/>ther Quadruple; and <lb/>&longs;o of the re&longs;t: and let <lb/>tho&longs;e Magnitudes be <lb/>taken in which there <lb/>is A; and let the &longs;ame <lb/>be done in the Magni­<lb/>tudes F, G, H, K. </s> <s>And <lb/>becau&longs;e in F the remaining Magnitude, to wit B, is equal to A; take it<emph.end type="italics"/><pb xlink:href="040/01/954.jpg" pagenum="261"/><emph type="italics"/>double in G, triple in H, &c. </s> <s>and let tho&longs;e Magnitudes be taken in <lb/>which there is B: and in the &longs;ame manner let tho&longs;e be taken in which is <lb/>C, D, and E: now all tho&longs;e in which there is A &longs;hall be equal to K: and <lb/>the compound of all the B B &longs;hall equal H; and the compound of C C <lb/>&longs;hall equal G; and the compound of all the D D &longs;hall equal F; and <lb/>E &longs;hall equal A. </s> <s>And becau&longs;e T I is double to I L, I &longs;hall be the point <lb/>of the<emph.end type="italics"/> Equilibrium <emph type="italics"/>of the Magnitudes compo&longs;ed of all the A A: and <lb/>likewi&longs;e &longs;ince S P is double to P L, P &longs;hall be the point of the<emph.end type="italics"/> Equilibri­<lb/>um <emph type="italics"/>of the compost of B B: and for the &longs;ame cau&longs;e N &longs;hall be the point <lb/>of the<emph.end type="italics"/> Equilibrium <emph type="italics"/>of the compo&longs;t of C C: and O of the compound <lb/>of D D: and L that of E. </s> <s>Therefore T L is a Beam on which at <lb/>equal di&longs;tances certain Magnitudes K, H, G, F, A do hang. </s> <s>And again <lb/>L I is another Ballance, on which, at di&longs;tances in like manner equal, do <lb/>hang &longs;uch a number of Magnitudes, and in the &longs;ame order equal to the <lb/>former. </s> <s>For the compound of all the A A, which hang on I, is equal to <lb/>K hanging at L; and the compo&longs;t of all B B, which is &longs;u&longs;pended at P, is <lb/>equal to H hanging at P; and likewi&longs;e the compound of C C, which <lb/>hangeth at N do equal G; and the compo&longs;t of D, which hang on O, <lb/>are equal to F; and E, hanging on L, is equal to A. </s> <s>Wherefore the <lb/>Ballances are divided in the &longs;ame proportion by the Center of the com­<lb/>pounds of the Magnitudes And the Center of the compound of, the &longs;aid <lb/>Magnitudes is one. </s> <s>Therefore the common point of the Right Line T L, <lb/>and of the Right Line L I &longs;hall be the Center, which let be X. </s> <s>Therefore <lb/>as T X is to X L, &longs;o &longs;hall L X be to X I; and the whole T L to the whole <lb/>L I. </s> <s>But T L is triple to L I: Wherefore T X &longs;hall al&longs;o be triple to X L.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If any number of Magnitudes be &longs;o taken, that the <lb/>&longs;econd addeth unto the fir&longs;t the triple of the <lb/>fir&longs;t, and the third addeth unto the &longs;econd the <lb/>quintuple of the fir&longs;t, and the fourth addeth <lb/>unto the third the &longs;eptuple of the fir&longs;t, and &longs;o <lb/>the re&longs;t, every one encrea&longs;ing above the next to <lb/>it, and proceedeth &longs;till to a new multiplex of <lb/>the fir&longs;t Magnitude according to the con&longs;e­<lb/>quent odd numbers, like as the Squares of <lb/>Lines equally exceeding one another do pro­<lb/>ceed, whereof the exce&longs;s is equal to the lea&longs;t, <lb/>and if they be &longs;u&longs;pended on a Ballance at equal <lb/>Di&longs;tances, the Center of <emph type="italics"/>Equilibrium<emph.end type="italics"/> of all the <lb/>compound Magnitudes &longs;o divideth the Beam <pb xlink:href="040/01/955.jpg" pagenum="262"/>that the part towards the le&longs;&longs;er Magnitudes is <lb/>more than triple the remaining part; and al&longs;o <lb/>one may take a di&longs;tance that is to the &longs;ame le&longs;s <lb/>than triple.</s></p><p type="main"> <s><emph type="italics"/>In the Ballance B E let there be Magnitudes, &longs;uch as were &longs;poken off, <lb/>from which let there be other Magnitudes taken away that were to <lb/>one another as they were di&longs;po&longs;ed in the precedent, and let it be of <lb/>the compound of all <lb/>the A A: the re&longs;t<emph.end type="italics"/><lb/><figure id="id.040.01.955.1.jpg" xlink:href="040/01/955/1.jpg"/><lb/><emph type="italics"/>in which are C <lb/>&longs;hall be di&longs;tributed <lb/>in the &longs;ame order, <lb/>but the greate&longs;t de­<lb/>ficient. </s> <s>Let E D be <lb/>triple to D B; and <lb/>G F triple to F B. <lb/></s> <s>D &longs;hall be the Center <lb/>of the<emph.end type="italics"/> Equilibrium <lb/><emph type="italics"/>of the compound con­<lb/>&longs;i&longs;ting of all the A A; <lb/>and F that of the <lb/>compound of all the <lb/>C C. </s> <s>Wherefore the <lb/>Center of the com­<lb/>pound of both A A <lb/>and C C falleth be­<lb/>tween D and F. </s> <s>Let <lb/>it be O. </s> <s>It is there­<lb/>fore manife&longs;t that <lb/>E O is more than triple to O B; but G O le&longs;s thantriple to the <lb/>&longs;ame O B: Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><pb xlink:href="040/01/956.jpg" pagenum="263"/><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If to any Cone or portion of a Cone a Eigure con­<lb/>&longs;i&longs;ting of Cylinders of equal heights be in&longs;cri­<lb/>bed and another circum&longs;cribed; and if its Axis <lb/>be &longs;o divided as that the part which lyeth be­<lb/>twixt the point of divi&longs;ion and the Vertex be <lb/>triple to the re&longs;t; the Center of Gravity of <lb/>the in&longs;cribed Figure &longs;hall be nearer to the Ba&longs;e <lb/>of the Cone than that point of divi&longs;ion: and <lb/>the Center of Gravity of the circum&longs;cribed <lb/>&longs;hall be nearer to the Vertex than that &longs;ame <lb/>point.</s></p><p type="main"> <s><emph type="italics"/>Take therefore a Cone, who&longs;e Axis is N M. </s> <s>Let it be divided <lb/>in S &longs;o, as that N S be triple to the remainder S M. </s> <s>I &longs;ay, that <lb/>the Center of Gravity of any Figure in&longs;cribed, as was &longs;aid, in <lb/>a Cone doth con&longs;i&longs;t in the Axis N M, and approacheth nearer to the Ba&longs;e <lb/>of the Cone than the point S: and that the Center of Gravity of the <lb/>Circum&longs;cribed is likewi&longs;e in the Axis N M, and nearer to the Vertex <lb/>than is S. </s> <s>Let a Figure therefore be &longs;uppo&longs;ed to be in&longs;cribed by the Cy­<lb/>linders who&longs;e Axis M C, C B, B E, E A are equal. </s> <s>Fir&longs;t therefore <lb/>the Cylinder who&longs;e Axis is M C hath<emph.end type="italics"/><lb/><figure id="id.040.01.956.1.jpg" xlink:href="040/01/956/1.jpg"/><lb/><emph type="italics"/>to the Cylinder who&longs;e Axis is C B the <lb/>&longs;ame proportion as its Ba&longs;e hath to <lb/>the Ba&longs;e of the other (for their Alti­<lb/>tudes are equal.) But this propor­<lb/>tion is the &longs;ame with that which the <lb/>Square C N hath to the Square N B. <lb/></s> <s>And &longs;o we might prove, that the Cy­<lb/>linder who&longs;e Axis is C B hath to the <lb/>Cylinder who&longs;e Axis is B E the &longs;ame <lb/>proportion, as the Square B N hath to <lb/>the Square N E: and the Cylinder <lb/>who&longs;e Axis is B E hath to the Cylin­<lb/>der who&longs;e Axis is E A the &longs;ame pro­<lb/>portion that the Square E N hath to <lb/>the Square N A. </s> <s>But the Lines N C, <lb/>N B, E N, and N A equally exceed one <lb/>another, and their exce&longs;s equalleth the <lb/>lea&longs;t, that is N A. </s> <s>Therefore they are certain Magnitudes, to wit, in­<lb/>&longs;cribed Cylinders having con&longs;equently to one another the &longs;ame proporti­<lb/>on as the Squares of Lines that equally exceed one another, and the ex-<emph.end type="italics"/><pb xlink:href="040/01/957.jpg" pagenum="264"/><emph type="italics"/>ce&longs;s of which is equal to the lea&longs;t: and they are &longs;o di&longs;po&longs;ed on the Beam <lb/>T I that their &longs;everal Centers of Gravity con&longs;i&longs;t in it, and that at equal <lb/>di&longs;tances. </s> <s>Therefore by the things above demon&longs;trated it appeareth that <lb/>the Center of Gravity of all &longs;o compo&longs;ed Magnitudes do &longs;o divide the <lb/>Balance T I, that the part to wards T is more than triple to the remain­<lb/>der. </s> <s>Let this Center be O. </s> <s>T O therefore is more than triple to O I. <lb/></s> <s>But T N is triple to I M. </s> <s>Therefore the whole M O will be le&longs;s than a <lb/>fourth part of the whole M N, who&longs;e fourth part was &longs;uppo&longs;ed to be <lb/>M S. </s> <s>It is manife&longs;t, therefore, that the point O doth nearer approach <lb/>the Ba&longs;e of the Cone than S. </s> <s>And let the circum&longs;cribed Figure be com­<lb/>po&longs;ed of the Cylinders who&longs;e Axis M C, C B, B E, E A and A N are <lb/>equal to each other, and, like as in tho&longs;e in&longs;cribed, let them be to one <lb/>another as the Squares of the Lines M N, N C, B N, N E, A N, <lb/>which equally exceed one another, and the exce&longs;s is equal to the lea&longs;t <lb/>A N. Wherefore, by the premi&longs;es, the Center of Gravity of all the Cy­<lb/>linders &longs;o di&longs;po&longs;ed, which let be V, doth &longs;o divide the Beam R I, that the <lb/>part towards R, to wit R V, is more than triple to the remaining part <lb/>V I: but T V &longs;hall be le&longs;s than triple to the &longs;ame. </s> <s>But N T is triple to <lb/>all I M: Therefore all V M is more than the fourth part of all M N, <lb/>who&longs;e fourth part was &longs;uppo&longs;ed to be M S. </s> <s>Therefore the point V is <lb/>nearer to the Vertex than the Point S. </s> <s>Which was to be demon&longs;tra­<lb/>ted.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>About a given Cone a Figure may be circum&longs;cri­<lb/>bed and another in&longs;cribed con&longs;i&longs;ting of Cylin­<lb/>ders of equal height, &longs;o, as that the Line which <lb/>lyeth betwixt the Center of Gravity of the <lb/>circum&longs;cribed, and the Center of Gravity of <lb/>the in&longs;cribed, may be le&longs;&longs;er than any Line <lb/>given.</s></p><p type="main"> <s><emph type="italics"/>Let a Cone be given, who&longs;e Axis is A B; and let the Right Line <lb/>given be K. </s> <s>I &longs;ay; Let there be placed by the Cylinder L <lb/>equal to that in&longs;cribed in the Cone, having for its Altitude half <lb/>of the Axis A B: and let A B be divided in C, &longs;o as that A C be tri­<lb/>ple to C B: And as A C is to K, &longs;o let the Cylinder L be to the Solid X. <lb/></s> <s>And about the Cone let there be a Figure circum&longs;cribed of Cylin­<lb/>ders that have equal Altitude, and let another be in&longs;cribed, &longs;o as that <lb/>the circum&longs;cribed exceed the in&longs;cribed a le&longs;s quantity than the Solid X. <lb/></s> <s>And let the Center of Gravity of the circum&longs;cribed be E; which falls <lb/>above C: and let the Center of the in&longs;cribed be S, falling beneath C.<emph.end type="italics"/><pb xlink:href="040/01/958.jpg" pagenum="265"/><emph type="italics"/>I &longs;ay now, that the Line E S is le&longs;&longs;er than K. </s> <s>For if not, then let C A <lb/>be &longs;uppo&longs;ed equal to E O. </s> <s>Becau&longs;e therefore O E hath to K the &longs;ame <lb/>proportion that L hath to X; and the in&longs;cribed Figure is not le&longs;s than <lb/>the Cylinder L; and the exce&longs;s with which the &longs;aid Figure is exceeded <lb/>by the circum&longs;cribed is le&longs;s than the Solid X: therefore the in&longs;cribed <lb/>Figure &longs;hall have to the &longs;aid exce&longs;s<emph.end type="italics"/><lb/><figure id="id.040.01.958.1.jpg" xlink:href="040/01/958/1.jpg"/><lb/><emph type="italics"/>greater proportion than O E hath to <lb/>K: But the proportion of O E to K is <lb/>not le&longs;s than that which O E hath to <lb/>E S with E S. </s> <s>Let it not be le&longs;s than <lb/>K. </s> <s>Therefore the in&longs;cribed Figure <lb/>hath to the exce&longs;s of the circum&longs;cri­<lb/>bed Figure above it greater propor­<lb/>tion than O E hath to E S. </s> <s>Therefore <lb/>as the in&longs;cribed is to the &longs;aid exce&longs;s, <lb/>&longs;o &longs;hall it be to the Line E S. </s> <s>Let E R <lb/>be a Line greater than E O; and the <lb/>Center of Gravity of the in&longs;cribed <lb/>Figure is S; and the Center of the cir­<lb/>cum&longs;cribed is E. </s> <s>It is manife&longs;t there­<lb/>fore, that the Center of Gravity of <lb/>the remaining proportions by which <lb/>the circum&longs;cribed exceedeth the in <lb/>&longs;cribed is in the Line R E, and in that point by which it is &longs;o termina­<lb/>ted, that as the in&longs;cribed Figure is to the &longs;aid proportions, &longs;o is the Line <lb/>included betwixt E and that point to the Line E S. </s> <s>And this propor­<lb/>tion hath R E to E S. </s> <s>Therefore the Center of Gravity of the remain­<lb/>ing proportions with which the circum&longs;cribed Figure exceeds the in­<lb/>&longs;cribed &longs;hall be R, which is impo&longs;&longs;ible. </s> <s>For the Plane drawn thorow <lb/>R equidi&longs;tant to the Ba&longs;e of the Cone doth not cut tho&longs;e proportions. </s> <s>It <lb/>is therefore fal&longs;e that the Line E S is not le&longs;&longs;er than K. </s> <s>It &longs;hall therefore <lb/>be le&longs;s. </s> <s>The &longs;ame al&longs;o may be done in a manner not unlike this in Pyra­<lb/>mides, as ne could demon&longs;trate.<emph.end type="italics"/></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it is manife&longs;t, that a given Cone may circum&longs;cribe one <lb/>Figure and in&longs;cribe another con&longs;i&longs;ting of Cylinders of equal <lb/>Altitudes &longs;o, as that the Lines which are intercepted betwixt <lb/>their Centers of Gravity and the point which &longs;o divides the <lb/>Axis of the Cone, as that the part towards the Vertex is tri­<lb/>ple to the le&longs;t, are le&longs;s than any given Line.</s></p><p type="main"> <s><emph type="italics"/>For, &longs;ince it hath been demon&longs;trated, that the &longs;aid point dividing the <lb/>Axis, as was &longs;aid, is alwaies found betwixt the Centers of Gravity<emph.end type="italics"/><pb xlink:href="040/01/959.jpg" pagenum="266"/><emph type="italics"/>of the Circum&longs;cribed and in&longs;cribed Figures: and that it's po&longs;&longs;ible, that <lb/>there be a Line in the middle betwixt tho&longs;e Centers that is le&longs;s than any <lb/>Line a&longs;&longs;igned; it followeth that the &longs;ame given Line be much le&longs;s that <lb/>lyeth betwixt one of the &longs;aid Centers and the &longs;aid point that divides <lb/>the Axis.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity divideth the Axis of any <lb/>Cone or Pyramid &longs;o, that the part next the <lb/>Vertex is triple to the remainder.</s></p><p type="main"> <s><emph type="italics"/>Let there be a Cone who&longs;e Axis is A B. </s> <s>And in C let it be divided, <lb/>&longs;o that A C be triple to the remaining part C B. </s> <s>It is to be proved, <lb/>that C is the Center of Gravity of the Cone. </s> <s>For if it be not, the <lb/>Cone's Center &longs;hall be either above or below the point C. </s> <s>Let it be fir&longs;t <lb/>beneath, and let it be E. </s> <s>And draw the Line L P, by it &longs;elf, equal to <lb/>C E; which divided at plea&longs;ure in N. </s> <s>And as both B E and P N to­<lb/>gether are to P N, &longs;o let the Cone be to the Solid X: and in&longs;cribe in the <lb/>Cone a Solid Figure of Cylinders that have equal Ba&longs;es, who&longs;e Center <lb/>of Gravity is le&longs;s di&longs;tant from the point C than is the Line L N, and <lb/>the exce&longs;s of the Cone above it le&longs;s than the Solid X. </s> <s>And that this <lb/>may be done is manife&longs;t from what hath been already demon&longs;trated. <lb/></s> <s>Now let the in&longs;cribed Figure be &longs;uch as<emph.end type="italics"/><lb/><figure id="id.040.01.959.1.jpg" xlink:href="040/01/959/1.jpg"/><lb/><emph type="italics"/>was required, who&longs;e Center of Gravity <lb/>let be I. </s> <s>The Line I E therefore &longs;hall be <lb/>greater than N P together with L P. </s> <s>Let <lb/>C E and I C le&longs;s L N be equal: And be­<lb/>cau&longs;e both together B E and N P is to N P <lb/>as the Cone to X: and the exce&longs;s by which <lb/>the Cone exceeds the in&longs;cribed Figure is <lb/>le&longs;s than the Solid X: Therefore the Cone <lb/>&longs;hall have greater proportion to the &longs;aid <lb/>X S than both B E and N P to N P: and, by <lb/>Divi&longs;ion, the in&longs;cribed Figure &longs;hall have <lb/>greater proportion to the exce&longs;s by which <lb/>the Cone exceeds it, than B E to N P: But B E hath le&longs;s proportion to <lb/>E I than to N P with I E. </s> <s>Let N P be greater. </s> <s>Then the in&longs;cribed Fi­<lb/>gure hath to the exce&longs;s of the Cone above it much greater proportion <lb/>than B E to E I. </s> <s>Therefore as the in&longs;cribed Figure is to the &longs;aid exce&longs;s, <lb/>&longs;o &longs;hall a Line bigger than B E be to E I. </s> <s>Let that Line be M E. Becau&longs;e, <lb/>therefore, M E is to E I as the in&longs;cribed Figure is to the exce&longs;s of the <lb/>Cone above the &longs;aid Figure, and D is the Center of Gravity of the <lb/>Cone, and I the Center of Gravity of the in&longs;cribed Figure: Therefore<emph.end type="italics"/><pb xlink:href="040/01/960.jpg" pagenum="267"/><emph type="italics"/>M &longs;hall be the Center of Gravity of the remaining proportions by which <lb/>the Cone exceeds the in&longs;cribed Figure. </s> <s>Which is impo&longs;&longs;ible. </s> <s>Therefore <lb/>the Center of Gravity of the Cone is not below the point C. </s> <s>Nor is it <lb/>above it. </s> <s>For if it may be, let it be R. </s> <s>And again a&longs;&longs;ume L P cut at <lb/>plea&longs;ure in N: And as both B C and N P together are to N L, &longs;o let the <lb/>Cone be to X. </s> <s>And let a Figure be, in like manner, circum&longs;cribed about <lb/>the Cone, which exceeds the &longs;aid Cone a le&longs;s quantity than the Solid X. <lb/></s> <s>And let the Line which intercepts bet wixt its Center of Gravity and C, <lb/>be le&longs;&longs;er than N P. </s> <s>Now take the circum&longs;cribed Figure, who&longs;e Center <lb/>let be O; the remainder O R &longs;hall be greater than the &longs;aid N L. </s> <s>And <lb/>becau&longs;e, as both together B C and P N is to N L, &longs;o is the Cone to X: <lb/>And the exce&longs;s by which the circum&longs;cribed exceeds the Cone is le&longs;&longs;er <lb/>than X: And B O is le&longs;&longs;er than B C and P N together: And O R grea­<lb/>ter than L N: The Cone therefore &longs;hall have much greater proportion to <lb/>the remaining proportions by which it was exceeded by the circum&longs;cribed <lb/>Figure, than B O to O R. </s> <s>Let it be as M O is to O R. </s> <s>M O &longs;hall <lb/>be greater than B C; and M &longs;hall be the Center of Gravity of the pro­<lb/>portions by which the Cone is exceeded by the circum&longs;cribed Figure. <lb/></s> <s>Which is inconvenient. </s> <s>Therefore the Center of Gravity of the Cone is <lb/>not above the point C. </s> <s>But neither is it below it; as hath been proved. <lb/></s> <s>Therefore it &longs;hall be C it &longs;elf. </s> <s>And &longs;o in like manner may it be demon­<lb/>&longs;trated in any Pyramid.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If there were four Lines continual proportionals; <lb/>and as the lea&longs;t of them were to the exce&longs;s by <lb/>which the greate&longs;t exceeds the lea&longs;t, &longs;o a Line <lb/>taken at plea&longs;ure &longs;hould be to 3/4 the exce&longs;s by <lb/>which the greate&longs;t exceeds the &longs;econd; and as <lb/>the Line equal to the&longs;e (<emph type="italics"/>viz.<emph.end type="italics"/> to the greate&longs;t, <lb/>double of the &longs;econd, and triple of the third) <lb/>is to the Line equal to the quadruple of the <lb/>fourth, the quadruple of the &longs;econd, and the <lb/>quadruple of the third, &longs;o &longs;hould another Line <lb/>taken be to the exce&longs;s of the greate&longs;t above the <lb/>&longs;econd: the&longs;e two Lines taken together &longs;hall <lb/>be a fourth part of the greate&longs;t of the propor­<lb/>tionals.</s></p><pb xlink:href="040/01/961.jpg" pagenum="268"/><p type="main"> <s><emph type="italics"/>For let A B, B C, B D, and B E be four proportional Lines. </s> <s>And <lb/>as B E is to E A, &longs;o let F G be to 3/4 of A C. </s> <s>And as the Line equal <lb/>to A B and to double B C and to triple B D is to the Line equal <lb/>to the quadruples of A B, B C, and B D, &longs;o let H G be to A C. </s> <s>It is <lb/>to be proved, that H F is a fourth part of A B. </s> <s>Fora&longs;much therefore <lb/>as A B, B C, B D, and B E<emph.end type="italics"/><lb/><figure id="id.040.01.961.1.jpg" xlink:href="040/01/961/1.jpg"/><lb/><emph type="italics"/>are proportionals, A C, <lb/>C D, and D E &longs;hall be in <lb/>the &longs;ame proportion: And <lb/>as the quadruple of the &longs;aid <lb/>A B, B C, and B D is to <lb/>A B with the double of B C and triple of B D, &longs;o is the quadruple of <lb/>A C, C D, and D E; that is, the quadruple of A E; to A C with the <lb/>double of C D, and triple of D E. </s> <s>And &longs;o is A C to H G. </s> <s>Therefore <lb/>as the triple of A E is to A C, with the double of C D and triple of <lb/>D E, &longs;o is 3/4 of A C to H G. </s> <s>And as the triple of A E is to the triple of <lb/>E B, &longs;o is 3/4 A C to G F: Therefore, by the Conver&longs;e of the twenty <lb/>fourth of the fifth, As triple A E is to A C with double C D and tri­<lb/>ple D B, &longs;o is 3/4 of A C to H F: And as the quadruple of A E is to A C <lb/>with the double of C D and triple of D B; that is, to A B with C B and <lb/>B D, &longs;o is A C to H F. And, by Permutation, as the quadruple of A E <lb/>is to A C, &longs;o is A B with C B and B D to H F. </s> <s>And as A C is to A E, &longs;o <lb/>is A B to A B with C B and B D. Therefore,<emph.end type="italics"/> ex æquali, <emph type="italics"/>by Perturbed <lb/>proportion, as quadruple A E is to A E, &longs;o is A B to H F. </s> <s>Wherefore it <lb/>is manife&longs;t that H F is the fourth part of A B.<emph.end type="italics"/></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity of the <emph type="italics"/>Fru&longs;tum<emph.end type="italics"/> of any Py­<lb/>ramid or Cone, cut equidi&longs;tant to the Plane <lb/>of the Ba&longs;e, is in the Axis, and doth &longs;o divide <lb/>the &longs;ame, that the part towards the le&longs;&longs;er Ba&longs;e <lb/>is to the remainder, as the triple of the greater <lb/>Ba&longs;e, with the double of the mean Space be­<lb/>twixt the greater and le&longs;&longs;er Ba&longs;e, together <lb/>with the le&longs;&longs;er Ba&longs;e is to the triple of the le&longs;&longs;er <lb/>Ba&longs;e, together with the &longs;ame double of the <lb/>mean Space, as al&longs;o of the greater Ba&longs;e.</s></p><pb xlink:href="040/01/962.jpg" pagenum="269"/><p type="main"> <s><emph type="italics"/>From a Cone or Pyramid who&longs;e Axis is A D, and equidi&longs;tant to <lb/>the Plane of the Ba&longs;e, let a<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>be cut who&longs;e Axis is V D. <lb/></s> <s>And as the triple of the greate&longs;t Ba&longs;e with the double of the <lb/>mean and lea&longs;t is to the triple of the lea&longs;t and double of the mean and <lb/>greate&longs;t, &longs;o is \ O to O D. </s> <s>It is to be proved that the Center of Gra­<lb/>vity of the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>is in O. </s> <s>Let V M be the fourth part of V D. <lb/></s> <s>Set the Line H X by the by, equal to A D: and let K X be equal to A V: <lb/>and unto H X K let X L be a third proportional, and X S a fourth. <lb/></s> <s>And as H S is to S X, &longs;o let M D be to the Line taken from O towards <lb/>A: which let be O N. </s> <s>And becau&longs;e the greater Ba&longs;e is in proportion <lb/>to that which is mean betwixt the <lb/>greater and le&longs;&longs;er as D A to A V; that<emph.end type="italics"/><lb/><figure id="id.040.01.962.1.jpg" xlink:href="040/01/962/1.jpg"/><lb/><emph type="italics"/>is, as H X, to X K, but the &longs;aid <lb/>mean is to the lea&longs;t as K X to X L; <lb/>the greater, mean, and le&longs;&longs;er Ba&longs;es <lb/>&longs;hall be in the &longs;ame proportion as <lb/>H X, X K, and X L. </s> <s>Wherefore as <lb/>triple the greater Ba&longs;e, with double <lb/>the mean and le&longs;&longs;er, is to triple the <lb/>lea&longs;t with double the mean and grea­<lb/>te&longs;t; that is, as V O is to O D; &longs;o is <lb/>triple H X with double X K and X L <lb/>to triple X L, with double X K and <lb/>X H: And by Compo&longs;ition and Converting the proportion, O D &longs;hall <lb/>be to V D, as H X, with double X K and triple X L, to quadruple H X, <lb/>X K, and X L. </s> <s>There are, therefore, four proportional Lines, H X, <lb/>X K, X L, and X S: And as X S is to S H, &longs;o is the Line taken N O <lb/>to 3/4 of D V, to wit, to D M; that is, to 3/4 of H K: And as H X <lb/>with double X K and triple X L is to quadruple H X, X K and X L; <lb/>&longs;o is another Line taken O D to D V; that is, to H K. Therefore, by <lb/>the things demon&longs;trated, D N &longs;hall be the fourth part of H X; that <lb/>is, of A D. </s> <s>Wherefore the point N &longs;hall be the Center of Gravity <lb/>of the Cone or Pyramid who&longs;e Axis is A D. </s> <s>Let the Center of Gra­<lb/>vity of the Pyramid or Cone who&longs;e Axis is A V be I. </s> <s>It is therefore <lb/>manife&longs;t that the Center of Gravity of the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>is in the Line <lb/>I N inclining towards the part N, and in that point of it which with <lb/>the point N include a Line to which I M hath the &longs;ame proportion that <lb/>the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>cut hath to the Pyramid or Cone who&longs;e Axis is A V. <lb/></s> <s>It remaineth therefore to prove that I N hath the &longs;ame proportion <lb/>to N O, that the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>hath to the Cone who&longs;e Axis is A V. </s> <s>But <lb/>as the Cone who&longs;e Axis is D A is to the Cone who&longs;e Axis is A V, &longs;o <lb/>is the Cube D A to the Cube D V; that is, the Cube H X to the <lb/>Cube X K: But this is the &longs;ame proportion that H X hath to X S. <lb/>Wherefore, by Divi&longs;ion, as H S is to S X, &longs;o &longs;hall the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>who&longs;e<emph.end type="italics"/><pb xlink:href="040/01/963.jpg" pagenum="270"/><emph type="italics"/>Axis is D V be to the Cone or Pyramid who&longs;e Axis is V A. </s> <s>And as <lb/>H S is to S X, &longs;o al&longs;o is M D to O N. </s> <s>Wherefore the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>is to the <lb/>Pyramid who&longs;e Axis is A V, as M D to N O. </s> <s>And becau&longs;e A N <lb/>is 3/4 of A D; and A I is 3/4 of A V; the remainder I N &longs;hall be 3/4 of the <lb/>remainder V D. </s> <s>Wherefore I N &longs;hall be equal to M D. <lb/></s> <s>And it hath been demon&longs;trated that M D is to N O, <lb/>as the<emph.end type="italics"/> Fru&longs;tum <emph type="italics"/>to the Cone A V. </s> <s>It is mani­<lb/>fe&longs;t, therefore, that I N hath likewi&longs;e <lb/>the &longs;ame proportion to N O: <lb/>Wherefore the Propo­<lb/>&longs;ition is manife&longs;t.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>FINIS.<emph.end type="italics"/><lb/></s></p> </chap> <pb xlink:href="040/01/964.jpg"/><chap> <pb xlink:href="040/01/965.jpg" pagenum="271"/><p type="head"> <s>GALILEUS, <lb/>HIS <lb/>MECHANICKS: <lb/>OF THE BENEFIT DERIVED <lb/>FROM THE SCIENCE OF MECHANICKS, <lb/>AND FROM ITS INSTRUMENTS.</s></p> </chap> <chap> <p type="main"> <s>I judged it extreamly nece&longs;&longs;ary, before our <lb/>de&longs;cending to the Speculation of Mecha­<lb/>nick In&longs;truments, to con&longs;ider how I might, <lb/>as it were, &longs;et before your eyes in a gene­<lb/>ral Di&longs;cour&longs;e, the many benefits that are <lb/>derived from the &longs;aid In&longs;truments: and <lb/>this I have thought my &longs;elf the more ob­<lb/>liged to do, for that (if I am not mi&longs;taken) <lb/>I have &longs;een the generality of <emph type="italics"/>M<emph.end type="italics"/>echaniti­<lb/>ans deceive them&longs;elves in going about to apply Machines to many <lb/>operations of their own nature impo&longs;&longs;ible; by the &longs;ucce&longs;&longs;e where­<lb/>of they have been di&longs;appointed, and others likewi&longs;e fru&longs;trate of <lb/>the hope which they had conceived upon the promi&longs;e of tho&longs;e pre­<lb/>&longs;umptuous undertakers: of which mi&longs;takes I think I have found <lb/>the principall cau&longs;e to be the belief and con&longs;tant opinion the&longs;e <pb xlink:href="040/01/966.jpg" pagenum="272"/>Artificers had, and &longs;till have, that they are able with a &longs;mall force <lb/>to move and rai&longs;e great weights; (in a certain manner with their <lb/>Machines cozening nature, who&longs;e In&longs;tinct, yea mo&longs;t po&longs;itive con­<lb/>&longs;titution it is, that no Re&longs;i&longs;tance can be overcome, but by a Force <lb/>more potent then it:) which conjecture how fal&longs;e it is, I hope by <lb/>the en&longs;uing true and nece&longs;&longs;ary Demon&longs;trations to evince.</s></p><p type="main"> <s>In the mean time, &longs;ince I have hinted, that the benefit and help <lb/>derived from Machines is not, to be able with le&longs;&longs;e Force, by help <lb/>of the Machine to move tho&longs;e weights, which, without it, could <lb/>not be moved by the &longs;ame Force: it would not be be&longs;ides the <lb/>purpo&longs;e to declare what the Commodities be which are derived to <lb/>us from &longs;uch like faculties, for if no profit were to be hoped for, <lb/>all endeavours employed in the acqui&longs;t thereof will be but lo&longs;t <lb/>labour.</s></p><p type="main"> <s>Proceeding therefore according to the nature of the&longs;e Studies, <lb/>let us fir&longs;t propo&longs;e four things to be con&longs;idered. </s> <s>Fir&longs;t, the weight <lb/>to be transferred from place to place; and &longs;econdly, the Force <lb/>and Power which &longs;hould move it; thirdly, the Di&longs;tance between <lb/>the one and the other Term of the Motion; Fourthly, the Time <lb/>in which that mutation is to be made: which Time becometh the <lb/>&longs;ame thing with the Dexterity, and Velocity of the Motion; we <lb/>determining that Motion to be more &longs;wift then another, which in <lb/>le&longs;&longs;e Time pa&longs;&longs;eth an equal Di&longs;tance.</s></p><p type="main"> <s>Now, any determinate Re&longs;i&longs;tance and limited Force what&longs;oever <lb/>being a&longs;&longs;igned, and any Di&longs;tance given, there is no doubt to be <lb/>made, but that the given Force may carry the given Weight to the <lb/>determinate Di&longs;tance; for, although the Force were extream <lb/>&longs;mall, yet, by dividing the Weight into many &longs;mall parts, none <lb/>of which remain &longs;uperiour to the Force, and by transferring them <lb/>one by one, it &longs;hall at la&longs;t have carried the whole Weight to the <lb/>a&longs;&longs;igned Term: and yet one cannot at the end of the Work with <lb/>Rea&longs;on &longs;ay, that that great Weight hath been moved, and tran&longs;­<lb/>ported by a Force le&longs;&longs;e then it &longs;elf, howbeit indeed it was done <lb/>by a Force, that many times reiterated that Motion, and that <lb/>Space, which &longs;hall have been mea&longs;ured but only once by the whole <lb/>Weight. </s> <s>From whence it appears, that the Velocity of the Force <lb/>hath been as many times Superiour to the Re&longs;i&longs;tance of the weight, <lb/>as the &longs;aid Weight was &longs;uperiour to the Force; for that in the <lb/>&longs;ame Time that the moving Force hath many times mea&longs;ured the <lb/>intervall between the Terms of the Motion, the &longs;aid Moveable <lb/>happens to have pa&longs;t it onely once: nor therefore ought we to <lb/>affirm a great Re&longs;i&longs;tance to have been overcome by a &longs;mall Force, <lb/>contrary to the con&longs;titution of Nature. </s> <s>Then onely may we &longs;ay <lb/>the Natural Con&longs;titution is overcome, when the le&longs;&longs;er Force tran&longs;­<lb/>fers the greater Re&longs;i&longs;tance, with a Velocity of Motion like to that <pb xlink:href="040/01/967.jpg" pagenum="273"/>wherewith it &longs;elf doth move; which we affirm ab&longs;olutely to be <lb/>impo&longs;&longs;ible to be done with any Machine imaginable. </s> <s>But becau&longs;e <lb/>it may &longs;ometimes come to pa&longs;&longs;e, that having but little Force, it is <lb/>required to move a great Weight all at once, without dividing it <lb/>in pieces, on this occa&longs;ion it will be necei&longs;ary to have recour&longs;e to <lb/>the Machine, by means whereof the propo&longs;ed Weight may be <lb/>transferred to the a&longs;&longs;igned Space by the Force given. </s> <s>But yet <lb/>this doth not hinder, but that the &longs;ame Force is to move, mea&longs;uring <lb/>that &longs;ame Space, or another equall to it, as many &longs;everall times as <lb/>it is exceeded by the &longs;aid Weight. </s> <s>So that in the end of the a­<lb/>ction we &longs;hall &longs;ind that we have received from the Machine no <lb/>other benefit tnen only that of tran&longs;porting the &longs;aid Weight with <lb/>the given Force to the Term given, all at once. </s> <s>Which Weight, <lb/>being divided into parts, would without any Machine have been <lb/>carried by the &longs;ame Force, in the &longs;ame Time, through the &longs;ame <lb/>Intervall. </s> <s>And this ought to pa&longs;&longs;e for one of the benefits taken <lb/>from the Mechanicks: for indeed it frequently happens, that be­<lb/>ing &longs;canted in Force but not Time, we are put upon moving great <lb/>Weights unitedly or in gro&longs;&longs;e: but he that &longs;hould hope, and at­<lb/>tempt to do the &longs;ame by the help of Machines without increa&longs;e of <lb/>Tardity in the Moveable, would certainly be deceived, and would <lb/>declare his ignorance of the u&longs;e of Mechanick In&longs;truments, and <lb/>the rea&longs;on of their effects.</s></p><p type="main"> <s>Another benefit is drawn from the In&longs;truments, which depend­<lb/>eth on the place wherein the operation is to be made: for all In­<lb/>&longs;truments cannot be made u&longs;e of in all places with equall conve­<lb/>nience. </s> <s>And &longs;o we &longs;ee (to explain our &longs;elves by an example) that <lb/>for drawing of Water out of a Well, we make u&longs;e of onely a <lb/>Rope and a Bucket fitted to receive and hold Water, wherewith <lb/>we draw up a determinate quantity of Water, in a certain Time, <lb/>with our limited &longs;trength: and he that &longs;hould think he could with <lb/>a Machine of what&longs;oever Force, with the &longs;ame &longs;trength, and in <lb/>the &longs;ame Time, take up a great quantity of Water, is in a gro&longs;&longs;e <lb/>Errour. </s> <s>And he &longs;hall find him&longs;elf &longs;o much the more deceived, <lb/>the more he &longs;hall vary and multiply his Inventions: Yet never­<lb/>thele&longs;&longs;e we &longs;ee Water drawn up with other Engines, as with a Pump <lb/>that drinks up Water in the Hold of Ships; where you mu&longs;t note <lb/>that the Pump was not imployed in tho&longs;e Offices, for that it draws <lb/>up more Water in the &longs;ame Time, and with the &longs;ame &longs;trength <lb/>then that which a bare Bucket would do, but becau&longs;e in that place <lb/>the u&longs;e of the Bucket or any &longs;uch like Ve&longs;&longs;el could not effect what <lb/>is de&longs;ired, namely to keep the Hold of the Ship quite dry from e­<lb/>very little quantity of Water; which the Bucket cannot do, for <lb/>that it cannot dimerge and dive, where there is not a con&longs;iderable <lb/>depth of Water. </s> <s>And thus we &longs;ee the Holds of Ships by the <pb xlink:href="040/01/968.jpg" pagenum="274"/>&longs;aid In&longs;trument kept dry, when Water cannot but onely oblique­<lb/>ly be drawn up, which the ordinary u&longs;e of the Bucket would not <lb/>effect, which ri&longs;eth and de&longs;cends with its Rope perpendicu­<lb/>larly.</s></p><p type="main"> <s>The third is a greater benefit, haply, then all the re&longs;t that are <lb/>derived from Mechanick In&longs;truments, and re&longs;pects the a&longs;&longs;i&longs;tance <lb/>which is borrowed of &longs;ome Force exanimate, as of the &longs;tream of a <lb/>River, or el&longs;e animate, but of le&longs;&longs;e expence by far, then that which <lb/>would be nece&longs;&longs;ary for maintaining humane &longs;trength: as when to <lb/>turn Mills, we make u&longs;e of the Current of a River, or the &longs;trength <lb/>of a Hor&longs;e, to effect that, which would require the &longs;trength of five <lb/>or fix Men. </s> <s>And this we may al&longs;o advantage our &longs;elves in rai&longs;ing <lb/>Water, or making other violent Motions, which mu&longs;t have been <lb/>done by Men, if there were no other helps; becau&longs;e with one &longs;ole <lb/>Ve&longs;&longs;el we may take Water, and rai&longs;e, and empty it where occa&longs;ion <lb/>requires; but becau&longs;e the Hor&longs;e, or &longs;uch other Mover wanteth <lb/>Rea&longs;on, and tho&longs;e In&longs;truments which are requi&longs;ite for holding and <lb/>emptying the Ve&longs;&longs;el in due time, returning again to fill it, and one­<lb/>ly is endued with Force, therefore it's nece&longs;&longs;ary that the Mecha­<lb/>nitian &longs;upply the naturall defect of that Mover, furni&longs;hing it with <lb/>&longs;uch devices and inventions, that with the &longs;ole application of it's <lb/>Force the defired effect may follow. </s> <s>And therein is very great <lb/>advantage, not becau&longs;e that a Wheel or other Machine can enable <lb/>one to tran&longs;port the &longs;ame Weight with le&longs;&longs;e Force, and greater <lb/>Dexterity, or a greater Space than an equall Force, without tho&longs;e <lb/>In&longs;truments, but having Judgment and proper Organs, could have <lb/>done; but becau&longs;e that the &longs;tream of a River co&longs;teth little or <lb/>nothing, and the charge of keeping of an Hor&longs;e or other Bea&longs;t, <lb/>who&longs;e &longs;trength is greater then that of eight, or it may be more <lb/>Men, is far le&longs;&longs;e then what &longs;o many Men would be kept <lb/>for.</s></p><p type="main"> <s>The&longs;e then are the benefits that may be derived from Mecha­<lb/>nick In&longs;truments, and not tho&longs;e which ignorant Engineers dream <lb/>of, to their own di&longs;grace, and the abu&longs;e of &longs;o many Princes, <lb/>whil&longs;t they undertake impo&longs;&longs;ible enterprizes; of which, both <lb/>by the little which hath been hinted, and by the much which <lb/>&longs;hall be demon&longs;trated in the Progre&longs;&longs;e of this Treati&longs;e, we &longs;hall <lb/>come to a&longs;&longs;ure our &longs;elves, if we attentively heed that which &longs;hall <lb/>be &longs;poken.</s></p><pb xlink:href="040/01/969.jpg" pagenum="275"/><p type="head"> <s>DEFINITIONS.</s></p><p type="main"> <s>That which in all Demon&longs;trative Sciences is nece&longs;&longs;ary to be <lb/>ob&longs;erved, we ought al&longs;o to follow in this Di&longs;cour&longs;e, that is; <lb/>to propound the Definitions of the proper Terms of this <lb/>Art, and the primary Suppo&longs;itions, from which, as from &longs;eeds full <lb/>of fecundity, may of con&longs;equence &longs;pring and re&longs;ult the cau&longs;es, <lb/>and true Demon&longs;trations, of the Nature of all the Mechanick <lb/>Engines which are u&longs;ed, for the mo&longs;t part about the Motions of <lb/>Grave Matters, therefore we will determine, fir&longs;t, what is <emph type="italics"/>GRA­<lb/>VITIE.<emph.end type="italics"/></s></p><p type="main"> <s>We call <emph type="italics"/>GRAVITIE<emph.end type="italics"/> then, That propen&longs;ion of moving <lb/>naturally downwards, which is found in &longs;olid Bodies, cau&longs;ed by <lb/>the greater or le&longs;&longs;e quantity of matter, whereof they are con&longs;ti­<lb/>tuted.</s></p><p type="main"> <s><emph type="italics"/>MOMENT<emph.end type="italics"/> is the propen&longs;ion of de&longs;cending, cau&longs;ed not &longs;o <lb/>much by the Gravity of the moveable, as by the di&longs;po&longs;ure which <lb/>divers Grave Bodies have in relation to one another; by means of <lb/>whichMoment, we oft &longs;ee a Body le&longs;s Grave counterpoi&longs;e another <lb/>of greater Gravity: as in the Stiliard, a great Weight is rai&longs;ed by <lb/>a very &longs;mall counterpoi&longs;e, not through exce&longs;s of Gravity, but <lb/>through the remotene&longs;&longs;e from the point whereby the Beam is up­<lb/>held, which conjoyned to the Gravity of the le&longs;&longs;er weight adds <lb/>thereunto Moment, and <emph type="italics"/>Impetus<emph.end type="italics"/> of de&longs;cending, wherewith the <lb/>Moment of the other greater Gravity may be exceeded. <emph type="italics"/>MO­<lb/>MENT<emph.end type="italics"/> then is that IMPETUS of de&longs;cending, compounded <lb/>of Gravity, Po&longs;ition, and the like, whereby that propenfion may <lb/>be occa&longs;ioned</s></p><p type="main"> <s>The <emph type="italics"/>CENTER<emph.end type="italics"/> of <emph type="italics"/>GRAVITY<emph.end type="italics"/> we define to be that point <lb/>in every Grave Body, about which con&longs;i&longs;t parts of equall Moment: <lb/>&longs;o that, imagining &longs;ome Grave Body to be &longs;u&longs;pended and &longs;u&longs;tain­<lb/>ed by the &longs;aid point, the parts on the right hand will Equilibrate <lb/>tho&longs;e on the left, the Anteriour, the Po&longs;teriour, and tho&longs;e above <lb/>tho&longs;e below; &longs;o that be it in any what&longs;oever fite, and po&longs;ition, <lb/>provided it be &longs;u&longs;pended by the &longs;aid <emph type="italics"/>CENTER,<emph.end type="italics"/> it &longs;hall &longs;tand <lb/>&longs;till: and this is that point which would gladly unite with the <lb/>univer&longs;all Center of Grave Bodies, namely withthat of the Earth, <lb/>if it might thorow &longs;ome free <emph type="italics"/>Medium<emph.end type="italics"/> de&longs;cend thither. </s> <s>From <lb/>whence we take the&longs;e Suppo&longs;itions.</s></p><pb xlink:href="040/01/970.jpg" pagenum="276"/><p type="head"> <s>SUPPOSITIONS.</s></p><p type="main"> <s>Any Grave Body, (as to what belongeth to it's proper ver­<lb/>tue) moveth downwards, &longs;o that the Center of it's Gravity <lb/>never &longs;trayeth out of that Right Line which is produced <lb/>from the &longs;aid Center placed in the fir&longs;t Term of the Motion unto <lb/>the univer&longs;al Center of Grave Bodies. </s> <s>Which is a Suppo&longs;ition <lb/>very manife&longs;t, becau&longs;e that &longs;ingle Center being obliged to endea­<lb/>vour to unite with the common Center, it's nece&longs;&longs;ary, unle&longs;&longs;e &longs;ome <lb/>impediment intervene, that it go &longs;eeking it by the &longs;horte&longs;t Line, <lb/>which is the Right alone: And from hence may we &longs;econdarily <lb/>&longs;uppo&longs;e</s></p><p type="main"> <s>Every Grave Body putteth the greate&longs;t &longs;tre&longs;&longs;e, and weigheth <lb/>mo&longs;t on the Center of it's Gravity, and to it, as to its proper &longs;eat, <lb/>all <emph type="italics"/>Impetus,<emph.end type="italics"/> all Pondero&longs;ity, and, in &longs;ome, all Moment hath re­<lb/>cour&longs;e.</s></p><p type="main"> <s>We la&longs;tly &longs;uppo&longs;e the Center of the Gravity of two Bodies e­<lb/>qually Grave to be in the mid&longs;t of that Right Line which conjoyns <lb/>the &longs;aid two Centers; or that two equall weights, &longs;u&longs;pended in <lb/>equall di&longs;tence, &longs;hall have the point of <emph type="italics"/>Equilibrium<emph.end type="italics"/> in the common <lb/>Center, or meeting of tho&longs;e equal Di&longs;tances. </s> <s>As for Example, <lb/>the Di&longs;tance C E being equall to the Di&longs;tance E D, and there be­<lb/>ing by them two equall weights &longs;u&longs;pended, A and B, we &longs;uppo&longs;e <lb/>the point of <emph type="italics"/>Equilibrium<emph.end type="italics"/> to be in the point E, there being no <lb/>greater rea&longs;on for inclining to <lb/>one, then to the other part. </s> <s>But <lb/><figure id="id.040.01.970.1.jpg" xlink:href="040/01/970/1.jpg"/><lb/>here is to be noted, that the Di­<lb/>&longs;tances ought to be mea&longs;ured <lb/>with Perpendicular Lines, which <lb/>from the point of Su&longs;pen&longs;ion E, <lb/>fall on the Right Lines, that from <lb/>the Center of the Gravity of the <lb/>Weights A and B, are drawn to <lb/>the common Center of things <lb/>Grave; and therefore if the Di&longs;tance E D were tran&longs;ported into <lb/>E F, the weight B would not counterpoi&longs;e the weight A, becau&longs;e <lb/>drawing from the Centers of Gravity two Right Lines to the Cen­<lb/>ter of the Earth, we &longs;hall &longs;ee that which cometh from the Center <lb/>of the Weight I, to be nearer to the Center E, then the other <lb/>produced from the Center of the weight A. </s> <s>Therefore our &longs;aying <lb/>that equal Weights are &longs;u&longs;pended by [or at] equal Di&longs;tances, is <lb/>to be under&longs;tood to be meant when as the Right Lines that go from <lb/>their Centers & to &longs;eek out the common Center of Gravity, &longs;hall be <lb/>equidi&longs;ta nt from that Right Line, which is produced from the &longs;aid <pb xlink:href="040/01/971.jpg" pagenum="277"/>Term of tho&longs;e Di&longs;tances, that is from the point of Su&longs;pen&longs;ion, to <lb/>the &longs;ame Center of the Earrh.</s></p><p type="main"> <s>The&longs;e things determined and &longs;uppo&longs;ed, we come to the explica­<lb/>tion of a Principle, the mo&longs;t common and materiall of the greater <lb/>part of Mechanick In&longs;truments: demon&longs;trating, that unequall <lb/>Weights weigh equally when &longs;u&longs;pended by [or at] unequal Di&longs;tan­<lb/>ces, which have contrary proportion to that which tho&longs;e weights <lb/>are found to have, See the Demon&longs;tration in the beginning of the <lb/>&longs;econd Dialogue of Local-Motions.</s></p><p type="head"> <s><emph type="italics"/>Some Adverii&longs;ements about what hath been &longs;aid.<emph.end type="italics"/></s></p><p type="main"> <s>Now being that Weights unequall come to acquire equall <lb/>Moment, by being alternately &longs;u&longs;pended at Di&longs;tances that <lb/>have the &longs;ame proportion with them; I think it not fit to <lb/>over pa&longs;&longs;e with &longs;ilence another congruicy and probability, which <lb/>may confirm the &longs;ame truth; for let the Ballance A B, be con&longs;ide­<lb/>red, as it is divided into unequal parts in the point C, and let the <lb/>Weights be of the &longs;ame propor­<lb/><figure id="id.040.01.971.1.jpg" xlink:href="040/01/971/1.jpg"/><lb/>tion that is between the Di&longs;tan­<lb/>ces B C, and C A, alternately <lb/>&longs;u&longs;pended by the points A, and <lb/>B: It is already manife&longs;t, that <lb/>the one will counterpoi&longs;e the <lb/>other, and con&longs;equently, that <lb/>were there added to one of them <lb/>a very &longs;mall Moment of Gravity, it would preponderate, rai&longs;ing <lb/>the other, &longs;o that an in&longs;en&longs;ible Weight put to the Grave B, the <lb/>Ballance would move and de&longs;cend from the point B towards E, <lb/>and the other extream A would a&longs;cend into D, and in regard that <lb/>to weigh down B, every &longs;mall Gravity is &longs;ufficient, therefore not <lb/>keeping any accompt of this in&longs;en&longs;ible Moment, we will put no <lb/>difference between one Weights <emph type="italics"/>&longs;u&longs;taining,<emph.end type="italics"/> and one Weights <lb/><emph type="italics"/>moving<emph.end type="italics"/> another. </s> <s>Now, let us con&longs;ider the Motion which the <lb/>Weight B makes, de&longs;cending into E, and that which the other <lb/>A makes in a&longs;cending into D, we &longs;hall without doubt find the <lb/>Space B E to be &longs;o much greater than the Space A D, as the Di­<lb/>&longs;tance B C is greater than C A, forming in the Center C two an­<lb/>gles D C A, and E C B, equall as being at the Cock, and con&longs;e­<lb/>quently two Circumferences A D and B E alike; and to have the <lb/>&longs;ame proportion to one another, as have the Semidiameters B C, <lb/>and C A, by which they are de&longs;cribed: &longs;o that then the Velocity <lb/>of the Motion of the de&longs;cending Grave B cometh to be &longs;o much <lb/>Superiour to the Velocity of the other a&longs;cending Moveable A, as <lb/>the Gravity of this exceeds the Gravity of that; and it not being <pb xlink:href="040/01/972.jpg" pagenum="278"/>po&longs;&longs;ible that the Weight A &longs;hould be rai&longs;ed to D, although &longs;low­<lb/>ly, unle&longs;&longs;e the other Weight B do move to E &longs;wiftly, it will not <lb/>be &longs;trange, or incon&longs;i&longs;tent with the Order of Nature, that the <lb/>Velocity of the Motion of the Grave B, do compen&longs;ate the greater <lb/>Re&longs;i&longs;tance of the Weight A, &longs;o long as it moveth &longs;lowly to D, <lb/>and the other de&longs;cendeth &longs;wiftly to E, and &longs;o on the contrary, <lb/>the Weight A being placed in the point D, and the other B in <lb/>the point E, it will not be unrea&longs;onable that that falling lea&longs;urely <lb/>to A, &longs;hould be able to rai&longs;e the other ha&longs;tily to B, recovering by <lb/>its Gravity what it had lo&longs;t by it's Tardity of Motion. </s> <s>And by <lb/>this Di&longs;cour&longs;e we may come to know how the Velocity of the <lb/>Motion is able to encrea&longs;e Moment in the Moveable, according to <lb/>that &longs;ame proportion by which the &longs;aid Velocity of the Motion is <lb/>augmented.</s></p><p type="main"> <s>There is al&longs;o another thing, before we proceed any farther, to <lb/>be confidered; and this is touching the Di&longs;tances, whereat, or <lb/>wherein Weights do hang: for it much imports how we are to <lb/>under&longs;tand Di&longs;tances equall, and unequall; and, in &longs;um, in what <lb/>manner they ought to be mea­<lb/><figure id="id.040.01.972.1.jpg" xlink:href="040/01/972/1.jpg"/><lb/>&longs;ured: for that A B being the <lb/>Right Line, and two equall <lb/>Weights being &longs;u&longs;pended at <lb/>the very ends thereof, the point <lb/>C being taken in the mid&longs;t of <lb/>the &longs;aid Line, there &longs;hall be an <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> upon the &longs;ame: <lb/>And the rea&longs;on is for that the <lb/>Di&longs;tance C B is equal to C A. <lb/></s> <s>But if elevating the Line C B, moving it about the point C, it <lb/>&longs;hall be transferred into CD, &longs;o that the Ballance &longs;tand according <lb/>to the two Lines A C, and C D, the two equall Weights hanging <lb/>at the Terms A and D, &longs;hall no longer weigh equally on that <lb/>point C, becau&longs;e the di&longs;tance of the Weight placed in D, is made <lb/>le&longs;&longs;e then it was when it hanged in B. </s> <s>For if we confider the Lines, <lb/>along [or by] which the &longs;aid Graves make their Impul&longs;e, and <lb/>would de&longs;cend, in ca&longs;e they were freely moved, there is no doubt <lb/>but that they would make or de&longs;cribe the Lines A G, D F, B H: <lb/>Therefore the Weight hanging on the point D, maketh it's Moment <lb/>and <emph type="italics"/>Impetus<emph.end type="italics"/> according to the Line D F: but when it hanged in <lb/>B, it made <emph type="italics"/>Impetus<emph.end type="italics"/> in the Line B H: and becau&longs;e the Line D F is <lb/>nearer to the Fulciment C, then is the Line B H Therefore we <lb/>are to under&longs;tand that the Weights hanging on the points A and D, <lb/>are not equi-di&longs;tant from the point C, as they be when they are <lb/>con&longs;tituted according to their Right Line A C B: And la&longs;tly, <lb/>we are to take notice, that the Di&longs;tance is to be mea&longs;ured by <pb xlink:href="040/01/973.jpg" pagenum="279"/>Lines, which fall at Right Angles on tho&longs;e whereon the Weights <lb/>hang, and would move, if &longs;o be they were permitted to de&longs;cend <lb/>freely.</s></p><p type="head"> <s>Of the BALLANCE and LEAVER.</s></p><p type="main"> <s>Having under&longs;tood by certain Demon&longs;tration, one of the <lb/>fir&longs;t Principles, from which, as from a plenti&longs;ul Fountain, <lb/>many of the Mechanical In&longs;truments are derived, we may <lb/>take occa&longs;ion without any difficulty to come to the knowledge of <lb/>the nature of them: and fir&longs;t &longs;peaking of the Stiliard, an In&longs;tru­<lb/>ment of mo&longs;t ordinary u&longs;e, with which divers Merchandizes are <lb/>weighed, &longs;u&longs;taining them, though very heavy, with a very &longs;mall <lb/>counterpoi&longs;e, which is com­<lb/>monly called the Roman or <lb/><figure id="id.040.01.973.1.jpg" xlink:href="040/01/973/1.jpg"/><lb/>Plummet, we &longs;hall prove that <lb/>there is no more to be done in <lb/>&longs;uch an operation, but to re­<lb/>duce into act and practice <lb/>what hath been above contemplated. </s> <s>For if we propo&longs;e the Bal­<lb/>lance A B, who&longs;e Fulciment or Lanquet is in the point C, by <lb/>which, at the &longs;mall Di&longs;tance C A, hangeth the heavy Weight D, <lb/>and if along the other greater C B, (which we call the Needle of <lb/>the Stiliard) we &longs;hould &longs;uppo&longs;e the Roman F, though of but little <lb/>weight in compari&longs;on of the Grave Body D to be &longs;lipped to and <lb/>fro, it &longs;hall be pof&longs;ible to place it &longs;o remotely from the Lanquet C, <lb/>that the &longs;ame proportion may be found between the two Weights <lb/>D and F, as is between the Di&longs;tances F C, and C A: and then &longs;hall <lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> &longs;ucceed; unequall Weights hanging at Di&longs;tances <lb/>alternately proportional to them.</s></p><p type="main"> <s>Nor is this In&longs;trument different from that other called <emph type="italics"/>Vectis,<emph.end type="italics"/><lb/><arrow.to.target n="marg1107"></arrow.to.target><lb/>and vulgarly the ^{*} Leaver, wherewith great Weights are moved <lb/>by &longs;mall Force; the application of which is according to the Fi­<lb/>gure prefixed; wherein the Leaver <lb/>is repre&longs;ented by the Bar of wood <lb/>or other &longs;olid matter, <emph type="italics"/>B<emph.end type="italics"/> C D, let <lb/><figure id="id.040.01.973.2.jpg" xlink:href="040/01/973/2.jpg"/><lb/>the heavy Weight to be rai&longs;ed be <lb/>A, and let the &longs;teadfa&longs;t &longs;upport <lb/>or Fulciment on which the Leaver <lb/>re&longs;ts and moves be &longs;uppo&longs;ed to be <lb/>E, and putting one end of the <lb/>Leaver under the Weight A, as <lb/>may be &longs;een in the point C, en­<lb/>crea&longs;ing the Weight or Force at the other end D, it will be able <lb/>to lift up the Weight A, though not much, whenever the Force in <pb xlink:href="040/01/974.jpg" pagenum="280"/>D hath the &longs;ame proportion to the Re&longs;i&longs;tance made by the Weight <lb/>A, in the point C: as the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> C hath to the Di&longs;tance C D, <lb/>whereby it's clear, that the nearer the Fulciment E &longs;hall approach <lb/>to the Term B, encrea&longs;ing the proportion of the Di&longs;tance D C to <lb/>the Di&longs;tance C <emph type="italics"/>B,<emph.end type="italics"/> the more may one dimini&longs;h the Force in D which <lb/>is to rai&longs;e the Weight A. </s> <s>And here it is to be noted, which I &longs;hall <lb/>al&longs;o in its place remember you of, that the benefit drawn from all <lb/>Mechanical In&longs;truments, is not that which the vulgar Mechanitians <lb/>do per&longs;wade us, to wit, &longs;uch, that there by Nature is overcome, and <lb/>in a certain manner deluded, a &longs;mall Force over-powring a very <lb/>great Re&longs;i&longs;tance with help of the Leaver; for we &longs;hall demon&longs;trate, <lb/>that without the help of the length of the Leaver, the &longs;ame Force, <lb/>in the &longs;ame Time, &longs;hall work the &longs;ame effect. </s> <s>For taking the &longs;ame <lb/>Leaver B C D, who&longs;e re&longs;t or Fulci­<lb/>ment is in C, let the Di&longs;tance C D <lb/><figure id="id.040.01.974.1.jpg" xlink:href="040/01/974/1.jpg"/><lb/>be &longs;uppo&longs;ed, for example, to be <lb/>in quintuple proportion to the <lb/>Di&longs;tance C <emph type="italics"/>B,<emph.end type="italics"/> & the &longs;aid Leaver to <lb/>be moved till it come to I C G: In <lb/>the Time that the Force &longs;hall have <lb/>pa&longs;&longs;ed the Space D I, the Weight <lb/>&longs;hall have been moved from B <lb/>to G: and becau&longs;e the Di&longs;tance <lb/>D C, was &longs;uppo&longs;ed quintuple to the other C B, it is manife&longs;t from <lb/>the things demon&longs;trated, that the Weight placed in B may be five <lb/>times greater then the moving Force &longs;uppo&longs;ed to be in D: but now, <lb/><arrow.to.target n="marg1108"></arrow.to.target><lb/>if on the contrary, we take notice of the ^{*} Way pa&longs;&longs;ed by <lb/>the Force from D unto I, whil&longs;t the Weight is moved from B unto <lb/>G, we &longs;hall find likewi&longs;e the Way D I, to be quintuple to the Space <lb/>B G. </s> <s>Moreover if we take the Di&longs;tance C L, equal to the Di&longs;tance <lb/>C B, and place the &longs;ame Force that was in D, in the point L, and <lb/>in the point B the fifth part onely of the Weight that was put there <lb/>at fir&longs;t, there is no que&longs;tion, but that the Force in L being now <lb/>equal to this Weight in B, and the Di&longs;tances L C and C B being <lb/>equall, the &longs;aid Force &longs;hall be able, being moved along the Space LM <lb/>to transfer the Weight equall to it &longs;elf, thorow the other equall <lb/>Space B G: which five times reiterating this &longs;ame action, &longs;hall tran&longs;­<lb/>port all the parts of the &longs;aid Weight to the &longs;ame Term G: But <lb/>the repeating of the Space L M, is certainly nothing more nor le&longs;&longs;e <lb/>then the onely once mea&longs;uring the Space D I, quintuple to the <lb/>&longs;aid L M. </s> <s>Therefore the transferring of the Weight from B to G, <lb/>requireth no le&longs;&longs;e Force, nor le&longs;&longs;e Time, nor a &longs;horter Way if it <lb/>wee placed in D, than it would need if the &longs;ame were applied <lb/>in L: And, in &longs;hort, the benefit that is derived from the length of <lb/>the Leaver C D, is no other, &longs;ave the enabling us to move that <pb xlink:href="040/01/975.jpg" pagenum="281"/>Body all at once, which would not have been moved by the &longs;ame <lb/>Force, in the &longs;ame Time, with an equall Motion, &longs;ave onely in <lb/>pieces, without the help of the Leaver.</s></p><p type="margin"> <s><margin.target id="marg1107"></margin.target>If of Iron, it is <lb/>called a Crow, <lb/>if of wood, a Bar <lb/>or Hand-&longs;pike.</s></p><p type="margin"> <s><margin.target id="marg1108"></margin.target>Or Space.</s></p><p type="head"> <s><emph type="italics"/>Of the<emph.end type="italics"/> CAPSTEN <emph type="italics"/>and of the<emph.end type="italics"/> CRANE.</s></p><p type="main"> <s>The In&longs;truments which we are now about to declare, have <lb/>immediate dependence upon the Leaver, nay, are no other <lb/>but a perpetual Vectis or Leaver. </s> <s>For if we &longs;hall &longs;uppo&longs;e the <lb/>Leaver B A C to be &longs;u&longs;tained in <lb/>the point A, and the Weight G to <lb/><figure id="id.040.01.975.1.jpg" xlink:href="040/01/975/1.jpg"/><lb/>hang at the point B, the Force be­<lb/>ing placed in C; It is manife&longs;t, <lb/>that transferring the Leaver unto <lb/>the points D A E, the Weight G <lb/>doth alter according to the Di­<lb/>&longs;tance B D, but cannot much far­<lb/>ther continue to rai&longs;e it, &longs;o that <lb/>if it were required to elevate it yet <lb/>higher, it would be nece&longs;&longs;ary to <lb/>&longs;tay it by &longs;ome other Fulciment <lb/>in this Po&longs;ition, and to remit or return the Leaver to its former Po­<lb/>&longs;ition B A C, and &longs;u&longs;pending the Weight anew thereat, to rai&longs;e it <lb/>once again to the like height B D; and in this manner repeating <lb/>the work, many times one &longs;hall come with an interrupted Motion <lb/>to effect the drawing up of the Weight, which for many re&longs;pects <lb/>will not prove very beneficial: whereupon this difficulty hath bin <lb/>thought on, and remedied, by finding out a way how to unite to­<lb/>gether almo&longs;t infinite Leavers, perpetuating the operation without <lb/>any interruption; and this hath been done by framing a Wheel <lb/>about the Center A, according to the Semidiameter A C, and an <lb/>Axis or Nave, about the &longs;ame Center, of which let the Line A B <lb/>be the Semidiameter; and all this of very tough wood, or of other <lb/>&longs;trong and &longs;olid matter, afterwards &longs;u&longs;taining the whole Machine <lb/>upon a Gudgeon or Pin of Iron planted in the point A, which <lb/>pa&longs;&longs;eth quite thorow, where it is held fa&longs;t by two fixed Fulciments, <lb/>and the Rope D B G, at which the weight G hangeth, being be-laid <lb/>or wound about the Axis or Barrell, and applying another Rope <lb/>about the greater Wheel, at which let the other Grave I be hang­<lb/>ed: It is manife&longs;t, that the length C A having to the other A B <lb/>the &longs;elf-&longs;ame proportion that the Weight G hath to the Weight I, <lb/>it may &longs;u&longs;tain the Grave G, and with any little Moment more &longs;hall <lb/>move it: and becau&longs;e the Axis turning round together with the <lb/>Wheel, the Ropes that &longs;u&longs;tain the Weights are alwaies pendent and <lb/>contingent with the extream Circumferences of that Wheel and <pb xlink:href="040/01/976.jpg" pagenum="282"/>Axis, &longs;o that they &longs;hall con&longs;tantly maintain alike Site and Po&longs;ition <lb/>in re&longs;pect of the Di&longs;tances B A and A C, the Motion &longs;hall be <lb/>perpetuated, the Weight I de&longs;cending, and forcing the other G <lb/>to a&longs;cend. </s> <s>Where we are to ob&longs;erve the nece&longs;&longs;ity of be-laying <lb/>or winding the Rope about the Wheel, that &longs;o the Weight I may <lb/>hang according to the Line that is tangent to the &longs;aid Wheel: for <lb/>if one &longs;hould &longs;u&longs;pend the &longs;aid Weight, &longs;o as that it did hang by the <lb/>point F, cutting the &longs;aid Wheel, as is &longs;een along the Line F N M, <lb/>the Motion would cea&longs;e, the Moment of the Weight M being di­<lb/>mini&longs;hed; which would weigh no more then if it did hang by the <lb/>point N: becau&longs;e the Di&longs;tance of its Su&longs;pen&longs;ion from the Center <lb/>A, cometh to be determined by the Line A N, which falleth per­<lb/>pendicularly upon the Rope F M, and is no longer terminated by <lb/>the Semidiameter of the Wheel A F, which falleth at unequall <lb/>Angles upon the &longs;aid Line F M. </s> <s>A violence therefore being offered <lb/>in the Circumference of the Wheel by a Grave and Exanimate <lb/>Body that hath no other <emph type="italics"/>Impetus<emph.end type="italics"/> then that of De&longs;cending, it is <lb/>nece&longs;&longs;ary that it be &longs;u&longs;tained by a Line that is contingent with <lb/>the Wheel, and not by one that cutteth it. </s> <s>But if in the &longs;ame <lb/>Circumference an Animate Force were employed, that had a Mo­<lb/>ment or Faculty of making an <emph type="italics"/>Impul&longs;e<emph.end type="italics"/> on all &longs;ides, the work might <lb/>be effected in any whatever place of the &longs;aid Circumference. </s> <s>And <lb/>thus being placed in F, it would draw up the Weight by turning <lb/>the Wheel about, pulling not according to the Line F M down­<lb/>wards, but &longs;ide-waies according to the Contingent Line F L, which <lb/>maketh a Right Angle, with that which is drawn from the Center <lb/>A unto the point of Contact F: &longs;o, that if in this manner one do <lb/>mea&longs;ure the Di&longs;tance from the Center A to the Force placed in <lb/>F, according to the Line A F perpendicular to F L, along which <lb/>the <emph type="italics"/>Impetus<emph.end type="italics"/> is made, a man &longs;hall not in any part have altered the <lb/>u&longs;e of the ordinary Leaver. </s> <s>And we mu&longs;t note, that the &longs;ame <lb/>would be po&longs;&longs;ible to be done likewi&longs;e with an Exanimate Force, <lb/>in ca&longs;e that a way were found out to cau&longs;e that its Moment might <lb/>make Impul&longs;e in the point F, drawing according to the Contingent <lb/>Line F L: which would be done by adjoyning beneath the Line F L <lb/>a turning Pulley, making the Rope wound about the Wheel to <lb/>pa&longs;&longs;e along upon it, as it is &longs;een to do by the Line F L X, &longs;u&longs;pending <lb/>at the end thereof the Weight X equall to the other I, which ex­<lb/>erci&longs;ing its Force according to the Line F L, &longs;hall alwaies keep a <lb/>Di&longs;tance from the Center A equall unto the Semidiameter of the <lb/>Wheel. </s> <s>And from what hath been declared we will gather for a <lb/>Conclu&longs;ion, That in this In&longs;trument the Force hath alwaies the <lb/>&longs;ame proportion to the Weight, as the Semidiameter of the Axis <lb/>or Barrell hath to the Semidiameter of the Wheel.</s></p><pb xlink:href="040/01/977.jpg" pagenum="283"/><p type="main"> <s>From the In&longs;trument la&longs;t de&longs;cribed, the other In&longs;trument which <lb/>we call the Crane is not much different, as to form, nay, differeth <lb/>nothing, &longs;ave in the way of applying or employing it: For that the <lb/>Cap&longs;ten moveth and is con&longs;tituted perpendicular to the Horizon, <lb/>and the Crane worketh with its Moment parallel to the &longs;ame Ho­<lb/><figure id="id.040.01.977.1.jpg" xlink:href="040/01/977/1.jpg"/><lb/>rizon. </s> <s>For if upon the Circle D A E we &longs;uppo&longs;e an Axis to be <lb/>placed Column-wi&longs;e, turning about the Center B, and about which <lb/>the Rope D H, fa&longs;tened to the Weight that is to be drawn, is be­<lb/>laid, and if the Bar F E B D be let into the &longs;aid Axis [<emph type="italics"/>by the Mor­<lb/>tace B<emph.end type="italics"/>] and the Force of a Man, of an Hor&longs;e, or of &longs;ome other <lb/>Animal apt to draw, be applyed at its end F, which moving round, <lb/>pa&longs;&longs;eth along the Circumference F G C, the Crane &longs;hall be framed <lb/>and fini&longs;hed, &longs;o that by carrying round the Bar F B D, the Barrell <lb/>or Axis E A D &longs;hall turn about, and the Rope which is twined a­<lb/>bout it, &longs;hall con&longs;train the Weight H to go forward: And becau&longs;e <lb/>the point of the Fulciment about which the Motion is made, is the <lb/>point B, and the Moment keeps at a Di&longs;tance from it according to <lb/>the Line B F, and the Re&longs;i&longs;tor at the Di&longs;tance B D, the Leaver <lb/>F B D is formed, by vertue of which the Force acquireth Moment <lb/>equall to the Re&longs;i&longs;tance, if &longs;o be, that it be in proportion to it, as <lb/>the Line B D is to B F, that is, as the Semidiameter of the Axis to <lb/>the Semidiameter of the Circle, along who&longs;e Circumference the <lb/>Force moveth. </s> <s>And both in this, and in the other In&longs;trument we <lb/>are to ob&longs;erve that which hath been frequently mentioned, that is, <lb/>That the benefit which is derived from the&longs;e Machines, is not that <lb/>which the generality of the Vulgar promi&longs;e them&longs;elves from the <lb/>Mechanicks; namely, that being too hard for Nature, its po&longs;&longs;ible <pb xlink:href="040/01/978.jpg" pagenum="284"/>with a Machine to overcome a Re&longs;i&longs;tance, though great, with a <lb/>&longs;mall Force, in regard, that we &longs;hall manife&longs;tly prove that the &longs;ame <lb/>Force placed in F, might in the &longs;ame Time conveigh the &longs;ame <lb/>Weight, with the &longs;ame Motion, unto the &longs;ame Di&longs;tance, without <lb/>any Machine at all: For &longs;uppo&longs;ing, for example, that the Re&longs;i&longs;tance <lb/>of the Grave H be ten times greater than the Force placed in F, it <lb/><figure id="id.040.01.978.1.jpg" xlink:href="040/01/978/1.jpg"/><lb/>will be requi&longs;ite for the mo­<lb/>ving of the &longs;aid Re&longs;i&longs;tance, <lb/>that the Line F B be decuple <lb/>to B D; and con&longs;equently, <lb/>that the Circumference of the <lb/>Circle F G C be al&longs;o decuple <lb/>to the Circumference E A D: <lb/>and becau&longs;e when the Force <lb/>&longs;hall be moved once along the <lb/>whole Circumference of the <lb/>Circle F G C, the Barrel EAD, <lb/>about which the Rope is be-laid which draweth the Weight, &longs;hall <lb/>likewi&longs;e have given one onely turn; it is manife&longs;t, that the Weight <lb/>H &longs;hall not have been moved more than the tenth part of that way <lb/>which the Mover &longs;hall have gone. </s> <s>If therefore the Force that is to <lb/>move a Re&longs;i&longs;tance that is greater than it &longs;elf, for &longs;uch an a&longs;&longs;igned <lb/>Space by help of this Machine, mu&longs;t of nece&longs;&longs;ity move ten times as <lb/>far, there is no doubt, but that dividing that Weight into ten parts, <lb/>each of them &longs;hall be equall to the Force, and con&longs;equently, might <lb/>have been tran&longs;ported one at a Time, as great a Space as that <lb/>which it &longs;elf did move, &longs;o that making ten journeys, each equal to <lb/>the Circumference E A D, it &longs;hall not have gone any farther than <lb/>if it did move but once alone about the Circumference F G C; <lb/>and &longs;hall have conveighed the &longs;ame Weight H to the &longs;ame Di­<lb/>&longs;tance. </s> <s>The benefit therefore that is to be derived from the&longs;e <lb/>Machines is, that they carry all the Weight together, but not with <lb/>le&longs;&longs;e Labour, or with greater Expedition, or a greater Way than <lb/>the &longs;ame Force might have done conveying it by parcels.</s></p><p type="head"> <s>Of PULLIES.</s></p><p type="main"> <s>The In&longs;truments, who&longs;e Natures are reducible unto the Bal­<lb/>lance, as to their Principle and Foundation, and others little <lb/>differing from them, have been already de&longs;cribed; now for <lb/>the under&longs;tanding of that which we have to &longs;ay touching Pullies, <lb/>it is requi&longs;ite, that we con&longs;ider in the fir&longs;t place another way to u&longs;e <lb/>the Leaver, which will conduce much towards the inve&longs;tigation of <lb/>the Force of Pullies, and towards the under&longs;tanding of other Me­<lb/>chanical Effects. </s> <s>The u&longs;e of the Leaver above declared &longs;uppo&longs;ed <pb xlink:href="040/01/979.jpg" pagenum="285"/>the Weight to be at one extream, and the Force at the other, and <lb/>the Fulciment placed in &longs;ome point between the extreams: but we <lb/>may make u&longs;e of the Leaver another way, yet, placing, as we &longs;ee, <lb/>the Fulciment in the extream A, the Force in the other extream C, <lb/>and &longs;uppo&longs;ing the Weight D to hang by &longs;ome point in the mid&longs;t, <lb/><figure id="id.040.01.979.1.jpg" xlink:href="040/01/979/1.jpg"/><lb/>as here we &longs;ee by the point B, in <lb/>this example it's manife&longs;t, that if <lb/>the Weight did hang at a point <lb/>Equi-di&longs;tant from the two ex­<lb/>treams A and C, as at the point F, <lb/>the labour of &longs;u&longs;taining it would <lb/>be equally divided betwixt the <lb/>two points A and C, &longs;o that half <lb/>the Weight would be felt by the <lb/>Force C, the other half being &longs;u­<lb/>&longs;tained by the Fulciment A: but if the Grave Body &longs;hall be hanged <lb/>at another place, as at B, we &longs;hall &longs;hew that the Force in C is &longs;uffi­<lb/>cient to &longs;u&longs;tain the Weight in B, as it hath the &longs;ame proportion <lb/>to it, that the Di&longs;tance, A B hath to the Di&longs;tance A C. </s> <s>For De­<lb/>mon&longs;tration of which, let us imagine the Line B A to be continued <lb/>right out unto G, and let the Di&longs;tance B A be equall to A G, and <lb/>let the Weight hanging at G, be &longs;uppo&longs;ed equall to D: It is ma­<lb/>nife&longs;t, that by rea&longs;on of the equality of the Weights D and E, and <lb/>of the Di&longs;tances G A and A B, the Moment of the Weight E <lb/>&longs;hall equalize the Moment of the Weight D, and is &longs;ufficient to <lb/>&longs;u&longs;tain it: Therefore whatever Force &longs;hall have Moment equall to <lb/>that of the Weight E, and that &longs;hall be able to &longs;u&longs;tain it, &longs;hall be <lb/>&longs;ufficient likewi&longs;e to &longs;u&longs;tain the Weight D: But for &longs;u&longs;taining the <lb/>Weight E, let there be placed in the point C &longs;uch a Force, who&longs;e <lb/>Moment hath that proportion to the Weight E, that the Di&longs;tance <lb/>G A hath to the Di&longs;tance A C, it &longs;hall be &longs;ufficient to &longs;u&longs;tain it: <lb/>Therefore the &longs;ame Force &longs;hall likewi&longs;e be able to &longs;u&longs;tain the <lb/>Weight D, who&longs;e Moment is equall to the of E: But look what <lb/>Proportion the Line G A hath to the Line A C; and A B al&longs;o hath <lb/>the &longs;ame to the &longs;aid A C, G A having been &longs;uppo&longs;ed equall to A B: <lb/>And becau&longs;e the Weights E and D are equall, each of them &longs;hall <lb/>have the &longs;ame proportion to the Force placed in C: Therefore the <lb/>Force in C is concluded to equall the Moment of the Weight D, <lb/>as often as it hath unto it the &longs;ame proportion that the Di&longs;tance B A <lb/>hath to the Di&longs;tance C A. </s> <s>And by moving the Weight, with the <lb/>Leaver u&longs;ed in this manner, it is gathered in this al&longs;o, as well as in <lb/>the other In&longs;truments, that what is gained in Force is lo&longs;t in Velo­<lb/>city: for the Force C rai&longs;ing the Leaver, and transferring it to A I, <lb/>the Weight is moved the Space B H, which is as much le&longs;&longs;er than <lb/>the Space C I pa&longs;&longs;ed by the Force, as the Di&longs;tance A B is le&longs;&longs;er <pb xlink:href="040/01/980.jpg" pagenum="286"/>than the Di&longs;tance A C; that is, as the Force is le&longs;&longs;e than the <lb/>Weight.</s></p><p type="main"> <s>The&longs;e Principles being declared, we will pa&longs;&longs;e to the Contem­<lb/>plation of Pullies, the compo&longs;ition and &longs;tructure of which, together <lb/>with their u&longs;e, &longs;hall be de&longs;cribed by us. </s> <s>And fir&longs;t let us &longs;uppo&longs;e the <lb/><arrow.to.target n="marg1109"></arrow.to.target><lb/>^{*} Little Pulley A B C, made of Mettall or hard Wood, voluble a­<lb/>bout it's Axis which pa&longs;&longs;eth thorow it's Center D, and about this <lb/><figure id="id.040.01.980.1.jpg" xlink:href="040/01/980/1.jpg"/><lb/>Pulley let the Rope E A B C be put, <lb/>at one end of whichlet the Weight E <lb/>hang, and at the other let us &longs;uppo&longs;e <lb/>the Force F. </s> <s>I &longs;ay, that the Weight <lb/>being &longs;u&longs;tained by a Force equall to <lb/>it &longs;elf in the upper Nut or Pulley <lb/>A B C, bringeth &longs;ome benefit, as the <lb/>moving or &longs;u&longs;taining of the &longs;aid <lb/>Weight with the Force placed in F: <lb/>For if we &longs;hall under&longs;tand, that from <lb/>the Center D, which is the place of the Fulciment, two Lines be <lb/>drawn out as far as the Circumference of the Pulley in the points <lb/>A and C, in which the pendent Cords touch the Circumference, we <lb/>&longs;hall have a Ballance of equal Arms which determine the Di&longs;tance <lb/>of the two Su&longs;pen&longs;ions from the Center and Fulciment D: Where­<lb/>upon it is manife&longs;t, that the Weight hanging at A cannot be &longs;u&longs;tain­<lb/>ed by a le&longs;&longs;er Weight hanging at G, but by one equal to it; &longs;uch <lb/>is the nature of equal Weights hanging at equal Di&longs;tances. </s> <s>And <lb/>although in moving downwards, the Force F cometh to turn about <lb/>the Pulley A B C, yet there followeth no alteration of the Alti­<lb/>tude or Re&longs;pect, that the Weight and Force have unto the two <lb/>Di&longs;tances A D and D C, nay, the Pulley encompa&longs;&longs;ed becometh a <lb/>Ballance equal to A C, but perpetuall. </s> <s>Whence we may learn, <lb/>how childi&longs;hly <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> deceiveth him&longs;elf, who holds, that by making <lb/>the &longs;mall Pulley A B C bigger, one might draw up the Weight with <lb/>a le&longs;&longs;er Force; he con&longs;idering that upon the enlargement of the <lb/>&longs;aid Pulley, the Di&longs;tance D C encrea&longs;ed, but not con&longs;idering that <lb/>there was as great an encrea&longs;e of the other Di&longs;tance of the Weight, <lb/>that is, the other Semidiameter D A. </s> <s>The benefit therefore that may <lb/>be drawn from the In&longs;trument above &longs;aid, is nothing at all as to the <lb/>diminution of the labour: and if any one &longs;hould ask how it hap­<lb/>pens, that on many occa&longs;ions of rai&longs;ing Weights, this means is made <lb/>u&longs;e of to help the Axis, as we &longs;ee, for example, in drawing up the <lb/>Water of Wells; it is an&longs;wered, that that is done, becau&longs;e that <lb/>by this means the manner of employing the Force is found more <lb/>commodious: for being to pull downwards, the proper Gravity of <lb/>our Arms and other parts help us, whereas if we were to draw <lb/>the fame Weight upwards with a meer Rope, by the &longs;ole &longs;trength <pb xlink:href="040/01/981.jpg" pagenum="287"/>of the Members and Mu&longs;cles, and as we u&longs;e to &longs;ay, by Force of <lb/>Armes, be&longs;ides the extern Weight, we are to lift up the Weight of <lb/>our own Armes, in which greater pains is required. </s> <s>Conclude we, <lb/>therefore, that this upper Pulley doth not bring any Facility to the <lb/>Force &longs;imply con&longs;idered, but onely to the manner of applying it: <lb/>but if we &longs;hall make u&longs;e of the like Machine <lb/><figure id="id.040.01.981.1.jpg" xlink:href="040/01/981/1.jpg"/><lb/>in another manner, as we are now about to <lb/>declare; we may rai&longs;e the Weight with di­<lb/>minution of Forces: For let the Pulley <lb/>B D C be voluble about the Center E placed <lb/>in it's Frame B L C, at which hang the <lb/>Grave G; and let the Rope A B D C F <lb/>pa&longs;&longs;e about the Pulley; of which let the end <lb/>A be fa&longs;tned to &longs;ome fixed &longs;tay, and in the <lb/>other F let the Force be placed; which <lb/>moving to wards H &longs;hall rai&longs;e the Machine <lb/>B L C, and con&longs;equently the Weight G: <lb/>and in this operation I &longs;ay, that the Force in <lb/>F is the half of the Weight &longs;u&longs;tained by it. <lb/></s> <s>For the &longs;aid Weight being kept to Rights by the two ^{*} Ropes A B <lb/><arrow.to.target n="marg1110"></arrow.to.target><lb/>and F C, it is manife&longs;t, that the Labour is equally &longs;hared betwixt <lb/>the Force F and the Fulciment A: and more &longs;ubtilly examining the <lb/>nature of this In&longs;trument, if we but continue forth the Diameter <lb/>B E C, we &longs;hall &longs;ee a Leaver to be made, at the mid&longs;t of which, that <lb/>is at the point E, the Grave doth hang, and the Fulciment cometh <lb/>to be at the end B, and the Force in the Term C: whereupon, by <lb/>what hath been above demon&longs;trated, the Force &longs;hall have the &longs;ame <lb/>proportion to the Weight, that the Di&longs;tance E B hath to the Di­<lb/>&longs;tance; Therefore it &longs;hall be the half of the &longs;aid Weight: And <lb/>becau&longs;e the Force ri&longs;ing towards A, the Pulley turneth round, <lb/>therefore that Re&longs;pect or Con&longs;titution which the Fulciment B and <lb/>Center E, on which the Weight and Term C, in which the Force <lb/>is employed do depend, &longs;hall not change all the while; but yet in <lb/>the Circuinduction the Terms B and C happen to vary in number, <lb/>but not in vertue, others and others continually &longs;ucceeding in their <lb/>place, whereby the Leaver B C cometh to be perpetuated. </s> <s>And <lb/>here (as hath been done in the other In&longs;truments, and &longs;hall be in <lb/>tho&longs;e that follow) we will not pa&longs;&longs;e without con&longs;idering how that <lb/>the journey that the Force maketh, is double to the Moment of the <lb/>Weight. </s> <s>For in ca&longs;e the Weight &longs;hall be moved &longs;o far, till that <lb/>the Line B C come to arrive with it's points B and C, at the points <lb/>A and F, it is nece&longs;&longs;ary that the two equal Ropes be di&longs;tended in <lb/>one &longs;ole Line F H, and con&longs;equently, when the Weight &longs;hall have <lb/>a&longs;cended along the Intervall B A, the Force &longs;hall have been moved <lb/>twice as far, that is, from <emph type="italics"/>F<emph.end type="italics"/> unto H. </s> <s>Then con&longs;idering that the <pb xlink:href="040/01/982.jpg" pagenum="288"/>Force in <emph type="italics"/>F,<emph.end type="italics"/> that it may rai&longs;e the Weight, mu&longs;t move upwards, which <lb/>to exanimate Movers, as being for the mo&longs;t part Grave Bodies, is al­<lb/><figure id="id.040.01.982.1.jpg" xlink:href="040/01/982/1.jpg"/><lb/>together impo&longs;&longs;ible, or at lea&longs;t more laborious, <lb/>than the making of the &longs;ame <emph type="italics"/>F<emph.end type="italics"/>orce down­<lb/>wards: Therefore to help this inconvenience, <lb/>a Remedy hath been found by adjoyning an­<lb/>other Nut or Pulley above, as in the adjacent <lb/><emph type="italics"/>F<emph.end type="italics"/>igure is &longs;een, where the Rope C E <emph type="italics"/>F<emph.end type="italics"/> hath <lb/>been made to pa&longs;s about the upper Pulley <emph type="italics"/>F<emph.end type="italics"/> G <lb/>upheld by the Hook L, &longs;o that the Rope pa&longs;&longs;ing <lb/>to H, and thither transferring the <emph type="italics"/>F<emph.end type="italics"/>orce E, it <lb/>&longs;hall be able to move the Weight X by pulling <lb/>downwards, but not that it may be le&longs;&longs;er than <lb/>it was in E: <emph type="italics"/>F<emph.end type="italics"/>or the Motions of the <emph type="italics"/>F<emph.end type="italics"/>orce <lb/><emph type="italics"/>F<emph.end type="italics"/> H, hanging at the equal Di&longs;tances <emph type="italics"/>F<emph.end type="italics"/> D and <lb/>D G of the upper Pulley, do alwaies continue <lb/>equal; nor doth that upper Pulley (as hath <lb/>been &longs;hewn above) come to produce any di­<lb/>minution in the Labour. </s> <s>Moreover it having been nece&longs;&longs;ary by <lb/>the addition of the upper Pulley to introduce the Appendix B, by <lb/>which it is &longs;u&longs;tained, it will prove of &longs;ome benefit to us to rai&longs;e <lb/>the other A, to which one end of the Rope was fa&longs;tned, transferring <lb/>it to a Ring annexed to the lower part of the <emph type="italics"/>F<emph.end type="italics"/>rame of the upper <lb/>Pulley, as we &longs;ee it done in M. </s> <s>Now finally, this Machine com­<lb/>pounded of upper and lower Pullies, is that which the Greeks call <lb/><arrow.to.target n="marg1111"></arrow.to.target><lb/><foreign lang="greek">*tpoxi/lion.</foreign></s></p><p type="margin"> <s><margin.target id="marg1109"></margin.target>*Called by &longs;ome <lb/>a Nut.</s></p><p type="margin"> <s><margin.target id="marg1110"></margin.target>* Or two ends of <lb/>the &longs;ame Rope.</s></p><p type="margin"> <s><margin.target id="marg1111"></margin.target>In Latine <emph type="italics"/>Tro­<lb/>chlea.<emph.end type="italics"/></s></p><p type="main"> <s>We have hitherto explained, how by help of Pullies one may <lb/>double the <emph type="italics"/>F<emph.end type="italics"/>orce, it remaineth that with the greate&longs;t brevity po&longs;­<lb/>&longs;ible, we &longs;hew the way how to encrea&longs;e it according to any Multi­<lb/>plicity. </s> <s>And fir&longs;t we will &longs;peak of the Multiplicity according to <lb/>the even numbers, and then the odde: To &longs;hew how we may mul­<lb/>tiply the <emph type="italics"/>F<emph.end type="italics"/>orce in a quadruple Proportion, we will propound the <lb/>following Speculation as the Soul of all that followeth.</s></p><p type="main"> <s>Take two Leavers, A B, C D, with the <emph type="italics"/>F<emph.end type="italics"/>ulciments in the ex­<lb/><figure id="id.040.01.982.2.jpg" xlink:href="040/01/982/2.jpg"/><lb/>treams A and C; and at the middles <lb/>of each of them let the Grave G hang, <lb/>&longs;u&longs;tained by two <emph type="italics"/>F<emph.end type="italics"/>orces of equal Mo­<lb/>ment placed in B and D. </s> <s>I &longs;ay, that <lb/>the Moment of each of them will <lb/>equal the Moment of the fourth part <lb/>of the Weight G. <emph type="italics"/>F<emph.end type="italics"/>or the two <emph type="italics"/>F<emph.end type="italics"/>or­<lb/>ces B and D bearing equally, it is <lb/>manife&longs;t, that the <emph type="italics"/>F<emph.end type="italics"/>orce D hath not <lb/>contra&longs;ted with more then one half of the Weight G: But if the <lb/><emph type="italics"/>F<emph.end type="italics"/>orce D do by benefit of the Leaver D C &longs;u&longs;tain the half of the <pb xlink:href="040/01/983.jpg" pagenum="289"/>Weight G hanging at <emph type="italics"/>F,<emph.end type="italics"/> it hath been already demon&longs;trated, that <lb/>the &longs;aid <emph type="italics"/>F<emph.end type="italics"/>orce D hath to the Weight &longs;o by it &longs;u&longs;tained, that &longs;ame <lb/>proportion which the Di&longs;tance <emph type="italics"/>F<emph.end type="italics"/> C hath to the Di&longs;tance C D: <lb/>Which is &longs;ubduple proportion: Therefore the Moment D is &longs;ub­<lb/>duple to the Moment of half of the Weight G &longs;u&longs;tained by it: <lb/>Wherefore it followeth, that it is the fourth part of the Moment <lb/>of the whole Weight. </s> <s>And in the &longs;ame manner the &longs;ame thing is <lb/>demon&longs;trated, of the Moment <emph type="italics"/>B<emph.end type="italics"/>; and it is but rea&longs;onable, that the <lb/>Weight G being &longs;u&longs;tained by the four points, A, <emph type="italics"/>B,<emph.end type="italics"/> C, D, each of <lb/>them &longs;hould feel an equall part of the Labour.</s></p><p type="main"> <s>Let us come now to apply this Con&longs;ideration to Pullies, and let <lb/>the Weight X be &longs;uppo&longs;ed to hang at the two Pullies A B and D E <lb/>entwining about them, and about the uppermo&longs;t Pulley G H, the <lb/>Rope, as we &longs;ee, I D E H G A B, &longs;u&longs;taining the whole Machine in <lb/>the point K. </s> <s>Now I &longs;ay, that placing the Force in L, it &longs;hall be able <lb/>to &longs;u&longs;tain the Weight X, if &longs;o be, it be equal to the fourth part of <lb/>it. </s> <s>For if we do imagine the two Diameters D E and A B, and the <lb/>Weights hanging at the middle points F and C, we &longs;hall have two <lb/>Leavers like to tho&longs;e before de&longs;cribed, the Fulciments of which an­<lb/>&longs;wer to the points D and A. </s> <s>Whereupon the Force placed in B, <lb/><figure id="id.040.01.983.1.jpg" xlink:href="040/01/983/1.jpg"/><lb/>or if you will, in L, &longs;hall be able to &longs;u­<lb/>&longs;tain the Weight X, being the fourth <lb/>part of it: And if we adde another Pul­<lb/>ley above the other two, making the <lb/>Rope or Cord to pa&longs;s along L M N, trans­<lb/>ferring the Force L into N, it &longs;hall be <lb/>able to bear the &longs;ame Weight gravitating <lb/>downwards, the upper Pulley neither aug­<lb/>menting or dimini&longs;hing the Force, as hath <lb/>been declared. </s> <s>And we will likewi&longs;e <lb/>note, that to make the: Weight a&longs;cend the <lb/><arrow.to.target n="marg1112"></arrow.to.target><lb/>four Ropes B L, E H, D I, and A G <lb/>ought to pa&longs;s, whereupon the Mover will <lb/>be to begin, as much as tho&longs;e Ropes are <lb/>long; and yet neverthele&longs;s the Weight <lb/>&longs;hall move but only as much as the length <lb/>of one of them: So that we may &longs;ay by <lb/>way of adverti&longs;ement, and for confirma­<lb/>tion of what hatn been many times &longs;po­<lb/>ken, namely, that look with what proportion the Labour of the <lb/><arrow.to.target n="marg1113"></arrow.to.target><lb/>Mover is dimini&longs;hed, the length of the Way, on the contrary, is <lb/>encrea&longs;ed with the &longs;ame proportion</s></p><p type="margin"> <s><margin.target id="marg1112"></margin.target>* Or four parts <lb/>of the &longs;ame Rope</s></p><p type="margin"> <s><margin.target id="marg1113"></margin.target>* The word <emph type="italics"/>Gy­<lb/>rilla<emph.end type="italics"/> &longs;ignifieth a <lb/>Shiver, Rundle, <lb/>or &longs;mall Wheel <lb/>of a Pulley, tran­<lb/>&longs;lated by we <lb/>&longs;ometimes Pul­<lb/>ley, &longs;ometimes <lb/>Nut or Girill.</s></p><p type="main"> <s>But if we would encrea&longs;e the Force in &longs;excuple proportion, it <lb/>will be requi&longs;ite that we adjoyn another ^{*} &longs;mall Pulley or Gyrill <lb/>to the inferiour Pulley which that you may the better under&longs;tand <pb xlink:href="040/01/984.jpg" pagenum="290"/>we will &longs;et before you the pre&longs;ent Contemplation. </s> <s>Suppo&longs;e, there­<lb/>fore, that A B, C D, and E F are three Leavers; and that on the <lb/>middle points of them G, H, and I the Weight K doth hang in <lb/>common, &longs;o that every one of them &longs;hall &longs;u&longs;tain the third part of <lb/><figure id="id.040.01.984.1.jpg" xlink:href="040/01/984/1.jpg"/><lb/>it: And becau&longs;e the Power in <lb/>B, &longs;u&longs;taining with the Leaver <lb/>B A thependent Weight in G, <lb/>hapneth to be the half of the <lb/>&longs;aid Weight, and it hath been <lb/>already &longs;aid, that it &longs;u&longs;taineth <lb/>the third part of the Weight <lb/>K: Therefore the Moment of <lb/>the Force B is equal to half of <lb/>the third part of the Weight K; that is, to the &longs;ixth part of it: <lb/>And the &longs;ame &longs;hall be demon&longs;trated of the other Forces D and F: <lb/>From whence we may ea&longs;ily gather, that putting three Gyrils or <lb/>Rundles into the inferiour Pulley, and two or three into the upper­<lb/><figure id="id.040.01.984.2.jpg" xlink:href="040/01/984/2.jpg"/><lb/>mo&longs;t, we may multiply the Force accor­<lb/><arrow.to.target n="marg1114"></arrow.to.target><lb/>ding to our ^{*} <emph type="italics"/>Senarius.<emph.end type="italics"/> And if we would <lb/>encrea&longs;e it according to any other even <lb/>Number, the Gyrils of the Pulley below <lb/>mu&longs;t be multiplyed according to the half <lb/>of that Number, according to which the <lb/>Force is to be multiplyed, circumpo&longs;ing <lb/>the Rope about the Pulleys, &longs;o as that one <lb/>of the ends be fa&longs;tned to the upper Pul­<lb/>ley, and let the Force be in the other; as <lb/>in this Figure adjoyning may manife&longs;tly <lb/>be gathered.</s></p><p type="margin"> <s><margin.target id="marg1114"></margin.target>* Or in Sexcuple <lb/>proportion.</s></p><p type="main"> <s>Now pa&longs;&longs;ing to the Declaration of the <lb/>manner how to multiply the Force ac­<lb/>cording to the odd Numbers, and begin­<lb/><figure id="id.040.01.984.3.jpg" xlink:href="040/01/984/3.jpg"/><lb/>ning at the triple proportion: fir&longs;t, let us <lb/>propo&longs;e the pre&longs;ent Contemplation, as <lb/>that, on the under&longs;tanding of which the <lb/>knowledge of all the Work in hand <lb/>doth depend. </s> <s>Let therefore the Leaver <lb/>be A B, its Fulciment A, and from the <lb/>middle of it, that is, at the point C let <lb/>the Grave D be hanged; and let it be &longs;u­<lb/>&longs;tained by two equal Forces; and let one of them be applied to the <lb/>point C, and the other to the term B. </s> <s>I &longs;ay, that each of tho&longs;e Powers <lb/>have Moment equal to the third part of the Weight D. </s> <s>For the <lb/>Force in C &longs;u&longs;taineth a Weight equal to it &longs;elf, being placed in the <lb/>&longs;ame Line in which the Weight D doth hang & Gravitate: But the <pb xlink:href="040/01/985.jpg" pagenum="291"/>Force in B &longs;u&longs;taineth a part of the Weight D double to it &longs;elf, its <lb/>Di&longs;tance from the Fulciment A, that is, the Line B A being dou­<lb/>ble to the Di&longs;tance A C at which the Grave hangeth: But becau&longs;e <lb/>the two Forces in B and C are &longs;uppo&longs;ed to be equal to each other: <lb/>Therefore the part of the Weight D, which is &longs;u&longs;tained by the <lb/>Force in B, is double to the part &longs;u&longs;tained by the Force in C. </s> <s>If <lb/>therefore, of the Grave D two parts be made, the one double to <lb/>the remainder, the greater is &longs;u&longs;tained by the Force in B, and the <lb/>le&longs;&longs;er by the Force in C: But this le&longs;&longs;er is the third part of the <lb/>Weight D: Therefore the Moment of the Force in C is equal to <lb/>the Moment of the third part of the Weight D; to which, of <lb/>con&longs;equence, the Force B &longs;hall be equal, we having &longs;uppo&longs;ed it <lb/>equal to the other Force C: Wherefore our intention is manifell, <lb/>which we were to demon&longs;trate, how that each of the two Powers <lb/>C and B is equal to the third part of the Weight D. </s> <s>Which be­<lb/>ing demon&longs;trated, we will pa&longs;s forwards to the Pulleys, and will <lb/>de&longs;cribe the inferiour Gyrils of A C B, voluble about the Center <lb/>G, and the Weight H hanging thereat, we will draw the other up­<lb/>per one E F, winding about them both the Rope D F E A C B I, <lb/>of which let the end D be fa&longs;tned to the inferiour Pulley, and to <lb/><figure id="id.040.01.985.1.jpg" xlink:href="040/01/985/1.jpg"/><lb/>the other I let the Force be applyed: <lb/>Which, I &longs;ay, &longs;u&longs;taining or moving the <lb/>Weight H, &longs;hall feele no more than the <lb/>third part of the Gravity of the &longs;ame. </s> <s>For <lb/>con&longs;idering the contrivance of this Ma­<lb/>chine, we &longs;hall find that the Diameter A B <lb/>&longs;upplieth the place of a Leaver, in who&longs;e <lb/>term B the Force I is applied, and in the <lb/>other A the <emph type="italics"/>F<emph.end type="italics"/>uiciment is placed, at the mid­<lb/>dle G the Grave H is hanged, and another <lb/><emph type="italics"/>F<emph.end type="italics"/>orce D applied at the &longs;ame place: &longs;o that <lb/><arrow.to.target n="marg1115"></arrow.to.target><lb/>the Weight is fa&longs;tned to the ^{*} three Ropes <lb/>I B, <emph type="italics"/>F<emph.end type="italics"/> D, and E A, which with equal Labour <lb/>&longs;u&longs;tain the Weight. </s> <s>Now, by what hath <lb/>already been contemplated, the two <emph type="italics"/>F<emph.end type="italics"/>orces <lb/>D and B being applied, one, to the mid&longs;t of the Leaver A B, and <lb/>the other to the extream term B, it is manife&longs;t, that each of them <lb/>holdeth no more but the third part of the Weight H: Therefore <lb/>the Power I, having a Moment equal to the third part of the <lb/>Weight H, &longs;hall be able to &longs;u&longs;tain and move it: but yet the Way <lb/>of the <emph type="italics"/>F<emph.end type="italics"/>orce in I &longs;hall be triple to the Way that the Weight &longs;hall <lb/>pa&longs;s; the &longs;aid Force being to di&longs;tend it &longs;elf according to the <lb/>Length of the three Ropes I B, <emph type="italics"/>F<emph.end type="italics"/> D, and E A, of which one alone <lb/>mea&longs;ureth the Way of the Weight H.</s></p><pb xlink:href="040/01/986.jpg" pagenum="292"/><p type="margin"> <s><margin.target id="marg1115"></margin.target>* Or three parts <lb/>of one Rope.</s></p><p type="head"> <s><emph type="italics"/>Of the<emph.end type="italics"/> SCREW.</s></p><p type="main"> <s>Among&longs;t the re&longs;t of Mechanick In&longs;truments for &longs;undry u&longs;es <lb/>found out by the Wit of Man, the Screw doth, in my opi­<lb/>nion, both for Invention and for Utility, hold the fir&longs;t <lb/>place, as that which is appo&longs;itely accommodated, and &longs;o contrived <lb/>not only to move, but al&longs;o to &longs;tay and pre&longs;s with very great Force, <lb/>that taking up but little room, it worketh tho&longs;e effects which other <lb/>In&longs;truments cannot, unle&longs;s they were reduced to a great Machine. <lb/></s> <s>The Screw therefore being of mo&longs;t ingenious and commodious <lb/>contrivance, we ought de&longs;ervedly to be at &longs;ome pains in explaining, <lb/>with all the plainne&longs;s that is po&longs;&longs;ible, the Original and Nature of <lb/>it. </s> <s>The which that we may do, we will begin at a Speculation, <lb/>which, though at fir&longs;t blu&longs;h it may appear &longs;omewhat remote from <lb/>the con&longs;ideration of this In&longs;trument, yet is the <emph type="italics"/>Ba&longs;is<emph.end type="italics"/> and Founda­<lb/>tion thereof.</s></p><p type="main"> <s>No doubt, but that Natures operation in the Motions of Grave <lb/>Bodies is &longs;uch, that any whatever Body that hath a Gravity in it <lb/>hath a propen&longs;ion of moving, being at liberty, towards the Cen­<lb/><arrow.to.target n="marg1116"></arrow.to.target><lb/>ter, and that not only ^{*} by the Right Line perpendicularly, but al­<lb/>&longs;o (when it cannot do otherwi&longs;e) by any other Line, which ha­<lb/>ving &longs;ome inclination towards the Center goeth more and more <lb/>aba&longs;ing. </s> <s>And thus we &longs;ee the Water not only to fall downwards <lb/>along the Perpendicular from &longs;ome eminent place, but al&longs;o to run <lb/>about the Surface of the Earth along Lines though very little en­<lb/>clined; as we &longs;ee in the Cour&longs;e of Rivers, the Waters of which, if &longs;o <lb/>be that the Bed have any the lea&longs;t declivity, go freely declining <lb/>downwards. </s> <s>Which very effect, like as it is di&longs;cerned in all Fluid <lb/>Bodies, would appear al&longs;o in hard Bodies, if &longs;o be, that their Fi­<lb/>gure and other Accidental and Extern Impediments did not hinder <lb/>it. </s> <s>So that we, having a Superficies very well &longs;moothed and poli­<lb/>&longs;hed, as for in&longs;tance, that of a Looking-gla&longs;s, and a Ball exactly <lb/>rotund and &longs;leek, either of Marble, or of Gla&longs;s, or of any other <lb/>Matter apt to be poli&longs;hed, this being placed upon that Superficies <lb/>&longs;hall trundle along, in ca&longs;e that this have any, though very &longs;mall, <lb/>inclination; and &longs;hall lie &longs;till only upon that Superficies which is <lb/>exactly levelled and parallel to the Plane of the Horizon: as is <lb/>that, for example, of a Lake or &longs;tanding Water being frozen, up­<lb/>on which the &longs;aid Spherical Body would &longs;tand &longs;till, but in a con­<lb/>dition of being moved by every &longs;mall Force. </s> <s>For we having &longs;up­<lb/>po&longs;ed that if that Plane did incline but an hairs breadth only, the <lb/>&longs;aid Ball would move along it &longs;pontaneou&longs;ly towards the part de­<lb/>clining, and on the oppo&longs;ite would have a Re&longs;i&longs;tance, nay, would <lb/>not be able without &longs;ome Violence to move towards the part <pb xlink:href="040/01/987.jpg" pagenum="293"/>ri&longs;ing or a&longs;cending: it of nece&longs;&longs;ity remaineth manife&longs;t, that in the <lb/>Superficies which is exactly equilibrated, the &longs;aid Ball remaineth in­<lb/>different and dubious between Motion and Re&longs;t, &longs;o that every &longs;mall <lb/>Force is &longs;ufficient to move it, as on the contrary, every &longs;mall Re&longs;i­<lb/>&longs;tance, and no greater than that of the meer Air that environs it, is <lb/>able to hold it &longs;till.</s></p><p type="margin"> <s><margin.target id="marg1116"></margin.target>* Or along.</s></p><p type="main"> <s>From whence we may take this Conclu&longs;ion for indubitable, That <lb/>Crave Bodies, all Extern and Adventitious Impediments being re­<lb/>moved, may be moved along the Plane of the Horizon by any ne­<lb/>ver &longs;o &longs;mall Force: but when the &longs;ame Grave is to be thrown along <lb/>an A&longs;cending Plane, then, it beginning to &longs;trive again&longs;t that a&longs;cent, <lb/>having an inclination to the contrary Motion, there &longs;hall be requi­<lb/>red greater Violence, and &longs;till greater the more Elevation that &longs;ame <lb/>Plane &longs;hall have. </s> <s>As for example, the Moveable G, being po&longs;ited <lb/>upon the Line A B parallel to the Horizon, it &longs;hall, as hath been <lb/>&longs;aid, be indifferent on it either to Motion or Re&longs;t, &longs;o that it may <lb/>be moved by a very &longs;mall Force: But if we &longs;hall have the Planes <lb/>Elevated, they &longs;hall not be driven along without Violence; which <lb/><figure id="id.040.01.987.1.jpg" xlink:href="040/01/987/1.jpg"/><lb/>Violence will be required to be <lb/>greater to move it along the Line <lb/>A D, than along A C; and &longs;till <lb/>greater along A E than along A D: <lb/>The which hapneth, becau&longs;e it hath <lb/>greater <emph type="italics"/>Impetus<emph.end type="italics"/> of going down­<lb/>wards along A E than along A D, <lb/>and along A D than along A C. </s> <s>So <lb/>that we may likewi&longs;e conclude <lb/>Grave Bodies to have greater Re&longs;i&longs;tance upon Planes differently <lb/>Elevared, to their being moved along the &longs;ame, according as one <lb/>&longs;hall be more or le&longs;s elevated than the other; and, in fine, that the <lb/>greate&longs;t Re&longs;i&longs;tance of the &longs;ame Grave to its being rai&longs;ed is in the <lb/>Perpendicular A F. </s> <s>But it will be nece&longs;&longs;ary to declare exactly what <lb/>proportion the Force mu&longs;t have to the Weight, that it may be able <lb/>to carry it along &longs;everal elevated Planes, before we proceed any <lb/>farther, to the end that we may perfectly under&longs;tand all that which <lb/>remains to be &longs;poken.</s></p><p type="main"> <s>Letting, therefore, Perpendiculars fall from the points C, D, <lb/>and E unto the Horizontal Line A B, which let be C H, D I, and <lb/>E K: it &longs;hall be demon&longs;trated that the &longs;ame Weight &longs;hall be mo­<lb/>ved along the Plane A C with le&longs;&longs;er Force than along the Perpendi­<lb/>cular A F, (where it is rai&longs;ed by a Force equal to it &longs;elf) accor­<lb/>ding to the proportion by which the Perpendicular C H is le&longs;s than <lb/>A C: and that along the Plane A D, the Force hath the &longs;ame pro­<lb/>portion to the Weight, that the Perpendicular I D hath to D A: <lb/>and, la&longs;tly, that in the Plane A E the <emph type="italics"/>F<emph.end type="italics"/>orce to the Weight ob&longs;er­<lb/>veth the proportion of E K and E A.</s></p><pb xlink:href="040/01/988.jpg" pagenum="294"/><p type="main"> <s>The pre&longs;ent Speculation hath been attempted by <emph type="italics"/>Pappus Alex­<lb/>andrinus<emph.end type="italics"/> in <emph type="italics"/>Lib.<emph.end type="italics"/> 8. <emph type="italics"/>de Collection. </s> <s>Mathemat.<emph.end type="italics"/> but, if I be in the <lb/>right, he hath not hit the mark, and was over&longs;een in the A&longs;&longs;umpti­<lb/>on that he maketh, where he &longs;uppo&longs;eth that the Weight ought to <lb/>be moved along the Horizontal Line by a <emph type="italics"/>F<emph.end type="italics"/>orce given; which is <lb/>fal&longs;e: there needing no &longs;en&longs;ible <emph type="italics"/>F<emph.end type="italics"/>orce (removing the Accidental <lb/>Impediments, which in the Theory are not regarded) to move the <lb/>given Weight along the Horizon, &longs;o that he goeth about in vain <lb/>afterwards to &longs;eek with what <emph type="italics"/>F<emph.end type="italics"/>orce it is to be moved along the <lb/>elevated Plane. </s> <s>It will be therefore better, the <emph type="italics"/>F<emph.end type="italics"/>orce that moveth <lb/>the Weight upwards perpendicularly, (which equalizeth the Gra­<lb/>vity of that Weight which is to be moved) being given, to <lb/>&longs;eek the <emph type="italics"/>F<emph.end type="italics"/>orce that moveth it along the Elevated Plane: Which <lb/>we will endeavour to do in a Method different from that of <lb/><emph type="italics"/>Pappus.<emph.end type="italics"/></s></p><p type="main"> <s>Let us therefore &longs;uppo&longs;e the Circle A I C, and in it the Diame­<lb/>ter A B C, and the Center B, and two Weights of equal Moment <lb/>in the extreams B and C; &longs;o that the Line A C being a Leaver, <lb/>or Ballance moveable about the Center B, the Weight C &longs;hall <lb/>come to be &longs;u&longs;tained by the Weight A. </s> <s>But if we &longs;hall imagine <lb/>the Arm of the Ballance B C to be inclined downwards according <lb/>to the Line B F, but yet in &longs;uch a manner that the two Lines <emph type="italics"/>A B<emph.end type="italics"/><lb/>and <emph type="italics"/>B F<emph.end type="italics"/> do continue &longs;olidly conjoyned in the point <emph type="italics"/>B,<emph.end type="italics"/> in this ca&longs;e <lb/>the Moment of the Weight C &longs;hall not be equal to the Moment <lb/><figure id="id.040.01.988.1.jpg" xlink:href="040/01/988/1.jpg"/><lb/>of the Weight <emph type="italics"/>A,<emph.end type="italics"/> for that the Di­<lb/>&longs;tance of the point <emph type="italics"/>F<emph.end type="italics"/> from the Line <lb/>of Direction, which goeth accord­<lb/>ing to B I, from the <emph type="italics"/>F<emph.end type="italics"/>ulciment B un­<lb/>to the Center of the Earth, is dimi­<lb/>ni&longs;hed: But if from the point <emph type="italics"/>F<emph.end type="italics"/> we <lb/>erect a Perpendicular unto B C, as is <lb/><emph type="italics"/>F<emph.end type="italics"/> K, the Moment of the Weight in <lb/><emph type="italics"/>F<emph.end type="italics"/> &longs;hall be as if it did hang by the <lb/>Line K <emph type="italics"/>F,<emph.end type="italics"/> and look how much the <lb/>Di&longs;tance K B is dimini&longs;hed by the <lb/>Di&longs;tance B <emph type="italics"/>A,<emph.end type="italics"/> &longs;o much is the Moment of the Weight <emph type="italics"/>F<emph.end type="italics"/> dimini&longs;hed <lb/>by the Moment of the <emph type="italics"/>W<emph.end type="italics"/>eight <emph type="italics"/>A. A<emph.end type="italics"/>nd in this fa&longs;hion inclining <lb/>the <emph type="italics"/>W<emph.end type="italics"/>eight more, as for in&longs;tance, according to B L, its Moment &longs;hall <lb/>&longs;till dimini&longs;h and &longs;hall be as if it did hang at the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> M, ac­<lb/>cording to the <emph type="italics"/>L<emph.end type="italics"/>ine M <emph type="italics"/>L,<emph.end type="italics"/> in which point <emph type="italics"/>L<emph.end type="italics"/> it &longs;hall be &longs;u&longs;tained by <lb/>a <emph type="italics"/>W<emph.end type="italics"/>eight placed in <emph type="italics"/>A,<emph.end type="italics"/> &longs;o much le&longs;s than it &longs;elf, by how much the <lb/>Di&longs;tance B <emph type="italics"/>A<emph.end type="italics"/> is greater than the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> M. </s> <s>See therefore that <lb/>the <emph type="italics"/>W<emph.end type="italics"/>eight placed in the extream of the <emph type="italics"/>L<emph.end type="italics"/>eaver B C, in inclining <lb/>downwards along the Circumference C <emph type="italics"/>F L<emph.end type="italics"/> I, cometh to dimini&longs;h <lb/>its Moment and <emph type="italics"/>Impetus<emph.end type="italics"/> of going downwards from time to time, <pb xlink:href="040/01/989.jpg" pagenum="295"/>more and le&longs;s, as it is more or le&longs;s &longs;u&longs;tained by the Lines B F and <lb/>B L: But the con&longs;idering that this Grave de&longs;cending, and &longs;u&longs;tained <lb/>by the Semidiameters B F and B L is one while le&longs;s, and another <lb/>while more con&longs;trained to pa&longs;s along the Circumference C F L, is <lb/>no other, than if we &longs;hould imagine the &longs;ame Circumference <lb/>C F L I to be a Super&longs;icies &longs;o curved, and put under the &longs;ame <lb/>Moveable: &longs;o that bearing it &longs;elf thereon it were con&longs;trained to <lb/>de&longs;cend along thereby; for if in the one and other manner the <lb/>Moveable de&longs;cribeth the &longs;ame Cour&longs;e or Way, it will nothing im­<lb/>port whether, if &longs;u&longs;pended at the Center B, it is &longs;u&longs;tained by the <lb/>Semidiameter of the Circle, or el&longs;e, whether that Fulciment being <lb/>taken away, it proceed along the Circumference C F L I: So that <lb/>we may confidently affirm, that the Grave de&longs;cending downwards <lb/>from the point C along the Circumference C F L I, its Moment <lb/>of De&longs;cent in the point C is total and entire, becau&longs;e it is not in <lb/>any part &longs;u&longs;tained by the Circumference: And there is not in that <lb/>fir&longs;t point C, any indi&longs;po&longs;ition to Motion different from that, which <lb/>being at liberty, it would make along the Perpendicular and Con­<lb/>tingent Line D C E: But if the Moveable &longs;hall be placed in the <lb/>point F, then its Gravity is in part &longs;u&longs;tained, and its Moment of <lb/>De&longs;cent is dimini&longs;hed by the Circular Path or Way that is placed <lb/>under it, in that proportion wherewith the <emph type="italics"/>L<emph.end type="italics"/>ine <emph type="italics"/>B<emph.end type="italics"/> K is overcome <lb/>by <emph type="italics"/>B<emph.end type="italics"/> C: But if when the Moveable is in F, at the fir&longs;t in&longs;tant of <lb/>&longs;uch its Motion, it be as if it were in the Plane elevated according <lb/>to the Contingent <emph type="italics"/>L<emph.end type="italics"/>ine G F H, for that rea&longs;on the inclination of the <lb/>Circumference in the point F differeth not from the inclination of <lb/>the Contingent <emph type="italics"/>L<emph.end type="italics"/>ine F G any more &longs;ave the in&longs;en&longs;ible Angle of <lb/>the Contact. </s> <s>And in the &longs;ame manner we &longs;hall find the Moment <lb/>of the &longs;aid Moveable to dimini&longs;h in the point <emph type="italics"/>L,<emph.end type="italics"/> as the <emph type="italics"/>L<emph.end type="italics"/>ine BM <lb/>is dimini&longs;hed by B C; &longs;o that in the Plane contingent to the Circle <lb/>in the point <emph type="italics"/>L,<emph.end type="italics"/> as for in&longs;tance, according to the <emph type="italics"/>L<emph.end type="italics"/>ine N <emph type="italics"/>L<emph.end type="italics"/> O, the <lb/>Moment of De&longs;cent dimini&longs;heth in the Moveable with the &longs;ame <lb/>proportion. </s> <s>If therefore ^{*} upon the Plane HG the Moment of the <lb/><arrow.to.target n="marg1117"></arrow.to.target><lb/>Moveable be dimini&longs;hed by the total <emph type="italics"/>Impetus<emph.end type="italics"/> which it hath in its <lb/>Perpendicular D C E, according to the proportion of the <emph type="italics"/>L<emph.end type="italics"/>ine K B <lb/>to the <emph type="italics"/>L<emph.end type="italics"/>ine B C, and B F, being by the Solicitude of the Triangles <lb/>K B F and K F H the &longs;ame proportion betwixt the <emph type="italics"/>L<emph.end type="italics"/>ines K F and <lb/>F H, as betwixt the &longs;aid K B and <emph type="italics"/>B<emph.end type="italics"/> F, we will conclude that the <lb/>proportion of the entire and ab&longs;olute Moment, that the Moveable <lb/>hath in the Perpendicular to the Horizon to that which it hath up­<lb/>on the Inclined Plane H F, hath the &longs;ame proportion that the <lb/><emph type="italics"/>L<emph.end type="italics"/>ine H F hath to the <emph type="italics"/>L<emph.end type="italics"/>ine F K; that is, that the <emph type="italics"/>L<emph.end type="italics"/>ength of the <lb/>Inclined Plane hath to the Perpendicular which &longs;hall fall from it <lb/>unto the Horizon. </s> <s>So that pa&longs;&longs;ing to a more di&longs;tinct Figure, &longs;uch <lb/>as this here pre&longs;ent, the Moment of De&longs;cending which the Move­<pb xlink:href="040/01/990.jpg" pagenum="296"/>able hath upon the inclined Plane C A hath to its total Moment <lb/>wherewith it gravitates in the Perpendicular to the Horizon C P the <lb/>&longs;ame proportion that the &longs;aid Line P C hath to C A. </s> <s>And if thus it <lb/>be, it is manife&longs;t, that like as the Force that &longs;u&longs;tai­<lb/>neth the Weight in the Perpendiculation P C ought <lb/><figure id="id.040.01.990.1.jpg" xlink:href="040/01/990/1.jpg"/><lb/>to be equal to the &longs;ame, &longs;o for &longs;u&longs;taining it in the <lb/>inclined Plane C A, it will &longs;uffice that it be &longs;o much <lb/>le&longs;&longs;er, by how much the &longs;aid Perpendicular C P wan­<lb/>teth of the Line C A: and becau&longs;e, as &longs;ometimes we <lb/>&longs;ce, it &longs;ufficeth, that the Force for moving of the <lb/>Weight do in&longs;en&longs;ibly &longs;uperate that which &longs;u&longs;taineth it, therefore <lb/>we will infer this univer&longs;al Propo&longs;ition, [That upon an Elevated <lb/>Plane the Force hath to the Weight the &longs;ame proportion, as the <lb/>Perpendicular let fall from the Plane unto the Horizon hath to the <lb/>Length of the &longs;aid Plane.]</s></p><p type="margin"> <s><margin.target id="marg1117"></margin.target>* Or along</s></p><p type="main"> <s>Returning now to our fir&longs;t Intention, which was to inve&longs;tigate <lb/>the Nature of the Screw, we will con&longs;ider the Triangle A B C, of <lb/>which the Line A B is Horizontal, B C perpendicular to the &longs;aid <lb/>Horizon, and A C a Plane elevated; upon which the Moveable D <lb/>&longs;hall be drawn by a Force &longs;o much le&longs;s than it, by how much the <lb/>Line B C is &longs;horter than C A: But to elevate or rai&longs;e the &longs;aid <lb/>Weight along the &longs;aid Plane A C, is as much as if the Triangle <lb/>C A B &longs;tanding &longs;till, the Weight <lb/><figure id="id.040.01.990.2.jpg" xlink:href="040/01/990/2.jpg"/><lb/>D be moved towards C, which is <lb/>the &longs;ame, as if the &longs;ame Weight <lb/>never removing from the Perpen­<lb/>dicular A E, the Triangle did <lb/>pre&longs;s forwards towards H. </s> <s>For if <lb/>it were in the Site F H G, the <lb/>Moveable would be found to <lb/>have mounted the height A I. <lb/>Now, in fine, the primary Form and E&longs;&longs;ence of the Screw is no­<lb/>thing el&longs;e but &longs;uch a Triangle A C B, which being forced for­<lb/>wards, &longs;hall work it &longs;elf under the Grave Body to be rai&longs;ed, and <lb/>lifteth it up, as we &longs;ay, by the ^{*} head and &longs;houlders. </s> <s>And this was <lb/><arrow.to.target n="marg1118"></arrow.to.target><lb/>its fir&longs;t Original: For its fir&longs;t Inventor (whoever he was) con&longs;i­<lb/>dering how that the Triangle A B C going forwards rai&longs;eth the <lb/>Weight D, he might have framed an In&longs;trument like to the &longs;aid <lb/>Triangle, of a very &longs;olid Matter, which being thru&longs;t forwards did <lb/>rai&longs;e up the propo&longs;ed Weight: But afterwards con&longs;idering better, <lb/>how that that &longs;ame Machine might be reduced into a much le&longs;&longs;er <lb/>and more commodious Form, taking the &longs;ame Triangle he twined <lb/>and wound it about the Cylinder A B C D in &longs;uch a fa&longs;hion, that <lb/>the height of the &longs;aid Triangle, that is the Line C B, did make the <lb/>Height of the Cylinder, and the A&longs;cending Plane did beget upon <pb xlink:href="040/01/991.jpg" pagenum="297"/>the &longs;aid Cylinder the Helical Line de&longs;cribed by the Line AEFGH, <lb/>which we vulgarly call the Wale of the Screw, which was produ­<lb/>ced by the Line A C. </s> <s>And in this manner is the In&longs;trument made, <lb/>which is by the Greeks called <foreign lang="greek">*ko/xlos,</foreign> and by us a Screw; which <lb/><arrow.to.target n="marg1119"></arrow.to.target><lb/>winding about <lb/>cometh to work <lb/><figure id="id.040.01.991.1.jpg" xlink:href="040/01/991/1.jpg"/><lb/>and in&longs;inu­<lb/>ate with its <lb/>Wales under <lb/>the Weight, and <lb/>with facility rai­<lb/>&longs;eth it. </s> <s>And we <lb/>having demon­<lb/>&longs;trated, That up­<lb/>on [<emph type="italics"/>or along<emph.end type="italics"/>] <lb/>the elevated Plane the Force hath the &longs;ame proportion to the <lb/>Weight, that the perpendicular Altitude of the &longs;aid Plane hath to <lb/>its Length; &longs;o, &longs;uppo&longs;ing that the Force in the Screw A B C D is <lb/>multiplied according to the proportion by which the Length of the <lb/>whole Wale exceedeth the Altitude C B, from hence we come <lb/>to know that making the Screw with its Helix's more thick or clo&longs;e <lb/>together, it becometh &longs;o much the more forceable, as being begot <lb/>by a Plane le&longs;s elevated, and who&longs;e Length regards its own Per­<lb/>pendicular Altitude with greater proportion. </s> <s>But we will not <lb/>omit to adverti&longs;e you, that de&longs;iring to find the Force of a propo­<lb/>&longs;ed Screw, it will not be needful that we mea&longs;ure the Length of <lb/>all its Wales, and the Altitude of the whole Cylinder, but it <lb/>will be enough if we &longs;hall but examine how many times the Di­<lb/>&longs;tance betwixt two &longs;ingle and Contiguous terms do enter into one <lb/>&longs;ole Turn of the &longs;ame Wale, as for example, how many times <lb/>the Di&longs;tance AF is contained in the Length of the Turn AEF: <lb/>For this is the &longs;ame proportion that the Altitude CB hath to all <lb/>the Wale.</s></p><p type="margin"> <s><margin.target id="marg1118"></margin.target><emph type="italics"/>Levar in capo<emph.end type="italics"/><lb/> &longs;ignfieth to lift <lb/>on high by force</s></p><p type="margin"> <s><margin.target id="marg1119"></margin.target>* <foreign lang="greek">*ko/xlos,</foreign> in La­<lb/>tine <emph type="italics"/>Cocblea,<emph.end type="italics"/> any <lb/>Screw winding <lb/>like the Shell of <lb/>a Snail.</s></p><p type="main"> <s>If all that be under&longs;tood which we have hitherto &longs;poken touch­<lb/>ing the Nature of this In&longs;trument, I do not doubt in the lea&longs;t but <lb/>that all the other circum&longs;tances may without difficulty be compre­<lb/>hended: as for in&longs;tance, that in&longs;teed of making the Weight to <lb/>mount upon the Screw if one accommodates its Nut with <lb/>the Helix incavated or made hollow, into which the Male Screw <lb/>that is the Wale entring, & then being turned round it rai&longs;eth and <lb/>lifteth up the Nut or Male Screw together with the Weight which <lb/>was hanged thereat. </s> <s>La&longs;tly, we are not to pa&longs;s over that Con&longs;idera­<lb/>tion with &longs;ilence which at the beginning hath been &longs;aid to be nece&longs;­<lb/>&longs;ary for us to have in all Mechanick In&longs;truments, to wit, That <lb/>what is gained in Force by their a&longs;&longs;i&longs;tance, is lo&longs;t again in Time, <pb xlink:href="040/01/992.jpg" pagenum="298"/>and in the Velocity: which peradventure, might not have &longs;eemed <lb/>to &longs;ome &longs;o true and manife&longs;t in the pre&longs;ent Contemplation; nay, <lb/>rather it &longs;eems, that in this ca&longs;e the Force is multiplied without the <lb/>Movers moving a longer way than the Moveable: In regard, that <lb/>if we &longs;hall in the Triangle A B C &longs;uppo&longs;e the Line A B to be the <lb/>Plane of the Horizon, A C the elevated Plane, who&longs;e Altitude is <lb/>mea&longs;ured by the Perpendicular C B, a Moveable placed upon the <lb/>Plane A C, and the Cord E D <emph type="italics"/>F<emph.end type="italics"/> tyed to it, and a <emph type="italics"/>F<emph.end type="italics"/>orce or Weight <lb/>applyed in <emph type="italics"/>F<emph.end type="italics"/> that hath to the <lb/>Gravity of the Weight E the <lb/><figure id="id.040.01.992.1.jpg" xlink:href="040/01/992/1.jpg"/><lb/>&longs;ame proportion that the Line <lb/>B C hath to C A; by what <lb/>hath been demon&longs;trated, the <lb/>Weight <emph type="italics"/>F<emph.end type="italics"/> &longs;hall de&longs;cend <lb/>downwards, drawing the <lb/>Moveable E along the eleva­<lb/>ted Plane; nor &longs;hall the Move­<lb/>able E mea&longs;ure a greater Space <lb/>when it &longs;hall have pa&longs;&longs;ed the <lb/>whole Line A <emph type="italics"/>C,<emph.end type="italics"/> than that which the &longs;aid Grave <emph type="italics"/>F<emph.end type="italics"/> mea&longs;ureth in its <lb/>de&longs;cent downwards. </s> <s>But here yet it mu&longs;t be adverti&longs;ed, that al­<lb/>though the Moveable E &longs;hall have pa&longs;&longs;ed the whole Line A C, in <lb/>the &longs;ame Time that the other Grave <emph type="italics"/>F<emph.end type="italics"/> &longs;hall have been aba&longs;ed the <lb/>like Space, neverthele&longs;s the Grave E &longs;hall not have retired from the <lb/>common Center of things Grave more than the Space of the Per­<lb/>pendicular <emph type="italics"/>C<emph.end type="italics"/> B. but yet the Grave <emph type="italics"/>F<emph.end type="italics"/> de&longs;cending Perpendicularly &longs;hall <lb/>be aba&longs;ed a Space equal to the whole Line A <emph type="italics"/>C.<emph.end type="italics"/> And becau&longs;e Grave <lb/>Bodies make no Re&longs;i&longs;tance to Tran&longs;ver&longs;al Motions, but only &longs;o <lb/>far as they happen to recede from the <emph type="italics"/>C<emph.end type="italics"/>enter of the Earth; There­<lb/>fore the Moveable E in all the Motion A <emph type="italics"/>C<emph.end type="italics"/> being rai&longs;ed no more <lb/>than the length of the Line <emph type="italics"/>C<emph.end type="italics"/>B, but the other <emph type="italics"/>F<emph.end type="italics"/> being aba&longs;ed per­<lb/>pendicularly the quantity of all the Line A <emph type="italics"/>C<emph.end type="italics"/>: Therefore we may <lb/>de&longs;ervedly affirm that Way of the <emph type="italics"/>F<emph.end type="italics"/>orce E maintaineth the &longs;ame <lb/>proportion to the <emph type="italics"/>F<emph.end type="italics"/>orce <emph type="italics"/>F<emph.end type="italics"/> that the <emph type="italics"/>L<emph.end type="italics"/>ine A <emph type="italics"/>C<emph.end type="italics"/> hath to <emph type="italics"/>C<emph.end type="italics"/> B; that is, <lb/>the Weight E to the Weight <emph type="italics"/>F.<emph.end type="italics"/> It very much importeth, therefore, <lb/>to con&longs;ider by [<emph type="italics"/>or along<emph.end type="italics"/>] what <emph type="italics"/>L<emph.end type="italics"/>ines the Motions are made, e&longs;pe­<lb/>cially in exanimate Grave Bodies, the Moments of which have their <lb/>total Vigour, and entire Re&longs;i&longs;tance in the <emph type="italics"/>L<emph.end type="italics"/>ine Perpendicular to <lb/>the Horizon; and in the others tran&longs;ver&longs;ally Elevated and Inclined <lb/>they feel the more or le&longs;s Vigour, <emph type="italics"/>Impetus,<emph.end type="italics"/> or Re&longs;i&longs;tance, the more <lb/>or le&longs;s tho&longs;e Inclinations approach unto the Perpendicular Inclina­<lb/>tion.</s></p><pb xlink:href="040/01/993.jpg" pagenum="299"/><p type="head"> <s><emph type="italics"/>Of the SCREW of<emph.end type="italics"/> ARCHIMEDES <lb/><emph type="italics"/>to draw Waier.<emph.end type="italics"/></s></p><p type="main"> <s>I Do not think it &longs;it in this place to pa&longs;s over with Silence the <lb/>Invention of <emph type="italics"/>Archimedes<emph.end type="italics"/> to rai&longs;e Wa er with the Screw, which <lb/>is not only marvellous, but miraculous: for we &longs;hall find that <lb/>the Water a&longs;cendeth in the Screw continually de&longs;cending; and in <lb/>a given Time, with a given Force doth rai&longs;e an un&longs;peakable quan­<lb/>tity therof. </s> <s>But before we proceed any farther, let us declare the u&longs;e <lb/>of the Screw in making Water to ri&longs;e: And in the en&longs;uing Figure, <lb/>let us con&longs;ider the Line I L O P Q <lb/><figure id="id.040.01.993.1.jpg" xlink:href="040/01/993/1.jpg"/><lb/>R S H being wrapped or twined <lb/>about the Collumn M I K H, <lb/>which Line you are to &longs;uppo&longs;e to <lb/>be a Chanel thorow which the <lb/>Water may run: If we &longs;hall put <lb/>the end I into the Water, making <lb/>the Screw to &longs;tand leaning, &longs;o as <lb/>the point L may be lower than <lb/>the fir&longs;t I, as the Diagram &longs;hew­<lb/>eth, and &longs;hall turn it round about <lb/>on the two Axes, T and V, the Water &longs;hall run thorow the Cha­<lb/>nel, till that in the end it &longs;hall di&longs;charge &longs;orth at the mouth H. <lb/></s> <s>Now I &longs;ay, that the Water, in its conveyance from the point I to <lb/>the point H, doth go all the way de&longs;cending, although the point H <lb/>be higher than the point I. </s> <s>Which that it is &longs;o, we will declare <lb/>in this manner. </s> <s>We will de&longs;cribe the Triangle A C B, which is <lb/>that of which the Screw H I is generated, in &longs;uch &longs;ort that the <lb/>Chanel of the Screw is repre&longs;ented by the Line A C, who&longs;e <lb/>A&longs;cent and Elevation is determined by the Angle C A B; that is <lb/>to &longs;ay, if &longs;o be, that that Angle &longs;hall be the third or fourth part of a <lb/>Right Angle, then the Elevation of the Chanel A C &longs;hall be ac­<lb/>cording to 1/3, or 1/4 of a Right Angle. </s> <s>And it is manife&longs;t; that the <lb/>Ri&longs;e of that &longs;ame Chanel A C will be taken away deba&longs;ing the <lb/>point C as far as to B: for then the Chanel A C &longs;hall have no <lb/>Elevation. </s> <s>And deba&longs;ing the point C a little below B, the Water <lb/>will naturally run along the Chanel A C downwards from the <lb/>point A towards C. </s> <s>Let us therefore conclude, that the Angle A <lb/>being 1/3 of a Right Angle, the Chanel A C &longs;hall no longer have any <lb/>Ri&longs;e, deba&longs;ing it on the part <emph type="italics"/>C<emph.end type="italics"/> for 1/3 of a Right Angle.</s></p><p type="main"> <s>The&longs;e things under&longs;tood, let us infold the Triangle about the <lb/>Column, and let us make the Screw B A E F G, &c. </s> <s>which if it <lb/>&longs;hall be placed at Right Angles with the end B in the Water, turn­<lb/>ing it about, it &longs;hall not this way draw up the Water, the Chanel <lb/>about the Column being elevated, as may be &longs;een by the part B A.</s> <pb xlink:href="040/01/994.jpg" pagenum="300"/><s>But although the Column &longs;tand erect at Right-Angles, yet for all <lb/>that, the Ri&longs;e along the Screw, folded about the Column, is not of <lb/>a greater Elevation than of 1/3 of a Right Angle, it being generated <lb/>by the Elevation of the Chanel A C: Therefore if we incline the <lb/>Column but 1/3 of the <lb/><figure id="id.040.01.994.1.jpg" xlink:href="040/01/994/1.jpg"/><lb/>&longs;aid Right Angle, and <lb/>a little more, as we &longs;ee <lb/>I K H M, there is a <lb/>Tran&longs;ition and Moti­<lb/>on along the Chanel <lb/>I L: Therefore the <lb/>Water from the point <lb/>I to the point L &longs;hall <lb/>move de&longs;cending, and <lb/>the Screw being turned <lb/>about, the other parts <lb/>of it &longs;hall &longs;ucce&longs;&longs;ively <lb/>di&longs;po&longs;e or pre&longs;ent <lb/>them&longs;elves to the Wa­<lb/>ter in the &longs;ame Po&longs;ition as the part I L: Whereupon the Water <lb/>&longs;hall go &longs;ucce&longs;&longs;ively de&longs;cending, and in the end &longs;hall be found to <lb/>be a&longs;cended from the point I to the point H. </s> <s>Which how admira­<lb/>ble a thing it is, I leave &longs;uch to judge who &longs;hall perfectly have un­<lb/>der&longs;tood it. </s> <s>And by what hath been &longs;aid, we come to know, That <lb/>the Screw for rai&longs;ing of Water ought to be inclined a little more <lb/>than the quantity of the Angle of the Triangle by which the &longs;aid <lb/>Screw is de&longs;cribed.</s></p><p type="head"> <s><emph type="italics"/>Of the Force of the <lb/>HAMMER, MALLET, or BEETLE.<emph.end type="italics"/></s></p><p type="main"> <s>The Inve&longs;tigation of the cau&longs;e of the Force of the&longs;e Percuti­<lb/>ents is nece&longs;&longs;ary for many Rea&longs;ons: and fir&longs;t, becau&longs;e that <lb/>there appeareth in it much more matter of admiration than <lb/>is ob&longs;erved in any other Mechanick In&longs;trument what&longs;oever. </s> <s>For <lb/>&longs;triking with the Hammer upon a Nail, which is to be driven into <lb/>a very tough Po&longs;t, or with the Beetle upon a Stake that is to pene­<lb/>trate into very &longs;tiffe ground, we &longs;ee, that by the &longs;ole vertue of the <lb/>blow of the Percutient both the one and the other is thru&longs;t for­<lb/>wards: &longs;o that without that, only laying the Beetle upon the <lb/>Nail or Stake it will not move then, nay, more, although you <lb/>&longs;hould lay upon them a Weight very much heavier than the &longs;aid <lb/>Beetle. </s> <s>An effect truly admirable, and &longs;o much the more worthy <lb/>of Contemplation, in that, as I conceive, none of tho&longs;e who have <pb xlink:href="040/01/995.jpg" pagenum="301"/>hitherto di&longs;cour&longs;ed upon it, have &longs;aid any thing that hits the mark; <lb/>which we may take for a certain Sign and Argument of the Ob&longs;cu­<lb/>rity and difficulty of this <emph type="italics"/>S<emph.end type="italics"/>peculation. </s> <s>For <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> or others, <lb/>who would reduce the cau&longs;e of this admirable Effect unto the <lb/>length of the <emph type="italics"/>Manubrium,<emph.end type="italics"/> or Handle, may, in my judgement, be <lb/>made to &longs;ee their mi&longs;take in the effect of tho&longs;e In&longs;truments, which <lb/>having no Handle, yet percu&longs;s, either in falling from on high <lb/>downwards, or by being thrown with Velocity &longs;idewaies. </s> <s>There­<lb/>fore it is requi&longs;ite, that we have recour&longs;e to &longs;ome other Principle, if <lb/>we would find out the truth of this bu&longs;ine&longs;s; the cau&longs;e of which, <lb/>although it be of its own nature &longs;omewhat ob&longs;cure, and of diffi­<lb/>cult con&longs;ideration, yet neverthele&longs;s we will attempt with the grea­<lb/>te&longs;t per&longs;picuity po&longs;&longs;ible to render it clear and obvious, &longs;hewing, for <lb/>a clo&longs;e of all, that the Principle and Original of this Effect is deri­<lb/>ved from no other Fountain than this, from which the rea&longs;ons of all <lb/>other Mechanick Effects do proceed: and this we will do, by &longs;etting <lb/>before your eyes that very thing which is &longs;een to befall in every <lb/>other Mechanick Operation, <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> That the Force, the Re&longs;i&longs;tance, <lb/>and the Space by which the Motion is made, do go alternately <lb/>with &longs;uch proportion operating, and with &longs;uch a rate an&longs;wering to <lb/>each other, that a Re&longs;i&longs;tance, equal to the Force, &longs;hall be moved by <lb/>the &longs;aid Force along an equal Space, with Velocity equal to that <lb/>with which it is moved. </s> <s>Likewi&longs;e, That a Force that is le&longs;s by half <lb/>than a Re&longs;i&longs;tance &longs;hall be able to move it, &longs;o that it be moved <lb/>with double Velocity, or, if you will, for a Di&longs;tance twice as great <lb/>as that which the moved Re&longs;i&longs;tance &longs;hall pa&longs;s: and, in a word, it <lb/>hath been &longs;een in all the other In&longs;truments, that any, never &longs;o great, <lb/>Re&longs;i&longs;tance may be moved by every &longs;mall Force given, provided, <lb/>that the Space, along which the Re&longs;i&longs;tance &longs;hall move, have the <lb/>&longs;ame proportion that is found to be betwixt the &longs;aid great Re&longs;i­<lb/>&longs;tance and the Force: and that this is according to the nece&longs;&longs;ary <lb/>Order and Con&longs;titution of Nature: So that inverting the Di&longs;cour&longs;e, <lb/>and Arguing the contrary way, what wonder &longs;hall it be, if that <lb/>Power that &longs;hall move a &longs;mall Re&longs;i&longs;tance a great way, &longs;hall carry <lb/>one an hundred times bigger an hundredth part of that Di&longs;tance? <lb/></s> <s>Certainly none at all: nay, it would be ab&longs;urd, yea, impo&longs;&longs;ible <lb/>that it &longs;hould be otherwi&longs;e. </s> <s>Let us therefore con&longs;ider, what the <lb/>Re&longs;i&longs;tance of the Beetle unto Motion may be in that point where <lb/>it is to &longs;trike, and how far, if it do not &longs;trike, it would be carryed <lb/>by the received Force beyond that point: and again, what Re&longs;i­<lb/>&longs;tance to Motion there is in him who &longs;triketh, and how much by <lb/>that &longs;ame Percu&longs;&longs;ion he is moved: and, having found that this <lb/>great Re&longs;i&longs;tance goeth forwards by a percu&longs;&longs;ion &longs;o much le&longs;s than <lb/>the Beetle driven by the <emph type="italics"/>Impetus<emph.end type="italics"/> of him that moveth it would do, <lb/>by how much that &longs;ame great Re&longs;i&longs;tance is greater than that of <pb xlink:href="040/01/996.jpg" pagenum="302"/>the Beetle; we &longs;hall cea&longs;e to wonder at the Effect, which doth not <lb/>in the lea&longs;t exceed the terms of Natural Con&longs;titutions, and of <lb/>what hath been &longs;poken. </s> <s>Let us, for better under&longs;tanding, give an <lb/>example thereof in particular Terms. </s> <s>There is a Beetle, which ha­<lb/>ving four degrees of Re&longs;i&longs;tance, is moved by &longs;uch a Force, that <lb/>being freed from it in that term where it maketh the Percu&longs;&longs;ion, it <lb/>would, meeting with no &longs;top, go ten Paces beyond it, and in that <lb/>term a great po&longs;t being oppo&longs;ed to it, who&longs;e Re&longs;i&longs;tance to Moti­<lb/>on is as four thou&longs;and, that is, a thou&longs;and times greater than that of <lb/>the Beetle, (but yet is not immoveable) &longs;o that it without mea­<lb/>&longs;ure or proportion exceeds the Re&longs;i&longs;tance of the Beetle, yet the <lb/>Percu&longs;&longs;ion being made on it, it &longs;hall be driven forwards, though in­<lb/>deed no more but the thou&longs;andth part of the ten Paces which the <lb/>Beetle &longs;hall be moved: and thus in an inverted method, changing <lb/>that which hath been &longs;poken touching the other Mechanical Effects, <lb/>we may inve&longs;tigate the rea&longs;on of the Force of the Percutient. </s> <s>I <lb/>know that here ari&longs;e difficulties and objections unto &longs;ome, which <lb/>they will not ea&longs;ily be removed from, but we will freely remit them <lb/><arrow.to.target n="marg1120"></arrow.to.target><lb/>to the ^{*} Problems Mechanical, which we &longs;hall adjoyn in the end of <lb/>this Di&longs;cour&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1120"></margin.target>* The&longs;e Pro­<lb/>blems he here <lb/>promi&longs;eth were <lb/>never yet ex­<lb/>tant.</s></p><pb xlink:href="040/01/997.jpg" pagenum="303"/><p type="head"> <s>THE <lb/>BALLANCE <lb/>OF <lb/><emph type="italics"/>Signeur GALILEO GALILEI<emph.end type="italics"/>;</s></p><p type="head"> <s>In which, in immitation of <emph type="italics"/>Archimedes<emph.end type="italics"/> in the <lb/>Problem of the Crown, he &longs;heweth how to <lb/>find the proportion of the Alloy of <lb/>Mixt-Metals; and how to make <lb/>the &longs;aid In&longs;trument.</s></p><p type="main"> <s>As it is well known, by &longs;uch who take the pains to read <lb/>old Authors, that <emph type="italics"/>Archimedes<emph.end type="italics"/> detected the Cheat of <lb/>the Gold&longs;mith in the Crown of ^{*} <emph type="italics"/>Hieron,<emph.end type="italics"/> &longs;o I think it <lb/><arrow.to.target n="marg1121"></arrow.to.target><lb/>hitherto unknown what method this Great Philo&longs;o­<lb/>pher ob&longs;erved in that Di&longs;covery: for the opinion, that he did per­<lb/>form it by putting the Crown into the Water, having fir&longs;t put in­<lb/><arrow.to.target n="marg1122"></arrow.to.target><lb/>to it &longs;uch another Ma&longs;s of pure Gold, and another of Silver &longs;eve­<lb/>rally, and that from the differences in their making the Water <lb/>more or le&longs;s ri&longs;e and run over, he came to know the Mixture or <lb/>Alloy of the Gold with the Silver, of which that Crown was <lb/>compounded; &longs;eems a thing (if I may &longs;peak it) very gro&longs;s, and <lb/>far from exactne&longs;s. </s> <s>And it will &longs;eem &longs;o much the more dull to <lb/>&longs;uch who have read and under&longs;tood the exqui&longs;ite Inventions of &longs;o <lb/>Divine a Man among&longs;t the Memorials that are extant of him; by <lb/>which it is very manife&longs;t that all other Wits are inferiour to that <lb/>of <emph type="italics"/>Archimedes.<emph.end type="italics"/> Indeed I believe, that Fame divulging it abroad, <lb/>that <emph type="italics"/>Archimedes<emph.end type="italics"/> had di&longs;covered that &longs;ame Fraud by means of the <lb/>Water, &longs;ome Writer of tho&longs;e Times committed the memory there­<lb/>of to Po&longs;terity, and that this per&longs;on, that he might add &longs;omething <lb/>to that little which he had heard by common Fame, did relate that <lb/><emph type="italics"/>Archimedes<emph.end type="italics"/> had made u&longs;e of the Water in that manner, as &longs;ince <lb/>hath been by the generality of men believed.</s></p><p type="margin"> <s><margin.target id="marg1121"></margin.target>* King of <emph type="italics"/>Sicily,<emph.end type="italics"/><lb/>and Kin&longs;man to <lb/>that Great Ma­<lb/>thematician.</s></p><p type="margin"> <s><margin.target id="marg1122"></margin.target><emph type="italics"/>Plutarch in Vit. <lb/></s> <s>Marcel.<emph.end type="italics"/></s></p><p type="main"> <s>But in regard I know, that that method is altogether fallacious, <lb/>and falls &longs;hort of that exactne&longs;s which is required in Mathematical <lb/>Matters, I have often thought in what manner, by help of the <lb/>Water, one might exactly find the Mixture of two Metals, and <lb/>in the end, after I had diligently peru&longs;ed that which <emph type="italics"/>Archimedes<emph.end type="italics"/><lb/>demon&longs;trateth in his Books <emph type="italics"/>De in&longs;identibus aquæ,<emph.end type="italics"/> and tho&longs;e others <pb xlink:href="040/01/998.jpg" pagenum="304"/><emph type="italics"/>De æquiponder antium,<emph.end type="italics"/> there came into my thoughts a Rule which <lb/>exqui&longs;itely re&longs;olveth our Que&longs;tion; which Rule I believe to be <lb/>the &longs;ame that <emph type="italics"/>Archimedes<emph.end type="italics"/> made u&longs;e of, &longs;eeing that be&longs;ides the <lb/>u&longs;e that is to be made of the Water, the exactne&longs;s of the Work <lb/>dependeth al&longs;o upon certain Demon&longs;trations found by the &longs;aid <lb/><emph type="italics"/>Archimedes.<emph.end type="italics"/></s></p><p type="main"> <s>The way is by help of a Ballance, who&longs;e Con&longs;truction and U&longs;e <lb/>&longs;hall be &longs;hewn by and by, after we &longs;hall have declared what is <lb/>nece&longs;&longs;ary for the knowledge thereof. </s> <s>You mu&longs;t know there­<lb/>fore, that the Solid Bodies that &longs;ink in the Water weigh &longs;o much <lb/>le&longs;s in the Water than in the Air, as a Ma&longs;s of Water equal to <lb/>the &longs;aid Solid doth weigh in the Air: which hath been demon­<lb/>&longs;trated by <emph type="italics"/>Archimedes.<emph.end type="italics"/> But, in regard his Demon&longs;tration is very <lb/>mediate, becau&longs;e I would not be over long, laying it a&longs;ide, I &longs;hall <lb/>declare the &longs;ame another way. </s> <s>Let us con&longs;ider, therefore, that <lb/>putting into the Water <emph type="italics"/>v. </s> <s>g.<emph.end type="italics"/> a Ma&longs;s of Gold, if that Ma&longs;s were <lb/>of Water it would have no weight at all: For the Water moveth <lb/>neither upwards, nor downwards in the Water: It remains, <lb/>therefore, that the Ma&longs;s of Gold weigheth in the Water only &longs;o <lb/>much as the Gravity of the Gold exceeds the Gravity of the Wa­<lb/>ter. </s> <s>And the like is to be under&longs;tood of other Metals. </s> <s>And be­<lb/>cau&longs;e the Metals are different from each other in Gravity, their <lb/>Gravity in the Water &longs;hall dimini&longs;h according to &longs;everal proporti­<lb/>ons. </s> <s>As for example: Let us &longs;uppo&longs;e that Gold weigheth twenty <lb/>times more than Water, it is manife&longs;t by that which hath been <lb/>&longs;poken, that the Gold will weigh le&longs;s in the Water than in the <lb/>Air by a twentieth part of its whole weight. </s> <s>Now, let us &longs;uppo&longs;e <lb/>that Silver, as being le&longs;s Grave than Gold, weigheth 12 times more <lb/>than Water: this then, being weighed in the Water, &longs;hall di­<lb/>mini&longs;h in Gravity the twelfth part of its whole weight. </s> <s>Therefore <lb/>the Gravity of Gold in the Water decrea&longs;eth le&longs;s than that of <lb/>Silver; for that dimini&longs;heth a twentieth part, and this a twelfth. <lb/></s> <s>If therefore in an exqui&longs;ite Ballance we &longs;hall hang a Metal at the <lb/>one Arm, and at the other a Counterpoi&longs;e that weigheth equally <lb/>with the &longs;aid Metal in the Water, leaving the Counterpoi&longs;e in the <lb/>Air, to the end that it may equivalate and compen&longs;ate the Me­<lb/>tal, it will be nece&longs;&longs;ary to hang it nearer the Perpendicular or <lb/>Cook. </s> <s>As for example, Let the Ballance be A B, its Perpendicu­<lb/><figure id="id.040.01.998.1.jpg" xlink:href="040/01/998/1.jpg"/><lb/>lar C, and let a <lb/>Ma&longs;s of &longs;ome <lb/>Metal be &longs;u­<lb/>&longs;pended at B, <lb/>counterpoi&longs;edby <lb/>the Weight D: putting the Weight B into the Water, the <lb/>Weight D in A would weigh more: therefore that they may <pb xlink:href="040/01/999.jpg" pagenum="305"/>weigh equally it would be nece&longs;&longs;ary to hang it nearer to the <lb/>Perpendicular C, as <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> in E: and look how many times the Di­<lb/>&longs;tance C A &longs;hall contain A E, &longs;o many times &longs;hall the Metal <lb/>weigh more than the Water. </s> <s>Let us therefore &longs;uppo&longs;e that the <lb/>Weight in B be Gold, and that weighed in the Water it with­<lb/>draws the Counterpoi&longs;e D into E; and then doing the &longs;ame with <lb/>pure Silver, let us &longs;uppo&longs;e that its Counterpoi&longs;e, when afterwards <lb/>it is weighed in the Water, returneth to F: which point &longs;hall be <lb/>nearer to the point C, as Experience &longs;heweth, becau&longs;e the Silver <lb/>is le&longs;s grave than the Gold: And the Di&longs;tance that is between <lb/>A and F &longs;hall have the &longs;ame Difference with the Di&longs;tance A E, <lb/>that the Gravity of the Gold hath with that of the Silver. </s> <s>But if <lb/>we have a Mixture of Gold and Silver, it is clear, that by rea&longs;on it <lb/>participates of Silver, it &longs;hall weigh le&longs;s than the pure Gold, and <lb/>by rea&longs;on it participates of Gold, it &longs;hall weigh more than the <lb/>pure Silver: and therefore being weighed in the Air, and de&longs;iring <lb/>that the &longs;ame Counterpoi&longs;e &longs;hould counterpoi&longs;e it, when that <lb/>Mixture &longs;hall be put into the Water it will be nece&longs;&longs;ary to draw <lb/>the &longs;aid Counterpoi&longs;e more towards the Perpendicular C, than the <lb/>point E is, which is the term of the Gold; and more from C <lb/>than F is, which is the term of the pure Silver; Therefore it &longs;hall <lb/>fall between the points E and F: And the proportion into which <lb/>the Di&longs;tance EF &longs;hall be divided, &longs;hall exactly give the proportion <lb/>of the two Metals which compound that Mixture. </s> <s>As for exam­<lb/>ple: Let us &longs;uppo&longs;e the Mixture of Gold and Silver to be in B, <lb/><figure id="id.040.01.999.1.jpg" xlink:href="040/01/999/1.jpg"/><lb/>counterpoi&longs;ed in <lb/>the Air by D, <lb/>which Counter­<lb/>poi&longs;e when the <lb/>Compound Me­<lb/>tal is put into the Water returneth into G: I &longs;ay now, that the <lb/>Gold and the Silver which compound this Mixture are to one ano­<lb/>ther in the &longs;ame proportion, as the Di&longs;tance F G is to the Di&longs;tance <lb/>G E. </s> <s>But you mu&longs;t know that the Di&longs;tance G F terminated in <lb/>the mark of the Silver, &longs;hall denote unto us the quantity of the <lb/>Gold, and the Di&longs;tance G E, terminated in the mark of the Gold, <lb/>&longs;hall &longs;hew us the quantity of the Silver: in&longs;omuch that if F G <lb/>&longs;hall prove double to G E, then that Mixture &longs;hall be two parts <lb/>Gold, and one part Silver: and in the &longs;ame method proceeding in<lb/>the examination of other Mixtures, one &longs;hall exactly find the <lb/>quantity of the &longs;imple Metals.</s></p><p type="main"> <s>To compo&longs;e the Ballance, therefore, take a Rod at lea&longs;t a yard <lb/>long, (and the longer it is, the exacter the In&longs;trument &longs;hall be) <lb/>and divide it in the mid&longs;t, where place the Perpendicular: then <lb/>adju&longs;t the Arms that they may &longs;tand in <emph type="italics"/>Equilibrium,<emph.end type="italics"/> by filing or <pb xlink:href="040/01/1000.jpg" pagenum="306"/>&longs;having that le&longs;s which weigheth mo&longs;t; and upon one of the Arms <lb/>note the terms to which the Counterpoi&longs;es of &longs;imple Metals return <lb/>when they &longs;hall be weighed in the Water: taking care to weigh the <lb/>pure&longs;t Metals that can be found. </s> <s>This being done, it remaineth <lb/>that we find out a way, how we may with facility di&longs;cover the <lb/>proportion, according to which, the Di&longs;tances between the terms <lb/>of the &longs;imple and pure Metals are divided by the Marks of the <lb/>Mixt Metals: Which &longs;hall be effected in this manner.</s></p><p type="main"> <s>We are to have two very &longs;mall Wires drawn thorow the &longs;ame <lb/>drawing-Iron, one of Steel, the other of Bra&longs;s, and above the <lb/>terms of the &longs;imple Metals we mu&longs;t wind the Steel Wyer; as for <lb/>example: above the point E, the term of the pure Gold, we are <lb/>to wind the Steel Wyer, and under it the other Bra&longs;s Wyre, and <lb/>having made ten folds of the Steel Wyer, we mu&longs;t make ten <lb/>more with that of Bra&longs;s, and thus we are to continue to do with <lb/>ten of Steel, and ten of Bra&longs;s, until that the whole Space be­<lb/>tween the points E and F, the terms of the pure Metals, be full; <lb/>cau&longs;ing tho&longs;e two terms to be alwaies vi&longs;ible and per&longs;picuous: <lb/>and thus the Di&longs;tance E F &longs;hall be divided into many equal parts, <lb/>and numbred by ten and ten. </s> <s>And if at any time we would know <lb/>the proportion that is between F G and G E, we mu&longs;t count the <lb/>Wyers F G, and the Wyers G E: and finding the Wyers F G <lb/>to be, for example, 40, and the Wyers G E, 21: we will &longs;ay that <lb/>there is in the mixt Metal 40 parts of Gold, and 21 of Silver. </s> <s>But <lb/>here you mu&longs;t note, that there is &longs;ome difficulty in the counting, <lb/>for tho&longs;e Wyers being very &longs;mall, as it is requi&longs;ite for exactne&longs;s <lb/>&longs;ake, it is not po&longs;&longs;ible with the eye to tell them, becau&longs;e the <lb/>&longs;malne&longs;s of the Spaces dazleth & confoundeth the Sight. </s> <s>Therefore <lb/>to number them with facility, take a Bodkin as &longs;harp as a Needle <lb/>and &longs;et it into an handle, or a very fine pointed Pen-knife, with <lb/>which we may ea&longs;ily run over all the &longs;aid Wyers, and this way <lb/>partly by help of hearing, partly by the impediments the hand <lb/>&longs;hall feel at every Wyer, tho&longs;e Wyers &longs;hall be counted; <lb/>the number of which, as I &longs;aid before, &longs;hall give us the exact <lb/>quantity of the &longs;unple Metals, of which the Mixt-Metal is com­<lb/>pounded: taking notice that the Simple an&longs;wer alternately to the <lb/>Di&longs;tances. </s> <s>As for example, in a Mixture of Gold and Silver, <lb/>the Wyers that &longs;hall be towards the term of Gold &longs;hall &longs;hew us <lb/>the quantity of the Silver: And the &longs;ame is to be under&longs;tood of <lb/>other Metals.</s></p><pb xlink:href="040/01/1001.jpg" pagenum="307"/><p type="head"> <s>Annotations of <emph type="italics"/>Dominico Mantovani<emph.end type="italics"/> upon the Bal­<lb/>lance of <emph type="italics"/>Signore Galileo Galilei.<emph.end type="italics"/></s></p><p type="main"> <s>Fir&longs;t, I conceive that the difficulty of Numbring the Wyres <lb/>is removed by wrapping about the Ballance ten of Steel, <lb/>and then ten of Bra&longs;s, which being divided by tens, there <lb/>only remains that tenth part to be numbred, in which the term <lb/>of the Mixt Metal falleth. </s> <s>For although <emph type="italics"/>Signore Galileo,<emph.end type="italics"/> who is <lb/>Author of this Invention, makes mention of two Wyres, one of <lb/>Steel, the other of Bra&longs;s, yet he doth not &longs;ay, that we are to <lb/>take ^{*} ten of the one, and ten of the other: which it may be <lb/><arrow.to.target n="marg1123"></arrow.to.target><lb/>hapneth by the negligence of him that hath tran&longs;cribed it; al­<lb/>though I mu&longs;t confe&longs;s that the Copy which came to my hands was <lb/>of his own writing.</s></p><p type="margin"> <s><margin.target id="marg1123"></margin.target>* <emph type="italics"/>Galileus<emph.end type="italics"/> &longs;aith it <lb/>expre&longs;ly in this <lb/>Copy which I fol­<lb/>low, but might <lb/>omit it in the Co­<lb/>py which came to <lb/>the hands of <emph type="italics"/>Man­<lb/>tovani.<emph.end type="italics"/></s></p><p type="main"> <s>Secondly, it is &longs;uppo&longs;ed in this Problem that the Compo&longs;ition <lb/>of two Metals do retain the &longs;ame proportion of Ma&longs;s in the <lb/>Mixture as the two Simple Metals, of which it is compounded, <lb/>had at fir&longs;t. </s> <s>I mean, that the Simple Metals retain and keep in <lb/>the Compo&longs;ition (after that they are incorporated and commix­<lb/>ed) the &longs;ame proportion in Ma&longs;s that the Simple Metals had <lb/>when they were &longs;eparated: Which in the Ca&longs;e of <emph type="italics"/>Signore Gali­<lb/>leo,<emph.end type="italics"/> touching the Commixtion of Gold and Silver, I do neither <lb/>deny, nor particularly confe&longs;s. </s> <s>But if one would, for example, <lb/>unite 101 pounds of Copper with 21 pounds of Tin, to make <lb/>thereof 120 pounds of Bell-Metal, (I abate two pounds, <lb/>&longs;uppo&longs;ed to be wa&longs;ted in the Melting) I do think that 120 <lb/>pounds of Compound Metal will have a le&longs;s Bulk than the 100 <lb/>pounds of pure Copper, and the 20 pounds of Tin unmixt, that <lb/>is, before they were incorporated and melted into one Ma&longs;s, and <lb/>that the Compo&longs;ition is more grave <emph type="italics"/>in Specie<emph.end type="italics"/> than the &longs;ingle Cop­<lb/>per, and the &longs;ingle Bra&longs;s: and in the Ca&longs;e of <emph type="italics"/>Signore Galileo<emph.end type="italics"/> the <lb/>Compo&longs;ition of Gold and Silver is &longs;uppo&longs;ed to be lighter <emph type="italics"/>in Specie<emph.end type="italics"/><lb/>than the pure Gold, and heavier <emph type="italics"/>in Specie<emph.end type="italics"/> than the pure Silver. </s> <s>Of <lb/>which it would be ea&longs;ie to make &longs;ome &longs;uch like experiment, melt­<lb/>ing together, <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> 10 pounds of Lead with 5 pounds of Tin, <lb/>and ob&longs;erving whether tho&longs;e 15 pounds, or whatever the Mixture <lb/>maketh, do give the difference betwixt the weight in the Water <lb/>to the weight in the Air, in the proportion that the 15 pounds of <lb/>the two Metals di&longs;-united gave before: I do not &longs;ay, the &longs;ame diffe­<lb/>rence, becau&longs;e I pre &longs;uppo&longs;e that they will wa&longs;te in melting down, <lb/>and that the Compound will be le&longs;s than 15 pounds, therefore I <lb/>&longs;ay in proportion.</s></p><p type="main"> <s>Thirdly, He doth al&longs;o &longs;uppo&longs;e, that one ought to take the <pb xlink:href="040/01/1002.jpg" pagenum="308"/>Simple Metals, that is, the Gold and the Silver, each of the &longs;ame <lb/>weight as the Mixture, although he doth not &longs;ay &longs;o; which may <lb/>be collected in that he marketh the ballance only betwixt the <lb/>Terms of the Gold and the Silver, which is the cau&longs;e of the great <lb/>facility in re&longs;olving the Problem by only counting the <lb/>Wyers.</s></p><p type="main"> <s>One might take the pure Gold, and pure Silver of the &longs;ame <lb/>weight, in re&longs;pect of one another, but yet different from the <lb/>weight of the Mixture, that is, either more or le&longs;s grave than the <lb/>Mixt Metal: and being equal in weight to one another they <lb/>might &longs;hew the proportion of the Ma&longs;s of the Gold to that of the <lb/>Silver; but yet with this difference, that the more grave will &longs;hew <lb/>the &longs;aid proportion more exactly than the &longs;mall and le&longs;s grave. <lb/></s> <s>But the Simple and pure Metals not being of the &longs;ame weight as <lb/>the Compound, it will be nece&longs;&longs;ary, having found the proportion <lb/>of the Ma&longs;s of the Gold to that of the Silver; to find by numbers <lb/>proportionally the exact quantity of each of the two Metals com­<lb/>pounding the Mixture.</s></p><p type="main"> <s>A man may likewi&longs;e u&longs;e the quantity of the &longs;imple Metals ac­<lb/>cording to nece&longs;&longs;ity and convenience, although of different <lb/>Weights, both as to each other, and to the Mixture, provided that <lb/>each of them be pure in its kind: but then we mu&longs;t after­<lb/>wards by numbers find the proportion of the Ma&longs;&longs;es of the two <lb/>Simple ones of equal weight (which is &longs;oon done, taking them of <lb/>equal weight as was &longs;aid before) and then according to this pro­<lb/>portion to find, by means of the Weight, and of the Ma&longs;s of the <lb/>Compound Metal, the di&longs;tinct quantity of each of the two Sim­<lb/>ple ones that make the Compo&longs;ition: of each of which Ca&longs;es <lb/>examples might be given. </s> <s>But to conclude, if the pure Gold, <lb/>and pure Silver, and the Mixt Metal &longs;hould be of equal Ma&longs;s, <lb/>they would be unequal in Weight, and it would not need to <lb/>weigh them in the Water, for being of equal Bulk, the differen­<lb/>ces of their Weights in the Air and in the Water would be al&longs;o <lb/>equal: for the difference of the weight of any Body in the Air <lb/>to its weight in the Water, is alwaies equal to the Weight of &longs;o <lb/>much Water as equalleth the &longs;ame Body in Ma&longs;s, by <emph type="italics"/>Archimedes<emph.end type="italics"/><lb/>his fifth Propo&longs;ition, <emph type="italics"/>De ijs quæ vehuntur in aqua.<emph.end type="italics"/></s></p><p type="main"> <s>And la&longs;t of all, the Simple and pure Metals may have the &longs;ame <lb/>proportion in Gravity, mutually or reciprocally, as their Bodies <lb/>have in Bulk: In which ca&longs;e, as well the Ma&longs;s, found by help of <lb/>the weight in Water, or by any other meanes, as their Weight in <lb/>the Air &longs;hall &longs;hew the proportion of their Specifical Gravities; as <lb/>their Weights in the Water do when their Weights in the Air <lb/>are equal; but yet alternately weighed: that is to &longs;ay, the Spe­<lb/>cifical Gravity of the Gold &longs;hall have &longs;uch proportion to the <pb xlink:href="040/01/1003.jpg" pagenum="309"/>Specifical Gravity of the Silver, as the Ma&longs;s of the Silver hath to <lb/>the Ma&longs;s of the Gold; that is, as the difference betwixt the <lb/>Weight in Water and Weight in Air of the Silver, hath to the <lb/>difference betwixt the Weight in Water and Weight in Air of <lb/>the Gold.</s></p><p type="main"> <s>With this &longs;ame Ballance one may with facility mea&longs;ure the <lb/>Ma&longs;s or Magnitude of any Body, in any manner what&longs;oever Irre­<lb/>gular in manner following, namely:</s></p><p type="main"> <s>We will have at hand a Solid Body of a &longs;ub&longs;tance more grave <lb/><emph type="italics"/>in Specie<emph.end type="italics"/> than the Water; as for in&longs;tance of Lead; or if it were <lb/>of Wood, or other matter more light <emph type="italics"/>in Specie<emph.end type="italics"/> than the Water, <lb/>it may be made heavier by fa&longs;tning unto it Lead, or &longs;ome other <lb/>thing that makes it &longs;ink in the Water, and let us take &longs;ome <lb/>known Mea&longs;ure, and with it mea&longs;ure the Irregular Solid; as for <lb/>in&longs;tance, the Roman Palm, the Geometrical Foot, or any other <lb/>known mea&longs;ure, or part of the &longs;ame, as the half Foot, the quar­<lb/>ter of a Foot, or any &longs;uch like part known; then let it be weighed <lb/>in the Air, and &longs;uppo&longs;e that it weigh 10 pounds; let the &longs;ame <lb/>Mea&longs;ure be weighed in the Air, and &longs;uppo&longs;e that it weigh 8 <lb/>pounds: and &longs;ub&longs;tract 8 pounds, the Weight in the Water, from <lb/>10 pounds, the Weight in the Air, and there remaineth 2 pounds <lb/>for the Weight of a Body of Water equal in Magnitude to the <lb/>Mea&longs;ure known. </s> <s>Now, if we would mea&longs;ure a Statue of Mar­<lb/>ble, let it be weighed fir&longs;t in the Air, and then in the Water, and <lb/>&longs;ub&longs;tract the Weight in the <emph type="italics"/>W<emph.end type="italics"/>ater from the <emph type="italics"/>W<emph.end type="italics"/>eight in the Air, and <lb/>the remainder &longs;hall be the weight of &longs;o much <emph type="italics"/>W<emph.end type="italics"/>ater as equalleth <lb/>the Statue in Ma&longs;s; which being divided by the difference betwixt <lb/>the <emph type="italics"/>W<emph.end type="italics"/>eight in <emph type="italics"/>W<emph.end type="italics"/>ater and the <emph type="italics"/>W<emph.end type="italics"/>eight in Air of the Mea&longs;ure known, <lb/>the Quotient will give how many times the Statue containeth the <lb/>&longs;ame given Mea&longs;ure. </s> <s>As for example; if the Statue in Air weigh <lb/>100 pounds, and in the <emph type="italics"/>W<emph.end type="italics"/>ater 80 pounds, 80 pounds being &longs;ub­<lb/>&longs;tracted from 100 there re&longs;teth 20 pounds for the <emph type="italics"/>W<emph.end type="italics"/>eight of &longs;o <lb/>much <emph type="italics"/>W<emph.end type="italics"/>ater in Ma&longs;s as equalleth the Statue. </s> <s>But becau&longs;e the <lb/>difference betwixt the <emph type="italics"/>W<emph.end type="italics"/>eight in <emph type="italics"/>W<emph.end type="italics"/>ater, and the <emph type="italics"/>W<emph.end type="italics"/>eight in Air <lb/>equal in Magnitude to the Mea&longs;ure known, was &longs;uppo&longs;ed to be <lb/>2 pounds; divide 18 pounds by two pounds, and the Quotient <lb/>is 9, for the number of times that the propo&longs;ed Statue containeth <lb/>the given Mea&longs;ure. </s> <s>The &longs;ame Method may be ob&longs;erved, if it <lb/>were required, to mea&longs;ure a Statue, or other Ma&longs;s of any kind of <lb/>Metal: only it mu&longs;t be adverti&longs;ed, that all the holes mu&longs;t be <lb/>&longs;topt, that the <emph type="italics"/>W<emph.end type="italics"/>ater may not enter into the Body of the Statue: <lb/>but he that de&longs;ireth only the Solid content of the Metal of the <lb/>&longs;aid Statue mu&longs;t open the holes, and with Tunnels fill the whole <lb/>cavity of the Statue with <emph type="italics"/>W<emph.end type="italics"/>ater. </s> <s>And if the Statue were of a <lb/>Sub&longs;tance lighter <emph type="italics"/>in Specie<emph.end type="italics"/> than the <emph type="italics"/>W<emph.end type="italics"/>ater; as, for example, of <pb xlink:href="040/01/1004.jpg" pagenum="310"/>Wax, it will be requi&longs;ite to add unto the Statue &longs;ome Counter­<lb/>poi&longs;e, that maketh it &longs;ink in the <emph type="italics"/>W<emph.end type="italics"/>ater, and then to mea&longs;ure the <lb/>Counterpoi&longs;e, as above, and to &longs;ub&longs;tract its mea&longs;ure from the <lb/>Compound Body, and there will remain the Mea&longs;ure of the <lb/>Statue of <emph type="italics"/>W<emph.end type="italics"/>ax. </s> <s>And la&longs;tly, to make u&longs;e of the &longs;aid Ballance, <lb/>in&longs;tead of &longs;eeking the numbers of the pounds of the Differences <lb/>of the <emph type="italics"/>W<emph.end type="italics"/>eights of the Mea&longs;ure known, and of the Solid <lb/>to be mea&longs;ured in <emph type="italics"/>W<emph.end type="italics"/>ater, and in Air, we may count the <lb/><emph type="italics"/>W<emph.end type="italics"/>yers of the Arm of the Ballance, which <lb/>being very &longs;mall will give the <lb/>Mea&longs;ure exactly.</s></p><p type="head"> <s><emph type="italics"/>FINIS.<emph.end type="italics"/></s></p></chap><chap> <pb xlink:href="040/01/1005.jpg" pagenum="311"/><p type="head"> <s>DISCOURSES <lb/>OF THE <lb/>MECHANICKS: <lb/>A MANVSCRIPT of <lb/>Mon&longs;ieur Des-Cartes.</s></p><p type="head"> <s>The Explication.</s></p><p type="main"> <s><emph type="italics"/>Of Engines, by help of which we may rai&longs;e a very great <lb/>weight with &longs;mall &longs;trength.<emph.end type="italics"/></s></p><p type="main"> <s>The Invention of all the&longs;e Engines de­<lb/>pends upon one &longs;ole Principle, which is, <lb/>That the &longs;ame Force that can lift up a <lb/>Weight, for example, of 100 pounds to <lb/>the height of one foot, can life up one of <lb/>200 pounds to the height of half a foot, <lb/>or one of 400 pounds to the height of a <lb/>fourth part of a foot, and &longs;o of the re&longs;t, <lb/>be there never &longs;o much applyed to it: and <lb/>this Principle cannot be denied if we con&longs;ider, that the Effect <lb/>ought to be proportioned to the Action that is nece&longs;&longs;ary for the <lb/>production of it; &longs;o that, if it be nece&longs;&longs;ary to employ an Action by <lb/>which we may rai&longs;e a Weight of 100 pounds to the height of two <lb/>foot, for to rai&longs;e one &longs;uch to the height of one foot only this &longs;ame <lb/>ought to weigh 200 pounds: for its the &longs;ame thing to rai&longs;e 100 <lb/>pounds to the height of one foot, and again yet another 100 <lb/>pounds to the height of one foot, as to rai&longs;e one of 200 pounds to <lb/>the height of one foot, and the &longs;ame, al&longs;o, as to rai&longs;e 100 pounds <lb/>to the height of two feet.</s></p><p type="main"> <s>Now, the Engines which &longs;erve to make this Application of a <lb/>Force which acteth at a great Space upon a <emph type="italics"/>W<emph.end type="italics"/>eight which it cau­<pb xlink:href="040/01/1006.jpg" pagenum="312"/>&longs;eth to be rai&longs;ed by a le&longs;&longs;er, are the Pulley, the Inclined Plane, the <lb/>Wedg, the Cap&longs;ten, or Wheel, the Screw, the Leaver, and &longs;ome <lb/>others, for if we will not apply or compare them one to another, <lb/>we cannot well number more, and if we will apply them we need <lb/>not in&longs;tance in &longs;o many.</s></p><p type="head"> <s>The PVLLEY, <emph type="italics"/>Trochlea.<emph.end type="italics"/></s></p><p type="main"> <s>Let A B C be a Chord put about the Pulley D, to which let <lb/>the Weight E be fa&longs;tned; and fir&longs;t, &longs;uppo&longs;ing that two <lb/>men &longs;u&longs;tain or pull up equally each of them one of the <lb/><figure id="id.040.01.1006.1.jpg" xlink:href="040/01/1006/1.jpg"/><lb/>ends of the &longs;aid Chord: <lb/>it is manife&longs;t, that if the <lb/>Weight weigheth 200 <lb/>pounds, each of tho&longs;e <lb/>men &longs;hal employ but the <lb/>half thereof, that is to &longs;ay, <lb/>the Force that is requi&longs;ite <lb/>for &longs;u&longs;taining or rai&longs;ing <lb/>of 100 pounds, for each <lb/>of them &longs;hal bear but the <lb/>half of it.</s></p><p type="main"> <s>Afterwards, let us &longs;up­<lb/>po&longs;e that A, one of the <lb/>ends of this Chord, being <lb/>made fa&longs;t to &longs;ome Nail, <lb/>the other C be again &longs;u­<lb/>&longs;tained by a Man; and it <lb/>is manife&longs;t, that this Man in C, needs not (no more than before) <lb/>for the &longs;u&longs;taining the Weight E, more Force than is requi&longs;ite for <lb/>the &longs;u&longs;taining of 100 pounds: becau&longs;e the Nail at A doth the <lb/>&longs;ame Office as the Man which we &longs;uppo&longs;ed there before. </s> <s>In fine, <lb/>let us &longs;uppo&longs;e that this Man in C do pull the Chord to make the <lb/>Weight E to ri&longs;e, and it is manife&longs;t, that if he there employeth <lb/>the Force which is requi&longs;ite for the rai&longs;ing of 100 pounds to the <lb/>height of two feet, he &longs;hall rai&longs;e this Weight E of 200 pounds to <lb/>the height of one foot: for the Chord A B C being doubled, as it <lb/>is, it mu&longs;t be pull'd two feet by the end C, to make the Weight E <lb/>ri&longs;e as much, as if two men did draw it, the one by the end A, <lb/>and the other by the end C, each of them the length of one foot <lb/>only.</s></p><p type="main"> <s>There is alwaies one thing that hinders the exactne&longs;s of the Cal­<lb/>culation, that is the pondero&longs;ity of the Chord or Pulley, and the <lb/>difficulty that we meet with in making the Chord to &longs;lip, and in <lb/>bearing it: but this is very &longs;mall in compari&longs;on of that which <pb xlink:href="040/01/1007.jpg" pagenum="313"/>rai&longs;eth it, and cannot be e&longs;timated &longs;ave wthin a &longs;mall matter.</s></p><p type="main"> <s>Moreover, it is nece&longs;&longs;ary to ob&longs;erve, that it is nothing but the <lb/>redoubling of the Chord, and not the Pulley, that cau&longs;eth this <lb/>Force: for if we fa&longs;ten yet another Pulley towards A, about <lb/>which we pa&longs;s the Chord A B C H, there will be required no le&longs;s <lb/>Force to draw H towards K, and &longs;o to lift up the Weight E, than <lb/>there was before to draw C towards G. </s> <s>But if to the&longs;e two Pul­<lb/>leys we add yet another towards D, to which we fa&longs;ten the Weight, <lb/>and in which we make the Chord to run or &longs;lip, ju&longs;t as we did in <lb/>the fir&longs;t, then we &longs;hall need no more Force to lift up this Weight <lb/>of 200 pounds than to lift up 50 pounds without the Pulley: be­<lb/>cau&longs;e that in drawing four feet of Chord we lift it up but one <lb/>foot. </s> <s>And &longs;o in multiplying of the Pulleys one may rai&longs;e the great­<lb/>e&longs;t Weights with the lea&longs;t Forces. </s> <s>It is requi&longs;ite al&longs;o to ob&longs;erve, <lb/>that a little more Force is alwaies nece&longs;&longs;ary for the rai&longs;ing of a <lb/>Weight than for the &longs;u&longs;taining of it: which is the rea&longs;on why I <lb/>have &longs;poken here di&longs;tinctly of the one and of the other.</s></p><p type="head"> <s><emph type="italics"/>The Inclined<emph.end type="italics"/> PLANE.</s></p><p type="main"> <s>If not having more Force than &longs;ufficeth to rai&longs;e 100 pounds, one <lb/>would neverthele&longs;s rai&longs;e this Body F, that weigheth 200 pounds, <lb/>to the height of the Line B A, there needs no more but to draw <lb/>or rowl it along the Inclined Plane C A, which I &longs;uppo&longs;e to be <lb/>twice as long as the Line <lb/><figure id="id.040.01.1007.1.jpg" xlink:href="040/01/1007/1.jpg"/><lb/>A B, for by this means, <lb/>for to make it arrive at <lb/>the point A, we mu&longs;t <lb/>there employ the Force <lb/>that is nece&longs;&longs;ary for the <lb/>rai&longs;ing 100 pounds twice <lb/>as high, and the more inclined this Plane &longs;hall be made, &longs;o much <lb/>the le&longs;s Force &longs;hall there need to rai&longs;e the Weight F. </s> <s>But yet there <lb/>is to be rebated from this Calculation the difficulty that there is <lb/>in moving the Body F, along the Plane A C, if that Plane were <lb/>laid down upon the Line B C, all the parts of which I &longs;uppo&longs;e to <lb/>be equidi&longs;tant from the Center of the Earth.</s></p><p type="main"> <s>It is true, that this impediment being &longs;o much le&longs;s as the Plane is <lb/>more united, more hard, more even, and more polite; it cannot <lb/>likewi&longs;e be e&longs;timated but by gue&longs;s, and it is not very con&longs;ide­<lb/>rable.</s></p><p type="main"> <s>We need not neither much to regard that the Line B C being a <lb/>part of a Circle that hath the &longs;ame Center with the Earth, the <lb/>Plane A C ought to be (though but very little) curved, and to <lb/>have the Figure of part of a Spiral, de&longs;cribed between two Circles, <pb xlink:href="040/01/1008.jpg" pagenum="314"/>which likewi&longs;e have for their Center that of the Earth, for that it <lb/>is not any way &longs;en&longs;ible.</s></p><p type="head"> <s><emph type="italics"/>The<emph.end type="italics"/> WEDGE, <emph type="italics"/>Cuneus.<emph.end type="italics"/></s></p><p type="main"> <s>The Force of the Wedge A B C D is ea&longs;ily under&longs;tood after <lb/>that which hath been &longs;poken above of the Inclined Plane, <lb/>for the Force wherewith we &longs;trike downwards acts as if it <lb/>were to make it move according to the Line B D; and the Wood, <lb/>or other thing and Body that it cleaveth, openeth not, or the <lb/>Weight that it rai&longs;eth doth not ri&longs;e, &longs;ave only according to the <lb/><figure id="id.040.01.1008.1.jpg" xlink:href="040/01/1008/1.jpg"/><lb/>Line A C, in&longs;omuch that the Force, <lb/>wherewith one driveth or &longs;triketh this <lb/>Wedge, ought to have the &longs;ame Pro­<lb/>portion to the Re&longs;i&longs;tance of this <lb/>Wood or Weight, that A C hath to <lb/>A B. </s> <s>Or el&longs;e again, to be exact, it <lb/>would be convenient that B D were <lb/>a part of a Circle, and A D and <lb/>C D two portions of Spirals that had the &longs;ame Center with the <lb/>Earth, and that the Wedge were of a Matter &longs;o perfectly hard <lb/>and polite, and of &longs;o &longs;mall weight, as that any little Force would <lb/>&longs;uffice to move it.</s></p><p type="head"> <s><emph type="italics"/>The<emph.end type="italics"/> CRANE, <emph type="italics"/>or the<emph.end type="italics"/> CAPSTEN, <lb/><emph type="italics"/>Axis in Peritrochio.<emph.end type="italics"/></s></p><p type="main"> <s>We &longs;ee al&longs;o very ea&longs;ily, that the Force wherewith the Wheel <lb/>A or Cogg B is turned, which make the Axis or Cylinder C <lb/>to move, about which a Chord is rolled, to which the <lb/>Weight D, which we would rai&longs;e, is fa&longs;tned, ought to have the <lb/><figure id="id.040.01.1008.2.jpg" xlink:href="040/01/1008/2.jpg"/><lb/>&longs;ame proportion to the &longs;aid <lb/>Weight, as the Circumference of <lb/>the Cylinder hath to the Cir­<lb/>cumference of a Circle which <lb/>that Force de&longs;cribeth, or that the <lb/>Diameter of the one hath unto <lb/>the Diameter of the other; for <lb/>that the Circumferences have the <lb/>&longs;ame proportion as the Diame­<lb/>ters: in&longs;omuch that the Cylinder C, having no more but one foot <lb/>in Diameter, if the Wheel AB be &longs;ix feet in its Diameter, and the <lb/>Weight D do weigh 600 pounds, it &longs;hall &longs;uffice that the Force in <lb/>B &longs;hall be capable to rai&longs;e 100 pounds, and &longs;o of others. </s> <s>One may <pb xlink:href="040/01/1009.jpg" pagenum="315"/>al&longs;o in&longs;tead of the Chord that rolleth about the Cylinder C, place <lb/>there a &longs;mall Wheel with teeth or Coggs, that may turn another <lb/>greater, and by that means multiply the power of the Force as <lb/>much as one &longs;hall plea&longs;e, without having any thing to deduct of <lb/>the &longs;ame, &longs;ave only the difficulty of moving the Machine, as in the <lb/>others.</s></p><p type="head"> <s><emph type="italics"/>The<emph.end type="italics"/> SCREW, <emph type="italics"/>Cochlea.<emph.end type="italics"/></s></p><p type="main"> <s>When once the Force of the Cap&longs;ten and of the In­<lb/>clined Plane is under&longs;tood, that of the Screw is ea&longs;ie <lb/>to be computed, for it is compo&longs;ed only of a Plane <lb/>much inclined, which windeth about a Cylinder: and if this Plane <lb/>be in &longs;uch manner Inclined, as that the Cylinder ought to make <lb/><emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> ten turns to advance forwards the length of a foot in the <lb/>Screw, and that the bigne&longs;s of the Circumference of the Circle <lb/><figure id="id.040.01.1009.1.jpg" xlink:href="040/01/1009/1.jpg"/><lb/>which the Force that turneth it <lb/>about doth de&longs;cribe be of ten <lb/>feet; fora&longs;much as ten times ten <lb/>are one hundred, one Man alone <lb/>&longs;hall be able to pre&longs;s as &longs;trongly <lb/>with this In&longs;trument, or Screw, as <lb/>one hundred without it, provided <lb/>alwaies, that we rebate the Force <lb/>that is required to the turning <lb/>of it.</s></p><p type="main"> <s>Now I &longs;peak here of Pre&longs;&longs;ing rather than of Rai&longs;ing, or Remo­<lb/>ving, in regard that it is about this mo&longs;t commonly that the Screw <lb/>is employed, but when we would make u&longs;e of it for the rai&longs;ing of <lb/>Weights, in&longs;tead of making it to advance into a Female Screw, we <lb/>joyn or apply unto it a Wheel of many Coggs, in &longs;uch &longs;ort <lb/>made, that if <emph type="italics"/>v. </s> <s>gr.<emph.end type="italics"/> this <emph type="italics"/>W<emph.end type="italics"/>heel have thirty Coggs, whil&longs;t the Screw <lb/>maketh one entire turn, it &longs;hall not cau&longs;e the <emph type="italics"/>W<emph.end type="italics"/>heel to make more <lb/>than the thirtieth part of a turn, and if the <emph type="italics"/>W<emph.end type="italics"/>eight be fa&longs;tned to <lb/>a Chord that rowling about the Axis of this <emph type="italics"/>W<emph.end type="italics"/>heel &longs;hall rai&longs;e it but <lb/>one foot in the time that the <emph type="italics"/>W<emph.end type="italics"/>heel makes one entire revolution, <lb/>and that the greatne&longs;s of the Circumference of the Circle that is <lb/>de&longs;cribed by the Force that turneth the Screw about be al&longs;o of ten <lb/>&longs;eet, by rea&longs;on that 10 times 30 make 300, one &longs;ingle Man &longs;hall be <lb/>able to rai&longs;e a <emph type="italics"/>W<emph.end type="italics"/>eight of that bigne&longs;s with this In&longs;trument, which <lb/>is called the Perpetual Screw, as would require 300 men with­<lb/>out it.</s></p><p type="main"> <s>Provided, as before, that we thence deduct the difficulty that <lb/>we meet with in turning of it, which is not properly cau&longs;ed by the <lb/>Pondero&longs;ity of the <emph type="italics"/>W<emph.end type="italics"/>eight, but by the Force or Matter of the In­<pb xlink:href="040/01/1010.jpg" pagenum="316"/>&longs;trument: which difficulty is more &longs;en&longs;ible in it than in tho&longs;e afore­<lb/>going, fora&longs;much as it hath greater Force.</s></p><p type="head"> <s>The LEAVER, <emph type="italics"/>Vectis.<emph.end type="italics"/></s></p><p type="main"> <s>I Have deferred to &longs;peak of the Leaver until the la&longs;t, in regard <lb/>that it is of all Engines for rai&longs;ing of Weights, the mo&longs;t diffi­<lb/>cult to be explained.</s></p><p type="main"> <s>Let us &longs;uppo&longs;e that C H is a Leaver, in &longs;uch manner &longs;upported <lb/>at the point O, (by means of an Iron Pin that pa&longs;&longs;eth thorow it <lb/>acro&longs;s, or otherwi&longs;e) that it may turn about on this point O, its <lb/>part C de&longs;cribing the Semicircle A B C D E, and its part H the <lb/><figure id="id.040.01.1010.1.jpg" xlink:href="040/01/1010/1.jpg"/><lb/>Semicircle F G H I K; and that <lb/>the Weight which we would <lb/>rai&longs;e by help of it were in H, <lb/>and the Force in C, the Line <lb/>C O being &longs;uppo&longs;ed triple of <lb/>O H. </s> <s>Then let us con&longs;ider that <lb/>in the Time whil&longs;t the Force <lb/>that moveth this Leaver de&longs;cri­<lb/>beth the whole Semicircle <lb/>A B C D E, and acteth accord­<lb/>ing to the Line A B C D E, al­<lb/>though that the Weight de&longs;cri­<lb/>beth likewi&longs;e the Semicircle <lb/>F G H I K, yet it is not rai&longs;ed to <lb/>the length of this curved Line <lb/>F G H I K, but only to that of the Line F O K; in&longs;omuch that the <lb/>Proportion that the Force which moveth this Weight ought to <lb/>have to its Pondero&longs;ity ought not to be mea&longs;ured by that which is <lb/>between the two Diameters of the&longs;e Circles, or between their two <lb/>Circumferences, as it hath been &longs;aid above of the Wheel, but ra­<lb/>ther by that which is betwixt the Circumference of the greater, <lb/>and the Diameter of the le&longs;&longs;er. </s> <s>Furthermore let us con&longs;ider, that <lb/>there is a nece&longs;&longs;ity that this Force needeth not to be &longs;o great, at <lb/>&longs;uch time as it is near to A, or near to E, for the turning of the <lb/>Leaver, as then when it is near to B, or to D; nor &longs;o great when <lb/>it is near to B or D, as then when it is near to C: of which the rea­<lb/>&longs;on is, that the Weights do there mount le&longs;s: as it is ea&longs;ie to un­<lb/>der&longs;tand, if having &longs;uppo&longs;ed that the Line C O H is parallel to the <lb/>Horizon, and that A O F cutteth it at Right Angles, we take the <lb/>point G equidi&longs;tant from the points F and H, and the point B equi­<lb/>di&longs;tant from A and C; and that having drawn G S perpendicular <lb/>to F O, we ob&longs;erve that the Line F S (which &longs;heweth how much <lb/>the Weight mounteth in the Time that the Force operates along <pb xlink:href="040/01/1011.jpg" pagenum="317"/>the Line A B) is much le&longs;&longs;er than the Line S O, which &longs;heweth <lb/>how much it mounteth in the Time that the Force opperates along <lb/>the Line B C.</s></p><p type="main"> <s>And to mea&longs;ure exactly what his Force ought to be in each Point <lb/>of the curved Line A B C D E, it is requi&longs;ite to know that it ope­<lb/>rates there ju&longs;t in the &longs;ame manner as if it drew the Weight along <lb/>a Plane Circularly Inclined, and that the Inclination of each of the <lb/>Points of this circular Plane were to be mea&longs;ured by that of the <lb/>right Line that toucheth the Circle in this Point. </s> <s>As for example, <lb/>when the Force is at the Point B, for to find the proportion that it <lb/>ought to have with the pondero&longs;ity of the Weight which is at that <lb/>time at the Point G, it is nece&longs;&longs;ary to draw the Contingent Line <lb/>G M, and to account that the pondero&longs;ity of the Weight is to the <lb/>Force which is required to draw it along this Plane, and con&longs;e­<lb/>quently to rai&longs;e it, according to the Circle F G H, as the Line G M <lb/>is to SM Again, for as much as B O is triple of O G, the Force <lb/>in B needs to be to the Weight in G but as the third part of the <lb/>Line SM is unto the whole Line G M. </s> <s>In the &longs;elf &longs;ame manner, <lb/>when the Force is at the Point D, to know how much the Weight <lb/>weigheth at I, it is nece&longs;&longs;ary to draw the Contingent Line betwixt <lb/>I and P, and the right Line I N perpendicular upon the Horizon, <lb/>and from the Point P taken at di&longs;cretion in the Line I P, provided <lb/>that it be below the Point I, you mu&longs;t draw P N parallel to the <lb/>&longs;ame Horizon, to the end you may have the proportion that is be­<lb/>twixt the Line I P and the third part of the Line I N, for that which <lb/>betwixt the pondero&longs;ity of the Weight, and the Force that ought to <lb/>be at the Point D for the moving of it: and &longs;o of others. </s> <s>Where, <lb/>neverthele&longs;s, you mu&longs;t except the Point H, at which the Contin­<lb/>gent Line being perpendicular upon the Horizon, the Weight can <lb/>be no other than triple the Force which ought to be in C for the <lb/>moving of it: in the Points F and K, at which the Contingent <lb/>Line being parallel unto the Horizon it &longs;elf, the lea&longs;t Force that <lb/>one can a&longs;&longs;ign is &longs;ufficient to move the Weight. </s> <s>Moreover, that you <lb/>may be perfectly exact, you mu&longs;t ob&longs;erve that the Lines S G and <lb/>P N ought to be parts of a Circle that have for their Center that <lb/>of the Earth; and GM and I P parts of Spirals drawn between two <lb/>&longs;uch Circles; and, la&longs;tly, that the right Lines S M and I N both <lb/>tending towards the Center of the Earth are not exactly Paral­<lb/>lels: and furthermore, that the Point H where I &longs;uppo&longs;e the <lb/>Contingent Line to be perpendicular unto the Horizon ought <lb/>to be &longs;ome &longs;mall matter nearer to the Point F than to K, at the <lb/>which F and K the Contingent Lines are Parallels unto the &longs;aid <lb/>Horizon.</s></p><p type="main"> <s>This done, we may ea&longs;ily re&longs;olve all the difficulties of the Ba­<lb/>lance, and &longs;hew, That then when it is mo&longs;t exact, and for in&longs;tance, <pb xlink:href="040/01/1012.jpg" pagenum="318"/>&longs;uppo&longs;ing it's Centre at O by which it is &longs;u&longs;tained to be no more <lb/>but an indivi&longs;ible Point, like as I have &longs;uppo&longs;ed here for the Leaver, <lb/>if the Armes be declined one way or the other, that which &longs;hall be <lb/>the lowermo&longs;t ought evermore to be adjudged the heavier; &longs;o that <lb/>the Centre of Gravity is not &longs;ixed and immoveable in each &longs;everal <lb/>Body, as the Ancients have &longs;uppo&longs;ed, which no per&longs;on, that I <lb/>know of, hath hitherto ob&longs;erved.</s></p><p type="main"> <s>But the&longs;e la&longs;t Con&longs;iderations are of no moment in Practice, and <lb/>it would be good for tho&longs;e who &longs;et them&longs;elves to invent new <lb/>Machines, that they knew nothing more of this bu&longs;i­<lb/>ne&longs;&longs;e than this little which I have now writ thereof, <lb/>for then they would not be in danger of decei­<lb/>ving them&longs;elves in their Computation, <lb/>as they frequently do in &longs;uppo&longs;ing <lb/>other Principles.</s></p><p type="head"> <s><emph type="italics"/>FINIS.<emph.end type="italics"/></s></p><figure id="id.040.01.1012.1.jpg" xlink:href="040/01/1012/1.jpg"/><pb xlink:href="040/01/1013.jpg" pagenum="319"/><p type="head"> <s>A <lb/>LETTER <lb/>OF <lb/>Mon&longs;ieur Des-Cartes <lb/>TO THE <lb/>REVEREND FATHER <lb/><emph type="italics"/>MARIN MERSENNE.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Reverend Father,<emph.end type="italics"/></s></p><p type="main"> <s>I Did think to have deferred writing unto you <lb/>yet eight or fifteen dayes, to the end I might <lb/>not trouble you too often with my Letters, <lb/>but I have received yours of the fir&longs;t of <emph type="italics"/>Sept.<emph.end type="italics"/><lb/>which giveth me to under&longs;tand that it is an <lb/>hard matter to admit the Principle which I <lb/>have &longs;uppo&longs;ed in my Examination of the <lb/>Geo&longs;tatick Que&longs;tion, and in regard that if it <lb/>be not true, all the re&longs;t that I have inferred from it would be yet <lb/>le&longs;&longs;e true: I would not one onely day defer &longs;ending you a more <lb/>particular Explication. </s> <s>It is requi&longs;ite above all things to con&longs;ider <lb/>that I did &longs;peak of the Force that &longs;erveth to rai&longs;e a Weight to &longs;ome <lb/>heighth, the which Force hath evermore two Dimen&longs;ions, and not <lb/>of that which &longs;erveth in each point to &longs;u&longs;tain it, which hath never <lb/>more than one Dimen&longs;ion, in&longs;omuch that the&longs;e two Forces differ <lb/>as much the one from the other, as a Superficies differs from a Line: <lb/>for the &longs;ame Force which a Nail ought to have for the &longs;u&longs;taining of <lb/>a Weight of 100 pound one moment of time, doth al&longs;o &longs;uffice for <lb/>to &longs;u&longs;tain it the &longs;pace of a year, provided that it do not dimini&longs;h, <lb/>but the &longs;ame Quantity of this Force which &longs;erveth to rai&longs;e the <lb/>Weight to the heighth of one foot, &longs;ufficeth not <emph type="italics"/>(eadem numero)<emph.end type="italics"/><lb/>to rai&longs;e it two feet; and it is not more manife&longs;t that two and two <lb/>make four, than it's manife&longs;t that we are to employ double as much <lb/>therein.</s></p><p type="main"> <s>Now, fora&longs;much as that this is nothing but the &longs;ame thing that <lb/>I have &longs;uppo&longs;ed for a Principle, I cannot gue&longs;&longs;e on what the Scruple <lb/>&longs;hould be grounded that men make of receiving it; but I &longs;hall in <pb xlink:href="040/01/1014.jpg" pagenum="320"/>this place &longs;peak of all &longs;uch as I &longs;u&longs;pect, which for the mo&longs;t part <lb/>ari&longs;e onely from this, that men are before-hand over-knowing in <lb/>the Mechanicks; that is to &longs;ay, that they are pre-occupied with <lb/>Principles that others prove touching the&longs;e matters, which not being <lb/>ab&longs;olutely true, they deceive the more, the more true they &longs;eem to <lb/>be.</s></p><p type="main"> <s>The fir&longs;t thing wherewith a man may be pre-occupied in this <lb/>bu&longs;ine&longs;&longs;e, is, that they many times confound the Con&longs;ideration of <lb/><figure id="id.040.01.1014.1.jpg" xlink:href="040/01/1014/1.jpg"/><lb/>Space, with that of Time, or of the Ve­<lb/>locity, &longs;o that, for Example, in the <lb/><emph type="italics"/>L<emph.end type="italics"/>eaver, or (which is the &longs;ame) the Ba­<lb/>llance A B C D having &longs;uppo&longs;ed that <lb/>the Arm A B is double to B C, and the <lb/>Weight in C double to the Weight <lb/>in A, and al&longs;o that they are in <emph type="italics"/>Equilibrium,<emph.end type="italics"/> in&longs;tead of &longs;aying, that <lb/>that which cau&longs;eth this <emph type="italics"/>Equilibrium<emph.end type="italics"/> is, that if the Weight C did <lb/>&longs;u&longs;tain, or was rai&longs;ed up by the Weight A, it did not pa&longs;&longs;e more <lb/>than half &longs;o much Space as it, they &longs;ay that it did move &longs;lower by <lb/>the half: which is a fault &longs;o much the more prejudicial, in that it is <lb/>very difficult to be known: for it is not the difference of <lb/><figure id="id.040.01.1014.2.jpg" xlink:href="040/01/1014/2.jpg"/><lb/>the Velocity that is the cau&longs;e why the&longs;e Weights are to be <lb/>one double to the other, but the difference of the Space, as <lb/>appeareth by this, that to rai&longs;e, for Example, the Weight F <lb/>with the hand unto G, it is not nece&longs;&longs;ary to employ a Force <lb/>that is preci&longs;ely double to that which one &longs;hould have <lb/>therein employed the fir&longs;t bout, to rai&longs;e it twice as quick­<lb/>ly, but it is requi&longs;ite to employ therein either more or le&longs;s <lb/>than the double, according to the different proportion that <lb/>this Velocity may have unto the Cau&longs;es that re&longs;i&longs;t it.</s></p><p type="main"> <s>In&longs;tead of requiring a Force ju&longs;t double for the rai&longs;ing of it with <lb/>the &longs;ame Velocity twice as high, unto H, I &longs;ay that it is ju&longs;t dou­<lb/>ble in counting (as two and two make four) that one and one make <lb/>two, for it is requi&longs;ite to employ a certain quantity of this Force <lb/>to rai&longs;e the Weight from F to G, and again al&longs;o, as much more of <lb/>the &longs;ame Force to rai&longs;e it from G to H.</s></p><p type="main"> <s>For if I had had a mind to have joyned the Con&longs;ideration of the <lb/>Velocity with that of the Space, it had been nece&longs;&longs;ary to have <lb/>a&longs;&longs;igned three Dimen&longs;ions to the Force, whereas I have a&longs;&longs;igned it <lb/>no more but two, on purpo&longs;e to exclude it. </s> <s>And if I have te&longs;tified <lb/>that there is &longs;o little of worth in any part of this &longs;mall Tract of the <lb/>Staticks, yet I de &longs;ire that men &longs;hould know, that there is more in <lb/>this alone than in all the re&longs;t: for it's impo&longs;&longs;ible to &longs;ay any thing <lb/>that is good and &longs;olid touching Velocity, without having rightly <lb/>explained what we are to under&longs;tand by Gravity, as al&longs;o the whole <lb/>Sy&longs;teme of the World. </s> <s>Now becau&longs;e I would not under take it, <pb xlink:href="040/01/1015.jpg" pagenum="321"/>I have thought good to omit this Con&longs;ideration, and in this manner <lb/>to &longs;ingle out the&longs;e others that I could explain without it: for <lb/>though there be no Motion but hath &longs;ome Velocity, neverthele&longs;s <lb/>it is onely the Augmentations and Diminutions of this Velocity <lb/>that are con&longs;iderable. </s> <s>And now that &longs;peaking of the Motion of a <lb/>Body, we &longs;uppo&longs;e that it is made according to the Velocity which <lb/>is mo&longs;t naturall to it, which is the &longs;ame as if we did not con&longs;ider it <lb/>at all.</s></p><p type="main"> <s>The other rea&longs;on that may have hindred men from rightly un­<lb/>der&longs;tanding my Principle is, that they have thought that they could <lb/>demon&longs;trate without it &longs;ome of tho&longs;e things which I demon&longs;trate <lb/>not without it: As, for example, touching the Pulley A B C, they <lb/>have thought that it was enough to know that the Nail in A did <lb/><figure id="id.040.01.1015.1.jpg" xlink:href="040/01/1015/1.jpg"/><lb/>&longs;u&longs;tain the half of the Weight B; to conclude <lb/>that the Hand in C had need but of half &longs;o much <lb/>Force to &longs;u&longs;tain or rai&longs;e the Weight, thus wound <lb/>about the Pulley, as it would need for to &longs;u&longs;tain <lb/>or rai&longs;e it without it. </s> <s>But howbeit that this ex­<lb/>plaineth very well, how the application of the <lb/>Force at C is made unto a Weight double to that <lb/>which it could rai&longs;e without a Pulley, and that I <lb/>my &longs;elf did make u&longs;e thereof, yet I deny that <lb/>this is &longs;imply, becau&longs;e that that the Nail A &longs;u­<lb/>&longs;taineth one part of the Weight B, that the Force <lb/>in C, which &longs;u&longs;taineth it, might be le&longs;s than if it <lb/>had been &longs;o &longs;u&longs;tained. </s> <s>For if that had been true, the Rope C E be­<lb/>ing wound about the Pulley D, the Force in E might by the &longs;ame <lb/>rea&longs;on be le&longs;s than the Force in C: for that the Nail A doth not <lb/>&longs;u&longs;tain the Weight le&longs;s than it did before, and that there is al&longs;o <lb/>another Nail that &longs;u&longs;tains it, to wit, that to wich the Pulley D is <lb/>fa&longs;tned. </s> <s>Thus therefore, that we may not be mi&longs;taken in this, that <lb/>the Nail A &longs;u&longs;taineth the half of the Weight B, we ought to con­<lb/>clude no more but this, that by this application the one of the Di­<lb/>men&longs;ions of the Force that ought to be in C <lb/><figure id="id.040.01.1015.2.jpg" xlink:href="040/01/1015/2.jpg"/><lb/>to rai&longs;e up this Weight is dimini&longs;hed the one <lb/>half; and that the other, of con&longs;equence, be­<lb/>cometh double, in &longs;uch &longs;ort that if the Line <lb/>F G repre&longs;ent the Force that is required for <lb/>the &longs;u&longs;taining the Weight B in a point, with­<lb/>out the help of any Machine, and the <lb/>Quadrangle G H that which is required for <lb/>the rai&longs;ing of it to the height of a foot, the <lb/>&longs;upport of the Nail A dimini&longs;heth the Di­<lb/>men&longs;ion which is repre&longs;ented by the Line F G the one half, and the <lb/>redoubling of the Rope A B C maketh the other Dimen&longs;ion to <pb xlink:href="040/01/1016.jpg" pagenum="322"/>double, which is repre&longs;ented by the Line FH; and &longs;o the Force <lb/>that ought to be in C for the rai&longs;ing of the Weight B to the height <lb/>of one foot is repre&longs;ented by the Quadrangle IK; and, as we know <lb/>in Geometry, that a Line being added to, or taken from a Superfi­<lb/>cies, neither augmenteth, nor dimini&longs;heth it in the lea&longs;t, &longs;o the <lb/>Force where with the Nail A &longs;u&longs;tains the Weight B, having but one <lb/>&longs;ole Dimen&longs;ion, cannot cau&longs;e that the Force in C, con&longs;idered ac­<lb/>cording to its two Dimen&longs;ions, ought to be le&longs;s for the rai&longs;ing in <lb/>like manner the Weight E, than for the rai&longs;ing it without any <lb/>Pulley.</s></p><p type="main"> <s>The third thing which may make men imagine &longs;ome Ob&longs;curity <lb/>in my Principle is, that they, it may be, have not had regard to all <lb/>the words by which I explain it; for I do not &longs;ay &longs;imply that the <lb/>Force that can rai&longs;e a Weight of 50 pounds to the height of four <lb/>feet can rai&longs;e one of 200 pounds to the height of one foot; but I <lb/>&longs;ay that it may do it, if &longs;o be that it be applyed to it: now it is <lb/>impo&longs;&longs;ible to apply the &longs;ame thereto, but by the means of &longs;ome Ma­<lb/>chine, or other Invention that &longs;hall cau&longs;e this Weight to a&longs;cend <lb/>but one, in the time whil&longs;t the Force pa&longs;&longs;eth the whole length <lb/>of four feet, and &longs;o that it do transform the Quandrangle, by <lb/>which the Force is repre&longs;ented that is required to rai&longs;e this <lb/>Weight of 400 pounds to the height of one foot into another <lb/>that is equall and like to that which repre&longs;ents the Force that is <lb/>required for to rai&longs;e a Weight of 50 pounds to the height of four <lb/>feet.</s></p><p type="main"> <s>In fine, it may be that men may have thought the wor&longs;e of my <lb/>Principle, becau&longs;e they have imagined that I have alledged the Ex­<lb/>amples of the Pulley, of the Inclined Plane, and of the Leaver, to <lb/>the end that I might better per&longs;warde the truth thereof, as if it had <lb/>been dubious, or el&longs;e that I had &longs;o ill di&longs;cour&longs;ed as to offer to a&longs;&longs;ume <lb/>from thence a Principle, which ought of it felf to be &longs;o clear, as not <lb/>to need any proof by things that are &longs;o difficult to comprehend as <lb/>that; it may be, they have never been well demon&longs;trated by any <lb/>man: but neither have I made u&longs;e of them, &longs;ave only with a de&longs;ign <lb/>to &longs;hew that this Principle extends it &longs;elf to all matters of which <lb/>one treateth in the Staticks: or, rather, I have made u&longs;e of this oc­<lb/>ca&longs;ion for to in&longs;ert them into my Treati&longs;e, for that I conceived <lb/>that it would have been too dry and barren if I had therein &longs;po­<lb/>ken of nothing el&longs;e but of this Que&longs;tion, that is of no u&longs;e, as of <lb/>that of the Geo&longs;taticks, which I purpo&longs;ed to examine.</s></p><p type="main"> <s>Now one may perceive, by what hath already been &longs;aid, how <lb/>the Forces of the Leaver and Pulley are demon&longs;trated by my <lb/>Principle &longs;o well, that there only remains the Inclined Plane, of <lb/>which you &longs;hall clearly &longs;ee the Demon&longs;tration by this Figure; in <lb/>which G F repre&longs;ents the fir&longs;t Dimen&longs;ion of the Force that the <pb xlink:href="040/01/1017.jpg" pagenum="323"/>Rectangle F H de&longs;cribeth whil&longs;t it draweth the Weight D along <lb/>the Plane B A, by the means of a Chord parallel to this Plane, and <lb/>pa&longs;&longs;ing about the Pulley E, in &longs;uch &longs;ort, that H G, that is the height <lb/>of this Rectangle, is equal to B A, along which the Weight D is to <lb/>move, whil&longs;t it mounteth to the height of the Line C A. </s> <s>And N O <lb/>repre&longs;ents the fir&longs;t Dimen&longs;ion of &longs;uch another Force, that is de­<lb/>&longs;cribed by the Rectan­<lb/>gle N P, in the time that <lb/><figure id="id.040.01.1017.1.jpg" xlink:href="040/01/1017/1.jpg"/><lb/>it is rai&longs;ing the Weight <lb/>L to M. </s> <s>And I &longs;uppo&longs;e <lb/>that L M is equal to B A, <lb/>or double to C A; and <lb/>that N O is to F G, as <lb/>O P is to G H. </s> <s>This <lb/>done, I con&longs;ider that at <lb/>&longs;uch time as the Weight <lb/>D is moved from B to­<lb/>wards A, one may ima­<lb/>gine its Motion to be <lb/>compo&longs;ed of two others, of which the one carrieth it from B R to­<lb/>wards C A, (to which operation there is no Force required, as all <lb/>tho&longs;e &longs;uppo&longs;e who treat of the Mechanicks) and the other rai&longs;eth <lb/>it from B C towards R A, for which alone the Force is required: <lb/>in&longs;omuch that it needs neither more nor le&longs;s Force to move it <lb/>along the Inclined Plane B A, than along the Perpendicular C A. <lb/></s> <s>For I &longs;uppo&longs;e that the unevenne&longs;&longs;es, <emph type="italics"/>&c.<emph.end type="italics"/> of the Plane do not <lb/>at all hinder it, like as it is alwaies &longs;uppo&longs;ed in treating of this <lb/>matter.</s></p><p type="main"> <s>So then the whole Force F H is employed only about the rai&longs;ing <lb/>of D to the height of C A: and fora&longs;much as it is exactly equal to <lb/>the Force N P, that is required for the rai&longs;ing of L to the Height <lb/>of L M, double to C A, I conclude by my Principle that the <lb/>Weight D is double to the Weight L. </s> <s>For in regard that it is <lb/>nece&longs;&longs;ary to employ as much Force for the one as for the other, <lb/>there is as much to be rai&longs;ed in the one as in the other; and no <lb/>more knowledge is required than to count unto two for the <lb/>knowing that it is alike facile to rai&longs;e 200 pounds from C to A, <lb/>as to rai&longs;e 100 pounds from L to M: &longs;ince that L M is double <lb/>to C A.</s></p><p type="main"> <s>You tell me, moreover, that I ought more particularly to ex­<lb/>plain the nature of the Spiral Line that repre&longs;enteth the Plane <lb/>equally enclined, which hath many qualities that render it &longs;uffi­<lb/>ciently knowable.</s></p><pb xlink:href="040/01/1018.jpg" pagenum="324"/><p type="main"> <s>For if A be the Center of the Earth, <lb/><figure id="id.040.01.1018.1.jpg" xlink:href="040/01/1018/1.jpg"/><lb/>and A N B C D the Spiral Line, having <lb/>drawn the Right Lines A B, A D, and the <lb/>like, there is the &longs;ame proportion betwixt <lb/>the Curved Line A N B and the Right Line <lb/>AB, as is betwixt the Curved Line A N B C, <lb/>and the Right Line A C; or betwixt <lb/>A N B C D and A D: and &longs;o of the <lb/>re&longs;t.</s></p><p type="main"> <s>And if one draw the Tangents D E, C F, <lb/>and B G, the Angles A D E, A C F, A B G, &c. <lb/></s> <s>&longs;hall be equal. </s> <s>As for the re&longs;t I will, &c.----</s></p><p type="main"> <s>Reverend Father,</s></p><p type="main"> <s>Your very humble Servant</s></p><p type="main"> <s><emph type="italics"/>DES-CARTES.<emph.end type="italics"/></s></p></chap> <chap> <pb xlink:href="040/01/1019.jpg" pagenum="325"/><p type="head"> <s>A <lb/>LETTER <lb/>OF <lb/>Mon&longs;ieur de Robberval <lb/>TO <lb/>Mon&longs;ieur de Fermates, <lb/>Coun&longs;ellour of <emph type="italics"/>THOULOUSE,<emph.end type="italics"/><lb/>Containing certain Propo&longs;itions in the <lb/>MECHANICKS.</s></p><p type="main"> <s>MONSIEUR,</s></p><p type="main"> <s>I have, according to my promi&longs;e, &longs;ent you the <lb/>Demon&longs;tration of the Fundamental Propo&longs;i­<lb/>tion of our Mechanicks, in which I follow the <lb/>common method of explaining, in the fir&longs;t <lb/>place, the Definitions and Principles of which <lb/>we make u&longs;e.</s></p><p type="main"> <s>We in general call that Quality a Force or <lb/>Power, by means of which any thing whatever <lb/>doth tend or a&longs;pire into another place than that in which it is, be it <lb/>downwards, upwards, or &longs;ide waies, whether this Quality naturally <lb/>belongeth to the Body, or be communicated to it from without. <lb/></s> <s>From which definition it followeth, that all Weights are a &longs;pecies <lb/>of Force, in regard that it is a Quality, by means whereof Bodies <lb/>do tend downwards. </s> <s>We often al&longs;o a&longs;&longs;ign the name of Force to <lb/>that very thing to which the Force belongeth, as a ponderous Bo­<lb/>dy is called a Weight, but with this pre-caution, that this is in re­<lb/>ference to the true Force, the which augmenting or dimini&longs;hing <lb/>&longs;hall be called a greater or le&longs;&longs;er Force, albeit that the thing to <lb/>which it belongeth do remain alwaies the &longs;ame.</s></p><p type="main"> <s>If a Force be &longs;u&longs;pended or fa&longs;tned to a Flexible Line that is <lb/>without Gravity, and that is made fa&longs;t by one end unto &longs;ome <emph type="italics"/>Ful­<lb/>ciment<emph.end type="italics"/> or &longs;tay, in &longs;uch &longs;ort as that it &longs;u&longs;tain the Force, drawing <pb xlink:href="040/01/1020.jpg" pagenum="326"/>without impediment by this Line, the Force and the Line &longs;hall <lb/>take &longs;ome certain po&longs;ition in which they &longs;hall re&longs;t, and the Line <lb/>&longs;hall of nece&longs;&longs;ity be &longs;treight, let that Line be termed <emph type="italics"/>the Pendant,<emph.end type="italics"/><lb/>or <emph type="italics"/>Line of Direction of the Force.<emph.end type="italics"/> And let the Point by which it is <lb/>fa&longs;tned to the Fulciment be called <emph type="italics"/>the Point of Su&longs;pen&longs;ion<emph.end type="italics"/>: which <lb/>may &longs;ometimes be the Arm of a Leaver or Ballance; and then let <lb/>the Line drawn from the Center of the Fulciment of the Leaver <lb/>or Ballance to the Point of Su&longs;pen&longs;ion be named <emph type="italics"/>the Di&longs;tance<emph.end type="italics"/> or <lb/><emph type="italics"/>the Arm of the Force<emph.end type="italics"/>: which we &longs;uppo&longs;e to be a Line fixed, and <lb/>con&longs;idered without Gravity. </s> <s>Moreover, let the Angle comprehen­<lb/>ded betwixt the Arm of the Force and the Line of Direction be <lb/>termed <emph type="italics"/>the Angle of the Direction of the Force.<emph.end type="italics"/></s></p><p type="head"> <s>AXIOM I.</s></p><p type="main"> <s>After the&longs;e Definitions we lay down for a Principle, that in the <lb/>Leaver, and in the Ballance, Equal Forces drawing by Arms <lb/>that are equal, and at equall Angles of Direction, do draw equal­<lb/>ly. </s> <s>And if in this Po&longs;ition they draw one again&longs;t the other they <lb/>&longs;hall make an <emph type="italics"/>Equilibrium<emph.end type="italics"/>: but if they draw together, or towards <lb/>the &longs;ame part, the Effect &longs;hall be double.</s></p><p type="main"> <s>If the Forces being equal, and the Augles of Direction al&longs;o <lb/>equal, the Arms be unequal, the Force that &longs;hall be &longs;u&longs;pended at <lb/>the greater Arm &longs;hall work the greater Effect.</s></p><p type="main"> <s>As in this Figure, the Center of the Ballance or Leaver being A, <lb/><figure id="id.040.01.1020.1.jpg" xlink:href="040/01/1020/1.jpg"/><lb/>if the Arms A B and A C are equal, <lb/>as al&longs;o the Angles A B D, and A C E, <lb/>the equal Forces D and E &longs;hall <lb/>draw equally, and make an <emph type="italics"/>Equili­<lb/>brium.<emph.end type="italics"/> So likewi&longs;e the Arm A F be­<lb/>ing equal to A B, the Angle A F G <lb/>to the Angle A B D, and the Force <lb/>G to D, the&longs;e two Forces ^{*} G and D <lb/><arrow.to.target n="marg1124"></arrow.to.target><lb/>draw equally; and in regard that <lb/>they draw both one way, the Effect <lb/>&longs;hall be double.</s></p><p type="margin"> <s><margin.target id="marg1124"></margin.target>* In the M. S. <lb/></s> <s>Copy it is <emph type="italics"/>C and <lb/>D.<emph.end type="italics"/></s></p><p type="main"> <s>In the &longs;ame manner the Forces G and E &longs;hall make an <emph type="italics"/>Equilibri­<lb/>um<emph.end type="italics"/>; as al&longs;o I and L &longs;hall counterpoi&longs;e, if (being equal) the Arms <lb/>A K and A H, and the Angles A H T, and A K L be equal.</s></p><p type="main"> <s>The &longs;ame &longs;hall befall in the Forces P and R, if all things be <lb/>di&longs;po&longs;ed as before. </s> <s>And in this ca&longs;e we make no other di&longs;tinction <lb/>betwixt Weights and other Forces &longs;ave only this, that Weights all <lb/>tend towards the Center of Grave Bodies, and Forces may be un­<lb/>der&longs;tood to tend all towards all parts of the Univer&longs;e, with &longs;o <lb/>much greater or le&longs;&longs;er <emph type="italics"/>Impetus<emph.end type="italics"/> than Weights. </s> <s>So that Weights and <pb xlink:href="040/01/1021.jpg" pagenum="327"/>their parts do draw by Lines of Direction, which all concur in one <lb/>and the &longs;ame Point; and Forces and their parts may be under&longs;tood <lb/>to draw in &longs;uch &longs;ort that all the Lines of Direction are parallel to <lb/>each other.</s></p><p type="head"> <s>AXIOM II.</s></p><p type="main"> <s>In the &longs;econd place, we &longs;uppo&longs;e that a Force and its Line of Di­<lb/>rection abiding alwaies in the &longs;ame po&longs;ition, as al&longs;o the Center <lb/>of the Ballance or Leaver, be the Arm what it will that is drawn <lb/>from the Center of the Ballance to the Line of Direction, the <lb/>Force drawing alwaies in the &longs;ame fa&longs;hion, will alwaies produce <lb/>the &longs;ame Effect.</s></p><p type="main"> <s>As, in this &longs;econd Figure, the Center of the Ballance being A, <lb/>the Force B, and the Line of Direction <lb/><figure id="id.040.01.1021.1.jpg" xlink:href="040/01/1021/1.jpg"/><lb/>B <emph type="italics"/>F<emph.end type="italics"/> prolonged, as occa&longs;ion &longs;hall re­<lb/>quire, in which the Arms A G, A C, and <lb/>A <emph type="italics"/>F<emph.end type="italics"/> do determine, in this po&longs;ition let <lb/>the Line B <emph type="italics"/>F<emph.end type="italics"/> be fa&longs;tned to the Arm <lb/>A <emph type="italics"/>F,<emph.end type="italics"/> or A C, or to another Arm drawn <lb/>from the Center A to the Line of Di­<lb/>rection ^{*} B <emph type="italics"/>F<emph.end type="italics"/>: we &longs;uppo&longs;e that this <lb/><arrow.to.target n="marg1125"></arrow.to.target><lb/><emph type="italics"/>F<emph.end type="italics"/>orce B &longs;hall alwaies work the &longs;ame <lb/>Effect upon the Ballance. </s> <s>And if <lb/>drawing by the Arm A C it make an <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> with the <emph type="italics"/>F<emph.end type="italics"/>orce <emph type="italics"/>D<emph.end type="italics"/> drawing by the <emph type="italics"/>A<emph.end type="italics"/>rm <emph type="italics"/>A<emph.end type="italics"/> E, when <lb/>ever it &longs;hall draw by the <emph type="italics"/>A<emph.end type="italics"/>rms <emph type="italics"/>A F<emph.end type="italics"/> or <emph type="italics"/>A<emph.end type="italics"/> G, it &longs;hall likewi&longs;e make <lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> with the <emph type="italics"/>F<emph.end type="italics"/>orce D drawing by the <emph type="italics"/>A<emph.end type="italics"/>rm <emph type="italics"/>A E.<emph.end type="italics"/> This <lb/>Principle although it be not expre&longs;ly found in <emph type="italics"/>A<emph.end type="italics"/>uthors, yet it is <lb/>tacitly &longs;uppo&longs;ed by all tho&longs;e that have writ on this <emph type="italics"/>A<emph.end type="italics"/>rgument, and <lb/>Experience con&longs;tantly confirmeth it.</s></p><p type="margin"> <s><margin.target id="marg1125"></margin.target>* In the Original <lb/>it is writ, but by <lb/>the mi&longs;take of <lb/>the Tran&longs;criber, <lb/><emph type="italics"/>a la ligue de<emph.end type="italics"/> di­<lb/>rection A F.</s></p><p type="head"> <s>AXIOM III.</s></p><p type="main"> <s>I<emph type="italics"/>f<emph.end type="italics"/> the Arms of a Ballance or Leaver are directly placed the one to <lb/>the other, and that being equal they &longs;u&longs;tain equal <emph type="italics"/>F<emph.end type="italics"/>orces, of which <lb/>the Angles of Direction are Right An­<lb/><figure id="id.040.01.1021.2.jpg" xlink:href="040/01/1021/2.jpg"/><lb/>gles, the&longs;e <emph type="italics"/>F<emph.end type="italics"/>orces do alwaies weigh <lb/>equally upon the Center of the Bal­<lb/>lance, whether that they be near to the <lb/>&longs;ame Center, or far di&longs;tant, or both <lb/>conjoyned in the Center it &longs;elf; as in <lb/>this <emph type="italics"/>F<emph.end type="italics"/>igure the Ballance being E D, <lb/>the Center A, the equal Arms A D <lb/>and <emph type="italics"/>A<emph.end type="italics"/> E, let us &longs;u&longs;tain equal <emph type="italics"/>F<emph.end type="italics"/>orces H and I, of which the <emph type="italics"/>A<emph.end type="italics"/>ngles <pb xlink:href="040/01/1022.jpg" pagenum="328"/>of Direction <emph type="italics"/>A<emph.end type="italics"/> D H and <emph type="italics"/>A<emph.end type="italics"/> E I are Right <emph type="italics"/>A<emph.end type="italics"/>ngles, we &longs;uppo&longs;e that <lb/>the&longs;e two <emph type="italics"/>F<emph.end type="italics"/>orces I and H weigh alike upon the Center <emph type="italics"/>A<emph.end type="italics"/> as if they <lb/>were nearer to the Center, at the equal Di&longs;tances <emph type="italics"/>A<emph.end type="italics"/> B and A C, <lb/>and we al&longs;o &longs;uppo&longs;e the &longs;ame if the&longs;e very <emph type="italics"/>F<emph.end type="italics"/>orces were &longs;u&longs;pended <lb/>both together in <emph type="italics"/>A,<emph.end type="italics"/> the <emph type="italics"/>A<emph.end type="italics"/>ngles of Directions being &longs;till Right <lb/><emph type="italics"/>A<emph.end type="italics"/>ngles.</s></p><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s>The&longs;e Principles agreed upon, we will ea&longs;ily demon&longs;trate, <lb/>in Imitation of <emph type="italics"/>Archimedes,<emph.end type="italics"/> that upon a &longs;traight Balance <lb/>the <emph type="italics"/>F<emph.end type="italics"/>orces, of which and of all their parts the Lines of Dire­<lb/>ction are parallel to one another, and perpendicular to the Balance, <lb/>&longs;hall couuterpoi&longs;e and make an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> when the &longs;aid <emph type="italics"/>F<emph.end type="italics"/>orces <lb/>&longs;hall be to one another in Reciprocal proportion of their Arms, <lb/>which we think to be &longs;o manife&longs;t to you, that we thence &longs;hall de­<lb/>rive the Demon&longs;tration of this Univer&longs;al Propo&longs;ition to which we <lb/>ha&longs;ten.</s></p><p type="head"> <s>PROPOS. II.</s></p><p type="main"> <s>In every Balance or Leaver, if the proportion of the <emph type="italics"/>F<emph.end type="italics"/>orces is <lb/>reciprocal to that of the Perpendicular Lines drawn from the <lb/>Center or Point of the <emph type="italics"/>F<emph.end type="italics"/>ulciment unto the Lines of Direction <lb/>of the <emph type="italics"/>F<emph.end type="italics"/>orces, drawing the one again&longs;t the other, they &longs;hall make <lb/>an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> and drawing on one and the &longs;ame &longs;ide, they &longs;hall <lb/>have a like Effect, that is to &longs;ay, that they &longs;hall have as much <emph type="italics"/>F<emph.end type="italics"/>orce <lb/>the one as the other, to move the Balance.</s></p><p type="main"> <s>In this <emph type="italics"/>F<emph.end type="italics"/>igure let the Center of the Balance be <emph type="italics"/>A,<emph.end type="italics"/> the <emph type="italics"/>A<emph.end type="italics"/>rm <emph type="italics"/>A<emph.end type="italics"/> B, <lb/>bigger than <emph type="italics"/>A<emph.end type="italics"/> C, and fir&longs;t let the <emph type="italics"/>L<emph.end type="italics"/>ines of Direction B D, and E C <lb/>be perpendicular to the <emph type="italics"/>A<emph.end type="italics"/>rms <emph type="italics"/>A<emph.end type="italics"/> B and <emph type="italics"/>A<emph.end type="italics"/> C, by which Lines the <lb/><emph type="italics"/>F<emph.end type="italics"/>orces D and E (which may be made of Weights if one will) do <lb/>draw; and that there is the &longs;ame rate <lb/><figure id="id.040.01.1022.1.jpg" xlink:href="040/01/1022/1.jpg"/><lb/>of the <emph type="italics"/>F<emph.end type="italics"/>orce D to the Force E as there <lb/>is betwixt the <emph type="italics"/>A<emph.end type="italics"/>rm <emph type="italics"/>A<emph.end type="italics"/> C to the Arm <lb/><emph type="italics"/>A<emph.end type="italics"/> B: the Forces drawing one again&longs;t <lb/>the other, I &longs;ay, that they will make an <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> upon the Balance <emph type="italics"/>C<emph.end type="italics"/> A B. <lb/></s> <s>For let the <emph type="italics"/>A<emph.end type="italics"/>rm C <emph type="italics"/>A<emph.end type="italics"/> be prolonged <lb/>unto F, &longs;o as that <emph type="italics"/>A<emph.end type="italics"/>F may be equal to <lb/><emph type="italics"/>A<emph.end type="italics"/> B: and let C <emph type="italics"/>A<emph.end type="italics"/> F be con&longs;idered as a <lb/>&longs;treight Balance, of which let the Center be <emph type="italics"/>A<emph.end type="italics"/>: and let there be <lb/>&longs;uppo&longs;ed two Forces G and H, of which and of all their parts the <lb/>Lines of Direction are parallel to the Line C E, and that the <lb/>Force G be equal to the Force D, and H to E, the one, to wit G, <pb xlink:href="040/01/1023.jpg" pagenum="329"/>drawing upon the Arm A <emph type="italics"/>F,<emph.end type="italics"/> and the other, to wit H, upon the Arm <lb/>A C: now, by the fir&longs;t Propo&longs;ition, G and H &longs;hall make an <emph type="italics"/>Equili­<lb/>brium<emph.end type="italics"/> upon the Balance C A F: But, by the fir&longs;t Principle, the Force <lb/>D upon the Arm A B worketh the &longs;ame effect as the Force G on <lb/>the Arm A F: Therefore the Force D upon the Arm A B maketh <lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> with the Force H upon A C: And the Force H <lb/>drawing in the &longs;ame manner upon the Arm <emph type="italics"/>A<emph.end type="italics"/> C as the Force E, by <lb/>the &longs;ame fir&longs;t <emph type="italics"/>A<emph.end type="italics"/>xiom, the Force D upon the Arm <emph type="italics"/>A<emph.end type="italics"/> B &longs;hall make an <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> with the Force E upon the Arm <emph type="italics"/>A<emph.end type="italics"/> C.</s></p><p type="main"> <s>Now, in the following Figure, let the Center of the Balance be <lb/><emph type="italics"/>A,<emph.end type="italics"/> the Arms A B and A C, the Lines of Direction B D and C E <lb/>which are not Perpendicular to the Arms, and the Forces D and E <lb/>drawing likewi&longs;e by the Lines of Direction, upon which Perpen­<lb/>diculars are erected unto the Center A, that is A F upon B D, and <lb/>A G upon E C, and that as A F is to A G, &longs;o is the Force E to the <lb/>Force D: which Forces draw one <lb/><figure id="id.040.01.1023.1.jpg" xlink:href="040/01/1023/1.jpg"/><lb/>again&longs;t the other: I &longs;ay, that they will <lb/>make an <emph type="italics"/>Equilibrium<emph.end type="italics"/> upon the Balance <lb/>C A B: For let the Lines A F and A G <lb/>be under&longs;tood to be the two Arms of <lb/>a Balance G A F, upon which the For­<lb/>ces D and E do draw by the Lines of <lb/>Direction F D and G E: The&longs;e Forces <lb/>&longs;hall make an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> by the fir&longs;t <lb/>part of this &longs;econd Propo&longs;ition; but, by the &longs;econd Axiom, the Force <lb/>D upon the Arm A F hath the &longs;ame Effect as upon the Arm A B: <lb/>Therefore the Force D upon the Arm A B maketh an <emph type="italics"/>Equilibrium<emph.end type="italics"/><lb/>with the Force E upon the Arm A C.</s></p><p type="main"> <s>There are many Ca&longs;es, according to the Series of Perpendicu­<lb/>lars, but it will be ea&longs;ie for you to &longs;ee that they have all but one <lb/>and the &longs;ame Demon&longs;tration.</s></p><p type="main"> <s>It is al&longs;o ea&longs;ie to demon&longs;trate, that if the Forces draw both on <lb/>one &longs;ide they &longs;hall make the &longs;ame Effect one as another, and that <lb/>the Effect of two together &longs;hall be double to that of one alone.</s></p><p type="head"> <s>OF THE <lb/>GEOSTATICKS.</s></p><p type="main"> <s>The Principle which you demand for the <emph type="italics"/>Geo&longs;taticks<emph.end type="italics"/> is, <lb/>That if two equal Weights are conjoyned by a right <lb/>Line fixed and void of Gravity, and that being &longs;o di­<lb/>&longs;po&longs;ed they may de&longs;cend freely, they will never re&longs;t till <lb/>that the middle of the Line, that is the Center of Gravitation of <lb/>the Ancients, unites it &longs;elf to the common Center of Grave Bodies.</s></p><pb xlink:href="040/01/1024.jpg" pagenum="330"/><p type="main"> <s>This Principle &longs;eems at the fir&longs;t very plau&longs;ible, but when <lb/>the Que&longs;tion concerneth a Principle, you know what Conditions <lb/>are required to it, that it may be received, the principal of which are <lb/>wanting in the Principle now in controver&longs;ie<emph type="italics"/>: &longs;cil.<emph.end type="italics"/> that we do not <lb/>know what is the radical Cau&longs;e why Grave Bodies de&longs;cend; and <lb/>whence the Original of this Gravity ari&longs;eth: as al&longs;o that we are to­<lb/>tally ignorant of that which would arrive at the Center whither <lb/>Grave Bodies do tend, nor to other places without the Surface of the <lb/>Earth, of which, in regard we inhabit upon it, we have &longs;ome Expe­<lb/>riments upon which we ground our Principles.</s></p><p type="main"> <s>For it may be, that Gravity is a Quality that re&longs;ides in the Body <lb/>it &longs;elf that falleth; it may be that it is in another that attracteth <lb/>that which de&longs;cends, as in the Earth: It may be, and it is very likely <lb/>that it is a Natural Attraction, or a Natural De&longs;ire of two Bodies to <lb/>unite together, as in the Iron and Load&longs;tone, which are &longs;uch, that <lb/>if the Load&longs;tone be &longs;taid, the Iron, if nothing hinder it, will go find <lb/>it out; and if the Iron be &longs;taid the Load&longs;tone will go towards it; <lb/>and if they be both at liberty, they will reciprocally approach one <lb/>another, yet after &longs;uch a fa&longs;hion, that the &longs;tronge&longs;t of the two <lb/>will move the lea&longs;t way.</s></p><p type="main"> <s>If the fir&longs;t be true, according to the common opinion, we &longs;ee not <lb/>how your Principle can &longs;ub&longs;i&longs;t, for Common Sen&longs;e tells us, that in <lb/>whatever place a Weight is, it alwaies weigheth alike, having ever­<lb/>more the &longs;ame Quality that maketh it to weigh, and that then a Bo­<lb/>dy will repo&longs;e at the Common Center of things Grave when the <lb/>parts of the Body which &longs;hall be on each part of the &longs;aid Center <lb/>&longs;hall be of equal Pondero&longs;ity to counterpoi&longs;e one another, without <lb/>having any regard whether they be little or much removed from the <lb/>Center. </s> <s>Since therefore that of the&longs;e three po&longs;&longs;ible Cau&longs;es of Gra­<lb/>vitation, we know not which is the right, nay, that we are not cer­<lb/>tain that it is any of them, it being po&longs;&longs;ibly that there is a fourth <lb/>from which one may draw Conclu&longs;ions very different, it &longs;eemeth to <lb/>me impo&longs;&longs;ible for us to lay down other Principles in this bufine&longs;s <lb/>than tho&longs;e of which we are a&longs;&longs;ured by a continual Experience, and <lb/>a &longs;ound Judgment. </s> <s>As for our parts, we call tho&longs;e Bodies equally <lb/>or unequally Grave which have an equal or unequal Force of mo­<lb/>ving towards the Common Center: and a Body is &longs;aid to have the <lb/>&longs;ame Weight when it alwaies hath this &longs;ame Force: but if this <lb/>Force augmenteth or dimini&longs;heth, then, although it be the &longs;ame Bo­<lb/>dy, we con&longs;ider it no longer as the &longs;ame Weight: Now &longs;ince that <lb/>this hapneth to Bodies that recede or approach to the Common <lb/>Center, this is it which we de&longs;ire to know, but finding nothing that <lb/>giveth me content upon this Subject, I will leave the Que&longs;tion un­<lb/>determined and unde&longs;cribed.</s></p> <p type="head"> <s>>FINIS.</s></p> </chap><pb xlink:href="040/01/1025.jpg"/><chap><p type="head"> <s>ARCHIMEDES <lb/>HIS TRACT <lb/>De Incidentibus Humido, <lb/>OR OF THE <lb/>NATATION OF BODIES VPON, <lb/>OR SVBMERSION IN, <lb/>THE <lb/>WATER <lb/>OR OTHER LIQUIDS.</s></p><p type="head"> <s>IN TWO BOOKS.</s></p><p type="head"> <s>Tran&longs;lated from the Original Greek,</s></p><p type="head"> <s>Fir&longs;t into Latine, and afterwards into Italian, by <emph type="italics"/>NICOLO <lb/>TARTAGLIA,<emph.end type="italics"/> and by him familiarly demon­<lb/>&longs;trated by way of Dialogue, with <emph type="italics"/>Richard Wentworth,<emph.end type="italics"/><lb/>a Noble Engli&longs;h Gentleman, and his Friend.</s></p><p type="head"> <s>Together with the Learned Commentaries of <emph type="italics"/>Federico <lb/>Commandino,<emph.end type="italics"/> who hath Re&longs;tored &longs;uch of the Demon&longs;trations <lb/>as, thorow the Injury of Time, were obliterated.</s></p><p type="head"> <s>Now compared with the ORIGINAL, and Engli&longs;hed <lb/>By <emph type="italics"/>THOMAS SALVSBVRY,<emph.end type="italics"/> <expan abbr="E&longs;q.">E&longs;que</expan></s></p><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/> Printed by <emph type="italics"/>W. Leybourn,<emph.end type="italics"/> 1662.</s></p></chap><chap><pb xlink:href="040/01/1026.jpg"/> <pb xlink:href="040/01/1027.jpg" pagenum="335[333]"/><p type="head"> <s>ARCHIMEDES <lb/>HIS TRACT <lb/><emph type="italics"/>De <lb/>INCIDENTIBUS HUMIDO,<emph.end type="italics"/><lb/>OR OF <lb/>The Natation of Bodies upon, or Submer&longs;ion in, <lb/>the Water, or other Liquids.</s></p></chap> <chap> <pb xlink:href="040/01/1028.jpg"/><p type="head"> <s>BOOK I.</s></p><p type="head"> <s>RICARDO.</s></p><p type="main"> <s><emph type="italics"/>Dear Companion,<emph.end type="italics"/> I have peru&longs;ed your <emph type="italics"/>Indu&longs;trious Invention,<emph.end type="italics"/><lb/>in which I find not any thing that will not certainly hold <lb/>true; but, truth is, there are many of your Conclu&longs;ions <lb/>of which I under&longs;tand uot the Cau&longs;e, and therefore, if it <lb/>be not a trouble to you, I would de&longs;ire you to declare them <lb/>to me, for, indeed, nothing plea&longs;eth me, if the Cau&longs;e <lb/>thereof be hid from me.</s></p><p type="main"> <s>NICOLO. </s> <s>My obligations unto you are &longs;o many and <lb/>great, <emph type="italics"/>Honoured Campanion,<emph.end type="italics"/> that no reque&longs;t of yours ought <lb/>to be trouble&longs;ome to me, and therefore tell me what tho&longs;e Perticulars are of which <lb/>you know not the Cau&longs;e, for I &longs;hall endeavour with the utmo&longs;t of my power and <lb/>under&longs;tanding to &longs;atisfie you in all your demands.</s></p><p type="main"> <s>RIC. </s> <s>In the fir&longs;t <emph type="italics"/>Direction<emph.end type="italics"/> of the fir&longs;t Book of that your <emph type="italics"/>Indu&longs;trious Invention<emph.end type="italics"/><lb/>you conclude, That it is impo&longs;&longs;ible that the Water &longs;hould wholly receive into it <lb/>any material Solid Body that is lighter than it &longs;eif (as to <emph type="italics"/>&longs;peciæ<emph.end type="italics"/>) nay, you &longs;ay, That <lb/>there will alwaies a part of the Body &longs;tay or remain above the Waters Surface <lb/>(that is uncovered by it;) and, That as the whole Solid Body put into the Water <lb/>is in proportion to that part of it that &longs;hall be immerged, or received, into the Wa­<lb/>ter, &longs;o &longs;hall the Gravity of the Water be to the Gravity <emph type="italics"/>(in &longs;peciæ)<emph.end type="italics"/> of that &longs;ame <lb/>material Body: And that tho&longs;e Solid Bodies, that are by nature more Grave than the <lb/>Water, being put into the Water, &longs;hall pre&longs;ently make the &longs;aid Water give place; <lb/>and, That they do not only wholly enter or &longs;ubmerge in the &longs;ame, but go continu­<lb/>ally de&longs;cending untill they arrive at <emph type="italics"/>t<emph.end type="italics"/>he Bottom; and, That they &longs;ink to the Bot­<lb/>tom &longs;o much fa&longs;ter, by how much they are more Grave than the Water. </s> <s>And, <lb/>again, That tho&longs;e which are preci&longs;ely of the &longs;ame Gravity with the Water, being <lb/>put into the &longs;ame, are of nece&longs;&longs;ity wholly received into, or immerged by it, but <lb/>yet retained in the Surface of the &longs;aid Water, and much le&longs;s will the Water con­<lb/>&longs;ent that it do de&longs;cend to the Bottom: and, now, albeit that all the&longs;e things are <lb/>manife&longs;t to Sen&longs;e and Experience, yet neverthele&longs;s would I be very glad, if it be <lb/>po&longs;&longs;ible, that you would demon&longs;trate to me the mo&longs;t apt and proper Cau&longs;e of <lb/>the&longs;e Effects.</s></p> <pb xlink:href="040/01/1029.jpg" pagenum="334"/><p type="main"> <s>NIC. </s> <s>The Cau&longs;e of all the&longs;e Effects is a&longs;&longs;igned by <emph type="italics"/>Archimedes,<emph.end type="italics"/> the <emph type="italics"/>Siracu&longs;an,<emph.end type="italics"/> in <lb/><arrow.to.target n="marg1126"></arrow.to.target><lb/>that Book <emph type="italics"/>De Incidentibus (^{*}) Aquæ,<emph.end type="italics"/> by me publi&longs;hed in Latine, and dedicated to <lb/>your &longs;elf, as I al&longs;o &longs;aid in the beginning of that my <emph type="italics"/>Indu&longs;trions Invention.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1126"></margin.target>* <emph type="italics"/>Aquæ,<emph.end type="italics"/> tan&longs;lated <lb/>by me <emph type="italics"/>Humido,<emph.end type="italics"/> as <lb/>the more Compre­<lb/>hen&longs;ive word, for <lb/>his Doctrine holds <lb/>true in all Liquids <lb/>as well as in Wa­<lb/>ter, <emph type="italics"/>&longs;oil.<emph.end type="italics"/> in Wine, <lb/>Oyl, Milk, <emph type="italics"/>&c.<emph.end type="italics"/></s></p><p type="main"> <s>RIC. </s> <s>I have &longs;een that &longs;ame <emph type="italics"/>Archimedes,<emph.end type="italics"/> and have very well under&longs;tood tho&longs;e <lb/>two Books in which he treateth <emph type="italics"/>De Centro Gravitatis æquerepentibus,<emph.end type="italics"/> or of the <lb/>Center of Gravity in Figures plain, or parallel to the Horizon; and likewi&longs;e tho&longs;e <lb/><emph type="italics"/>De Quadratura Parabolæ,<emph.end type="italics"/> or, of Squaring the Parabola; but ^{*}<emph type="italics"/>that<emph.end type="italics"/> in which he treat­<lb/>eth of Solids that Swim upon, or &longs;ink in Liquids, is &longs;o ob&longs;cure, that, to &longs;peak the <lb/>truth, there are many things in <emph type="italics"/>it<emph.end type="italics"/> which I do not under&longs;tand, and therefore before <lb/><arrow.to.target n="marg1127"></arrow.to.target><lb/>we proceed any farther, I &longs;hould take it for a favour if you would declare it to me <lb/>in your Vulgar Tongue, beginning with his fir&longs;t <emph type="italics"/>Suppo&longs;ition,<emph.end type="italics"/> which &longs;peaketh in this <lb/>manner.</s></p><p type="margin"> <s><margin.target id="marg1127"></margin.target>* He &longs;peaks of but <lb/>one Book, <emph type="italics"/>Tartag­<lb/>lia<emph.end type="italics"/> having tran&longs;la­<lb/>ted no more.</s></p><p type="head"> <s>SVPPOSITION I.</s></p><p type="main"> <s><emph type="italics"/>It is &longs;uppo&longs;ed that the Liquid is of &longs;uch a nature, that <lb/>its parts being equi-jacent and contiguous, the le&longs;s <lb/>pre&longs;&longs;ed are repul&longs;ed by the more pre&longs;&longs;ed. </s> <s>And <lb/>that each of its parts is pre&longs;&longs;ed or repul&longs;ed by the <lb/>Liquor that lyeth over it, perpendicularly, if the <lb/>Liquid be de&longs;cending into any place, or pre&longs;&longs;ed any <lb/>whither by another.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>Every Science, Art, or Doctrine (as you know, <emph type="italics"/>Honoured Companion,<emph.end type="italics"/>) <lb/>hath its fir&longs;t undemon&longs;trable Principles, by which (they being <lb/>granted or &longs;uppo&longs;ed) the &longs;aid Science is proved, maintained, or de­<lb/>mon&longs;trated. </s> <s>And of the&longs;e Principles, &longs;ome are called <emph type="italics"/>Petitions,<emph.end type="italics"/><lb/>and others <emph type="italics"/>Demands,<emph.end type="italics"/> or <emph type="italics"/>Suppo&longs;itions.<emph.end type="italics"/> I &longs;ay, therefore, that the Science or Doctrine <lb/>of tho&longs;e Material Solids that Swim or Sink in Liquids, hath only two undemon­<lb/>&longs;trable <emph type="italics"/>Suppo&longs;itions,<emph.end type="italics"/> one of which is that above alledged, the which in compliance <lb/>with your de&longs;ire I have &longs;et down in our Vulgar Tongue.</s></p><p type="main"> <s>RIC. </s> <s>Before you proceed any farther tell me, how we are to under&longs;tand the <lb/>parts of a Liquid to be <emph type="italics"/>Equijacent.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>When they are equidi&longs;tant from the Center of the World, or of the <lb/>Earth (which is the &longs;ame, although ^{*} &longs;ome hold that the Centers of the Earth <lb/>and Worldare different.)</s></p><p type="main"> <s>RIC. </s> <s>I under&longs;tand you not unle&longs;s you give me &longs;ome Example thereof in <lb/>Figure.<lb/><arrow.to.target n="marg1128"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1128"></margin.target>* The Coperni­<lb/>cans.</s></p><p type="main"> <s>NIC. </s> <s>To exemplifie this particular, Let us &longs;uppo&longs;e a quantity of Liquor (as <lb/>for in&longs;tance of Water) to be upon the Earth; then let us with the Imagination <lb/>cut the whole Earth together with that Water into two equal parts, in &longs;uch a <lb/>manner as that the &longs;aid Section may pa&longs;s ^{*} by the Center of the Earth: And let <lb/>us &longs;uppo&longs;e that one part of the Superficies of that Section, as well of the Water <lb/>as of the Earth, be the Superficies A B, and that the Center of the Earth be the <lb/>point K. </s> <s>This being done, let us in our Imagination de&longs;cribe a Circle upon the </s></p><p type="main"> <s><arrow.to.target n="marg1129"></arrow.to.target><lb/>&longs;aid Center K, of &longs;uch a bigne&longs;s as that the Circumference may pa&longs;s by the Super­<lb/>ficies of the Section of the Water: Now let this Circumference be E F G: and <lb/>let many Lines be drawn from the point K to the &longs;aid Circumference, cutting the <lb/>&longs;ame, as KE, KHO, KFQ KLP, KM. </s> <s>Now I &longs;ay, that all the&longs;e parts of <lb/>the &longs;aid Water, terminated in that Circumference, are Equijacent, as being all <pb xlink:href="040/01/1030.jpg" pagenum="335"/>equidi&longs;tant from the point K, the Center of the World, which parts are G M, <lb/>M L, L F, F H, H E.</s></p><p type="margin"> <s><margin.target id="marg1129"></margin.target>* Or through.</s></p><p type="main"> <s>RIC. </s> <s>I under&longs;tand you very well, as to this particular: But tell me a little; he <lb/>&longs;aith that each of the parts of the Liquid is pre&longs;&longs;ed or repul&longs;ed by the Liquid that <lb/>is above it, according to the Perpendicular: I know not what that Liquid is that <lb/>lieth upon a part of another Perpendicularly.</s></p><p type="main"> <s>NIC. </s> <s>Imagining a Line that cometh from the Center of the Earth penetrating <lb/>thorow &longs;ome Water, each part of the Water that is in that Line he &longs;uppo&longs;eth to <lb/>be pre&longs;&longs;ed or repul&longs;ed by the Water that lieth above it in that &longs;ame Line, and that <lb/>that repul&longs;e is made according to the &longs;ame Line, (that is, directly towards the <lb/>Center of the World) which Line is called a Perpendicular; becau&longs;e every <lb/>Right-Line that departeth from any point, and goeth directly towards the Worlds <lb/>Center is called a Perpendicular. </s> <s>And that you may the better under&longs;tand me, let <lb/><figure id="id.040.01.1030.1.jpg" xlink:href="040/01/1030/1.jpg"/><lb/>us imagine <lb/>the Line KHO, <lb/>and in that <lb/>let us imagine <lb/>&longs;everal parts, <lb/>as &longs;uppo&longs;e RS, <lb/>S T, T V, V H, <lb/>H O. </s> <s>I &longs;ay, <lb/>that he &longs;up­<lb/>po&longs;eth that <lb/>the part V H <lb/>is pre&longs;&longs;ed by <lb/>that placed a­<lb/>bove it, H O, <lb/>according to <lb/>the Line OK; <lb/>the which <lb/>O K, as hath been &longs;aid above, is called the Perpendicular pa&longs;&longs;ing thorow tho&longs;e two <lb/>parts. </s> <s>In like manner, I &longs;ay that the part T V is expul&longs;ed by the part V H, ac­<lb/>cording to the &longs;aid Line O K: and &longs;o the part S T to be pre&longs;&longs;ed by T V, according <lb/>to the &longs;aid Perpendicular O K, and R S by S T. </s> <s>And this you are to under&longs;tand <lb/>in all the other Lines that were protracted from the &longs;aid Point K, penetrating the <lb/>&longs;aid Water, As for Example, in <emph type="italics"/>K<emph.end type="italics"/> G, <emph type="italics"/>K<emph.end type="italics"/> M, <emph type="italics"/>K<emph.end type="italics"/> L, <emph type="italics"/>K<emph.end type="italics"/> F, <emph type="italics"/>K<emph.end type="italics"/> E, and infinite others of the <lb/>like kind.</s></p><p type="main"> <s>RIC. Indeed, <emph type="italics"/>Dear Companion,<emph.end type="italics"/> this your Explanation hath given megreat &longs;a­<lb/>tisfaction; for, in my Judgment, it &longs;eemeth that all the difficulty of this Suppo&longs;ition <lb/>con&longs;i&longs;ts in the&longs;e two particulars which you have declared to me.</s></p><p type="main"> <s>NIC. </s> <s>It doth &longs;o; for having under&longs;tood that the parts E H, H F, F L, L M, and <lb/>MG, determining in the Circumference of the &longs;aid Circle are equijacent, it is an <lb/>ea&longs;ie matter to under&longs;tand the fore&longs;aid <emph type="italics"/>Suppo&longs;ition<emph.end type="italics"/> in Order, which &longs;aith, <emph type="italics"/>That it is <lb/>&longs;uppo&longs;ed that the Liquid is of &longs;uch a nature, that the part thereof le&longs;s pre&longs;&longs;ed or thrust is re­<lb/>pul&longs;ed by the more thru&longs;t or pre&longs;&longs;ed.<emph.end type="italics"/> As for example, if the part E H were by chance <lb/>more thru&longs;t, crowded, or pre&longs;&longs;ed from above downwards by the Liquid, or &longs;ome <lb/>other matter that was over it, than the part H F, contiguous to it, it is &longs;uppo&longs;ed <lb/>that the &longs;aid part H F, le&longs;s pre&longs;&longs;ed, would be repul&longs;ed by the &longs;aid part E H. </s> <s>And <lb/>thus we ought to under&longs;tand of the other parts equijacent, in ca&longs;e that they be <lb/>contiguous, and not &longs;evered. </s> <s>That each of the parts thereof is pre&longs;&longs;ed and repul. <lb/></s> <s>&longs;ed by the <emph type="italics"/>L<emph.end type="italics"/>iquid that lieth over it Perpendicularly, is manife&longs;t by that which was <lb/>&longs;aid above, to wit, that it &longs;hould be repul&longs;ed, in ca&longs;e the <emph type="italics"/>L<emph.end type="italics"/>iquid be de&longs;cending into <lb/>any place, and thru&longs;t, or driven any whither by another.</s></p><p type="main"> <s>RIC. </s> <s>I under&longs;tand this Suppo&longs;ition very well, but yet me thinks that before <lb/>the Suppo&longs;ition, the Author ought to have defined tho&longs;e two particulars, which <lb/>you fir&longs;t declared to me, that is, how we are to under&longs;tand the parts of the <emph type="italics"/>L<emph.end type="italics"/>iquid <lb/>equijacent, and likewi&longs;e the Perpendicular.</s></p> <pb xlink:href="040/01/1031.jpg" pagenum="336"/><p type="main"> <s>NIC. </s> <s>You &longs;ay truth.</s></p><p type="main"> <s>RIC. </s> <s>I have another que&longs;tion to aske you, which is this, Why the Author <lb/>u&longs;eth the word <emph type="italics"/>L<emph.end type="italics"/>iquid, or Humid, in&longs;tead of Water.</s></p><p type="main"> <s>NIC. </s> <s>It may be for two of the&longs;e two Cau&longs;es; the one is, that Water being the <lb/>principal of all <emph type="italics"/>L<emph.end type="italics"/>iquids, therefore &longs;aying <emph type="italics"/>Humidum<emph.end type="italics"/> he is to be under&longs;tood to mean <lb/>the chief Liquid, that is Water: The other, becau&longs;e that all the Propo&longs;itions of <lb/>this Book of his, do not only hold true in Water, but al&longs;o in every other <emph type="italics"/>L<emph.end type="italics"/>iquid, <lb/>as in Wine, Oyl, and the like: and therefore the Author might have u&longs;ed the word <lb/><emph type="italics"/>Humidum,<emph.end type="italics"/> as being a word more general than <emph type="italics"/>Aqua.<emph.end type="italics"/></s></p><p type="main"> <s>RIC. </s> <s>This I under&longs;tand, therefore let us come to the fir&longs;t <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> which, as <lb/>you know, in the Original &longs;peaks in this manner.</s></p><p type="head"> <s>PROP. I. THEOR. I.</s></p><p type="main"> <s><emph type="italics"/>If any Superficies &longs;hall be cut by a Plane thorough any <lb/>Point, and the Section be alwaies the Circumference <lb/>of a Circle, who&longs;e Center is the &longs;aid Point: that Su­<lb/>perficies &longs;hall be Spherical.<emph.end type="italics"/></s></p><p type="main"> <s>Let any Superficies be cut at plea&longs;ure by a Plane thorow the <lb/>Point K; and let the Section alwaies de&longs;cribe the Circumfe­<lb/>rence of a Circle that hath for its Center the Point K: I &longs;ay, <lb/>that that &longs;ame Superficies is Sphærical. </s> <s>For were it po&longs;&longs;ible that the <lb/>&longs;aid Superficies were not Sphærical, then all the Lines drawn <lb/>through the &longs;aid Point K unto that Superficies would not be equal, <lb/>Let therefore A and B be two <lb/>Points in the &longs;aid Superficies, &longs;o that <lb/><figure id="id.040.01.1031.1.jpg" xlink:href="040/01/1031/1.jpg"/><lb/>drawing the two Lines K A and <lb/>K B, let them, if po&longs;&longs;ible, be une­<lb/>qual: Then by the&longs;e two Lines let <lb/>a Plane be drawn cutting the &longs;aid <lb/>Superficies, and let the Section in <lb/>the Superficies make the Line <lb/>D A B G: Now this Line D A B G <lb/>is, by our pre-&longs;uppo&longs;al, a Circle, and <lb/>the Center thereof is the Point K, for &longs;uch the &longs;aid Superficies was <lb/>&longs;uppo&longs;ed to be. </s> <s>Therefore the two Lines K A and K B are equal: <lb/>But they were al&longs;o &longs;uppo&longs;ed to be unequal; which is impo&longs;&longs;ible: <lb/>It followeth therefore, of nece&longs;&longs;ity, that the &longs;aid Superficies be <lb/>Sphærical, that is, the Superficies of a Sphære.</s></p><p type="main"> <s>RIC. </s> <s>I under&longs;tand you very well; now let us proceed to the &longs;econd <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/><lb/>which, you know, runs thus.</s></p> <pb xlink:href="040/01/1032.jpg" pagenum="337"/><p type="head"> <s>PROP. II. THEOR. II.</s></p><p type="main"> <s><emph type="italics"/>The Superficies of every Liquid that is con&longs;i&longs;tant and <lb/>&longs;etled &longs;hall be of a Sphærical Figure, which Figure <lb/>&longs;hall have the &longs;ame Center with the Earth.<emph.end type="italics"/></s></p><p type="main"> <s>Let us &longs;uppo&longs;e a Liquid that is of &longs;uch a con&longs;i&longs;tance as that it <lb/>is not moved, and that its Superficies be cut by a Plane along <lb/>by the Center of the Earth, and let the Center of the Earth <lb/>be the Point K: and let the Section of the Superficies be the Line <lb/>A B G D. </s> <s>I &longs;ay that the Line A B G D is the Circumference of a <lb/><figure id="id.040.01.1032.1.jpg" xlink:href="040/01/1032/1.jpg"/><lb/>Circle, and that the Center <lb/>thereof is the Point K And <lb/>if it be po&longs;&longs;ible that it may <lb/>not be the Circumference <lb/>of a Circle, the Right­<lb/><arrow.to.target n="marg1130"></arrow.to.target><lb/>Lines drawn ^{*} by the Point <lb/>K to the &longs;aid Line A B G D <lb/>&longs;hall not be equal. </s> <s>There­<lb/>fore let a Right-Line be <lb/>taken greater than &longs;ome of tho&longs;e produced from the Point K unto <lb/>the &longs;aid Line A B G D, and le&longs;&longs;er than &longs;ome other; and upon the <lb/>Point K let a Circle be de&longs;cribed at the length of that Line, <lb/>Now the Circumference of this Circle &longs;hall fall part without the <lb/>&longs;aid Line A B G D, and part within: it having been pre&longs;uppo&longs;ed <lb/>that its Semidiameter is greater than &longs;ome of tho&longs;e Lines that may <lb/>be drawn from the &longs;aid Point K unto the &longs;aid Line A B G D, and <lb/>le&longs;&longs;er than &longs;ome other. </s> <s>Let the Circumference of the de&longs;cribed <lb/>Circle be R B G H, and from B to K draw the Right-Line B K: and <lb/>drawn al&longs;o the two Lines K R, and K E L which make a Right­<lb/>Angle in the Point K: and upon the Center K de&longs;cribe the Circum­<lb/>ference X O P in the Plane and in the Liquid. </s> <s>The parts, there­<lb/>fore, of the Liquid that are ^{*} according to the Circumference <lb/><arrow.to.target n="marg1131"></arrow.to.target><lb/>X O P, for the rea&longs;ons alledged upon the fir&longs;t <emph type="italics"/>Suppo&longs;ition,<emph.end type="italics"/> are equi­<lb/>jacent, or equipo&longs;ited, and contiguous to each other; and both <lb/>the&longs;e parts are pre&longs;t or thru&longs;t, according to the &longs;econd part of the <lb/><emph type="italics"/>Suppo&longs;ition,<emph.end type="italics"/> by the Liquor which is above them. </s> <s>And becau&longs;e the <lb/>two Angles E K B and B K R are &longs;uppo&longs;ed equal [<emph type="italics"/>by the<emph.end type="italics"/> 26. <emph type="italics"/>of<emph.end type="italics"/> 3. <lb/><emph type="italics"/>of Euclid,<emph.end type="italics"/>] the two Circumferences or Arches B E and B R &longs;hall <lb/>be equal (fora&longs;much as R B G H was a Circle de&longs;cribed for &longs;atis­<lb/>faction of the Oponent, and K its Center:) And in like manner <lb/>the whole Triangle B E K &longs;hall be equal to the whole Triangle <lb/>B R K. </s> <s>And becau&longs;e al&longs;o the Triangle O P K for the &longs;ame rea&longs;on <pb xlink:href="040/01/1033.jpg" pagenum="338"/>&longs;hall be equal to the Triangle O X K; Therefore (by common <lb/>Notion) &longs;ub&longs;tracting tho&longs;e two &longs;mall Triangles O P K and O X K <lb/>from the two others B E K and B R K, the two Remainders &longs;hall <lb/>be equal: one of which Remainders &longs;hall be the Quadrangle <lb/>B E O P, and the other B R X O. </s> <s>And becau&longs;e the whole Quadran­<lb/>gle B E O P is full of Liquor, and of the Quadrangle B R X O, <lb/>the part B A X O only is full, and the re&longs;idue B R A is wholly void <lb/>of Water: It followeth, therefore, that the Quadrangle B E O P <lb/>is more ponderous than the Quadrangle B R X O. </s> <s>And if the &longs;aid <lb/>Quadrangle B E O P be more Grave than the Quadrangle <lb/>B R X O, much more &longs;hall the Quadrangle B L O P exceed in Gra­<lb/>vity the &longs;aid Quadrangle B R X O: whence it followeth, that the <lb/>part O P is more pre&longs;&longs;ed than the part O X. But, by the fir&longs;t part <lb/>of the Suppo&longs;ition, the part le&longs;s pre&longs;&longs;ed &longs;hould be repul&longs;ed by the <lb/>part more pre&longs;&longs;ed: Therefore the part O X mu&longs;t be repul&longs;ed by <lb/>the part O P: But it was pre&longs;uppo&longs;ed that the Liquid did not <lb/>move: Wherefore it would follow that the le&longs;s pre&longs;&longs;ed would not <lb/>be repul&longs;ed by the more pre&longs;&longs;ed: And therefore it followeth of <lb/>nece&longs;&longs;ity that the Line A <emph type="italics"/>B<emph.end type="italics"/> G D is the Circumference of a Circle, <lb/>and that the Center of it is the point K. </s> <s>And in like manner &longs;hall <lb/>it be demon&longs;trated, if the Surface of the Liquid be cut by a Plane <lb/>thorow the Center of the Earth, that the Section &longs;hall be the Cir­<lb/>cumference of a Circle, and that the Center of the &longs;ame &longs;hall be <lb/>that very Point which is Center of the Earth. </s> <s>It is therefore mani­<lb/>fe&longs;t that the Superficies of a Liquid that is con&longs;i&longs;tant and &longs;etled <lb/>&longs;hall have the Figure of a Sphære, the Center of which &longs;hall be <lb/>the &longs;ame with that of the Earth, by the fir&longs;t <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/>; for it is <lb/>&longs;uch that being ever cut thorow the &longs;ame Point, the Section or Di­<lb/>vi&longs;ion de&longs;cribes the Circumference of a Circle which hath for Cen­<lb/>ter the &longs;elf-&longs;ame Point that is Center of the Earth: Which was to <lb/>be demon&longs;trated.</s></p><p type="margin"> <s><margin.target id="marg1130"></margin.target>* O: through.</s></p><p type="margin"> <s><margin.target id="marg1131"></margin.target>* <emph type="italics"/>i.e.<emph.end type="italics"/> Parallel.</s></p><p type="main"> <s>RIC. </s> <s>I do thorowly under&longs;tand the&longs;e your Rea&longs;ons, and &longs;ince there is in them <lb/>no umbrage of Doubting, let us proceed to his third <emph type="italics"/>Propo&longs;ition.<emph.end type="italics"/></s></p><p type="head"> <s>PROP. III. THEOR. III.</s></p><p type="main"> <s><emph type="italics"/>Solid Magnitudes that being of equal Ma&longs;s with the <lb/>Liquid are al&longs;o equal to it in Gravity, being demit-<emph.end type="italics"/><lb/><arrow.to.target n="marg1132"></arrow.to.target><lb/><emph type="italics"/>ted into the [^{*} &longs;etled] Liquid do &longs;o &longs;ubmerge in the <lb/>&longs;ame as that they lie or appear not at all above the <lb/>Surface of the Liquid, nor yet do they &longs;ink to the <lb/>Bottom.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1034.jpg" pagenum="339"/><p type="margin"> <s><margin.target id="marg1132"></margin.target>* I add the word <lb/>&longs;etled, as nece&longs;&longs;ary <lb/>in making the Ex­<lb/>periment.</s></p><p type="main"> <s>NIC. </s> <s>In this <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> it is affirmed that tho&longs;e Solid Magnitules that hap­<lb/>pen to be equal in &longs;pecifical Gravity with the Liquid being lefeat liber­<lb/>ty in the &longs;aid Liquid do &longs;o &longs;ubmerge in the &longs;ame, as that they lie or ap­<lb/>pear not at all above the Surface of the Liquid, nor yet do they go or &longs;ink to the <lb/>Bottom.</s></p><p type="main"> <s>For &longs;uppo&longs;ing, on the contrary, that it were po&longs;&longs;ible for one of <lb/>tho&longs;e Solids being placed in the Liquid to lie in part without the <lb/>Liquid, that is above its Surface, (alwaies provided that the &longs;aid <lb/>Liquid be &longs;etled and undi&longs;turbed,) let us imagine any Plane pro­<lb/>duced thorow the Center of the Earth, thorow the Liquid, and <lb/>thorow that Solid Body: and let us imagine that the Section of the <lb/>Liquid is the Superficies A B G D, and the Section of the Solid <lb/>Body that is within it the Super&longs;icies E Z H T, and let us &longs;uppo&longs;e <lb/>the Center of the Earth to be the Point K: and let the part of the <lb/>&longs;aid Solid &longs;ubmerged in the Liquid be B G H T, and let that above <lb/>be B E Z G: and let the Solid Body be &longs;uppo&longs;ed to be comprized in <lb/>a Pyramid that hath its Parallelogram Ba&longs;e in the upper Surface of <lb/>the Liquid, and its Summity or Vertex in the Center of the Earth: <lb/>which Pyramid let us al&longs;o &longs;uppo&longs;e to be cut or divided by the &longs;ame <lb/>Plane in which is the Circumference A B G D, and let the Sections <lb/><figure id="id.040.01.1034.1.jpg" xlink:href="040/01/1034/1.jpg"/><lb/>of the Planes of the &longs;aid <lb/>Pyramid be K L and <lb/>K M: and in the Liquid <lb/>about the Center K let <lb/>there be de&longs;cribed a Su­<lb/>perficies of another <lb/>Sphære below E Z H T, <lb/>which let be X O P; <lb/>and let this be cut by <lb/>the Superficies of the Plane: And let there be another Pyramid ta­<lb/>ken or &longs;uppo&longs;ed equal and like to that which compri&longs;eth the &longs;aid <lb/>Solid Body, and contiguous and conjunct with the &longs;ame; and let <lb/>the Sections of its Superficies be K M and K N: and let us &longs;uppo&longs;e <lb/>another Solid to be taken or imagined, of Liquor, contained in that <lb/>&longs;ame Pyramid, which let be R S C Y, equal and like to the partial <lb/>Solid B H G T, which is immerged in the &longs;aid Liquid: But the <lb/>part of the Liquid which in the fir&longs;t Pyramid is under the Super­<lb/>ficies X O, and that, which in the other Pyramid is under the Su­<lb/>perficies O P, are equijacent or equipo&longs;ited and contiguous, but <lb/>are not pre&longs;&longs;ed equally; for that which is under the Superficies <lb/>X O is pre&longs;&longs;ed by the Solid T H E Z, and by the Liquor that is <lb/>contained between the two Spherical Superficies X O and L M <lb/>and the Planes of the Pyramid, but that which proceeds accord­<lb/>ing to F O is pre&longs;&longs;ed by the Solid R S C Y, and by the Liquid <pb xlink:href="040/01/1035.jpg" pagenum="340"/>contained between the Sphærical Superficies that proceed accord­<lb/>ing to P O and M N and the Planes of the Pyramid; and the Gra­<lb/>vity of the Liquid, which is according to M N O P, &longs;hall be le&longs;&longs;er <lb/>than that which is according to L M X O; becau&longs;e that Solid of <lb/>Liquor which proceeds according to R S C Y is le&longs;s than the Solid <lb/>E Z H T (having been &longs;uppo&longs;ed to be equal in quantity to only <lb/>the part H B G T of that:) And the &longs;aid Solid E Z H T hath been <lb/>&longs;uppo&longs;ed to be equally grave with the Liquid: Therefore the Gra­<lb/>vity of the <emph type="italics"/>L<emph.end type="italics"/>iquid compri&longs;ed betwixt the two Sphærical Superfi­<lb/>cies L M and <emph type="italics"/>X<emph.end type="italics"/> O, and betwixt the &longs;ides L <emph type="italics"/>X<emph.end type="italics"/> and M O of the <lb/><figure id="id.040.01.1035.1.jpg" xlink:href="040/01/1035/1.jpg"/><lb/>Pyramid, together with <lb/>the whole Solid EZHT, <lb/>&longs;hall exceed the Gravity <lb/>of the Liquid compri­<lb/>&longs;ed betwixt the other <lb/>two Sphærical Superfi­<lb/>cies M N and O P, and <lb/>the Sides M O and N P <lb/>of the Pyramid, toge­<lb/>ther with the Solid of Liquor R S C Y by the quantity of the Gra­<lb/>vity of the part E B Z G, &longs;uppo&longs;ed to remain above the Surface of <lb/>the Liquid: And therefore it is manife&longs;t that the part which pro­<lb/>ceedeth according to the Circumference O P is pre&longs;&longs;ed, driven, and <lb/>repul&longs;ed, according to the <emph type="italics"/>Suppo&longs;ition,<emph.end type="italics"/> by that which proceeds ac­<lb/>cording to the Circumference X O, by which means the Liquid <lb/>would not be &longs;etled and &longs;till: But we did pre&longs;uppo&longs;e that it was <lb/>&longs;etled, namely &longs;o, as to be without motion: It followeth, therefore, <lb/>that the &longs;aid Solid cannot in any part of it exceed or lie above the <lb/>Superficies of the Liquid: And al&longs;o that being dimerged in the Li­<lb/>quid it cannot de&longs;cend to the Bottom, for that all the parts of the <lb/>Liquid equijacent, or di&longs;po&longs;ed equally, are equally pre&longs;&longs;ed, becau&longs;e <lb/>the Solid is equally grave with the Liquid, by what we pre&longs;uppo&longs;ed.</s></p><p type="main"> <s>RIC. </s> <s>I do under&longs;tand your Argumentation, but I under&longs;tand not that Phra&longs;e <lb/><emph type="italics"/>Solid Magnitudes.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>I will declare this Term unto you. <emph type="italics"/>Magnitude<emph.end type="italics"/> is a general Word that <lb/>re&longs;pecteth all the Species of Continual Quantity; and the Species of Continual <lb/>Quantity are three, that is, the <emph type="italics"/>L<emph.end type="italics"/>ine, the Superficies, and the Body; which Body <lb/>is al&longs;o called a Solid, as having in it &longs;elf <emph type="italics"/>L<emph.end type="italics"/>ength, Breadth, and Thickne&longs;s, or Depth: <lb/>and therefore that none might equivocate or take that Term <emph type="italics"/>Magnitudes<emph.end type="italics"/> to be <lb/>meant of <emph type="italics"/>L<emph.end type="italics"/>ines, or Superficies, but only of Solid <emph type="italics"/>Magnitudes,<emph.end type="italics"/> that is, Bodies, he <lb/>did &longs;pecifie it by that manner of expre&longs;&longs;ion, as was &longs;aid. </s> <s>The truth is, that he <lb/>might have expre&longs;t that <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> in this manner: <emph type="italics"/>Solids (or Bodies) which being <lb/>of equal Gravity with an equal Ma&longs;s of the Liquid,<emph.end type="italics"/> &c. </s> <s>And this <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> would have <lb/>been more cleer and intelligible, for it is as &longs;ignificant to &longs;ay, a <emph type="italics"/>Solid,<emph.end type="italics"/> or, a <emph type="italics"/>Body,<emph.end type="italics"/> as <lb/>to &longs;ay, a <emph type="italics"/>Solid Magnitude:<emph.end type="italics"/> therefore wonder not if for the future I u&longs;e the&longs;e three <lb/>kinds of words indifferently.</s></p><p type="main"> <s>RIC. </s> <s>You have &longs;ufficiently &longs;atisfied me, wherefore that we may lo&longs;e no time <lb/>let us go forwards to the fourth <emph type="italics"/>Propo&longs;ition.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1036.jpg" pagenum="341"/><p type="head"> <s>PROP. IV. THEOR. IV.</s></p><p type="main"> <s><emph type="italics"/>Solid Magnitudes that are lighter than the Liquid, <lb/>being demitted into the &longs;etled Liquid, will not total­<lb/>ly &longs;ubmerge in the &longs;ame, but &longs;ome part thereof will <lb/>lie or &longs;tay above the Surface of the Liquid.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>In this fourth <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> it is concluded, that every Body or Solid that is <lb/>lighter (as to Specifical Gravity) than the <emph type="italics"/>L<emph.end type="italics"/>iquid, being put into the <lb/><emph type="italics"/>L<emph.end type="italics"/>iquid, will not totally &longs;ubmerge in the &longs;ame, but that &longs;ome part of it <lb/>will &longs;tay and appear without the <emph type="italics"/>L<emph.end type="italics"/>iquid, that is above its Surface.</s></p><p type="main"> <s>For &longs;uppo&longs;ing, on the contrary, that it were po&longs;&longs;ible for a Solid <lb/>more light than the Liquid, being demitted in the Liquid to &longs;ub­<lb/>merge totally in the &longs;ame, that is, &longs;o as that no part thereof re­<lb/>maineth above, or without the &longs;aid Liquid, (evermore &longs;uppo&longs;ing <lb/>that the Liquid be &longs;o con&longs;tituted as that it be not moved,) let us <lb/>imagine any Plane produced thorow the Center of the Earth, tho­<lb/>row the Liquid, and thorow that Solid Body: and that the Surface <lb/>of the Liquid is cut by this Plane according to the Circumference <lb/>A <emph type="italics"/>B<emph.end type="italics"/> G, and the Solid <emph type="italics"/>B<emph.end type="italics"/>ody according to the Figure R; and let the <lb/>Center of the Earth be K. </s> <s>And let there be imagined a Pyramid <lb/><figure id="id.040.01.1036.1.jpg" xlink:href="040/01/1036/1.jpg"/><lb/>that compri&longs;eth the Figure <lb/>R, as was done in the pre. <lb/></s> <s>cedent, that hath its Ver­<lb/>tex in the Point K, and let <lb/>the Superficies of that <lb/>Pyramid be cut by the <lb/>Superficies of the Plane <lb/>A <emph type="italics"/>B<emph.end type="italics"/> G, according to A K <lb/>and K <emph type="italics"/>B<emph.end type="italics"/>. </s> <s>And let us ima­<lb/>gine another Pyramid equal and like to this, and let its Superficies <lb/>be cut by the Superficies A <emph type="italics"/>B<emph.end type="italics"/> G according to K <emph type="italics"/>B<emph.end type="italics"/> and K <emph type="italics"/>G<emph.end type="italics"/>; and let <lb/>the Superficies of another Sphære be de&longs;cribed in the Liquid, upon <lb/>the Center K, and beneath the Solid R; and let that be cut by the <lb/>&longs;ame Plane according to <emph type="italics"/>X<emph.end type="italics"/> O P. And, la&longs;tly, let us &longs;uppo&longs;e ano­<lb/>ther Solid taken ^{*} from the Liquid, in this &longs;econd Pyramid, which <lb/><arrow.to.target n="marg1133"></arrow.to.target><lb/>let be H, equal to the Solid R. </s> <s>Now the parts of the Liquid, name­<lb/>ly, that which is under the Spherical Superficies that proceeds ac­<lb/>cording to the Superficies or Circumference <emph type="italics"/>X<emph.end type="italics"/> O, in the fir&longs;t Py­<lb/>ramid, and that which is under the Spherical Superficies that pro­<lb/>ceeds according to the Circumference O P, in the &longs;econd Pyramid, <lb/>are equijacent, and contiguous, but are not pre&longs;&longs;ed equally; for <pb xlink:href="040/01/1037.jpg" pagenum="342"/>that of the fir&longs;t Pyramid is pre&longs;&longs;ed by the Solid R, and by the Liquid <lb/>which that containeth, that is, that which is in the place of the Py­<lb/>ramid according to A B O X: but that part which, in the other Py­<lb/>ramid, is pre&longs;&longs;ed by the Solid H, &longs;uppo&longs;ed to be of the &longs;ame Li­<lb/>quid, and by the Liquid which that containeth, that is, that which <lb/>is in the place of the &longs;aid Pyramid according to P O B G: and the <lb/>Gravity of the Solid R is le&longs;s than the Gravity of the Liquid <lb/>H, for that the&longs;e two Magnitudes were &longs;uppo&longs;ed to be equal in <lb/>Ma&longs;s, and the Solid R was &longs;uppo&longs;ed to be lighter than the Liquid: <lb/>and the Ma&longs;&longs;es of the two Pyramids of Liquor that containeth the&longs;e <lb/><arrow.to.target n="marg1134"></arrow.to.target><lb/>two Solids R and H are equal ^{*} by what was pre&longs;uppo&longs;ed: There­<lb/>fore the part of the Liquid that is under the Superficies that pro­<lb/>ceeds according to the Circumference O P is more pre&longs;&longs;ed; and, <lb/>therefore, by the <emph type="italics"/>Suppo&longs;ition,<emph.end type="italics"/> it &longs;hall repul&longs;e that part which is le&longs;s <lb/>pre&longs;&longs;ed, whereby the &longs;aid Liquid will not be &longs;etled: But it was be­<lb/>fore &longs;uppo&longs;ed that it was &longs;etled: Therefore that Solid R &longs;hall not <lb/>totally &longs;ubmerge, but &longs;ome part thereof will remain without the <lb/>Liquid, that is, above its Surface, Which was the <emph type="italics"/>Propo&longs;ition.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1133"></margin.target>* That is a Ma&longs;s of <lb/>the Liquid.</s></p><p type="margin"> <s><margin.target id="marg1134"></margin.target>* For that the Py­<lb/>ramids were &longs;uppo­<lb/>&longs;ed equal.</s></p><p type="main"> <s>RIC. </s> <s>I have very well under&longs;tood you, therefore let us come to the fifth <emph type="italics"/>Pro­<lb/>po&longs;ition,<emph.end type="italics"/> which, as you know, doth thus &longs;peak.</s></p><p type="head"> <s>PROP. V. THEOR. V.</s></p><p type="main"> <s><emph type="italics"/>Solid Magnitudes that are lighter than the Liquid, <lb/>being demitted in the (&longs;etled) Liquid, will &longs;o far <lb/>&longs;ubmerge, till that a Ma&longs;s of Liquor, equal to the <lb/>Part &longs;ubmerged, doth in Gravity equalize the <lb/>whole Magnitude.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>It having, in the precedent, been demon&longs;trared that Solids lighter than <lb/>the Liquid, being demitted in the <emph type="italics"/>L<emph.end type="italics"/>iquid, alwaies a part of them remains <lb/>without the <emph type="italics"/>L<emph.end type="italics"/>iquid, that is above its Surface; In this fifth <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> it is <lb/>a&longs;&longs;erted, that &longs;o much of &longs;uch a Solid &longs;hall &longs;ubmerge, as that a Ma&longs;s of the <lb/><emph type="italics"/>L<emph.end type="italics"/>iquid equal to the part &longs;ubmerged, &longs;hall have equal Gravity with the whole <lb/>Solid.</s></p><p type="main"> <s>And to demon&longs;trate this, let us a&longs;&longs;ume all the &longs;ame Schemes <lb/>as before, in <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> 3. and likewi&longs;e let the Liquid be &longs;et­<lb/>led, and let the Solid E Z H T be lighter than the Liquid. <lb/></s> <s>Now if the &longs;aid Liquid be &longs;etled, the parts of it that are equija­<lb/>cent are equally pre&longs;&longs;ed: Therefore the Liquid that is beneath <pb xlink:href="040/01/1038.jpg" pagenum="343"/>the Superficies that proceed according to the Circumferences X O <lb/>and P O are equally pre&longs;&longs;ed; whereby the Gravity pre&longs;&longs;ed is equal. <lb/><figure id="id.040.01.1038.1.jpg" xlink:href="040/01/1038/1.jpg"/><lb/>But the Gravity of the <lb/>Liquid which is in the <lb/><arrow.to.target n="marg1135"></arrow.to.target><lb/>fir&longs;t Pyramid ^{*} without <lb/>the Solid B H T G, is <lb/>equal to the Gravity of <lb/>the Liquid which is in <lb/>the other Pyramid with­<lb/>out the Liquid R S C Y: <lb/>It is manife&longs;t, therefore, <lb/>that the Gravity of the Solid E Z H T, is equal to the Gravity of <lb/>the Liquid R S C Y: Therefore it is manife&longs;t that a Ma&longs;s of Liquor <lb/>equal in Ma&longs;s to the part of the Solid &longs;ubmerged is equal in Gra­<lb/>vity to the whole Solid.</s></p><p type="margin"> <s><margin.target id="marg1135"></margin.target>* <emph type="italics"/>Without, i.e.<emph.end type="italics"/> that <lb/>being deducted.</s></p><p type="main"> <s>RIC. </s> <s>This was a pretty Demon&longs;tration, and becau&longs;e I very well under&longs;tand <lb/>it, let us lo&longs;e no time, but proceed to the &longs;ixth <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> &longs;peaking thus.</s></p><p type="head"> <s>PROP. VI. THEOR. VI.</s></p><p type="main"> <s><emph type="italics"/>Solid Magnitudes lighter than the Liquid being thru&longs;t <lb/>into the Liquid, are repul&longs;ed upwards with a Force <lb/>as great as is the exce&longs;s of the Gravity of a Ma&longs;s <lb/>of Liquor equal to the Magnitude above the Gra­<lb/>vity of the &longs;aid Magnitude.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>This &longs;ixth <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> &longs;aith, that the Solids lighter than the Liquid <lb/>demitted, thru&longs;t, or trodden by Force underneath the Liquids Sur­<lb/>face, are returned or driven upwards with &longs;o much Force, by <lb/>how much a quantity of the Liquid equal to the. </s> <s>Solid &longs;hall <lb/>exceed the &longs;aid Solid in Gravity.</s></p><p type="main"> <s>And to delucidate this <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> let the Solid A be lighter <lb/>than the <emph type="italics"/>L<emph.end type="italics"/>iquid, and let us &longs;uppo&longs;e that the Gravity of the &longs;aid <lb/>Solid A is B: and let the Gravity of a <emph type="italics"/>L<emph.end type="italics"/>iquid, equal in Ma&longs;s to A, <lb/>be B G. </s> <s>I &longs;ay, that the Solid A depre&longs;&longs;ed or demitted with Force <lb/>into the &longs;aid <emph type="italics"/>L<emph.end type="italics"/>iquid, &longs;hall be returned and repul&longs;ed upwards with <lb/>a Force equal to the Gravity G. </s> <s>And to demon&longs;trate this <emph type="italics"/>Propo­<lb/>&longs;ition,<emph.end type="italics"/> take the Solid D, equal in Gravity to the &longs;aid G. </s> <s>Now <lb/>the Solid compounded of the two Solids A and D will be lighter <lb/>than the <emph type="italics"/>L<emph.end type="italics"/>iquid: for the Gravity of the Solid compounded of <lb/>them both is BG, and the Gravity of as much Liquor as equal­<lb/>leth in greatne&longs;s the Solid A, is greater than the &longs;aid Gravity BG, <pb xlink:href="040/01/1039.jpg" pagenum="344"/>for that B G is the Gravity of the Liquid equal in Ma&longs;s unto it: <lb/>Therefore the Solid compounded of tho&longs;e two Solids A and D <lb/>being dimerged, it &longs;hall, by the precedent, &longs;o much of it &longs;ubmerge, <lb/>as that a quantity of the Liquid equal to the &longs;aid &longs;ubmerged part <lb/>&longs;hall have equal Gravity with the &longs;aid compounded Solid. </s> <s>And <lb/><figure id="id.040.01.1039.1.jpg" xlink:href="040/01/1039/1.jpg"/><lb/>for an example of that <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> let the Su­<lb/>perficies of any Liquid be that which pro­<lb/>ceedeth according to the Circumference <lb/>A B G D: Becau&longs;e now a Ma&longs;s or quantity <lb/>of Liquor as big as the Ma&longs;s A hath equal <lb/>Gravity with the whole compounded Solid <lb/>A D: It is manife&longs;t that the &longs;ubmerged part <lb/>thereof &longs;hall be the Ma&longs;s A: and the remain­<lb/>der, namely, the part D, &longs;hall be wholly a­<lb/>top, that is, above the Surface of the Liquid. <lb/></s> <s>It is therefore evident, that the part A hath &longs;o much virtue or <lb/>Force to return upwards, that is, to ri&longs;e from below above the Li­<lb/>quid, as that which is upon it, to wit, the part D, hath to pre&longs;s it <lb/>downwards, for that neither part is repul&longs;ed by the other: But D <lb/>pre&longs;&longs;eth downwards with a Gravity equal to G, it having been &longs;up­<lb/>po&longs;ed that the Gravity of that part D was equal to G: Therefore <lb/>that is manife&longs;t which was to be demon&longs;trated.</s></p><p type="main"> <s>RIC. </s> <s>This was a fine Demon&longs;tration, and from this I perceive that you colle­<lb/>cted your <emph type="italics"/>Indu&longs;trious Invention<emph.end type="italics"/>; and e&longs;pecially that part of it which you in&longs;ert in <lb/>the fir&longs;t Book for the recovering of a Ship &longs;unk: and, indeed, I have many Que­<lb/>&longs;tions to ask you about that, but I will not now interrupt the Di&longs;cour&longs;e in hand, but <lb/>de&longs;ire that we may go on to the &longs;eventh <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> the purport whereof is this.</s></p><p type="head"> <s>PROP. VII. THEOR. VII.</s></p><p type="main"> <s><emph type="italics"/>Solid Magnitudes beavier than the Liquid, being de­<lb/>mitted into the [&longs;etled] Liquid, are boren down­<lb/>wards as far as they can de&longs;cend: and &longs;hall be lighter <lb/>in the Liquid by the Gravity of a Liquid Ma&longs;s of <lb/>the &longs;ame bigne&longs;s with the Solid Magnitude.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>This &longs;eventh <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> hath two parts to be demon&longs;trated.</s></p><p type="main"> <s>The fir&longs;t is, That all Solids heavier than the Liquid, being demit­<lb/>ted into the <emph type="italics"/>L<emph.end type="italics"/>iquid, are boren by their Gravities downwards as far <lb/>as they can de&longs;cend, that is untill they arrive at the Bottom. </s> <s>Which <lb/>fir&longs;t part is manife&longs;t, becau&longs;e the Parts of the <emph type="italics"/>L<emph.end type="italics"/>iquid, which &longs;till lie <lb/>under that Solid, are more pre&longs;&longs;ed than the others equijacent, <lb/>becau&longs;e that that Solid is &longs;uppo&longs;ed more grave than the Liquid. <pb xlink:href="040/01/1040.jpg" pagenum="345"/>But now that that Solid is lighter in the Liquid than out of it, as <lb/>is affirmed in the &longs;econd part, &longs;hall be demon&longs;trated in this man­<lb/>ner. </s> <s>Take a Solid, as &longs;uppo&longs;e A, that is more grave than the Li­<lb/>quid, and &longs;uppo&longs;e the Gravity of that &longs;ame Solid A to be BG. <lb/></s> <s>And of a Ma&longs;s of <emph type="italics"/>L<emph.end type="italics"/>iquor of the &longs;ame bigne&longs;s with the Solid A, &longs;up­<lb/>po&longs;e the Gravity to be B: It is to be demon&longs;trated that the Solid <lb/>A, immerged in the Liquid, &longs;hall have a Gravity equal to G. </s> <s>And <lb/>to demon&longs;trate this, let us imagine another Solid, as &longs;uppo&longs;e D, <lb/>more light than the Liquid, but of &longs;uch a quality as that its Gravi­<lb/>ty is equal to B: and let this D be of &longs;uch a Magnitude, that a <lb/>Ma&longs;s of <emph type="italics"/>L<emph.end type="italics"/>iquor equal to it hath its Gravity equal to the Gravity <lb/>B G. </s> <s>Now the&longs;e two Solids D and A being compounded toge­<lb/>ther, all that Solid compounded of the&longs;e two &longs;hall be equally <lb/>Grave with the Water: becau&longs;e the Gravity of the&longs;e two Solids <lb/>together &longs;hall be equal to the&longs;e two Gravities, that is, to B G, and <lb/><figure id="id.040.01.1040.1.jpg" xlink:href="040/01/1040/1.jpg"/><lb/>to B; and the Gravity of a Liquid that hath its <lb/>Ma&longs;s equal to the&longs;e two Solids A and D, &longs;hall be <lb/>equal to the&longs;e two Gravities B G and B. <emph type="italics"/>L<emph.end type="italics"/>et <lb/>the&longs;e two Solids, therefore, be put in the <emph type="italics"/>L<emph.end type="italics"/>iquid, <lb/><arrow.to.target n="marg1136"></arrow.to.target><lb/>and they &longs;hall ^{*} remain in the Surface of that <emph type="italics"/>L<emph.end type="italics"/>i­<lb/>quid, (that is, they &longs;hall not be drawn or driven <lb/>upwards, nor yet downwards:) For if the Solid <lb/>A be more grave than the Liquid, it &longs;hall be <lb/>drawn or born by its Gravity downwards to­<lb/>wards the Bottom, with as much Force as by the Solid D it is thru&longs;t <lb/>upwards: And becau&longs;e the Solid D is lighter than the <emph type="italics"/>L<emph.end type="italics"/>iquid, it <lb/>&longs;hall rai&longs;e it upward with a Force as great as the Gravity G: Be­<lb/>cau&longs;e it hath been demon&longs;trated, in the &longs;ixth <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> That So­<lb/>lid Magnitudes that are lighter than the Water, being demitted in <lb/>the &longs;ame, are repul&longs;ed or driven upwards with a Force &longs;o much the <lb/>greater by how much a <emph type="italics"/>L<emph.end type="italics"/>iquid of equal Ma&longs;s with the Solid is more <lb/>Grave than the &longs;aid Solid: But the <emph type="italics"/>L<emph.end type="italics"/>iquid which is equal in Ma&longs;s <lb/>with the Solid D, is more grave than the &longs;aid Solid D, by the Gra­<lb/>vity G: Therefore it is manife&longs;t, that the Solid A is pre&longs;&longs;ed or <lb/>born downwards towards the Centre of the World, with a Force <lb/>as great as the Gravity G: Which was to be demon&longs;trated.</s></p><p type="margin"> <s><margin.target id="marg1136"></margin.target>* Or, according to <lb/><emph type="italics"/>Commandine,<emph.end type="italics"/> &longs;hall <lb/>be equall in Gravi­<lb/>ty to the Liquid, <lb/>neither moving up­<lb/>wards or down­<lb/>wards.</s></p><p type="main"> <s>RIC. </s> <s>This hath been an ingenuous Demon&longs;tration; and in regard I do &longs;uffici­<lb/>ently under&longs;tand it, that we may lo&longs;e no time, we will proceed to the &longs;econd <emph type="italics"/>Suppo­<lb/>&longs;ition,<emph.end type="italics"/> which, as I need not tell you, &longs;peaks thus.</s></p> <pb xlink:href="040/01/1041.jpg" pagenum="346"/><p type="head"> <s>SVPPOSITION II.</s></p><p type="main"> <s><emph type="italics"/>It is &longs;uppo&longs;ed that tho&longs;e Solids which are moved up­<lb/>wards, do all a&longs;cend according to the Perpendicular <lb/>which is produced thorow their Centre of Gravity.<emph.end type="italics"/></s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s><emph type="italics"/>And tho&longs;e which are moved downwards, de&longs;cend, likewi&longs;e, according to the Perpendicular <lb/>that is produced thorow their Centre of Gravity, which he pretermitted either as known, <lb/>or as to be collected from what went before.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>For under&longs;tanding of this &longs;econd <emph type="italics"/>Suppo&longs;ition,<emph.end type="italics"/> it is requi&longs;ite to take notice <lb/>that every Solid that is lighter than the Liquid being by violence, or by &longs;ome other <lb/>occa&longs;ion, &longs;ubmerged in the Liquid, and then left at liberty, it &longs;hall, by that which <lb/>hath been proved in the &longs;ixth <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> be thru&longs;t or born up wards by the Liquid, <lb/>and that impul&longs;e or thru&longs;ting is &longs;uppo&longs;ed to be directly according to the Perpendi­<lb/>cular that is produced thorow the Centre of Gravity of that Solid; which Per­<lb/>pendicular, if you well remember, is that which is drawn in the Imagination <lb/>from the Centre of the World, or of the Earth, unto the Centre of Gravity of <lb/>that Body, or Solid.</s></p><p type="main"> <s>RIC. </s> <s>How may one find the Centre of Gravity of a Solid?</s></p><p type="main"> <s>NIC. </s> <s>This he &longs;heweth in that Book, intituled <emph type="italics"/>De Centris Gravium, vel de Æqui­<lb/>ponderantibus<emph.end type="italics"/>; and therefore repair thither and you &longs;hall be &longs;atisfied, for to declare <lb/>it to you in this place would cau&longs;e very great confu&longs;ion.</s></p><p type="main"> <s>RIC. </s> <s>I under&longs;tand you: &longs;ome other time we will talk of this, becau&longs;e I have <lb/>a mind at pre&longs;ent to proceed to the la&longs;t <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> the Expo&longs;ition of which &longs;eemeth <lb/>to me very confu&longs;ed, and, as I conceive, the Author hath not therein &longs;hewn all <lb/>the Subject of that <emph type="italics"/>Propo&longs;ition<emph.end type="italics"/> in general, but only a part: which Propo&longs;ition <lb/>&longs;peaketh, as you know, in this form.</s></p><p type="head"> <s>PROP. VIII. THEOR. VIII.<lb/><arrow.to.target n="marg1137"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1137"></margin.target>A</s></p><p type="main"> <s><emph type="italics"/>If any Solid Magnitude, lighter than the Liquid, that <lb/>hath the Figure of a Portion of a Sphære, &longs;hall be<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1138"></arrow.to.target><lb/><emph type="italics"/>demitted into the Liquid in &longs;uch a manner as that <lb/>the Ba&longs;e of the Portion touch not the Liquid, the <lb/>Figure &longs;hall &longs;tand erectly, &longs;o, as that the Axis of <lb/>the &longs;aid Portion &longs;hall be according to the Perpen­<lb/>dicular. </s> <s>And if the Figure &longs;hall be inclined to any <lb/>&longs;ide, &longs;o, as that the Ba&longs;e of the Portion touch the <lb/>Liquid, it &longs;hall not continue &longs;o inclined as it was de­<lb/>mitted, but &longs;hall return to its uprightne&longs;s.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1042.jpg" pagenum="347"/><p type="margin"> <s><margin.target id="marg1138"></margin.target>B</s></p><p type="main"> <s>For the declaration of this <emph type="italics"/>Propo&longs;ition,<emph.end type="italics"/> let a Solid Magnitude <lb/>that hath the Figure of a portion of a Sphære, as hath been &longs;aid, <lb/>be imagined to be de­<lb/><figure id="id.040.01.1042.1.jpg" xlink:href="040/01/1042/1.jpg"/><lb/>mitted into the Liquid; and <lb/>al&longs;o, let a Plain be &longs;uppo&longs;ed <lb/>to be produced thorow the <lb/>Axis of that portion, and <lb/>thorow the Center of the <lb/>Earth: and let the Section <lb/>of the Surface of the Liquid <lb/>be the Circumference A B <lb/>C D, and of the Figure, the <lb/>Circumference E F H, & let <lb/>E H be a right line, and F T <lb/>the Axis of the Portion. </s> <s>If now <lb/>it were po&longs;&longs;ible, for &longs;atisfact­<lb/>ion of the Adver&longs;ary, Let <lb/>it be &longs;uppo&longs;ed that the &longs;aid Axis were not according to the <emph type="italics"/>(a)<emph.end type="italics"/> Per­<lb/><arrow.to.target n="marg1139"></arrow.to.target><lb/>pendicular; we are then to demon&longs;trate, that the Figure will not <lb/>continue as it was con&longs;tituted by the Adver&longs;ary, but that it will re­<lb/>turn, as hath been &longs;aid, unto its former po&longs;ition, that is, that the <lb/>Axis F T &longs;hall be according to the Perpendicular. </s> <s>It is manife&longs;t, by <lb/>the <emph type="italics"/>Corollary<emph.end type="italics"/> of the 1. of 3. <emph type="italics"/>Euclide,<emph.end type="italics"/> that the Center of the Sphære <lb/>is in the Line F T, fora&longs;much as that is the Axis of that Figure. <lb/></s> <s>And in regard that the Por­<lb/><figure id="id.040.01.1042.2.jpg" xlink:href="040/01/1042/2.jpg"/><lb/>tion of a Sphære, may be <lb/>greater or le&longs;&longs;er than an He­<lb/>mi&longs;phære, and may al&longs;o be <lb/>an Hemi&longs;phære, let the Cen­<lb/>tre of the Sphære, in the He­<lb/>mi&longs;phære, be the Point T, <lb/>and in the le&longs;&longs;er Portion the <lb/>Point P, and in the greater, <lb/>the Point K, and let the Cen­<lb/>tre of the Earth be the Point <lb/>L. </s> <s>And &longs;peaking, fir&longs;t, of <lb/>that greater Portion which <lb/>hath its Ba&longs;e out of, or a­<lb/>bove, the Liquid, thorew the Points K and L, draw the Line KL <lb/>cutting the Circumference E F H in the Point N, Now, becau&longs;e <lb/><arrow.to.target n="marg1140"></arrow.to.target><lb/>every Portion of a Sphære, hath its Axis in the Line, that from the <lb/>Centre of the Sphære is drawn perpendicular unto its Ba&longs;e, and hath <lb/>its Centre of Gravity in the Axis; therefore that Portion of the Fi­<lb/>gure which is within the Liquid, which is compounded of two Por­ <pb xlink:href="040/01/1043.jpg" pagenum="348"/>tions of a Sphære, &longs;hall have its Axis in the Perpendicular, that is <lb/>drawn through the point K; and its Centre of Gravity, for the &longs;ame <lb/>rea&longs;on, &longs;hall be in the Line N K: let us &longs;uppo&longs;e it to be the Point R: <lb/><arrow.to.target n="marg1141"></arrow.to.target><lb/>But the Centre of Gravity of the whole Portion is in the Line F T, <lb/>betwixt the Point R and <lb/><figure id="id.040.01.1043.1.jpg" xlink:href="040/01/1043/1.jpg"/><lb/>the Point F; let us &longs;uppo&longs;e <lb/>it to be the Point <emph type="italics"/>X<emph.end type="italics"/>: The re­<lb/>mainder, therefore, of that <lb/><arrow.to.target n="marg1142"></arrow.to.target><lb/>Figure elivated above the <lb/>Surface of the Liquid, hath <lb/>its Centre of Gravity in <lb/>the Line R X produced or <lb/>continued right out in the <lb/>Part towards X, taken &longs;o, <lb/>that the part prolonged may <lb/>have the &longs;ame proportion to <lb/>X R, that the Gravity of <lb/>that Portion that is demer­<lb/>ged in the Liquid hath to <lb/>the Gravity of that Figure which is above the Liquid; let us &longs;uppo&longs;e <lb/><arrow.to.target n="marg1143"></arrow.to.target><lb/>that ^{*} that Centre of the &longs;aid Figure be the Point S: and thorow that <lb/><arrow.to.target n="marg1144"></arrow.to.target><lb/>&longs;ame Centre S draw the Perpendicular L S. </s> <s>Now the Gravity of the Fi­<lb/>gure that is above the Liquid &longs;hall pre&longs;&longs;e from above downwards ac­<lb/>cording to the Perpendicular S L; & the Gravity of the Portion that <lb/>is &longs;ubmerged in the Liquid, &longs;hall pre&longs;&longs;e from below upwards, accor­<lb/>ding to the Perpendicular R L. </s> <s>Therefore that Figure will not conti­<lb/>nue according to our Adver&longs;aries Propo&longs;all, but tho&longs;e parts of the <lb/>&longs;aid Figure which are towards E, &longs;hall be born or drawn downwards, <lb/>& tho&longs;e which are towards H &longs;hall be born or driven upwards, and <lb/>this &longs;hall be &longs;o long untill that the Axis F T comes to be according <lb/>to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1139"></margin.target>(a) <emph type="italics"/>Perpendicular <lb/>is taken kere, as <lb/>in all other places, <lb/>by this Author for <lb/>the Line K L <lb/>drawn thorow the <lb/>Centre and Cir­<lb/>cumference of the <lb/>Earth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1140"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1141"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1142"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1143"></margin.target>* <emph type="italics"/>i. </s> <s>e,<emph.end type="italics"/> The Center <lb/>of Gravity.</s></p><p type="margin"> <s><margin.target id="marg1144"></margin.target>F</s></p><p type="main"> <s>And this &longs;ame Demon&longs;tration is in the &longs;ame manner verified in <lb/>the other <emph type="italics"/>P<emph.end type="italics"/>ortions. </s> <s>As, fir&longs;t, in the Hæmi&longs;phere that lieth with its <lb/>whole Ba&longs;e above or without the <emph type="italics"/>L<emph.end type="italics"/>iquid, the Centre of the Sphære <lb/>hath been &longs;uppo&longs;ed to be the <emph type="italics"/>P<emph.end type="italics"/>oint T; and therefore, imagining T <lb/>to be in the place, in which, in the other above mentioned, the <lb/><emph type="italics"/>P<emph.end type="italics"/>oint R was, arguing in all things el&longs;e as you did in that, you &longs;hall <lb/>find that the Figure which is above the <emph type="italics"/>L<emph.end type="italics"/>iquid &longs;hall pre&longs;s from <lb/>above downwards according to the <emph type="italics"/>P<emph.end type="italics"/>erpendicular S <emph type="italics"/>L<emph.end type="italics"/>; and the <lb/><emph type="italics"/>P<emph.end type="italics"/>ortion that is &longs;ubmerged in the <emph type="italics"/>L<emph.end type="italics"/>iquid &longs;hall pre&longs;s from below up­<lb/>wards according to the <emph type="italics"/>P<emph.end type="italics"/>erpendicular R <emph type="italics"/>L.<emph.end type="italics"/> And therefore it &longs;hall <lb/>follow, as in the other, namely, that the parts of the whole Figure <lb/>which are towards E, &longs;hall be born or pre&longs;&longs;ed downwards, and tho&longs;e <lb/><arrow.to.target n="marg1145"></arrow.to.target><lb/>that are towards H, &longs;hall be born or driven upwards: and this &longs;hall <lb/>be &longs;o long untill that the Axis F T come to &longs;tand ^{*} <emph type="italics"/>P<emph.end type="italics"/>erpendicular­ <pb xlink:href="040/01/1044.jpg" pagenum="349"/>ly. </s> <s>The like &longs;hall al&longs;o hold true in the <emph type="italics"/>P<emph.end type="italics"/>ortion of the Sphære <lb/>le&longs;s than an Hemi&longs;phere that lieth with its whole Ba&longs;e above the <lb/>Liquid.</s></p><p type="margin"> <s><margin.target id="marg1145"></margin.target>* Or according <lb/>to the Perpendi­<lb/>cular.</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s><emph type="italics"/>The Demon&longs;tration of this Propo&longs;ition is defaced by the Injury of Time, which we have re­<lb/>&longs;tored, &longs;o far as by the Figures that remain, one may collect the Meaning of<emph.end type="italics"/> Archimedes, <lb/><emph type="italics"/>for we thought it not good to alter them: and what was wanting to their declaration and ex­<lb/>planation we have &longs;upplyed in our Commentaries, as we have al&longs;o determined to do in the &longs;e­<lb/>cond Propo&longs;ition of the &longs;econd Book.<emph.end type="italics"/></s></p><p type="main"> <s>If any Solid Magnitude lighter than the Liquid.] <emph type="italics"/>The&longs;e words, light-<emph.end type="italics"/><lb/><arrow.to.target n="marg1146"></arrow.to.target><lb/><emph type="italics"/>er than the Liquid, are added by us, and are not to be found in the Tran&longs;iation; for of the&longs;e <lb/>kind of Magnitudes doth<emph.end type="italics"/> Archimedes <emph type="italics"/>&longs;peak in this Propo&longs;ition.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1146"></margin.target>A</s></p><p type="main"> <s>Shall be demitted into the Liquid in &longs;uch a manner as that the <lb/><arrow.to.target n="marg1147"></arrow.to.target><lb/>Ba&longs;e of the Portion touch not the Liquid.] <emph type="italics"/>That is, &longs;hall be &longs;o demitted into <lb/>the Liquid as that the Ba&longs;e &longs;hall be upwards, and the<emph.end type="italics"/> Vertex <emph type="italics"/>downwards, which he oppo&longs;eth <lb/>to that which he &longs;aith in the Propo&longs;ition following<emph.end type="italics"/>; Be demitted into the Liquid, &longs;o, as <lb/>that its Ba&longs;e be wholly within the Liquid; <emph type="italics"/>For the&longs;e words &longs;ignifie the Portion demit­<lb/>ted the contrary way, as namely, with the<emph.end type="italics"/> Vertex <emph type="italics"/>upwards and the Ba&longs;e downwards. </s> <s>The <lb/>&longs;ame manner of &longs;peech is frequently u&longs;ed in the &longs;econd Book; which treateth of the Portions <lb/>of Rectangle Conoids.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1147"></margin.target>B</s></p><p type="main"> <s>Now becau&longs;e every Portion of a Sphære hath its Axis in the Line <lb/><arrow.to.target n="marg1148"></arrow.to.target><lb/>that from the Center of the Sphære is drawn perpendicular to its <lb/>Ba&longs;e.] <emph type="italics"/>For draw a Line from B to C, and let K L cut the Circumference A B C D in the <lb/>Point G, and the Right Line B C in M<emph.end type="italics"/>: <lb/><figure id="id.040.01.1044.1.jpg" xlink:href="040/01/1044/1.jpg"/><lb/><emph type="italics"/>and becau&longs;e the two Circles A B C D, and <lb/>E F H do cut one another in the Points <lb/>B and C, the Right Line that conjoyneth <lb/>their Centers, namely, K L, doth cut the <lb/>Line B C in two equall parts, and at <lb/>Right Angles; as in our Commentaries <lb/>upon<emph.end type="italics"/> Prolomeys <emph type="italics"/>Plani&longs;phære we do <lb/>prove: But of the Portion of the Circle <lb/>B N C the Diameter is M N; and of the <lb/>Portion B G C the Diameter is M G;<emph.end type="italics"/><lb/><arrow.to.target n="marg1149"></arrow.to.target><lb/><emph type="italics"/>for the<emph.end type="italics"/> (a) <emph type="italics"/>Right Lines which are drawn <lb/>on both &longs;ides parallel to B C do make<emph.end type="italics"/><lb/><arrow.to.target n="marg1150"></arrow.to.target><lb/><emph type="italics"/>Right Angles with N G; and<emph.end type="italics"/> (b) <emph type="italics"/>for <lb/>that cau&longs;e are thereby cut in two equall <lb/>parts: Therefore the Axis of the Portion <lb/>of the Sphære B N C is N M; and the <lb/>Axis of the Portion B G C is M G: <lb/>from whence it followeth that the Axis of <lb/>the Portion demerged in the Liquid is <lb/>in the Line K L, namely N G. </s> <s>And &longs;ince the Center of Gravity of any Portion of a Sphære is <lb/>in the Axis, as we have demonstrated in our Book<emph.end type="italics"/> De Centro Gravitatis Solidorum, <emph type="italics"/>the <lb/>Centre of Gravity of the Magnitude compounded of both the Portions B N C & B G C, that is, <lb/>of the Portion demerged in the Water, is in the Line N G that doth conjoyn the Centers of Gra­<lb/>vity of tho&longs;e Portions of Sphæres. </s> <s>For &longs;uppo&longs;e, if po&longs;&longs;ible, that it be out of the Line N G, as <lb/>in Q, and let the Center of the Gravity of the Portion B N C, be V, and draw V <expan abbr="q.">que</expan> Becau&longs;e <lb/>therefore from the Portion demerged in the Liquid the Portion of the Sphære B N C, not ha­<lb/>ving the &longs;ame Center of Gravity, is cut off, the Center of Gravity of the Remainder of the <lb/>Portion B G C &longs;hall, by the 8 of the fir&longs;t Book of<emph.end type="italics"/> Archimedes, De Centro Gravitatis <pb xlink:href="040/01/1045.jpg" pagenum="350"/>Planotum, <emph type="italics"/>be in the Line V Q prolonged: But that is impo&longs;&longs;ible; for it is in the Axis <lb/>G: It followeth, therefore, that the Center of Gravity of the Portion demerged in <lb/>Liquid be in the Line N K: which we propounded to be proved.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1148"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1149"></margin.target><emph type="italics"/>(a)<emph.end type="italics"/> By 29. of the <lb/>fir&longs;t of <emph type="italics"/>Encl.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1150"></margin.target><emph type="italics"/>(b)<emph.end type="italics"/> By 3. of the <lb/>third.</s></p><p type="main"> <s>But the Centre of Gravity of the whole Portion is in the Line <lb/><arrow.to.target n="marg1151"></arrow.to.target><lb/>T, betwixt the Point R and the Point F; let us &longs;uppo&longs;e it to be<lb/>the Point X.] <emph type="italics"/>Let the Sphære becompleated, &longs;o as that there be added of that Portion<lb/>the Axis T Y, and the Center of Gravity Z. </s> <s>And becau&longs;e that from the whole Sphære,<lb/>who&longs;e Centre of Gravity is K, as we have al&longs;o demon&longs;trated in the (c) Book before named, the <lb/>is cut off the Portion E Y H, having the Centre of Gravity Z; the Centre of the remaind<emph.end type="italics"/><lb/><arrow.to.target n="marg1152"></arrow.to.target><lb/><emph type="italics"/>of the Portion E F H &longs;hall be in the Line Z K prolonged: And therefore it mu&longs;t of nece&longs;&longs;ity<lb/>fall betwixt K and F.<emph.end type="italics"/><lb/><arrow.to.target n="marg1153"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1151"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1152"></margin.target>(c) <emph type="italics"/>By 8 of the <lb/>fir&longs;t<emph.end type="italics"/> of Archimedes.</s></p><p type="margin"> <s><margin.target id="marg1153"></margin.target>E</s></p><p type="main"> <s>The remainder, therefore, of the Figure, elevated above the Sur­<lb/>face of the Liquid, hath its Center of Gravity in the <emph type="italics"/>L<emph.end type="italics"/>ine R X<lb/>prolonged.] <emph type="italics"/>By the &longs;ame 8 of the fir&longs;t Book of<emph.end type="italics"/> Archimedes, de Centro Gravita­<lb/>tis Planorum.</s></p><p type="main"> <s>Now the Gravity of the Figure that is above the <emph type="italics"/>L<emph.end type="italics"/>iquid &longs;hall<arrow.to.target n="marg1154"></arrow.to.target><lb/>pre&longs;s from above downwards according to S L; and the Gravit <lb/>of the Portion that is &longs;ubmerged in the <emph type="italics"/>L<emph.end type="italics"/>iquid &longs;hall pre&longs;s from be <lb/>low upwards, according to the Perpendicular R L.] <emph type="italics"/>By the &longs;econd Sup­<lb/>po&longs;ition of this. </s> <s>For the Magnitude that is demerged in the Liquid is moved upwards with as<lb/>much Force along R L, as that which is above the Liquid is moved downwards along S L; as<lb/>may be &longs;hewn by Propo&longs;ition 6. of this. </s> <s>And becau&longs;e they are moved along &longs;everall other Lines,<lb/>neither cau&longs;eth the others being le&longs;s moved; the which it continually doth when the Portion<lb/>is &longs;et according to the Perpendicular: For then the Centers of Gravity of both the Magnitudes<lb/>do concur in one and the &longs;ame Perpendicular, namely, in the Axis of the Portion: and look<lb/>with what force or<emph.end type="italics"/> Impetus <emph type="italics"/>that which is in the Lipuid tendeth upwards, and with the like<lb/>doth that which is above or without the Liquid tend downwards along the &longs;ame Line: And<emph.end type="italics"/><lb/><arrow.to.target n="marg1155"></arrow.to.target><lb/><emph type="italics"/>therefore, in regard that the one doth not ^{*} exceed the other, the Portion &longs;hall no longer move <lb/>but &longs;hall &longs;tay and re&longs;t allwayes in one and the &longs;ame Po&longs;ition, unle&longs;s &longs;ome extrin&longs;ick Cau&longs;e<lb/>chance to intervene.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1154"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1155"></margin.target>* <emph type="italics"/>Or overcome.<emph.end type="italics"/></s></p><p type="head"> <s>PROP. IX. THEOR. IX.<lb/><arrow.to.target n="marg1156"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1156"></margin.target>* In &longs;ome Greek <lb/>Coppies this is no <lb/>di&longs;tinct Propo&longs;i­<lb/>tion, but all <lb/>Commentators, <lb/>do divide it <lb/>from the Prece­<lb/>dent, as having a <lb/>di&longs;tinct demon­<lb/>&longs;tration in the <lb/>Originall.</s></p><p type="main"> <s>^{*} <emph type="italics"/>But if the Figure, lighter than the Liquid, be demit­<lb/>ted into the Liquid, &longs;o, as that its Ba&longs;e be wholly<lb/>within the &longs;aid Liquid, it &longs;hall continue in &longs;uch <lb/>manner erect, as that its Axis &longs;hall &longs;tand according <lb/>to the Perpendicular.<emph.end type="italics"/></s></p><p type="main"> <s>For &longs;uppo&longs;e, &longs;uch a Magnitude as that aforenamed to be de <lb/>mitted into the Liquid; and imagine a Plane to be produced<lb/>thorow the Axis of the Portion, and thorow the Center of the <lb/>Earth: And let the <emph type="italics"/>S<emph.end type="italics"/>ection of the Surface of the Liquid, be the Cir­<lb/>cumference A B C D, and of the Figure the Circumference E F <emph type="italics"/>H<emph.end type="italics"/><lb/>And let E H be a Right Line, and F T the Axis of the Portion. </s> <s>If<lb/>now it were po&longs;&longs;ible, for &longs;atisfaction of the Adver&longs;ary, let it be <lb/>&longs;uppo&longs;ed that the &longs;aid Axis were not according to the Perpendicu­<lb/>lar: we are now to demon&longs;trate that the Figure will not &longs;o conti­ <pb xlink:href="040/01/1046.jpg" pagenum="351"/>nue, but will return to be according to the <lb/><figure id="id.040.01.1046.1.jpg" xlink:href="040/01/1046/1.jpg"/><lb/>Perpendieular. </s> <s>It is manife&longs;t that the Gen­<lb/>tre of the Sphære is in the Line F T. </s> <s>And <lb/>again, fora&longs;much as the Portion of a Sphære <lb/>may be greater or le&longs;&longs;er than an Hemi&longs;­<lb/>phære, and may al&longs;o be an Hemi&longs;phære, let <lb/>the Centre of the Sphære in the Hemi&longs;­<lb/>phære be the Point T, & in the le&longs;&longs;er Por­<lb/>tion the Point P, and in the Greater the </s></p><p type="main"> <s><arrow.to.target n="marg1157"></arrow.to.target><lb/>Point R. </s> <s>And &longs;peaking fir&longs;t of that greater <lb/>Portion which hath its Ba&longs;e within the <lb/>Liquid, thorow R and L, the Earths Cen­<lb/><figure id="id.040.01.1046.2.jpg" xlink:href="040/01/1046/2.jpg"/><lb/>tre, draw the line RL. </s> <s>The Portion that is <lb/>above the Liquid, hath its Axis in the Per­<lb/>pendicular pa&longs;&longs;ing thorow R; and by <lb/>what hath been &longs;aid before, its Centre of <lb/>Gravity &longs;hall be in the Line N R; let it <lb/>be the Point R: But the Centre of Gra­<lb/>vity of the whole Portion is in the line F <lb/>T, betwixt R and F; let it be X: The re­<lb/>mainder therefore of that Figure, which is <lb/>within the Liquid &longs;hall have its Centre in <lb/>the Right Line R <emph type="italics"/>X<emph.end type="italics"/> prolonged in the part <lb/><figure id="id.040.01.1046.3.jpg" xlink:href="040/01/1046/3.jpg"/><lb/>towards <emph type="italics"/>X,<emph.end type="italics"/> taken &longs;o, that the part pro­<lb/>longed may have the &longs;ame Proportion to <lb/>X R, that the Gravity of the Portion that <lb/>is above the Liquid hath to the Gravity <lb/>of the Figure that is within the Liquid. <lb/></s> <s>Let O be the Centre of that &longs;ame Figure: <lb/>and thorow O draw the Perpendicular L <lb/>O. </s> <s>Now the Gravity of the Portion that <lb/>is above the Liquid &longs;hall pre&longs;s according <lb/>to the Right Line R L downwards; and <lb/>the Gravity of the Figure that is in the <lb/>Liquid according to the Right Line O L upwards: There the Figure <lb/>&longs;hall not continue; but the parts of it towards H &longs;hall move down­<lb/>wards, and tho&longs;e towards E upwards: & <lb/><figure id="id.040.01.1046.4.jpg" xlink:href="040/01/1046/4.jpg"/><lb/>this &longs;hall ever be, &longs;o long as F T is accord­<lb/>ing to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1157"></margin.target>A</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s>The Portion that is above the Liquid <lb/><arrow.to.target n="marg1158"></arrow.to.target><lb/>hath its Axis in the Perpendicular pa&longs;&longs;ing <lb/>thorow K.] <emph type="italics"/>For draw B C cutting the Line N K in <lb/>M; and let N K out the Circumference<emph.end type="italics"/> A B <emph type="italics"/>C D in G. </s> <s>In <lb/>the &longs;ame manner as before me will demon&longs;trate, that the Axis<emph.end type="italics"/> <pb xlink:href="040/01/1047.jpg" pagenum="352"/><emph type="italics"/>of the Portion of the Sphære is N M; and of the Portion B G C the Axis is G M: Wherefore <lb/>the Centre of Gravity of them both &longs;hall be in the Line N M: And becau&longs;e that from the Por­<lb/>tion B N C the Portion B G C, not having the &longs;ame Centre of Gravity, is cut off, the Centre <lb/>of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid &longs;hall be <lb/>in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the &longs;aid <lb/>Portions by the fore&longs;aid 8 of<emph.end type="italics"/> Archimedis de Centro Gravitatis Planorum.</s></p><p type="margin"> <s><margin.target id="marg1158"></margin.target>A</s></p><p type="main"> <s>NIC. </s> <s>Truth is, that in &longs;ome of the&longs;e Figures C is put for X, and &longs;o it was in <lb/>the Greek Copy that I followed.</s></p><p type="main"> <s>RIC. </s> <s>This Demo&longs;tration is very difficult, to my thinking; but I believe that <lb/>it is becau&longs;e I have not in memory the Propo&longs;itions of that Book entituled <emph type="italics"/>De Cen­<lb/>tris Gravium.<emph.end type="italics"/></s></p><p type="main"> <s>NIC. </s> <s>It is &longs;o.</s></p><p type="main"> <s>RIC. </s> <s>We will take a more convenient time to di&longs;cour&longs;e of that, and now return <lb/><arrow.to.target n="marg1159"></arrow.to.target><lb/>to &longs;peak of the two la&longs;t Propo&longs;itions. </s> <s>And I &longs;ay that the Figures incerted in the <lb/>demon&longs;tration would in my opinion, have been better and more intelligble unto <lb/>me, drawing the Axis according to its proper Po&longs;ition; that is in the half Arch of <lb/>the&longs;e Figures, and then, to &longs;econd the Objection of the Adver&longs;ary, to &longs;uppo&longs;e <lb/>that the &longs;aid Figures &longs;tood &longs;omewhat Obliquely, to the end that the &longs;aid Axis, if it <lb/>were po&longs;&longs;ible, did not &longs;tand according to the Perpendicular &longs;o often mentioned, <lb/>which doing, the Propo&longs;ition would be proved in the &longs;ame manner as before: <lb/>and this way would be more naturall and clear.<lb/><arrow.to.target n="marg1160"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1159"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1160"></margin.target>B</s></p><p type="main"> <s>NIC. </s> <s>You are in the right, but becau&longs;e thus they were in the Greek Copy, <lb/>I thought not fit to alter them, although unto the better.</s></p><p type="main"> <s>RIC. Companion, you have thorowly &longs;atisfied me in all that in the beginning <lb/>of our Di&longs;cour&longs;e I asked of you, to morrow, God permitting, we will treat of <lb/>&longs;ome other ingenious Novelties.</s></p><p type="head"> <s>THE TRANSLATOR.</s></p><p type="main"> <s>I &longs;ay that the Figures, &c. </s> <s>would have been more intelligible to </s></p><p type="main"> <s><arrow.to.target n="marg1161"></arrow.to.target><lb/>me, drawing the Axis Z T according to its proper Po&longs;ition, that <lb/>is in the half Arch of the&longs;e Figures.] <emph type="italics"/>And in this con&longs;ideration I have followed <lb/>the Schemes of<emph.end type="italics"/> Commandine, <emph type="italics"/>who being the Re&longs;torer of the Demon&longs;trations of the&longs;e two la&longs;t <lb/>Propo&longs;itions, hath well con&longs;idered what<emph.end type="italics"/> Ricardo <emph type="italics"/>here propo&longs;eth, and therefore hath drawn the <lb/>&longs;aid Axis (which in the Manu&longs;cripts that he had by him is lettered F T, and not as in that of<emph.end type="italics"/><lb/>Tartaylia <emph type="italics"/>Z T,) according to that its proper Po&longs;ition.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1161"></margin.target>A</s></p><p type="main"> <s>But becau&longs;e thus they were in the Greek Copy, I thought not <lb/><arrow.to.target n="marg1162"></arrow.to.target><lb/>fit to alter them although unto the better.] <emph type="italics"/>The Schemes of tho&longs;e Manu-<emph.end type="italics"/><lb/><figure id="id.040.01.1047.1.jpg" xlink:href="040/01/1047/1.jpg"/><lb/><emph type="italics"/>&longs;cripts that<emph.end type="italics"/> Tartaylia <emph type="italics"/>had &longs;een were more imperfect then tho&longs;e <lb/>in Commandines Copies; but for variety &longs;ake, take here one <lb/>of<emph.end type="italics"/> Tartaylia, <emph type="italics"/>it being that of the Portion of a Sphære, equall <lb/>to an Hemi&longs;phære, with its Axis oblique, and its Ba&longs;e dimitted <lb/>into the Liquid, and Lettered as in this Edition.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1162"></margin.target>B</s></p><p type="main"> <s><emph type="italics"/>Now Courteous Readers, I hope that you may, amid&longs;t the <lb/>great Ob&longs;curity of the Originall in the Demon&longs;trations of the&longs;e <lb/>two la&longs;t Propo&longs;itions, be able from the joynt light of the&longs;e two Famous Commentators of our <lb/>more famous Author, to di&longs;cern the truth of the Doctrine affirmed, namely, That Solids of the <lb/>Figure of Portions of Sphæres demitted into the Liquid with their Ba&longs;es upwards &longs;hall &longs;tand <lb/>erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the <lb/>Earth unto its Circumference: And that if the &longs;aid Portions be demitted with their Ba&longs;es <lb/>oblique and touching the Liquid in one Point, they &longs;hall not rest in that Obliquity, but &longs;hall <lb/>return to Rectitude: And that la&longs;tly, if the&longs;e Portions be demitted with their Ba&longs;es downwards, <lb/>they &longs;hall continue erect with their Axis according to the Perpendicular afore&longs;aid: &longs;o that no <lb/>more remains to be done, but that we&longs;et before you the 2 Books of this our Admirable Author.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1048.jpg" pagenum="353"/><p type="head"> <s>ARCHIMEDES, <lb/>HIS TRACT <lb/><emph type="italics"/>DE <lb/>INSIDENTIBUS HUMIDO,<emph.end type="italics"/><lb/>OR, <lb/>Of the NATATION of BODIES Upon, or <lb/>Submer&longs;ion In the WATER, or other LIQUIDS.</s></p><p type="head"> <s><emph type="italics"/>BOOK<emph.end type="italics"/> II.</s></p><p type="head"> <s>PROP. I. THEOR. I.</s></p><p type="main"> <s><emph type="italics"/>If any Magnitude lighter than the Liquid be demitted <lb/>into the &longs;aid Liquid, it &longs;hall have the &longs;ame proporti­<lb/>on in Gravity to a Liquid of equal Ma&longs;&longs;e, that the <lb/>part of the Magnitude demerged hath unto the <lb/>whole Magnitude.<emph.end type="italics"/></s></p><p type="main"> <s>For let any Solid Magnitude, as for in­<lb/>&longs;tance F A, lighter than the Liquid, be de­<lb/>merged in the Liquid, which let be F A: <lb/>And let the part thereof immerged be A, <lb/>and the part above the Liquid F, It is to <lb/>be demon&longs;trated that the Magnitude F A <lb/>hath the &longs;ame proportion in Gravity to a <lb/>Liquid of Equall Ma&longs;&longs;e that A hath to F <lb/>A. </s> <s>Take any Liquid Magnitude, as &longs;up­<lb/>po&longs;e N I, of equall Ma&longs;&longs;e with F A; and let F be equall to N, and <lb/>A to I: and let the Gravity of the whole Magnitude F A be B, and <lb/>let that of the Magnitude N I be O, <lb/>and let that of I be R. </s> <s>Now the <lb/><figure id="id.040.01.1048.1.jpg" xlink:href="040/01/1048/1.jpg"/><lb/>Magnitude F A hath the &longs;ame pro­<lb/>portion unto N I that the Gravity B <lb/>hath to the Gravity O R: But for <lb/>a&longs;much as the Magnitude F A demit­<lb/>ted into the Liquid is lighter than <lb/>the &longs;aid Liquid, it is manife&longs;t that a Ma&longs;&longs;e of the Liquid, I, equall <lb/>to the part of the Magnitude demerged, A, hath equall Gravity <lb/><arrow.to.target n="marg1163"></arrow.to.target><lb/>with the whole Magnitnde, F A: For this was <emph type="italics"/>(a)<emph.end type="italics"/> above demon­<lb/>&longs;trated: But B is the Gravity of the Magnitude F A, and R of I: <pb xlink:href="040/01/1049.jpg" pagenum="354"/>Therefore B and R are equall. </s> <s>And becau&longs;e that of the Magni­<lb/>tude FA the <emph type="italics"/>G<emph.end type="italics"/>ravity is B: Therefore of the Liquid Body <emph type="italics"/>N<emph.end type="italics"/> I the <lb/>Gravity is O R. </s> <s>As F A is to N I, &longs;o is B to O R, or, &longs;o is R to <lb/>O R: But as R is to O R, &longs;o is I to N I, and A to F A: Therefore <lb/><arrow.to.target n="marg1164"></arrow.to.target><lb/>I is to N I, as F A to N I: And as I to N I &longs;o is <emph type="italics"/>(b)<emph.end type="italics"/> A to F A. <lb/></s> <s>Therefore F A is to N I, as A is to F A: Which was to be demon­<lb/>&longs;trated.</s></p><p type="margin"> <s><margin.target id="marg1163"></margin.target>(a) <emph type="italics"/>By 5. of the <lb/>fir&longs;t of this.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1164"></margin.target>(b) <emph type="italics"/>By 11. of the <lb/>fifth of<emph.end type="italics"/> Eucl.</s></p><p type="head"> <s>PROP. II. THEOR. II.<lb/><arrow.to.target n="marg1165"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1165"></margin.target>A</s></p><p type="main"> <s>^{*} <emph type="italics"/>The Right Portion of a Right angled Conoide, when it <lb/>&longs;hall have its Axis le&longs;&longs;e than<emph.end type="italics"/> &longs;e&longs;quialter ejus quæ ad <lb/>Axem (<emph type="italics"/>or of its<emph.end type="italics"/> Semi-parameter) <emph type="italics"/>having any what <lb/>ever proportion to the Liquid in Gravity, being de­<lb/>mitted into the Liquid &longs;o as that its Ba&longs;e touch not <lb/>the &longs;aid Liquid, and being &longs;et &longs;tooping, it &longs;hall not <lb/>remain &longs;tooping, but &longs;hall be restored to uprightne&longs;&longs;e. <lb/></s> <s>I &longs;ay that the &longs;aid Portion &longs;hall &longs;tand upright when <lb/>the Plane that cuts it &longs;hall be parallel unto the Sur­<lb/>face of the Liquid.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a Portion of a Rightangled Conoid, as hath been <lb/>&longs;aid; and let it lye &longs;tooping or inclining: It is to be demon­<lb/>&longs;trated that it will not &longs;o continue but &longs;hall be re&longs;tored to re­<lb/>ctitude. </s> <s>For let it be cut through the Axis by a plane erect upon <lb/>the Surface of the Liquid, and let the Section of the Portion be <lb/>A PO L, the Section of a Rightangled Cone, and let the Axis <lb/><figure id="id.040.01.1049.1.jpg" xlink:href="040/01/1049/1.jpg"/><lb/>of the Portion and Diameter of the <lb/>Section be N O: And let the Sect­<lb/>ion of the Surface of the Liquid be <lb/>I S. </s> <s>If now the Portion be not <lb/>erect, then neither &longs;hall A L be Pa­<lb/>rallel to I S: Wherefore N O will <lb/>not be at Right Angles with I S. </s></p><p type="main"> <s><arrow.to.target n="marg1166"></arrow.to.target><lb/>Draw therefore K <foreign lang="greek">w,</foreign> touching the Section of the Cone I, in the <lb/>Point P [that is parallel to I S: and from the Point P unto I S <lb/><arrow.to.target n="marg1167"></arrow.to.target><lb/>draw P F parallel unto O N, ^{*} which &longs;hall be the Diameter of the <lb/>Section I P O S, and the Axis of the Portion demerged in the <emph type="italics"/>L<emph.end type="italics"/>i­<lb/><arrow.to.target n="marg1168"></arrow.to.target><lb/>quid. </s> <s>In the next place take the Centres of Gravity: ^{*} and of <lb/>the Solid Magnitude A P O L, let the Centre of Gravity be R; and <lb/><arrow.to.target n="marg1169"></arrow.to.target><lb/>of I P O S let the Centre be B: ^{*} and draw a Line from B to R <lb/>prolonged unto G; which let be the Centre of Gravity of the <pb xlink:href="040/01/1050.jpg" pagenum="355"/>remaining Figure I S L A. </s> <s>Becau&longs;e now that N O is <emph type="italics"/>Se&longs;quialter<emph.end type="italics"/><lb/>of R O, but le&longs;s than <emph type="italics"/>Se&longs;quialter ejus quæ u&longs;que ad Axem<emph.end type="italics"/> (or of its <lb/><emph type="italics"/>Semi-parameter<emph.end type="italics"/>;) ^{*} R O &longs;hall be le&longs;&longs;e than <emph type="italics"/>quæ u&longs;que ad Axem<emph.end type="italics"/> (or <lb/><arrow.to.target n="marg1170"></arrow.to.target><lb/>than the <emph type="italics"/>Semi-parameter<emph.end type="italics"/>;) ^{*} whereupon the Angle R P <foreign lang="greek">w</foreign> &longs;hall be <lb/><arrow.to.target n="marg1171"></arrow.to.target><lb/>acute. </s> <s>For &longs;ince the Line <emph type="italics"/>quæ u&longs;que ad Axem<emph.end type="italics"/> (or <emph type="italics"/>Semi-parameter<emph.end type="italics"/>) <lb/>is greater than R O, that Line which is drawn from the Point R, <lb/>and perpendicular to K <foreign lang="greek">w,</foreign> namely RT, meeteth with the line F P <lb/>without the Section, and for that cau&longs;e mu&longs;t of nece&longs;&longs;ity fall be­<lb/>tween the Points <emph type="italics"/>P<emph.end type="italics"/> and <foreign lang="greek">w;</foreign> Therefore if <emph type="italics"/>L<emph.end type="italics"/>ines be drawn through <lb/>B and G, parallel unto R T, they &longs;hall contain Right Angles with <lb/>the Surface of the Liquid: ^{*} and the part that is within the Li­<lb/><arrow.to.target n="marg1172"></arrow.to.target><lb/>quid &longs;hall move upwards according to the Perpendicular that is <lb/>drawn thorow B, parallel to R T, and the part that is above the Li­<lb/>quid &longs;hall move downwards according to that which is drawn tho­<lb/>row G; and the Solid A P O L &longs;hall not abide in this Po&longs;ition; for <lb/>that the parts towards A will move upwards, and tho&longs;e towards <lb/>B downwards; Wherefore N O &longs;hall be con&longs;tituted according to <lb/>the Perpendicular.]</s></p><p type="margin"> <s><margin.target id="marg1166"></margin.target>* <emph type="italics"/>Supplied by<emph.end type="italics"/> Fe­<lb/>derico Comman­<lb/>dino.</s></p><p type="margin"> <s><margin.target id="marg1167"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1168"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1169"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1170"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1171"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1172"></margin.target>G</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s><emph type="italics"/>The Demon&longs;tration of this propo&longs;ition hath been much de&longs;ired; which we have (in like man­<lb/>ner as the 8 Prop. </s> <s>of the fir&longs;t Book) re&longs;tored according to<emph.end type="italics"/> Archimedes <emph type="italics"/>his own Schemes, and <lb/>illustrated it with Commentaries.<emph.end type="italics"/></s></p><p type="main"> <s>The Right Portion of a Rightangled Conoid, when it &longs;hall <lb/><arrow.to.target n="marg1173"></arrow.to.target><lb/>have its Axis le&longs;&longs;e than <emph type="italics"/>Se&longs;quialter ejus quæ u&longs;que ad Axem<emph.end type="italics"/> (or of <lb/>its <emph type="italics"/>Semi-parameter] In the Tran&longs;lation of<emph.end type="italics"/> Nicolo Tartaglia <emph type="italics"/>it is fal&longs;lyread<emph.end type="italics"/> great­<lb/>er then Se&longs;quialter, <emph type="italics"/>and &longs;o its rendered in the following Propo&longs;ition; but it is the Right <lb/>Portion of a Concid cut by a Plane at Right Angles, or erect, unto the Axis: and we &longs;ay <lb/>that Conoids are then con&longs;tituted erect when the cutting Plane, that is to &longs;ay, the Plane of the <lb/>Ba&longs;e, &longs;hall be parallel to the Surface of the Liquid.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1173"></margin.target>A</s></p><p type="main"> <s>Which &longs;hall be the Diameter of the Section I P O S, and the <lb/><arrow.to.target n="marg1174"></arrow.to.target><lb/>Axis of the Portion demerged in the Liquid.] <emph type="italics"/>By the 46 of the fir&longs;t of <lb/>the Conicks of<emph.end type="italics"/> Apollonious, <emph type="italics"/>or by the Corol­<lb/>lary of the 51 of the &longs;ame.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1174"></margin.target>B</s></p><figure id="id.040.01.1050.1.jpg" xlink:href="040/01/1050/1.jpg"/><p type="main"> <s>And of the Solid Magnitude A P <lb/><arrow.to.target n="marg1175"></arrow.to.target><lb/>O L, let the Centre of Gravity be R; <lb/>and of I P O S let the Centre be B.] <lb/><emph type="italics"/>For the Centre of Gravity of the Portion of a Right­<lb/>angled Conoid is in its Axis, which it &longs;o divideth <lb/>as that the part thereof terminating in the vertex, <lb/>be double to the other part terminating in the Ba&longs;e; as <lb/>in our Book<emph.end type="italics"/> De Centro Gravitatis Solidorum Propo. </s> <s>29. <emph type="italics"/>we have demon&longs;trated. </s> <s>And <lb/>&longs;ince the Centre of Gravity of the Portion A P O L is R, O R &longs;hall be double to RN and there­<lb/>fore N O &longs;hall be Se&longs;quialter of O R. </s> <s>And for the &longs;ame rea&longs;on, B the Centre of Gravity of the Por­<lb/>tion I P O S is in the Axis P F, &longs;o dividing it as that P B is double to B F;<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1175"></margin.target>C</s></p><p type="main"> <s>And draw a Line from B to R prolonged unto G; which let <lb/><arrow.to.target n="marg1176"></arrow.to.target><lb/>be the Centre of Gravity of the remaining Eigure I S L A.] <pb xlink:href="040/01/1051.jpg" pagenum="356"/><emph type="italics"/>For if, the Line B R being prolonged unto G, G R hath the &longs;ame proportion to R B as the Por­<lb/>tion of the Conoid I P O S hath to the remaining Figure that lyeth above the Surface of the <lb/>Liquid, the Toine G &longs;hall be its Centre of Gravity; by the 8 of the &longs;econd of<emph.end type="italics"/> Archimedes <lb/>de Centro Gravitatis Planorum, vel de <emph type="italics"/>Æ<emph.end type="italics"/>quiponderantibus.<lb/><arrow.to.target n="marg1177"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1176"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1177"></margin.target>E</s></p><p type="main"> <s>R O &longs;hall be le&longs;s than <emph type="italics"/>quæ u&longs;que ad Axem<emph.end type="italics"/> (or than the Semi­<lb/>parameter.] <emph type="italics"/>By the 10 Propofit. </s> <s>of<emph.end type="italics"/> Euclids <emph type="italics"/>fifth Book of Elements. </s> <s>The Line<emph.end type="italics"/> quæ <lb/>u&longs;que ad Axem, <emph type="italics"/>(or the Semi-parameter) according to<emph.end type="italics"/> Archimedes, <emph type="italics"/>is the half of that<emph.end type="italics"/><lb/>juxta quam po&longs;&longs;unt, quæ á Sectione ducuntur, (<emph type="italics"/>or of the Parameter;) as appeareth <lb/>by the 4 Propo&longs;it of his Book<emph.end type="italics"/> De Conoidibus & Shpæroidibus: <emph type="italics"/>and for what rea&longs;on it is <lb/>&longs;o called, we have declared in the Commentaries upon him by us publi&longs;hed.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1178"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1178"></margin.target>F</s></p><p type="main"> <s>Whereupon the Angle R P <foreign lang="greek">w</foreign> &longs;hall be acute.] <emph type="italics"/>Let the Line N O be <lb/>continued out to H, that &longs;o RH may be equall to <lb/>the Semi-parameter. </s> <s>If now from the Point H<emph.end type="italics"/><lb/><figure id="id.040.01.1051.1.jpg" xlink:href="040/01/1051/1.jpg"/><lb/><emph type="italics"/>a Line be drawn at Right Angles to N H, it &longs;hall <lb/>meet with FP without the Section; for being <lb/>drawn thorow O parallel to A L, it &longs;hall fall <lb/>without the Section, by the 17 of our &longs;irst Book of<emph.end type="italics"/><lb/>Conicks; <emph type="italics"/>Therefore let it meet in V: and <lb/>becau&longs;e F P is parallel to the Diameter, and H <lb/>V perpendicular to the &longs;ame Diameter, and R H <lb/>equall to the Semi-parameter, the Line drawn <lb/>from the Point R to V &longs;hall make Right Angles <lb/>with that Line which the Section toucheth in the Point P: that is with K<emph.end type="italics"/> <foreign lang="greek">w,</foreign> <emph type="italics"/>as &longs;hall anon be <lb/>demonstrated: Wherefore the Perpendidulat R T falleth betwixt A and<emph.end type="italics"/> <foreign lang="greek">w;</foreign> <emph type="italics"/>and the Argle R<emph.end type="italics"/><lb/>P <foreign lang="greek">w</foreign> <emph type="italics"/>&longs;hall be an Acute Angle.<emph.end type="italics"/></s></p><p type="main"> <s>Let A B C be the Section of a Rightangled Cone, or a Parabola, <lb/>and its Diameter B D; and let the Line E F touch the <lb/>&longs;ame in the Point G: and in the Diameter B D take the Line <lb/>H K equall to the Semi-parameter: and thorow G, G L be­<lb/>ing drawn parallel to the Diameter, draw KM from the <lb/><emph type="italics"/>P<emph.end type="italics"/>oint K at Right Angles to B D cutting G L in M: I &longs;ay <lb/>that the Line prolonged thorow Hand Mis perpendicular to <lb/>E F, which it cutteth in N.</s></p><p type="main"> <s><emph type="italics"/>For from the Point G draw the Line G O at Right Angles to E F cutting the Diameter in <lb/>O: and again from the &longs;ame Point draw G P perpendicular to the Diameter: and let the <lb/>&longs;aid Diameter prolonged cut the Line E F in <expan abbr="q.">que</expan> P B &longs;hall be equall to B Q, by the 35 of<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1179"></arrow.to.target><lb/><emph type="italics"/>our fir&longs;t Book of<emph.end type="italics"/> Conick <emph type="italics"/>Sections,<emph.end type="italics"/> (a) <emph type="italics"/>and G<emph.end type="italics"/><lb/><figure id="id.040.01.1051.2.jpg" xlink:href="040/01/1051/2.jpg"/><lb/><emph type="italics"/>P a Mean-proportion all betmixt Q P and PO<emph.end type="italics"/>; <lb/><arrow.to.target n="marg1180"></arrow.to.target><lb/>(b) <emph type="italics"/>and therefore the Square of G P &longs;hall be e­<lb/>quall to the Rectangle of O P Q: But it is al&longs;o <lb/>equall to the Rectangle comprehended under P B <lb/>and the Line<emph.end type="italics"/> juxta quam po&longs;&longs;unt, <emph type="italics"/>or the Par­<lb/>ameter, by the 11 of our fir&longs;t Book of<emph.end type="italics"/> Conicks: <lb/><arrow.to.target n="marg1181"></arrow.to.target><lb/>(c) <emph type="italics"/>Therefore, look what proportion Q P hath to <lb/>P B, and the &longs;ame hath the Parameter unto P O: <lb/>But Q P is double unto<emph.end type="italics"/> P B, <emph type="italics"/>for that<emph.end type="italics"/> P B <emph type="italics"/>and B <lb/>Q are equall, as hath been &longs;aid: And therefore <lb/>the Parameter &longs;hall be double to the &longs;aid P O: <lb/>and by the &longs;ame Rea&longs;on P O is equall to that which we call the Semi-parameter, that is, to K H<emph.end type="italics"/>: <lb/><arrow.to.target n="marg1182"></arrow.to.target><lb/><emph type="italics"/>But<emph.end type="italics"/> (d) <emph type="italics"/>P G is equall to K M, and<emph.end type="italics"/> (e) <emph type="italics"/>the Angle O P G to the Angle H K M; for they are both<emph.end type="italics"/><lb/><arrow.to.target n="marg1183"></arrow.to.target><lb/><emph type="italics"/>Right Angles: And therefore O G al&longs;o is equall to H M, and the Angle P O G unto the<emph.end type="italics"/> <pb xlink:href="040/01/1052.jpg" pagenum="357"/><figure id="id.040.01.1052.1.jpg" xlink:href="040/01/1052/1.jpg"/><lb/><emph type="italics"/>Angle K H M: Therefore<emph.end type="italics"/> (f) O G <emph type="italics"/>and H N are parallel,<emph.end type="italics"/><lb/><arrow.to.target n="marg1184"></arrow.to.target><lb/><emph type="italics"/>and the<emph.end type="italics"/> (g) <emph type="italics"/>Angle H N F equall to the Angle O G F; for <lb/>that G O being Perpendicular to E F, H N &longs;hall al&longs;o be per-<emph.end type="italics"/><lb/><arrow.to.target n="marg1185"></arrow.to.target><lb/><emph type="italics"/>pandicnlar to the &longs;ame: Which was to be demon &longs;trated.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1179"></margin.target>(a) <emph type="italics"/>By Cor. </s> <s>of 8. of <lb/>6. of<emph.end type="italics"/> Euclide.</s></p><p type="margin"> <s><margin.target id="marg1180"></margin.target>(b) <emph type="italics"/>By 17. of the<emph.end type="italics"/><lb/>6.</s></p><p type="margin"> <s><margin.target id="marg1181"></margin.target>(c) <emph type="italics"/>By 14. of the<emph.end type="italics"/><lb/>6.</s></p><p type="margin"> <s><margin.target id="marg1182"></margin.target>(d) <emph type="italics"/>By 33. of the<emph.end type="italics"/><lb/>1.</s></p><p type="margin"> <s><margin.target id="marg1183"></margin.target>(e) <emph type="italics"/>By 4. of the<emph.end type="italics"/> 1.</s></p><p type="margin"> <s><margin.target id="marg1184"></margin.target>(f) <emph type="italics"/>By 28. of the<emph.end type="italics"/><lb/>1.</s></p><p type="margin"> <s><margin.target id="marg1185"></margin.target>(g) <emph type="italics"/>By 29. of th<emph.end type="italics"/><lb/>1</s></p><p type="main"> <s>And the part which is within the Liquid <lb/><arrow.to.target n="marg1186"></arrow.to.target><lb/>doth move upwards according to the Per­<lb/>pendicular that is drawn thorow B parallel <lb/>to R T.] <emph type="italics"/>The rea&longs;on why this moveth upwards, and that <lb/>other downwards, along the Perpendicular Line, hath been &longs;hewn above in the 8 of the fir&longs;t <lb/>Book of this; &longs;o that we have judged it needle&longs;&longs;e to repeat it either in this, or in the re&longs;t <lb/>that follow.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1186"></margin.target>G</s></p><p type="head"> <s>THE TRANSLATOR.</s></p><p type="main"> <s><emph type="italics"/>In the<emph.end type="italics"/> Antient <emph type="italics"/>Parabola (namely that a&longs;&longs;umed in a Rightangled <lb/>Cone) the Line<emph.end type="italics"/> juxta quam Po&longs;&longs;unt quæ in Sectione ordinatim du­<lb/>cuntur <emph type="italics"/>(which I, following<emph.end type="italics"/> Mydorgius, <emph type="italics"/>do call the<emph.end type="italics"/> Parameter<emph type="italics"/>) is<emph.end type="italics"/> (a) <lb/><arrow.to.target n="marg1187"></arrow.to.target><lb/><emph type="italics"/>double to that<emph.end type="italics"/> quæ ducta e&longs;t à Vertice Sectionis u&longs;que ad Axem, <emph type="italics"/>or in<emph.end type="italics"/><lb/>Archimedes <emph type="italics"/>phra&longs;e,<emph.end type="italics"/> <foreign lang="greek">ta_s us/xri tou_ a)/con<34>;</foreign> <emph type="italics"/>which I for that cau&longs;e, and <lb/>for want of a better word, name the<emph.end type="italics"/> Semiparameter: <emph type="italics"/>but in<emph.end type="italics"/> Modern <lb/><emph type="italics"/>Parabola's it is greater or le&longs;&longs;er then double. </s> <s>Now that throughout this <lb/>Book<emph.end type="italics"/> Archimedes <emph type="italics"/>&longs;peaketh of the Parabola in a Rectangled Cone, is mani­<lb/>fe&longs;t both by the fir&longs;t words of each Propo&longs;ition, & by this that no Parabola <lb/>hath its Parameter double to the Line<emph.end type="italics"/> quæ e&longs;t a Sectione ad Axem, <emph type="italics"/>&longs;ave <lb/>that which is taken in a Rightangled Cone. </s> <s>And in any other Parabola, for <lb/>the Line<emph.end type="italics"/> <foreign lang="greek">ta_s ms/xritou_ a)/eon<34></foreign> <emph type="italics"/>or<emph.end type="italics"/> quæ u&longs;que ad Axem <emph type="italics"/>to u&longs;urpe the Word<emph.end type="italics"/> Se­<lb/>miparameter <emph type="italics"/>would be neither proper nor true: but in this ca&longs;e it may pa&longs;s<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1187"></margin.target>(a) Rîvalt. <emph type="italics"/>in<emph.end type="italics"/> Ar­<lb/>chimed. <emph type="italics"/>de Cunoid <lb/>& Sphæroid.<emph.end type="italics"/> Prop. <lb/></s> <s>3. Lem. </s> <s>1.</s></p><p type="head"> <s>PROP. III. THEOR. III.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Rightangled Conoid, when it <lb/>&longs;hall have its Axis le&longs;&longs;e than &longs;e&longs;quialter of the Se­<lb/>mi-parameter, the Axis having any what ever pro­<lb/>portion to the Liquid in Gravity, being demitted into <lb/>the Liquid &longs;o as that its Ba&longs;e be wholly within the <lb/>&longs;aid Liquid, and being &longs;et inclining, it &longs;hall not re­<lb/>main inclined, but &longs;hall be &longs;o re&longs;tored, as that its Ax­<lb/>is do &longs;tand upright, or according to the Perpendicular.<emph.end type="italics"/></s></p><p type="main"> <s>Let any Portion be demitted into the Liquid, as was &longs;aid; and <lb/>let its Ba&longs;e be in the <emph type="italics"/>L<emph.end type="italics"/>iquid; <lb/><figure id="id.040.01.1052.2.jpg" xlink:href="040/01/1052/2.jpg"/><lb/>and let it be cut thorow the <lb/>Axis, by a Plain erect upon the Sur­<lb/>face of the Liquid, and let the Se­<lb/>ction be A P O <emph type="italics"/>L,<emph.end type="italics"/> the Section of a <lb/>Right angled Cone: and let the Axis <lb/>of the Portion and Diameter of the <pb xlink:href="040/01/1053.jpg" pagenum="356"/>Section of the Portion be A P O L, the Section of a Rightangled <lb/>Cone; and let the Axis of the Portion and Diameter of the Section <lb/>be N O, and the Section of the Surface of the Liquid I S. </s> <s>If now <lb/>the Portion be not erect, then N O &longs;hall not be at equall Angles with <lb/>I S. </s> <s>Draw R <foreign lang="greek">w</foreign> touching the Section of the Rightangled Conoid <lb/>in P, and parallel to I S: and from the Point P and parall to O N <lb/>draw <emph type="italics"/>P<emph.end type="italics"/> F: and take the Centers of Gravity; and of the Solid A <lb/><emph type="italics"/>P<emph.end type="italics"/> O L let the Centre be R; and of that which lyeth within the <lb/>Liquid let the Centre be B; and draw a Line from B to R pro­<lb/>longing it to G, that G may be the Centre of Gravity of the Solid <lb/>that is above the Liquid. </s> <s>And becau&longs;e N O is &longs;e&longs;quialter of R <lb/>O, and is greater than &longs;e&longs;quialter of the Semi-Parameter; it is ma­<lb/><arrow.to.target n="marg1188"></arrow.to.target><lb/>nife&longs;t that <emph type="italics"/>(a)<emph.end type="italics"/> R O is greater than the <lb/><figure id="id.040.01.1053.1.jpg" xlink:href="040/01/1053/1.jpg"/><lb/>Semi-parameter. ^{*}Let therefore R <lb/><arrow.to.target n="marg1189"></arrow.to.target><lb/>H be equall to the Semi-Parameter, <lb/><arrow.to.target n="marg1190"></arrow.to.target><lb/>^{*} and O <emph type="italics"/>H<emph.end type="italics"/> double to H M. </s> <s>Fora&longs;­<lb/>much therefore as N O is &longs;e&longs;quialter <lb/><arrow.to.target n="marg1191"></arrow.to.target><lb/>of R O, and M O of O H, <emph type="italics"/>(b)<emph.end type="italics"/> the <lb/>Remainder N M &longs;hall be &longs;e&longs;quialter <lb/>of the Remainder R H: Therefore <lb/>the Axis is greater than &longs;e&longs;quialter <lb/>of the Semi parameter by the quan­<lb/>tity of the Line M O. </s> <s>And let it be <lb/>&longs;uppo&longs;ed that the Portion hath not le&longs;&longs;e proportion in Gravity unto <lb/>the Liquid of equall Ma&longs;&longs;e, than the Square that is made of the <lb/>Exce&longs;&longs;e by which the Axis is greater than &longs;e&longs;quialter of the Semi­<lb/>parameter hath to the Square made of the Axis: It is therefore ma­<lb/>nife&longs;t that the Portion hath not le&longs;&longs;e proportion in Gravity to the <lb/>Liquid than the Square of the Line M O hath to the Square of N <lb/>O: But look what proportion the <emph type="italics"/>P<emph.end type="italics"/>ortion hath to the Liquid in <lb/>Gravity, the &longs;ame hath the <emph type="italics"/>P<emph.end type="italics"/>ortion &longs;ubmerged to the whole Solid: <lb/>for this hath been demon&longs;trated <emph type="italics"/>(c)<emph.end type="italics"/> above: ^{*}And look what pro­<lb/><arrow.to.target n="marg1192"></arrow.to.target><lb/>portion the &longs;ubmerged Portion hath to the whole <emph type="italics"/>P<emph.end type="italics"/>ortion, the <lb/><arrow.to.target n="marg1193"></arrow.to.target><lb/>&longs;ame hath the Square of <emph type="italics"/>P<emph.end type="italics"/> F unto the Square of N O: For it hath <lb/>been demon&longs;trated in <emph type="italics"/>(d) Lib. de Conoidibus,<emph.end type="italics"/> that if from a Right­<lb/><arrow.to.target n="marg1194"></arrow.to.target><lb/>angled Conoid two <emph type="italics"/>P<emph.end type="italics"/>ortions be cut by Planes in any fa&longs;hion pro­<lb/>duced, the&longs;e <emph type="italics"/>P<emph.end type="italics"/>ortions &longs;hall have the &longs;ame Proportion to each <lb/>other as the Squares of their Axes: The Square of P F, therefore, <lb/>hath not le&longs;&longs;e proportion to the Square of N O than the Square of <lb/>M O hath to the Square of N O: ^{*}Wherefore P F is not le&longs;&longs;e than <lb/><arrow.to.target n="marg1195"></arrow.to.target><lb/>M O, ^{*}nor B P than H O. ^{*}If therefore, a Right Line be drawn <lb/><arrow.to.target n="marg1196"></arrow.to.target><lb/>from H at Right Angles unto N O, it &longs;hall meet with B <emph type="italics"/>P,<emph.end type="italics"/> and &longs;hall <lb/><arrow.to.target n="marg1197"></arrow.to.target><lb/>fall betwixt B and P; let it fall in T: <emph type="italics"/>(e)<emph.end type="italics"/> And becau&longs;e <emph type="italics"/>P<emph.end type="italics"/> F is <lb/><arrow.to.target n="marg1198"></arrow.to.target><lb/>parallel to the Diameter, and H T is perpendicular unto the &longs;ame <lb/>Diameter, and R H equall to the Semi-parameter; a Line drawn <lb/>from R to T and prolonged, maketh Right Angles with the Line <pb xlink:href="040/01/1054.jpg" pagenum="360"/>contingent unto the Section in the Point P: Wherefore it al&longs;o <lb/>maketh Right Angles with the Surface of the Liquid: and that <lb/>part of the Conoidall Solid which is within the Liquid &longs;hall move <lb/>upwards according to the Perpendicular drawn thorow B parallel <lb/>to R T; and that part which is above the Liquid &longs;hall move down­<lb/>wards according to that drawn thorow G, parallel to the &longs;aid R T: <lb/>And thus it &longs;hall continue to do &longs;o long untill that the Conoid be <lb/>re&longs;tored to uprightne&longs;&longs;e, or to &longs;tand according to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1188"></margin.target>(a) <emph type="italics"/>By 10. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1189"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1190"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1191"></margin.target>(b) <emph type="italics"/>By 19. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1192"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1193"></margin.target>(c) <emph type="italics"/>By 1. of this <lb/>&longs;econd Book.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1194"></margin.target>(d) <emph type="italics"/>By<emph.end type="italics"/> 6. De Co­<lb/>noilibus & <emph type="italics"/>S<emph.end type="italics"/>phæ­<lb/>roidibus <emph type="italics"/>of<emph.end type="italics"/> Archi­<lb/>medes.</s></p><p type="margin"> <s><margin.target id="marg1195"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1196"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1197"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1198"></margin.target>(e) <emph type="italics"/>By 2. of this <lb/>&longs;econd Book.<emph.end type="italics"/></s></p><p type="head"> <s>COMMANDINE.<lb/><arrow.to.target n="marg1199"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1199"></margin.target>A</s></p><p type="main"> <s>Let therefore R H be equall to the Semi-parameter.] <emph type="italics"/>So it is to be <lb/>read, and not R M, as<emph.end type="italics"/> Tartaglia's <emph type="italics"/>Tran&longs;lation hath is; which may be made appear from <lb/>that which followeth.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1200"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1200"></margin.target>B</s></p><p type="main"> <s>And O H double to H M.] <emph type="italics"/>In the Tran&longs;lation aforenamed it is fal&longs;ly render­<lb/>ed,<emph.end type="italics"/> O N <emph type="italics"/>double to<emph.end type="italics"/> R M.</s></p><p type="main"> <s><arrow.to.target n="marg1201"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1201"></margin.target>C</s></p><p type="main"> <s>And look what proportion the Submerged Portion hath to the whole <lb/>Portion, the &longs;ame hath the Square of P F unto the Square of N O.] <lb/><emph type="italics"/>This place we have re&longs;tored in our Tran&longs;lation, at the reque&longs;t of &longs;ome friends: But it is demon­<lb/>&longs;trated by<emph.end type="italics"/> Archimedes in Libro de Conoidibus & Sphæroidibus, Propo. </s> <s>26.</s></p><p type="main"> <s><arrow.to.target n="marg1202"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1202"></margin.target>D</s></p><p type="main"> <s>Wherefore P F is not le&longs;&longs;e than M O.] <emph type="italics"/>For by 10 of the fifth it followeth <lb/>that the Square of P F is not le&longs;&longs;e than the Square of M O: and therefore neither &longs;hall the <lb/>Line P F be leße than the Line M O, by 22 of the<emph.end type="italics"/></s></p><figure id="id.040.01.1054.1.jpg" xlink:href="040/01/1054/1.jpg"/><p type="main"> <s><arrow.to.target n="marg1203"></arrow.to.target><lb/><emph type="italics"/>&longs;ixth.<emph.end type="italics"/><lb/><arrow.to.target n="marg1204"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1203"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1204"></margin.target>(a) <emph type="italics"/>By 14. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="main"> <s>Nor B P than H O,] <emph type="italics"/>For as P F is to <lb/>P B, &longs;o is M O to H O: and, by Permutation, as<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1205"></arrow.to.target><lb/><emph type="italics"/>P F is to M O, &longs;o is B P to H O; But P F is not <lb/>le&longs;&longs;e than M O as hath bin proved; (a) Therefore <lb/>neither &longs;hall B P be le&longs;&longs;e than H O.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1205"></margin.target>F</s></p><p type="main"> <s>If therefore a Right Line be drawn <lb/>from H at Right Angles unto N O, it <lb/>&longs;hall meet with B P, and &longs;hall fall be­<lb/>twixt B and P.] <emph type="italics"/>This Place was corrupt in the <lb/>Tran&longs;lation of<emph.end type="italics"/> Tartaglia<emph type="italics"/>: But it is thus demonstra­<lb/>ted. </s> <s>In regard that P F is not le&longs;&longs;e than O M, nor P B than O H, if we &longs;uppo&longs;e P F equall to <lb/>O M, P B &longs;hall be likewi&longs;e equall to O H: Wherefore the Line drawn thorow O, parallel to A L <lb/>&longs;hall fall without the Section, by 17 of the fir&longs;t of our Treati&longs;e of Conicks; And in regard that <lb/>B P prolonged doth meet it beneath P; Therefore the Perpendicular drawn thorow H doth <lb/>al&longs;o meet with the &longs;ame beneath B, and it doth of nece&longs;&longs;ity fall betwixt B and P: But the <lb/>&longs;ame is much more to follow, if we &longs;uppo&longs;e P F to be greater than O M.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1055.jpg" pagenum="361"/><p type="head"> <s>PROP. V. THEOR. V.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Right-Angled Conoid lighter <lb/>than the Liquid, when it &longs;hall have its Axis great­<lb/>er than<emph.end type="italics"/> Se&longs;quialter <emph type="italics"/>of the Semi-parameter, if it have <lb/>not greater proportion in Gravity to the Liquid [of <lb/>equal Ma&longs;s] than the Exce&longs;&longs;e by which the Square <lb/>made of the Axis is greater than the Square made <lb/>of the Exce&longs;&longs;e by which the Axis is greater than<emph.end type="italics"/><lb/>&longs;e&longs;quialter <emph type="italics"/>of the Semi-Parameter hath to the <lb/>Square made of the Axis being demitted into the Li­<lb/>quid, &longs;o as that its Ba&longs;e be wholly within the Liquid, <lb/>and being &longs;et inclining, it &longs;hall not remain &longs;o inclined, <lb/>but &longs;hall turn about till that its Axis &longs;hall be accor­<lb/>ding to the Perpendicular.<emph.end type="italics"/></s></p><p type="main"> <s>For let any Portion be demitted into the Liquid, as hath been <lb/>&longs;aid; and let its Ba&longs;e be wholly within the Liquid, And being <lb/>cut thorow its Axis by a Plain erect upon the Surface of the <lb/>Liquid; its Section &longs;hall be the Section <lb/><figure id="id.040.01.1055.1.jpg" xlink:href="040/01/1055/1.jpg"/><lb/>of a Rightangled Cone: Let it be <lb/>A P O L, and let the Axis of the Por­<lb/>tion and Diameter of the Section be <lb/>N O; and the Section of the Surface of <lb/>the Liquid I S. </s> <s>And becau&longs;e the Axis <lb/>is not according to the Perpendicu­<lb/>lar, N O will not be at equall angles <lb/>with I S. </s> <s>Draw K <foreign lang="greek">w</foreign> touching the Se­<lb/>ction A P O L in P, and parallel unto <lb/>I S: and thorow P, draw P F parallel unto N O: and take the <lb/>Centres of Gravity; and of the Solid A P O L let the Centre be <lb/>R; and of that which lyeth above the Liquid let the Centre be B; <lb/>and draw a Line from B to R, prolonging it to G; which let be the <lb/>Centre of Gravity of the Solid demerged within the Liquid: and <lb/>moreover, take R H equall to the Semi-parameter, and let O H be <lb/>double to H M; and do in the re&longs;t as hath been &longs;aid <emph type="italics"/>(a)<emph.end type="italics"/> above. <lb/><arrow.to.target n="marg1206"></arrow.to.target><lb/>Now fora&longs;much as it was &longs;uppo&longs;ed that the Portion hath not greater <lb/>proportion in Gravity to the Liquid, than the Exce&longs;&longs;e by which <lb/>the Square N O is greater than the Square M O, hath to the &longs;aid <lb/>Square N O: And in regard that whatever proportion in Gravity <pb xlink:href="040/01/1056.jpg" pagenum="362"/>the Portion hath to the Liquid of equall Ma&longs;&longs;e, the &longs;ame hath the <lb/>Magnitude of the Portion &longs;ubmerged unto the whole Portion; as <lb/>hath been demon&longs;trated in the fir&longs;t Propo&longs;ition; The Magnitude <lb/>&longs;ubmerged, therefore, &longs;hall not have greater proportion to the <lb/><arrow.to.target n="marg1207"></arrow.to.target><lb/>whole <emph type="italics"/>(b)<emph.end type="italics"/> Portion, than that which hath been mentioned: ^{*}And <lb/>therefore the whole Portion hath not greater proportion unto that <lb/><arrow.to.target n="marg1208"></arrow.to.target><lb/>which is above the Liquid, than the Square N O hath to the Square <lb/><arrow.to.target n="marg1209"></arrow.to.target><lb/>M O: But the <emph type="italics"/>(c)<emph.end type="italics"/> whole Portion hath the &longs;ame proportion unto <lb/>that which is above the Liquid that the Square N O hath to the <lb/>Square P F: Therefore the Square N O hath not greater propor­<lb/><arrow.to.target n="marg1210"></arrow.to.target><lb/>tion unto the Square P F, than it hath unto the Square M O: ^{*}And <lb/>hence it followeth that P F is not le&longs;&longs;e than O M, nor P B than O <lb/><arrow.to.target n="marg1211"></arrow.to.target><lb/>H: ^{*} A Line, therefore, drawn from H at Right Angles unto N O <lb/>&longs;hall meet with B P betwixt P and B: Let it be in T: And be­<lb/>cau&longs;e that in the Section of the Rectangled Cone P F is parallel unto <lb/>the Diameter N O; and H T perpendicular unto the &longs;aid Diame­<lb/>ter; and R H equall to the Semi-parameter: It is manife&longs;t that <lb/>R T prolonged doth make Right Angles with K P <foreign lang="greek">w</foreign>: And there­<lb/>fore doth al&longs;o make Right Angles with I S: Therefore R T is per­<lb/>pendicular unto the Surface of the Liquid; And if thorow the <lb/>Points B and G Lines be drawn parallel unto R T, they &longs;hall be <lb/>perpendicular unto the Liquids Surface. </s> <s>The Portion, therefore, <lb/>which is above the Liquid &longs;hall move downwards in the Liquid ac­<lb/>cording to the Perpendicular drawn thorow B; and that part <lb/>which is within the Liquid &longs;hall move upwards according to the <lb/>Perpendicular drawn thorow G; and the Solid Portion A P O L <lb/>&longs;hall not continue &longs;o inclined, [<emph type="italics"/>as it was at its demer&longs;ion<emph.end type="italics"/>], but &longs;hall <lb/>move within the Liquid untill &longs;uch time that N O do &longs;tand accor­<lb/>ding to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1206"></margin.target>(a) <emph type="italics"/>In 4. Prop. of <lb/>this.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1207"></margin.target>(a) <emph type="italics"/>By 11. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1208"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1209"></margin.target>(b) <emph type="italics"/>By 26. of the <lb/>Book<emph.end type="italics"/> De Conoid. <lb/></s> <s>& Sphæroid.</s></p><p type="margin"> <s><margin.target id="marg1210"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1211"></margin.target>C</s></p><p type="head"> <s>COMMANDINE.<lb/><arrow.to.target n="marg1212"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1212"></margin.target>A</s></p><p type="main"> <s>And therefore the whole Portion hath not greater proportion <lb/>unto that which is above the Liquid, than the Square N O hath to <lb/>the Square M O.] <emph type="italics"/>For in regard that the Magnitude of the Portion demerged <lb/>within the Liquid hath not greater proportion unto the whole Portion than the Exce&longs;&longs;e by which <lb/>the Square N O is greater than the Square M O hath to the &longs;aid Square N O; Converting of <lb/>the Proportion, by the 26. of the fifth of<emph.end type="italics"/> Euclid, <emph type="italics"/>of<emph.end type="italics"/> Campanus <emph type="italics"/>his Tran&longs;lation, the whole <lb/>Portion &longs;hall not have le&longs;&longs;er proportion unto the Magnitude &longs;ubmerged, than the Square N O <lb/>hath unto the Exce&longs;&longs;e by which N O is greater than the Square M O. </s> <s>Let a Portion be taken; <lb/>and let that part of it which is above the Liquid be the fir&longs;t Magnitude; the part of it which <lb/>is &longs;ubmerged the &longs;econd: and let the third Magnitude be the Square M O; and let the Exce&longs;&longs;e <lb/>by which the Square N O is greater than the Square M O be the fourth. </s> <s>Now of the&longs;e Mag­<lb/>nitudes, the proportion of the fir&longs;t and &longs;econd, unto the &longs;econd, is not le&longs;&longs;e than that of the third & <lb/>fourth unto the fourth: For the Square M O together with the Exce&longs;&longs;e by which the Square <lb/>N O exceedeth the Square M O is equall unto the &longs;aid Square N O: Wherefore, by Conver&longs;i­<lb/>on of Proportion, by 30 of the &longs;aid fifth Book, the proportion of the fir&longs;t and &longs;econd unto the <lb/>fir&longs;t, &longs;hall not be greater than that of the third and fourth unto the third: And, for the &longs;ame<emph.end type="italics"/> <pb xlink:href="040/01/1057.jpg" pagenum="363"/><emph type="italics"/>the proportion of the whole Portion unto that part thereof which is above the Liquid &longs;hall not be <lb/>greater than that of the Square N O unto the Square M O: Which was to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s>And hence it followeth that P F is not le&longs;&longs;e than O M, nor P B </s></p><p type="main"> <s><arrow.to.target n="marg1213"></arrow.to.target><lb/>than O H.] <emph type="italics"/>This followeth by the 10 and 14 of the fifth, and by the 22 of the &longs;ixth of<emph.end type="italics"/><lb/>Euclid, <emph type="italics"/>as hath been &longs;aid above.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1213"></margin.target>B</s></p><p type="main"> <s>A <emph type="italics"/>L<emph.end type="italics"/>ine, therefore, drawn from Hat Right Angles unto N O &longs;hall <lb/><arrow.to.target n="marg1214"></arrow.to.target><lb/>meet with P B betwixt P and B.] <emph type="italics"/>Why this &longs;o falleth out, we will &longs;hew in the <lb/>next.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1214"></margin.target>C</s></p><p type="head"> <s>PROP. VI. THEOR. VI.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Rightangled Conoid lighter <lb/>than the Liquid, when it &longs;hall have its Axis greater <lb/>than &longs;e&longs;quialter of the Semi-parameter, but le&longs;&longs;e than <lb/>to be unto the Semi-parameter in proportion as fifteen <lb/>to fower, being demitted into the Liquid &longs;o as that <lb/>its Ba&longs;e do touch the Liquid, it &longs;hall never stand &longs;o <lb/>enclined as that its Ba&longs;e toucheth the Liquid in one <lb/>Point only.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a Portion, as was &longs;aid; and demit it into the Li­<lb/>quid in &longs;uch fa&longs;hion as that its Ba&longs;e do touch the Liquid in <lb/>one only Point: It is to be demon&longs;trated that the &longs;aid Portion <lb/><arrow.to.target n="marg1215"></arrow.to.target><lb/>&longs;hall not continue &longs;o, but &longs;hall turn about in &longs;uch manner as that <lb/>its Ba&longs;e do in no wi&longs;e touch the Surface of the Liquid. </s> <s>For let it be <lb/>cut thorow its Axis by a Plane erect <lb/><figure id="id.040.01.1057.1.jpg" xlink:href="040/01/1057/1.jpg"/><lb/>upon the <emph type="italics"/>L<emph.end type="italics"/>iquids Surface: and let <lb/>the Section of the Superficies of the <lb/>Portion be A P O L, the Section of <lb/>a Rightangled Cone; and the Sect­<lb/>ion of the Surface of the <emph type="italics"/>L<emph.end type="italics"/>iquid be <lb/>A S; and the Axis of the Portion <lb/>and Diameter of the Section N O: <lb/>and let it be cut in F, &longs;o as that O <lb/>F be double to F N; and in <foreign lang="greek">w</foreign> &longs;o, as that N O may be to F <foreign lang="greek">w</foreign> in the <lb/>&longs;ame proportion as fifteen to four; and at Right Angles to N O <lb/>draw <foreign lang="greek">w</foreign> <emph type="italics"/>N<emph.end type="italics"/>ow becau&longs;e N O hath greater proportion unto F <foreign lang="greek">w</foreign> than <lb/>unto the Semi-parameter, let the Semi-parameter be equall to F B: <lb/><arrow.to.target n="marg1216"></arrow.to.target><lb/>and draw P C parallel unto A S, and touching the Section A P O L <lb/>in P; and P I parallel unto <emph type="italics"/>N O<emph.end type="italics"/>; and fir&longs;t let P I cut K<foreign lang="greek">w</foreign> in H. For­<lb/><arrow.to.target n="marg1217"></arrow.to.target><lb/>a&longs;much, therefore, as in the Portion A P O L, contained betwixt <lb/>the Right <emph type="italics"/>L<emph.end type="italics"/>ine and the Section of the Rightangled Cone, K <foreign lang="greek">w</foreign> is <lb/>parallel to A L, and P I parallel unto the Diameter, and cut by the <pb xlink:href="040/01/1058.jpg" pagenum="364"/>&longs;aid K <foreign lang="greek">w</foreign> in H, and A S is parallel unto the <emph type="italics"/>L<emph.end type="italics"/>ine that toucheth in <lb/>P; It is nece&longs;&longs;ary that P I hath unto P H either the &longs;ame proportion <lb/>that <emph type="italics"/>N<emph.end type="italics"/> <foreign lang="greek">w</foreign> hath to <foreign lang="greek">w</foreign> O, or greater; for this hath already been de­<lb/>mon&longs;trated: But <emph type="italics"/>N<emph.end type="italics"/> <foreign lang="greek">w</foreign> is &longs;e&longs;quialter of <foreign lang="greek">w</foreign> O; and P I, therefore, is <lb/>either Se&longs;quialter of H P, or more than &longs;e&longs;quialter: Wherefore <lb/><arrow.to.target n="marg1218"></arrow.to.target><lb/>P H is to H I either double, or le&longs;&longs;e than double. <emph type="italics"/>L<emph.end type="italics"/>et P T be <lb/>double to T I: the Centre of Gravity of the part which is within <lb/>the <emph type="italics"/>L<emph.end type="italics"/>iquid &longs;hall be the Point T. </s> <s>Therefore draw a <emph type="italics"/>L<emph.end type="italics"/>ine from T <lb/>to F prolonging it; and let the Centre of <lb/><figure id="id.040.01.1058.1.jpg" xlink:href="040/01/1058/1.jpg"/><lb/>Gravity of the part which is above the <emph type="italics"/>L<emph.end type="italics"/>iquid <lb/>be G: and from the Point B at Right Angles <lb/>unto <emph type="italics"/>N O<emph.end type="italics"/> draw B R. </s> <s>And &longs;eeing that P I is <lb/>parallel unto the Diameter <emph type="italics"/>N O,<emph.end type="italics"/> and B R <lb/>perpendicular unto the &longs;aid Diameter, and F <lb/>B equall to the Semi-parameter; It is mani­<lb/>fe&longs;t that the <emph type="italics"/>L<emph.end type="italics"/>ine drawn thorow the Points <lb/>F and R being prolonged, maketh equall <lb/>Angles with that which toucheth the Section <lb/>A P O L in the Point P: and therefore doth al&longs;o make Right An­<lb/>gles with A S, and with the Surface of the <emph type="italics"/>L<emph.end type="italics"/>iquid: and the <emph type="italics"/>L<emph.end type="italics"/>ines <lb/>drawn thorow T and G parallel unto F R &longs;hall be al&longs;o perpendicu­<lb/>lar to the Surface of the <emph type="italics"/>L<emph.end type="italics"/>iquid: and of the Solid Magnitude A P <lb/>O L, the part which is within the <emph type="italics"/>L<emph.end type="italics"/>iquid moveth upwards according <lb/>to the Perpendicular drawn thorow T; and the part which is above <lb/>the <emph type="italics"/>L<emph.end type="italics"/>iquid moveth downwards according to that drawn thorow G: <lb/><arrow.to.target n="marg1219"></arrow.to.target><lb/>The Solid A <emph type="italics"/>P<emph.end type="italics"/> O L, therefore, &longs;hall turn about, and its Ba&longs;e &longs;hall <lb/>not in the lea&longs;t touch the Surface of the <emph type="italics"/>L<emph.end type="italics"/>iquid, And if <emph type="italics"/>P<emph.end type="italics"/> I do not <lb/>cut the <emph type="italics"/>L<emph.end type="italics"/>ine K <foreign lang="greek">w,</foreign> as in the &longs;econd Figure, it is manife&longs;t that the <lb/><emph type="italics"/>P<emph.end type="italics"/>oint T, which is the Centre of Gravity of the &longs;ubmerged <emph type="italics"/>P<emph.end type="italics"/>ortion, <lb/>falleth betwixt <emph type="italics"/>P<emph.end type="italics"/> and I: And for the other particulars remaining, <lb/>they are demon&longs;trated like as before.</s></p><p type="margin"> <s><margin.target id="marg1215"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1216"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1217"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1218"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1219"></margin.target>E</s></p><p type="head"> <s>COMMANDINE.<lb/><arrow.to.target n="marg1220"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1220"></margin.target>A</s></p><p type="main"> <s>It is to be demon&longs;trated that the &longs;aid <emph type="italics"/>P<emph.end type="italics"/>ortion &longs;hall not continue <lb/>&longs;o, but &longs;hall turn about in &longs;uch manner as that its Ba&longs;e do in no wi&longs;e <lb/>touch the Surface of the Liquid.] <emph type="italics"/>The&longs;e words are added by us, as having been <lb/>omitted by<emph.end type="italics"/> Tartaglia.</s></p><p type="main"> <s><emph type="italics"/>N<emph.end type="italics"/>ow becau&longs;e N O hath greater proportion to F <foreign lang="greek">w</foreign> than unto </s></p><p type="main"> <s><arrow.to.target n="marg1221"></arrow.to.target><lb/>the Semi parameter.] <emph type="italics"/>For the Diameter of the Portion N O hath unto F<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>the <lb/>&longs;ame proportion as fifteen to fower: But it was &longs;uppo&longs;ed to have le&longs;&longs;e proportion unto the <lb/>Semi-parameter than fifteen to fower: Wherefore N O hath greater proportion unto F<emph.end type="italics"/> <foreign lang="greek">w</foreign><lb/><emph type="italics"/>than unto the Semi-parameter: And therefore<emph.end type="italics"/> (a) <emph type="italics"/>the Semi-parameter &longs;hall be greater<emph.end type="italics"/><lb/><arrow.to.target n="marg1222"></arrow.to.target><lb/><emph type="italics"/>than the &longs;aid F<emph.end type="italics"/> <foreign lang="greek">w.</foreign></s></p><p type="margin"> <s><margin.target id="marg1221"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1222"></margin.target>(a) <emph type="italics"/>By 10. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>Fora&longs;much, therefore, as in the <emph type="italics"/>P<emph.end type="italics"/>ortion <emph type="italics"/>A P O L,<emph.end type="italics"/> contained, be­<lb/><arrow.to.target n="marg1223"></arrow.to.target><lb/>twixt the Right <emph type="italics"/>L<emph.end type="italics"/>ine and the Section of the Rightangled Cone K <lb/><foreign lang="greek">w</foreign> is parallel to A L, and <emph type="italics"/>P I<emph.end type="italics"/> parallel unto the Diameter, and cut by <pb xlink:href="040/01/1059.jpg" pagenum="365"/>the &longs;aid K <foreign lang="greek">w</foreign> in H, and A S is parallel unto the Line that toucheth <lb/>in P; It is nece&longs;&longs;ary that P I hath unto P H either the &longs;ame propor­<lb/>tion that N <foreign lang="greek">w</foreign> hath to <foreign lang="greek">w</foreign> O, or greater; for this hath already been <lb/>demon&longs;trated.] <emph type="italics"/>Where this is demon&longs;trated either by<emph.end type="italics"/> Archimedes <emph type="italics"/>him&longs;elf, or by <lb/>any other, doth not appear; touching which we will here in&longs;ert a Demon&longs;tration, after that <lb/>we have explained &longs;ome things that pertaine thereto.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1223"></margin.target>C</s></p><p type="head"> <s>LEMMA I.</s></p><p type="main"> <s>Let the Lines A B and A C contain the Angle B A C; and from <lb/>the point D, taken in the Line A C, draw D E and D F at <lb/>plea&longs;ure unto A B: and in the &longs;ame Line any Points G and L <lb/>being taken, draw G H & L M parallel to D E, & G K and <lb/>L N parallel unto F D: Then from the Points D & G as farre <lb/>as to the Line M L draw D O P, cutting G H in O, and G Q <lb/>parallel unto B A. </s> <s>I &longs;ay that the Lines that lye betwixt the Pa­<lb/>rallels unto F D have unto tho&longs;e that lye betwixt the Par­<lb/>allels unto D E (namely K N to G Q or to O P; F K to D O; <lb/>and F N to D P) the &longs;ame mutuall proportion: that is to &longs;ay, <lb/>the &longs;ame that A F hath to A E.</s></p><p type="main"> <s><emph type="italics"/>For in regard that the Triangles A F D, A K G, and A N L<emph.end type="italics"/><lb/><figure id="id.040.01.1059.1.jpg" xlink:href="040/01/1059/1.jpg"/><lb/><emph type="italics"/>are alike, and E F D, H K G, and M N L are al&longs;o alike: There-<emph.end type="italics"/><lb/><arrow.to.target n="marg1224"></arrow.to.target><lb/><emph type="italics"/>fore,<emph.end type="italics"/> (a) <emph type="italics"/>as A F is to F D, &longs;o &longs;hall A K be to K G; and as F D is to <lb/>F E, &longs;o &longs;hall K G be to K H: Wherefore,<emph.end type="italics"/> ex equali, <emph type="italics"/>as A F is to F <lb/>E, &longs;o &longs;hall A K be to K H: And, by Conver&longs;ion of proportion, as <lb/>A F is to A E, &longs;o &longs;hall A K be to K H. </s> <s>It is in the &longs;ame manner <lb/>proved that, as A F is to A E, &longs;o &longs;hall A N be to A M. </s> <s>Now A<emph.end type="italics"/><lb/><arrow.to.target n="marg1225"></arrow.to.target><lb/><emph type="italics"/>N being to A M, as A K is to A H; The<emph.end type="italics"/> (b) <emph type="italics"/>Remainder K N &longs;hall <lb/>be unto the Remainder H M, that is unto G Q, or unto O P, as <lb/>A N is to A M; that is, as A F is to A E: Again, A K is to <lb/>A H, as A F is to A E; Therefore the Remainder F K &longs;hall be to <lb/>the Remainder E H, namely to D O, as A F is to A E. </s> <s>We might in <lb/>like manner demonstrate that &longs;o is F N to D P: Which is that that <lb/>was required to be demonstrated.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1224"></margin.target>(a) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1225"></margin.target>(b) <emph type="italics"/>By 5. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s>In the &longs;ame Line A B let there be two Points R and S, &longs;o di&longs;po­<lb/>&longs;ed, that A S may have the &longs;ame Proportion to A R that <lb/>A F hath to A E; and thorow R draw R T parallel to E D, <lb/>and thorow S draw S T parallel to F D, &longs;o, as that it may <lb/>meet with R T in the Point T. </s> <s>I &longs;ay that the Point T fall­<lb/>eth in the Line A C.</s></p> <pb xlink:href="040/01/1060.jpg" pagenum="366"/><figure id="id.040.01.1060.1.jpg" xlink:href="040/01/1060/1.jpg"/><p type="main"> <s><emph type="italics"/>For if it be po&longs;&longs;ible, let it fall &longs;hort of it: and let R T be pro­<lb/>longed as farre as to A C in V: and then thorow V draw V X pa­<lb/>rallel to F D. Now, by the thing we have last demon&longs;trated, A X <lb/>&longs;hall have the &longs;ame proportion unto A R, as A F hath to A E. <lb/></s> <s>But A S hath al&longs;o the &longs;ame proportion to A R: Wherefore<emph.end type="italics"/> (a) <lb/><arrow.to.target n="marg1226"></arrow.to.target><lb/>A S <emph type="italics"/>is equall to A X, the part to the whole, which is impo&longs;&longs;i­<lb/>ble. </s> <s>The &longs;ame ab&longs;urdity will follow if we &longs;uppo&longs;e the Toint <lb/>T to fall beyond the Line A C: It is therefore nece&longs;&longs;ary that <lb/>it do fall in the &longs;aid A C. </s> <s>Which we propounded to be demonstrated.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1226"></margin.target>(a) <emph type="italics"/>By 9. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA III.</s></p><p type="main"> <s>Let there be a Parabola, who&longs;e Diameter <lb/><arrow.to.target n="marg1227"></arrow.to.target><lb/>let be A B; and let the Right Lines A C and B D be ^{*} con­<lb/>tingent to it, A C in the Point C, and B D in B: And two <lb/>Lines being drawn thorow C, the one C E, parallel unto <lb/>the Diameter; the other C F, parallel to B D; take any <lb/>Point in the Diameter, as G; and as F B is to B G, &longs;o let B <lb/>G be to B H: and thorow G and H draw G K L, and H E <lb/>M, parallel unto B D; and thorow M draw M N O parallel <lb/>to <emph type="italics"/>A C,<emph.end type="italics"/> and cutting the Diameter in O: and the Line <emph type="italics"/>N P<emph.end type="italics"/><lb/>being drawn thorow <emph type="italics"/>N<emph.end type="italics"/> unto the Diameter let it be parallel <lb/>to B D. </s> <s>I &longs;ay that H O is double to G B.</s></p><p type="margin"> <s><margin.target id="marg1227"></margin.target>* Or touch it.</s></p><p type="main"> <s><emph type="italics"/>For the Line M N O cutteth the Diameter either in G, or in other Points: and if it do <lb/>cut it in G, one and the &longs;ame Point &longs;hall be noted by the two letters G and O. </s> <s>Therfore F C, <lb/>P N, and H E M being Parallels, and A C being Parallels to M N O, they &longs;hall make the<emph.end type="italics"/><lb/><figure id="id.040.01.1060.2.jpg" xlink:href="040/01/1060/2.jpg"/><lb/><emph type="italics"/>Triangles A F C, O P N and O H M like to<emph.end type="italics"/><lb/><arrow.to.target n="marg1228"></arrow.to.target><lb/><emph type="italics"/>each other: Wherefore<emph.end type="italics"/> (a) <emph type="italics"/>O H &longs;hall be to <lb/>H M, as A F to FC: and<emph.end type="italics"/> ^{*} Permutando, <lb/><arrow.to.target n="marg1229"></arrow.to.target><lb/><emph type="italics"/>O H &longs;hall be to A F, as H M to F C: But <lb/>the Square H M is to the Square G L as the Line <lb/>H B is to the Line B G, by 20. of our fir&longs;t Book <lb/>of<emph.end type="italics"/> Conicks; <emph type="italics"/>and the Square G L is unto the <lb/>Square F C, as the Line G B is to the Line B F: <lb/>and the Lines H B, B G and B F are thereupon<emph.end type="italics"/><lb/><arrow.to.target n="marg1230"></arrow.to.target><lb/><emph type="italics"/>Proportionals: Therefore the<emph.end type="italics"/> (b) <emph type="italics"/>Squares <lb/>H M, G L and F C and there Sides, &longs;hall al&longs;o be <lb/>Proportionals: And, therefore, as the (c) <lb/>Square H M is to the Square G L, &longs;o is the Line<emph.end type="italics"/><lb/><arrow.to.target n="marg1231"></arrow.to.target><lb/><emph type="italics"/>H M to the Line F C: But as H M is to F C, &longs;o <lb/>is O H to A F; and as the Square H M is to <lb/>the Square G L, &longs;o is the Line H B to B G; that <lb/>is, B G to B F: From whence it followeth that <lb/>O H is to A F, as B G to B F: And<emph.end type="italics"/> Permu­<lb/>tando, <emph type="italics"/>O H is to B G, as A F to F B; But A F is double to F B: Therefore A B and B F <lb/>are equall, by 35. of our fir&longs;t Book of<emph.end type="italics"/> Conicks: <emph type="italics"/>And therefore N O is double to G B: <lb/>Which was to be demon&longs;trated.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1061.jpg" pagenum="367"/><p type="margin"> <s><margin.target id="marg1228"></margin.target>(a) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1229"></margin.target>* Or permitting.</s></p><p type="margin"> <s><margin.target id="marg1230"></margin.target>(b) <emph type="italics"/>By 22. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1231"></margin.target>(c) <emph type="italics"/>By<emph.end type="italics"/> Cor. <emph type="italics"/>of 20. <lb/>of the &longs;ixth.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA IV.</s></p><p type="main"> <s>The &longs;ame things a&longs;&longs;umed again, and M Q being drawn from the <lb/>Point M unto the Diameter, let it touch the Section in the <lb/>Point M. </s> <s>I &longs;ay that H Q hath to Q O, the &longs;ame proportion <lb/>that G H hath to C N.</s></p><p type="main"> <s><emph type="italics"/>For make H R equall to G F; and &longs;eeing that<emph.end type="italics"/><lb/><figure id="id.040.01.1061.1.jpg" xlink:href="040/01/1061/1.jpg"/><lb/><emph type="italics"/>the Triangles A F C and O P N are alike, and <lb/>P N equall to F C, we might in like manner de­<lb/>mon&longs;trate P O and F A to be equall to each other: <lb/>Wherefore P O &longs;hall be double to F B: But H O <lb/>is double to G B: Therefore the Remainder P H <lb/>is al&longs;o double to the Remainder F G; that is, to <lb/>R H: And therefore is followeth that P R, R H <lb/>and F G are equall to one another; as al&longs;o that <lb/>R G and P F are equall: For P G is common to <lb/>both R P and G F. </s> <s>Since therefore, that H B is <lb/>to B G, as G B is to B F, by Conver&longs;ion of Pro­<lb/>portion, B H &longs;hall be to H G, as B G is to G F: <lb/>But Q H is to H B, as H O to B G. </s> <s>For by 35 <lb/>of our fir&longs;t Book of<emph.end type="italics"/> Conicks, <emph type="italics"/>in regard that Q <lb/>M toucheth the Section in the Point M, H B and <lb/>B Q &longs;hall be equall, and Q H double to H B: <lb/>Therefore,<emph.end type="italics"/> ex æquali, <emph type="italics"/>Q H &longs;hall be to H G, as <lb/>H O to G F; that is, to H R: and,<emph.end type="italics"/> Permu­<lb/>tando, <emph type="italics"/>Q H &longs;hall be to H O, as H G to H R: again, by Conver&longs;ion, H Q &longs;hall be to Q <lb/>O, as H G to G R; that is, to P F; and, by the &longs;ame rea&longs;on, to C N: Whichwas to be de­<lb/>mon&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s>The&longs;e things therefore being explained, we come now to that <lb/>which was propounded. </s> <s>I &longs;ay, therefore, fir&longs;t that <emph type="italics"/>N C<emph.end type="italics"/> hath <lb/>to C K the &longs;ame proportion that H G hath to G B.</s></p><p type="main"> <s><emph type="italics"/>For &longs;ince that H Q is to Q O, as H G to C N<emph.end type="italics"/>; <lb/><figure id="id.040.01.1061.2.jpg" xlink:href="040/01/1061/2.jpg"/><lb/><emph type="italics"/>that is, to A O, equall to the &longs;aid C N: The Re­<lb/>mainder G Q &longs;hall be to the Remainder Q A, as <lb/>H Q to Q O: and, for the &longs;ame cau&longs;e, the Lines <lb/>A C and G L prolonged, by the things that wee <lb/>have above demonstrated, &longs;hall inter&longs;ect or meet <lb/>in the Line Q M. Again, G Q is to Q A, <lb/>as H Q to Q O: that is, as H G to F P; as<emph.end type="italics"/><lb/><arrow.to.target n="marg1232"></arrow.to.target><lb/>(a) <emph type="italics"/>was bnt now demonstrated, But unto<emph.end type="italics"/> (b) <emph type="italics"/>G<emph.end type="italics"/><lb/><arrow.to.target n="marg1233"></arrow.to.target><lb/><emph type="italics"/>Q two Lines taken together, Q B that is H B, and <lb/>B G are equall: and to Q A H F is equall; for <lb/>if from the equall Magnitudes H B and B Q there <lb/>be taken the equall Magnitudes F B and B A, the <lb/>Re mainder &longs;hall be equall; Therefore taking H <lb/>G from the two Lines H B and B G, there &longs;hall re­<lb/>main a Magnitude double to B G; that is, O H: <lb/>and P F taken from F H, the Remainder is H P: <lb/>Wherefore<emph.end type="italics"/> (c) <emph type="italics"/>O H is to H P, as G Q to Q A:<emph.end type="italics"/><lb/><arrow.to.target n="marg1234"></arrow.to.target><lb/><emph type="italics"/>But as G Q is to Q A, &longs;o is H Q to Q O;<emph.end type="italics"/> <pb xlink:href="040/01/1062.jpg" pagenum="368"/><arrow.to.target n="marg1235"></arrow.to.target><lb/><emph type="italics"/>that is, H G to N C: and as<emph.end type="italics"/> (d) <emph type="italics"/>O H is to H P, &longs;o is G B to C K; For O H is double <lb/>to G B, and H P al&longs;o double to G F; that is, to C K; Therefore H G hath the &longs;ame propor­<lb/>tion to N C, that G B hath to C K: And<emph.end type="italics"/> Permutando, <emph type="italics"/>N C hath to C K the &longs;ame proportion <lb/>that H G hath to G B.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1232"></margin.target>(a) <emph type="italics"/>By<emph.end type="italics"/> 2. Lemma.</s></p><p type="margin"> <s><margin.target id="marg1233"></margin.target>(b) <emph type="italics"/>By<emph.end type="italics"/> 4. Lemma.</s></p><p type="margin"> <s><margin.target id="marg1234"></margin.target>(b) <emph type="italics"/>By 19. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1235"></margin.target>(d) <emph type="italics"/>By 15. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>Then take &longs;ome other Point at plea&longs;ure in the Section, which <lb/>let be S: and thorow S draw two Lines, the one S T paral­<lb/>lel to D B, and cutting the Diameter in the Point T; the <lb/>other S V parallel to A C, and cutting C E in V. </s> <s>I &longs;ay <lb/>that V C hath greater proportion to C K, than T G hath <lb/>to G B.</s></p><p type="main"> <s><emph type="italics"/>For prolong V S unto the Line Q M in X; and from the Point X draw X Y unto the <lb/>Diameter parallel to B D: G T &longs;hall be le&longs;&longs;e than G Y, in regard that V S is leße than V X: <lb/>And, by the fir&longs;t Lemma, Y G &longs;hall be to V C, as H G to N C; that is, as G B to C K, which <lb/>was demon&longs;trated but now: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>Y G &longs;hall be to G B, as V C to C K: But <lb/>T G, for that it is le&longs;&longs;e than Y G, hath le&longs;&longs;e proportion to G B, than Y G hath to the &longs;ame; <lb/>Therefore V C hath greater proportion to C K. than T G hath to G B: Which was to be de­<lb/>mon&longs;trated. </s> <s>Therefore a Po&longs;ition given G K, there &longs;hall be in the Section one only Point, to <lb/>wit M, from which two Lines M E H and M N O being drawn, N C &longs;hall have the &longs;ame pro­<lb/>portion to C K, that H G hath to G B; For if they be drawn from any other, that which fall­<lb/>eth betwixt A C, and the Line parallel unto it &longs;hall alwayes have greater proportion to C K, <lb/>than that which falleth betwixt G K and the Line parallel unto it hath to G B. That, there­<lb/>fore, is manife&longs;t which was affirmed by<emph.end type="italics"/> Archimedes, <emph type="italics"/>to wit, that the Line P I hath unto P H, <lb/>either the &longs;ame proportion that N<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>hath to<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>O, or greater.<emph.end type="italics"/><lb/><arrow.to.target n="marg1236"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1236"></margin.target>D</s></p><p type="main"> <s>Wherefore P H is to H I either double, or le&longs;&longs;e than double.] <lb/><emph type="italics"/>If le&longs;&longs;e than double, let P T be double to T I: The Centre of Gravity of that part of the <lb/>Portion that is within the Liquid &longs;hall be the<emph.end type="italics"/><lb/><figure id="id.040.01.1062.1.jpg" xlink:href="040/01/1062/1.jpg"/><lb/><emph type="italics"/>Point T: But if P H be double to H I, H &longs;hall <lb/>be the Centre of Gravity; And draw H F, and <lb/>prolong it unto the Centre of that part of the Por­<lb/>tion which is above the Liquid, namely, unto G, <lb/>and the re&longs;t is demon&longs;trated as before. </s> <s>And the <lb/>&longs;ame is to be under&longs;tood in the Propo&longs;ition that <lb/>followeth.<emph.end type="italics"/></s></p><p type="main"> <s>The Solid A P O L, therefore, <lb/>&longs;hall turn about, and its Ba&longs;e &longs;hall <lb/>not in the lea&longs;t touch the Surface <lb/>of the Liquid.] <emph type="italics"/>In<emph.end type="italics"/> Tartaglia's <emph type="italics"/>Tran&longs;lation it is rendered<emph.end type="italics"/> ut Ba&longs;is ip&longs;ius non tangent <lb/>&longs;uperficiem humidi &longs;ecundum unum &longs;ignum; <emph type="italics"/>but we have cho&longs;en to read<emph.end type="italics"/> ut Ba&longs;is ip&longs;ius <lb/>nullo modo humidi &longs;uperficiem contingent, <emph type="italics"/>both here, and in the following Propo&longs;itions, <lb/>becau&longs;e the Greekes frequently u&longs;e<emph.end type="italics"/> <foreign lang="greek">w(de\ei)=s, w(de\<gap/></foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">w)dei\s<gap/> & ou)di\n</foreign>: <emph type="italics"/>&longs;o that<emph.end type="italics"/> <foreign lang="greek">ou)de)/sinoudei/s,</foreign> nullus <lb/>e&longs;t; <foreign lang="greek">ou)d<gap/>u(p)e(ro\s</foreign> à nullo, <emph type="italics"/>and &longs;o of others of the like nature.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1063.jpg" pagenum="369"/><p type="head"> <s>PROP. VII. THE OR. VII.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Rightangled Conoid lighter <lb/>than the Liquid, when it &longs;hall have its Axis greater <lb/>than Se&longs;quialter of the Semi-parameter, but le&longs;&longs;e <lb/>than to be unto the &longs;aid Semi-parameter in proportion <lb/>as fi&longs;teen to fower, being demitted into the Liquid &longs;o <lb/>as that its Ba&longs;e be wholly within the Liquid, it &longs;hall <lb/>never &longs;tand &longs;o as that its Ba&longs;e do touch the Surface <lb/>of the Liquid, but &longs;o, that it be wholly within the <lb/>Liquid, and &longs;hall not in the lea&longs;t touch its Surface.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a Portion as hath been &longs;aid; and let it be de­<lb/>mitted into the Liquid, as we have &longs;uppo&longs;ed, &longs;o as that its <lb/>Ba&longs;e do touch the Surface in one Point only: It is to be de­<lb/>mon&longs;trated that the &longs;ame &longs;hall not &longs;o <lb/><figure id="id.040.01.1063.1.jpg" xlink:href="040/01/1063/1.jpg"/><lb/>continue, but &longs;hall turn about in <lb/>&longs;uch manner as that its Ba&longs;e do in no <lb/>wi&longs;e touch the Surface of the Liquid. <lb/></s> <s>For let it be cut thorow its Axis by <lb/>a Plane erect upon the Liquids Sur­<lb/>face: and let the Section be A P O L, <lb/>the Section of a Rightangled <lb/>Cone; the Section of the Liquids <lb/>Surface S L; and the Axis of the <lb/>Portion and Diameter of the Section P F: and let P F be cut in <lb/>R, &longs;o, as that R P may be double to R F, and in <foreign lang="greek">w</foreign> &longs;o as that P F <lb/>may be to R <foreign lang="greek">w</foreign> as fifteen to fower: and draw <foreign lang="greek">w</foreign> K at Right Angles </s></p><p type="main"> <s><arrow.to.target n="marg1237"></arrow.to.target><lb/>to P F: <emph type="italics"/>(a)<emph.end type="italics"/> R <foreign lang="greek">w</foreign> &longs;hall be le&longs;&longs;e than the Semi-parameter. </s> <s>There­<lb/>fore let R H be &longs;uppo&longs;ed equall to the Semi-parameter: and <lb/>draw C O touching the Section in O and parallel unto S L; and <lb/>let N O be parallel unto P F; and fir&longs;t let N O cut K <foreign lang="greek">w</foreign> in the Point <lb/>I, as in the former Schemes: It &longs;hall be demon&longs;trated that N O is <lb/>to O I either &longs;e&longs;quialter, or greater than &longs;e&longs;quialter. </s> <s>Let O I be <lb/>le&longs;&longs;e than double to I N; and let O B be double to B N: and let <lb/>them be di&longs;po&longs;ed like as before. </s> <s>We might likewi&longs;e demon&longs;trate <lb/>that if a Line be drawn thorow R and T it will make Right Angles <lb/>with the Line C O, and with the Surface of the Liquid: Where­<lb/>fore Lines being drawn from the Points B and G parallels unto <lb/>R T, they al&longs;o &longs;hall be Perpendiculars to the Surface of the Liquid: <lb/>The Portion therefore which is above the Liquid &longs;hall move down­ <pb xlink:href="040/01/1064.jpg" pagenum="370"/><figure id="id.040.01.1064.1.jpg" xlink:href="040/01/1064/1.jpg"/><lb/>wards according to that &longs;ame Perpendicular <lb/>which pa&longs;&longs;eth thorow B; and the Portion <lb/>which is within the Liquid &longs;hall move up­<lb/>wards acording to that pa&longs;&longs;ing thorow G: <lb/>From whence it is manife&longs;t that the Solid <lb/>&longs;hall turn about in &longs;uch manner, as that <lb/>its Ba&longs;e &longs;hall in no wi&longs;e touch the Surface <lb/>of the Liquid; for that now when it touch­<lb/>eth but in one Point only, it moveth down­<lb/>wards on the part towards L. </s> <s>And though <lb/>N O &longs;hould not cut <foreign lang="greek">w</foreign> K, yet &longs;hall the &longs;ame hold true.</s></p><p type="margin"> <s><margin.target id="marg1237"></margin.target>(a) <emph type="italics"/>By 10 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="head"> <s>PROP. VIII. THE OR. VIII.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Rightangled Conoid, when it <lb/>&longs;hall have its Axis greater than &longs;e&longs;quialter of the Se­<lb/>mi-parameter, but le&longs;&longs;e than to be unto the &longs;aid Semi­<lb/>parameter, in proportion as fifteen to fower, if it <lb/>have a le&longs;&longs;er proportion in Gravity to the Liquid, than <lb/>the Square made of the Exce&longs;&longs;e by which the Axis is <lb/>greater than Se&longs;quialter of the Semi-parameter hath <lb/>to the Square made of the Axis, being demitted into <lb/>the Liquid, &longs;o as that its Ba&longs;e touch not the Liquid, <lb/>it &longs;hall neither return to Perpendicularity, nor conti­<lb/>nue inclined, &longs;ave only when the Axis makes an <lb/>Angle with the Surface of the Liquid, equall to that <lb/>which we &longs;hall pre&longs;ently &longs;peak of.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a Portion as hath been &longs;aid; and let B D be equall <lb/>to the Axis: and let B K be double to K D; and R K equall <lb/><arrow.to.target n="marg1238"></arrow.to.target><lb/>to the Semi-parameter: and let C B be Se&longs;quialter of B R: <lb/>C D &longs;hall be al&longs;o Sefquialter of K R. </s> <s>And as the Portion is to the <lb/>Liquid in Gravity, &longs;o let the Square F Q be to the Square D B; <lb/>and let F be double to Q: It is manife&longs;t, therefore, that F Q hath <lb/>to D B, le&longs;s proportion than C B hath to B D; For C B is the <lb/>Exce&longs;s by which the Axis is greater than Se&longs;quialter of the Semi­<lb/><arrow.to.target n="marg1239"></arrow.to.target><lb/>parameter: And, therefore, F Q is le&longs;s than B C; and, for the <lb/><arrow.to.target n="marg1240"></arrow.to.target><lb/>&longs;ame rea&longs;on, F is le&longs;s than B R. </s> <s>Let R <foreign lang="greek">y</foreign> be equall to F; and draw <lb/><foreign lang="greek">y</foreign> E perpendicular to B D; which let be in power or contence the <lb/>half of that which the Lines K R and <foreign lang="greek">y</foreign> B containeth; and <lb/>draw a Line from B to E: It is to be demon&longs;trated, that the <pb xlink:href="040/01/1065.jpg" pagenum="371"/>Portion demitted into the Liquid, like as hath been &longs;aid, &longs;hall &longs;tand <lb/>enclined &longs;o as that its Axis do make an Angle with the Surface of <lb/>the Liquid equall unto the Angle E B <foreign lang="greek">*y.</foreign> For demit any Portion <lb/>into the Liquid &longs;o as that its Ba&longs;e <lb/><figure id="id.040.01.1065.1.jpg" xlink:href="040/01/1065/1.jpg"/><lb/>touch not the Liquids Surface; <lb/>and, if it can be done, let the <lb/>Axis not make an Angle with the <lb/>Liquids Surface equall to the <lb/>Angle E B <foreign lang="greek">*y</foreign>; but fir&longs;t, let it be <lb/>greater: and the Portion being <lb/>cut thorow the Axis by a Plane e­<lb/>rect unto [<emph type="italics"/>or upon<emph.end type="italics"/>] the Surface of <lb/>the Liquid, let the Section be A P <lb/>O L the Section of a Rightangled <lb/>Cone; the Section of the Surface of the Liquid X S; and let the <lb/>Axis of the Portion and Diameter of the Section be N O: and <lb/>draw P Y parallel to X S, and touching the Section A P O L in P; <lb/>and P M parallel to N O; and P I perpendicular to N O: and <lb/>moreover, let B R be equall to O <foreign lang="greek">w,</foreign> and R K to T <foreign lang="greek">w;</foreign> and let <foreign lang="greek">w</foreign> H <lb/>be perpendicular to the Axis. </s> <s>Now becau&longs;e it hath been &longs;uppo&longs;ed <lb/><arrow.to.target n="marg1241"></arrow.to.target><lb/>that the Axis of the Portion doth make an Angle with the Surface <lb/>of the Liquid greater than the Angle B, the Angle P Y I &longs;hall be <lb/>greater than the Angle B: Therefore the Square P I hath greater <lb/><arrow.to.target n="marg1242"></arrow.to.target><lb/>proportion to the Square Y I, than the Square E <foreign lang="greek">*y</foreign> hath to the <lb/>Square <foreign lang="greek">*y</foreign> B: But as the Square P I is to the Square Y I, &longs;o is the <lb/><arrow.to.target n="marg1243"></arrow.to.target><lb/>Line K R unto the Line I Y; and as the Square E <foreign lang="greek">*y</foreign> is to the Square <lb/><arrow.to.target n="marg1244"></arrow.to.target><lb/><foreign lang="greek">*y</foreign> B, &longs;o is half of the Line K R unto the Line <foreign lang="greek">*y</foreign> B: Wherefore <lb/><emph type="italics"/>(a)<emph.end type="italics"/> K R hath greater proportion to I Y, than the half of K R hath <lb/><arrow.to.target n="marg1245"></arrow.to.target><lb/>to <foreign lang="greek">*y</foreign> B: And, con&longs;equently, I Y isle&longs;&longs;e than the double of <foreign lang="greek">*y</foreign> B, <lb/>and is the double of O I: Therefore O I is le&longs;&longs;e than <foreign lang="greek">*y</foreign> B; and I <foreign lang="greek">w</foreign><lb/><arrow.to.target n="marg1246"></arrow.to.target><lb/>greater than <foreign lang="greek">*y</foreign> R: but <foreign lang="greek">*y</foreign> R is equall to F: Therefore I <foreign lang="greek">w</foreign> is greater <lb/><arrow.to.target n="marg1247"></arrow.to.target><lb/>than F. </s> <s>And becau&longs;e that the Portion is &longs;uppo&longs;ed to be in Gra­<lb/>vity unto the Liquid, as the Square F Q is to the Square B D; and <lb/>&longs;ince that as the Portion is to the Liquid in Gravity, &longs;o is the part <lb/>thereof &longs;ubmerged unto the whole Portion; and in regard that as <lb/>the part thereof &longs;ubmerged is to the whole, &longs;o is the Square P M to <lb/>the Square O N; It followeth, that the Square P M is to the Square <lb/>N O, as the Square F Q is to the Square B D: And therefore F <lb/><arrow.to.target n="marg1248"></arrow.to.target><lb/>Q is equall to P M: But it hath been demon&longs;trated that P H is <lb/><arrow.to.target n="marg1249"></arrow.to.target><lb/>greater than F: It is manife&longs;t, therefore, that P M is le&longs;&longs;e than <lb/>&longs;e&longs;quialter of P H: And con&longs;equently that P H is greater than <lb/>the double of H M. </s> <s>Let P Z be double to Z M: T &longs;hall be the Cen­<lb/>tre of Gravity of the whole Solid; the Centre of that part of it <lb/>which is within the Liquid, the Point Z; and of the remaining <lb/><arrow.to.target n="marg1250"></arrow.to.target><lb/>part the Centre &longs;hall be in the Line Z T prolonged unto G. </s> <s>In <pb xlink:href="040/01/1066.jpg" pagenum="372"/>the &longs;ame manner we might demon­<lb/><figure id="id.040.01.1066.1.jpg" xlink:href="040/01/1066/1.jpg"/><lb/>&longs;trate the <emph type="italics"/>L<emph.end type="italics"/>ine T H to be perpendi­<lb/>cular unto the Surface of the Liquid: <lb/>and that the Portion demerged with­<lb/>in the <emph type="italics"/>L<emph.end type="italics"/>iquid moveth or a&longs;cend­<lb/>eth out of the <emph type="italics"/>L<emph.end type="italics"/>iquid according to <lb/>the Perpendicular that &longs;hall be <lb/>drawn thorow Z unto the Surface <lb/>of the Liquid; and that the part <lb/>that is above the Liquid de&longs;cendeth <lb/>into the Liquid according to that <lb/>drawn thorow G: therefore the Portion will not continue &longs;o inclined <lb/>as was &longs;uppo&longs;ed: But neither &longs;hall it return to Rectitude or Per­<lb/>pendicularity; For that of the Perpendiculars drawn thorow Z and <lb/>G, that pa&longs;&longs;ing thorow Z doth fall on tho&longs;e parts which are to­<lb/>wards L; and that that pa&longs;&longs;eth thorow G on tho&longs;e towards A: <lb/>Wherefore it followeth that the Centre Z do move upwards, <lb/>and G downwards: Therefore the parts of the whole Solid which <lb/>are towards A &longs;hall move downwards, and tho&longs;e towards L up­<lb/>wards. </s> <s>Again let the Propo&longs;ition run in other termes; and let <lb/>the Axis of the Portion make an Angle with the Surface of the <lb/><arrow.to.target n="marg1251"></arrow.to.target><lb/>Liquid le&longs;&longs;e than that which is at B. </s> <s>Therefore the Square P I <lb/>hath le&longs;&longs;er Proportion unto the Square <lb/><figure id="id.040.01.1066.2.jpg" xlink:href="040/01/1066/2.jpg"/><lb/>I Y, than the Square E <foreign lang="greek">*y</foreign> hath to the <lb/>Square <foreign lang="greek">*y</foreign> B: Wherefore K R hath <lb/>le&longs;&longs;er proportion to I Y, than the half <lb/>of K R hath to <foreign lang="greek">*y</foreign> B: And, for the <lb/>&longs;ame rea&longs;on, I Y is greater than dou­<lb/>ble of <foreign lang="greek">*y</foreign> B: but it is double of O I: <lb/>Therefore O I &longs;hall be greater than <lb/><foreign lang="greek">*y</foreign> B: But the Totall O <foreign lang="greek">w</foreign> is equall <lb/>to R B, and the Remainder <foreign lang="greek">w</foreign> I le&longs;&longs;e <lb/>than <foreign lang="greek">y</foreign> R: Wherefore P H &longs;hall al&longs;o <lb/>be le&longs;&longs;e than F. And, in regard that <lb/>M P is equall to F Q, it is manife&longs;t that P M is greater than &longs;e&longs;qui­<lb/>alter of P H; and that P H is le&longs;&longs;e than double of <emph type="italics"/>H<emph.end type="italics"/> M. <emph type="italics"/>L<emph.end type="italics"/>et P Z <lb/>be double to Z M. </s> <s>The Centre of Gravity of the whole Solid &longs;hall <lb/>again be T; that of the part which is within the Liquid Z; and <lb/>drawing a Line from Z to T, the Centre of Gravity of that which <lb/>is above the Liquid &longs;hall be found in that Line portracted, that is <lb/>in G: Therefore, Perpendiculars being drawn thorow Z and G <lb/><arrow.to.target n="marg1252"></arrow.to.target><lb/>unto the Surface of the Liquid that are parallel to T H, it followeth <lb/>that the &longs;aid Portion &longs;hall not &longs;tay, but &longs;hall turn about till <lb/>that its Axis do make an Angle with the Waters Surface greater than <lb/>that which it now maketh. </s> <s>And becau&longs;e that when before we <pb xlink:href="040/01/1067.jpg" pagenum="373"/>did &longs;uppo&longs;e that it made an Angle greater than the Angle B, the <lb/>Poriton did not re&longs;t then neither; It is manife&longs;t that it &longs;hall &longs;tay <lb/><arrow.to.target n="marg1253"></arrow.to.target><lb/>or re&longs;t when it &longs;hall make an Angle eqnall to B. </s> <s>For &longs;o &longs;hall I O <lb/>be equall to <foreign lang="greek">*y</foreign> <emph type="italics"/>B<emph.end type="italics"/>; and <foreign lang="greek">w</foreign> I equall to <lb/><figure id="id.040.01.1067.1.jpg" xlink:href="040/01/1067/1.jpg"/><lb/><foreign lang="greek">*y</foreign> R; and P H equall to F: There­<lb/>fore <emph type="italics"/>M P<emph.end type="italics"/> &longs;hall be &longs;e&longs;quialter of <emph type="italics"/>P H,<emph.end type="italics"/><lb/>and <emph type="italics"/>P H<emph.end type="italics"/> double of H M: And there­<lb/>fore &longs;ince H is the Centre of Gravity <lb/>of that part of it which is within the <lb/>Liquid, it &longs;hall move upwards along <lb/>the &longs;ame <emph type="italics"/>P<emph.end type="italics"/>erpendicular according to <lb/>which the whole <emph type="italics"/>P<emph.end type="italics"/>ortion moveth; <lb/>and along the &longs;ame al&longs;o &longs;hall the part <lb/>which is above move downwards: <lb/>The <emph type="italics"/>P<emph.end type="italics"/>ortion therefore &longs;hall re&longs;t; for­<lb/>a&longs;much as the parts are not repul&longs;ed by each other.</s></p><p type="margin"> <s><margin.target id="marg1238"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1239"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1240"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1241"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1242"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1243"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1244"></margin.target>G</s></p><p type="margin"> <s><margin.target id="marg1245"></margin.target>(a) <emph type="italics"/>By 13. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1246"></margin.target>H</s></p><p type="margin"> <s><margin.target id="marg1247"></margin.target>K</s></p><p type="margin"> <s><margin.target id="marg1248"></margin.target>L</s></p><p type="margin"> <s><margin.target id="marg1249"></margin.target>M</s></p><p type="margin"> <s><margin.target id="marg1250"></margin.target>N</s></p><p type="margin"> <s><margin.target id="marg1251"></margin.target>O</s></p><p type="margin"> <s><margin.target id="marg1252"></margin.target>P</s></p><p type="margin"> <s><margin.target id="marg1253"></margin.target>Q</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s>And let <emph type="italics"/>C B<emph.end type="italics"/> be &longs;e&longs;quialter of <emph type="italics"/>B R<emph.end type="italics"/>: C D &longs;hall al&longs;o be &longs;e&longs;quialter <lb/><arrow.to.target n="marg1254"></arrow.to.target><lb/>of K R.] <emph type="italics"/>In the Tran&longs;lation it is read thus:<emph.end type="italics"/> Sit autem & CB quidem hemeolia <lb/>ip&longs;ius B R: C D autem ip&longs;ius K R. <emph type="italics"/>But we at the reading of this pa&longs;&longs;age have thought <lb/>fit thus to correctit; for it is not &longs;uppo&longs;ed &longs;o to be, but from the things &longs;uppo&longs;ed is proved to <lb/>be &longs;o. </s> <s>For if B<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>be double of<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>D, D B &longs;hall be &longs;e&longs;quialter of B<emph.end type="italics"/> <foreign lang="greek">y.</foreign> <emph type="italics"/>And becau&longs;e E B is <lb/>&longs;e&longs;quialter of B R, it followeth that the<emph.end type="italics"/> (a) <emph type="italics"/>Remainder C D is &longs;e&longs;quialter of<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>R; that is, of<emph.end type="italics"/><lb/><arrow.to.target n="marg1255"></arrow.to.target><lb/><emph type="italics"/>the Semi-parameter: Wherefore B C &longs;hall be the Exce&longs;&longs;e by which the Axis is greater than <lb/>&longs;e&longs;quialter of the Semi-parameter.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1254"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1255"></margin.target>(a) <emph type="italics"/>By 19. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>And therefore F Q is le&longs;&longs;e than <emph type="italics"/>B C.] For in regard that the Portion hath<emph.end type="italics"/><lb/><arrow.to.target n="marg1256"></arrow.to.target><lb/><emph type="italics"/>the &longs;ame proportion in Gravity unto the Liquid, as the Square F Q hath to the Square D B; <lb/>and hath le&longs;&longs;er proportion than the Square made of the Exce&longs;&longs;e by which the Axis <lb/>is greater than Se&longs;quialter of the Semi parameter, hath to the Square made of the Axis; that <lb/>is, leßer than the Square C B hath to the Square B D; for the Line B D was &longs;uppo&longs;ed to be <lb/>equall unto the Axis: Therefore the Square F Q &longs;hall have to the Square D B le&longs;&longs;er proporti­<lb/>on than the Sqnare C B to the &longs;ame Square B D: And therefore the Square<emph.end type="italics"/> (b) <emph type="italics"/>F Q &longs;hall be<emph.end type="italics"/><lb/><arrow.to.target n="marg1257"></arrow.to.target><lb/><emph type="italics"/>leße than the Square C B: And, for that rea&longs;on, the Line F Q &longs;hall be leße than B C.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1256"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1257"></margin.target>(b) <emph type="italics"/>By 8 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>And, for the &longs;ame rea&longs;on, F is le&longs;&longs;e than <emph type="italics"/>B R.] For C B being &longs;e&longs;qui-<emph.end type="italics"/><lb/><arrow.to.target n="marg1258"></arrow.to.target><lb/><emph type="italics"/>alter of B R, and F Q &longs;e&longs;quialter of F<emph.end type="italics"/>: (c) F <emph type="italics"/>Q &longs;hall be likewi&longs;e le&longs;&longs;e than B C; and F<emph.end type="italics"/><lb/><arrow.to.target n="marg1259"></arrow.to.target><lb/><emph type="italics"/>leße than B R.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1258"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1259"></margin.target>(c) <emph type="italics"/>By 14 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>Now becau&longs;e it hath been &longs;uppo&longs;ed that the Axis of the <emph type="italics"/>P<emph.end type="italics"/>ortion <lb/><arrow.to.target n="marg1260"></arrow.to.target><lb/>doth make an Angle with the Surface of the Liquid greater than <lb/>the Angle <emph type="italics"/>B,<emph.end type="italics"/> the Angle <emph type="italics"/>P Y I<emph.end type="italics"/> &longs;hall be greater than the Angle <emph type="italics"/>B.] <lb/>For the Line P Y being parallel to the Surface of the Liquid, that is, to XS<emph.end type="italics"/>; (d) <emph type="italics"/>the Angle<emph.end type="italics"/><lb/><arrow.to.target n="marg1261"></arrow.to.target><lb/><emph type="italics"/>P Y I &longs;hall be equall to the Angle contained betwixt the Diameter of the Portion N O, and the <lb/>Line X S: And therefore &longs;hall be greater than the Angle B.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1260"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1261"></margin.target>(d) <emph type="italics"/>By 29 of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="main"> <s>Therefore the Square <emph type="italics"/>P I<emph.end type="italics"/> hath greater proportion to the Square <lb/><arrow.to.target n="marg1262"></arrow.to.target><lb/>Y I, than the Square E <foreign lang="greek">*y</foreign> hath to the Square <foreign lang="greek">*y</foreign> <emph type="italics"/>B] Let the Triangles P I Y <lb/>and E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B, be de&longs;cribed apart: And &longs;eeing that the Angle P Y I is greater <lb/>than the Angle E B<emph.end type="italics"/> <foreign lang="greek">y,</foreign> <emph type="italics"/>unto the Line I Y, and at the Point Y a&longs;&longs;igned in<emph.end type="italics"/><lb/><figure id="id.040.01.1067.2.jpg" xlink:href="040/01/1067/2.jpg"/><lb/><emph type="italics"/>the &longs;ame, make the Angle V Y I equall to the Angle E B<emph.end type="italics"/> <foreign lang="greek">y</foreign>; <emph type="italics"/>But <lb/>the Right Angle at I, is equall unto the Right Angle at<emph.end type="italics"/> <foreign lang="greek">y;</foreign> <emph type="italics"/>therefore the<emph.end type="italics"/> <pb xlink:href="040/01/1068.jpg" pagenum="374"/><emph type="italics"/>Remaining Angle Y V I is equall to the Remaining Angle B E<emph.end type="italics"/> <foreign lang="greek">y.</foreign> <emph type="italics"/>And therefore the<emph.end type="italics"/><lb/><arrow.to.target n="marg1263"></arrow.to.target><lb/>(e) <emph type="italics"/>Line V I hath to the Line I Y the &longs;ame proportion that the Line E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>hath to<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B: But <lb/>the<emph.end type="italics"/> (f) <emph type="italics"/>Line P I, which is greater than V I, hath unto I Y greater proportion than V I hath un-<emph.end type="italics"/><lb/><arrow.to.target n="marg1264"></arrow.to.target><lb/><emph type="italics"/>to the &longs;ame: Therefore<emph.end type="italics"/> (g) <emph type="italics"/>T I &longs;hall have greater proportion unto I Y, than E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>hath to<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B: <lb/>And, by the &longs;ame rea&longs;on, the Square T I &longs;hall have greater proportion to the Square I Y, than<emph.end type="italics"/><lb/><arrow.to.target n="marg1265"></arrow.to.target><lb/><emph type="italics"/>the Square E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>hath to the Square<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B.<emph.end type="italics"/><lb/><arrow.to.target n="marg1266"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1262"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1263"></margin.target>(e) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1264"></margin.target>(f) <emph type="italics"/>By 8. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1265"></margin.target>(g) <emph type="italics"/>By 13 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1266"></margin.target>F</s></p><p type="main"> <s>But as the Square P I is to the Square Y I, &longs;o is the Line K R unto <lb/>the Line I Y] <emph type="italics"/>For by 11. of the fir&longs;t of our<emph.end type="italics"/> Conicks, <emph type="italics"/>the Square P I is equall <lb/>to the Rectangle contained under the Line I O, and under the Parameter; which <lb/>we &longs;uppo&longs;ed to be eqnall to the Semi-parameter; that is, the double of K R<emph.end type="italics"/>: </s></p><p type="main"> <s><arrow.to.target n="marg1267"></arrow.to.target><lb/><emph type="italics"/>But I Y is double of I O, by 33 of the &longs;ame: And, therefore, the<emph.end type="italics"/> (h) <emph type="italics"/>Rectangle made of K R <lb/>and I Y, is equall to the Rectangle contained under the Line I O, and under the Parameter;<emph.end type="italics"/><lb/><arrow.to.target n="marg1268"></arrow.to.target><lb/><emph type="italics"/>that is, to the Square P I: But as the<emph.end type="italics"/> (i) <emph type="italics"/>Rectangle compounded of K R and I Y is to the <lb/>Square I Y, &longs;o is the Line K R unto the Line I Y: Therefore the Line K R &longs;hall have unto I <lb/>Y, the &longs;ame proportion that the Rectangle compounded of K R and I Y; that is, the Square P I <lb/>hath to the Square I Y.<emph.end type="italics"/><lb/><arrow.to.target n="marg1269"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1267"></margin.target>(h) <emph type="italics"/>By 26. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1268"></margin.target>(i) <emph type="italics"/>By<emph.end type="italics"/> Lem. </s> <s>22 <emph type="italics"/>of <lb/>the tenth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1269"></margin.target>G</s></p><p type="main"> <s>And as the Square E <foreign lang="greek">*y</foreign> is to the Square <foreign lang="greek">*y</foreign> B, &longs;o is half of the <lb/>Line K R unto the Line <foreign lang="greek">y</foreign> B.] <emph type="italics"/>For the Square E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>having been &longs;uppo&longs;ed equall <lb/>to half the Rectangle contained under the Line K R and<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B; that is, to that contained under <lb/>the half of K R and the Line<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B; and &longs;eeing that as the<emph.end type="italics"/> (k) <emph type="italics"/>Rectangle made of half K R<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1270"></arrow.to.target><lb/><emph type="italics"/>and of B<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>is to the Square<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B, &longs;o is half K R unto the Line<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B; the half of K R &longs;hall have <lb/>the &longs;ame proportion to<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B, as the Square E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>hath to the Square<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B.<emph.end type="italics"/><lb/><arrow.to.target n="marg1271"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1270"></margin.target>(k) <emph type="italics"/>By<emph.end type="italics"/> Lem. </s> <s>22 <emph type="italics"/>of <lb/>the tenth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1271"></margin.target>H</s></p><p type="main"> <s>And, con&longs;equently, I Y is le&longs;&longs;e than the double of <foreign lang="greek">y</foreign> B.] <lb/><emph type="italics"/>For, as half K R is to<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B, &longs;o is K R to another Line: it &longs;hall be<emph.end type="italics"/> (1) <emph type="italics"/>greater than I Y; that<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1272"></arrow.to.target><lb/><emph type="italics"/>is, than that to which K R hath le&longs;&longs;er proportion; and it &longs;hall be double of<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B: Therefore <lb/>I Y is le&longs;&longs;e than the double of<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B.<emph.end type="italics"/><lb/><arrow.to.target n="marg1273"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1272"></margin.target>(l) <emph type="italics"/>By 10 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1273"></margin.target>K</s></p><p type="main"> <s>And I <foreign lang="greek">w</foreign> greater than <foreign lang="greek">y</foreign> R.] <emph type="italics"/>For O having been &longs;uppo&longs;ed equall to B R, <lb/>if from B R,<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B be taken, and from O<emph.end type="italics"/> <foreign lang="greek">w,</foreign> <emph type="italics"/>O I, which is le&longs;&longs;er than B, be taken; the <lb/>Remainder I<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>&longs;hall be greater than the Remainder<emph.end type="italics"/> <foreign lang="greek">*y</foreign> <emph type="italics"/>R.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1274"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1274"></margin.target>L</s></p><p type="main"> <s>And, therefore, F Q is equall to P M.] <emph type="italics"/>By the fourteenth of the fifth of<emph.end type="italics"/><lb/>Euclids <emph type="italics"/>Elements: For the Line O N is equall to B D.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1275"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1275"></margin.target>M</s></p><p type="main"> <s>But it hath been demon&longs;trated that P H is greater than F.] <lb/><emph type="italics"/>For it was demon&longs;trated that I<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>is greater than F: And P H is equall to I<emph.end type="italics"/> <foreign lang="greek">w.</foreign></s></p><p type="main"> <s><arrow.to.target n="marg1276"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1276"></margin.target>N</s></p><p type="main"> <s>In the &longs;ame manner we might demon&longs;trate the Line T H <lb/>to be Perpendicular unto the Surface of the Liquid.] <emph type="italics"/>For T<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>is equall <lb/>to K R; that is, to the Semi-parameter: And, therefore, by the things above demonstrated, <lb/>the Line T H &longs;hall be drawn Perpendicular unto the Liquids Surface.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1277"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1277"></margin.target>O</s></p><p type="main"> <s>Therefore, the Square P I hath le&longs;&longs;er proportion unto the <lb/>Square I Y, than the Square E <foreign lang="greek"><gap/></foreign> hath to the Square <foreign lang="greek">y</foreign> B.] <lb/><emph type="italics"/>The&longs;e, and other particulars of the like nature, that follow both in this and the following <lb/>Propo&longs;itions, &longs;hall be demon&longs;trated by us no otherwi&longs;e than we have done above.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1278"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1278"></margin.target>P</s></p><p type="main"> <s>Therefore Perpendiculars being drawn thorow Z and G, unto <lb/>the Surface of the Liquid, that are parallel to T H, it followeth <lb/>that the &longs;aid Portion &longs;hall not &longs;tay, but &longs;hall turn about till that its <lb/>Axis do make an Angle with the Waters Surface greater than that <lb/>which it now maketh.] <emph type="italics"/>For in that the Line drawn thorow G, doth fall perpendicu­<lb/>larly towards tho&longs;e parts which are next to L; but that thorow Z, towards tho&longs;e next to A; <lb/>It is nece&longs;&longs;ary that the Centre G do move downwards, and Z upwards: and, therefore, the <lb/>parts of the Solid next to L &longs;hall move downwards, and tho&longs;e towards A upwards, that the <lb/>Axis may makea greater Angle with the Surface of the Liquid.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1279"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1279"></margin.target>Q</s></p><p type="main"> <s>For &longs;o &longs;hall I O be equall to <foreign lang="greek">y</foreign> B; and <foreign lang="greek">w</foreign> I equall to I R; and <lb/>P H equall to F.] <emph type="italics"/>This plainly appeareth in the third Figure, which is added by us.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1069.jpg" pagenum="375"/><p type="head"> <s>PROP. IX. THE OR. IX.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Rightangled Conoid, when it <lb/>&longs;hall have its Axis greater than Se&longs;quialter of the <lb/>Semi-parameter, but le&longs;&longs;er than to be unto the &longs;aid <lb/>Semi-parameter in proportion as fifteen to four, and <lb/>hath greater proportion in Gravity to the Liquid, than <lb/>the exce&longs;s by which the Square made of the Axis is <lb/>greater than the Square made of the Exce&longs;s, by which <lb/>the Axis is greater than Se&longs;quialter of the Semi­<lb/>parameter, hath to the Square made of the Axis, <lb/>being demitted into the Liquid, &longs;o as that its Ba&longs;e <lb/>be wholly within the Liquid, and being &longs;et inclining<lb/>it &longs;hall neither turn about, &longs;o as that its Axis &longs;tand <lb/>according to the Perpendicular, nor remain inclined, <lb/>&longs;ave only when the Axis makes an Angle with <lb/>the Surface of the Liquid, equall to that aßigned <lb/>as before.<emph.end type="italics"/></s></p><p type="main"> <s>Let there be a Portion as was &longs;aid; and &longs;uppo&longs;e D B equall to <lb/>the Axis of the <emph type="italics"/>P<emph.end type="italics"/>ortion: and let B K be double to K D; and <lb/>K R equall to the Semi-parameter: and C B Se&longs;quialter of <lb/>B R. </s> <s>And as the Portion is to the Liquid in Gravity, &longs;o let the Ex­<lb/>ce&longs;&longs;e by which the Square B D exceeds the Square F Q be to the <lb/>Square B D: and let F be double to Q: It is manife&longs;t, therefore, <lb/>that the Exce&longs;&longs;e by which the <lb/><figure id="id.040.01.1069.1.jpg" xlink:href="040/01/1069/1.jpg"/><lb/>Square B D is greater than the <lb/>Square B C hath le&longs;ser proportion <lb/>to the Square B D, than the Exce&longs;s <lb/>by which the Square B D is greater <lb/>than the Square F Q hath to the <lb/>Square B D; for B C is the Exce&longs;s <lb/>by which the Axis of the Portion is <lb/>greater than Se&longs;quialter of the <lb/>Semi-parameter: And, therefore, </s></p><p type="main"> <s><arrow.to.target n="marg1280"></arrow.to.target><lb/>the Square B D doth more exceed <lb/>the Square F Q, than doth the <lb/>Square B C: And, con&longs;equently, the Line F Q is le&longs;s than B C; <pb xlink:href="040/01/1070.jpg" pagenum="376"/>and F le&longs;s than B R. </s> <s>Let R <foreign lang="greek">*y</foreign> be equall to F; and draw <foreign lang="greek">*y</foreign> E <lb/>perpendicular to B D; which let be in power the half of that <lb/>which the Lines K R and <foreign lang="greek">*y</foreign> B containeth; and draw a Line from <lb/>B to E: I &longs;ay that the Portion demitted into the Liquid, &longs;o as that <lb/>its Ba&longs;e be wholly within the Liquid, &longs;hall &longs;o &longs;tand, as that its Axis <lb/>do make an Angle with the Liquids Surface, equall to the Angle B. <lb/></s> <s>For let the <emph type="italics"/>P<emph.end type="italics"/>ortion be demitted into the Liquid, as hath been &longs;aid; <lb/>and let the Axis not make an Angle with the Liquids Surface, equall <lb/>to B, but fir&longs;t a greater: and the &longs;ame being cut thorow the Axis <lb/>by a Plane erect unto the Surface of the Liquid, let the Section of <lb/>the Portion be A P O L, the Section of a Rightangled Cone; the <lb/>Section of the Surface of the Liquid <foreign lang="greek">*g</foreign> I; and the Axis of the <lb/>Portion and Diameter of the Section N O; which let be cut in <lb/>the Points <foreign lang="greek">w</foreign> and T, as before: and draw Y P, parallelto <foreign lang="greek">*g</foreign> I, and <lb/>touching the Section in P, and MP parallel to N O, and P S perpen­<lb/>dicular to the Axis. </s> <s>And becau&longs;e now that the Axis of the Portion <lb/>maketh an <emph type="italics"/>A<emph.end type="italics"/>ngle with the Liquids Surface greater than the Angle <lb/>B, the Angle S Y P &longs;hall al&longs;o be greater than the Angle B: And, <lb/>therefore, the Square P S hath greater proportion to the Square <lb/><arrow.to.target n="marg1281"></arrow.to.target><lb/>S Y, than the Square <foreign lang="greek">*y</foreign> E hath to the Square <foreign lang="greek">*y</foreign> B: And, for that <lb/>cau&longs;e, K R hath greater proportion to S Y, than the half of K R <lb/>hath to <foreign lang="greek">*y</foreign> B: Therefore, S Y is le&longs;s than the double of <foreign lang="greek">*y</foreign> B; and <lb/><arrow.to.target n="marg1282"></arrow.to.target><lb/>S O le&longs;s than <foreign lang="greek">y</foreign> B: <emph type="italics"/>A<emph.end type="italics"/>nd, therefore, S <foreign lang="greek">w</foreign> is greater than R <foreign lang="greek">y</foreign>; and <lb/><arrow.to.target n="marg1283"></arrow.to.target><lb/>P H greater than F. <emph type="italics"/>A<emph.end type="italics"/>nd, becau&longs;e that the <emph type="italics"/>P<emph.end type="italics"/>ortion hath the <lb/>&longs;ame proportion in Gravity unto the Liquid, that the Exce&longs;s by <lb/>which the Square B D, is greater than the Square F Q, hath unto <lb/>the Square B D; and that as the Portion is in proportion to the <lb/>Liquid in Gravity, &longs;o is the part thereof &longs;ubmerged unto the whole <lb/>Portion; It followeth that the part &longs;ubmerged, hath the &longs;ame <lb/>proportion to the whole <emph type="italics"/>P<emph.end type="italics"/>ortion, that the Exce&longs;s by which the <lb/>Square B D is greater than the Square F Q hath unto the Square <lb/>B D: <emph type="italics"/>A<emph.end type="italics"/>nd, therefore, the whole <emph type="italics"/>P<emph.end type="italics"/>ortion &longs;hall have the &longs;ame propor­<lb/><arrow.to.target n="marg1284"></arrow.to.target><lb/>tion to that part which is above the <lb/><figure id="id.040.01.1070.1.jpg" xlink:href="040/01/1070/1.jpg"/><lb/>Liquid, that the Square B D hath to <lb/>the Square F Q: But as the whole <lb/>Portion is to that part which is above <lb/>the Liquid, &longs;o is the Square N O unto <lb/>the Square P M: Therefore, P M <lb/>&longs;hall be equall to F Q: But it <lb/>hath been demon&longs;trated, that P H is <lb/>greater than F. And, therefore, <lb/>MH &longs;hall be le&longs;s than <expan abbr="q;">que</expan> and P H <lb/>greater than double of H M. </s> <s>Let <lb/>therefore, P Z be double to Z M: <pb xlink:href="040/01/1071.jpg" pagenum="377"/>and drawing a Line from Z to T pro­<lb/><figure id="id.040.01.1071.1.jpg" xlink:href="040/01/1071/1.jpg"/><lb/>long it unto G. </s> <s>The Centre of <lb/>Gravity of the whole Portion &longs;hall <lb/>be T; of that part which is above <lb/>the Liquid Z; and of the Remain­<lb/>der which is within the Liquid, the <lb/>Centre &longs;hall be in the Line Z T pro­<lb/>longed; let it be in G: It &longs;hall be <lb/>demon&longs;trated, as before, that T H <lb/>is perpendicular to the Surface of <lb/>the Liquid, and that the Lines <lb/>drawn thorow Z and G parallel to the &longs;aid T H, are al&longs;o perpen­<lb/>diculars unto the &longs;ame: Therefore, the Part which is above the <lb/>Liquid &longs;hall move downwards, along that which pa&longs;seth thorow Z; <lb/>and that which is within it, &longs;hall move upwards, along that which <lb/>pa&longs;seth thorow G: And, therefore, the Portion &longs;hall not remain <lb/>&longs;o inclined, nor &longs;hall &longs;o turn about, as that its Axis be perpendicular <lb/><arrow.to.target n="marg1285"></arrow.to.target><lb/>unto the Surface of the Liquid; for the parts towards L &longs;hall move <lb/>downwards, and tho&longs;e towards <emph type="italics"/>A<emph.end type="italics"/> upwards; as may appear by <lb/>the things already demon&longs;trated. </s> <s>And, if the Axis &longs;hould make <lb/>an Angle with the Surface of the Liquid, le&longs;s than the Angle B; <lb/>it &longs;hall in like manner be demon&longs;trated, that the Portion will not <lb/><arrow.to.target n="marg1286"></arrow.to.target><lb/>re&longs;t, but incline untill that its Axis do make an Angle with the <lb/>Surface of the Liquid, equall to the Angle B.</s></p><p type="margin"> <s><margin.target id="marg1280"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1281"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1282"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1283"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1284"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1285"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1286"></margin.target>G</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s>And, therefore, the Square B D doth more exceed the Square <lb/><arrow.to.target n="marg1287"></arrow.to.target><lb/>F Q, than doth the Square B C: And, con&longs;equently, the Line <lb/>F Q, is le&longs;s than B C; and F le&longs;s than B R.] <emph type="italics"/>Becau&longs;e the Exce&longs;s by <lb/>which the Square B D exceedeth the Square B C; having le&longs;s proportion unto the Square B D, <lb/>than the Exce&longs;s by which the Square B D exceedeth the Square F Q, hath to the &longs;aid Square<emph.end type="italics"/>; <lb/>(a) <emph type="italics"/>the Exce&longs;s by which the Square B D exceedeth the Square B C &longs;hall be le&longs;s than the Exce&longs;s<emph.end type="italics"/><lb/><arrow.to.target n="marg1288"></arrow.to.target><lb/><emph type="italics"/>by which it exceedeth the Square F Q: Therefore, the Square F Q is le&longs;s than the Square B C: <lb/>and, con&longs;quently, the Line F Q le&longs;s than the Line BC: But F Q hath the &longs;ameproportion <lb/>to F, that B C hath to B R; for the Antecedents are each Se&longs;quialter of their con&longs;equents: <lb/>And<emph.end type="italics"/> (b) <emph type="italics"/>F Q being le&longs;s than B C, F &longs;hall al&longs;o be le&longs;s than B R.<emph.end type="italics"/><lb/><arrow.to.target n="marg1289"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1287"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1288"></margin.target>(a) <emph type="italics"/>By 8. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1289"></margin.target>(b) <emph type="italics"/>By 14. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>And, for that cau&longs;e, K R hath greater proportion to S Y, than <lb/>the half of K R hath to <foreign lang="greek">y</foreign> B.] <emph type="italics"/>For K R is to S Y, as the Square P S is to the Square<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1290"></arrow.to.target><lb/><emph type="italics"/>S Y: and the half of the Line K R is to the Line<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B, as the Square E<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>is to the Square<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>B.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1290"></margin.target>B</s></p><p type="main"> <s>And S O le&longs;s than <foreign lang="greek">y</foreign> B.] <emph type="italics"/>For S Y is double of S O.<emph.end type="italics"/><lb/><arrow.to.target n="marg1291"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1291"></margin.target>C</s></p><p type="main"> <s>And P H greater than F.] <emph type="italics"/>For P H is equall to S<emph.end type="italics"/> <foreign lang="greek">w,</foreign> <emph type="italics"/>and R<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>equall to F.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1292"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1292"></margin.target>D</s></p><p type="main"> <s>And, therefore, the whole Portion &longs;hall have the &longs;ame propor­</s></p><p type="main"> <s><arrow.to.target n="marg1293"></arrow.to.target><lb/>tion to that part which is above the Liquid, that the Square B D <lb/>hath to the Square F Q] <emph type="italics"/>Becau&longs;e that the part &longs;ubmerged, being to the whole Portion <lb/>as the Exce&longs;s by which the Square B D is greater than the Square F Q, is to the Square B D; <lb/>the whole Portion, Converting, &longs;hall be to the part thereof &longs;ubmerged, as the Square B D is to<emph.end type="italics"/> <pb xlink:href="040/01/1072.jpg" pagenum="378"/><emph type="italics"/>the Exce&longs;s by which it exceedeth the Square F Q: And, therefore, by Conver&longs;ion of Proportion, <lb/>the whole Portion is to the part thereof above the Liquid, as the Square B D is to the Square, <lb/>F <expan abbr="q;">que</expan> for the Square B D is &longs;o much greater than the Exce&longs;s by which it exceedeth the Squar, <lb/>F Q as is the &longs;aid Square F <expan abbr="q.">que</expan><emph.end type="italics"/><lb/><arrow.to.target n="marg1294"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1293"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1294"></margin.target>F</s></p><p type="main"> <s>For the parts towards L &longs;hall move downwards, and tho&longs;e to­<lb/>wards A upwards.] <emph type="italics"/>We thus carrect the&longs;e words, for in<emph.end type="italics"/> Tartaglia's <emph type="italics"/>Tran&longs;lation it <lb/>is fal&longs;ly, as I conceive, read<emph.end type="italics"/> Quoniam quæ ex parte L ad &longs;uperiora ferentur, <emph type="italics"/>becau&longs;e <lb/>the Line thàt pa&longs;&longs;eth thorow Z falls perpendicularly on the parts towards L, and that thorow<lb/>G falleth perpendicularly on the parts towards A: Whereupon the Centre Z, together with tho&longs;e <lb/>parts which are towards L &longs;hall move downwards; and the Centre G, together with the parts <lb/>which are towards A upwards.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1295"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1295"></margin.target>G</s></p><p type="main"> <s>It &longs;hall in like manner be demon&longs;trated that the Portion &longs;hall not <lb/>re&longs;t, but incline untill that its Axis do make an Angle with the <lb/>Surface of the Liquid, equall to the Angle B.] <emph type="italics"/>This may be ea&longs;ily demon­<lb/>&longs;tratred, as nell from what hath been &longs;aid in the precedent Propo&longs;ition, as al&longs;o from the two <lb/>latter Figures, by us in&longs;erted<emph.end type="italics"/></s></p><p type="head"> <s>PROP. X. THEOR. X.</s></p><p type="main"> <s><emph type="italics"/>The Right Portion of a Rightangled Conoid, lighter <lb/>than the Liquid, when it &longs;hall have its Axis greater <lb/>than to be unto the Semiparameter, in proportion as <lb/>fifteen to four, being demitted into the Liquid, &longs;o as<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1296"></arrow.to.target><lb/><emph type="italics"/>that its Ba&longs;e touch not the &longs;ame, it &longs;hall &longs;ometimes<emph.end type="italics"/><lb/><arrow.to.target n="marg1297"></arrow.to.target><lb/><emph type="italics"/>&longs;tand perpendicular; &longs;ometimes inclined; and &longs;ome­<lb/>times &longs;o inclined, as that its Ba&longs;e touch the Surface <lb/>of the Liquid in one Point only, and that in two Po-<emph.end type="italics"/><lb/><arrow.to.target n="marg1298"></arrow.to.target><lb/><emph type="italics"/>&longs;itions; &longs;ometimes &longs;o that its Ba&longs;e be more &longs;ubmer-<emph.end type="italics"/><lb/><arrow.to.target n="marg1299"></arrow.to.target><lb/><emph type="italics"/>ged in the Liquid; and &longs;ometimes &longs;o as that it doth <lb/>not in the lea&longs;t touch the Surface of the Liquid;<emph.end type="italics"/><lb/><arrow.to.target n="marg1300"></arrow.to.target><lb/><emph type="italics"/>according to the proportion that it hath to the Liquid <lb/>in Gravity. </s> <s>Every one of which Ca&longs;es &longs;hall be anon <lb/>demon&longs;trated.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1296"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1297"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1298"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1299"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1300"></margin.target>E</s></p><p type="main"> <s>Let there be a Portion, as hath been &longs;aid; and it being cut <lb/>thorow its Axis, by a Plane erect unto the Superficies of the <lb/>Liquid, let the Section be A P O L, the Section of a Right <lb/>angled Cone; and the Axis of the Portion and Diameter of the <lb/>Section B D: and let B D be cut in the Point K, &longs;o as that B K <lb/>be double of K D; and in C, &longs;o as that B D may have the &longs;ame <lb/><arrow.to.target n="marg1301"></arrow.to.target><lb/>proportion to K C, as fifteen to four: It is manife&longs;t, therefore, <lb/><arrow.to.target n="marg1302"></arrow.to.target><lb/>that K C is greater than the Semi-parameter: Let the Semi­ <pb xlink:href="040/01/1073.jpg" pagenum="379"/>parameter be equall to K R: and <lb/><figure id="id.040.01.1073.1.jpg" xlink:href="040/01/1073/1.jpg"/><lb/><arrow.to.target n="marg1303"></arrow.to.target><lb/>let D S be Se&longs;quialter of K R: but <lb/>S B is al&longs;o Se&longs;quialter of B R: <lb/>Therefore, draw a Line from A to <lb/>B; and thorow C draw C E Per­<lb/>pendicular to B D, cutting the Line <lb/>A B in the Point E; and thorow E <lb/>draw E Z parallel unto B D. Again, <lb/>A B being divided into two equall <lb/>parts in T, draw T H parallel to the <lb/>&longs;ame B D: and let Sections of <lb/>Rightangled Cones be de&longs;cribed, A E I about the Diameter E Z; <lb/>and A T D about the Diameter T H; and let them be like to the <lb/><arrow.to.target n="marg1304"></arrow.to.target><lb/>Portion A B L: Now the Section of the Cone A E I, &longs;hall pa&longs;s <lb/><arrow.to.target n="marg1305"></arrow.to.target><lb/>thorow K; and the Line drawn from R perpendicular unto B D, <lb/>&longs;hall cut the &longs;aid A E I; let it cut it in the Points Y G: and <lb/>thorow Y and G draw P Y Q and O G N parallels unto B D, and <lb/>cutting A T D in the Points F and X: la&longs;tly, draw P <foreign lang="greek">*f</foreign> and O X <lb/>touching the Section A P O L in the <emph type="italics"/>P<emph.end type="italics"/>oints P and O. </s> <s>In regard, <lb/><arrow.to.target n="marg1306"></arrow.to.target><lb/>therefore, that the three <emph type="italics"/>P<emph.end type="italics"/>ortions A P O L, A E I, and A T D are <lb/>contained betwixt Right Lines, and the Sections of Rightangled <lb/>Cones, and are right alike and unequall, touching one another, upon <lb/>one and the &longs;ame Ba&longs;e; and N X G O being drawn from the <lb/><emph type="italics"/>P<emph.end type="italics"/>oint N upwards, and Q F Y P from Q: O G &longs;hall have to G X <lb/>a proportion compounded of the proportion, that I L hath to L A, <lb/>and of the proportion that A D hath to DI: But I L is to L A, <lb/>as two to five: And C B is to B D, as &longs;ix to fifteen; that is, as two <lb/><arrow.to.target n="marg1307"></arrow.to.target><lb/>to five: And as C B is to B D, &longs;o is <emph type="italics"/>E B to B A<emph.end type="italics"/>; and D Z to <lb/><arrow.to.target n="marg1308"></arrow.to.target><lb/>D A: And of D Z and D A, L I and L A are double: and A D <lb/><arrow.to.target n="marg1309"></arrow.to.target><lb/>is to D I, as five to one: <emph type="italics"/>B<emph.end type="italics"/>ut the proportion compounded of the <lb/>proportion of two to five, and of the proportion of five to one, is <lb/><arrow.to.target n="marg1310"></arrow.to.target><lb/>the &longs;ame with that of two to one: and two is to one, in double <lb/>proportion: Therefore, O G is double of GX: and, in the &longs;ame <lb/>manner is P Y proved to be double of Y F: Therefore, &longs;ince that <lb/>D S is Se&longs;quialter of K R; <emph type="italics"/>B S<emph.end type="italics"/> &longs;hall be the Exce&longs;s by which the <lb/>Axis is greater than Se&longs;quialter of the Semi-parameter. </s> <s>If there­<lb/>fore, the <emph type="italics"/>P<emph.end type="italics"/>ortion have the &longs;ame proportion in Gravity unto the <lb/>Liquid, as the Square made of the Line <emph type="italics"/>B S,<emph.end type="italics"/> hath to the Square <lb/>made of <emph type="italics"/>B D,<emph.end type="italics"/> or greater, being demitted into the Liquid, &longs;o as hat <lb/>its <emph type="italics"/>B<emph.end type="italics"/>a&longs;e touch not the Liquid, it &longs;hall &longs;tand erect, or perpendicular: <lb/>For it hath been demon&longs;trated above, that the <emph type="italics"/>P<emph.end type="italics"/>ortion who&longs;e <lb/><arrow.to.target n="marg1311"></arrow.to.target><lb/>Axis is greater than Se&longs;quialter of the Semi-parameter, if it have <lb/>not le&longs;ser proportion in Gravity unto the Liquid, than the Square <pb xlink:href="040/01/1074.jpg" pagenum="380"/>made of the Exce&longs;s by which the Axis is greater than Se&longs;quialter <lb/>of the Semi-parameter, hath to the Square made of the Axis, being <lb/>demitted into the Liquid, &longs;o as hath been &longs;aid, it &longs;hall &longs;tand erect, <lb/>or <emph type="italics"/>P<emph.end type="italics"/>erpendicular.</s></p><p type="margin"> <s><margin.target id="marg1301"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1302"></margin.target>G</s></p><p type="margin"> <s><margin.target id="marg1303"></margin.target>H</s></p><p type="margin"> <s><margin.target id="marg1304"></margin.target>K</s></p><p type="margin"> <s><margin.target id="marg1305"></margin.target>L</s></p><p type="margin"> <s><margin.target id="marg1306"></margin.target>M</s></p><p type="margin"> <s><margin.target id="marg1307"></margin.target>N</s></p><p type="margin"> <s><margin.target id="marg1308"></margin.target>O</s></p><p type="margin"> <s><margin.target id="marg1309"></margin.target>P</s></p><p type="margin"> <s><margin.target id="marg1310"></margin.target>Q</s></p><p type="margin"> <s><margin.target id="marg1311"></margin.target>R</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s><emph type="italics"/>The particulars contained in this Tenth Propo&longs;ition, are divided by<emph.end type="italics"/> Archimedes <lb/><emph type="italics"/>into five Parts and Conclu&longs;ions, each of which he proveth by a di&longs;tinct Demon&longs;tration.<emph.end type="italics"/><lb/><arrow.to.target n="marg1312"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1312"></margin.target>A</s></p><p type="main"> <s>It &longs;hall &longs;ometimes &longs;tand perpendicular.] <emph type="italics"/>This is the fir&longs;t Conclu&longs;ion, the <lb/>Demonstration of which he hath &longs;ubjoyned to the Propo&longs;ition.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1313"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1313"></margin.target>B</s></p><p type="main"> <s>And &longs;ometimes &longs;o inclined, as that its Ba&longs;e touch the Surface <lb/>of the Liquid, in one Point only.] <emph type="italics"/>This is demon&longs;trated in the third Con­<lb/>clu&longs;ion.<emph.end type="italics"/></s></p><p type="main"> <s>Sometimes, &longs;o that its Ba&longs;e be mo&longs;t &longs;ubmerged in the Liquid.] </s></p><p type="main"> <s><arrow.to.target n="marg1314"></arrow.to.target><lb/><emph type="italics"/>This pertaineth unto the fourth Conclu&longs;ion.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1314"></margin.target>C</s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/>nd, &longs;ometimes, &longs;o as that it doth not in the lea&longs;t touch the Sur­<lb/><arrow.to.target n="marg1315"></arrow.to.target><lb/>face of the Liquid.] <emph type="italics"/>This it doth hold true two wayes, one of which is explained is <lb/>the &longs;econd, and the other in the fifth Conclu&longs;ion.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1315"></margin.target>D</s></p><p type="main"> <s>According to the proportion, that it hath to the Liquid in Gra­<lb/><arrow.to.target n="marg1316"></arrow.to.target><lb/>vity. </s> <s>Every one of which Ca&longs;es &longs;hall be anon demon&longs;trated.] <lb/><emph type="italics"/>In<emph.end type="italics"/> Tartaglia's <emph type="italics"/>Ver&longs;ion it is rendered, to the confu&longs;ion of the &longs;ence,<emph.end type="italics"/> Quam autem pro­<lb/>portionem habeant ad humidum in Gravitate fingula horum demon&longs;trabuntur.</s></p><p type="margin"> <s><margin.target id="marg1316"></margin.target>E</s></p><p type="main"> <s>It is manife&longs;t, therefore, that K C is greater than the Semi­<lb/><arrow.to.target n="marg1317"></arrow.to.target><lb/>parameter] <emph type="italics"/>For, &longs;ince B D hath to K C the &longs;ame proportion, as fifteen to four, and <lb/>hath unto the Semi-parameter greater proportion; (a) the Semi-parameter &longs;hall be le&longs;s<emph.end type="italics"/><lb/><arrow.to.target n="marg1318"></arrow.to.target><lb/><emph type="italics"/>than K C.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1317"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1318"></margin.target>(a) <emph type="italics"/>By 10. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>Let the Semi-parameter be equall to KR.] <emph type="italics"/>We have added the&longs;e words,<emph.end type="italics"/><lb/><arrow.to.target n="marg1319"></arrow.to.target><lb/><emph type="italics"/>which are not to be found in<emph.end type="italics"/> Tartaglia.</s></p><p type="margin"> <s><margin.target id="marg1319"></margin.target>G</s></p><p type="main"> <s>But S B is al&longs;o Se&longs;quialter of BR.] <emph type="italics"/>For, D B is &longs;uppo&longs;ed Se&longs;quialter of<emph.end type="italics"/><lb/><arrow.to.target n="marg1320"></arrow.to.target><lb/><emph type="italics"/>B K; and D S al&longs;o is Se&longs;quialter of K R: Wherefore as<emph.end type="italics"/> (b) <emph type="italics"/>the whole D B, is to the whole <lb/>B K, &longs;o is the part D S to the part K R. Therefore, the Remainder S B, is al&longs;o to the<emph.end type="italics"/><lb/><arrow.to.target n="marg1321"></arrow.to.target><lb/><emph type="italics"/>Remainder B R, as D B is to B K.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1320"></margin.target>H</s></p><p type="margin"> <s><margin.target id="marg1321"></margin.target>(b) <emph type="italics"/>By 19 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/>nd let them be like to the <emph type="italics"/>P<emph.end type="italics"/>ortion <emph type="italics"/>A B L.<emph.end type="italics"/>] Apollonius <emph type="italics"/>thus defineth<emph.end type="italics"/><lb/><arrow.to.target n="marg1322"></arrow.to.target><lb/><emph type="italics"/>like Portions of the Sections of a Cone, in<emph.end type="italics"/> Lib. 6. Conicornm, <emph type="italics"/>as<emph.end type="italics"/> Eutocius <emph type="italics"/>writeth<emph.end type="italics"/> ^{*}; <lb/><arrow.to.target n="marg1323"></arrow.to.target><lb/><foreign lang="greek">o)/n oi(_s a)x deisw_n o)/n e(xa/sw| warallh/lwn th_ <35>a\sei, i(/swn to\ plh_o<34>, ai( para/llhlos, kai\ a(i <35>a/seis wro\s ta/s apotrm<gap/><lb/>nome/nas a)po\ <gap/> diame/tswn tw_s korufai_s e)n toi_s a)ntoi_s lo/gois ei)si, kai\ ai( a)potemno/menai wro\s ta\s a) temnomi/nas<gap/></foreign><lb/><emph type="italics"/>that is,<emph.end type="italics"/> In both of which an equall number of Lines being drawn parallel to the <lb/>Ba&longs;e; the parallel and the Ba&longs;es have to the parts of the Diameters, cut off from <lb/>the Vertex, the &longs;ameproportion: as al&longs;o, the parts cut off, to the parts cut off. <lb/><emph type="italics"/>Now the Lines parallel to the Ba&longs;es are drawn, as I &longs;uppo&longs;e, by making a Rectilineall Figure (cal-<emph.end type="italics"/><lb/><arrow.to.target n="marg1324"></arrow.to.target><lb/><emph type="italics"/>led)<emph.end type="italics"/> Signally in&longs;cribed [<foreign lang="greek">xh_ma giwri/mws e)gn\<36>ro/menon</foreign>] <emph type="italics"/>in both portions, having an equall num­<lb/>ber of Sides in both. </s> <s>Therefore, like Portions are cut off from like Sections of a Cone; and <lb/>their Diameters, whether they be perpendicular to their Ba&longs;es, or making equall Angles with their <lb/>Ba&longs;es, have the &longs;ame proportion unto their Ba&longs;es.<emph.end type="italics"/><lb/><arrow.to.target n="marg1325"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1322"></margin.target>K</s></p><p type="margin"> <s><margin.target id="marg1323"></margin.target>* <emph type="italics"/>Upon prop. 3 lib.<emph.end type="italics"/> 2 <lb/>Archim. <emph type="italics"/>Æqui­<lb/>pond.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1324"></margin.target><emph type="italics"/>Vide<emph.end type="italics"/> Archim, <emph type="italics"/>ante <lb/>prop. 2. lib. 2. <lb/>Æquipond.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1325"></margin.target>L</s></p><p type="main"> <s>Now the Section of the Cone <emph type="italics"/>A E I<emph.end type="italics"/> &longs;hall pa&longs;s thorow K.] <lb/><emph type="italics"/>For, if it be po&longs;&longs;ible, let it not pa&longs;s thorow K, but thorow &longs;ome other Point of the Line D B, as <lb/>thorow V. Inregard, therefore, that in the Section of the Right-angled Cone A E I, who&longs;e <lb/>Diameter is E Z, A E is drawn and prolonged; and D B parallel unto the Diameter, cutteth <lb/>both A E and A I; A E in B, and A I in D; D B &longs;hall have to B V, the &longs;ame proportion<emph.end type="italics"/> <pb xlink:href="040/01/1075.jpg" pagenum="381"/><emph type="italics"/>that A Z hath to Z D; by the fourth Propo&longs;ition of<emph.end type="italics"/> Archimedes, De quadratura Para­<lb/>bolæ: <emph type="italics"/>But A Z is Se&longs;quialter of Z D; for it is as three to two, as we &longs;hallanon demon-<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1326"></arrow.to.target><lb/><emph type="italics"/>&longs;trate: Therefore D B is Se&longs;quialter of B V; but D B and B K are Se&longs;quialter: <lb/>And, therefore, the Lines<emph.end type="italics"/> (c) <emph type="italics"/>B V and B K are equall: Which is impos&longs;ible: <lb/>Therefore the Section of the Right-angled Cone A E I, &longs;hall pa&longs;s thorow the Point K; which <lb/>we would demonstrate.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1326"></margin.target>(c) <emph type="italics"/>By 9 of the <lb/>fifth,<emph.end type="italics"/></s></p><p type="main"> <s>In regard, therefore, that the three <emph type="italics"/>P<emph.end type="italics"/>ortions A P O L, A E I <lb/><arrow.to.target n="marg1327"></arrow.to.target><lb/>and A T D are contained betwixt Right Lines and the Sections <lb/>of Right-angled Cones, and are Right, alike and unequall, <lb/>touching one another, upon one and the &longs;ame Ba&longs;e.] <emph type="italics"/>After the&longs;e words,<emph.end type="italics"/><lb/>upon one and the &longs;ame Ba&longs;e, <emph type="italics"/>we may &longs;ee that &longs;omething is obliterated, that is to be <lb/>de&longs;ired: and for the Demon&longs;tration of the&longs;e particulars, it is requi&longs;ite in this place to <lb/>premi&longs;e &longs;ome things: which will al&longs;o be nece&longs;&longs;ary unto the things that follow.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1327"></margin.target>M</s></p><p type="head"> <s>LEMMA. I.</s></p><p type="main"> <s>Let there be a Right <emph type="italics"/>L<emph.end type="italics"/>ine A B; and let it be cut by two <emph type="italics"/>L<emph.end type="italics"/>ines, <lb/>parallel to one another, A C and D E, &longs;o, that as <emph type="italics"/>A B<emph.end type="italics"/> is to <lb/>B D. &longs;o <emph type="italics"/>A C<emph.end type="italics"/> may be to D E. </s> <s>I &longs;ay that the Line that con­<lb/>joyneth the Points C and B &longs;hall likewi&longs;e pa&longs;s by E.</s></p><figure id="id.040.01.1075.1.jpg" xlink:href="040/01/1075/1.jpg"/><p type="main"> <s><emph type="italics"/>For, if po&longs;&longs;ible, let it not pa&longs;s by E, but either <lb/>above or below it. </s> <s>Let it first pa&longs;s below it, <lb/>as by F. </s> <s>The Triangles A B C and D B F &longs;hall <lb/>be alike: And, therefore, as<emph.end type="italics"/> (a) <emph type="italics"/>A B is to B D,<emph.end type="italics"/><lb/><arrow.to.target n="marg1328"></arrow.to.target><lb/><emph type="italics"/>&longs;o is A C to D F: But as A B is to B D, &longs;o was <lb/>A C to D E: Therefore<emph.end type="italics"/> (b) <emph type="italics"/>D F &longs;hall be equall to<emph.end type="italics"/><lb/><arrow.to.target n="marg1329"></arrow.to.target><lb/><emph type="italics"/>D E: that is, the part to the whole: Which is <lb/>ab&longs;urd. </s> <s>The &longs;ame ab&longs;urditie will follow, if the <lb/>Line C B be &longs;uppo&longs;ed to pa&longs;s above the Point E: <lb/>And, therefore, C B mu&longs;t of neces&longs;ity pa&longs;s thorow <lb/>E: Which was required to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1328"></margin.target>(a) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1329"></margin.target>(b) <emph type="italics"/>By 9. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA. II.</s></p><p type="main"> <s>Let there be two like <emph type="italics"/>P<emph.end type="italics"/>ortions, contained betwixt Right Lines, <lb/>and the Sections of Right-angled Cones; A B C the great­<lb/>er, who&longs;e Diameter let be B D; and E F C the le&longs;ser, who&longs;e <lb/>Diameter let be F G: and, let them be &longs;o applyed to one <lb/>another, that the greater include the le&longs;ser; and let their <lb/>Ba&longs;es A C and E C be in the &longs;ame Right Line, that the &longs;ame <lb/>Point C, may be the term or bound of them both: And, <lb/>then in the Section A B C, take any Point, as H; and draw <lb/>a Line from H to C. </s> <s>I &longs;ay, that the Line H C, hath to that <lb/>part of it &longs;elf, that lyeth betwixt C and the Section E F C, the <lb/>&longs;ame proportion that A C hath to C E.</s></p><p type="main"> <s><emph type="italics"/>Draw B C, which &longs;hall pa&longs;s thorow F, For, in regard, that the Portions are alike, the <lb/>Diameters with the Ba&longs;es contain equall Angles: And, therefore, B D and F G are parallel <lb/>to one another: and B D is to A C, as F G it to E C: and,<emph.end type="italics"/> Permutando, <emph type="italics"/>B D is to F G, as <lb/>A C is to C E; that is,<emph.end type="italics"/> (a) <emph type="italics"/>as their halfes D C to C G; therefore, it followeth, by the<emph.end type="italics"/><lb/><arrow.to.target n="marg1330"></arrow.to.target><lb/><emph type="italics"/>preceding Lemma, that the Line B C &longs;hall pa&longs;s by the Point F. Moreover, from the Point <lb/>H unto the Diameter B D, draw the Line H K, parallel to the Ba&longs;e A C: and, draw a Line<emph.end type="italics"/> <pb xlink:href="040/01/1076.jpg" pagenum="382"/><figure id="id.040.01.1076.1.jpg" xlink:href="040/01/1076/1.jpg"/><lb/><emph type="italics"/>from K to C, cutting the Diameter F G in L: <lb/>and, thorow L, unto the Section E F. G, on the <lb/>part E, draw the Line L M, parallel unto the <lb/>&longs;ame Ba&longs;e A C. And, of the Section A B C, <lb/>let the Line B N be the Parameter; and, of the <lb/>Section E F C, let F O be the Parameter. </s> <s>And, <lb/>becau&longs;e the Triangles C B D and C F G are alike<emph.end type="italics"/>; <lb/>(b) <emph type="italics"/>therefore, as B C is to C F, &longs;o &longs;hall D C be<emph.end type="italics"/><lb/><arrow.to.target n="marg1331"></arrow.to.target><lb/><emph type="italics"/>to C G, and B D to F G. Again, becau&longs;e the <lb/>Triangles C K B and C L F, are al&longs;o alike to <lb/>one another; therefore, as B C is to C F, that is, <lb/>as B D is to F G, &longs;o &longs;hall K C be to C L, and B K to F L: Wherefore, K C to C L, and,<emph.end type="italics"/><lb/><arrow.to.target n="marg1332"></arrow.to.target><lb/><emph type="italics"/>B K to F L, are as D C to C G; that is,<emph.end type="italics"/> (c) <emph type="italics"/>as their duplicates A C and C E: But as <lb/>B D is to F G, &longs;o is D C to C G; that is, A D to E G: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>as B D is to <lb/>A D, &longs;o is F G to E G: But the Square A D, is equall to the Rectangle D B N, by the 11 <lb/>of our fir&longs;t of<emph.end type="italics"/> Conicks: <emph type="italics"/>Therefore, the<emph.end type="italics"/> (d) <emph type="italics"/>three Lines B D, A D and B N are<emph.end type="italics"/><lb/><arrow.to.target n="marg1333"></arrow.to.target><lb/><emph type="italics"/>Proportionalls. </s> <s>By the &longs;ame rea&longs;on, likewi&longs;e, the Square E G being equall to the Rectangle <lb/>G F O, the three other Lines F G, E G and F O, &longs;hall be al&longs;o Proportionals: And, as B D is <lb/>to A D, &longs;o is F G to E G: And, therefore, as A D is to B N, &longs;o is E G to F O:<emph.end type="italics"/> Ex equali, <lb/><emph type="italics"/>therefore, as D B is to B N, &longs;o is G F to F O: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>as D B is to G F, &longs;o is <lb/>B N to F O: But as D B is to G F, &longs;o is B K to F L: Therefore, B K is to F L, as <lb/>B N is to F O: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>as B K is to B N, &longs;o is F L to F O. Again, <lb/>becau&longs;e the<emph.end type="italics"/> (e) <emph type="italics"/>Square H K is equall to the Rectangle B N; and the Square M L, equall<emph.end type="italics"/><lb/><arrow.to.target n="marg1334"></arrow.to.target><lb/><emph type="italics"/>to the Rectangle L F O, therefore, the three Lines B K, K H and B N &longs;hall be Proportionals: <lb/>and F L, L M, and F O &longs;hall al&longs;o be Proportionals: And, therefore,<emph.end type="italics"/> (f) <emph type="italics"/>as the Line<emph.end type="italics"/><lb/><arrow.to.target n="marg1335"></arrow.to.target><lb/><emph type="italics"/>B K is to the Line B N, &longs;o &longs;hall the Square B K, be to the Square H K: And, as the <lb/>Line F L is to the Line F O, &longs;o &longs;hall the Square F L be to the Square L M: <lb/>Therefore, becau&longs;e that as B K is to B N, &longs;o is F L to F O; as the Square<emph.end type="italics"/><lb/><arrow.to.target n="marg1336"></arrow.to.target><lb/><emph type="italics"/>B K is to the Square K H, &longs;o &longs;hall the Square F L be to the Square L M: Therefore,<emph.end type="italics"/><lb/>(g) <emph type="italics"/>as the Line B K is to the Line K H, &longs;o is the Line F L to L M: And,<emph.end type="italics"/> Permutando, <lb/><emph type="italics"/>as B K is to F L, &longs;o is K H to L M: But B K was to F L, as K C to C L: Therefore, <lb/>K H is to L M, as K C to C L: And, therefore, by the preceding Lemma, it is manife&longs;t that <lb/>the Line H C al&longs;o &longs;hall pa&longs;s thorow the Point M: As K C, therefore, is to C L, that is, <lb/>as A C to C E, &longs;o is H C to C M; that is, to the &longs;ame part of it &longs;elf, that lyeth betwixt C and <lb/>the Section E F C. And, in like manner might we demon&longs;trate, that the &longs;ame happeneth <lb/>in other Lines, that are produced from the Point C, and the Sections E B C. And, that <lb/>B C hath the &longs;ame proportion to C F, plainly appeareth; for B C is to C F, as D C to C G; <lb/>that is, as their Duplicates A C to C E.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1330"></margin.target>(a) <emph type="italics"/>By 15. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1331"></margin.target>(b) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1332"></margin.target>(c) <emph type="italics"/>By 15. of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1333"></margin.target>(d) <emph type="italics"/>By 17. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1334"></margin.target>(e) <emph type="italics"/>By 11 of our <lb/>fir&longs;t of<emph.end type="italics"/> Conicks.</s></p><p type="margin"> <s><margin.target id="marg1335"></margin.target>(f) <emph type="italics"/>By<emph.end type="italics"/> Cor. <emph type="italics"/>of 20. <lb/>of the &longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1336"></margin.target>(g) <emph type="italics"/>By 23. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="main"> <s>From whence it is manife&longs;t, that all Lines &longs;o drawn, &longs;hall be cut by the <lb/>&longs;aid Section in the &longs;ame proportion. </s> <s>For, by Divi&longs;ion and Conver&longs;ion, <lb/>C M is to M H, and C F to F B, as C E to E A.</s></p><p type="head"> <s>LEMMA. III.</s></p><p type="main"> <s>And, hence it may al&longs;o be proved, that the Lines which are <lb/>drawn in like Portions, &longs;o, as that with the Ba&longs;es, they con­<lb/>tain equall Angles, &longs;hall al&longs;o cut off like Portions; that is, <lb/>as in the foregoing Figure, the Portions H B C and M F C, <lb/>which the Lines C H and C M do cut off, are al&longs;o alike to <lb/>each other.</s></p><p type="main"> <s><emph type="italics"/>For let C H and C M be divided in the midst in the Points P and <expan abbr="q;">que</expan> and thorow tho&longs;e <lb/>Points draw the Lines R P S and T Q V parallel to the Diameters. </s> <s>Of the Portion <lb/>H S C the Diameter &longs;hall be P S, and of the Portion M V C the Diameter &longs;hall be<emph.end type="italics"/> <pb xlink:href="040/01/1077.jpg" pagenum="383"/><emph type="italics"/>Q V. And, &longs;uppo&longs;e that as the Square C R is to the Square C P, &longs;o is the Line B N unto <lb/>another Line; which let be S X: And, as the Square C T is to the Square C Q &longs;o let F O <lb/>be to V Y. </s> <s>Now it is manife&longs;t, by the things which we have demon&longs;trated, in our Commentaries, <lb/>upon the fourth Propo&longs;ition of<emph.end type="italics"/> Archimedes, De Conoidibus & Spheæroidibus, <emph type="italics"/>that the <lb/>Square C P is equall to the Rectangle P S X; and al&longs;o, that the Square C Q is equall to <lb/>the Rectangle Q V Y; that is, the Lines S X and V Y, are the Parameters of the Sections H S C <lb/>and M V C: But &longs;ince the Triangles C P R and C Q T are alike; C R &longs;hall have to C P, the <lb/>&longs;ame Proportion that C T hath to C Q: And, therefore, the<emph.end type="italics"/> (a) <emph type="italics"/>Square C R &longs;hall have<emph.end type="italics"/><lb/><arrow.to.target n="marg1337"></arrow.to.target><lb/><emph type="italics"/>to the Square C P, the &longs;ame proportion that the<emph.end type="italics"/><lb/><figure id="id.040.01.1077.1.jpg" xlink:href="040/01/1077/1.jpg"/><lb/><emph type="italics"/>Square C T hath to the Square C Q: There­<lb/>fore, al&longs;o, the Line B N &longs;hall be to the Line <lb/>S X, as the Line F O is to V Y: But H C was <lb/>to C M, as A C to C E: And, therefore, al&longs;o, <lb/>their halves C P and C Q, are al&longs;o to one <lb/>another, as A D and E G: And.<emph.end type="italics"/> Permu­<lb/>tando, <emph type="italics"/>C P is to A D, as C Q is to E G: <lb/>But it hath been proved, that A D is to B N, <lb/>as E G to F O; and B N to S X, as F O to <lb/>V Y: Therefore,<emph.end type="italics"/> exæquali, <emph type="italics"/>C P &longs;hall be <lb/>to S X, as C Q is to V Y. And, &longs;ince the <lb/>Square C P is equall to the Rectangle P S X, and the Square C Q to the Rectangle Q V Y, <lb/>the three Lines S P, PC and S X &longs;hall be proportionalls, and V Q, Q C and V Y &longs;hal be <lb/>Proportionalls al&longs;o: And therefore al&longs;o S P &longs;hall be to P C as V Q to Q C And as P C <lb/>is to C H, &longs;o &longs;hall Q C. be to C M: Therefore,<emph.end type="italics"/> ex æquali, <emph type="italics"/>as S P the Diameter of the <lb/>Portion H S C is to its Ba&longs;e C H, &longs;o is V Q the Diameter of the portion M V S the <lb/>Ba&longs;e C M; and the Angles which the Diameter with the Ba&longs;es do contain, are equall; and the <lb/>Lines S P and V Q are parallel: Therefore the Portions, al&longs;o, H S C and M V C &longs;hall be alike: <lb/>Which was propo&longs;ed to be demon&longs;trated<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1337"></margin.target>(a) <emph type="italics"/>By 22. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA. IV.</s></p><p type="main"> <s><emph type="italics"/>L<emph.end type="italics"/>et there be two <emph type="italics"/>L<emph.end type="italics"/>ines A <emph type="italics"/>B<emph.end type="italics"/> and C D; and let them be cut in the <lb/>Points E and F, &longs;o that as A E is to E B, C F may be to F D: <lb/>and let them be cut again in two other Points G and H; and <lb/>let C H be to H D, as A G is to G B. </s> <s>I &longs;ay that C F &longs;hall be to <lb/>F H as A E is E G.</s></p><p type="main"> <s><emph type="italics"/>For in regard that as A E is to E B, &longs;o is C F to F D; it followeth that, by Compounding, <lb/>as A B is to E B, &longs;o &longs;hall C D be to F D. Again, &longs;ince that as A G is to G B, &longs;o is C H, to <lb/>H D; it followeth that, by Compounding and Converting, as G B is to A B, &longs;o &longs;hall H D be<emph.end type="italics"/><lb/><figure id="id.040.01.1077.2.jpg" xlink:href="040/01/1077/2.jpg"/><lb/><emph type="italics"/>C D: Therefore,<emph.end type="italics"/> ex æquali, <emph type="italics"/>and Converting as E B <lb/>is to G B, &longs;o &longs;hall F D be to H D; And, by Conver­<lb/>&longs;ion of Propo&longs;ition, as E B is to E G, &longs;o &longs;hall F D <lb/>be to F H: But as A E is to E B, &longs;o is C F to F D:<emph.end type="italics"/><lb/>Ex æquali, <emph type="italics"/>therefore, as A E is to E G, &longs;o <lb/>&longs;hall CF be to F H.<emph.end type="italics"/> Again, another way. <emph type="italics"/>Let <lb/>the Lines A B and C D be applyed to one another, <lb/>&longs;o as that they doe make an Angle at the parts A and C; <lb/>and let A and C be in one and the &longs;ame Point: then <lb/>draw Lines from D to B, from H to G, and from F to E. </s> <s>And &longs;ince that as A E is to E B, <lb/>&longs;o is C F, that is A F to F D; therefore F E &longs;hall be parallel to D B<emph.end type="italics"/>; (a) <emph type="italics"/>and likewi&longs;e<emph.end type="italics"/><lb/><arrow.to.target n="marg1338"></arrow.to.target><lb/><emph type="italics"/>H G &longs;hall be parallel to D B; for that A H is to H D, as A G to G B<emph.end type="italics"/>: (b) <emph type="italics"/>Therefore F E <lb/>and H G are parallel to each other: And con&longs;equently, as A E is to E G, &longs;o is A H, that is,<emph.end type="italics"/><lb/><arrow.to.target n="marg1339"></arrow.to.target><lb/><emph type="italics"/>C F to F H: Which was to be demon&longs;trated.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1078.jpg" pagenum="384"/><p type="margin"> <s><margin.target id="marg1338"></margin.target>(a) <emph type="italics"/>By 2. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1339"></margin.target>(b) <emph type="italics"/>By 30 of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA. V.</s></p><p type="main"> <s>Again, let there be two like Portions, contained betwixt Right <lb/>Lines and the Sections of Right-angled Cones, as in the fore­<lb/>going figure, A B C, who&longs;e Diameter is B D; and E F C, <lb/>who&longs;e Diameter is F G; and from the Point E, draw the <lb/>Line E H parallel to the Diameters B D and F G; and let it <lb/>cut the Section A B C in K: and from the Point C draw C H <lb/>touching the Section A B C in C, and meeting with the Line <lb/>E H in H; which al&longs;o toucheth the Section E F C in the &longs;ame <lb/>Point C, as &longs;hall be demon&longs;trated: I &longs;ay that the Line drawn <lb/>from C <emph type="italics"/>H<emph.end type="italics"/> unto the Section E F C &longs;o as that it be parallel to <lb/>the Line E H, &longs;hall be divided in the &longs;ame proportion by the <lb/>Section A B C, in which the <emph type="italics"/>L<emph.end type="italics"/>ine C A is divided by the Section <lb/>E F C; and the part of the <emph type="italics"/>L<emph.end type="italics"/>ine C A which is betwixt the <lb/>two Sections, &longs;hall an&longs;wer in proportion to the part of the Line <lb/>drawn, which al&longs;o falleth betwixt the &longs;ame Sections: that is, <lb/>as in the foregoing Figure, if D B be produced untill it meet <lb/>with C H in L, that it may inter&longs;ect the Section E F C in the <lb/>Point M, the <emph type="italics"/>L<emph.end type="italics"/>ine <emph type="italics"/>L<emph.end type="italics"/> B &longs;hall have to B M the &longs;ame proportion <lb/>that C E hath to E A.</s></p><p type="main"> <s><emph type="italics"/>For let G F be prolonged untill it meet the &longs;ame Line C H in N, cutting the Section A B C <lb/>in O; and drawing a Line from B to C, which &longs;hall pa&longs;&longs;e by F, as hath been &longs;hewn, the<emph.end type="italics"/><lb/><figure id="id.040.01.1078.1.jpg" xlink:href="040/01/1078/1.jpg"/><lb/><emph type="italics"/>Triangles C G F and C D B &longs;hall be alike; as <lb/>al&longs;o the Triangles C F N and C B L: Wherefore<emph.end type="italics"/><lb/>(a) <emph type="italics"/>as G F is to D B, &longs;o &longs;hall C F b to C B:<emph.end type="italics"/><lb/><arrow.to.target n="marg1340"></arrow.to.target><lb/><emph type="italics"/>And as<emph.end type="italics"/> (b) <emph type="italics"/>C F is to C B, &longs;o &longs;hall F N be <lb/>to B L: Therefore G F &longs;hall be to D B, as F N<emph.end type="italics"/><lb/><arrow.to.target n="marg1341"></arrow.to.target><lb/><emph type="italics"/>to B L: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>G F &longs;hall be to <lb/>F N, as D B to B L: But D B is equall to <lb/>B L, by 35 of our Fir&longs;t Book of<emph.end type="italics"/> Conicks: <lb/><emph type="italics"/>Therefore<emph.end type="italics"/> (c) <emph type="italics"/>G F al&longs;o &longs;hall be equall to F N:<emph.end type="italics"/><lb/><arrow.to.target n="marg1342"></arrow.to.target><lb/><emph type="italics"/>And by 33 of the &longs;ame, the Line C H touch­<lb/>eth the Section E F C in the &longs;ame Point. </s> <s>There­<lb/>fore, drawing a Line from C to M, prolong it <lb/>untill it meet with the Section A B C in P; and <lb/>from P unto A C draw P Q parallel to B D. <lb/>Becau&longs;e, now, that the Line C H toucheth the <lb/>Section E F C in the Point C; L M &longs;hall have <lb/>the &longs;ame proportion to M D that C D hath to D E, <lb/>by the Fifth Propo&longs;ition of<emph.end type="italics"/> Archimedes <emph type="italics"/>in his <lb/>Book<emph.end type="italics"/> De Quadratura Patabolæ: <emph type="italics"/>And by <lb/>rea&longs;on of the Similitude of the Triangles C M D <lb/>and C P Q, as C M is to C D, &longs;o &longs;hall C P <lb/>be to C Q: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>as C M is to <lb/>C P, &longs;o &longs;hall C D be to C Q: But as C M is to C P, &longs;o is C E to C A,; as we have but <lb/>even now demon&longs;trated: And therefore, as C E is to C A, &longs;o is C D to C <expan abbr="q;">que</expan> that is as the <lb/>whole is to the whole, &longs;o is the part to the part: The remainder, therefore, D E is to the <lb/>Remainder Q A, as C E is to C A; that is, as C D is to C Q: And,<emph.end type="italics"/> Permutando, <emph type="italics"/>C D <lb/>is to D E, as C Q is to Q A: And L M is al&longs;o to M D, as C D to D E: Therefore L M is<emph.end type="italics"/> <pb xlink:href="040/01/1079.jpg" pagenum="385"/><emph type="italics"/>to M D, as C Q to Q A: But L B is to B D, by 5 of<emph.end type="italics"/> Archimedes, <emph type="italics"/>before recited, as C D <lb/>to D A: It is manife&longs;t therefore, by the precedent Lemma, that C D is to D Q, as L B is to <lb/>B M: But as C D is to D Q, &longs;o is C M to M P: Therefore L B is to B M, as C M to M P:<emph.end type="italics"/><lb/><arrow.to.target n="marg1343"></arrow.to.target><lb/><emph type="italics"/>And it haveing been demon&longs;trated, that C M is to M P, as C E to E A; L B &longs;hall be to B M,<lb/>as C E to E A. </s> <s>And in like manner it &longs;hall be demonstrated that &longs;o is N O to O F; as al&longs;o the <lb/>Remainders. </s> <s>And that al&longs;o H K is to K E, as C E to E A, doth plainly appeare by the &longs;ame<emph.end type="italics"/><lb/>5. <emph type="italics"/>of<emph.end type="italics"/> Archimedes<emph type="italics"/>: Which is that that we propounded to be demon&longs;trated.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1340"></margin.target>(a) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1341"></margin.target>(b) <emph type="italics"/>By 11 of the <lb/>fifth,<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1342"></margin.target>(c) <emph type="italics"/>By 14 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1343"></margin.target><emph type="italics"/>By 2. of the &longs;ixth<emph.end type="italics"/></s></p><p type="head"> <s>LEMMA. VI.</s></p><p type="main"> <s>And, therefore, let the things &longs;tand as above; and de&longs;cribe <lb/>yet another like Portion, contained betwixt a Right Line, and <lb/>the Section of the Rightangled Cone D R C, who&longs;e Diameter <lb/>is R S, that it may cut the Line F G in T; and prolong S R <lb/>unto the <emph type="italics"/>L<emph.end type="italics"/>ine C H in V, which meeteth the Section A B C in <lb/>X, and E F C in Y. </s> <s>I &longs;ay, that B M hath to M D, a propor­<lb/>tion compounded of the proportion that E A hath to A C; <lb/>and of that which C D hath to D E.</s></p><p type="main"> <s><emph type="italics"/>For, we &longs;hall fir&longs;t demon&longs;trate, that the Line C H toucheth the Section D R C in the <lb/>Point C; and that L M is to M D, as al&longs;o N F to F T, and V Y to Y R, as C D is to E D. <lb/>And, becau&longs;e now that L B is to B M, as C E is to E A; therefore, Compounding and Conver­<lb/>ting, B M &longs;hall be to L M, as E A to A C: And, as L M is to M D, &longs;o &longs;hall C D be to <lb/>D E: The proportion, therefore, of B M to M D, is compounded of the proportion that <lb/>B M hath to L M, and of the proportion that L M hath to M D: Therefore, the proportion <lb/>of B M to M D, &longs;hall al&longs;o be compounded of the proportion that E A hath to A C, and of <lb/>that which C D hath to D E. </s> <s>In the &longs;ame manner it &longs;hal be demon&longs;trated, that O F hath to <lb/>F T, and al&longs;o X Y to Y R, a proportion compounded of tho&longs;e &longs;ame proportions; and &longs;o in <lb/>the re&longs;t: Which was to be demonstrated.<emph.end type="italics"/></s></p><p type="main"> <s>By which it appeareth that the <emph type="italics"/>L<emph.end type="italics"/>ines &longs;o drawn; which fall betwixt <lb/>the Sections A B C and D R C, &longs;hall be divided by the Section E F C <lb/>in the &longs;ame Proportion.</s></p><p type="main"> <s>And C B is to B D, as &longs;ix to fifteen.] <emph type="italics"/>For we have &longs;uppo&longs;ed that B K is<emph.end type="italics"/><lb/><arrow.to.target n="marg1344"></arrow.to.target><lb/><emph type="italics"/>double of K D: Wherefore, by Compo&longs;ition B D &longs;hall be to K D as three to one; that is, as <lb/>fifteen to five: But B D was to K C as fifteen to four; Therefore B D is to D C as fifteen to nine: <lb/>And, by Conver&longs;ion of proportion and Convert­<lb/>ing, C B is to B D, as &longs;ix to &longs;ifteen.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1344"></margin.target>N</s></p><figure id="id.040.01.1079.1.jpg" xlink:href="040/01/1079/1.jpg"/><p type="main"> <s>And as C B is to B D, &longs;o is <lb/><arrow.to.target n="marg1345"></arrow.to.target><lb/>E B to B A; and D Z to D A.] <lb/><emph type="italics"/>For the Triangles C B E and D B A being <lb/>alike; As C B is to B E, &longs;o &longs;hall D B be to B A: <lb/>And,<emph.end type="italics"/> Permutando, <emph type="italics"/>as C B is to B D, &longs;o &longs;hall <lb/>E B be to B A: Againe, as B C is to C E &longs;o <lb/>&longs;hall B D be to D A, And,<emph.end type="italics"/> Permutando, <emph type="italics"/>as <lb/>C B is to B D, &longs;o &longs;hall C E, that is, D Z <lb/>equall to it, be to D A.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1345"></margin.target>O</s></p><p type="main"> <s>And of D Z and D A, L I and <lb/><arrow.to.target n="marg1346"></arrow.to.target><lb/>L A are double.] <emph type="italics"/>That the Line L A is <lb/>double of D A, is manife&longs;t, for that B D is the Diameter of the Portion. </s> <s>And that L I is <lb/>dovble to D Z &longs;hall be thus demon&longs;trated. </s> <s>For as much as ZD is to D A, as two to five: <lb/>therefore, Converting and Dividing, A Z, that is, I Z, &longs;hall be to Z D, as three to two:<emph.end type="italics"/> <pb xlink:href="040/01/1080.jpg" pagenum="386"/><emph type="italics"/>Again, by dividing, I D &longs;hall be to D Z, as one to two: But Z D was to D A, that is, to D L, <lb/>as two to five: Therefore,<emph.end type="italics"/> ex equali, <emph type="italics"/>and Converting, L D is to D I, as five to one: and, by <lb/>Conver&longs;ion of Proportion, D L is to D I, as five to four: But D Z was to D L, as two to <lb/>five: Therefore, again,<emph.end type="italics"/> ex equali, <emph type="italics"/>D Z is to L I, as two to four: Therefort L I is double <lb/>of D Z: Which was to be demon&longs;trated.<emph.end type="italics"/><lb/><arrow.to.target n="marg1347"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1346"></margin.target>P</s></p><p type="margin"> <s><margin.target id="marg1347"></margin.target>Q</s></p><p type="main"> <s>And, A D is to D I, as five to one.] <emph type="italics"/>This we have but ju&longs;t now demon­<lb/>&longs;trated.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1348"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1348"></margin.target>R</s></p><p type="main"> <s>For it hath been demon&longs;trated, above, that the Portion who&longs;e <lb/>Axis is greater than Se&longs;quialter of the Semi-parameter, if it have <lb/>not le&longs;&longs;er proportion in Gravity to the Liquid, &c.] <emph type="italics"/>He hath demonstra­<lb/>ted this in the fourth Propo&longs;ition of this Book.<emph.end type="italics"/></s></p><p type="head"> <s>CONCLVSION II.</s></p><p type="main"> <s><emph type="italics"/>If the Portion have le&longs;&longs;er proportion in Gravity to the<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1349"></arrow.to.target><lb/><emph type="italics"/>Liquid, than the Square S B hath to the Square <lb/>B D, but greater than the Square X O hath to the <lb/>Square B D, being demitted into the Liquid, &longs;o in­<lb/>clined, as that its Ba&longs;e touch not the Liquid, it &longs;hall <lb/>continue inclined, &longs;o, as that its Ba&longs;e &longs;hall not in the <lb/>lea&longs;t touch the Surface of the Liquid, and its Axis <lb/>&longs;hall make an Angle with the Liquids Surface, greater <lb/>than the Angle X.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1349"></margin.target>A</s></p><p type="main"> <s>Therfore repeating the fir&longs;t figure, let the Portion have unto <lb/>the Liquid in Gravitie a proportion greater than the Square <lb/>X O hath to the &longs;quare B D, but le&longs;&longs;er than the Square made of <lb/>the Exce&longs;&longs;e by which the Axis is greater than Se&longs;quialter of the Semi­<lb/><figure id="id.040.01.1080.1.jpg" xlink:href="040/01/1080/1.jpg"/><lb/>Parameter, that is, of S B, hath to <lb/>the Square B D: and as the Portion <lb/>is to the Liquid in Gravity, &longs;o let <lb/>the Square made of the Line <foreign lang="greek">y</foreign> be <lb/>to the Square B D: <foreign lang="greek">y</foreign> &longs;hall be great­<lb/><arrow.to.target n="marg1350"></arrow.to.target><lb/>er than X O, but le&longs;&longs;er than the <lb/>Exce&longs;&longs;e by which the Axis is grea­<lb/>ter than Se&longs;quialter of the Semi­<lb/>parameter, that is, than S B. </s> <s>Let <lb/>a Right Line M N be applyed to <lb/>fall between the Conick-Sections <lb/>A M Q L and A <emph type="italics"/>X<emph.end type="italics"/> D, [<emph type="italics"/>parallel to <lb/>B D falling betwixt O X and B D,<emph.end type="italics"/>] and equall to the Line <foreign lang="greek">y</foreign>: and let <lb/>it cut the remaining Conick Section A H I in the point H, and the <lb/><arrow.to.target n="marg1351"></arrow.to.target><lb/>Right Line R G in V. </s> <s>It &longs;hall be demon&longs;trated that M H is double to <lb/>H N, like as it was demon&longs;trated that O G is double to G X. <pb xlink:href="040/01/1081.jpg" pagenum="387"/><figure id="id.040.01.1081.1.jpg" xlink:href="040/01/1081/1.jpg"/><lb/>And from the Point M draw M Y <lb/>touching the Section A M Q L in M; <lb/>and M C perpendicular to B D: and <lb/>la&longs;tly, having drawn A N & prolong­<lb/>ed it to Q, the Lines A N & N Q &longs;hall <lb/>be equall to each other. </s> <s>For in <lb/>regard that in the Like Portions <lb/><arrow.to.target n="marg1352"></arrow.to.target><lb/>A M Q L and A <emph type="italics"/>X<emph.end type="italics"/> D the Lines A Q <lb/>and A N are drawn from the Ba&longs;es <lb/>unto the Portions, which Lines <lb/>contain equall Angles with the &longs;aid <lb/>Ba&longs;es, Q A &longs;hall have the &longs;ame proportion to A M that L A hath <lb/>to A D: Therefore A N is equall to N Q, and A Q parallel to M Y. <lb/><arrow.to.target n="marg1353"></arrow.to.target><lb/>It is to be demon&longs;trated that the Portion being demitted into the <lb/>Liquid, and &longs;o inclined as that its Ba&longs;e touch not the Liquid, it <lb/>&longs;hall continue inclined &longs;o as that its Ba&longs;e &longs;hall not in the lea&longs;t touch <lb/>the Surface of the Liquid, and its Axis &longs;hall make an Angle with <lb/>the Liquids Surface greater than the Angle X. </s> <s>Let it be demitted <lb/>into the Liquid, and let it &longs;tand, &longs;o, as that its Ba&longs;e do touch the <lb/>Surface of the Liquid in one Point only; and let the Portion be cut <lb/>thorow the Axis by a Plane erect unto the Surface of the Liquid, <lb/><figure id="id.040.01.1081.2.jpg" xlink:href="040/01/1081/2.jpg"/><lb/>and Let the Section of the Super­<lb/>ficies of the Portion be A P O L, <lb/>the Section of a Rightangled Cone, <lb/>and let the Section of the Liquids <lb/>Surface be A O; And let the Axis <lb/>of the Portion and Diameter of the <lb/>Section be <emph type="italics"/>B<emph.end type="italics"/> D: and let B D be <lb/><arrow.to.target n="marg1354"></arrow.to.target><lb/>cut in the Points K and R as hath <lb/>been &longs;aid; al&longs;o draw P G Parallel to <lb/>A O and touching the Section <lb/>A P O L in P; and from that Point <lb/>draw P T Parallel to B D, and P S perpendicular to the &longs;ame B D. <lb/>Now, fora&longs;much as the Portion is unto the Liquid in Gravity, as <lb/>the Square made of the Line <foreign lang="greek">y</foreign> is to the Square B D; and &longs;ince that <lb/>as the portion is unto the Liquid in Gravitie, &longs;o is the part thereof <lb/>&longs;ubmerged unto the whole Portion; and that as the part &longs;ubmerged <lb/>is to the whole, &longs;o is the Square T P to the Square B D; It follow­<lb/>eth that the Line <foreign lang="greek">y</foreign> &longs;hall be equall to T P: And therefore the Lines <lb/>M N and P T, as al&longs;o the Portions A M Q and A P O &longs;hall like­<lb/>wi&longs;e be equall to each other. </s> <s>And &longs;eeing that in the Equall and <lb/>Like Portions A P O L and A M Q L the Lines A O and A Q <lb/><arrow.to.target n="marg1355"></arrow.to.target><lb/>are drawn from the extremites of their Ba&longs;es, &longs;o, as that the Portions <lb/>cut off do make Equall Angles with their Diameters; as al&longs;o the <pb xlink:href="040/01/1082.jpg" pagenum="388"/>Angles at Y and G being equall; therefore the Lines Y B and G B, <lb/>and B C and B S &longs;hall al&longs;o be equall: And therefore C R and S R, <lb/>and M V and P Z, and V N and Z T, &longs;hall be equall likewi&longs;e. <lb/><arrow.to.target n="marg1356"></arrow.to.target><lb/>Since therefore M V is Le&longs;&longs;er than double of V N, it is manife&longs;t that <lb/>P Z is le&longs;&longs;er than double of Z T. <emph type="italics"/>L<emph.end type="italics"/>et P <foreign lang="greek">w</foreign> be double of <foreign lang="greek">w</foreign> T; and <lb/>drawing a <emph type="italics"/>L<emph.end type="italics"/>ine from <foreign lang="greek">w</foreign> to K, prolong it to E. </s> <s>Now the Centre of <lb/>Gravity of the whole Portion &longs;hall be the point K; and the Centre <lb/>of that part which is in the Liquid &longs;hall be <foreign lang="greek">w,</foreign> and of that which is <lb/>above the Liquid &longs;hall be in the <emph type="italics"/>L<emph.end type="italics"/>ine K E, which let be E: But the <lb/><emph type="italics"/>L<emph.end type="italics"/>ine K Z &longs;hall be perpendicular unto the Surface of the <emph type="italics"/>L<emph.end type="italics"/>iquid: <lb/>And therefore al&longs;o the Lines drawn thorow the Points E and <foreign lang="greek">w</foreign> parall­<lb/><arrow.to.target n="marg1357"></arrow.to.target><lb/>lell unto K Z, &longs;hall be perpendicular sunto the &longs;ame: Therefore the <lb/>Portion &longs;hall not abide, but &longs;hall turn about &longs;o, as that its <emph type="italics"/>B<emph.end type="italics"/>a&longs;e <lb/>do not in the lea&longs;t touch the Surface of the <emph type="italics"/>L<emph.end type="italics"/>iquid; in regard that <lb/>now when it toucheth in but one Point only, it moveth upwards, on <lb/><arrow.to.target n="marg1358"></arrow.to.target><lb/>the part towards A: It is therefore per&longs;picuous, that the Portion <lb/>&longs;hall con&longs;i&longs;t &longs;o, as that its Axis &longs;hall make an Angle with the <emph type="italics"/>L<emph.end type="italics"/>iquids <lb/>Surface greater than the Angle X.</s></p><p type="margin"> <s><margin.target id="marg1350"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1351"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1352"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1353"></margin.target>E F</s></p><p type="margin"> <s><margin.target id="marg1354"></margin.target>G</s></p><p type="margin"> <s><margin.target id="marg1355"></margin.target>H</s></p><p type="margin"> <s><margin.target id="marg1356"></margin.target>K</s></p><p type="margin"> <s><margin.target id="marg1357"></margin.target>L</s></p><p type="margin"> <s><margin.target id="marg1358"></margin.target>M</s></p><p type="head"> <s>COMMANDINE.<lb/><arrow.to.target n="marg1359"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1359"></margin.target>A</s></p><p type="main"> <s>If the Portion have le&longs;&longs;er proportion in Gravity to the Liquid, <lb/>than the Square S B hath to the Square B D, but greater than the <lb/>Square X O hath to the Square B D.] <emph type="italics"/>This is the &longs;econd part of the Tenth <lb/>propo&longs;ition; and the other pat is with their Demon&longs;trations, &longs;hall hereafter follow in the &longs;ame Order.<emph.end type="italics"/></s></p><p type="main"> <s><foreign lang="greek">*y</foreign> &longs;hall be greater than <emph type="italics"/>X<emph.end type="italics"/> O, but le&longs;&longs;er than the Exce&longs;s by </s></p><p type="main"> <s><arrow.to.target n="marg1360"></arrow.to.target><lb/>which the Axis is greater than Se&longs;quialter of the Semi-parameter, <lb/>that is than S B.] <emph type="italics"/>This followeth from the 10 of the fifth Book of<emph.end type="italics"/> Euclids <emph type="italics"/>Elements.<emph.end type="italics"/><lb/><arrow.to.target n="marg1361"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1360"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1361"></margin.target>C</s></p><p type="main"> <s>It &longs;hall be demon&longs;trated, that M H is double to H N, like as it <lb/>was demon&longs;trated, that O G is double to G X.] <emph type="italics"/>As in the fir&longs;t Conclu&longs;ion <lb/>of this Propo&longs;ition, and from what we have but even now written, thereupon appeareth:<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1362"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1362"></margin.target>D</s></p><p type="main"> <s>For in regard that in the like Portions A M Q L and A X D, the <lb/>Lines A Q and A N are drawn from the Ba&longs;es unto the Portions, <lb/>which Lines contain equall Angles with the &longs;aid Ba&longs;es, Q A &longs;hall <lb/>have the &longs;ame proportion to A N, that L A hath to A D.] <lb/><emph type="italics"/>This we have demonstrated above.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1363"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1363"></margin.target>E</s></p><p type="main"> <s>Therefore A N is equall to N Q] <emph type="italics"/>For &longs;ince that Q A is to A N, as L A to <lb/>A D; Dividing and Converting, A N &longs;hall be to N Q as A D to D L: But A D <lb/>is equall to D L; for that D B is &longs;uppo&longs;ed to be the Diameter of the Portion: Therefore<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1364"></arrow.to.target><lb/><emph type="italics"/>al&longs;o<emph.end type="italics"/> (a) <emph type="italics"/>A N is equall to N <expan abbr="q.">que</expan><emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1364"></margin.target>(a) <emph type="italics"/>By 14 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="main"> <s>And A Q parallel to M Y.] <emph type="italics"/>By the fifth of the &longs;econd Book of<emph.end type="italics"/> Apollonius <emph type="italics"/>his Conicks.<emph.end type="italics"/><lb/> </s><s><arrow.to.target n="marg1365"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1365"></margin.target>F</s></p><p type="main"> <s>And let B D be cut in the Points K and R as hath been &longs;aid.] </s></p><p type="main"> <s><arrow.to.target n="marg1366"></arrow.to.target><lb/><emph type="italics"/>In the fir&longs;t Conciu&longs;ion of this Propo&longs;ition: And let it be cut in K, &longs;o, as that B K be double to <lb/>K D, and in R &longs;o, as that K R may be equall to the Semi-parameter.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1366"></margin.target>G</s></p><p type="main"> <s>And, &longs;eeing that in the Equall and Like Portions A P O L and <lb/><arrow.to.target n="marg1367"></arrow.to.target><lb/>A <emph type="italics"/>M<emph.end type="italics"/> Q L, the Lines A O and A Q are drawn from the Extremities <lb/>of their Ba&longs;es, &longs;o, as that the Portions cut off, do make equall Angles <pb xlink:href="040/01/1083.jpg" pagenum="389"/>with their Diameters; as al&longs;o, the Angles at Y and G being equall; <lb/>Therefore, the Lines Y B and G B, & B C & B S, &longs;hall al&longs;o be equall.] <lb/><emph type="italics"/>Let the Line A Q cut the Diameter D B in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>and let it cut A O in<emph.end type="italics"/> <foreign lang="greek">d.</foreign> <emph type="italics"/>Now becau&longs;e that in<emph.end type="italics"/><lb/><figure id="id.040.01.1083.1.jpg" xlink:href="040/01/1083/1.jpg"/><lb/><emph type="italics"/>the equall and like Portions A P O L & A M Q L, <lb/>from the Extremities of their Ba&longs;es, A O and <lb/>A Q are drawn, that contain equall Angles with <lb/>tho&longs;e Ba&longs;es; and &longs;ince the Angles at D, are both <lb/>Right; Therefore, the Remaining Angles A<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>D <lb/>and A<emph.end type="italics"/> <foreign lang="greek">g</foreign> D <emph type="italics"/>&longs;hall be equall to one another: But <lb/>the Line P G is parallel unto the Line A O; al&longs;o <lb/>M Y is parallel to A <expan abbr="q;">que</expan> and P S and M C to <lb/>A D: Therefore the Triangles P G S and M Y C, <lb/>as al&longs;o the Triangles A<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>D and A<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>D, are all <lb/>alike to each other<emph.end type="italics"/>: (b) <emph type="italics"/>And as A D is to A<emph.end type="italics"/> <foreign lang="greek">d,</foreign><lb/><arrow.to.target n="marg1368"></arrow.to.target><lb/><emph type="italics"/>&longs;o is A D to A<emph.end type="italics"/> <foreign lang="greek">g</foreign><emph type="italics"/>: and,<emph.end type="italics"/> Permutando, <emph type="italics"/>the Lines <lb/>A D and A D are equall to each other: Therefore, <lb/>A<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>and A<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>are al&longs;o equall: But A O and <lb/>A Q are equall to each other; as al&longs;o their halves <lb/>A T and A N: Therefore the Remainders T<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>and N<emph.end type="italics"/> <foreign lang="greek">g</foreign><emph type="italics"/>; that is, TG and MY, are al&longs;o<emph.end type="italics"/><lb/><arrow.to.target n="marg1369"></arrow.to.target><lb/><figure id="id.040.01.1083.2.jpg" xlink:href="040/01/1083/2.jpg"/><lb/><emph type="italics"/>equall. </s> <s>And, as<emph.end type="italics"/> (c) <emph type="italics"/>P G is to G S, &longs;o is M Y to <lb/>Y C: and<emph.end type="italics"/> Permutando, <emph type="italics"/>as P G is to M Y, &longs;o is <lb/>G S to Y C: And, therefore, G S and Y C are <lb/>equall; as al&longs;o their halves B S and B C: From <lb/>whence it followeth, that the Remainders S R and C R <lb/>are al&longs;o equall: And, con&longs;equently, that P Z and <lb/>M V, and V N and Z T, are lkiewi&longs;e equall to one <lb/>another.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1367"></margin.target>H</s></p><p type="margin"> <s><margin.target id="marg1368"></margin.target>(b) <emph type="italics"/>By 4. of the <lb/>&longs;ixth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1369"></margin.target>(c) <emph type="italics"/>By 34 of the <lb/>fir&longs;t,<emph.end type="italics"/></s></p><p type="main"> <s>Since, therefore, that N V is le&longs;&longs;er <lb/><arrow.to.target n="marg1370"></arrow.to.target><lb/>than double of V N.] <emph type="italics"/>For M H is double of <lb/>H N, and M V is le&longs;&longs;er than M H: Therefore, M V <lb/>is le&longs;&longs;er than double of H N, and much le&longs;&longs;er than <lb/>double of V N.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1370"></margin.target>K</s></p><p type="main"> <s>Therefore, the Portion &longs;hall not abide, but &longs;hall turn about, <lb/><arrow.to.target n="marg1371"></arrow.to.target><lb/>&longs;o, as that its Ba&longs;e do not in the lea&longs;t touch the Surface of <lb/>the Liquid; in regard that now when it toucheth in but one Point <lb/>only, it moveth upwards on the part towards A.] Tartaglia's <emph type="italics"/>his Tran&longs;la­<lb/>tion hath it thus,<emph.end type="italics"/> Non ergo manet Portio &longs;ed inclinabitur ut Ba&longs;is ip&longs;ius, nec &longs;ecundum <lb/>unum tangat Superficiem Humidi, quon am nunc &longs;ecundum unum tacta ip&longs;a reclina­<lb/>tur<emph type="italics"/>: Which we have thought fit in this manner to correct, from other Places of<emph.end type="italics"/><lb/>Archimedes, <emph type="italics"/>that the &longs;en&longs;e might be the more per&longs;picuous. </s> <s>For in the &longs;ixth Propo&longs;ition of this, <lb/>he thus writeth (as we al&longs;o have it in the Tran&longs;lation,)<emph.end type="italics"/> The Solid A P O L, therefore, &longs;hall <lb/>turn about, and its Ba&longs;e &longs;hall not in the lea&longs;t touch the Surface of the Liquid. <emph type="italics"/>Again, <lb/>in the &longs;eventh Propo&longs;ition<emph.end type="italics"/>; From whence it is manife&longs;t, that its Ba&longs;e &longs;hall turn about in <lb/>&longs;uch manner, a that its Ba&longs;e doth in no wi&longs;e touch the Surface of the Liquid; For <lb/>that now when it toucheth but in one Point only, it moveth downwards on the part <lb/>towards L. <emph type="italics"/>And that the Portion moveth upwards, on the part towards A, doth plainly ap­<lb/>pear: For &longs;ince that the Perpendiculars unto the Surface of the Liquid, that pa&longs;s thorow <foreign lang="greek">w</foreign>, de <lb/>fall on the part towards A, and tho&longs;e that pa&longs;s thorow E, on the part towards L; it is nece&longs;&longs;ary <lb/>that the Centre<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>do move upwards, and the Centre E downwards.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1371"></margin.target>L</s></p><p type="main"> <s>It is therefore per&longs;picuous, that the Portion &longs;hall con&longs;i&longs;t, &longs;o, as that <lb/>its Axis &longs;hall make an Angle with the Liquids Surface greater than <lb/>the Angle <emph type="italics"/>X.] For dræwing a Line from A to X, prolong it untill it do cut the Diamter<emph.end type="italics"/> <pb xlink:href="040/01/1084.jpg" pagenum="390"/><figure id="id.040.01.1084.1.jpg" xlink:href="040/01/1084/1.jpg"/><lb/><emph type="italics"/>B D in<emph.end type="italics"/> <foreign lang="greek">l</foreign><emph type="italics"/>; and from the Point O, and parallel to <lb/>A<emph.end type="italics"/> <foreign lang="greek">l,</foreign> <emph type="italics"/>draw O X; and let it touch the Section in O, <lb/>as in the first Figure: And the<emph.end type="italics"/> (d) <emph type="italics"/>Angle at X,<emph.end type="italics"/><lb/><arrow.to.target n="marg1372"></arrow.to.target><lb/><emph type="italics"/>&longs;hall be equall al&longs;o to the angle<emph.end type="italics"/> <foreign lang="greek">l</foreign><emph type="italics"/>: But the angle at Y <lb/>is equall to the Angle at<emph.end type="italics"/> <foreign lang="greek">g;</foreign> <emph type="italics"/>and the<emph.end type="italics"/> (e) <emph type="italics"/>Angle<emph.end type="italics"/><lb/><arrow.to.target n="marg1373"></arrow.to.target><lb/>A <foreign lang="greek">*g</foreign> D <emph type="italics"/>greater than the Angle A<emph.end type="italics"/> <foreign lang="greek">l</foreign> <emph type="italics"/>D, which falleth <lb/>without it: Therefore the Angle at Y &longs;hall be great­<lb/>er than that at X. </s> <s>And becau&longs;e now the Portion <lb/>turneth about, &longs;o, as that the Ba&longs;e doth not touch <lb/>the Liquid, the Axis &longs;hall make an Angle with its <lb/>Surface greater than the Angle G; that is, than the <lb/>Angle Y: And, for that rea&longs;on, much greater than <lb/>the Angle X.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1372"></margin.target>(d) <emph type="italics"/>By 29 of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1373"></margin.target>(e) <emph type="italics"/>By 16. of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="head"> <s>CONCLUSION III.</s></p><p type="main"> <s><emph type="italics"/>If the Portion have the &longs;ame proportion in Gravity to the <lb/>Liquid, that the Square X O hath to the Square<emph.end type="italics"/><lb/>BD, <emph type="italics"/>being demitted into the Liquid, &longs;o inclined, as that <lb/>its Ba&longs;e touch not the Liquid, it &longs;hall &longs;tand and <lb/>continue inclined, &longs;o, as that its Ba&longs;e touch the Sur­<lb/>face of the Liquid, in one Point only, and its Axis &longs;hall <lb/>make an Angle with the Liquids Surface equall to the <lb/>Angle X. And, if the Portion have the &longs;ame proportion <lb/>in Gravity to the Liquid, that the Square P F hath <lb/>to the Square B D, being demitted into the Liquid, <lb/>& &longs;et &longs;o inclined, as that its Ba&longs;e touch not the Liquid, <lb/>it &longs;hall &longs;tand inclined, &longs;o, as that its Ba&longs;e touch the <lb/>Surface of the Liquid in one Point only, & its Axis &longs;hall <lb/>make an Angle with it, equall to the Angle<emph.end type="italics"/> <foreign lang="greek">*f.</foreign></s></p><p type="main"> <s>Let the Portion have the &longs;ame proportion in Gravity to tho <lb/>Liquid that the Square <emph type="italics"/>X<emph.end type="italics"/>O hath to the Square B D; and let <lb/>it be demitted into the Liquid &longs;o inclined, as that its Ba&longs;e touch <lb/><figure id="id.040.01.1084.2.jpg" xlink:href="040/01/1084/2.jpg"/><lb/>not the Liquid. </s> <s>And cutting it by <lb/>a Plane thorow the Axis, erect unto <lb/>the Surface of the Liquid, let the <lb/>Section of the Solid, be the Section <lb/>of a Right-angled Cone, A P M L; <lb/>let the Section of the Surface of the <lb/>Liquid be I M; and the Axis of the <lb/>Portion and Diameter of the Section <lb/>B D; and let B D be divided as be­<lb/>fore; and draw PN parallel to IM <pb xlink:href="040/01/1085.jpg" pagenum="391"/>and touching the Section in P, and T P parallel to B D; and P S perpen­<lb/>dicular unto B D. </s> <s>It is to be demon&longs;trated that the Portion &longs;hall <lb/><figure id="id.040.01.1085.1.jpg" xlink:href="040/01/1085/1.jpg"/><lb/>not &longs;tand &longs;o, but &longs;hall encline until <lb/>that the Ba&longs;e touch the Surface of <lb/>the Liquid, in one Point only, for let <lb/>the &longs;uperior figure &longs;tand as it was, <lb/>and draw O C, Perpendicular to B D; <lb/>and drawing a <emph type="italics"/>L<emph.end type="italics"/>ine from A to <emph type="italics"/>X,<emph.end type="italics"/><lb/>prolong it to Q: A X &longs;halbe equall <lb/>to <emph type="italics"/>X<emph.end type="italics"/> <expan abbr="q.">que</expan> Then draw O X parallel <lb/>to A <expan abbr="q.">que</expan> And becau&longs;e the Portion <lb/>is &longs;uppo&longs;ed to have the &longs;ame pro­<lb/>portion in Gravity to the Liquid <lb/>that the &longs;quare X O hath to the <lb/>Square B D; the part thereof &longs;ubmerged &longs;hall al&longs;o have the &longs;ame <lb/>proportion to the whole; that is, the Square T P to the Square <lb/><arrow.to.target n="marg1374"></arrow.to.target><lb/>B D; and &longs;o T P &longs;hall be equal to <emph type="italics"/>X<emph.end type="italics"/> O: And &longs;ince that of the <emph type="italics"/>P<emph.end type="italics"/>ortions <lb/>I P M and A O Q the Diameters are equall, the portions &longs;hall al&longs;o be <lb/><arrow.to.target n="marg1375"></arrow.to.target><lb/>equall. <emph type="italics"/>A<emph.end type="italics"/>gain, becau&longs;e that in the Equall and <emph type="italics"/>L<emph.end type="italics"/>ike <emph type="italics"/>P<emph.end type="italics"/>ortions A O Q L <lb/><arrow.to.target n="marg1376"></arrow.to.target><lb/>and AP ML the Lines A Q and I M, which cut off equall <emph type="italics"/>P<emph.end type="italics"/>or­<lb/>tions, are drawn, that, from the Extremity of the <emph type="italics"/>B<emph.end type="italics"/>a&longs;e, and this <lb/>not from the Extremity; it appeareth that that which is drawn from <lb/>the end or Extremity of the <emph type="italics"/>B<emph.end type="italics"/>a&longs;e, &longs;hall make the Acute Angle with <lb/>the Diameter of the whole <emph type="italics"/>P<emph.end type="italics"/>ortion le&longs;set. <emph type="italics"/>A<emph.end type="italics"/>nd the Angle at <emph type="italics"/>X<emph.end type="italics"/><lb/><arrow.to.target n="marg1377"></arrow.to.target><lb/>being le&longs;&longs;e than the Angle at N, B C &longs;hall be greater than B S; and <lb/>C R le&longs;&longs;er than S R: <emph type="italics"/>A<emph.end type="italics"/>nd, therfore O G &longs;hall be le&longs;&longs;er than P Z; <lb/>and G <emph type="italics"/>X<emph.end type="italics"/> greater than Z T: Therfore P Z is greater than double of <lb/>Z T; being that O G is double of G X. </s> <s>Let P H be double to H T; <lb/>and drawing a Line from H to K, prolong it to <foreign lang="greek">w.</foreign> The Center of <lb/>Gravity of the whole Portion &longs;hall be K; the Center of the part <lb/>which is within the Liquid H, and that of the part which is above <lb/>the Liquid in the Line K <foreign lang="greek">w</foreign>; which &longs;uppo&longs;ed to be <foreign lang="greek">w.</foreign> Therefore it <lb/>&longs;hall be demon&longs;trated, both, that K H is perpendicular to the Surface <lb/>of the Liquid, and tho&longs;e Lines al&longs;o that are drawn thorow the Points <lb/>Hand <foreign lang="greek">w</foreign> parallel to K H: And therfore the Portion &longs;hall not re&longs;t, but <lb/>&longs;hall encline untill that its Ba&longs;e do touch the Surface of the Liquid <lb/>in one Point; and &longs;o it &longs;hall continue. </s> <s>For in the Equall Portions <lb/>A O Q L and A P M L, the <lb/><figure id="id.040.01.1085.2.jpg" xlink:href="040/01/1085/2.jpg"/><lb/>Lines A Q and A M, that cut off <lb/>equall Portions, &longs;hall be dawn <lb/>from the Ends or Terms of the Ba&longs;es; <lb/>and A O Q and A P M &longs;hall be <lb/>demon&longs;trated, as in the former, to <lb/><arrow.to.target n="marg1378"></arrow.to.target><lb/>be equall: Therfore A Q and A M, <lb/>do make equall Acute Angles with <lb/>the Diameters of the Portions; and <pb xlink:href="040/01/1086.jpg" pagenum="392"/>the Angles at X and N are equall. </s> <s>And, therefore, if drawing HK, <lb/>it be prolonged to <foreign lang="greek">w,</foreign> the Centre of Gravity of the whole Portion &longs;hall <lb/>be K; of the part which is within the Liquid H; and of the part which <lb/>is above the Liquid in K <foreign lang="greek">w)</foreign> as &longs;uppo&longs;e in <foreign lang="greek">w;</foreign> and H K perpendicular to <lb/><figure id="id.040.01.1086.1.jpg" xlink:href="040/01/1086/1.jpg"/><lb/>the Surface of the Liquid. </s> <s>Therfore <lb/>along the &longs;ame Right Lines &longs;hall the <lb/>part which is within the Liquid move <lb/>upwards, and the part above it down­<lb/>wards: And therfore the Portion <lb/>&longs;hall re&longs;t with one of its Points <lb/>touching the Surface of the Liquid, <lb/>and its Axis &longs;hall make with the <lb/><arrow.to.target n="marg1379"></arrow.to.target><lb/>&longs;ame an Angle equall to X. </s> <s>It is <lb/>to be demon&longs;trated in the &longs;ame <lb/>manner that the Portion that hath <lb/>the &longs;ame proportion in Gravity to the Liquid, that the Square P F hath <lb/>to the Square B D, being demitted into the Liquid, &longs;o, as that its <lb/>Ba&longs;e touch not the Liquid, it &longs;hall &longs;tand inclined, &longs;o, as that its Ba&longs;e <lb/>touch the Surface of the Liquid in one Point only; and its Axis &longs;hall <lb/>make therwith an Angle equall to the Angle <foreign lang="greek">f.</foreign></s></p><p type="margin"> <s><margin.target id="marg1374"></margin.target>A</s></p><p type="margin"> <s><margin.target id="marg1375"></margin.target>B</s></p><p type="margin"> <s><margin.target id="marg1376"></margin.target>C</s></p><p type="margin"> <s><margin.target id="marg1377"></margin.target>D</s></p><p type="margin"> <s><margin.target id="marg1378"></margin.target>E</s></p><p type="margin"> <s><margin.target id="marg1379"></margin.target>F</s></p><p type="head"> <s>COMMANDINE.<lb/><arrow.to.target n="marg1380"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1380"></margin.target>A</s></p><p type="main"> <s>That is the Square T P to the Square B D.] <emph type="italics"/>By the twenty &longs;ixth of the Book<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1381"></arrow.to.target><lb/><emph type="italics"/>of<emph.end type="italics"/> Archimedes, De Conoidibus & Sphæroidibus: <emph type="italics"/>Therefore, (a) the Square T P <lb/>&longs;hall be equall to the Square X O: And for that rea&longs;on, the Line T P equall to the <lb/>Line X O.<emph.end type="italics"/><lb/><arrow.to.target n="marg1382"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1381"></margin.target>(a) <emph type="italics"/>By 9 of the <lb/>fifth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1382"></margin.target>B</s></p><p type="main"> <s>The Portions &longs;hall al&longs;o be equall.] <emph type="italics"/>By the twenty fifth of the &longs;ame Book.<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1383"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1383"></margin.target>C</s></p><p type="main"> <s>Again, becau&longs;e that in the Equall and Like Portions, A O Q L <lb/>and A P M L.] <emph type="italics"/>For, in the Portion A P M L, de&longs;cribe the Portion A O Q equall <lb/>to the Portion I P M: The Point Q falleth beneath M; for otherwi&longs;e, the Whole would be <lb/>equall to the Part. </s> <s>Then draw I V parallel to A Q, and cutting the Diameter is<emph.end type="italics"/> <foreign lang="greek">y;</foreign> <emph type="italics"/>and <lb/>let I M cut the &longs;ame<emph.end type="italics"/> <foreign lang="greek">s;</foreign> <emph type="italics"/>and A Q in<emph.end type="italics"/> <foreign lang="greek">s.</foreign> <emph type="italics"/>I &longs;ay <lb/>that the Angle A<emph.end type="italics"/> <foreign lang="greek">u</foreign> <emph type="italics"/>D, is le&longs;&longs;er than the Angle<emph.end type="italics"/><lb/><figure id="id.040.01.1086.2.jpg" xlink:href="040/01/1086/2.jpg"/><lb/><emph type="italics"/>I<emph.end type="italics"/> <foreign lang="greek">s</foreign> <emph type="italics"/>D. </s> <s>For the Angle I<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>D is equall to the <lb/>Angle A<emph.end type="italics"/> <foreign lang="greek">u</foreign> <emph type="italics"/>D: (b) But the interiour Angle<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1384"></arrow.to.target><lb/><emph type="italics"/>I<emph.end type="italics"/> <foreign lang="greek">y</foreign> <emph type="italics"/>D is le&longs;&longs;er than the exteriour I<emph.end type="italics"/> <foreign lang="greek">s</foreign> <emph type="italics"/>D: There-<emph.end type="italics"/><lb/><arrow.to.target n="marg1385"></arrow.to.target><lb/><emph type="italics"/>fore, (c) A<emph.end type="italics"/> <foreign lang="greek">u</foreign> <emph type="italics"/>D &longs;hall al&longs;o be lefter than I<emph.end type="italics"/> <foreign lang="greek">s</foreign> <emph type="italics"/>D.<emph.end type="italics"/><lb/><arrow.to.target n="marg1386"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1384"></margin.target>(b) <emph type="italics"/>By 29 of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1385"></margin.target><emph type="italics"/>(c) By 16 of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1386"></margin.target>D</s></p><p type="main"> <s>And the Angle at X, being le&longs;&longs;e <lb/>than the Angle at N.] <emph type="italics"/>Thorow O draw twe <lb/>Lines, O C perpendicular to the Diameter B D, and <lb/>O X touching the Section in the Point O, and cutting<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1387"></arrow.to.target><lb/><emph type="italics"/>the Diameter in X: (d) O X &longs;hall be parallel <lb/>to A <expan abbr="q;">que</expan> and the<emph.end type="italics"/> (e) <emph type="italics"/>Angle at X, &longs;hall be equall to<emph.end type="italics"/><lb/><arrow.to.target n="marg1388"></arrow.to.target><lb/><emph type="italics"/>that at<emph.end type="italics"/> <foreign lang="greek">u</foreign>: <emph type="italics"/>Therefore, the<emph.end type="italics"/> (f) <emph type="italics"/>Angle at X,<emph.end type="italics"/><lb/><arrow.to.target n="marg1389"></arrow.to.target><lb/><emph type="italics"/>&longs;hall be le&longs;&longs;er than the Angle at<emph.end type="italics"/> <foreign lang="greek">s;</foreign> <emph type="italics"/>that is, to <lb/>that at N: And, con&longs;equently, X &longs;hall fall beneath N: Therefore, the Line X B is greater than <lb/>N B. And, &longs;ince B C is equall to X B, and B S equall to N B; B C &longs;hall be greater than B S.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1087.jpg" pagenum="397"/><p type="margin"> <s><margin.target id="marg1387"></margin.target><emph type="italics"/>(d) By 5 of our &longs;e­<lb/>cond of<emph.end type="italics"/> Conicks.</s></p><p type="margin"> <s><margin.target id="marg1388"></margin.target>(e) <emph type="italics"/>By 29 of the <lb/>fir&longs;t.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1389"></margin.target>(f) <emph type="italics"/>By 39 of our <lb/>fir&longs;t of<emph.end type="italics"/> Conicks.</s></p><p type="main"> <s>Therefore, A Q and A M do make equall Acute Angles with <lb/><arrow.to.target n="marg1390"></arrow.to.target><lb/>the Diameters of the Portions.] <emph type="italics"/>We demon&longs;trate this as in the Commentaries <lb/>upon the &longs;econd Conclu&longs;ion.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1390"></margin.target>E</s></p><p type="main"> <s>It is to be demon&longs;trated in the &longs;ame manner, that the Portion <lb/><arrow.to.target n="marg1391"></arrow.to.target><lb/>that hath the &longs;ame proportion in Gravity to the Liquid, that the <lb/>Square P F hath to the Square B D, <lb/>being demitted into the Liquid, &longs;o, <lb/><figure id="id.040.01.1087.1.jpg" xlink:href="040/01/1087/1.jpg"/><lb/>as that its Ba&longs;e touch not the Li­<lb/>quid, it &longs;hall &longs;tand inclined, &longs;o, as <lb/>that its Ba&longs;e touch the Surface of the <lb/>Liquid in one point only; and its Axis <lb/>&longs;hall make therewith an angle equall <lb/>to the Angle <foreign lang="greek">f.</foreign>] <emph type="italics"/>Let the Portion be to the <lb/>Liquid in Gravity, as the Square P F to the <lb/>Square B D: and being demitted into the <lb/>Liquid, &longs;o inclined, as that its Ba&longs;e touch not <lb/>the Liquid, let it be cut thorow the Axis by a <lb/>Plane erect to the Surface of the Liquid, that <lb/>that the Section may be A M O L, the Section <lb/>of a Rightangled Cone; and, let the Section of the Liquids Surface be I O; and the Axit <lb/>of the Portion and Diameter of the Section B D; which let be cut into the &longs;ame parts as <lb/>we &longs;aid before, and draw M N parallel to I O, that it may touch the Section in the Point <lb/>M; and M T parallel to B D, and P M S perpe ndicular to the &longs;ame. </s> <s>It is to be demon­<lb/>strated, that the Portion &longs;hall not re&longs;t, but &longs;hall incline, &longs;o, as that it touch the Liquids <lb/>Surface, in one Point of its Ba&longs;e only. </s> <s>For,<emph.end type="italics"/><lb/><figure id="id.040.01.1087.2.jpg" xlink:href="040/01/1087/2.jpg"/><lb/><emph type="italics"/>draw P C perpendicular to B D; and drawing <lb/>a Line from A to F, prolong it till it meet with <lb/>the Section in <expan abbr="q;">que</expan> and thorow P draw P<emph.end type="italics"/> <foreign lang="greek">f</foreign> <emph type="italics"/>pa­<lb/>rallel to A Q: Now, by the things allready de­<lb/>mon&longs;trated by us, A F and F Q &longs;hall be equall <lb/>to one another. </s> <s>And being that the Portion hath <lb/>the &longs;ame proportion in Gravity unto the Liquid, <lb/>that the Square P F hath to the Square B D; and <lb/>&longs;eeing that the part &longs;ubmerged, hath the &longs;ame pro-<emph.end type="italics"/><lb/><arrow.to.target n="marg1392"></arrow.to.target><lb/><emph type="italics"/>partion to the whole Portion; that is, the Squàre <lb/>M T to the Square B D; (g) the Square M T <lb/>&longs;hall be equall to the Square P F; and, by the <lb/>&longs;ame rea&longs;on, the Line M T equall to the Line <lb/>P F. </s> <s>So that there being drawn in the equall & like <lb/>portions A P Q Land A M O L, the Lines A Q and I O which cut off equall Portions, the <lb/>fir&longs;t from the Extreme term of the Ba&longs;e, the la&longs;t not from the Extremity; it followeth, that <lb/>A Q drawn from the Extremity, containeth a le&longs;&longs;er Acute Angle with the Diameter of the <lb/>Portion, than I O: But the Line P<emph.end type="italics"/> <foreign lang="greek">f</foreign> <emph type="italics"/>is parallel to the Line A Q, and M N to I O: There­<lb/>fore, the Angle at<emph.end type="italics"/> <foreign lang="greek">f</foreign> <emph type="italics"/>&longs;hall be le&longs;&longs;er than the Angle at N; but the Line B C greater than B S; <lb/>and S R, that is, M X, greater than C R, that is, than P Y: and, by the &longs;ame rea&longs;on, X T <lb/>le&longs;&longs;er than Y F. And, &longs;ince P Y is double to Y F, M X &longs;hall be greater than double to <lb/>Y F, and much greater than double of X T. </s> <s>Let M H be double to H T, and draw a <lb/>Line from H to K, prolonging it. </s> <s>Now, the Centre of Gravity of the whole Portion <lb/>&longs;hall be the Point K; of the part within the Liquid H; and of the Remaining part above <lb/>the Liquid in the Line H K produced, as &longs;uppo&longs;e in<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>It &longs;hall be demon&longs;trated in the &longs;ame <lb/>manner, as before, that both the Line K H and tho&longs;e that are drawn thorow the Points H <lb/>and<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>parallel to the &longs;aid K H, are perpendicular to the Surface of the Liquid: The <lb/>Portion therefore, &longs;hall not re&longs;t; but when it &longs;hall be enclined &longs;o far as to touch the Sur­<lb/>face of the Liquid in one Point and no more, then it &longs;hall &longs;tay. </s> <s>For the Angle at N<emph.end type="italics"/> <pb xlink:href="040/01/1088.jpg" pagenum="398"/><figure id="id.040.01.1088.1.jpg" xlink:href="040/01/1088/1.jpg"/><lb/><emph type="italics"/>&longs;hall be equall to the Angle at<emph.end type="italics"/> <foreign lang="greek">f;</foreign> <emph type="italics"/>and the Line B S <lb/>equall to the Line B C; and S R to C R: Where­<lb/>fore, M H &longs;hall be likewi&longs;e equall to P Y. There­<lb/>fore, having drawn HK and prolonged it; the <lb/>Centre of Gravity of the whole Portion &longs;hall be <lb/>K; of that which is in the Liquid H; and of <lb/>that which is above it, the Centre &longs;hall be in <lb/>the Line prolonged: let it be in<emph.end type="italics"/> <foreign lang="greek">w.</foreign> <emph type="italics"/>There­<lb/>fore, along that &longs;ame Line K H, which is per­<lb/>pendicular to the Surface of the Liquid, &longs;hall <lb/>the part which is within the Liquid move up­<lb/>wards, and that which is above the Liquld <lb/>downwards: And, for this cau&longs;e, the Portion, <lb/>&longs;hall be no longer moved, but &longs;hall &longs;tay, and <lb/>re&longs;t, &longs;o, as that its Ba&longs;e do touch the Liquids Surface in but one Point; and its Axis <lb/>maketh an Angle therewith equall to the Angle<emph.end type="italics"/> <foreign lang="greek">f</foreign><emph type="italics"/>; And, this is that which we were to <lb/>demon&longs;trate.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1391"></margin.target>F</s></p><p type="margin"> <s><margin.target id="marg1392"></margin.target>(g) <emph type="italics"/>By 9 of t <lb/>fifth.<emph.end type="italics"/></s></p><p type="head"> <s>CONCLVSION IV.</s></p><p type="main"> <s><emph type="italics"/>If the Portion have greater proportion in Gravity <lb/>to the Liquid, than the Square F P to the Square <lb/>B D, but le&longs;&longs;er than that of the Square X O to the <lb/>Square B D, being demitted into the Liquid, <lb/>and inclined, &longs;o, as that its Ba&longs;e touch not the <lb/>Liquid, it &longs;hall &longs;tand and re&longs;t, &longs;o, as that its Ba&longs;e <lb/>&longs;hall be more &longs;ubmerged in the Liquid.<emph.end type="italics"/></s></p><p type="main"> <s>Again, let the Portion have greater proportion in <lb/>Gravity to the Liquid, than the Square F P to the <lb/>Square B D, but le&longs;&longs;er than that of the Square X O to <lb/>the Square B D; and as the Portion is in Gravity to the Liquid, <lb/>&longs;o let the Square made of the Line <foreign lang="greek">y</foreign> be to the Square B D. <foreign lang="greek">*y</foreign><lb/>&longs;hall be greater than F P, and le&longs;&longs;er than X O. Apply, therefore, <lb/>the right Line I V to fall betwixt the Portions A V Q L and A X D; <lb/>and let it be equall to <foreign lang="greek">y,</foreign> and parallel to B D; and let it meet <lb/>the Remaining Section in Y: V Y &longs;hall al&longs;o be proved double <lb/>to Y I, like as it hath been demon&longs;trated, that O G is double off <lb/>G X. And, draw from V, the Line V <foreign lang="greek">w,</foreign> touching the Section <lb/>A V Q L in V; and drawing a Line from A to I, prolong it unto <lb/><expan abbr="q.">que</expan> We prove in the &longs;ame manner, that the Line A I is equall <lb/>to I <expan abbr="q;">que</expan> and that A Q is parallel to V <foreign lang="greek">w.</foreign> It is to be demon&longs;trated, <lb/>that the Portion being demitted into the Liquid, and &longs;o inclined, <lb/>as that its Ba&longs;e touch not the Liquid, &longs;hall &longs;tand, &longs;o, that its Ba&longs;e <lb/>&longs;hall be more &longs;ubmerged in the Liquid, than to touch it Surface in <pb xlink:href="040/01/1089.jpg" pagenum="399"/>but one Point only. </s> <s>For let it be de­<lb/><figure id="id.040.01.1089.1.jpg" xlink:href="040/01/1089/1.jpg"/><lb/>mitted into the Liquid, as hath been <lb/>&longs;aid; and let it fir&longs;t be &longs;o inclined, as <lb/>that its Ba&longs;e do not in the lea&longs;t <lb/>touch the Surface of the Liquid. </s> <s>And <lb/>then it being cut thorow the Axis, <lb/>by a Plane erect unto the Surface of <lb/>the Liquid, let the Section of the <lb/>Portion be A N Z G; that of the <lb/>Liquids Surface E Z; the Axis of <lb/>the Portion and Diameter of the <lb/>Section B D; and let B D be cut in <lb/>the Points K and R, as before; and <lb/>draw N L parallel to E Z, and touching the Section A N Z G <lb/>in N, and N S perpendicular to <lb/><figure id="id.040.01.1089.2.jpg" xlink:href="040/01/1089/2.jpg"/><lb/>B D. Now, &longs;eeing that the Por­<lb/>tion is in Gravity unto the Liquid, <lb/>as the Square made of the Line <lb/>is to the Square B D; <foreign lang="greek">y</foreign> &longs;hall <lb/>be equall to N T: Which is to <lb/>be demon&longs;trated as above: And, <lb/>therefore, N T is al&longs;o equall to <lb/>V I: The Portions, therefore, <lb/>A V Q and E N Z are equall to <lb/>one another. </s> <s>And, &longs;ince that in <lb/>the Equall and like Portions A V <lb/>Q L and A N Z G, there are drawn A Q and E Z, cutting off <lb/>equall Portions, that from the <lb/><figure id="id.040.01.1089.3.jpg" xlink:href="040/01/1089/3.jpg"/><lb/>Extremity of the Ba&longs;e, this not <lb/>from the Extreme, that which is <lb/>drawn from the Extremity of the <lb/>Ba&longs;e, &longs;hall make the Acute Angle <lb/>with the Diameter of the Portion <lb/>le&longs;&longs;er: and in the Triangles N L S <lb/>and V <foreign lang="greek">w</foreign> C, the Angle at L is <lb/>greater than the Angle at <foreign lang="greek">w</foreign>: <lb/>Therefore, B S &longs;hall be le&longs;&longs;er <lb/>than B C; and S R le&longs;&longs;er than <lb/>C R: and, con&longs;equently, N X <lb/>greater than V H; and X T le&longs;&longs;er than H I. Seeing, therefore, <lb/>that V Y is double to Y I; It is manife&longs;t, that N X is greater than <lb/>double to X T. </s> <s>Let N M be double to M T: It is manife&longs;t, from what <lb/>hath been &longs;aid, that the Portion &longs;hall not re&longs;t, but will incline, untill <lb/>that its Bafe do touch the Surface of the Liquid: and it toucheth it in <lb/>one Point only, as appeareth in the Figure: And other things <pb xlink:href="040/01/1090.jpg" pagenum="400"/><figure id="id.040.01.1090.1.jpg" xlink:href="040/01/1090/1.jpg"/><lb/>&longs;tanding as before, we will again <lb/>demon&longs;trate, that N T is equall to <lb/>V I; and that the Portions A V Q <lb/>and A N Z are equall to each other. <lb/></s> <s>Therefore, in regard, that in the <lb/>Equall and Like Portions A V Q L <lb/>and A N Z G, there are drawn <lb/>A Q and A Z cutting off equall Por­<lb/>tions, they &longs;hall with the Diameters <lb/>of the Portions, contain equall <lb/>Angles. </s> <s>Therefore, in the Triangles <lb/>N L S and V <foreign lang="greek">w</foreign> C, the Angles at <lb/>the Points <emph type="italics"/>L<emph.end type="italics"/> and <foreign lang="greek">w</foreign> are equall; and the Right Line B S equall to <lb/>B C; S R to C R; N X to V H; and X T to H I: And, &longs;ince <lb/>V Y is double to Y I, N X &longs;hall be greater than double of X T. <lb/></s> <s>Let therefore, N M be double to M T. </s> <s>It is hence again manife&longs;t, <lb/>that the Portion will not remain, but &longs;hall incline on the part <lb/>towards A: But it was &longs;uppo&longs;ed, that the &longs;aid Portion did <lb/>touch the Surface of the Liquid in one &longs;ole Point: Therefore, <lb/>its Ba&longs;e mu&longs;t of nece&longs;&longs;ity &longs;ubmerge farther into the Liquid.</s></p><p type="head"> <s>CONCLVSION V.</s></p><p type="main"> <s><emph type="italics"/>If the Portion have le&longs;&longs;er proportion in Gravity to <lb/>the Liquid, than the Square F P to the Square <lb/>B D, being demitted into the Liquid, and in­<lb/>clined, &longs;o, as that its Ba&longs;e touch not the Liquid, <lb/>it &longs;hall &longs;tand &longs;o inclined, as that its Axis &longs;hall <lb/>make an Angle with the Surface of the Liquid, <lb/>le&longs;&longs;e than the Angle<emph.end type="italics"/> <foreign lang="greek">y;</foreign> <emph type="italics"/>And its Ba&longs;e &longs;hall <lb/>not in the lea&longs;t touch the Liquids Surface.<emph.end type="italics"/></s></p><p type="main"> <s>Finally, let the Portion have le&longs;&longs;er proportion to the Liquid <lb/>in Gravity, than the Square F P hath to the Square B D; and <lb/>as the Portion is in Gravity to the Liquid, &longs;o let the <lb/>Square made of the Line <foreign lang="greek">y</foreign> be to the Square B D. <foreign lang="greek">y</foreign> &longs;hall be <lb/>le&longs;&longs;er than P F. Again, apply any Right Line as G I, falling <lb/>betwixt the Sections A G Q L and A X D, and parallel to B D; <lb/>and let it cut the Middle Conick Section in the Point H, and <pb xlink:href="040/01/1091.jpg" pagenum="401"/>the Right Line R Y in Y. </s> <s>We <lb/><figure id="id.040.01.1091.1.jpg" xlink:href="040/01/1091/1.jpg"/><lb/>&longs;hall demon&longs;trate G H to be double <lb/>to H I, as it hathbeen demon&longs;tra­<lb/>ted, that O G is double to G X. <lb/></s> <s>Then draw G <foreign lang="greek">w</foreign> touching the Section <lb/>A G Q L in G; and G C perpen di­<lb/>cular to B D; and drawing a Line <lb/>from A to I, prolong it to <expan abbr="q.">que</expan> Now <lb/>A I &longs;hall be equall to I <expan abbr="q;">que</expan> and <lb/>A Q parallel to G <foreign lang="greek">w.</foreign> It is to be <lb/>demon&longs;trated, that the Portion being <lb/>demitted into the Liquid, and inclined, &longs;o, as that its Ba&longs;e touch <lb/>the Liquid, it &longs;hall &longs;tand &longs;o incli­<lb/><figure id="id.040.01.1091.2.jpg" xlink:href="040/01/1091/2.jpg"/><lb/>ned, as that its Axis &longs;hall make <lb/>an Angle with the Surface of the <lb/>Liquid le&longs;&longs;e than the Angle <foreign lang="greek">f;</foreign><lb/>and its Ba&longs;e &longs;hall not in the lea&longs;t <lb/>touch the Liquids Surface. </s> <s>For <lb/>let it be demitted into the Liquid, <lb/>and let it &longs;tand, &longs;o, as that its Ba&longs;e <lb/>do touch the Surface of the Liquid <lb/>in one Point only: and the Portion <lb/>being cut thorow the Axis by a <lb/>Plane erect unto the Surface of the Liquid, let the Section of <lb/><figure id="id.040.01.1091.3.jpg" xlink:href="040/01/1091/3.jpg"/><lb/>the Portion be A N Z L, the Section <lb/>of a Rightangled Cone; that of <lb/>the Surface of the Liquid A Z; and <lb/>the Axis of the Portion and Dia­<lb/>meter of the Section B D; and let <lb/>B D be cut in the Points K and R <lb/>as hath been &longs;aid above; and draw <lb/>N F parallel to A Z, and touching <lb/>the Section of the Cone in the Point <lb/>N; and N T parallel to B D; and <lb/>N S perpendicular to the &longs;ame. </s> <s>Be­<lb/>cau&longs;e, now, that the Portion is in Gravity to the Liquid, as <lb/>the Square made of <foreign lang="greek">y</foreign> is to the Square B D; and &longs;ince that as the <lb/>Portion is to the Liquid in Gravity, &longs;o is the Square N T to the <lb/>Square B D, by the things that have been &longs;aid; it is plain, that <lb/>N T is equall to the Line <foreign lang="greek">y</foreign>: And, therefore, al&longs;o, the Portions <lb/>A N Z and A G Q are equall. </s> <s>And, &longs;eeing that in the Equall and <lb/>Like Portions A G Q L and A N Z L; there are drawn from the <lb/>Extremities of their Ba&longs;es, A Q and A Z which cut off equall Porti­<lb/>ons: It is obvious, that with the Diameters of the Portions they <pb xlink:href="040/01/1092.jpg" pagenum="402"/>make equall Angles; and that in the Triangles N F S and G <foreign lang="greek">w</foreign> C <lb/>the Angles at F and <foreign lang="greek">w</foreign> are equall; as al&longs;o, that S B and B C, and<lb/>S R and C R are equall to one another: And, therefore, N X and<lb/>G Y are al&longs;o equall; and X T and Y I. </s> <s>And &longs;ince G H is double<lb/>to H I, N X &longs;hall be le&longs;&longs;er than double of X T. </s> <s>Let N M therefore<lb/>be double to M T; and drawing a Line from M to K, prolong it<lb/>unto E. </s> <s>Now the Centre of Gravity of the whole &longs;hall be the<lb/>Point K; of the part which is in the Liquid the Point M; and<lb/>that of the part which is above the Liquid in the Line prolonged <lb/>as &longs;uppo&longs;e in E. Therefore, by what was even now demon&longs;trated <lb/>it is manife&longs;t that the Portion &longs;hall not &longs;tay thus, but &longs;hall incline, &longs;o <lb/>as that its Ba&longs;e do in no wi&longs;e touch the Surface of the Liquid <lb/>And that the Portion will &longs;tand, &longs;o, as to make an Angle with the<lb/>Surface of the Liquid le&longs;&longs;er than<lb/><figure id="id.040.01.1092.1.jpg" xlink:href="040/01/1092/1.jpg"/><lb/>the Angle <foreign lang="greek">f,</foreign> &longs;hall thus be demon <lb/>&longs;trated. </s> <s>Let it, if po&longs;&longs;ible, &longs;tand,<lb/>&longs;o, as that it do not make an Angle<lb/>le&longs;&longs;er than the Angle <foreign lang="greek">f;</foreign> and di&longs;po&longs;e<lb/>all things el&longs;e in the &longs;ame manner a <lb/>before; as is done in the pre&longs;et <lb/>Figure. </s> <s>We are to demon&longs;trat <lb/>in the &longs;ame method, that N T is e­<lb/>quall to <foreign lang="greek">y;</foreign> and by the &longs;ame rea&longs;or <lb/>equall al&longs;o to G I. </s> <s>And &longs;ince that in<lb/>the Triangles P <foreign lang="greek">f</foreign> C and N F S, the Angle F is not le&longs;&longs;er than the<lb/>Angle <foreign lang="greek">f,</foreign> B F &longs;hall not be greater than B C: And, therefore, neither<lb/>&longs;hall S R be le&longs;&longs;er than C R; nor N X than P Y: But &longs;ince P F is<lb/>greater than N T, let P F be Se&longs;quialter of P Y: N T &longs;hall be le&longs;&longs;er<lb/>than Se&longs;quialter of N X: And, therefore, N X &longs;hall be greate <lb/>than double of X T. </s> <s>Let N M be double of M T; and drawing <lb/>Line from M to K prolong it. </s> <s>It is manife&longs;t, now, by what hath<lb/>been &longs;aid, that the Portion &longs;hall not continue in this po&longs;ition, but &longs;hall<lb/>turn about, &longs;o, as that its Axis do make an Angle with the Surface<lb/>of the Liquid, le&longs;&longs;er than the Angle <foreign lang="greek">f.</foreign> </s></p><p type="head"> <s><emph type="italics"/>FINIS.<emph.end type="italics"/></s></p></chap><pb xlink:href="040/01/1093.jpg"/> <chap> <p type="head"> <s>A <lb/>DISCOURSE <lb/><emph type="italics"/>PRESENTED<emph.end type="italics"/><lb/>TO THE MOST SERENE <lb/>Don Co&longs;imo II. <lb/>GREAT DUKE <lb/><emph type="italics"/>OF<emph.end type="italics"/><lb/>TUSCANY, <lb/>CONCERNING <lb/>The <emph type="italics"/>NATATION<emph.end type="italics"/> of BODIES Vpon, <lb/>And <emph type="italics"/>SUBMERSION<emph.end type="italics"/> In, <lb/>THE <lb/>WATER.</s></p><p type="head"> <s>By GALILEUS GALILEI: Philo&longs;opher and <lb/>Mathematician, unto His mo&longs;t Serene Highne&longs;&longs;e.</s></p><p type="head"> <s>Engli&longs;hed from the Second Edition of the ITALIAN, <lb/>compared with the Manu&longs;cript Copies, and reduced <lb/>into PROPOSITIONS: <lb/>By <emph type="italics"/>THOMAS SALUSBURY,<emph.end type="italics"/> <expan abbr="E&longs;q;">E&longs;que</expan></s></p><p type="head"> <s><emph type="italics"/>LONDON<emph.end type="italics"/>: <lb/>Printed by WILLIAM LEYBOURN: <lb/><emph type="italics"/>M D C LXIII.<emph.end type="italics"/></s></p></chap><chap> <pb xlink:href="040/01/1094.jpg" pagenum="401"/><p type="head"> <s>A DISCOVRSE <lb/>Pre&longs;ented to the Mo&longs;t Serene DON COSIMO II. <lb/>GREATDUKE of <emph type="italics"/>TUSC ANY:<emph.end type="italics"/><lb/>CONCERNING<lb/><emph type="italics"/>The Natation of BODIES Upon, or Submer&longs;ion <lb/>In, the WATER.<emph.end type="italics"/></s> </p></chap> <chap><p type="main"> <s>Con&longs;idering (Mo&longs;t Serene Prince) that the <lb/>publi&longs;hing this pre&longs;ent Treati&longs;e, of &longs;o <lb/>different an Argument from that which <lb/><arrow.to.target n="marg1393"></arrow.to.target><lb/>many expect, and which according to the <lb/>intentions I propo&longs;ed in my ^{*} A&longs;tronomi­<lb/>call <emph type="italics"/>Advi&longs;o,<emph.end type="italics"/> I &longs;hould before this time <lb/>have put forth, might peradventure make <lb/>&longs;ome thinke, either that I had wholly <lb/>relinqui&longs;hed my farther imployment <lb/>about the new Cele&longs;tiall Ob&longs;ervations, <lb/>or that, at lea&longs;t, I handled them very <lb/>remi&longs;&longs;ely; I have judged fit to render an account, a&longs;well of my <lb/>deferring that, as of my writing, and publi&longs;hing this treati&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1393"></margin.target>His Nuncio Sl­<lb/>derio.</s></p><p type="main"> <s>As to the fir&longs;t, the la&longs;t di&longs;coveries of <emph type="italics"/>Saturn<emph.end type="italics"/> to be tricorporeall, and <lb/>of the mutations of Figure in <emph type="italics"/>Venus,<emph.end type="italics"/> like to tho&longs;e that are &longs;een in the <lb/>Moon, together with the Con&longs;equents depending thereupon, have <lb/>not &longs;o much occa&longs;ioned the demur, as the inve&longs;tigation of the times <lb/>of the Conver&longs;ions of each of the Four Medicean Planets about <emph type="italics"/>Ju­ <lb/>piter,<emph.end type="italics"/> which I lighted upon in <emph type="italics"/>April<emph.end type="italics"/> the year pa&longs;t, 1611, at my being in <lb/><emph type="italics"/>Rome<emph.end type="italics"/>; where, in the end, I a&longs;&longs;ertained my &longs;elfe, that the fir&longs;t and neere&longs;t <lb/>to <emph type="italics"/>Jupiter,<emph.end type="italics"/> moved about 8 <emph type="italics"/>gr.<emph.end type="italics"/> & 29 <emph type="italics"/>m.<emph.end type="italics"/> of its Sphere in an houre, make­ <lb/>ing its whole revolution in one naturall day, and 18 hours, and almo&longs;t <lb/>an halfe. </s><s>The &longs;econd moves in its Orbe 14 <emph type="italics"/>gr. </s><s>13 min.<emph.end type="italics"/> or very neer, <lb/>in an hour, and its compleat conver&longs;ion is con&longs;ummate in 3 dayes, 13 <lb/>hours, and one third, or thereabouts. </s><s>The third pa&longs;&longs;eth in an hour, <lb/>2 <emph type="italics"/>gr. </s><s>6 min.<emph.end type="italics"/> little more or le&longs;s of its Circle, and mea&longs;ures it all in 7 <lb/>dayes, 4 hours, or very neer. </s><s>The fourth, and more remote than the <lb/>re&longs;t, goes in one houre, o <emph type="italics"/>gr 54 min.<emph.end type="italics"/> and almo&longs;t an halfe of its Sphere, <lb/>and fini&longs;heth it all in 16 dayes, and very neer 18 hours. </s><s>But be­ <lb/>cau&longs;e the exce&longs;&longs;ive velocity of their returns or re&longs;titutions, requires a <lb/>mo&longs;t &longs;crupulous preci&longs;ene&longs;&longs;e to calculate their places, in times pa&longs;t <pb xlink:href="040/01/1095.jpg" pagenum="402"/>and future, e&longs;pecially if the time be for many Moneths or Years; I <lb/>am therefore forced, with other Ob&longs;ervations, and more exact than <lb/>the former, and in times more remote from one another, to correct <lb/>the Tables of &longs;uch Motions, and limit them even to the &longs;horte&longs;t mo­ <lb/>ment: for &longs;uch exactne&longs;&longs;e my fir&longs;t Ob&longs;ervations &longs;uffice not; not only <lb/>in regard of the &longs;hort intervals of Time, but becau&longs;e I had not as then <lb/>found out a way to mea&longs;ure the di&longs;tances between the &longs;aid Planets <lb/>by any In&longs;trument: I Ob&longs;erved &longs;uch Intervals with &longs;imple relation <lb/>to the Diameter of the Body of <emph type="italics"/>Jupiter<emph.end type="italics"/>; taken, as we have &longs;aid, by <lb/>the eye, the which, though they admit not errors of above a Minute, <lb/>yet they &longs;uffice not for the determination of the exact greatne&longs;s of the <lb/>Spheres of tho&longs;e Stars. </s><s>But now that I have hit upon a way of ta­ <lb/>king &longs;uch mea&longs;ures without failing, &longs;carce in a very few Seconds, I will <lb/>continue the ob&longs;ervation to the very occultation of <emph type="italics"/>JVPITER,<emph.end type="italics"/> <lb/>which &longs;hall &longs;erve to bring us to the perfect knowledge of the Moti­ <lb/>ons, and Magnitudes of the Orbes of the &longs;aid Planets, together <lb/><arrow.to.target n="marg1394"></arrow.to.target> <lb/>al&longs;o with &longs;ome other con&longs;equences thence ari&longs;ing. </s><s>I adde to the&longs;e <lb/>things the ob&longs;ervation of &longs;ome ob&longs;cure Spots, which are di&longs;cover­ <lb/>ed in the Solar Body, which changing, po&longs;ition in that, propounds <lb/>to our con&longs;ideration a great argument either that the Sun revolves in <lb/>it &longs;elfe, or that perhaps other Starts, in like manner as <emph type="italics"/>Venus<emph.end type="italics"/> and <lb/><emph type="italics"/>Mercury,<emph.end type="italics"/> revolve about it, invi&longs;ible in other times, by rea&longs;on of their <lb/>&longs;mall digre&longs;&longs;ions, le&longs;&longs;e than that of <emph type="italics"/>Mercury,<emph.end type="italics"/> and only vi&longs;ible when <lb/>they interpo&longs;e between the Sun and our eye, or el&longs;e hint the truth <lb/>of both this and that; the certainty of which things ought not to be <lb/>contemned, nor omitted.</s></p><p type="margin"> <s><margin.target id="marg1394"></margin.target>The Authors <lb/>Ob&longs;ervations of <lb/>the Solar Spots.</s></p><p type="main"> <s><emph type="italics"/>Continuall ob&longs;ervation hath at la&longs;t a&longs;&longs;ured me that the&longs;e Spots are <lb/>matters contiguous to the Body of the Sun, there continually produced <lb/>in great number, and afterwards di&longs;&longs;olved, &longs;ome in a &longs;horter, &longs;ome in a <lb/>longer time, and to be by the Conver&longs;ion or Revolution of the Sun in it <lb/>&longs;elfe, which in a Lunar Moneth, or thereabouts, fini&longs;heth its Period, <lb/>caried about in a Circle, an accident great of it &longs;elfe, and greater for <lb/>its Con&longs;equences.<emph.end type="italics"/> <lb/><arrow.to.target n="marg1395"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1395"></margin.target>The occa&longs;ion in­ <lb/>ducing the Au­ <lb/>thor to write <lb/>this Treati&longs;e.</s></p><p type="main"> <s>As to the other particular in the next place. ^{*} Many cau&longs;es have <lb/>moved me to write the pre&longs;ent Tract, the &longs;ubject whereof, is the <lb/>Di&longs;pute which I held &longs;ome dayes &longs;ince, with &longs;ome learned men of <lb/>this City, about which, as your Highne&longs;&longs;e knows, have followed <lb/>many Di&longs;cour&longs;es: The principall of which Cau&longs;es hath been the <lb/>Intimation of your Highne&longs;&longs;e, having commended to me Writing, <lb/>as a &longs;ingular means to make true known from fal&longs;e, reall from appa­ <lb/>rent Rea&longs;ons, farr better than by Di&longs;puting vocally, where the <lb/>one or the other, or very often both the Di&longs;putants, through too <pb xlink:href="040/01/1096.jpg" pagenum="403"/>greate heate, or exalting of the voyce, either are not under&longs;tood, <lb/>or el&longs;e being tran&longs;ported by o&longs;tentation of not yeilding to one ano­ <lb/>ther, farr from the fir&longs;t Propo&longs;ition, with the novelty, of the <lb/>various Propo&longs;als, confound both them&longs;elves and their Auditors.</s></p><p type="main"> <s>Moreover, it &longs;eemed to me convenient to informe your High­ <lb/>ne&longs;&longs;e of all the &longs;equell, concerning the Controver&longs;ie of which I <lb/>treat, as it hath been adverti&longs;ed often already by others: and becau&longs;e <lb/>the Doctrine which I follow, in the di&longs;cu&longs;&longs;ion of the point in hand, <lb/>is different from that of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; and interferes with his Principles, <lb/>I have con&longs;idered that again&longs;t the Authority of that mo&longs;t famous <lb/>Man, which among&longs;t many makes all &longs;u&longs;pected that comes not from <lb/>the Schooles of the Peripateticks, its farr better to give ones Rea&longs;ons <lb/>by the Pen than by word of mouth and therfore I re&longs;olved to write the <lb/>pre&longs;ent di&longs;cour&longs;e: in which yet I hope to demon&longs;trate that it was not <lb/>out of capritiou&longs;ne&longs;&longs;e, or for that I had not read or under&longs;tood <lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that I &longs;ometimes &longs;werve from his opinion, but becau&longs;e <lb/>&longs;everall Rea&longs;ons per&longs;wade me to it, and the &longs;ame <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath </s></p><p type="main"> <s><arrow.to.target n="marg1396"></arrow.to.target> <lb/>tought me to fix my judgment on that which is grounded upon <lb/>Rea&longs;on, and not on the bare Authority of the Ma&longs;ter; and it is <lb/>mo&longs;t certaine according to the &longs;entence of <emph type="italics"/>Alcinoos,<emph.end type="italics"/> that philo&longs;opha­ <lb/><arrow.to.target n="marg1397"></arrow.to.target> <lb/>ting &longs;hould be free. </s><s>Nor is the re&longs;olution of our Que&longs;tion in my <lb/>judgment without &longs;ome benefit to the Univer&longs;all, fora&longs;much as <lb/>treating whether the figure of Solids operates, or not, in their going, <lb/>or not going to the bottome in Water, in occurrences of building <lb/>Bridges or other Fabricks on the Water, which happen commonly <lb/>in affairs of grand import, it may be of great availe to know the <lb/>truth.</s></p><p type="margin"> <s><margin.target id="marg1396"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> prefers <lb/>Rea&longs;on to the <lb/>Authority ofan <lb/>Author.</s></p><p type="margin"> <s><margin.target id="marg1397"></margin.target>The benefit of <lb/>this Argument.</s></p><p type="main"> <s>I &longs;ay therfore, that being the la&longs;t Summer in company with certain <lb/><arrow.to.target n="marg1398"></arrow.to.target> <lb/>Learned men, it was &longs;aid in the argumentation; That Conden&longs;ation <lb/>was the propriety of Cold, and there was alledged for in&longs;tance, the <lb/>example of Ice: now I at that time &longs;aid, that, in my judgment, <lb/>the Ice &longs;hould be rather Water rarified than conden&longs;ed, and my <lb/><arrow.to.target n="marg1399"></arrow.to.target> <lb/>rea&longs;on was, becau&longs;e Conden&longs;ation begets diminution of Ma&longs;s, and <lb/>augmentation of gravity, and Rarifaction cau&longs;eth greater Lightne&longs;s, <lb/>and augmentarion of Ma&longs;&longs;e: and Water in freezing, encrea&longs;eth in <lb/>Ma&longs;&longs;e, and the Ice made thereby is lighter than the Water on which <lb/>it &longs;wimmeth.</s></p><p type="margin"> <s><margin.target id="marg1398"></margin.target>Conden&longs;ation <lb/>the Propriety of <lb/>Cold, according <lb/>to the Peripate­ <lb/>ticks.</s></p><p type="margin"> <s><margin.target id="marg1399"></margin.target>Ice rather water <lb/>rarified, than <lb/>conden&longs;ed, and <lb/>why:</s></p><p type="main"> <s><emph type="italics"/>What I &longs;ay, is manife&longs;t, becau&longs;e, the medium &longs;ubtracting from the <lb/>whole Gravity of Sollids the weight of &longs;uch another Ma&longs;&longs;e of the &longs;aid<emph.end type="italics"/> <lb/><arrow.to.target n="marg1400"></arrow.to.target> <lb/><emph type="italics"/>Medium; was<emph.end type="italics"/> Archimedes <emph type="italics"/>proves in his ^{*} Fir&longs;t Booke<emph.end type="italics"/> De In&longs;identibus <lb/>Humido; <emph type="italics"/>when ever the Ma&longs;&longs;e of the &longs;aid Solid encrea&longs;eth by Di&longs;traction, <lb/>the more &longs;hall the<emph.end type="italics"/> Medium <emph type="italics"/>detract from its entire Gravity; and le&longs;&longs;e, <lb/>when by Compre&longs;&longs;ion it &longs;hall be conden&longs;ed and reduced to a le&longs;&longs;e Ma&longs;&longs;e.<emph.end type="italics"/></s></p><p type="margin"> <pb xlink:href="040/01/1097.jpg" pagenum="404"/> <s><margin.target id="marg1400"></margin.target>In lib: 1. of Na­ <lb/>tation of Bodies <lb/>Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1401"></margin.target>Figure operates <lb/>not in the Nata­ <lb/>tion of Sollids.</s></p><p type="main"> <s>It was an&longs;wered me, that that proceeded not from the greater Levity; <lb/><arrow.to.target n="marg1401"></arrow.to.target> <lb/>but from the Figure, large and flat, which not being able to pene­ <lb/>trate the Re&longs;i&longs;tance of the Water, is the cau&longs;e that it &longs;ubmergeth not. <lb/></s><s>I replied, that any piece of Ice, of what&longs;oever Figure, &longs;wims upon <lb/>the Water, a manife&longs;t &longs;igne, that its being never &longs;o flat and broad, <lb/>hath not any part in its floating: and added, that it was a manife&longs;t <lb/>proofe hereof to &longs;ee a piece of Ice of very broad Figure being thru&longs;t <lb/>to the botome of the Water, &longs;uddenly return to flote atoppe, which <lb/>had it been more grave, and had its &longs;wimming proceeded from its <lb/>Forme, unable to penetrate the Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> that <lb/>would be altogether impo&longs;&longs;ible; I concluded therefore, that the Figure <lb/>was in &longs;ort a Cau&longs;e of the Natation or Submer&longs;ion of Bodies, <lb/>but the greater or le&longs;&longs;e Gravity in re&longs;pect of the Water: and there­ <lb/>fore all Bodyes heavier than it of what Figure &longs;oever they be, indiffe­ <lb/>rently go to the bottome, and the lighter, though of any figure, float <lb/>indifferently on the top: and I &longs;uppo&longs;e that tho&longs;e which hold other­ <lb/>wi&longs;e, were induced to that beliefe, by &longs;eeing how that diver&longs;ity <lb/>of Formes or Figures, greatly altereth the Velo&longs;ity, and Tardity <lb/>of Motion; &longs;o that Bodies of Figure broad and thin, de&longs;cend <lb/>far more lea&longs;urely into the Water, than tho&longs;e of a more compacted <lb/>Figure, though both made of the &longs;ame Matter: by which &longs;ome <lb/>might be induced to believe that the Dilatation of the Figure might <lb/>reduce it to &longs;uch amplene&longs;&longs;e that it &longs;hould not only retard but wholly <lb/>impede and take away the Motion, which I hold to be fal&longs;e. </s><s>Upon <lb/>this Conclu&longs;ion, in many dayes di&longs;cour&longs;e, was &longs;poken much, and <lb/>many things, and divers Experiments produced, of which your <lb/>Highne&longs;&longs;e heard, and &longs;aw &longs;ome, and in this di&longs;cour&longs;e &longs;hall have <lb/>all that which hath been produced again&longs;t my A&longs;&longs;ertion, and what <lb/>hath been &longs;ugge&longs;ted to my thoughts on this matter, and for con­ <lb/>firmation of my Conclu&longs;ion: which if it &longs;hall &longs;uffice to remove that <lb/>(as I e&longs;teem hitherto fal&longs;e) Opinion, I &longs;hall thinke I have not <lb/>unprofitably &longs;pent my paynes and time. </s><s>and although that come <lb/>not to pa&longs;&longs;e, yet ought I to promi&longs;e another benefit to my &longs;elfe, <lb/>namely, of attaining the knowledge of the truth, by hearing my <lb/>Fallacyes confuted, and true demon&longs;trations produced by tho&longs;e <lb/>of the contrary opinion.</s></p><p type="main"> <s>And to proceed with the greate&longs;t plainne&longs;s and per&longs;picuity that <lb/>I can po&longs;&longs;ible, it is, I conceive, nece&longs;&longs;ary, fir&longs;t of all to declare <lb/>what is the true, intrin&longs;ecall, and totall Cau&longs;e, of the a&longs;cending of <lb/>&longs;ome Sollid Bodyes in the Water, and therein floating; or on the <lb/>contrary, of their &longs;inking. </s><s>and &longs;o much the rather in a&longs;much as I <lb/>cannot &longs;atisfie my &longs;elfe in that which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath left written on <lb/>this Subject.</s></p><p type="margin"> <s><margin.target id="marg1402"></margin.target>The cau&longs;e of the <lb/>Natation & &longs;ub­</s></p> <p type="main"> <s>I &longs;ay then the Cau&longs;e why &longs;ome Sollid Bodyes de&longs;cend to the <lb/><arrow.to.target n="marg1402"></arrow.to.target> <pb xlink:href="040/01/1098.jpg" pagenum="405"/>Bottom of Water, is the exce&longs;&longs;e of their Gravity, above the <lb/><arrow.to.target n="marg1403"></arrow.to.target> <lb/>Gravity of the Water; and on the contrary, the exce&longs;s of the <lb/>Waters Gravity above the Gravity of tho&longs;e, is the Cau&longs;e that others <lb/>do not de&longs;cend, rather that they ri&longs;e from the Bottom, and a&longs;cend <lb/>to the Surface. </s><s>This was &longs;ubtilly demon&longs;trated by <emph type="italics"/>Archimedes<emph.end type="italics"/> in <lb/>his Book Of the NATATION of BODIES: Conferred afterwards <lb/>by a very grave Author, but, if I erre not invi&longs;ibly, as below for <lb/>defence of him, I &longs;hall endeavour to prove.</s></p><p type="margin"> <s><margin.target id="marg1403"></margin.target>mer&longs;ion of Sol­ <lb/>ids in the Wa­ <lb/>ter.</s></p><p type="main"> <s>I, with a different Method, and by other meanes, will endeavour <lb/>to demon&longs;trate the &longs;ame, reducing the Cau&longs;es of &longs;uch Effects to <lb/>more intrin&longs;ecall and immediate Principles, in which al&longs;o are di&longs;co­ <lb/>vered the Cau&longs;es of &longs;ome admirable and almo&longs;t incredible Acci­ <lb/>dents, as that would be, that a very little quantity of Water, &longs;hould <lb/>be able, with its &longs;mall weight, to rai&longs;e and &longs;u&longs;tain a Solid Body, an <lb/>hundred or a thou&longs;and times heavier than it.</s></p><p type="main"> <s>And becau&longs;e demon&longs;trative Order &longs;o requires, I &longs;hall define cer­ <lb/>tain Termes, and afterwards explain &longs;ome Propo&longs;itions, of which, <lb/>as of things true and obvious, I may make u&longs;e of to my pre&longs;ent pur­ <lb/>po&longs;e.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s><emph type="italics"/>I then call equally Grave<emph.end type="italics"/> in &longs;pecie, <emph type="italics"/>tho&longs;e Matters <lb/>of which equall Ma&longs;&longs;es weigh equally.<emph.end type="italics"/></s></p><p type="main"> <s>As if for example, two Balls, one of Wax, and the other of &longs;ome <lb/>Wood of equall Ma&longs;&longs;e, were al&longs;o equall in Weight, we &longs;ay, that <lb/>&longs;uch Wood, and the Wax are <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> equally grave.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s><emph type="italics"/>But equally grave in Ab&longs;olute Gravity, we call two <lb/>Sollids, weighing equally, though of Ma&longs;s they be <lb/>unequall.<emph.end type="italics"/></s></p><p type="main"> <s>As for example, a Ma&longs;s of Lead, and another of Wood, that <lb/>weigh each ten pounds, I call equall in Ab&longs;olute Gravity, though <lb/>the Ma&longs;s of the Wood be much greater then that of the Lead.</s></p><p type="main"> <s><emph type="italics"/>And, con&longs;equently, le&longs;s Grave<emph.end type="italics"/> in &longs;pecie.</s></p><p type="head"> <s>DEFINITION III.</s></p><p type="main"> <s><emph type="italics"/>I call a Matter more Grave<emph.end type="italics"/> in &longs;pecie <emph type="italics"/>than another, of <lb/>which a Ma&longs;s, equall to a Ma&longs;s of the other, &longs;hall <lb/>weigh more.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1099.jpg" pagenum="406"/><p type="main"> <s>And &longs;o I &longs;ay, that Lead is more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than Tinn, becau&longs;e <lb/>if you take of them two equall Ma&longs;&longs;es, that of the Lead weigheth <lb/>more.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s><emph type="italics"/>But I call that Body more grave ab&longs;olutely than this, if <lb/>that weigh more than this, without any re&longs;pect had to <lb/>the Ma&longs;&longs;es.<emph.end type="italics"/></s></p><p type="main"> <s>And thus a great piece of Wood is &longs;aid to weigh more than a <lb/>little lump of Lead, though the Lead be <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> more heavy than <lb/>the Wood. </s><s>And the &longs;ame is to be under&longs;tood of the le&longs;s grave <emph type="italics"/>in <lb/>&longs;pecie,<emph.end type="italics"/> and the le&longs;s grave ab&longs;olutely.</s></p><p type="main"> <s>The&longs;e Termes defined, I take from the Mechanicks two Princi­ <lb/>ples: the fir&longs;t is, that</s></p><p type="head"> <s>AXIOME. I.</s></p><p type="main"> <s><emph type="italics"/>Weights ab&longs;olutely equall, moved with equall Velocity, <lb/>are of equall Force and Moment in their operations.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>DEFINITION V.<emph.end type="italics"/></s></p><p type="main"> <s>Moment, among&longs;t Mechanicians, &longs;igrifieth that <lb/>Vertue, that Force, or that Efficacy, with which <lb/>the Mover moves, and the Moveable re&longs;i&longs;ts.</s></p><p type="main"> <s><emph type="italics"/>Which Vertue dependes not only on the &longs;imple Gravity, but on the <lb/>Velocity of the Motion, and on the diver&longs;e Inclinations of the Spaces <lb/>along which the Motion is made: For a de&longs;cending Weight makes a <lb/>greater<emph.end type="italics"/> Impetus <emph type="italics"/>in a Space much declining, than in one le&longs;s declining; <lb/>and in &longs;umme, what ever is the occa&longs;ion of &longs;uch Vertue, it ever retaines <lb/>the name of<emph.end type="italics"/> Moment; <emph type="italics"/>nor in my Judgement, is this &longs;ence new in our <lb/>Idiome, for, if I mistake not, I think we often &longs;ay; This is a weighty <lb/>bu&longs;ine&longs;&longs;e, but the other is of &longs;mall moment: and we con&longs;ider lighter mat­ <lb/>ters and let pa&longs;s tho&longs;e of Moment; a Metaphor, I &longs;uppo&longs;e, taken from <lb/>the Mechanicks.<emph.end type="italics"/></s></p><p type="main"> <s>As for example, two weights equall in ab&longs;olute Gravity, being <lb/>put into a Ballance of equall Arms, they &longs;tand in <emph type="italics"/>Equilibrium,<emph.end type="italics"/> nei­ <lb/>ther one going down, nor the other up: becau&longs;e the equality of the <lb/>Di&longs;tances of both, from the Centre on which the Ballance is &longs;uppor­ <lb/>ted, and about which it moves, cau&longs;eth that tho&longs;e weights, the &longs;aid <lb/>Ballance moving, &longs;hall in the &longs;ame Time move equall Spaces, that is, <lb/>&longs;hall move with equall Velocity, &longs;o that there is no rea&longs;on for which <pb xlink:href="040/01/1100.jpg" pagenum="407"/>this Weight &longs;hould de&longs;cend more than that, or that more than this; <lb/>and therefore they make an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> and their Moments continue <lb/>of &longs;emblable and equall Vertue.</s></p><p type="main"> <s>The &longs;econd Principle is; That</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s><emph type="italics"/>The Moment and Force of the Gravity, is encrea&longs;ed by <lb/>the Velocity of the Motion.<emph.end type="italics"/></s></p><p type="main"> <s>So that Weights ab&longs;olutely equall, but conjoyned with Velocity <lb/>unequall, are of Force, Moment and Vertue unequall: and the <lb/>more potent, the more &longs;wift, according to the proportion of the Ve­ <lb/>locity of the one, to the Velocity of the other. </s><s>Of this we have a <lb/>very pertinent example in the Balance or Stiliard of unequall Arms, <lb/>at which Weights ab&longs;olutely equall being &longs;u&longs;pended, they do not <lb/>weigh down, and gravitate equally, but that which is at a greater <lb/>di&longs;tance from the Centre, about which the Beam moves, de&longs;cends, <lb/>rai&longs;ing the other, and the Motion of this which a&longs;cends is &longs;low, and <lb/>the other &longs;wift: and &longs;uch is the Force and Vertue, which from the <lb/>Velocity of the Mover, is conferred on the Moveable, which receives <lb/>it, that it can exqui&longs;itely compen&longs;ate, as much more Weight added to <lb/>the other &longs;lower Moveable: &longs;o that if of the Arms of the Balance, <lb/>one were ten times as long as the other, whereupon in the Beames <lb/>moving about the Centre, the end of that would go ten times as far <lb/>as the end of this, a Weight &longs;u&longs;pended at the greater di&longs;tance, may <lb/>&longs;u&longs;tain and poy&longs;e another ten times more grave ab&longs;olutely than it: <lb/>and that becau&longs;e the Stiliard moving, the le&longs;&longs;er Weight &longs;hall move <lb/>ten times fa&longs;ter than the bigger. </s><s>It ought alwayes therefore to be <lb/>under&longs;tood, that Motions are according to the &longs;ame Inclinations, <lb/>namely, that if one of the Moveables move perpendicularly to the <lb/>Horizon, then the other makes its Motion by the like Perpendicular; <lb/>and if the Motion of one were to be made Horizontally; that then <lb/>the other is made along the &longs;ame Horizontall plain: and in &longs;umme, <lb/>alwayes both in like Inclinations. </s><s>This proportion between the <lb/>Gravity and Velocity is found in all Mechanicall In&longs;truments: and <lb/>is con&longs;idered by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> as a Principle in his <emph type="italics"/>Mechanicall Que&longs;tions<emph.end type="italics"/>; <lb/>whereupon we al&longs;o may take it for a true A&longs;&longs;umption, That</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s><emph type="italics"/>Weights ab&longs;olutely unequall, do alternately counterpoy&longs;e <lb/>and become of equall Moments, as oft as their Gravi­ <lb/>ties, with contrary proportion, an&longs;wer to the Velocity of <lb/>their Motions.<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1101.jpg" pagenum="408"/><p type="main"> <s>That is to &longs;ay, that by how much the one is le&longs;s grave than the other, <lb/>by &longs;o much is it in a con&longs;titution of moving more &longs;wiftly than that.</s></p><p type="main"> <s>Having prefatically explicated the&longs;e things, we may begin to en­ <lb/>quire, what Bodyes tho&longs;e are which totally &longs;ubmerge in Water, and <lb/>go to the Bottom, and which tho&longs;e that by con&longs;traint float on the <lb/>top, &longs;o that being thru&longs;t by violence under Water, they return to <lb/>&longs;wim, with one part of their Ma&longs;s vi&longs;ible above the Surface of the <lb/>Water: and this we will do by con&longs;idering the re&longs;pective operati­ <lb/>on of the &longs;aid Solids, and of Water: Which operation followes <lb/>the Submer&longs;ion and &longs;inking; and this it is, That in the Submer&longs;ion <lb/><arrow.to.target n="marg1404"></arrow.to.target> <lb/>that the Solid maketh, being depre&longs;&longs;ed downwards by its proper <lb/>Gravity, it comes to drive away the water from the place where it <lb/>&longs;ucce&longs;&longs;ively &longs;ubenters, and the water repul&longs;ed ri&longs;eth and a&longs;cends <lb/>above its fir&longs;t levell, to which A&longs;cent on the other &longs;ide it, as being a <lb/>grave Body of its own nature, re&longs;i&longs;ts: And becau&longs;e the de&longs;cending <lb/>Solid more and more immerging, greater and greater quantity of <lb/>Water a&longs;cends, till the whole Sollid be &longs;ubmerged; its nece&longs;&longs;ary to <lb/>compare the Moments of the Re&longs;i&longs;tance of the water to A&longs;cen&longs;ion, <lb/>with the Moments of the pre&longs;&longs;ive Gravity of the Solid: And if the <lb/>Moments of the Re&longs;i&longs;tance of the water, &longs;hall equalize the Moments <lb/><arrow.to.target n="marg1405"></arrow.to.target> <lb/>of the Solid, before its totall Immer&longs;ion; in this ca&longs;e doubtle&longs;s there <lb/>&longs;hall be made an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> nor &longs;hall the Body &longs;ink any farther. <lb/></s><s>But if the Moment of the Solid, &longs;hall alwayes exceed the Moments <lb/><arrow.to.target n="marg1406"></arrow.to.target> <lb/>wherewith the repul&longs;ed water &longs;ucce&longs;&longs;ively makes Re&longs;i&longs;tance, that <lb/>Solid &longs;hall not only wholly &longs;ubmerge under water, but &longs;hall de&longs;cend <lb/>to the Bottom. </s><s>But if, la&longs;tly, in the in&longs;tant of totall Submer&longs;ion, <lb/><arrow.to.target n="marg1407"></arrow.to.target> <lb/>the equality &longs;hall be made between the Moments of the prement <lb/>Solid, and the re&longs;i&longs;ting Water; then &longs;hall re&longs;t en&longs;ue, and the &longs;aid <lb/>Solid &longs;hall be able to re&longs;t indifferently, in what&longs;oever part of the <lb/>water. </s><s>By this time is manife&longs;t the nece&longs;&longs;ity of comparing the <lb/><arrow.to.target n="marg1408"></arrow.to.target> <lb/>Gravity of the water, and of the Solid; and this compari&longs;on might <lb/>at fir&longs;t &longs;ight &longs;eem &longs;ufficient to conclude and determine which are the <lb/>Solids that float a-top, and which tho&longs;e that &longs;ink to the Bottom in the <lb/>water, a&longs;&longs;erting that tho&longs;e &longs;hall float which are le&longs;&longs;e grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> <lb/>than the water, and tho&longs;e &longs;ubmerge, which are <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> more grave. <lb/></s><s>For it &longs;eems in appearance, that the Sollid in &longs;inking continually, <lb/>rai&longs;eth &longs;o much Water in Ma&longs;s, as an&longs;wers to the parts of its own <lb/>Bulk &longs;ubmerged: whereupon it is impo&longs;&longs;ible, that a Solid le&longs;s grave <lb/><emph type="italics"/>in &longs;pecie,<emph.end type="italics"/> than water, &longs;hould wholly &longs;ink, as being unable to rai&longs;e a <lb/>weight greater than its own, and &longs;uch would a Ma&longs;s of water equall <lb/>to its own Ma&longs;s be. </s><s>And likewi&longs;e it &longs;eems nece&longs;&longs;ary, that the graver <lb/>Solids do go to the Bottom, as being of a Force more than &longs;ufficient <lb/>for the rai&longs;ing a Ma&longs;&longs;e of water, equall to its own, though inferiour <lb/>in weight. </s><s>Neverthele&longs;s the bu&longs;ine&longs;s &longs;ucceeds otherwi&longs;e: and <pb xlink:href="040/01/1102.jpg" pagenum="409"/>though the Conclu&longs;ions are true, yet are the Cau&longs;es thus a&longs;&longs;igned <lb/>deficient, nor is it true, that the Solid in &longs;ubmerging, rai&longs;eth and <lb/>repul&longs;eth Ma&longs;&longs;es of Water, equall to the parts of it &longs;elf &longs;ubmerged; <lb/>but the Water repul&longs;ed, is alwayes le&longs;s than the parts of the Solid <lb/><arrow.to.target n="marg1409"></arrow.to.target> <lb/>&longs;ubmerged: and &longs;o much the more by how much the Ve&longs;&longs;ell in <lb/>which the Water is contained is narrower: in &longs;uch manner that it <lb/>hinders not, but that a Solid may &longs;ubmerge all under Water, with­ <lb/>out rai&longs;ing &longs;o much Water in Ma&longs;s, as would equall the tenth or <lb/>twentieth part of its own Bulk: like as on the contrary, a very <lb/><arrow.to.target n="marg1410"></arrow.to.target> <lb/>&longs;mall quantity of Water, may rai&longs;e a very great Solid Ma&longs;s, though <lb/>&longs;uch Solid &longs;hould weigh ab&longs;olutely a hundred times as much, or <lb/>more, than the &longs;aid Water, if &longs;o be that the Matter of that &longs;ame <lb/>Solid be <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> le&longs;s grave than the Water. </s><s>And thus a great <lb/>Beam, as &longs;uppo&longs;e of a 1000 weight, may be rai&longs;ed and born afloat <lb/>by Water, which weighs not 50: and this happens when the Mo­ <lb/>ment of the Water is compen&longs;ated by the Velocity of its Motion.</s></p><p type="margin"> <s><margin.target id="marg1404"></margin.target>How the &longs;ub­ <lb/>mer&longs;ion of So­ <lb/>lids in the Wa­ <lb/>ter, is effected.</s></p><p type="margin"> <s><margin.target id="marg1405"></margin.target>What Solids <lb/>&longs;hall float on the <lb/>Water.</s></p><p type="margin"> <s><margin.target id="marg1406"></margin.target>What Solids <lb/>&longs;hall &longs;inke to the <lb/>botome.</s></p><p type="margin"> <s><margin.target id="marg1407"></margin.target>What Solids <lb/>&longs;hall re&longs;t in all <lb/>places of the Wa­ <lb/>ter.</s></p><p type="margin"> <s><margin.target id="marg1408"></margin.target>The Gravitie of <lb/>the Water and <lb/><emph type="italics"/>S<emph.end type="italics"/>olid mu&longs;t be <lb/>compared in all <lb/>Problems, of Na­ <lb/>tation of Bodies.</s></p><p type="margin"> <s><margin.target id="marg1409"></margin.target>The water re­ <lb/>pul&longs;ed is ever le&longs;s <lb/>than the parts of <lb/>the Sollid &longs;ub­ <lb/>merged.</s></p><p type="margin"> <s><margin.target id="marg1410"></margin.target><emph type="italics"/>A<emph.end type="italics"/> &longs;mall quantity <lb/>of water, may <lb/>float a very <lb/>great Solid Ma&longs;s.</s></p><p type="main"> <s>But becau&longs;e &longs;uch things, propounded thus in ab&longs;tract, are &longs;ome­ <lb/>what difficult to be comprehended, it would be good to demon&longs;trate <lb/>them by particular examples; and for facility of demon&longs;tration, we <lb/>will &longs;uppo&longs;e the Ve&longs;&longs;els in which we are to put the Water, and place <lb/>the Solids, to be inviron'd and included with &longs;ides erected perpendi­ <lb/>cular to the Plane of the Horizon, and the Solid that is to be put <lb/>into &longs;uch ve&longs;&longs;ell to be either a &longs;treight Cylinder, or el&longs;e an upright <lb/>Pri&longs;me</s></p><p type="main"> <s><emph type="italics"/>The which propo&longs;ed and declared, I proceed to demonstrate the truth <lb/>of what hath been hinted, forming the en&longs;uing Theoreme.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>THEOREME I.<emph.end type="italics"/></s></p><p type="main"> <s>The Ma&longs;s of the Water whicha&longs;cends in the &longs;ub­ <lb/><arrow.to.target n="marg1411"></arrow.to.target> <lb/>merging of a Solid, Pri&longs;me or Cylinder, or that <lb/>aba&longs;eth in taking it out, is le&longs;s than the Ma&longs;s of <lb/>the &longs;aid Solid, &longs;o depre&longs;&longs;ed or advanced: and <lb/>hath to it the &longs;ame proportion, that the Surface <lb/>of the Water circumfu&longs;ing the Solid, hath to the <lb/>&longs;ame circumfu&longs;ed Surface, together with the Ba&longs;e <lb/>of the Solid.</s></p><p type="margin"> <s><margin.target id="marg1411"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he Proportion <lb/>of the water rai­ <lb/>&longs;ed to the <emph type="italics"/>S<emph.end type="italics"/>olid <lb/>&longs;ubmerged.</s></p><p type="main"> <s><emph type="italics"/>Let the Ve&longs;&longs;ell be A B C D, and in it the Water rai&longs;ed up to the <lb/>Levell E F G, before the Solid Pri&longs;me H I K be therein immerged; <lb/>but after that it is depre&longs;&longs;ed under Water, let the Water be rai&longs;ed as <lb/>high as the Levell L M, the Solid H I K &longs;hall then be all under Water, <lb/>and the Ma&longs;s of the elevated Water &longs;hall be L G, which is le&longs;s than the<emph.end type="italics"/> <pb xlink:href="040/01/1103.jpg" pagenum="410"/><figure id="id.040.01.1103.1.jpg" xlink:href="040/01/1103/1.jpg"/> <lb/><emph type="italics"/>Ma&longs;&longs;e of the Solid depre&longs;&longs;ed, namely of <lb/>H I K, being equall to the only part E I K, <lb/>which is contained under the fir&longs;t Levell <lb/>E F G. </s><s>Which is manife&longs;t, becau&longs;e if <lb/>the Solid H I K be taken out, the Water <lb/>I G &longs;hall return into the place occupied by <lb/>the Ma&longs;s E I K, where it was continuate be­ <lb/>fore the &longs;ubmer&longs;ion of the Pri&longs;me. </s><s>And <lb/>the Ma&longs;s L G being equall to the Ma&longs;s <lb/>E K: adde thereto the Ma&longs;s E N, and it <lb/>&longs;hall be the whole Ma&longs;s E M, compo&longs;ed of the parts of the Pri&longs;me E N, <lb/>and of the Water N F, equall to the whole Solid H I K: And, there­ <lb/>fore, the Ma&longs;s L G &longs;hall have the &longs;ame proportion to E M, as to the <lb/>Ma&longs;s H I K: But the Ma&longs;s L G hath the &longs;ame proportion to the Ma&longs;s <lb/>E M, as the Surface L M hath to the Surface M H: Therefore it is ma­ <lb/>nife&longs;t, that the Ma&longs;s of Water repul&longs;ed L G, is in proportion to the Ma&longs;s <lb/>of the Solid &longs;ubmerged H I K; as the Surface L M, namely, that of the <lb/>Water ambient about the Sollid, to the whole Surface H M, compounded <lb/>of the &longs;aid ambient water, and the Ba&longs;e of the Pri&longs;me H N. </s><s>But if we <lb/>&longs;uppo&longs;e the fir&longs;t Levell of the Water the according to the Surface H M, <lb/>and the Pri&longs;me allready &longs;ubmerged H I K; and after to be taken out and <lb/>rai&longs;ed to E A O, and the Water to be faln from the fir&longs;t Levell H L M as <lb/>low as E F G; It is manife&longs;t, that the Pri&longs;me E A O being the &longs;ame with <lb/>H I K, its &longs;uperiour part H O, &longs;hall be equall to the inferiour E I K: <lb/>and remove the common part E N, and, con&longs;equently, the Ma&longs;s of the <lb/>Water L G is equall to the Ma&longs;s H O; and, therefore, le&longs;s than the <lb/>Solid, which is without the Water, namely, the whole Pri&longs;me E A O, to <lb/>which likewi&longs;e, the &longs;aid Ma&longs;s of Water abated L G, hath the &longs;ame propor­ <lb/>tion, that the Surface of the Waters circumfu&longs;ed L M hath to the &longs;ame <lb/>circumfu&longs;ed Surface, together with the Ba&longs;e of the Pri&longs;me A O: which <lb/>hath the &longs;ame demon&longs;tration with the former ca&longs;e above.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>And from hence is inferred, that the Ma&longs;s of the Water, that ri&longs;eth in <lb/>the immer&longs;ion of the Solid, or that ebbeth in elevating it, is not equall to <lb/>all the Ma&longs;s of the Solid, which is &longs;ubmerged or elevated, but to that <lb/>part only, which in the immer&longs;ion is under the fir&longs;t Levell of the Water, <lb/>and in the elevation remaines above the fir&longs;t Levell: Which is that <lb/>which was to be demon&longs;trated. </s><s>We will now pur&longs;ue the things that <lb/>remain.<emph.end type="italics"/></s></p><p type="main"> <s>And fir&longs;t we will demon&longs;trate that,</s></p> <pb xlink:href="040/01/1104.jpg" pagenum="411"/><p type="head"> <s>THEOREME II.</s></p><p type="main"> <s><emph type="italics"/>When in one of the above &longs;aid Ve&longs;&longs;els, of what ever<emph.end type="italics"/> <lb/><arrow.to.target n="marg1412"></arrow.to.target> <lb/><emph type="italics"/>breadth, whether wide or narrow, there is placed &longs;uch <lb/>a Pri&longs;me or Cylinder, inviron'd with Water, if we ele­ <lb/>vate that Solid perpendicularly, the Water circumfu­ <lb/>&longs;ed &longs;hall abate, and the Abatement of the Water, <lb/>&longs;hall have the &longs;ame proportion to the Elevation of the <lb/>Pri&longs;me, as one of the Ba&longs;es of the Pri&longs;me, hath to <lb/>the Surface of the Water Circumfu&longs;ed.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1412"></margin.target>The proportion <lb/>of the water aba­ <lb/>ted, to the Solid <lb/>rai&longs;ed.</s></p><p type="main"> <s>Imagine in the Ve&longs;&longs;ell, as is afore&longs;aid, the <lb/><figure id="id.040.01.1104.1.jpg" xlink:href="040/01/1104/1.jpg"/> <lb/>Pri&longs;me A C D B to be placed, and in the <lb/>re&longs;t of the Space the Water to be dif­ <lb/>fu&longs;ed as far as the Levell E A: and rai­ <lb/>&longs;ing the Solid, let it be transferred to <lb/>G M, and let the Water be aba&longs;ed from <lb/>E A to N O: I &longs;ay, that the de&longs;cent of <lb/>the Water, mea&longs;ured by the Line A O, <lb/>hath the &longs;ame proportion to the ri&longs;e of the <lb/>Pri&longs;me, mea&longs;ured by the Line G A, as the Ba&longs;e of the Solid G H <lb/>hath to the Surface of the Water N O. </s><s>The which is manife&longs;t: <lb/>becau&longs;e the Ma&longs;s of the Solid G A B H, rai&longs;ed above the fir&longs;t Levell <lb/>E A B, is equall to the Ma&longs;s of Water that is aba&longs;ed E N O A. <lb/>Therefore, E N O A and G A B H are two equall Pri&longs;mes; for of <lb/>equall Pri&longs;mes, the Ba&longs;es an&longs;wer contrarily to their heights: There­ <lb/>fore, as the Altitude A O is to the Altitude A G, &longs;o is the Superfi­ <lb/>cies or Ba&longs;e G H to the Surface of the Water N O. </s><s>If therefore, <lb/>for example, a Pillar were erected in a wa&longs;te Pond full of Water, <lb/>or el&longs;e in a Well, capable of little more then the Ma&longs;s of the &longs;aid <lb/>Pillar, in elevating the &longs;aid Pillar, and taking it out of the Water, <lb/>according as it ri&longs;eth, the Water that invirons it will gradually abate, <lb/>and the aba&longs;ement of the Water at the in&longs;tant of lifting out the <lb/>Pillar, &longs;hall have the &longs;ame proportion, that the thickne&longs;s of the Pillar <lb/>hath to the exce&longs;s of the breadth of the &longs;aid Pond or Well, above <lb/>the thickne&longs;s of the &longs;aid Pillar: &longs;o that if the breadth of the Well <lb/>were an eighth part larger than the thickne&longs;s of the Pillar, and the <lb/><arrow.to.target n="marg1413"></arrow.to.target> <lb/>breadth of the Pond twenty five times as great as the &longs;aid thickne&longs;s, <lb/>in the Pillars a&longs;cending one foot, the water in the Well &longs;hall de&longs;cend <lb/>&longs;even foot, and that in the Pond only 1/25 of a foot.</s></p><p type="margin"> <s><margin.target id="marg1413"></margin.target>Why a Solid <lb/>le&longs;s grave <emph type="italics"/>in &longs;pe­ <lb/>cie<emph.end type="italics"/> than water, <lb/>&longs;tayeth not un­ <lb/>der water, in ve­ <lb/>ry &longs;mall depthst.</s></p><p type="main"> <s>This Demon&longs;trated, it will not be difficult to &longs;hew the true <lb/>cau&longs;e, how it comes to pa&longs;s, that,</s></p> <pb xlink:href="040/01/1105.jpg" pagenum="412"/><p type="head"> <s>THEOREME III.</s></p><p type="main"> <s><emph type="italics"/>A Pri&longs;me or regular Cylinder, of a &longs;ub&longs;tance &longs;pecifically <lb/>le&longs;s grave than Water, if it &longs;hould be totally &longs;ubmerged <lb/>in Water, &longs;tayes not underneath, but ri&longs;eth, though the <lb/>Water circumfu&longs;ed be very little, and in ab&longs;olute <lb/>Gravity, never &longs;o much inferiour to the Gravity of the <lb/>&longs;aid Pri&longs;me.<emph.end type="italics"/></s></p><p type="main"> <s>Let then the Pri&longs;me A E F B, be put into the Ve&longs;&longs;ell C D F B, the <lb/>&longs;ame being le&longs;s grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the Water: and let the <lb/>Water infu&longs;ed ri&longs;e to the height of the Pri&longs;me: I &longs;ay, that the <lb/>Pri&longs;me left at liberty, it &longs;hall ri&longs;e, being born up <lb/>by the Water circumfu&longs;ed C D E A. </s><s>For the <lb/><figure id="id.040.01.1105.1.jpg" xlink:href="040/01/1105/1.jpg"/> <lb/>Water C E being &longs;pecifically more grave than <lb/>the Solid A F, the ab&longs;olute weight of the water <lb/>C E, &longs;hall have greater proportion to the ab&longs;o­ <lb/>lute weight of the Pri&longs;me A F, than the Ma&longs;s <lb/>C E hath to the Ma&longs;s A F (in regard the Ma&longs;s <lb/>hath the &longs;ame proportion to the Ma&longs;s, that the <lb/>weight ab&longs;olute hath to the weight ab&longs;olute, <lb/>in ca&longs;e the Ma&longs;&longs;es are of the &longs;ame Gravity <emph type="italics"/>in &longs;pecie.<emph.end type="italics"/>) But <lb/>the Ma&longs;s C E is to the Ma&longs;s A F, as the Surface of the water A C, is <lb/>to the Superficies, or Ba&longs;e of the Pri&longs;me A B; which is the &longs;ame pro­ <lb/>portion as the a&longs;cent of the Pri&longs;me when it ri&longs;eth, hath to the de&longs;cent <lb/>of the water circumfu&longs;ed C E.</s></p><p type="main"> <s>Therefore, the ab&longs;olute Gravity of the water C E, hath greater <lb/>proportion to the ab&longs;olute Gravity of the Pri&longs;me A F; than the <lb/>A&longs;cent of the Pri&longs;me A F, hath to the de&longs;cent of the &longs;aid <lb/>water C E. </s><s>The Moment, therefore, compounded of the ab&longs;olute <lb/>Gravity of the water C E, and of the Velocity of its de&longs;cent, whil&longs;t <lb/>it forceably repul&longs;eth and rai&longs;eth the Solid A F, is greater than the <lb/>Moment compounded of the ab&longs;olute Gravity of the Pri&longs;me A F, and <lb/>of the Tardity of its a&longs;cent, with which Moment it contra&longs;ts and re­ <lb/>fi&longs;ts the repul&longs;e and violence done it by the Moment of the water: <lb/>Therefore, the Pri&longs;me &longs;hall be rai&longs;ed. <lb/><arrow.to.target n="marg1414"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1414"></margin.target>The Proportion <lb/>according to <lb/>which the Sub­ <lb/>mer&longs;ion & Na <lb/>tation of Solids <lb/>is made.</s></p><p type="main"> <s>It followes, now, that we proceed forward to demon&longs;trate more <lb/>particularly, how much &longs;uch Solids &longs;hall be inferiour in Gravity to <lb/>the water elevated; namely, what part of them &longs;hall re&longs;t &longs;ubmerged, <lb/>and what &longs;hall be vi&longs;ible above the Surface of the water: but fir&longs;t <lb/>it is nece&longs;&longs;ary to demon&longs;trate the &longs;ub&longs;equent Lemma.</s></p> <pb xlink:href="040/01/1106.jpg" pagenum="413"/><p type="head"> <s>LEMMA I.</s></p><p type="main"> <s><emph type="italics"/>The ab&longs;olute Gravities of Solids, have a proportion com-<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1415"></arrow.to.target> <lb/><emph type="italics"/>pounded of the proportions of their &longs;pecificall Gravities, <lb/>and of their Ma&longs;&longs;es.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1415"></margin.target>The ab&longs;olute <lb/>Gravity of So­ <lb/>lids, are in a pro­ <lb/>portion com­ <lb/>pounded of their <lb/>Specifick Gravi­ <lb/>ties, and of their <lb/>Ma&longs;&longs;es.</s></p><p type="main"> <s>Let A and B be two Solids. </s><s>I &longs;ay, that the Ab&longs;olute Gravity <lb/>of A, hath to the Ab&longs;olute Gravity of B, a proportion com­ <lb/>pounded of the proportions of the &longs;pecificall Gravity of A, to <lb/>the Specificall Gravity of B, and of the Ma&longs;s <lb/>A to the Ma&longs;s B. </s><s>Let the Line D have the <lb/><figure id="id.040.01.1106.1.jpg" xlink:href="040/01/1106/1.jpg"/> <lb/>&longs;ame proportion to E, that the &longs;pecifick <lb/>Gravity of A, hath to the &longs;pecifick Gravity <lb/>of B; and let E be to F, as the Ma&longs;s A to the <lb/>Ma&longs;s B: It is manife&longs;t, that the proportion <lb/>of D to F, is compounded of the proportions <lb/>D and E; and E and F. </s><s>It is requi&longs;ite, <lb/>therefore, to demon&longs;trate, that as D is to F, &longs;o the ab&longs;olute Gravity <lb/>of A, is to the ab&longs;olute Gravity of B. </s><s>Take the Solid C, equall in <lb/>Ma&longs;s to the Solid A, and of the &longs;ame Gravity <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> with the Solid <lb/>B. Becau&longs;e, therefore, A and C are equall in Ma&longs;s, the ab&longs;olute <lb/>Gravity of A, &longs;hall have to the ab&longs;olute Gravity of C, the &longs;ame pro­ <lb/>portion, as the &longs;pecificall Gravity of A, hath to the &longs;pecificall Gravity <lb/>of C, or of B, which is the &longs;ame <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>; that is, as D is to E. And, be­ <lb/>cau&longs;e, C and B are of the &longs;ame Gravity <emph type="italics"/>in &longs;pecie,<emph.end type="italics"/> it &longs;hall be, that as <lb/>the ab&longs;olute weight of C, is to the ab&longs;olute weight of B, &longs;o the Ma&longs;s <lb/>C, or the Ma&longs;s A, is to the Ma&longs;s B; that is, as the Line E to the Line <lb/>F. </s><s>As therefore, the ab&longs;olute Gravity of A, is to the ab&longs;olute <lb/>Gravity of C, &longs;o is the Line D to the Line E: and, as the ab&longs;olute <lb/>Gravity of C, is to the ab&longs;olute Gravity of B, &longs;o is the Line E to the <lb/>Line F: Therefore, by Equality of proportion, the ab&longs;olute Gra­ <lb/>vity of A, is to the ab&longs;olute Gravity of B, as the Line D to the <lb/>Line F: which was to be demon&longs;trated. </s><s>I proceed now to demon­ <lb/>&longs;trate, how that,</s></p> <pb xlink:href="040/01/1107.jpg" pagenum="414"/><p type="head"> <s>THEOREME IV. <lb/><arrow.to.target n="marg1416"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1416"></margin.target>The proportion <lb/>of water requi­ <lb/>&longs;ite to make a <lb/>Solid &longs;wim.</s></p><p type="main"> <s><emph type="italics"/>If a Solid, Cylinder, or Pri&longs;me, le&longs;&longs;e grave &longs;pecifically <lb/>than the Water, being put into a Ve&longs;&longs;el, as above, of <lb/>what&longs;oever greatne&longs;&longs;e, and the Water, be afterwards <lb/>infu&longs;ed, the Solid &longs;hall re&longs;t in the bottom, unrai&longs;ed, till <lb/>the Water arrive to that part of the Altitude, of the <lb/>&longs;aid Pri&longs;me, to which its whole Altitude hath the <lb/>&longs;ame proportion, that the Specificall Gravity of the <lb/>Water, hath to the Specificall Gravity of the &longs;aid <lb/>Solid: but infu&longs;ing more Water, the Solid &longs;hall a&longs;cend.<emph.end type="italics"/></s></p><p type="main"> <s>Let the Ve&longs;&longs;ell be M L G N of any bigne&longs;s, and let there be pla­ <lb/>ced in it the Solid Pri&longs;me D F G E, le&longs;s grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the <lb/>water; and look what proportion the <emph type="italics"/>S<emph.end type="italics"/>pecificall Gravity of <lb/>the water, hath to that of the Pri&longs;me, &longs;uch let the Altitude D F, have <lb/>to the Altitude F B. </s><s>I &longs;ay, that infu&longs;ing water to the Altitude F B, <lb/>the Solid D G &longs;hall not float, but &longs;hall &longs;tand in <emph type="italics"/>Equilibrium,<emph.end type="italics"/> &longs;o, that <lb/>that every little quantity of water, that is infu&longs;ed, &longs;hall rai&longs;e it. </s><s>Let <lb/>the water, therefore, be infu&longs;ed to the Levell A B C, and, becau&longs;e <lb/>the Specifick Gravity of the Solid D G, is to the Specifick Gravity of <lb/>the water, as the altitude B F is to the altitude F D; that is, as the Ma&longs;s <lb/>B G to the Ma&longs;s G D; as the proportion of the Ma&longs;s B G is to the <lb/>Ma&longs;s G D, as the proportion of the Ma&longs;s G D is to the Ma&longs;s A F, they <lb/>compo&longs;e the Proportion of the Ma&longs;s B G to the Ma&longs;s A F. Therefore, <lb/>the Ma&longs;s B G is to the Ma&longs;s A F, in a proportion compounded of the <lb/>proportions of the Specifick Gravity of the Solid G D, to the Speci­ <lb/>fick Gravity of the water, and of the Ma&longs;s G D <lb/>to the Ma&longs;s A F: But the &longs;ame proportions <lb/><figure id="id.040.01.1107.1.jpg" xlink:href="040/01/1107/1.jpg"/> <lb/>of the Specifick Gravity of G D, to the Specifick <lb/>Gravity of the water, and of the Ma&longs;s G D to <lb/>the Ma&longs;s A F, do al&longs;o by the precedent <emph type="italics"/>Lemma,<emph.end type="italics"/> <lb/>compound the proportion of the ab&longs;olute Gra­ <lb/>vity of the Solid D G, to the ab&longs;olute Gravity <lb/>of the Ma&longs;s of the water A F: Therefore, <lb/>as the Ma&longs;s B G is to the Ma&longs;s A F, &longs;o is the <lb/>Ab&longs;olute Gravity of the Solid D G, to the Ab­ <lb/>&longs;olute Gravity of the Ma&longs;s of the water A F. </s><s>But as the Ma&longs;s B G <lb/>is to the Ma&longs;s A F; &longs;o is the Ba&longs;e of the Pri&longs;me D E, to the Surface <lb/>of the water AB; and &longs;o is the de&longs;cent of the water A B, to the <lb/>Elevation of the Pri&longs;me D G; Therefore, the de&longs;cent of the <pb xlink:href="040/01/1108.jpg" pagenum="415"/>water is to the elevation of the Pri&longs;me, as the ab&longs;olute Gravity of <lb/>the Pri&longs;me, is to the ab&longs;olute Gravity of the water: Therefore, the <lb/>Moment re&longs;ulting from the ab&longs;olute Gravity of the water A F, and <lb/>the Velocity of the Motion of declination, with which Moment it <lb/>forceth the Pri&longs;me D G, to ri&longs;e and a&longs;cend, is equall to the Moment <lb/>that re&longs;ults from the ab&longs;olute Gravity of the Pri&longs;me D G, and from <lb/>the Velocity of the Motion, wherewith being rai&longs;ed, it would a&longs;cend: <lb/>with which Moment it re&longs;i&longs;ts its being rai&longs;ed: becau&longs;e, therefore, <lb/>&longs;uch Moments are equall, there &longs;hall be an <emph type="italics"/>Equilibrium<emph.end type="italics"/> between the <lb/>water and the Solid. </s><s>And, it is manife&longs;t, that putting a little more <lb/>water unto the other A F, it will increa&longs;e the Gravity and Moment, <lb/>whereupon the Pri&longs;me D G, &longs;hall be overcome, and elevated till that <lb/>the only part B F remaines &longs;ubmerged. </s><s>Which is that that was to <lb/>be demon&longs;trated.</s></p><p type="head"> <s>COROLLARY I.</s></p><p type="main"> <s><emph type="italics"/>By what hath been demon&longs;trated, it is manife&longs;t, that Solids le&longs;s grave<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1417"></arrow.to.target> <lb/>in &longs;pecie <emph type="italics"/>than the water, &longs;ubmerge only &longs;o far, that as much water in <lb/>Ma&longs;s, as is the part of the Solid &longs;ubmerged, doth weigh ab&longs;olutely as <lb/>much as the whole Solid.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1417"></margin.target><emph type="italics"/>H<emph.end type="italics"/>ow far Solids <lb/>le&longs;s grave <emph type="italics"/>in &longs;pe­ <lb/>cie<emph.end type="italics"/> than water, <lb/>do &longs;ubmerge.</s></p><p type="main"> <s>For, it being &longs;uppo&longs;ed, that the Specificall Gravity of the water, <lb/>is to the Specificall Gravity of the Pri&longs;me D G, as the Altitude <lb/>D F, is to the Altitude F B; that is, as the Solid D G is to the <lb/>Solid B G; we might ea&longs;ily demon&longs;trate, that as much water in Ma&longs;s <lb/>as is equall to the Solid B G, doth weigh ab&longs;olutely as much as the <lb/>whole Solid D G; For, by the <emph type="italics"/>Lemma<emph.end type="italics"/> foregoing, the Ab&longs;olute <lb/>Gravity of a Ma&longs;s of water, equall to the Ma&longs;s B G, hath to the Ab­ <lb/>&longs;olute Gravity of the Pri&longs;me D G, a proportion compounded of the <lb/>proportions, of the Ma&longs;s B G to the Ma&longs;s G D, and of the Specifick <lb/>Gravit 7 of the water, to the Specifick Gravity of the Pri&longs;me: But <lb/>the Gravity <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> of the water, to the Gravity <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> of the <lb/>Pri&longs;me, is &longs;uppo&longs;ed to be as the Ma&longs;s G D to the Ma&longs;s G B. There­ <lb/>fore, the Ab&longs;olute Gravity of a Ma&longs;s of water, equall to the Ma&longs;s <lb/>B G, is to the Ab&longs;olute Gravity of the Solid D G, in a proportion <lb/>compounded of the proportions, of the Ma&longs;s B G to the Ma&longs;s G D, <lb/>and of the Ma&longs;s D G to the Ma&longs;s G B; which is a proportion of <lb/>equalitie. </s><s>The Ab&longs;olute Gravity, therefore, of a Ma&longs;s of Water <lb/>equall to the part of the Ma&longs;s of the Pri&longs;me B G, is equall to the Ab­ <lb/>&longs;olute Gravity of the whole Solid D G.</s></p> <pb xlink:href="040/01/1109.jpg" pagenum="416"/><p type="head"> <s>COROLLARY II. <lb/><arrow.to.target n="marg1418"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1418"></margin.target><emph type="italics"/>A<emph.end type="italics"/> Rule to equi­ <lb/>librate <emph type="italics"/>S<emph.end type="italics"/>olids in <lb/>the water.</s></p><p type="main"> <s><emph type="italics"/>It followes, moreover, that a Solid le&longs;s grave than the water, being put <lb/>into a Ve&longs;&longs;ell of any imaginable greatne&longs;s, and water being circumfu&longs;ed <lb/>about it to &longs;uch a height, that as much water in Ma&longs;s, as is the part of <lb/>the Solid &longs;ubmerged, doth/> weigh ab&longs;olutely as much as the whole Solid; <lb/>it &longs;hall by that water be ju&longs;tly &longs;u&longs;tained, be the circumfu&longs;ed Water in <lb/>quantity greater or le&longs;&longs;er.<emph.end type="italics"/></s></p><p type="main"> <s>For, if the Cylinder or Pri&longs;me M, le&longs;s grave than the water, <emph type="italics"/>v. <lb/></s><s>gra.<emph.end type="italics"/> in Sub&longs;equiteriall proportion, &longs;hall be put into the capaci­ <lb/>ous Ve&longs;&longs;ell A B C D, and the water rai&longs;ed about it, to three <lb/>quarters of its height, namely, to its Levell A D: it &longs;hall be &longs;u&longs;tained <lb/>and exactly poy&longs;ed in <emph type="italics"/>Equi­ <lb/>librium.<emph.end type="italics"/> The &longs;ame will hap­ <lb/>pen, if the Ve&longs;&longs;ell E N S F <lb/><figure id="id.040.01.1109.1.jpg" xlink:href="040/01/1109/1.jpg"/> <lb/>were very &longs;mall, &longs;o, that be­ <lb/>tween the Ve&longs;&longs;ell and the So­ <lb/>lid M, there were but a very <lb/>narrow &longs;pace, and only capable of &longs;o much water, as the hundredth <lb/>part of the Ma&longs;s M, by which it &longs;hould be likewi&longs;e rai&longs;ed and erected, <lb/>as before it had been elevated to three fourths of the height of the <lb/>Solid: which to many at the fir&longs;t &longs;ight, may &longs;eem a notable Paradox, <lb/>and beget a conceit, that the Demon&longs;tration of the&longs;e effects, were <lb/>&longs;ophi&longs;ticall and fallacious: but, for tho&longs;e who &longs;o repute it, the Ex­ <lb/>periment is a means that may fully &longs;atisfie them. </s><s>But he that &longs;hall <lb/>but comprehend of what Importance Velocity of Motion is, and how <lb/>it exactly compen&longs;ates the defect and want of Gravity, will cea&longs;e to <lb/>wonder, in con&longs;idering that at the elevation of the Solid M, the great <lb/>Ma&longs;s of water A B C D abateth very little, but the little Ma&longs;s of <lb/>water E N S F decrea&longs;eth very much, and in an in&longs;tant, as the Solid <lb/>M before did li&longs;e, howbeit for a very &longs;hort &longs;pace: Whereupon the <lb/>Moment, compounded of the &longs;mall Ab&longs;olute Gravity of the water <lb/>E N S F, and of its great Velocity in ebbing, equalizeth the Force and <lb/>and Moment, that re&longs;ults from the compo&longs;icion of the immen&longs;e Gra­ <lb/>vity of the water A B C D, with its great &longs;lowne&longs;&longs;e of ebbing; <lb/>&longs;ince that in the Elevation of the Sollid M, the aba&longs;ement of the le&longs;­</s></p><p type="main"> <s><arrow.to.target n="marg1419"></arrow.to.target> <lb/>&longs;er water E S, is performed ju&longs;t &longs;o much more &longs;wiftly than the great <lb/>Ma&longs;s of water A C, as this is more in Ma&longs;s than that which we thus <lb/>demon&longs;trate.</s></p><p type="margin"> <s><margin.target id="marg1419"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he proportion <lb/>according to <lb/>which water ri­ <lb/>&longs;eth and falls in <lb/>different Ve&longs;&longs;els <lb/>at the Immer&longs;i­ <lb/>on and Elevati­ <lb/>on of <emph type="italics"/>s<emph.end type="italics"/>olids.</s></p><p type="main"> <s>In the ri&longs;ing of the Solid M, its elevation hath the &longs;ame proportion <lb/>to the circumfu&longs;ed water E N S F, that the Surface of the &longs;aid water, <lb/>hath to the Superficies or Ba&longs;e of the &longs;aid Solid M; which Ba&longs;e hath <lb/>the &longs;ame proportion to the Surface of the water A D, that the aba&longs;e­ <pb xlink:href="040/01/1110.jpg" pagenum="417"/>ment or ebbing of the water A C, hath to the ri&longs;e or elevation of <lb/>the &longs;aid Solid M. Therefore, by Perturbation of proportion, in the <lb/>a&longs;cent of the &longs;aid Solid M, the aba&longs;ement of the water A B C D, to <lb/>the aba&longs;ement of the water E N S F, hath the &longs;ame proportion, that the <lb/>Surface of the water E F, hath to the Surface of the water A D; <lb/>that is, that the whole Ma&longs;s of the water E N S F, hath to the whole <lb/>Ma&longs;s A B C D, being equally high: It is manife&longs;t, therefore, that <lb/>in the expul&longs;ion and elevation of the Solid M, the water E N S F <lb/>&longs;hall exceed in Velocity of <emph type="italics"/>M<emph.end type="italics"/>otion the water A B C D, a&longs;much as it <lb/>on the other &longs;ide is exceeded by that in quantity: whereupon their <lb/>Moments in &longs;uch operations, are mutually equall.</s></p><p type="main"> <s><emph type="italics"/>And, for ampler confirmation, and clearer explication of this, let us <lb/>con&longs;ider the pre&longs;ent Figure, (which if I be not deceived, may &longs;erve to <lb/>detect the errors of &longs;ome Practick Mechanitians, who upon a fal&longs;e founda­ <lb/>tion &longs;ome times attempt impo&longs;&longs;ible enterprizes,) in which, unto the large <lb/>Ve&longs;&longs;ell E I D F, the narrow Funnell or Pipe I C A B is continued, and &longs;up­ <lb/>po&longs;e water infu&longs;ed into them, unto the Levell L G H, which water &longs;hall <lb/>re&longs;t in this po&longs;ition, not without admiration in &longs;ome, who cannot conceive<emph.end type="italics"/> <lb/><figure id="id.040.01.1110.1.jpg" xlink:href="040/01/1110/1.jpg"/> <lb/><emph type="italics"/>how it can be, that the heavie charge of the great <lb/>Ma&longs;s of water G D, pre&longs;&longs;ing downwards, &longs;hould <lb/>not elevate and repul&longs;e the little quantity of the <lb/>other, contained in the Funnell or Pipe C L, by <lb/>which the de&longs;cent of it is re&longs;isted and hindered: <lb/>But &longs;uch wonder &longs;hall cea&longs;e, if we begin to &longs;uppo&longs;e <lb/>the water G D to be aba&longs;ed only to Q D, and <lb/>&longs;hall afterwards con&longs;ider, what the water C L <lb/>hath done, which to give place to the other, which <lb/>is de&longs;cended from the Levell G H, to the Levell <lb/>Q O, &longs;hall of nece&longs;&longs;ity have a&longs;cended in the &longs;ame <lb/>time, from the Levell Lunto A B. </s><s>And the <lb/>a&longs;cent L B, &longs;hall be &longs;o much greater than the de­ <lb/>&longs;cent G Q, by how much the breadth of the Ve&longs;&longs;ell <lb/>G D, is greater than that of the Funnell I C; <lb/>which, in &longs;umme, is as much as the water G D, <lb/>is more than the water L C: but in regard that the Moment of the Velocity <lb/>of the Motion, in one Moveable, compen&longs;ates that of the Gravity of ano­ <lb/>ther, what wonder is it, if the &longs;wift a&longs;cent of the le&longs;&longs;er Water C L, &longs;hall <lb/>re&longs;i&longs;t the &longs;low de&longs;cent of the greater G D<emph.end type="italics"/>?</s></p><p type="main"> <s>The &longs;ame, therefore, happens in this operation, as in the Stilliard, <lb/>in which a weight of two pounds counterpoy&longs;eth an other of 200, <lb/>asoften as that &longs;hall move in the &longs;ame time, a &longs;pace 100 times great­ <lb/>er than this: which falleth out when one Arme of the Beam is an <pb xlink:href="040/01/1111.jpg" pagenum="418"/>hundred times as long as the other. </s><s>Let the erroneous opinion o <lb/><arrow.to.target n="marg1420"></arrow.to.target> <lb/>tho&longs;e therefore cea&longs;e, who hold that a Ship is better, and ea&longs;ter born <lb/>up in a great abundance of water, then in a le&longs;&longs;er quantity, (<emph type="italics"/>this was <lb/>believed by<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>in his Problems, Sect. </s><s>23, Probl.<emph.end type="italics"/> 2.) it being or <lb/>the contrary true, that its po&longs;&longs;ible, that a Ship may as well float in <lb/>ten Tun of water, as in an Ocean. <lb/><arrow.to.target n="marg1421"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1420"></margin.target>A &longs;hip flotes as <lb/>well in ten Tun <lb/>of water as in an <lb/>Ocean.</s></p><p type="margin"> <s><margin.target id="marg1421"></margin.target>A Solid &longs;peci­ <lb/>fiaclly graver <lb/>than the water, <lb/>cannot be born <lb/>up by any quan­ <lb/>tity of it.</s></p><p type="main"> <s>But following our matter, I &longs;ay, that by what hath been hitherto <lb/>demon&longs;trated, we may under&longs;tand how, that</s></p><p type="head"> <s>COROLLARY III.</s></p><p type="main"> <s><emph type="italics"/>One of the above named Solids, when more grave<emph.end type="italics"/> in &longs;pecie <emph type="italics"/>than the water, <lb/>can never be &longs;u&longs;tained, by any whatever quantity of it.<emph.end type="italics"/></s></p><p type="main"> <s>For having &longs;een how that the Moment wherewith &longs;uch a Solid <lb/>as grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> as the water, contra&longs;ts with the Moment of any Ma&longs;s <lb/>of water what&longs;oever, is able to retain it, even to its totall Submer&longs;ion: <lb/>without its ever a&longs;cending; it remaineth, manife&longs;t, that the water is <lb/>far le&longs;s able to rai&longs;e it up, when it exceeds the &longs;ame <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>: &longs;o, <lb/>that though you infu&longs;e water till its totall Submer&longs;ion, it &longs;hall &longs;till <lb/>&longs;tay at the Bottome, and with &longs;uch Gravity, and Re&longs;i&longs;tance to Eleva­ <lb/>tion, as is the exce&longs;s of its Ab&longs;olute Gravity, above the Ab&longs;olute Gra­ <lb/>vity of a Ma&longs;s equall to it, made of water, or of a Matter <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> <lb/>equally grave with the water: and, though you &longs;hould moreover <lb/>adde never &longs;o much water above the Levell of that which equalizeth <lb/>the Altitude of the Solid, it &longs;hall not, for all that, encrea&longs;e the Pre&longs;&longs;ion <lb/>or Gravitation, of the parts circumfu&longs;ed about the &longs;aid Solid, by <lb/>which greater pre&longs;&longs;ion, it might come to be repul&longs;ed, becau&longs;e, the <lb/>Re&longs;i&longs;tance is not made, but only by tho&longs;e parts of the water, which <lb/>at the Motion of the &longs;aid Solid do al&longs;o move, and the&longs;e are tho&longs;e <lb/>only, which are comprehended by the two Superficies equidi&longs;tant to <lb/>the Horizon, and their parallels, that comprehend the Altitude of the <lb/>Solid immerged in the water.</s></p><p type="main"> <s>I conceive, I have by this time &longs;ufficiently declared and opened <lb/>the way to the contemplation of the true, intrin&longs;ecall and proper <lb/>Cau&longs;es of diver&longs;e Motions, and of the Re&longs;t of many Solid Bodies in <lb/>diver&longs;e <emph type="italics"/>Mediums,<emph.end type="italics"/> and particularly in the water, &longs;hewing how all ii <lb/>effect, depend on the mutuall exce&longs;&longs;es of the Gravity of the Movea­ <lb/>bles and of the <emph type="italics"/>Mediums<emph.end type="italics"/>: and, that which did highly import, re­ <lb/>moving the Objection, which peradventure would have begotter <lb/>much doubting, and &longs;cruple in &longs;ome, about the verity of my Con­ <lb/>clu&longs;ion, namely, how that notwith&longs;tanding, that the exce&longs;s of the <lb/>Gravity of the water, above the Gravity of the Solid, demitted into <lb/>it, be the cau&longs;e of its floating and ri&longs;ing from the Bottom to the Sur­ <lb/>face, yet a quantity of water, that weighs not ten pounds, can rai&longs;e <pb xlink:href="040/01/1112.jpg" pagenum="419"/>Solid that weighs above 100 pounds: in that we have demon&longs;tra­ <lb/>ted, That it &longs;ufficeth, that &longs;uch difference be found between the <lb/>Specificall Gravities of the <emph type="italics"/>Mediums<emph.end type="italics"/> and Moveables, let the particular <lb/>and ab&longs;olute Gravities be what they will: in&longs;omuch, that a Solid, <lb/>provided that it be Specifically le&longs;s grave than the water, although <lb/>its ab&longs;olute weight were 1000 pounds, yet may it be born up and <lb/>elevated by ten pounds of water, and le&longs;s: and on the contrary, a­ <lb/>nother Solid, &longs;o that it be Specifically more grave than the water, <lb/>though in ab&longs;olute Gravity it were not above a pound, yet all the <lb/>water in the Sea, cannot rai&longs;e it from the Bottom, or float it. </s><s>This <lb/>&longs;ufficeth me, for my pre&longs;ent occa&longs;ion, to have, by the above declared <lb/>Examples, di&longs;covered and demon&longs;trated, without extending &longs;uch <lb/>matters farther, and, as I might have done, into a long Treati&longs;e: <lb/>yea, but that there was a nece&longs;&longs;ity of re&longs;olving the above propo&longs;ed <lb/>doubt, I &longs;hould have contented my &longs;elf with that only, which is <lb/>demon&longs;trated by <emph type="italics"/>Archimedes,<emph.end type="italics"/> in his fir&longs;t Book <emph type="italics"/>De In&longs;identibus hu­ <lb/>mido<emph.end type="italics"/>: where in generall termes he infers and confirms the &longs;ame </s></p><p type="main"> <s><arrow.to.target n="marg1422"></arrow.to.target> <lb/><arrow.to.target n="marg1423"></arrow.to.target> <lb/>Conclu&longs;ions, namely, that Solids (<emph type="italics"/>a<emph.end type="italics"/>) le&longs;s grave than water, &longs;wim or <lb/><arrow.to.target n="marg1424"></arrow.to.target> <lb/>float upon it, the (<emph type="italics"/>b<emph.end type="italics"/>) more grave go to the Bottom, and the (<emph type="italics"/>c<emph.end type="italics"/>) e­ <lb/><arrow.to.target n="marg1425"></arrow.to.target> <lb/>qually grave re&longs;t indifferently in all places, yea, though they &longs;hould <lb/>be wholly under water.</s></p><p type="margin"> <s><margin.target id="marg1422"></margin.target><emph type="italics"/>Of Natation<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1423"></margin.target>(a) <emph type="italics"/>Lib. 1. Prop.<emph.end type="italics"/> 4.</s></p><p type="margin"> <s><margin.target id="marg1424"></margin.target>(b) <emph type="italics"/>Id. </s><s>Lib. </s><s>1. <lb/>Prop.<emph.end type="italics"/> 3.</s></p><p type="margin"> <s><margin.target id="marg1425"></margin.target>(c) <emph type="italics"/>Id. </s><s>Lib. 1. <lb/>Prop.<emph.end type="italics"/> 3.</s></p><p type="main"> <s>But, becau&longs;e that this Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> peru&longs;ed, tran&longs;cri­ <lb/><arrow.to.target n="marg1426"></arrow.to.target> <lb/>bed and examined by <emph type="italics"/>Signor France&longs;co Buonamico,<emph.end type="italics"/> in his <emph type="italics"/>fifth Book <lb/>of Motion, Chap.<emph.end type="italics"/> 29, and afterwards by him confuted, might by the <lb/>Authority of &longs;o renowned, and famous a Philo&longs;opher, be rendered <lb/>dubious, and &longs;u&longs;pected of fal&longs;ity; I have judged it nece&longs;&longs;ary to de­ <lb/>fend it, if I am able &longs;o to do, and to clear <emph type="italics"/>Archimedes,<emph.end type="italics"/> from tho&longs;e <lb/>cen&longs;ures, with which he appeareth to be charged. <emph type="italics"/>Buonamico<emph.end type="italics"/> re­ <lb/><arrow.to.target n="marg1427"></arrow.to.target> <lb/>jecteth the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> fir&longs;t, as not con&longs;entaneous with <lb/>the Opinion of <emph type="italics"/>Aristotle,<emph.end type="italics"/> adding, that it was a &longs;trange thing to him, <lb/><arrow.to.target n="marg1428"></arrow.to.target> <lb/>that the Water &longs;hould exceed the Earth in Gravity, &longs;eeing on the <lb/>contrary, that the Gravity of water, increa&longs;eth, by means of the parti­ <lb/><arrow.to.target n="marg1429"></arrow.to.target> <lb/>cipation of Earth. </s><s>And he &longs;ubjoyns pre&longs;ently after, that he was <lb/>not &longs;atisfied with the Rea&longs;ons of <emph type="italics"/>Archimedes,<emph.end type="italics"/> as not being able with <lb/>that Doctrine, to a&longs;&longs;ign the cau&longs;e whence it comes, that a Boat and <lb/>a Ve&longs;&longs;ell, which otherwi&longs;e, floats above the water, doth &longs;ink to the <lb/>Bottom, if once it be filled with water; that by rea&longs;on of the e­ <lb/>quality of Gravity, between the water within it, and the other water <lb/>without, it &longs;hould &longs;tay a top; but yet, neverthele&longs;s, we &longs;ee it to go to <lb/>the Bottom. <lb/><arrow.to.target n="marg1430"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1426"></margin.target>The <emph type="italics"/>Authors<emph.end type="italics"/> <lb/>defence of <emph type="italics"/>Ar­ <lb/>chimedes<emph.end type="italics"/> his Do­ <lb/>ctrine, again&longs;t <lb/>the oppo&longs;itions <lb/>of <emph type="italics"/>Buonamico.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1427"></margin.target>His fir&longs;t Objecti­ <lb/>on again&longs;t the <lb/>Doctrine of <emph type="italics"/>Ar­ <lb/>chimedes.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1428"></margin.target>His Second Ob­ <lb/>jection.</s></p><p type="margin"> <s><margin.target id="marg1429"></margin.target>His third Obje­ <lb/>ction.</s></p><p type="margin"> <s><margin.target id="marg1430"></margin.target>His &longs;ourth Ob­ <lb/>jection.</s></p><p type="main"> <s>He farther addes, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had clearly confuted the Ancients, <lb/>who &longs;aid, that light Bodies moved upwards, driven by the impul&longs;e </s></p><p type="main"> <s><arrow.to.target n="marg1431"></arrow.to.target> <lb/>of the more grave Ambient: which if it were &longs;o, it &longs;hould &longs;eem of <lb/>nece&longs;&longs;ity to follow, that all naturall Bodies are by nature heavy, <pb xlink:href="040/01/1113.jpg" pagenum="420"/>and none light: For that the &longs;ame would befall the Fire and Air, <lb/>if put in the Bottom of the water. </s><s>And, howbeit, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> grants <lb/>a Pul&longs;ion in the Elements, by which the Earth is reduced into a Sphe­ <lb/>ricall Figure, yet neverthele&longs;s, in his judgement, it is not &longs;uch that it <lb/>can remove grave Bodies from their naturall places, but rather, that <lb/>it &longs;end them toward the Centre, to which (as he &longs;omewhat ob&longs;curely <lb/>continues to &longs;ay,) the water principally moves, if it in the interim <lb/>meet not with &longs;omething that re&longs;i&longs;ts it, and, by its Gravity, thru&longs;ts <lb/>it out of its place: in which ca&longs;e, if it cannot directly, yet at lea&longs;t <lb/>as well as it can, it tends to the Centre: but it happens, that light <lb/>Bodies by &longs;uch Impul&longs;ion, do all a&longs;cend upward: but this properly <lb/>they have by nature, as al&longs;o, that other of &longs;wimming. </s><s>He concludes, <lb/><arrow.to.target n="marg1432"></arrow.to.target> <lb/>la&longs;tly, that he concurs with <emph type="italics"/>Archimedes<emph.end type="italics"/> in his Conclu&longs;ions; but not <lb/>in the Cau&longs;es, which he would referre to the facile and difficult Sepa­ <lb/>ration of the <emph type="italics"/>Medium,<emph.end type="italics"/> and to the predominance of the Elements, &longs;o <lb/>that when the Moveable &longs;uperates the power of the <emph type="italics"/>Medium<emph.end type="italics"/>; as for <lb/>example, Lead doth the Continuity of water, it &longs;hall move thorow it, <lb/>el&longs;e not.</s></p><p type="margin"> <s><margin.target id="marg1431"></margin.target>The <emph type="italics"/>Ancients<emph.end type="italics"/> <lb/>denved <emph type="italics"/>Ao&longs;olute<emph.end type="italics"/> <lb/>Levity.</s></p><p type="margin"> <s><margin.target id="marg1432"></margin.target>The cau&longs;es of <lb/>Natation & Sub­ <lb/>mer&longs;ion, accord­ <lb/>ing to the Peri­ <lb/>pateticks.</s></p><p type="main"> <s>This is all that I have been able to collect, as produced again&longs;t <lb/><emph type="italics"/>Archimedes<emph.end type="italics"/> by <emph type="italics"/>Signor Buonamico<emph.end type="italics"/>: who hath not well ob&longs;erved the <lb/>Principles and Suppo&longs;itions of <emph type="italics"/>Archimedes<emph.end type="italics"/>; which yet mu&longs;t be <lb/>fal&longs;e, if the Doctrine be fal&longs;e, which depends upon them; but is <lb/>contented to alledge therein &longs;ome Inconveniences, and &longs;ome Repug­ <lb/>nances to the Doctrine and Opinion of <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/> In an&longs;wer to which <lb/>Objections, I &longs;ay, fir&longs;t, That the being of <emph type="italics"/>Archimedes<emph.end type="italics"/> Doctrine, &longs;im­ <lb/><arrow.to.target n="marg1433"></arrow.to.target> <lb/>ply different from the Doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> ought not to move any <lb/>to &longs;u&longs;pect it, there being no cau&longs;e, why the Authority of this &longs;hould <lb/>be preferred to the Authority of the other: but, becau&longs;e, where the <lb/>decrees of Nature are indifferently expo&longs;ed to the intellectuall eyes of <lb/>each, the Authority of the one and the other, lo&longs;eth all anthentical­ <lb/>ne&longs;s of Per&longs;wa&longs;ion, the ab&longs;olute power re&longs;iding in Rea&longs;on; therefore <lb/>I pa&longs;s to that which he alledgeth in the &longs;econd place, as an ab&longs;urd con­ <lb/><arrow.to.target n="marg1434"></arrow.to.target> <lb/>&longs;equent of the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> namely, That water &longs;hould <lb/>be more grave than Earth. </s><s>But I really find not, that ever <emph type="italics"/>Archi­ <lb/>medes<emph.end type="italics"/> &longs;aid &longs;uch a thing, or that it can be rationally deduced from his <lb/>Conclu&longs;ions: and if that were manife&longs;t unto me, I verily believe, I <lb/>&longs;hould renounce his Doctrine, as mo&longs;t erroneous. </s><s>Perhapsthis Dedu­ <lb/>ction of <emph type="italics"/>Buonamico,<emph.end type="italics"/> is founded upon that which he citeth of the Ve­ <lb/>&longs;&longs;el, which &longs;wims as long as its voyd of water, but once full it &longs;inks to <lb/>the Bottom, and under&longs;tanding it of a Ve&longs;&longs;el of Earth, he infers again&longs;t <lb/><emph type="italics"/>Archimedes<emph.end type="italics"/> thus: Thou &longs;ay&longs;t that the Solids which &longs;wim, are le&longs;s grave <lb/>than water: this Ve&longs;&longs;ell &longs;wimmeth: therefore, this Ve&longs;&longs;ell is le&longs;&longs;e grave <lb/>than water. </s><s>If this be the Illation. </s><s>I ea&longs;ily an&longs;wer, granting that this <lb/>Ve&longs;&longs;ell is le&longs;&longs;e grave than water, and denying the other con&longs;equence, <pb xlink:href="040/01/1114.jpg" pagenum="421"/>namely, that Earth is le&longs;s Grave than Water. </s><s>The Ve&longs;&longs;el that &longs;wims <lb/>occupieth in the water, not only a place equall to the Ma&longs;s of the <lb/>Earth, of which it is formed; but equall to the Earth and to the Air <lb/>together, contained in its concavity. </s><s>And, if &longs;uch a Ma&longs;s compoun­ <lb/>ded of Earth and Air, &longs;hall be le&longs;s grave than &longs;uch another quantity <lb/>of water, it &longs;hall &longs;wim, and &longs;hall accord with the Doctrine of <emph type="italics"/>Archi­ <lb/>medes<emph.end type="italics"/>; but if, again, removing the Air, the Ve&longs;&longs;ell &longs;hall be filled <lb/>with water, &longs;o that the Solid put in the water, be nothing but <lb/>Earth, nor occupieth other place, than that which is only po&longs;&longs;e&longs;t by <lb/>Earth, it &longs;hall then go to the Bottom, by rea&longs;on that the Earth is <lb/>heavier than the water: and this corre&longs;ponds well with the meaning <lb/>of <emph type="italics"/>Archimedes.<emph.end type="italics"/> See the &longs;ame effect illu&longs;trated, with &longs;uch another <lb/>Experiment, In pre&longs;&longs;ing a Viall Gla&longs;s to the Bottom of the water, <lb/>when it is full of Air, it will meet with great re&longs;i&longs;tance, becau&longs;e it is <lb/>not the Gla&longs;s alone, that is pre&longs;&longs;ed under water, but together with <lb/>the Gla&longs;s a great Ma&longs;s of Air, and &longs;uch, that if you &longs;hould take as <lb/>much water, as the Ma&longs;s of the Gla&longs;s, and of the Air contained in it, <lb/>you would have a weight much greater than that of the Viall, and of <lb/>its Air: and, therefore, it will not &longs;ubmerge without great violence: <lb/>but if we demit only the Gla&longs;s into the water, which &longs;hall be when <lb/>you &longs;hall fill the Gla&longs;s with water, then &longs;hall the Gla&longs;s de&longs;cend to <lb/>the Bottom; as &longs;uperiour in Gravity to the water.</s></p><p type="margin"> <s><margin.target id="marg1433"></margin.target>The Authors an­ <lb/>&longs;wer to the fir&longs;t <lb/>Objection.</s></p><p type="margin"> <s><margin.target id="marg1434"></margin.target>The Authors an­ <lb/>&longs;wer to the &longs;e­ <lb/>cond Objection.</s></p><p type="main"> <s>Returning, therefore, to our fir&longs;t purpo&longs;e; I &longs;ay, that Earth is <lb/>more grave than water, and that therefore, a Solid of Earth goeth to <lb/>the bottom of it; but one may po&longs;&longs;ibly make a compo&longs;ition of Earth <lb/>and Air, which &longs;hall be le&longs;s grave than a like Ma&longs;s of Water; and <lb/>this &longs;hall &longs;wim: and yet both this and the other experiment &longs;hall <lb/>very well accord with the Doctrine of <emph type="italics"/>Archimedes.<emph.end type="italics"/> But becau&longs;e that <lb/>in my judgment it hath nothing of difficulty in it, I will not po&longs;itive­ <lb/>ly affirme that <emph type="italics"/>Signor Buonamico,<emph.end type="italics"/> would by &longs;uch a di&longs;cour&longs;e object <lb/>unto <emph type="italics"/>Archimedes<emph.end type="italics"/> the ab&longs;urdity of inferring by his doctrine, that Earth <lb/>was le&longs;s grave than Water, though I know not how to conceive what <lb/>other accident he could have induced thence.</s></p><p type="main"> <s>Perhaps &longs;uch a Probleme (in my judgement fal&longs;e) was read by <lb/><emph type="italics"/>Signor Buonamico<emph.end type="italics"/> in &longs;ome other Author, by whom peradventure it <lb/>was attributed as a &longs;ingular propertie, of &longs;ome particular Water, and <lb/>&longs;o comes now to be u&longs;ed with a double errour in confutation of <emph type="italics"/>Ar­ <lb/>chimedes,<emph.end type="italics"/> &longs;ince he &longs;aith no &longs;uch thing, nor by him that did &longs;ay it was it <lb/>meant of the common Element of Water.</s></p><p type="main"> <s>The third difficulty in the doctrine of <emph type="italics"/>Archimedes<emph.end type="italics"/> was, that he <lb/><arrow.to.target n="marg1435"></arrow.to.target> <lb/>could not render a rea&longs;on whence it aro&longs;e, that a piece of Wood, <lb/>and a Ve&longs;&longs;ell of Wood, which otherwi&longs;e floats, goeth to the bottom, <lb/>if filled with Water. <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> hath &longs;uppo&longs;ed that a Ver&longs;&longs;ell <lb/>of Wood, and of Wood that by nature &longs;wims, as before is &longs;aid, <pb xlink:href="040/01/1115.jpg" pagenum="422"/>goes to the bottom, if it be filled with water; of which he in the fol­ <lb/>lowing Chapter, which is the 30 of the fifth Book copiou&longs;ly di&longs;cour&longs;­ <lb/>eth: but I (&longs;peaking alwayes without diminution of his &longs;ingular <lb/>Learning) dare in defence of <emph type="italics"/>Archimedes<emph.end type="italics"/> deny this experiment, being <lb/>certain that a piece of Wood which by its nature &longs;inks not in Water, <lb/>&longs;hall not &longs;inke though it be turned and converted into the forme of a­ <lb/>ny Ve&longs;&longs;ell what&longs;oever, and then filled with Water: and he that would <lb/>readily &longs;ee the Experiment in &longs;ome other tractable Matter, and that is <lb/>ea&longs;ily reduced into &longs;everal Figures, may take pure Wax, and ma­ <lb/>king it fir&longs;t into a Ball or other &longs;olid Figure, let him adde to it &longs;o <lb/>much Lead as &longs;hall ju&longs;t carry it to the bottome, &longs;o that being a graine <lb/>le&longs;s it could not be able to &longs;inke it, and making it afterwards into <lb/>the forme of a Di&longs;h, and filling it with Water, he &longs;hall finde that with­ <lb/>out the &longs;aid Lead it &longs;hall not &longs;inke, and that with the Lead it &longs;hall de­ <lb/>&longs;cend with much &longs;lowne&longs;s: & in &longs;hort he &longs;hall &longs;atisfie him&longs;elf, that the <lb/>Water included makes no alteration. </s><s>I &longs;ay not all this while, but that <lb/>its po&longs;&longs;ible of Wood to make Barkes, which being filled with water, <lb/>&longs;inke; but that proceeds not through its Gravity, encrea&longs;ed by the <lb/>Water, but rather from the Nailes and other Iron Workes, &longs;o that <lb/>it no longer hath a Body le&longs;s grave than Water, but one mixt of Iron <lb/>and Wood, more grave than a like Ma&longs;&longs;e of Water. </s><s>Therefore let <lb/><emph type="italics"/>Signor Buonamico<emph.end type="italics"/> de&longs;i&longs;t from de&longs;iring a rea&longs;on of an effect, that is <lb/>not in nature: yea if the &longs;inking of the Woodden Ve&longs;&longs;ell when its full <lb/>of Water, may call in que&longs;tion the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> which <lb/>he would not have you to follow, is on the contrary con&longs;onant and a­ <lb/>greeable to the Doctrine of the Peripateticks, &longs;ince it aptly a&longs;&longs;ignes a <lb/>rea&longs;on why &longs;uch a Ve&longs;&longs;ell mu&longs;t, when its full of Water, de&longs;cend to the <lb/>bottom; converting the Argument the other way, we may with <lb/>&longs;afety &longs;ay that the Doctrine of <emph type="italics"/>Archimedes<emph.end type="italics"/> is true, &longs;ince it aptly agre­ <lb/>eth with true experiments, and que&longs;tion the other, who&longs;e Deducti­ <lb/>ons are fa&longs;tened upon etroneou&longs;s Conclu&longs;ions. </s><s>As for the other point <lb/>hinted in this &longs;ame In&longs;tance, where it &longs;eemes that <emph type="italics"/>Benonamico<emph.end type="italics"/> under­ <lb/>&longs;tands the &longs;ame not only of a piece of wood, &longs;haped in the forme of a <lb/>Ve&longs;&longs;ell, but al&longs;o of ma&longs;&longs;ie Wood, which filled, <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> as I believe, he <lb/>would &longs;ay, &longs;oaked and &longs;teeped in Water, goes finally to the bottom <lb/>that happens in &longs;ome poro&longs;e Woods, which, while their Poro&longs;ity is re­ <lb/>pleni&longs;hed with Air, or other Matter le&longs;s grave than Water, are Ma&longs;­ <lb/>&longs;es &longs;pecificially le&longs;s grave than the &longs;aid Water, like as is that Viall of <lb/>Gla&longs;s while&longs;t it is full of Air: but when, &longs;uch light Matter depart­ <lb/>ing, there &longs;ucceedeth Water into the &longs;ame Poro&longs;ities and Cavities, <lb/>there re&longs;ults a compound of Water and Gla&longs;s more grave than a like <lb/>Ma&longs;s of Water: but the exce&longs;s of its Gravity con&longs;i&longs;ts in the Matter <lb/>of the Gla&longs;s, and not in the Water, which cannot be graver than it <lb/>&longs;elf: &longs;o that which remaines of the Wood, the Air of its Cavi­ <pb xlink:href="040/01/1116.jpg" pagenum="423"/>ties departing, if it &longs;hall be more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than Water, fil but its <lb/>Poro&longs;ities with Water, and you &longs;hal have a Compo&longs;t of Water and <lb/>of Wood more grave than Water, but not by vertue of the Water re­ <lb/>ceived into and imbibed by the Poro&longs;ities, but of that Matter of the <lb/>Wood which remains when the Air is departed: and being &longs;uch it <lb/>&longs;hall, according to the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> goe to the bottom, <lb/>like as before, according to the &longs;ame Doctrine it did &longs;wim.</s></p><p type="margin"> <s><margin.target id="marg1435"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he Authors an­ <lb/>&longs;wer to the third <lb/>Objection.</s></p><p type="main"> <s>As to that finally which pre&longs;ents it &longs;elf in the fourth place, namely, <lb/><arrow.to.target n="marg1436"></arrow.to.target> <lb/>that the <emph type="italics"/>Ancients<emph.end type="italics"/> have been heretofore confuted by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who <lb/>denying Po&longs;itive and Ab&longs;olute Levity, and truely e&longs;teeming all Bo­ <lb/>dies to be grave, &longs;aid, that that which moved upward was driven by <lb/>the circumambient Air, and therefore that al&longs;o the Doctrine of <lb/><emph type="italics"/>Archimedes,<emph.end type="italics"/> as an adherent to &longs;uch an Opinion was con­ <lb/>victed and confuted: I an&longs;wer fir&longs;t, that <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> in my <lb/>judgement hath impo&longs;ed upon <emph type="italics"/>Archimedes,<emph.end type="italics"/> and deduced from his <lb/>words more than ever he intended by them, or may from his Propo­ <lb/>&longs;itions be collected, in regard that <emph type="italics"/>Archimedes<emph.end type="italics"/> neither denies, nor ad­ <lb/>mitteth Po&longs;itive Levity, nor doth he &longs;o much as mention it: &longs;o that <lb/>much le&longs;s ought <emph type="italics"/>Buonamico<emph.end type="italics"/> to inferre, that he hath denyed that it <lb/>might be the Cau&longs;e and Principle of the A&longs;cen&longs;ion of Fire, and other <lb/>Light Bodies: having but only demon&longs;trated, that Solid Bodies <lb/><arrow.to.target n="marg1437"></arrow.to.target> <lb/>more grave than Water de&longs;cend in it, according to the exce&longs;s of their <lb/>Gravity above the Gravity of that, he demon&longs;trates likewi&longs;e, how the <lb/><arrow.to.target n="marg1438"></arrow.to.target> <lb/>le&longs;s grave a&longs;cend in the &longs;ame Water, accordng to its exce&longs;s of Gra­ <lb/>ty, above the Gravity of them. </s><s>So that the mo&longs;t that can be gather­ <lb/>ed from the Dem on&longs;tration of <emph type="italics"/>Archimedes<emph.end type="italics"/> is, that like as the exce&longs;s <lb/>of the Gravity of the Moveable above the Gravity of the Water, is <lb/>the Cau&longs;e that it de&longs;cends therein, &longs;o the exce&longs;s of the Gravity of <lb/>the water above that of the Moveable, is a &longs;ufficient Cau&longs;e why it de&longs;­ <lb/>cends not, but rather betakes it &longs;elf to &longs;wim: not enquiring whe­ <lb/>ther of moving upwards there is, or is not any other Cau&longs;e contrary <lb/>to Gravity: nor doth <emph type="italics"/>Archimedes<emph.end type="italics"/> di&longs;cour&longs;e le&longs;s properly than if one <lb/>&longs;hould &longs;ay: If the South Winde &longs;hall a&longs;&longs;ault the Barke with greater <lb/><emph type="italics"/>Impetus<emph.end type="italics"/> than is the violence with which the Streame of the River car­ <lb/>ries it towards the South, the motion of it &longs;hall be towards the North: <lb/>but if the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Water &longs;hall overcome that of the Winde, its <lb/>motion &longs;hall be towards the South. </s><s>The di&longs;cour&longs;e is excellent and <lb/>would be unworthily contradicted by &longs;uch as &longs;hould oppo&longs;e it, &longs;aying: <lb/>Thou mi&longs;-alledge&longs;t as Cau&longs;e of the motion of the Bark towards the <lb/>South, the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Stream of the Water above that of the <lb/>South Winde; mi&longs;-alledge&longs;t I &longs;ay, for it is the Force of the North <lb/>Winde oppo&longs;ite to the South, that is able to drive the Bark towards <lb/>the South. </s><s>Such an Objection would be &longs;uperfluous, becau&longs;e he which <lb/>alledgeth for Cau&longs;e of the Motion the &longs;tream of the Water, denies not <pb xlink:href="040/01/1117.jpg" pagenum="424"/>but that the Winde oppo&longs;ite to the South may do the &longs;ame, but only <lb/>affirmeth that the force of the Water prevailing over the South <lb/>Wind, the Bark &longs;hall move towards the South: and &longs;aith no more <lb/>than is true. </s><s>And ju&longs;t thus when <emph type="italics"/>Archimedes<emph.end type="italics"/> &longs;aith, that the Gravity <lb/>of the Water prevailing over that by which the moveable de&longs;cends to <lb/>the Bottom, &longs;uch moveable &longs;hall be rai&longs;ed from the Bottom to the Sur­ <lb/>face alledgeth a very true Cau&longs;e of &longs;uch an Accident, nor doth he af­ <lb/>firm or deny that there is, or is not, a vertue contrary to Gravity, called <lb/>by &longs;ome Levity, that hath al&longs;o a power of moving &longs;ome Matters up <lb/>wards. </s><s>Let therefore the Weapons of <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> be directed a­ <lb/><arrow.to.target n="marg1439"></arrow.to.target> <lb/>gain&longs;t <emph type="italics"/>Plato,<emph.end type="italics"/> and other <emph type="italics"/>Ancients,<emph.end type="italics"/> who totally denying <emph type="italics"/>Levity,<emph.end type="italics"/> and taking <lb/>all Bodies to be grave, &longs;ay that the Motion upwards is made, not <lb/>from an intrin&longs;ecal Principle of the Moveable, but only by the Im­ <lb/>pul&longs;e of the <emph type="italics"/>Medium<emph.end type="italics"/>; and let <emph type="italics"/>Archimedes<emph.end type="italics"/> and his Doctrine e&longs;cape <lb/>him, &longs;ince he hath given him no Cau&longs;e of quarelling with him <lb/>But if this Apologie, produced in defence of <emph type="italics"/>Archimedes,<emph.end type="italics"/> &longs;hould &longs;een <lb/>to &longs;ome in&longs;ufficient to free him from the Objections and Arguments <lb/>produced by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> again&longs;t <emph type="italics"/>Plato,<emph.end type="italics"/> and the other <emph type="italics"/>Ancients,<emph.end type="italics"/> as if they <lb/>did al&longs;o fight again&longs;t <emph type="italics"/>Archimedes,<emph.end type="italics"/> alledging the Impul&longs;e of the Water <lb/><arrow.to.target n="marg1440"></arrow.to.target> <lb/>as the Cau&longs;e of the &longs;wimming of &longs;ome Bodies le&longs;s grave than it, I would <lb/>not que&longs;tion, but that I &longs;hould be able to maintaine the Doctrine of <lb/><emph type="italics"/>Plato<emph.end type="italics"/> and tho&longs;e others to be mo&longs;t true, who ab&longs;olutely deny Levity, <lb/>and affirm no other Intrin&longs;ecal Principle of Motion to be in Elemen­ <lb/>tary Bodies &longs;ave only that towards the Centre of the Earth, nor no <lb/><arrow.to.target n="marg1441"></arrow.to.target> <lb/>other Cau&longs;e of moving upwards, &longs;peaking of that which hath the re­ <lb/>&longs;emblance of natural Motion, but only the repul&longs;e of the <emph type="italics"/>Medium,<emph.end type="italics"/> &longs;luid, <lb/>and exceeding the Gravity of the Moveable: and as to the Rea&longs;ons <lb/>of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> on the contrary, I believe that I could be able fully to <lb/><arrow.to.target n="marg1442"></arrow.to.target> <lb/>an&longs;wer them, and I would a&longs;&longs;ay to do it, if it were ab&longs;olutely nece&longs;&longs;a­ <lb/>ry to the pre&longs;ent Matter, or were it not too long a Digre&longs;&longs;ion for this <lb/>&longs;hort Treati&longs;e. </s><s>I will only &longs;ay, that if there were in &longs;ome of our Elle­ <lb/>mentary Bodies an Intrin&longs;ecall Principle and Naturall Inclination <lb/>to &longs;hun the Centre of the Earth, and to move towards the Concave <lb/>of the Moon, &longs;uch Bodies, without doubt, would more &longs;wiftly a&longs;cend <lb/>through tho&longs;e <emph type="italics"/>Mediums<emph.end type="italics"/> that lea&longs;t oppo&longs;e the Velocity of the Moveable, <lb/>and the&longs;e are the more tenuous and &longs;ubtle; as is, for example, the <lb/>Air in compari&longs;on of the Water, we daily proving that we can with <lb/><arrow.to.target n="marg1443"></arrow.to.target> <lb/>farre more expeditious Velocity move a Hand or a Board to and a­ <lb/>gain in one than in the other: neverthele&longs;s, we never could finde any <lb/>Body, that did not a&longs;cend much more &longs;wiftly in the water than in the <lb/><arrow.to.target n="marg1444"></arrow.to.target> <lb/>Air. </s><s>Yea of Bodies which we &longs;ee continually to a&longs;cend in the Water, <lb/>there is none that having arrived to the confines of the Air, do not whol­ <lb/>ly lo&longs;e their Motion; even the Air it &longs;elf, which ri&longs;ing with great Ce­ <lb/>lerity through the Water, being once come to its Region it lo&longs;eth all</s></p> <pb xlink:href="040/01/1118.jpg" pagenum="425"/><p type="margin"> <s><margin.target id="marg1436"></margin.target>The Authors <lb/>an&longs;wer to the <lb/>fourth Object­ <lb/>ion.</s></p><p type="margin"> <s><margin.target id="marg1437"></margin.target>Of Natation, <lb/>Lib. 1. Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1438"></margin.target>Of Natation, <lb/>Lib. </s><s>1. Prop. </s><s>4.</s></p><p type="margin"> <s><margin.target id="marg1439"></margin.target><emph type="italics"/>Plato<emph.end type="italics"/> denyeth <lb/>Po&longs;itive Levi­ <lb/>ty.</s></p><p type="margin"> <s><margin.target id="marg1440"></margin.target>The Authors <lb/>defence of the <lb/>doctrine of <emph type="italics"/>Plato<emph.end type="italics"/> <lb/>and the <emph type="italics"/>Ancients,<emph.end type="italics"/> <lb/>who ab&longs;olutely <lb/>deny Levity:</s></p><p type="margin"> <s><margin.target id="marg1441"></margin.target>According to <lb/><emph type="italics"/>Plato<emph.end type="italics"/> there is no <lb/>Principle of the <lb/>Motion of de­ <lb/>&longs;cent in Naturall <lb/>Bodies, &longs;ave that <lb/>to the Centre.</s></p><p type="margin"> <s><margin.target id="marg1442"></margin.target>No cau&longs;e of <lb/>the motion of <lb/><emph type="italics"/>A<emph.end type="italics"/> cent, &longs;ave the <lb/>Impul&longs;e of the <lb/><emph type="italics"/>Medium,<emph.end type="italics"/> exceed­ <lb/>ing the Move­ <lb/>able in Gravi­ <lb/>tie.</s></p><p type="margin"> <s><margin.target id="marg1443"></margin.target>Bodies a&longs;cend <lb/>much &longs;wifter in <lb/>the Water, than <lb/>in the Air.</s></p><p type="margin"> <s><margin.target id="marg1444"></margin.target>All Bodies a&longs;­ <lb/>cending through <lb/>Water, lo&longs;e <lb/>their Motion, <lb/>comming to the <lb/>confines of the <lb/>Air.</s></p><p type="main"> <s>And, howbeit, Experience &longs;hewes, that the Bodies, &longs;ucce&longs;&longs;ively <lb/><arrow.to.target n="marg1445"></arrow.to.target> <lb/>le&longs;s grave, do mo&longs;t expeditiou&longs;ly a&longs;cend in water, it cannot be doubt­ <lb/>ed, but that the Ignean Exhalations do a&longs;cend more &longs;wiftly <lb/><arrow.to.target n="marg1446"></arrow.to.target> <lb/>through the water, than doth the Air: which Air is &longs;een by Experi­ <lb/>ence to a&longs;cend more &longs;wiftly through the Water, than the Fiery Exha­ <lb/>lations through the Air: Therefore, we mu&longs;t of nece&longs;&longs;ity conclude, <lb/>that the &longs;aid Exhalations do much more expeditiou&longs;ly a&longs;cend through <lb/>the Water, than through the Air; and that, con&longs;equently, they are <lb/>moved by the Impul&longs;e of the Ambient <emph type="italics"/>Medium,<emph.end type="italics"/> and not by an intrin­ <lb/>&longs;ick Principle that is in them, of avoiding the Centre of the Earth; <lb/>to which other grave Bodies tend.</s></p><p type="margin"> <s><margin.target id="marg1445"></margin.target>The lighter <lb/>Bodies al&longs;end <lb/>more &longs;wiftly <lb/>through Water.</s></p><p type="margin"> <s><margin.target id="marg1446"></margin.target>Fiery Exhalati­ <lb/>ons ascend tho­ <lb/>row the Water <lb/>more &longs;wiftly <lb/>than doth the <lb/>Air; & the Air <lb/>a&longs;cends more <lb/>&longs;wiftly thorow <lb/>the Water, than <lb/><emph type="italics"/>F<emph.end type="italics"/>ire thorow the <lb/>Air.</s></p><p type="main"> <s>To that which for a finall conclu&longs;ion, <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> produceth <lb/><arrow.to.target n="marg1447"></arrow.to.target> <lb/>of going about to reduce the de&longs;cending or not de&longs;cending, to the <lb/>ea&longs;ie and unea&longs;ie Divi&longs;ion of the <emph type="italics"/>Medium,<emph.end type="italics"/> and to the predominancy <lb/>of the Elements: I an&longs;wer, as to the fir&longs;t part, that that cannot in any <lb/>manner be admitted as a Cau&longs;e, being that in none of the Fluid <lb/><emph type="italics"/>Mediums,<emph.end type="italics"/> as the Air, the Water, and other Liquids, there is any <lb/><arrow.to.target n="marg1448"></arrow.to.target> <lb/>Re&longs;i&longs;tance again&longs;t Divi&longs;ion, but all by every the lea&longs;t Force, are di­ <lb/>vided and penetrated, as I will anon demon&longs;trate: &longs;o, that of &longs;uch <lb/>Re&longs;i&longs;tance of Divi&longs;ion there can be no Act, &longs;ince it &longs;elf is not in be­ <lb/>ing. </s><s>As to the other part, I &longs;ay, that the predominancy of the Ele­ <lb/><arrow.to.target n="marg1449"></arrow.to.target> <lb/>ments in Moveables, is to be con&longs;idered, as far as to the exce&longs;&longs;e or <lb/>defect of Gravity, in relation to the <emph type="italics"/>Medium<emph.end type="italics"/>: for in that Action, <lb/>the Elements operate not, but only, &longs;o far as they are grave or light: <lb/>therefore, to &longs;ay that the Wood of the Firre &longs;inks not, becau&longs;e Air <lb/>predominateth in it, is no more than to &longs;ay, becau&longs;e it is le&longs;s grave <lb/>than the Water. </s><s>Yea, even the immediate Cau&longs;e, is its being le&longs;s <lb/>grave than the Water: and it being under the predominancy of the <lb/><arrow.to.target n="marg1450"></arrow.to.target> <lb/>Air, is the Cau&longs;e of its le&longs;s Gravity: Therefore, he that alledgeth the <lb/>predominancy of the Element for a Cau&longs;e, brings the Cau&longs;e of the <lb/>Cau&longs;e, and not the neere&longs;t and immediate Cau&longs;e. </s><s>Now, who knows <lb/>not that the true Cau&longs;e is the immediate, and not the mediate? <lb/><arrow.to.target n="marg1451"></arrow.to.target> <lb/>Moreover, he that alledgeth Gravity, brings a Cau&longs;e mo&longs;t per&longs;picuous <lb/>to Sence: The cau&longs;e we may very ea&longs;ily a&longs;&longs;ertain our &longs;elves; <lb/>whether Ebony, for example, and Firre, be more or le&longs;s grave than <lb/>water: but whether Earth or Air predominates in them, who &longs;hall <lb/><arrow.to.target n="marg1452"></arrow.to.target> <lb/>make that manife&longs;t? </s><s>Certainly, no Experiment can better do it <lb/>than to ob&longs;erve whether they &longs;wim or &longs;ink. </s><s>So, that he who knows, <lb/>not whether &longs;uch a Solid &longs;wims, unle&longs;s when he knows that Air pre­ <lb/>dominates in it, knows not whether it &longs;wim, unle&longs;s he &longs;ees it &longs;wim, <lb/>for then he knows that it &longs;wims, when he knows that it is Air that <lb/>predominates, but knows not that Air hath the predominance, unle&longs;s <lb/>he &longs;ees it &longs;wim: therefore, he knows not if it &longs;wims, till &longs;uch time <lb/>as he hath &longs;een it &longs;wim.</s></p> <pb xlink:href="040/01/1119.jpg" pagenum="426"/><p type="margin"> <s><margin.target id="marg1447"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he Authors <lb/>confutation of <lb/>the Peripateticks <lb/>Cau&longs;es of Nata­ <lb/>tion & Submer&longs;i­ <lb/>on.</s></p><p type="margin"> <s><margin.target id="marg1448"></margin.target>Water & other <lb/>fluids void of <lb/>Re&longs;i&longs;tance a­ <lb/>gain&longs;t Divi&longs;ion.</s></p><p type="margin"> <s><margin.target id="marg1449"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he predomi­ <lb/>nancy of Ele­ <lb/>ments in Move­ <lb/>ables to be con­ <lb/>&longs;idered only in <lb/>relation to their <lb/>excefs or defect <lb/>of Gravity in <lb/>reference to the <lb/><emph type="italics"/>Medium.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1450"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he immedi­ <lb/>ate Cau&longs;e of Na­ <lb/>tation is that the <lb/>Moveable is le&longs;s <lb/>grave than the <lb/>Water.</s></p><p type="margin"> <s><margin.target id="marg1451"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he <emph type="italics"/>P<emph.end type="italics"/>eripate­ <lb/>ticks alledge for <lb/>the rea&longs;on of <lb/>Natation the <lb/>Cau&longs;e of the <lb/>Cau&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1452"></margin.target>Gravity a <lb/>Cau&longs;e mo&longs;t per­ <lb/>&longs;picuous to <lb/>&longs;ence:</s></p><p type="main"> <s>Let us not then de&longs;pi&longs;e tho&longs;e Hints, though very dark, which <lb/>Rea&longs;on, after &longs;ome contemplation, offereth to our Intelligence, and <lb/>lets be content to be taught by <emph type="italics"/>Archimedes,<emph.end type="italics"/> that then any Body &longs;hall <lb/><arrow.to.target n="marg1453"></arrow.to.target> <lb/>&longs;ubmerge in water, when it &longs;hall be &longs;pecifically more grave than it <lb/>and that if it &longs;hall be le&longs;s grave, it &longs;hall of nece&longs;&longs;ity &longs;wim, and <lb/><arrow.to.target n="marg1454"></arrow.to.target> <lb/>that it will re&longs;t indifferently in any place under water, if its Gravity <lb/>be perfectly like to that of the water. <lb/><arrow.to.target n="marg1455"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1453"></margin.target>Lib 1. of Na­ <lb/>tation Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1454"></margin.target>Id. </s><s>Lib. 1. <lb/>Prop. </s><s>4.</s></p><p type="margin"> <s><margin.target id="marg1455"></margin.target>Id. </s><s>Lib. </s><s>1: <lb/>Prop. </s><s>3.</s></p><p type="main"> <s>The&longs;e things explained and proved, I come to con&longs;ider that which <lb/>offers it &longs;elf, touching what the Diver&longs;ity of figure given unto the <lb/>&longs;aid Moveable hath to do with the&longs;e Motions and Re&longs;ts; and pro­ <lb/>ceed to affirme, that,</s></p><p type="head"> <s>THEOREME V.</s></p><p type="main"> <s><emph type="italics"/>The diver&longs;ity of Figures given to this or that Solid<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1456"></arrow.to.target> <lb/><emph type="italics"/>cannot any way be a Cau&longs;e of its ab&longs;olute Sinking or <lb/>Swimming.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1456"></margin.target>Diver&longs;ity of <lb/>Figure no Cau&longs;e <lb/>of its ab&longs;olute <lb/>Natation or Sub­ <lb/>mer&longs;ion.</s></p><p type="main"> <s>So that if a Solid being formed, for example, into a Spherical <lb/>Figure, doth &longs;ink or &longs;wim in the water, I &longs;ay, that being formed <lb/>into any other Figure, the &longs;ame figure in the &longs;ame water, &longs;hall <lb/>&longs;ink or &longs;wim: nor can &longs;uch its Motion by the Expan&longs;ion or by o­ <lb/>ther mutation of Figure, be impeded or taken away. <lb/><arrow.to.target n="marg1457"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1457"></margin.target>The Expan&longs;i­ <lb/>on of <emph type="italics"/>F<emph.end type="italics"/>igure, re­ <lb/>tards the Veloci­ <lb/>ty of the a&longs;cent <lb/>or de&longs;cent of the <lb/>Moveable in the <lb/>water; but doth <lb/>not deprive it of <lb/>all Motion.</s></p><p type="main"> <s>The Expan&longs;ion of the Figure may indeed retard its Velocity, a&longs; <lb/>well of a&longs;cent as de&longs;cent, and more and more according as the &longs;aid Fi­ <lb/>gure is reduced to a greater breadth and thinne&longs;s: but that it may bere <lb/>duced to &longs;uch a form as that that &longs;ame matter be wholly hindred from <lb/>moving in the &longs;ame water, that I hold to be impo&longs;&longs;ible. </s><s>In this I have <lb/>met with great contradictors, who producing &longs;ome Experiments, and <lb/>in perticular a thin Board of Ebony, and a Ball of the &longs;ame Wood <lb/>and &longs;hewing how the Ball in Water de&longs;cended to the bottom, and <lb/>the Board being put lightly upon the Water &longs;ubmerged not, but re&longs;t­ <lb/>ed; have held, and with the Authority of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> confirmed them <lb/>&longs;elves in their Opinions, that the Cau&longs;e of that Re&longs;t was the breadth <lb/>of the Figure, u able by its &longs;mall weight to pierce and penetrate the <lb/>Re&longs;i&longs;tance of the Waters Cra&longs;&longs;itude, which Re&longs;i&longs;tance is readily o­ <lb/>vercome by the other Sphericall Figure.</s></p><p type="main"> <s>This is the Principal point in the pre&longs;ent Que&longs;tion, in which I per­ <lb/>&longs;wade my &longs;elf to be on the right &longs;ide.</s></p><p type="main"> <s>Therefore, beginning to inve&longs;tigate with the examination of ex­ <lb/>qui&longs;ite Experiments that really the Figure doth not a jot alter the de&longs;­ <lb/>cent or A&longs;cent of the &longs;ame Solids, and having already demon&longs;tra­ <lb/>ted that the greater or le&longs;s Gravity of the Solid in relation to the Gra­ <lb/>vity of the <emph type="italics"/>Medium<emph.end type="italics"/> is the cau&longs;e of De&longs;cent or A&longs;cent: when ever we <pb xlink:href="040/01/1120.jpg" pagenum="427"/>would make proof of that, which about this Effect the diver&longs;ity of Fi­ <lb/>gure worketh, its nece&longs;&longs;ary to make the Experiment with Matter <lb/>wherein variety of Gravities hath no place. </s><s>For making u&longs;e of Mat­ <lb/>ters which may be different in their Specifical Gravities, and meeting <lb/>with varieties of effects of A&longs;cending and De&longs;cending, we &longs;hall al­ <lb/>wayes be left un&longs;atisfied whether that diver&longs;ity derive it &longs;elf really <lb/>from the &longs;ole Figure, or el&longs;e from the divers Gravity al&longs;o. </s><s>We may <lb/>remedy this by takeing one only Matter, that is tractable and ea&longs;ily <lb/>reduceable into every &longs;ort of Figure. </s><s>Moreover, it wil be an excellent <lb/>expedient to take a kinde of Matter, exactly alike in Gravity unto the <lb/>Water: for that Matter, as far as pertaines to the Gravity, is in­ <lb/>different either to A&longs;cend or De&longs;cend; &longs;o that we may pre&longs;ently ob­ <lb/>&longs;erve any the lea&longs;t difference that derives it &longs;elf from the diver&longs;ity of <lb/>Figure.</s></p><p type="main"> <s>Now to do this, Wax is mo&longs;t apt, which, be&longs;ides its incapacity of </s></p><p type="main"> <s><arrow.to.target n="marg1458"></arrow.to.target> <lb/>receiveing any &longs;en&longs;ible alteration from its imbibing of Water, is duct­ <lb/>ile or pliant, and the &longs;ame piece is ea&longs;ily reduceable into all Figures: <lb/>and being <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> a very incon&longs;iderable matter inferiour in Gravity <lb/>to the Water, by mixing therewith a little of the fileings of Lead it is <lb/>reduced to a Gravity exactly equall to that of the Water.</s></p><p type="margin"> <s><margin.target id="marg1458"></margin.target>An Experi­ <lb/>ment in Wax, <lb/>that proveth Fi­ <lb/>gute to have no <lb/>Operation in <lb/>Natation & Sub­ <lb/>mer&longs;ion.</s></p><p type="main"> <s>This Matter prepared, and, for example, a Ball being made there­ <lb/>of as bigge as an Orange or biger, and that made &longs;o grave as to <lb/>&longs;ink to the bottom, but &longs;o lightly, that takeing thence one only Grain <lb/>of Lead, it returnes to the top, and being added, it &longs;ubmergeth to <lb/>the bottom, let the &longs;ame Wax afterwards be made into a very broad <lb/>and thin Flake or Cake; and then, returning to make the &longs;ame Ex­ <lb/>periment, you &longs;hall &longs;ee that it being put to the bottom, it &longs;hall, with the <lb/>Grain of Lead re&longs;t below, and that Grain deducted, it &longs;hall a&longs;cend to <lb/>the very Surface, and added again it &longs;hall dive to the bottom. </s><s>And <lb/>this &longs;ame effect &longs;hall happen alwaies in all &longs;ort of Figures, as wel re­ <lb/>gular as irregular: nor &longs;hall you ever finde any that will &longs;wim with­ <lb/>out the removall of the Grain of Lead, or &longs;inke to the bottom unle&longs;s <lb/>it be added: and, in &longs;hort, about the going or not going to the Bot­ <lb/>tom, you &longs;hall di&longs;cover no diver&longs;ity, although, indeed, you &longs;hall about <lb/>the quick and &longs;low de&longs;cent: for the more expatiated and di&longs;tended <lb/>Figures move more &longs;lowly a&longs;wel in the diveing to the bottom as in <lb/>the ri&longs;ing to the top; and the other more contracted and compact Fi­ <lb/>gures, more &longs;peedily. </s><s>Now I know not what may be expected from <lb/>the diver&longs;ity of Figures, if the mo&longs;t contrary to one another operate <lb/>not &longs;o much as doth a very &longs;mall Grain of Lead, added or removed.</s></p><p type="main"> <s>Me thinkes I hear &longs;ome of the Adver&longs;aries to rai&longs;e a doubt upon <lb/><arrow.to.target n="marg1459"></arrow.to.target> <lb/>my produced Experiment. </s><s>And fir&longs;t, that they offer to my con&longs;idera­ <lb/>tion, that the Figure, as a Figure &longs;imply, and disjunct from the Matter <lb/>workes not any effect, but requires to be conjoyned with the Matter­ <pb xlink:href="040/01/1121.jpg" pagenum="428"/>and, furthermore, not with every Matter, but with tho&longs;e only, <lb/>wherewith it may be able ro execute the de&longs;ired operation. </s><s>Like <lb/>as we &longs;ee it verified by Experience, that the Acute and &longs;harp Angle is <lb/>more apt to cut, than the Obtu&longs;e; yet alwaies provided, that both <lb/>the one and the other, be joyned with a Matter apt to cut, as for <lb/>example, with Steel. </s><s>Therefore, a Knife with a fine and &longs;harp <lb/>edge, cuts Bread or Wood with much ea&longs;e, which it will not do, if <lb/>the edge be blunt and thick: but he that will in&longs;tead of Steel, take <lb/>Wax, and mould it into a Knife, undoubtedly &longs;hall never know the <lb/>effects of &longs;harp and blunt edges: becau&longs;e neither of them will cut, <lb/>the Wax being unable by rea&longs;on of its flexibility, to overcome the <lb/>hardne&longs;s of the Wood and Bread. </s><s>And, therefore, applying the <lb/>like di&longs;cour&longs;e to our purpo&longs;e, they &longs;ay, that the difference of Figure <lb/>will &longs;hew different effects, touching Natation and Submer&longs;ion, but <lb/>not conjoyned with any kind of Matter, but only with tho&longs;e Matters <lb/>which, by their Gravity, are apt to re&longs;i&longs;t the Velocity of the water, <lb/>whence he that would elect for the Matter, Cork or other light wood <lb/>unable, through its Levity, to &longs;uperate the Cra&longs;&longs;itude of the water, <lb/>and of that Matter &longs;hould forme Solids of divers Figures, woulld in <lb/>vain &longs;eek to find out what operation Figure hath in Natation or Sub­ <lb/>mer&longs;ion; becau&longs;e all would &longs;wim, and that not through any property <lb/>of this or that Figure, but through the debility of the Matter, want­ <lb/>ing &longs;o much Gravity, as is requi&longs;ite to &longs;uperate and overcome the <lb/>Den&longs;ity and Cra&longs;&longs;itude of the water.</s></p><p type="margin"> <s><margin.target id="marg1459"></margin.target>An objection a­ <lb/>gain&longs;t the Expe­ <lb/>riment in Wax.</s></p><p type="main"> <s>Its needfull, therefore, if wee would &longs;ee the effect wrought by the <lb/>Diver&longs;ity of Figure, fir&longs;t to make choice of a Matter of its nature <lb/>apt to penetrate the Cra&longs;&longs;itude of the water. </s><s>And, for this effect, <lb/><arrow.to.target n="marg1460"></arrow.to.target> <lb/>they have made choice of &longs;uch a Matter, as fit, that being readily re­ <lb/>duced into Sphericall Figure, goes to the Bottom; and it is Ebony <lb/>of which they afterwards making a &longs;mall Board or Splinter, as thin as <lb/>a Lath, have illu&longs;trated how that this, put upon the Surface of the <lb/>water, re&longs;ts there without de&longs;cending to the Bottom: and making, on <lb/>the other&longs;ide, of the &longs;ame wood a Ball, no le&longs;s than a hazell Nut, <lb/>they &longs;hew, that this &longs;wims not, but de&longs;cendes. </s><s>From which Experi­ <lb/>ment, they think they may frankly conclude, that the Breadth ofthe <lb/>Figure in the flat Lath or Board, is the cau&longs;e of its not de&longs;cendingto <lb/>the Bottom, fora&longs;much as a Ball of the &longs;ame Matter, not different <lb/>from the Board in any thing but in Figure, &longs;ubmergeth in the &longs;ame <lb/>water to the Bottom. </s><s>The di&longs;cour&longs;e and the Experiment hath really <lb/>&longs;o much of probability and likely hood of truth in it, that it would be <lb/>no wonder, if many per&longs;waded by a certain cur&longs;ory ob&longs;ervation, <lb/>&longs;hould yield credit to it; neverthele&longs;s, I think I am able to di&longs;cover, <lb/>how that it is not free from falacy.</s></p><p type="margin"> <s><margin.target id="marg1460"></margin.target>An Experi­ <lb/>ment in Ebany, <lb/>brought to di&longs;­ <lb/>prove the Expe­ <lb/>timent in Wax.</s></p><p type="main"> <s>Beginning, therefore, to examine one by one, all the particulars that <pb xlink:href="040/01/1122.jpg" pagenum="429"/>have been produced, I &longs;ay, that Figures, as &longs;imple Figures, not only <lb/><arrow.to.target n="marg1461"></arrow.to.target> <lb/>operate not in naturall things, but neither are they ever &longs;eperated <lb/>from the Corporeall &longs;ub&longs;tance: nor have I ever alledged them &longs;tript <lb/>of &longs;en&longs;ible Matter, like as al&longs;o I freely admit, that in our endeavour­ <lb/>ing to examine the Diver&longs;ity of Accidents, dependant upon the va­ <lb/>riety of Figures, it is nece&longs;&longs;ary to apply them to Matters, which ob­ <lb/>&longs;truct not the various operations of tho&longs;e various Figures: and I ad­ <lb/>mit and grant, that I &longs;hould do very ill, if I would experiment the in­ <lb/>fluence of Acutene&longs;&longs;e of edge with a Knife of Wax, applying it to cut <lb/>an Oak, becau&longs;e there is no Acutene&longs;s in Wax able to cut that <lb/>very hard wood. </s><s>But yet &longs;uch an Experiment of this Knife, would <lb/>not be be&longs;ides the purpo&longs;e, to cut curded Milk, or other very yielding <lb/>Matter: yea, in &longs;uch like Matters, the Wax is more commodious <lb/>than Steel; for finding the diver&longs;ity depending upon Angles, more or <lb/>le&longs;s Acute, for that Milk is indifferently cut with a Rai&longs;or, and with <lb/>a Knife, that hath a blunt edge. </s><s>It needs, therefore, that regard be <lb/>had, not only to the hardne&longs;s, &longs;olidity or Gravity of Bodies, which <lb/>under divers figures, are to divide and penetrate &longs;ome Matters, but it <lb/>forceth al&longs;o, that regard be had, on the other &longs;ide, to the Re&longs;i&longs;tance <lb/>of the Matters, to be divided and penetrated. </s><s>But &longs;ince I have in <lb/>making the Experiment concerning our Conte&longs;t, cho&longs;en a Matter <lb/>which penetrates the Re&longs;i&longs;tance of the water; and in all figures de&longs;­ <lb/>cendes to the Bottome, the Adver&longs;aries can charge me with no defect; <lb/>yea, I have propounded &longs;o much a more excellent Method than they, <lb/>in as much as I have removed all other Cau&longs;es, of de&longs;cending or <lb/>not de&longs;cending to the Bottom, and retained the only &longs;ole and pure <lb/>variety of Figures, demon&longs;trating that the &longs;ame Figures all de&longs;cende <lb/>with the only alteration of a Grain in weight: which Grain being <lb/>removed, they return to float and &longs;wim; it is not true, therefore, <lb/>(re&longs;uming the Example by them introduced) that I have gon about <lb/>to experiment the efficacy of Acutene&longs;s, in cutting with Matters un­ <lb/>able to cut, but with Matters proportioned to our occa&longs;ion; &longs;ince <lb/>they are &longs;ubjected to no other variety, then that alone which depends <lb/>on the Figure more or le&longs;s a cute. <lb/><arrow.to.target n="marg1462"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1461"></margin.target>Figure is un­ <lb/>&longs;eperable from <lb/>Corporeall Sub­ <lb/>&longs;tance.</s></p><p type="margin"> <s><margin.target id="marg1462"></margin.target>The an&longs;wer to <lb/>the Objection a­ <lb/>gain&longs;t the Expe­ <lb/>riment of the <lb/>Wax.</s></p><p type="main"> <s>But let us proceed a little farther, and ob&longs;erve, how that indeed <lb/>the Con&longs;ideration, which, they &longs;ay, ought to be had about the Election <lb/>of the Matter, to the end, that it may be proportionate for the ma­ <lb/>king of our experiment, is needle&longs;ly introduced, declaring by the ex­ <lb/>ample of Cutting, that like as Acutene&longs;s is in&longs;ufficient to cut, unle&longs;s <lb/>when it is in a Matter hard and apt to &longs;uperate the Re&longs;i&longs;tance of the <lb/>wood or other Matter, which we intend to cut; &longs;o the aptitude of <lb/>de&longs;cending or notde&longs;cending in water, ought and can only be known <lb/>in tho&longs;e Matters, that are able to overcome the Renitence, and &longs;upe­ <lb/>rate the Cra&longs;&longs;itude of the water. </s><s>Unto which, I &longs;ay, that to make <lb/>di&longs;tinction and election, more of this than of that Matter, on which to <pb xlink:href="040/01/1123.jpg" pagenum="430"/>impre&longs;s the Figures for cutting or penetrating this or that Body, <lb/>as the &longs;olidity or obduratene&longs;s of the &longs;aid Bodies &longs;hall be greater <lb/>or le&longs;s, is very nece&longs;&longs;ary: but withall I &longs;ubjoyn, that &longs;uch di&longs;tinct­ <lb/>ion, election and caution would be &longs;uperfluous and unprofitable, if <lb/>the Body to be cut or penetrated, &longs;hould have no Re&longs;i&longs;tance, or <lb/>&longs;hould not at all with&longs;tand the Cutting or Penitration: and if the <lb/>Knife were to be u&longs;ed in cutting a Mi&longs;t or Smoak, one of Paper <lb/>would be equally &longs;erviceable with one of <emph type="italics"/>Dama&longs;cus<emph.end type="italics"/> Steel: and &longs;o <lb/>by rea&longs;on the water hath not any Re&longs;i&longs;tance again&longs;t the Penitration <lb/>of any Solid Body, all choice of Matter is &longs;uperfluous and needle&longs;s, <lb/>and the Election which I &longs;aid above to have been well made of a <lb/>Matter reciprocall in Gravity to water, was not becau&longs;e it was ne­ <lb/>ce&longs;&longs;ary, for the overcoming of the cra&longs;&longs;iitude of the water, but its <lb/>Gravity, with which only it re&longs;i&longs;ts the &longs;inking of Solid Bodies: and <lb/>for what concerneth the Re&longs;i&longs;tance of the cra&longs;&longs;itude, if we narrowly <lb/>con&longs;ider it, we &longs;hall find that all Solid Bodies, as well tho&longs;e that <lb/>&longs;ink, as tho&longs;e that &longs;wim, are indifferently accomodated and apt to <lb/>bring us to the knowledge of the truth in que&longs;tion. </s><s>Nor will I <lb/>be frighted out of the belief of the&longs;e Conclu&longs;ions, by the Experi­ <lb/>ments which may be produced again&longs;t me, of many &longs;everall Woods, <lb/>Corks, Galls, and, moreover, of &longs;ubtle &longs;lates and plates of all &longs;orts <lb/>of Stone and Mettall, apt by means of their Naturall Gravity, to <lb/>move towards the Centre of the Earth, the which, neverthele&longs;s, be­ <lb/>ing impotent, either through the Figure (as the Adver&longs;aries thinke) <lb/>or through Levity, to break and penetrate the Continuity of the <lb/>parts of the water, and to di&longs;tract its union, do continue to &longs;wimm <lb/>without &longs;ubmerging in the lea&longs;t: nor on the other &longs;ide, &longs;hall the <lb/>Authority of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> move me, who in more than one place, a&longs;&longs;ir­ <lb/>meth the contrary to this, which Experience &longs;hews me.</s></p><p type="main"> <s><arrow.to.target n="marg1463"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1463"></margin.target>No Solid of <lb/>&longs;uch Levity, nor <lb/>of &longs;uch Figure, <lb/>but that it doth <lb/>penetrate the <lb/>Cra&longs;&longs;itude of <lb/>the Water.</s></p><p type="main"> <s>I return, therefore, to a&longs;&longs;ert, that there is not any Solid of &longs;uch <lb/>Levity, nor of &longs;uch Figure, that being put upon the water, doth not <lb/>divide and penetrate its Cra&longs;&longs;itude: yea if any with a more per­ <lb/>&longs;picatious eye, &longs;hall return to ob&longs;erve more exactly the thin Boards <lb/>of Wood, he &longs;hall &longs;ee them to be with part of their thickne&longs;s under </s></p><p type="main"> <s><arrow.to.target n="marg1464"></arrow.to.target> <lb/>water, and not only with their inferiour Superficies, to ki&longs;&longs;e the <lb/>Superiour of the water, as they of nece&longs;&longs;ity mu&longs;t have believed, who <lb/>have &longs;aid, that &longs;uch Boards &longs;ubmerge not, as not being able to di­ <lb/>vide the Tenacity of the parts of the water: and, moreover, he <lb/>&longs;hall &longs;ee, that &longs;ubtle &longs;hivers of Ebony, Stone or Metall, when they <lb/>float, have not only broak the Continuity of the water, but are with <lb/>all their thickne&longs;s, under the Surface of it; and more and more, <lb/>according as the Matters are more grave: &longs;o that a thin Plate of <lb/>Lead, &longs;hall be lower than the Surface of the circumfu&longs;ed water, by <lb/>at lea&longs;t twelve times the thickne&longs;s of the Plate, and Gold &longs;hall dive <pb xlink:href="040/01/1124.jpg" pagenum="431"/>below the Levell of the water, almo&longs;t twenty times the thickne&longs;s <lb/>of the Plate, as I &longs;hall anon declare.</s></p><p type="margin"> <s><margin.target id="marg1464"></margin.target>Bodies of all <lb/>Figures, laid up­ <lb/>on the water, do <lb/>penetrate its <lb/>Cra&longs;&longs;itude, and <lb/>in what propor­ <lb/>tion.</s></p><p type="main"> <s>But let us proceed to evince, that the water yields and &longs;ufters it <lb/>&longs;elf to be penetrated by every the lighte&longs;t Body; and therewithall <lb/>demon&longs;trate, how, even by Matters that &longs;ubmerge not, we may <lb/>come to know that Figure operates nothing about the going or <lb/>not going to the Bottom, &longs;eeing that the water &longs;uffers it &longs;elf to be <lb/>penetrated equally by every Figure.</s></p><p type="main"> <s>Make a Cone, or a Piramis of Cypre&longs;s, of Firre, or of other <lb/><arrow.to.target n="marg1465"></arrow.to.target> <lb/>Wood of like Gravity, or of pure Wax, and let its height be &longs;ome­ <lb/>what great, namely a handfull, or more, and put it into the water <lb/>with the Ba&longs;e downwards: fir&longs;t, you &longs;hall &longs;ee that it will penetrate <lb/>the water, nor &longs;hall it be at all impeded by the largene&longs;s of the Ba&longs;e, <lb/>nor yet &longs;hall it &longs;ink all under water, but the part towards the point <lb/>&longs;hall lye above it: by which &longs;hall be manife&longs;t, fir&longs;t, that that Solid <lb/>forbeares not to &longs;ink out of an inabillity to divide the Continuity <lb/>of the water, having already divided it with its broad part, that in <lb/>the opinion of the Adver&longs;aries is the le&longs;s apt to make the divi&longs;ion. <lb/></s><s>The Piramid being thus fixed, note what part of it &longs;hall be &longs;ub­ <lb/>merged, and revert it afterwards with the point downwards, and <lb/>you &longs;hall &longs;ee that it &longs;hall not dive into the water more than before, <lb/>but if you ob&longs;erve how far it &longs;hall &longs;ink, every per&longs;on expert in <lb/>Geometry, may mea&longs;ure, that tho&longs;e parts that remain out of the <lb/>water, both in the one and in the other Experiment are equall to <lb/>an hair: whence he may manife&longs;tly conclude, that the acute Figure <lb/>which &longs;eemed mo&longs;t apt to part and penetrate the water, doth not <lb/>part or penetrate it more than the large and &longs;pacious.</s></p><p type="margin"> <s><margin.target id="marg1465"></margin.target>The Experi­ <lb/>ment of a Cone, <lb/>demitted with <lb/>its Ba&longs;e, and af­ <lb/>ter with its <lb/>Point down­ <lb/>wards.</s></p><p type="main"> <s>And he that would have a more ea&longs;ie Experiment, let him take <lb/>two Cylinders of the &longs;ame Matter, one long and &longs;mall, and the o­ <lb/>ther &longs;hert, but very broad, and let him put them in the water, not <lb/>di&longs;tended, but erect and endways: he &longs;hall &longs;ee, if he diligently <lb/>mea&longs;ure the parts of the one and of the other, that in each of them <lb/>the part &longs;ubmerged, retains exactly the &longs;ame proportion to that <lb/>out of the water, and that no greater part is &longs;ubmerged of that <lb/>long and &longs;mall one, than of the other more &longs;pacious and broad: <lb/>howbeit, this re&longs;ts upon a very large, and that upon a very little <lb/>Superficies of water: therefore the diver&longs;ity of Figure, occa&longs;ioneth <lb/>neither facility, nor difficulty, in parting and penetrating the Con­ <lb/>tinuity of the water; and, con&longs;equently, cannot be the Cau&longs;e of the <lb/>Natation or Submer&longs;ion. </s><s>He may likewi&longs;e di&longs;cover the non­ <lb/>operating of variety of Figures, in ari&longs;ing from the Bottom of the <lb/>water, towards the Surface, by taking Wax, and tempering it with <lb/>a competent quantity of the filings of Lead, &longs;o that it may become <lb/>a con&longs;iderable matter graver than the water: then let him make <pb xlink:href="040/01/1125.jpg" pagenum="432"/>it into a Ball, and thru&longs;t it unto the Bottom of the water; and <lb/>fa&longs;ten to it as much Cork, or other light matter, as ju&longs;t &longs;erveth to <lb/>rai&longs;e it, and draw it towards the Surface: for afterwards changing <lb/>the &longs;ame Wax into a thin Cake, or into any other Figure, that <lb/>&longs;ame Cork &longs;hall rai&longs;e it in the &longs;ame manner to a hair.</s></p><p type="main"> <s>This &longs;ilenceth not my Antagoni&longs;ts, but they &longs;ay, that all the <lb/>di&longs;cour&longs;e hitherto made by me little importeth to them, and that it <lb/>&longs;erves their turn, that they have demon&longs;trated in one only parti­ <lb/>cular, and in what matter, and under what Figure plea&longs;eth them, <lb/>namely, in a Board and in a Ball of Ebony, that this put in the <lb/>water, de&longs;cends to the Bottom, and that &longs;tays atop to &longs;wim: <lb/>and the Matter being the &longs;ame, and the two Bodies differing in no­ <lb/>thing but in Figure, they affirm, that they have with all per&longs;picuity <lb/>demon&longs;trated and &longs;en&longs;ibly manife&longs;ted what they undertook; and <lb/>la&longs;tly, that they have obtained their intent. </s><s>Neverthele&longs;s, I believe, <lb/>and thinke, I can demon&longs;trate, that that &longs;ame Experiment proveth <lb/>nothing again&longs;t my Conclu&longs;ion.</s></p><p type="main"> <s>And fir&longs;t, it is fal&longs;e, that the Ball de&longs;cends, and the Board not: <lb/><arrow.to.target n="marg1466"></arrow.to.target> <lb/>for the Board &longs;hall al&longs;o de&longs;cend, if you do to both the Figures, as <lb/>the words of our Que&longs;tion requireth; that is, if you put them both <lb/>into the water. <lb/><arrow.to.target n="marg1467"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1466"></margin.target>In Experi­ <lb/>ments of Nata­ <lb/>tion, the Solid <lb/>is to be put into, <lb/>not upon the <lb/>water.</s></p><p type="margin"> <s><margin.target id="marg1467"></margin.target>The Que&longs;tion <lb/>of Natation &longs;ta­ <lb/>ted.</s></p><p type="main"> <s><emph type="italics"/>The words were the&longs;e. </s><s>That the Antagoni&longs;ts having an opinion, that <lb/>the Figure would alter the Solid Bodies, in relation to the de&longs;cending <lb/>or not de&longs;cending, a&longs;cending or not a&longs;cending in the &longs;ame<emph.end type="italics"/> Medium, <emph type="italics"/>as<emph.end type="italics"/> <lb/>v. </s><s>gr. <emph type="italics"/>in the &longs;ame water, in &longs;uch &longs;ort, that, for Example, a Solid that <lb/>being of a Sphericall Figure, &longs;hall de&longs;cend to the Bottom, being reduced <lb/>into &longs;ome other Figure, &longs;hall not de&longs;cend: I holding the contrary, do <lb/>affirm, that a Corporeall Solid Body, which reduced into a Sphericall Fi­ <lb/>gure, or any other, &longs;hall go to the Bottom, &longs;hall do the like under what&longs;oever <lb/>other Figure, &c.<emph.end type="italics"/></s></p><p type="main"> <s>But to be in the water, implies to be placed in the water, and by </s></p><p type="main"> <s><arrow.to.target n="marg1468"></arrow.to.target> <lb/><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> own Definition of place, to be placed, importeth to be in­ <lb/>vironed by the Superficies of the Ambient Body, therefore, then <lb/>&longs;hall the two Figures be in the water, when the Superficies of the <lb/>water, &longs;hall imbrace and inviron them: but when the Adver&longs;aries <lb/>&longs;hew the Board of Ebony not de&longs;cending to the Bottom, they put it <lb/>not into the water, but upon the water, where being by a certain im­ <lb/>pediment (as by and by we will &longs;hew) retained, it is invironed, part <lb/>by water, and part by air, which thing is contrary to our agreement, <lb/>that was, that the Bodies &longs;hould be in the water, and not part in <lb/>water, and part in air.</s></p> <pb xlink:href="040/01/1126.jpg" pagenum="433"/><p type="margin"> <s><margin.target id="marg1468"></margin.target>Place defined <lb/>according to <lb/><emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>The which is again made manifest, by the que&longs;tions being put as well <lb/>about the things which go to the Bottom, as tho&longs;e which ari&longs;e from the <lb/>Bottom to &longs;wimme, and who &longs;ees not that things placed in the Bottom, <lb/>mu&longs;t have water about them.<emph.end type="italics"/></s></p><p type="main"> <s>It is now to be noted, that the Board of Ebany and the Ball, put <lb/><arrow.to.target n="marg1469"></arrow.to.target> <lb/><emph type="italics"/>into<emph.end type="italics"/> the water, both &longs;ink, but the Ball more &longs;wiftly, and the Board <lb/>more &longs;lowly; and &longs;lower and &longs;lower, according as it &longs;hall be more <lb/>broad and thin, and of this Tardity the breadth of the Figure is the <lb/>true Cau&longs;e: But the&longs;e broad Boards that &longs;lowly de&longs;cend, are the <lb/>&longs;ame, that being put lightly upon the water, do &longs;wimm: Therefore, <lb/>if that were true which the Adver&longs;aries affirm, the &longs;ame numerical <lb/>Figure, would in the &longs;ame numericall water, cau&longs;e one while Re&longs;t, and <lb/>another while Tardity of Motion, which is impo&longs;&longs;ible: for every per­ <lb/><arrow.to.target n="marg1470"></arrow.to.target> <lb/>ticular Figure which de&longs;cends to the Bottom, hath of nece&longs;&longs;ity its own <lb/>determinate Tardity and &longs;lowne&longs;s, proper and naturall unto it, accor­ <lb/>ding to which it moveth, &longs;o that every other Tardity, greater or le&longs;&longs;er <lb/>is improper to its nature: if, therefore, a Board, as &longs;uppo&longs;e of a foot <lb/>&longs;quare, de&longs;cendeth naturally with &longs;ix degrees of Tardity, it is impo&longs;&longs;i­ <lb/>ble, that it &longs;hould de&longs;cend with ten or twenty, unle&longs;s &longs;ome new impe­ <lb/>diment do arre&longs;t it. </s><s>Much le&longs;s can it, by rea&longs;on of the &longs;ame Figure <lb/>re&longs;t, and wholly cea&longs;e to move; but it is nece&longs;&longs;ary, that when ever it <lb/>re&longs;teth, there do &longs;ome greater impediment intervene than the breadth <lb/>of the Figure. </s><s>Therefore, it mu&longs;t be &longs;omewhat el&longs;e, and not the Fi­ <lb/>gure, that &longs;tayeth the Board of Ebany above water, of which Eigure <lb/>the only Effect is the retardment of the Motion, according to which <lb/>it de&longs;cendeth more &longs;lowly than the Ball. </s><s>Let it be confe&longs;&longs;ed, there­ <lb/>fore, rationally di&longs;cour&longs;ing, that the true and &longs;ole Cau&longs;e of the Ebanys <lb/>going to the Bottom, is the exce&longs;s of its Gravity above the Gravity of <lb/>the water: and the Cau&longs;e of the greater or le&longs;s Tardity, the breadth <lb/>of this Figure, or the contractedne&longs;s of that: but of its Re&longs;t, it can <lb/>by no means be allowed, that the quallity of the Figure, is the Cau&longs;e <lb/>thereof: a&longs;well, becau&longs;e, making the Tardity greater, according as <lb/>the Figure more dilateth, there cannot be &longs;o immen&longs;e a Dilatation, to <lb/>which there may not be found a corre&longs;pondent immence Tardity. <lb/></s><s>without redu&longs;ing it to Nullity of Motion; as, becau&longs;e the Figures <lb/>produced by the Antagoni&longs;ts for effecters of Re&longs;t, are the &longs;elf &longs;ame <lb/>that do al&longs;o go to the Bottom. <lb/><arrow.to.target n="marg1471"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1469"></margin.target>The con&longs;utati­ <lb/>on of the Expe­ <lb/>riment in the <lb/>Ebany.</s></p><p type="margin"> <s><margin.target id="marg1470"></margin.target>Every perticular <lb/>Figure hath its <lb/>own peculiat <lb/>Tardity.</s></p><p type="margin"> <s><margin.target id="marg1471"></margin.target>* The Figure & <lb/>Re&longs;i&longs;tance of <lb/>the Medium a­ <lb/>gain&longs;t Divi&longs;ion, <lb/>have nothing to <lb/>do with the Ef­ <lb/>fect of Natation <lb/>or Submer&longs;ion, <lb/>by an Experi­ <lb/>ment in Wall­ <lb/>nut tree,</s></p><p type="main"> <s>I will not omit another rea&longs;on, founded al&longs;o upon Experience, and <lb/>if I deceive not my &longs;elf, manife&longs;tly concluding, how that the Intro­ <lb/>ducton of the breadth or amplitude of Figure, and the Re&longs;i&longs;tance of <lb/>the water again&longs;t penetration, have nothing to do in the Effect of de­ <lb/>&longs;cending, or a&longs;cending, or re&longs;ting in the water. ^{*}Take a piece of wood <lb/>or other Matter, of which a Ball a&longs;cends from the Bottom of the water <pb xlink:href="040/01/1127.jpg" pagenum="434"/>to the Surface, more &longs;lowly than a Ball of Ebony of the &longs;ame bigne&longs;&longs;e, <lb/>&longs;o that it is manife&longs;t, that the Ball of Ebony more readily divideth the <lb/>water in de&longs;cending, than the other in a&longs;cending; as for Example, let <lb/>the Wood be Walnut-tree. </s><s>Then take a Board of Walnut-tree, like <lb/>and equall to that of Ebony of the Antagoni&longs;ts, which &longs;wims; and if <lb/>it be true, that this floats above water, by rea&longs;on of the Figure, unable <lb/>through its breadth, to pierce the Cra&longs;&longs;itude of the &longs;ame, the other of <lb/>Wallnut-tree, without all que&longs;tion, being thru&longs;t unto the Bottom, will <lb/>&longs;tay there, as le&longs;s apt, through the &longs;ame impediment of Figure, to di­ <lb/>vide the &longs;aid Re&longs;i&longs;tance of the water. </s><s>But if we &longs;hall find, and by <lb/>experience &longs;ee, that not only the thin Board, but every other Figure <lb/>of the &longs;ame Wallnut-tree will return to float, as undoubtedly we &longs;hall, <lb/>then I mu&longs;t de&longs;ier my oppo&longs;ers to forbear to attribute the floating of <lb/>the Ebony, unto the Figure of the Board, in regard that the Re&longs;i&longs;tance <lb/>of the water is the &longs;ame, as well to the a&longs;cent, as to the de&longs;cent, and the <lb/>force of the Wallnut-trees a&longs;cen&longs;ion, is le&longs;&longs;e than the Ebonys force in <lb/>going to the Bottom.</s></p><p type="main"> <s>Nay, I will &longs;ay more, that if we &longs;hall con&longs;ider Gold in compari&longs;on <lb/><arrow.to.target n="marg1472"></arrow.to.target> <lb/>of water, we &longs;hall find, that it exceeds it in Gravity almo&longs;t twenty times, <lb/>&longs;o that the Force and Impetus, wherewith a Ball of Gold goes to the <lb/>Bottom, is very great. </s><s>On the contrary, there want not matters, as <lb/>Virgins Wax, and &longs;ome Woods, which are not above a fiftieth part le&longs;s <lb/>grave than water, whereupon their A&longs;cen&longs;ion therein is very &longs;low, and <lb/>a thou&longs;and times weaker than the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Golds de&longs;cent: yet <lb/>notwith&longs;tanding, a plate of Gold &longs;wims without de&longs;cending to the <lb/>Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin <lb/>Board of Wood, which put in the Bottom of the Water, &longs;hall re&longs;t there <lb/>without a&longs;cending. </s><s>Now if the Figure can ob&longs;truct the Penetration, <lb/>and impede the de&longs;cent of Gold, that hath &longs;o great an <emph type="italics"/>Impetus,<emph.end type="italics"/> how <lb/>can it choo&longs;e but &longs;uffice to re&longs;i&longs;t the &longs;ame Penetration of the other mat­ <lb/>ter in a&longs;cending, when as it hath &longs;carce a thou&longs;andth part of the <emph type="italics"/>Impetus<emph.end type="italics"/> <lb/>that the Gold hath in de&longs;cending? </s><s>Its therefore, nece&longs;&longs;ary, that that <lb/>which &longs;u&longs;pends the thin Plate of Gold, or Board of Ebony, upon the <lb/>water, be &longs;ome thing that is wanting to the other Cakes and Boards of <lb/>Matters le&longs;s grave than the water; &longs;ince that being put to the Bottom, <lb/>and left at liberty, they ri&longs;e up to the Surface, without any ob&longs;truction: <lb/>But they want not for flatne&longs;s and breadth of Figure: Therefore, the <lb/>&longs;paciou&longs;ne&longs;&longs;e of the Figure, is not that which makes the Gold and Ebony <lb/>to &longs;wim.</s></p><p type="margin"> <s><margin.target id="marg1472"></margin.target>An Experi­ <lb/>ment in Gold, to <lb/>prove the non­ <lb/>operating of Fi­ <lb/>gure in Natation <lb/>and Submer&longs;ion.</s></p><p type="main"> <s>And, becau&longs;e, that the exce&longs;s of their Gravity above the Gravity of <lb/>the water, is que&longs;tionle&longs;s the Cau&longs;e of the &longs;inking of the flat piece of <lb/>Ebony, and the thin Plate of Gold, when they go to the Bottom, there­ <lb/>fore, of nece&longs;&longs;ity, when they float, the Cau&longs;e of their &longs;taying above <lb/>water, proceeds from Levity, which in that ca&longs;e, by &longs;ome Accident, <pb xlink:href="040/01/1128.jpg" pagenum="435"/>peradventure not hitherto ob&longs;erved, cometh to meet with the &longs;aid <lb/>Board, rendering it no longer as it was before, whil&longs;t it did fink more <lb/>ponderous than the water, but le&longs;s.</s></p><p type="main"> <s>Now, let us return to take the thin Plate of Gold, or of Silver, or the <lb/>thin Board of Ebony, and let us lay it lightly upon the water, &longs;o that it <lb/>&longs;tay there without &longs;inking, and diligently ob&longs;erve its effect. </s><s>And <lb/>fir&longs;t, &longs;ee how fal&longs;e the a&longs;&longs;ertion of <emph type="italics"/>Aristotle,<emph.end type="italics"/> and our oponents is, to wit, <lb/>that it &longs;tayeth above water, through its unability to pierce and pene­ <lb/>trate the Re&longs;i&longs;tance of the waters Cra&longs;&longs;itude: for it will manife&longs;tly <lb/>appear, not only that the &longs;aid Plates have penetrated the water, but <lb/>al&longs;o that they are a con&longs;iderable matter lower than the Surface of the <lb/>&longs;ame, the which continueth eminent, and maketh as it were a Rampert <lb/>on all &longs;ides, round about the &longs;aid Plates, the profundity of which they <lb/>&longs;tay &longs;wimming: and, according as the &longs;aid Plates &longs;hall be more grave <lb/>than the water, two, four, ten or twenty times, it is nece&longs;&longs;ary, that <lb/>their Superficies do &longs;tay below the univer&longs;all Surface of the water, &longs;o <lb/>much more, than the thickne&longs;s of tho&longs;e Plates, as we &longs;hal more di&longs;tinctly <lb/>&longs;hew anon. </s><s>In the mean &longs;pace, for the more ea&longs;ie under&longs;tanding of what <lb/>I &longs;ay, ob&longs;erve with me a little the pre&longs;ent <lb/><figure id="id.040.01.1128.1.jpg" xlink:href="040/01/1128/1.jpg"/> <lb/>Scheme: in which let us &longs;uppo&longs;e the Surface <lb/>of the water to be di&longs;tended, according to the <lb/>Lines F L D B, upon which if one &longs;hall put a <lb/>board of matter &longs;pecifically more grave than <lb/>water, but &longs;o lightly that it &longs;ubmetge not, it <lb/>&longs;hall not re&longs;t any thing above, but &longs;hall enter with its whole thickne&longs;s <lb/>into the water: and, moreover, &longs;hall &longs;ink al&longs;o, as we &longs;ee by the Board <lb/>A I, O I, who&longs;e breadth is wholly &longs;unk into the water, the little Ram­ <lb/>perts of water L A and D O incompa&longs;&longs;ing it, who&longs;e Superficies is no­ <lb/>tably higher than the Superficies of the Board. </s><s>See now whether it be <lb/>true, that the &longs;aid Board goes not to the Bottom, as being of Figure <lb/>unapt to penetrate the Cra&longs;&longs;itude of the water.</s></p><p type="main"> <s>But, if it hath already penetrated, and overcome the Continuity of <lb/><arrow.to.target n="marg1473"></arrow.to.target> <lb/>the water, & is of its own nature more grave than the &longs;aid water, why <lb/>doth it not proceed in its &longs;inking, but &longs;top and &longs;u&longs;pend its &longs;elf within <lb/>that little dimple or cavitie, which with its pondero&longs;ity it hath made in <lb/>the water? </s><s>I an&longs;wer; becau&longs;e that in &longs;ubmerging it &longs;elf, &longs;o far as till its <lb/>Superficies come to the Levell with that of the water, it lo&longs;eth a part <lb/>of its Gravity, and lo&longs;eth the re&longs;t of it as it &longs;ubmergeth & de&longs;cends be­ <lb/>neath the Surface of the water, which maketh Ramperts and Banks <lb/>round about it, and it &longs;u&longs;taines this lo&longs;s by means of its drawing after it, <lb/>and carrying along with it, the Air that is above it, and by Contact ad­ <lb/>herent to it, which Air &longs;ucceeds to fill the Cavity that is invironed by <lb/>the Ramperts of water: &longs;o that that which in this ca&longs;e de&longs;cends and is <lb/>placed in the water, is not only the Board of Ebony or Plate of Iron, <pb xlink:href="040/01/1129.jpg" pagenum="436"/>but a compo&longs;ition of Ebony and Air, from which re&longs;ulteth a Solid <lb/>no longer &longs;uperiour in Gravity to the water, as was the &longs;imple Ebony, <lb/>or the &longs;imple Gold. </s><s>And, if we exactly con&longs;ider, what, and how <lb/>great the Solid is, that in this Experiment enters into the water, and <lb/>contra&longs;ts with the Gravity of the &longs;ame, it will be found to be all that <lb/>which we find to be beneath the Surface of the water, the which is <lb/>an aggregate and Compound of a Board of Ebony, and of almo&longs;t <lb/>the like quantity of Air, or a Ma&longs;s compounded of a Plate of Lead, <lb/>and ten or twelve times as much Air. </s><s>But, Genrlemen, you that <lb/>are my Antagoni&longs;ts in our Que&longs;tion, we require the Identity of <lb/>Matter, and the alteration only of the Figure; therefore, you mu&longs;t <lb/>remove that Air, which being conjoyned with the Board, makes it <lb/>become another Body le&longs;s grave than the Water, and put only the <lb/>Ebony into the Water, and you &longs;hall certainly &longs;ee the Board de&longs;cend <lb/>to the Bottom; and, if that do not happen, you have got the day. <lb/><arrow.to.target n="marg1474"></arrow.to.target> <lb/>And to &longs;eperate the Air from the Ebony, there needs no more but <lb/>only to bath the Superficies of the &longs;aid Board with the &longs;ame Water: <lb/>for the Water being thus interpo&longs;ed between the Board and the Air, <lb/>the other circumfu&longs;ed Water &longs;hall run together without any impedi­ <lb/>ment, and &longs;hall receive into it the &longs;ole and bare Ebony, as it was to do.</s></p><p type="margin"> <s><margin.target id="marg1473"></margin.target>Why &longs;olids <lb/>having penitra­ <lb/>ted the Water, <lb/>do not proceed <lb/>to a totail Sub­ <lb/>mer&longs;ion.</s></p><p type="margin"> <s><margin.target id="marg1474"></margin.target>How to &longs;epe­ <lb/>rate the Air from <lb/>Solids in demit­ <lb/>ting them into <lb/>the water.</s></p><p type="main"> <s>But, me thinks I hear &longs;ome of the Adver&longs;aries cunningly oppo&longs;ing <lb/>this, and telling me, that they will not yield, by any means, that <lb/>their Board be wetted, becau&longs;e the weight added thereto by the <lb/>Water, by making it heavier than it was before, draws it to the <lb/>Bottom, and that the addition of new weight is contrary to our a­ <lb/>greement, which was, that the Matter be the &longs;ame.</s></p><p type="main"> <s>To this, I an&longs;wer, fir&longs;t; that treating of the operation of Figure <lb/>in Bodies put into the Water, none can &longs;uppo&longs;e them to be put into <lb/>the Water without being wet; nor do I de&longs;ire more to be done to <lb/>the Board, then I will give you leave to do to the Ball. </s><s>Moreover, <lb/>it is untrue, that the Board &longs;inks by vertue of the new Weight added <lb/>to it by the Water, in the &longs;ingle and &longs;light bathing of it: for I will <lb/>put ten or twenty drops of Water upon the &longs;ame Board, whil&longs;t it is <lb/>&longs;u&longs;tained upon the water, which drops, becau&longs;e not conjoyned with <lb/>the other Water circumfu&longs;ed, &longs;hall not &longs;o encrea&longs;e the weight of it, as <lb/>to make it &longs;ink: but if the Board being taken out, and all the water <lb/>wiped off that was added thereto, I &longs;hould bath all its Superficies <lb/>with one only very &longs;mall drop, and put it again upon the water, with­ <lb/>out doubt it &longs;hall &longs;ink, the other Water running to cover it, not be­ <lb/>ing retained by the &longs;uperiour Air; which Air by the interpo&longs;ition of <lb/>the thin vail of water, that takes away its Contiguity unto the Ebony, <lb/>&longs;hall without Renitence be &longs;eperated, nor doth it in the lea&longs;t oppo&longs;e <lb/>the &longs;ucce&longs;&longs;ion of the other Water: but rather, to &longs;peak better, it <lb/>&longs;hall de&longs;cend freely; becau&longs;e it &longs;hall be all invironed and covered <pb xlink:href="040/01/1130.jpg" pagenum="437"/>with water, as &longs;oon as its &longs;uperiour Superficies, before vailed with <lb/>water, doth arrive to the Levell of the univer&longs;all Surface of the &longs;aid <lb/>water. </s><s>To &longs;ay, in the next place, that water can encrea&longs;e the weight <lb/><arrow.to.target n="marg1475"></arrow.to.target> <lb/>of things that are demitted into it, is mo&longs;t fal&longs;e, for water hath no <lb/>Gravity in water, &longs;ince it de&longs;cends not: yea, if we would well con&longs;i­ <lb/>der what any immen&longs;e Ma&longs;s of water doth put upon a grave Body; <lb/><arrow.to.target n="marg1476"></arrow.to.target> <lb/>that is placed in it, we &longs;hall find experimentally, that it, on the con­ <lb/>trary, will rather in a great part demini&longs;h the weight of it, and that <lb/>we may be able to lift an huge Stone from the Bottom of the water, <lb/>which the water being removed, we are not able to &longs;tir. </s><s>Nor let <lb/>them tell me by way of reply, that although the &longs;uperpo&longs;ed water <lb/>augment not the Gravity of things that are in it, yet it increa&longs;eth the <lb/>pondero&longs;ity of tho&longs;e that &longs;wim, and are part in the water and part <lb/><arrow.to.target n="marg1477"></arrow.to.target> <lb/>in the Air, as is &longs;een, for Example, in a Bra&longs;s Ketle, which whil&longs;t it <lb/>is empty of water, and repleni&longs;hed only with Air &longs;hall &longs;wim, but <lb/>pouring of Water therein, it &longs;hall become &longs;o grave, that it &longs;hall &longs;ink <lb/>to the Bottom, and that by rea&longs;on of the new weight added thereto. <lb/></s><s>To this I will return an&longs;wer, as above, that the Gravity of the <lb/>Water, contained in the Ve&longs;&longs;el is not that which &longs;inks it to the Bot­ <lb/>tom, but the proper Gravity of the Bra&longs;s, &longs;uperiour to the Specificall <lb/><arrow.to.target n="marg1478"></arrow.to.target> <lb/>Gravity of the Water: for if the Ve&longs;&longs;el were le&longs;s grave than <lb/>water, the Ocean would not &longs;uffice to &longs;ubmerge it. </s><s>And, give me <lb/>leave to repeat it again, as the fundamentall and principall point in <lb/>this Ca&longs;e, that the Air contained in this Ve&longs;&longs;el before the infu&longs;ion of <lb/>the Water, was that which kept it a-float, &longs;ince that there was made <lb/><arrow.to.target n="marg1479"></arrow.to.target> <lb/>of it, and of the Bra&longs;s, a Compo&longs;ition le&longs;s grave than an equall quanti­ <lb/>ty of Water: and the place that the Ve&longs;&longs;el occupyeth in the <lb/>Water whil&longs;t it floats, is not equall to the Bra&longs;s alone, but to the <lb/>Bra&longs;s and to the Air together, which filleth that part of the Ve&longs;&longs;el <lb/>that is below the Levell of the water: Moreover, when the Water <lb/>is infu&longs;ed, the Air is removed, and there is a compo&longs;ition made of <lb/>Bra&longs;s and of water, more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the &longs;imple water, but <lb/>not by vertue of the water infu&longs;ed, as having greater Specifick <lb/>Gravity than the other water, but through the proper Gravity of <lb/>the Bra&longs;s, and through the alienation of the Air. </s><s>Now, as he that <lb/>&longs;hould &longs;ay that Bra&longs;s, that by its nature goes to the Bottom, being <lb/><arrow.to.target n="marg1480"></arrow.to.target> <lb/>formed into the Figure of a Ketle, acquireth from that Figure a <lb/>vertue of lying in the Water without &longs;inking, would &longs;ay that which <lb/>is fal&longs;e; becau&longs;e that Bra&longs;s fa&longs;hioned into any whatever Figure, <lb/>goeth always to the Bottom, provided, that that which is put into the <lb/>water be &longs;imple Bra&longs;s; and it is not the Figure of the Ve&longs;&longs;el that <lb/>makes the Bra&longs;s to float, but it is becau&longs;e that that is not purely <lb/>Bra&longs;s which is put into the water, but an aggregate of Bra&longs;s and of <lb/>Air: &longs;o is it neither more nor le&longs;s fal&longs;e, that a thin Plate of Bra&longs;s <pb xlink:href="040/01/1131.jpg" pagenum="438"/>or of Ebony, &longs;wims by vertue of its dilated & broad Figure: for the <lb/>truth is, that it bares up without &longs;ubmerging, becau&longs;e that that which <lb/>is put in the water, is not pure Bra&longs;s or &longs;imple Ebony, but an ag­ <lb/>gregate of Bra&longs;s and Air, or of Ebony and Air. </s><s>And, this is not <lb/>contrary unto my Conclu&longs;ion, the which, (having many a time &longs;een <lb/>Ve&longs;&longs;els of Mettall, and thin pieces of diver&longs;e grave Matters float, by <lb/>vertue of the Air conjoyned with them) did affirm, That Figure <lb/>was not the Cau&longs;e of the Natation or Submer&longs;ion of &longs;uch Solids as <lb/>were placed in the water. </s><s>Nay more, I cannot omit, but mu&longs;t tell <lb/>my Antagoni&longs;ts, that this new conceit of denying that the Superfi­ <lb/>cies of the Board &longs;hould be bathed, may beget in a third per&longs;on an <lb/>opinion of a poverty of Arguments of defence on their part, &longs;ince <lb/>that &longs;uch bathing was never in&longs;i&longs;ted upon by them in the beginning <lb/>of our Di&longs;pute, and was not que&longs;tioned in the lea&longs;t, being that the <lb/>Originall of the di&longs;cour&longs;e aro&longs;e upon the &longs;wiming of Flakes of Ice, <lb/>wherein it would be &longs;implicity to require that their Superficies might <lb/>bedry: be&longs;ides, that whether the&longs;e pieces of Ice be wet or dry they <lb/>alwayes &longs;wim, and as the Adver&longs;aries &longs;ay, by rea&longs;on of the Figure. </s></p><p type="margin"> <s><margin.target id="marg1475"></margin.target>Water hath <lb/>no Gravity in <lb/>Water.</s></p><p type="margin"> <s><margin.target id="marg1476"></margin.target>Water de­ <lb/>mini&longs;heth the <lb/>Gravity of So­ <lb/>lids immerged <lb/>therein.</s></p><p type="margin"> <s><margin.target id="marg1477"></margin.target>The Experi­ <lb/>ment of a Bra&longs;s <lb/>Ketle &longs;wiming <lb/>when empty, & <lb/>&longs;inking when <lb/>full, alledged to <lb/>prove that water <lb/>gravitates in <lb/>water, an&longs;wered.</s></p><p type="margin"> <s><margin.target id="marg1478"></margin.target>An Ocean &longs;uf­ <lb/>ficeth not to <lb/>&longs;ink a Ve&longs;&longs;el &longs;pe­ <lb/>cifically le&longs;s <lb/>grave than wa­ <lb/>ter.</s></p><p type="margin"> <s><margin.target id="marg1479"></margin.target>Air, the Cau&longs;e <lb/>of the Natation <lb/>of empty Ve&longs;&longs;els <lb/>of Matters gra­ <lb/>ver <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than <lb/>the water.</s></p><p type="margin"> <s><margin.target id="marg1480"></margin.target>Neither Figure, <lb/>nor the breadth <lb/>of Figure, is the <lb/>Cau&longs;e of Nata­ <lb/>tion.</s></p><p type="main"> <s>Some peradventure, by way of defence, may &longs;ay, that wetting the <lb/>Board of Ebony, and that in the &longs;uperiour Superficies, it would, <lb/>though of it &longs;elf unable to pierce and penetrate the water, be born <lb/>downwards, if not by the weight of the additionall water, at lea&longs;t <lb/>by that de&longs;ire and propen&longs;ion that the &longs;uperiour parts of the water <lb/>have to re-unite and rejoyn them&longs;elves: by the Motion of which <lb/>parts, the &longs;aid Board cometh in a certain manner, to be depre&longs;&longs;ed <lb/>downwards. <lb/><arrow.to.target n="marg1481"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1481"></margin.target>The Bathed <lb/>Solid de&longs;cends <lb/>not out of any <lb/>affectation of u­ <lb/>nion in the upper <lb/>parts of the wa­ <lb/>ter.</s></p><p type="main"> <s>This weak Refuge will be removed, if we do but con&longs;ider, that <lb/>the repugnancy of the inferiour parts of the water, is as great against <lb/>Di&longs;-union, as the Inclination of its &longs;uperiour parts is to union: nor can <lb/>the uper unite them&longs;elves without depre&longs;&longs;ing the board, nor can it <lb/>de&longs;cend without di&longs;uniting the parts of the nether Water: &longs;o that <lb/>it doth follow, by nece&longs;&longs;ary con&longs;equence, that for tho&longs;e re&longs;pects, it &longs;hall <lb/>not de&longs;cend. </s><s>Moreover, the &longs;ame that may be &longs;aid of the upper <lb/>parts of the water, may with equall rea&longs;on be &longs;aid of the nethe, <lb/>namely, that de&longs;iring to unite, they &longs;hall force the &longs;aid Board <lb/>upwards.</s></p><p type="main"> <s>Happily, &longs;ome of the&longs;e Gentlemen that di&longs;&longs;ent from me, will won­ <lb/>der, that I affirm, that the contiguous &longs;uperiour Air is able to &longs;u&longs;tain <lb/>that Plate of <emph type="italics"/>B<emph.end type="italics"/>ra&longs;s or of Silver, that &longs;tayeth above water; as if I <lb/><arrow.to.target n="marg1482"></arrow.to.target> <lb/>would in a certain &longs;ence allow the Air, a kind of Magnetick vertue <lb/>of &longs;u&longs;taining the grave <emph type="italics"/>B<emph.end type="italics"/>odies, with which it is contiguous. </s><s>To &longs;a­ <lb/>tis&longs;ie all I may, to all doubts, I have been con&longs;idering how by &longs;ome <lb/>other &longs;en&longs;ible Experiment I might demon&longs;trate, how truly that little <lb/>contiguous and &longs;uperiour Air &longs;u&longs;taines tho&longs;e Solids, which being by <pb xlink:href="040/01/1132.jpg" pagenum="439"/>nature apt to de&longs;cend to the Bottom, being placed lightly on the water <lb/>&longs;ubmerge not, unle&longs;s they be fir&longs;t thorowly bathed; and have found, <lb/>that one of the&longs;e Bodies having de&longs;cended to the Bottom, by conveigh­ <lb/>ing to it (without touching it in the lea&longs;t) a little Air, which conjoyneth <lb/>with the top of the &longs;ame; it becometh &longs;ufficient, not only, as before to <lb/>&longs;u&longs;tain it, but al&longs;o to rai&longs;e it, and to carry it back to the top, where it <lb/>&longs;tays and abideth in the &longs;ame manner, till &longs;uch time, as the a&longs;&longs;i&longs;tance <lb/>of the conjoyned Air is taken away. </s><s>And to this effect, I have taken a <lb/>Ball of Wax, and made it with a little Lead, &longs;o grave, that it lea&longs;urely <lb/>de&longs;cends to the Bottom, making with all its Superficies very &longs;mooth and <lb/>pollite: and this being put gently into the water, almo&longs;t wholly &longs;ub­ <lb/><arrow.to.target n="marg1483"></arrow.to.target> <lb/>mergeth, there remaining vi&longs;&longs;ible only a little of the very top, the which <lb/>solong as it is conjoyned with the Air, &longs;hall retain the Ball a-top, but <lb/>the Contiguity of the Air taken away by wetting it, it &longs;hall de&longs;cend to <lb/>the Bottom and there remain. </s><s>Now to make it by vertue of the Air, that <lb/>before &longs;u&longs;tained it to return again to the top, and &longs;tay there, thru&longs;t into <lb/>the water a Gla&longs;s rever&longs;ed with the mouth downwards, the which &longs;hall <lb/>carry with it the Air it contains, and move this towards the Ball, aba&longs;ing <lb/>it till &longs;uch time that you &longs;ee, by the tran&longs;parency of the Gla&longs;s, that the <lb/><arrow.to.target n="marg1484"></arrow.to.target> <lb/>contained Air do arrive to the &longs;ummity of the <emph type="italics"/>B<emph.end type="italics"/>all: then gently with­ <lb/>draw the Gla&longs;s upwards, and you &longs;hall &longs;ee the <emph type="italics"/>B<emph.end type="italics"/>all to ri&longs;e, and afterwards <lb/><arrow.to.target n="marg1485"></arrow.to.target> <lb/>stay on the top of the water, if you carefully part the Gla&longs;s and the water <lb/>without overmuch commoving and di&longs;turbing it. </s><s>There is, therefore, a <lb/>certain affinity between the Air and other <emph type="italics"/>B<emph.end type="italics"/>odies, which holds them uni­ <lb/>ed, &longs;o, that they &longs;eperate not without a kind of violence. </s><s>The &longs;ame <lb/><arrow.to.target n="marg1486"></arrow.to.target> <lb/>likewi&longs;e is &longs;een in the water; for if we &longs;hall wholly &longs;ubmerge &longs;ome <emph type="italics"/>B<emph.end type="italics"/>ody <lb/>in it, &longs;o that it be thorowly bathed, in the drawing of it afterwards gent­ <lb/>ly out again, we &longs;hall &longs;ee the water follow it, and ri&longs;e notably above its <lb/>Surface, before it &longs;eperates from it. </s><s>Solid <emph type="italics"/>B<emph.end type="italics"/>odies, al&longs;o, if they be equall <lb/><arrow.to.target n="marg1487"></arrow.to.target> <lb/>and alike in Superficies, &longs;o, that they make an exact Contact without <lb/>the interpo&longs;ition of the lea&longs;t Air, that may part them in the &longs;eperation <lb/>and yield untill that the ambient <emph type="italics"/>Medium<emph.end type="italics"/> &longs;ucceeds to repleni&longs;h the place, <lb/>do hold very firmly conjoyned, and are not to be &longs;eperated without great <lb/>force but, becau&longs;e, the Air, Water, and other Liquids, very expedi­ <lb/>tiou&longs;ly &longs;hape them&longs;elves to contact with any Solid <emph type="italics"/>B<emph.end type="italics"/>odies, &longs;o that their <lb/>Superficies do exqui&longs;itely adopt them&longs;elves to that of the Solids, without <lb/>any thing remaining between them, therefore, the effect of this Con­ <lb/>junction and Adherence is more manife&longs;tly and frequently ob&longs;erved in <lb/>them, than in hard and inflexible <emph type="italics"/>B<emph.end type="italics"/>odies, who&longs;e Superficies do very rate­ <lb/>ly conjoyn with exactne&longs;s of Contact. </s><s>This is therefore that Magne­ <lb/><arrow.to.target n="marg1488"></arrow.to.target> <lb/>tick vertue, which with firm Connection conjoyneth all Bodies, that do <lb/>touch without the interpo&longs;ition of flexible fluids; and, who knows, but <lb/>that that a Contact, when it is very exact, may be a &longs;ufficient Cau&longs;e of <lb/>the Union and Continuity of the parts of a naturall <emph type="italics"/>B<emph.end type="italics"/>ody?</s></p> <pb xlink:href="040/01/1133.jpg" pagenum="440"/><p type="margin"> <s><margin.target id="marg1482"></margin.target><emph type="italics"/>A<emph.end type="italics"/> Magneti&longs;me in <lb/>the <emph type="italics"/>A<emph.end type="italics"/>ir, by which <lb/>it bears up tho&longs;e <lb/>Solids in the wa­ <lb/>ter, that are con­ <lb/>tiguous with it.</s></p><p type="margin"> <s><margin.target id="marg1483"></margin.target>The Effect of <lb/>the Airs Conti­ <lb/>guity in the Na­ <lb/>tation of Solids.</s></p><p type="margin"> <s><margin.target id="marg1484"></margin.target>The force of <lb/>Contact.</s></p><p type="margin"> <s><margin.target id="marg1485"></margin.target><emph type="italics"/>A<emph.end type="italics"/>n affectati­ <lb/>on of Conjunct­ <lb/>ion betwixt So­ <lb/>lids and the Air <lb/>contiguous to <lb/>them.</s></p><p type="margin"> <s><margin.target id="marg1486"></margin.target>The like affect­ <lb/>ation of Con­ <lb/>junction be­ <lb/>twixt Solids & <lb/>the water.</s></p><p type="margin"> <s><margin.target id="marg1487"></margin.target>Al&longs;o the like <lb/>affectation and <lb/>Conjunction be­ <lb/>twixt Solids <lb/>them&longs;eives.</s></p><p type="margin"> <s><margin.target id="marg1488"></margin.target>Contact may <lb/>be the Cau&longs;e of <lb/>the Continuity <lb/>of Naturall Bo­ <lb/>dies.</s></p><p type="main"> <s>Now, pur&longs;uing my purpo&longs;e, I &longs;ay; that it needs not, that we have <lb/>recour&longs;e to the Tenacity, that the parts of the water have among&longs;t them­ <lb/>&longs;elves, by which they re&longs;i&longs;t and oppo&longs;e Divi&longs;ion, Di&longs;traction, and Seper­ <lb/>ration, becau&longs;e there is no &longs;uch Coherence and Re&longs;i&longs;tance of Divi&longs;ion <lb/>for if there were, it would be no le&longs;s in the internall parts than in tho&longs;e <lb/>nearer the &longs;uperiour or externall Surface, &longs;o that the &longs;ame Board, find­ <lb/>ing alwayes the &longs;ame Re&longs;i&longs;tance and Renitence, would no le&longs;s &longs;top in <lb/>the middle of the water than about the Surface, which is fal&longs;e. More­ <lb/></s><s>over, what Re&longs;i&longs;tance can we place in the Continuity of the water <lb/>if we &longs;ee that it is impo&longs;&longs;ible to &longs;ind any Body of what&longs;oever Matter <lb/>Figure or Magnitude, which being put into the water, &longs;hall be ob&longs;tructed <lb/>and impeded by the Tenacity of the parts of the water to one another <lb/>&longs;o, but that it is moved upwards or downwards, according as the Cau&longs;e <lb/>of their Motion tran&longs;ports it? </s><s>And, what greater proof of it can we de­ <lb/>&longs;ier, than that which we daily &longs;ee in Muddy waters, which being put into <lb/>Ve&longs;&longs;els to be drunk, and being, after &longs;ome hours &longs;etling, &longs;till, as we &longs;ay <lb/><arrow.to.target n="marg1489"></arrow.to.target> <lb/>thick in the end, after four or &longs;ix dayes they are wholly &longs;etled, and be­ <lb/>come pure and clear? </s><s>Nor can their Re&longs;i&longs;tance of Penetration &longs;tay tho&longs;e <lb/>impalpable and in&longs;en&longs;ible Atomes of Sand, which by rea&longs;on of their <lb/>exceeding &longs;mall force, &longs;pend &longs;ix dayes in de&longs;cending the &longs;pace of half <lb/>a yard.</s></p><p type="margin"> <s><margin.target id="marg1489"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he &longs;ettlement <lb/>of <emph type="italics"/>M<emph.end type="italics"/>uddy Wa­ <lb/>ter, proveth that <lb/>that Element <lb/>hath no aver&longs;i­ <lb/>on to Divi&longs;ion.</s></p><p type="main"> <s><emph type="italics"/>Nor let them &longs;ay, that the &longs;eeing of &longs;uch &longs;mall Bodies, con&longs;ume &longs;ix dayes in <lb/>de&longs;cending &longs;o little a way, is a &longs;ufficient Argument of the Waters Re&longs;i&longs;tance <lb/>of Divi&longs;ion; becau&longs;e that is no re&longs;i&longs;ting of Divi&longs;ion, but a retarding of<emph.end type="italics"/> <lb/><arrow.to.target n="marg1490"></arrow.to.target> <lb/><emph type="italics"/>Motion; and it would be &longs;implicity to &longs;ay, that a thing oppo&longs;eth Divi&longs;ion <lb/>and that in the &longs;ame in&longs;tant, it permits it &longs;elf to be divided: nor doth the <lb/>Retardation of Motion at all favour the Adver&longs;aries cau&longs;e, for that they are <lb/>to in&longs;tance in a thing that wholly prohibiteth Motion, and procureth Re&longs;t; <lb/>it is nece&longs;&longs;ary, therefore, to find out Bodies that &longs;tay in the water, if one would <lb/>&longs;hew its repugnancy to Divi&longs;ion, and not &longs;uch as move in it, howbeit <lb/>&longs;lowly.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1490"></margin.target>Water cannot <lb/>oppo&longs;e divi&longs;ion, <lb/>and at the &longs;ame <lb/>time permit it <lb/>&longs;elf to be divi­ <lb/>ded.</s></p><p type="main"> <s>What then is this Cra&longs;&longs;itude of the water, with which it re&longs;i&longs;teth Di­ <lb/>vi&longs;ion? </s><s>What, I be&longs;eech you, &longs;hould it be, if we (as we have &longs;aid above) <lb/>with all diligence attempting the reduction of a Matter into &longs;o like a <lb/>Gravity with the water, that forming it into a dilated Plate it re&longs;ts &longs;u&longs;­ <lb/>pended as we have &longs;aid, between the two waters, it be impo&longs;&longs;ible to <lb/>effect it, though we bring them to &longs;uch an Equiponderance, that as <lb/>much Lead as the fourth part of a Grain of Mu&longs;terd-&longs;eed, added to the <lb/>&longs;ame expanded Plate, that in Air [<emph type="italics"/>i. </s><s>e. </s><s>out of the water<emph.end type="italics"/>] &longs;hall weigh four <lb/>or fix pounds, &longs;inketh it to the Bottom, and being &longs;ub&longs;tracted, it a&longs;cends <lb/>to the Surface of the water? </s><s>I cannot &longs;ee, (if what I &longs;ay be true, as it is <lb/>mo&longs;t certain) what minute vertue and force we can po&longs;&longs;ibly find or ima­ <lb/>gine, to which the Re&longs;i&longs;tance of the water again&longs;t Divi&longs;ion and Penetra­ <pb xlink:href="040/01/1134.jpg" pagenum="441"/>tion is not inferiour; whereupon, we mu&longs;t of nece&longs;&longs;ity conclude <lb/>that it is nothing: becan&longs;e, if it were of any &longs;en&longs;ible power, &longs;ome <lb/>large Plate might be found or compounded of a Matter alike in Gra­ <lb/>vity to the water, which not only would &longs;tay between the two wa­ <lb/>ters; but, moreover, &longs;hould not be able to de&longs;cend or a&longs;cend with­ <lb/>out notable force. </s><s>We may likewi&longs;e collect the &longs;ame from an o­ <lb/><arrow.to.target n="marg1491"></arrow.to.target> <lb/>ther Experiment, &longs;hewing that the Water gives way al&longs;o in the &longs;ame <lb/>manner to tran&longs;ver&longs;all Divi&longs;ion; for if in a &longs;etled and &longs;tanding water <lb/>we &longs;hould place any great Ma&longs;s that goeth not to the bottom, draw­ <lb/>ing it with a &longs;ingle (Womans) Hair, we might carry it from place to <lb/>place without any oppo&longs;ition, and this whatever Figure it hath, <lb/>though that it po&longs;&longs;e&longs;s a great &longs;pace of water, as for in&longs;tance, a great <lb/>Beam would do moved &longs;ide-ways. </s><s>Perhaps &longs;ome might oppo&longs;e me <lb/>and &longs;ay, that if the Re&longs;i&longs;tance of water again&longs;t Divi&longs;ion, as I affirm, <lb/>were nothing; Ships &longs;hould not need &longs;uch a force of Oars and Sayles <lb/>for the moving of them from place to place in a tranquile Sea, or <lb/>&longs;tanding Lake. </s><s>To him that &longs;hould make &longs;uch an objection, I would <lb/><arrow.to.target n="marg1492"></arrow.to.target> <lb/>reply, that the water contra&longs;teth not again&longs;t, nor &longs;imply re&longs;i&longs;teth <lb/>Divi&longs;ion, but a &longs;udden Divi&longs;ion, and with &longs;o much greater Reni­ <lb/>tence, by how much greater the Velocity is: and the Cau&longs;e of this <lb/>Re&longs;i&longs;tance depends not on Cra&longs;&longs;itude, or any other thing that ab&longs;o­ <lb/>lutely oppo&longs;eth Divi&longs;ion, but becau&longs;e that the parts of the water <lb/>divided, in giving way to that Solid that is moved in it, are them­ <lb/>&longs;elves al&longs;o nece&longs;&longs;itated locally to move, &longs;ome to the one &longs;ide, and &longs;ome <lb/>to the other, and &longs;ome downwards: and this mu&longs;t no le&longs;s be done <lb/>by the waves before the Ship, or other Body &longs;wimming through the <lb/>water, than by the po&longs;teriour and &longs;ub&longs;equent; becau&longs;e, the Ship <lb/>proceeding forwards, to make it &longs;elf a way to receive its Bulk, it is <lb/>requi&longs;ite, that with the Prow it repul&longs;e the adjacent parts of the <lb/>water, as well on one hand as on the other, and that it move them <lb/>as much tran&longs;ver&longs;ly, as is the half of the breadth of the Hull: and <lb/>the like removall mu&longs;t tho&longs;e waves make, that &longs;ucceeding the Poump <lb/>do run from the remoter parts of the Ship towards tho&longs;e of the <lb/>middle, &longs;ucce&longs;&longs;ively to repleni&longs;h the places, which the Ship in ad­ <lb/>vancing forwards, goeth, leaving vacant. </s><s>Now, becau&longs;e, all Moti­ <lb/><arrow.to.target n="marg1493"></arrow.to.target> <lb/>tions are made in Time, and the longer in greater time: and it being <lb/>moreover true, that tho&longs;e Bodies that in a certain time are moved <lb/>by a certain power &longs;uch a certain &longs;pace, &longs;hall not be moved the &longs;ame <lb/>&longs;pace, and in a &longs;horter Time, unle&longs;s by a greater Power: therefore, <lb/>the broader Ships move &longs;lower than the narrower, being put on by <lb/>an equall Force: and the &longs;ame Ve&longs;&longs;el requires &longs;o much greater <lb/>force of Wind, or Oars, the fa&longs;ter it is to move.</s></p> <pb xlink:href="040/01/1135.jpg" pagenum="442"/><p type="margin"> <s><margin.target id="marg1491"></margin.target>An hair will <lb/>draw a great <lb/>Ma&longs;s thorow the <lb/>Water; which <lb/>proveth, that it <lb/>hath no Re&longs;i&longs;t­ <lb/>ance again&longs;t <lb/>tran&longs;ver&longs;all Di­ <lb/>vi&longs;ion.</s></p><p type="margin"> <s><margin.target id="marg1492"></margin.target>How &longs;hips are <lb/>moved in the <lb/>water.</s></p><p type="margin"> <s><margin.target id="marg1493"></margin.target>Bodies moved <lb/>a certain &longs;pace in <lb/>a certain Time, <lb/>by a certain <lb/>power, cannot be <lb/>moved the <lb/>&longs;ame &longs;pace, and <lb/>in a &longs;horter time, <lb/>but by a greater <lb/>power.</s></p><p type="main"> <s><emph type="italics"/>But yet for all this, any great Ma&longs;s &longs;wimming in a &longs;tanding Lake, may <lb/>be moved by any petit force; only it is true, that a le&longs;&longs;er force more <lb/>&longs;lowly moves it: but if the waters Re&longs;i&longs;tance of Divi&longs;ion, were in any <lb/>manner &longs;en&longs;ible, it would follow, that the &longs;aid Ma&longs;s, &longs;hould, notwith­ <lb/>&longs;tanding the percu&longs;&longs;ion of &longs;ome &longs;en&longs;ible force, continue immoveable, which is<emph.end type="italics"/> <lb/><arrow.to.target n="marg1494"></arrow.to.target> <lb/><emph type="italics"/>not &longs;o. </s><s>Yea, I will &longs;ay farther, that &longs;hould we retire our &longs;elves into the <lb/>more internall contemplation of the Nature of water and other Fluids, <lb/>perhaps we &longs;hould di&longs;cover the Con&longs;titution of their parts to be &longs;uch, that <lb/>they not only do not oppo&longs;e Divi&longs;ion, but that they have not any thing in <lb/>them to be divided: &longs;o that the Re&longs;i&longs;tance that is ob&longs;erved in moving<emph.end type="italics"/> <lb/><arrow.to.target n="marg1495"></arrow.to.target> <lb/><emph type="italics"/>through the water, is like to that which we meet with in pa&longs;&longs;ing through <lb/>a great Throng of People, wherein we find impediment, and not by any <lb/>difficulty in the Divi&longs;ion, for that none of tho&longs;e per&longs;ons are divided <lb/>whereof the Croud is compo&longs;ed, but only in moving of tho&longs;e per&longs;ons &longs;ide­ <lb/>ways which were before divided and disjoyned: and thus we find <lb/>Re&longs;i&longs;tance in thru&longs;ting a Stick into an heap of Sand, not becau&longs;e any part <lb/>of the Sand is to be cut in pieces, but only to be moved and rai&longs;ed. two <emph.end type="italics"/> <lb/><arrow.to.target n="marg1496"></arrow.to.target> <lb/><emph type="italics"/>manners of Penetration, therefore, offer them&longs;elves to us, one in Bodies, <lb/>who&longs;e parts were continuall, and here Divi&longs;ion &longs;eemeth nece&longs;&longs;ary; the <emph.end type="italics"/> <lb/><arrow.to.target n="marg1497"></arrow.to.target> <lb/><emph type="italics"/>other in the aggregates of parts not continuall, but contiguous only, and <lb/>here there is no nece&longs;&longs;ity of dividing but of moving only. </s><s>Now, I am <lb/>not well re&longs;olved, whether water and other Fluids may be e&longs;teemed to <lb/>be of parts continuall or contiguous only; yet I find my &longs;elf indeed incli­<emph.end type="italics"/> <lb/><arrow.to.target n="marg1498"></arrow.to.target> <lb/><emph type="italics"/>ned to think that they are rather contiguous (if there be in Naturno <lb/>other manner of aggregating, than by the union, or by the touching of the <lb/>extreams:) and I am induced thereto by the great difference that I &longs;ee > <lb/>between the Conjunction of the parts of an hard or Solid Body, and the<emph.end type="italics"/> <lb/><arrow.to.target n="marg1499"></arrow.to.target> <lb/><emph type="italics"/>Conjunction of the &longs;ame parts when the &longs;ame Body &longs;hall be made Liquid <lb/>and Fluid: for if, for example, I take a Ma&longs;s of Silver or other Solid <lb/>and hard Mettall, I &longs;hall in dividing it into two parts, find not only the <emph.end type="italics"/> <lb/><arrow.to.target n="marg1500"></arrow.to.target> <lb/><emph type="italics"/>re&longs;i&longs;tance that is found in the moving of it only, but an other incomparably <lb/>greater, dependent on that vertue, whatever it be, which holds the parts <lb/>united: and &longs;o if we would divide again tho&longs;e two parts into other two <lb/>and &longs;ucce&longs;&longs;ively into others and others, we &longs;hould &longs;till find a like Re&longs;i&longs;t­ <lb/>ance, but ever le&longs;s by how much &longs;maller the parts to be divided &longs;hall be; <lb/>but if, la&longs;tly, employing mo&longs;t &longs;ubtile and acute In&longs;truments, &longs;uch as are <lb/>the mo&longs;t tenuous parts of the Fire, we &longs;hall re&longs;olve it (perhaps) into its <lb/>la&longs;t and lea&longs;t Particles, there &longs;hall not be left in them any longer either <lb/>Re&longs;i&longs;tance of Divi&longs;ion, or &longs;o much as a capacity of being farther divi­ <lb/>ded, e&longs;pecially by In&longs;truments more gro&longs;&longs;e than the acuities of Fire: and <lb/>what Knife or Ra&longs;or put into well melted Silver can we finde, that will <lb/>divide a thing which &longs;urpa&longs;&longs;eth the &longs;eparating power of Fire? </s><s>Certainly <lb/>none: becau&longs;e either the whole &longs;hall be reduced to the mo&longs;t minute and <lb/>ultimate Divi&longs;ions, or if there remain parts capable &longs;till of other Suddi­<emph.end type="italics"/> <pb xlink:href="040/01/1136.jpg" pagenum="443"/><emph type="italics"/>divi&longs;ions, they cannot receive them, but only from acuter Divi&longs;ors than <lb/>Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not <lb/>&longs;uch a one. </s><s>Of a like Con&longs;titution and Con&longs;i&longs;tence, I account the parts<emph.end type="italics"/> <lb/><arrow.to.target n="marg1501"></arrow.to.target> <lb/><emph type="italics"/>of Water, and other Liquids to be, namely, incapable of Divi&longs;ion by <lb/>rea&longs;on of their Temtity; or if not ab&longs;olutely indivi&longs;ible, yet at lea&longs;t <lb/>not to be divided by a Board, or other Solid Body, palpable unto the <lb/>band, the Sector being alwayes required to be more &longs;harp than the Solid <lb/>to be cut. </s><s>Solid Bodies, therefore, do only move, and not divide the<emph.end type="italics"/> <lb/><arrow.to.target n="marg1502"></arrow.to.target> <lb/><emph type="italics"/>Water, when put into it; who&longs;e parts being before divided to the ex­ <lb/>treame&longs;t minuity, and therefore capable of being moved, either many of <lb/>them at once, or few, or very few, they &longs;oon give place to every &longs;mall Cor­ <lb/>pu&longs;cle, that de&longs;cends in the &longs;ame: for that, it being little and light, de­ <lb/>&longs;cending in the Air, and arriving to the Surface of the Water, it meets <lb/>with Particles of Water more &longs;mall, and of le&longs;s Re&longs;i&longs;tance again&longs;t <lb/>Motion and Extru&longs;ion, than is its own prement and extru&longs;ive force, <lb/>whereupon it &longs;ubmergeth, and moveth &longs;uch a portion of them, as is pro­ <lb/>portionate to its Power. </s><s>There is not, therefore, any Re&longs;i&longs;tance in <lb/>Water again&longs;t Divi&longs;ion, nay, there is not in it any divi&longs;ible parts. </s><s>I <lb/>adde, moreover, that in ca&longs;e yet there &longs;bould be any &longs;mall Re&longs;i&longs;tance<emph.end type="italics"/> <lb/><arrow.to.target n="marg1503"></arrow.to.target> <lb/><emph type="italics"/>found (which is ab&longs;olutely fal&longs;e) haply in attempting with an Hair to <lb/>move a very great natant Machine, or in e&longs;&longs;aying by the addition of one <lb/>&longs;mall Grain of Lead to &longs;ink, or by removall of it to rai&longs;e a very broad <lb/>Plate of Matter, equall in Gravity with Water, (which likewi&longs;e will <lb/>not happen, in ca&longs;e we proceed with dexterity) we may ob&longs;erve that that <lb/>Re&longs;i&longs;tance is a very different thing from that which the Adver&longs;aries pro­ <lb/>duce for the Cau&longs;e of the Natation of the Plate of Lead or Board of Ebo­ <lb/>ny, for that one may make a Board of Ebony, which being put upon the <lb/>Water &longs;wimmeth, and cannot be &longs;ubmerged, no not by the addition of an <lb/>bundred Grains of Lead put upon the &longs;ame, and afterwards being ba­ <lb/>thed, not only &longs;inks, though the &longs;aid Lead be taken away, but though <lb/>moreover a quantity of Cork, or of &longs;ome other light Body fa&longs;tened to it, <lb/>&longs;ufficeth not to hinder it from &longs;inking unto the bottome: &longs;o that you <lb/>&longs;ee, that although it were granted that there is a certain &longs;mall Re&longs;i&longs;t­ <lb/>ance of Divi&longs;ion found in the &longs;ubstance of the Water, yet this hath no­ <lb/>thing to do with that Cau&longs;e which &longs;upports the Board above the Water, <lb/>with a Re&longs;i&longs;tance an hundred times greater than that which men can <lb/>find in the parts of the Water: nor let them tell me, that only the Sur-<emph.end type="italics"/> <lb/><arrow.to.target n="marg1504"></arrow.to.target> <lb/><emph type="italics"/>face of the Water hath &longs;uch Re&longs;i&longs;tance, and not the internall parts, or <lb/>that &longs;uch Re&longs;i&longs;tance is found greate&longs;t in the beginning of the Submer&longs;ion, <lb/>as it al&longs;o &longs;eems that in the beginning, Motion meets with greater oppo&longs;iti­ <lb/>on, than in the continuance of it; becau&longs;e, fir&longs;t, I will permit, that the<emph.end type="italics"/> <lb/><arrow.to.target n="marg1505"></arrow.to.target> <lb/><emph type="italics"/>Water be &longs;tirred, and that the &longs;uperiour parts be mingled with the mid­ <lb/>dle, and inferiour parts, or that tho&longs;e above be wholly removed, and <lb/>tho&longs;e in the middle only made u&longs;e off, and yet you &longs;hall &longs;ee the effect for<emph.end type="italics"/> <pb xlink:href="040/01/1137.jpg" pagenum="444"/><emph type="italics"/>all that, to be still the &longs;ame: Moreover, that Hair which draws a <lb/>Beam through the Water, is likewi&longs;e to divide the upperparts, and is <lb/>al&longs;o to begin the Motion, and yet it begins it, and yet it divides it: and <lb/>finally, let the Board of Ebony be put in the midway, betwixt the bottome <lb/>and the top of the Water, and let it there for a while be &longs;u&longs;pended and <lb/>&longs;etled, and afterwards let it be left at liberty, and it will instantly begin <lb/>its Motion, and will continue it unto the bottome. </s><s>Nay, more, the Board <lb/>&longs;o &longs;oon as it is dimitted upon the Water, hath not only begun to move <lb/>and divide it, but is for a good &longs;pace dimerged into it.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1494"></margin.target>The parts of <lb/>Liquids, &longs;o farte <lb/>from re&longs;i&longs;ting <lb/>Divi&longs;ion, that <lb/>they contain not <lb/>any thing that <lb/>may be divided.</s></p><p type="margin"> <s><margin.target id="marg1495"></margin.target>The Re&longs;i&longs;t­ <lb/>ance a Solid <lb/>findeth in mo­ <lb/>ving through <lb/>the water, like <lb/>to that we meet <lb/>with in pa&longs;&longs;ing <lb/>through a <lb/>throng of peo­ <lb/>ple;</s></p><p type="margin"> <s><margin.target id="marg1496"></margin.target>Or in thru&longs;t­ <lb/>ing a Stick into <lb/>an heap of Sand.</s></p><p type="margin"> <s><margin.target id="marg1497"></margin.target>Two kinds of <lb/>Penetration, one <lb/>in Bodies conti­ <lb/>nuall, the other <lb/>in Bodies only <lb/>contiguous.</s></p><p type="margin"> <s><margin.target id="marg1498"></margin.target>Water con&longs;i&longs;ts <lb/>not of continu­ <lb/>all, but only <lb/>of contiguous <lb/>parts.</s></p><p type="margin"> <s><margin.target id="marg1499"></margin.target><emph type="italics"/>Set what &longs;atis­ <lb/>faction he hath <lb/>given, as to this <lb/>point, in Lib. de <lb/>Motu. </s><s>Dial.<emph.end type="italics"/> 2.</s></p><p type="margin"> <s><margin.target id="marg1500"></margin.target>Great differ­ <lb/>ence betwixt the <lb/>Conjunction of <lb/>the parts of a Bo­ <lb/>dy when Solid, <lb/>and when fluid.</s></p><p type="margin"> <s><margin.target id="marg1501"></margin.target>Water con&longs;i&longs;ts <lb/>of parts that ad­ <lb/>mit of no fat­ <lb/>ther divi&longs;ion.</s></p><p type="margin"> <s><margin.target id="marg1502"></margin.target>Solids dimit­ <lb/>ted into the wa­ <lb/>ter, do onely <lb/>move, and not <lb/>divide it.</s></p><p type="margin"> <s><margin.target id="marg1503"></margin.target>If there were <lb/>any Re&longs;i&longs;tance <lb/>of Divi&longs;ion in <lb/>water, it mu&longs;t <lb/>needs be &longs;mall, <lb/>in that it is over­ <lb/>come by an <lb/>Hair, a Grain of <lb/>Lead, or a &longs;light <lb/>bathing of the <lb/>Solid.</s></p><p type="margin"> <s><margin.target id="marg1504"></margin.target>The uper parts <lb/>of the Water, do <lb/>no more re&longs;i&longs;t <lb/>Divi&longs;ion, than <lb/>the middle or <lb/>lowe&longs;t parts.</s></p><p type="margin"> <s><margin.target id="marg1505"></margin.target>Waters Re­ <lb/>&longs;i&longs;tance of divi­ <lb/>&longs;ion, not greater <lb/>in the begin­ <lb/>ning of the Sub­ <lb/>mer&longs;ion.</s></p><p type="main"> <s>Let us receive it, therefore, for a true and undoubted Conclu&longs;i­ <lb/>on, That the Water hath not any Renitence again&longs;t &longs;imple Divi&longs;i­ <lb/>on, and that it is not po&longs;&longs;ible to find any Solid Body, be it of what <lb/>Figure it will, which being put into the Water, its Motion upwards <lb/>or downwards, according as it exceedeth, or &longs;hall be exceeded by <lb/>the Water in Gravity (although &longs;uch exce&longs;&longs;e and difference be in­ <lb/>&longs;en&longs;ible) &longs;hall be prohibited, and taken away, by the Cra&longs;&longs;itude of <lb/>the &longs;aid Water. </s><s>When, therefore, we &longs;ee the Board of Ebony, or <lb/>of other Matter, more grave than the Water, to &longs;tay in the Con­ <lb/>fines of the Water and Air, without &longs;ubmerging, we mu&longs;t have re­ <lb/>cour&longs;e to &longs;ome other Originall, for the inve&longs;ting the Cau&longs;e of that <lb/>Effect, than to the breadth of the Figure, unable to overcome the <lb/>Renitence with which the Water oppo&longs;eth Divi&longs;ion, &longs;ince there is <lb/>no Re&longs;i&longs;tance; and from that which is not in being, we can expect <lb/>no Action. </s><s>It remains mo&longs;t true, therefore, as we have &longs;aid before, that <lb/>this &longs;o &longs;ucceds, for that that which in &longs;uch manner put upon the wa­ <lb/>ter, not the &longs;ame Body with that which is put <emph type="italics"/>into<emph.end type="italics"/> the Water: becau&longs;e <lb/>this which is put <emph type="italics"/>into<emph.end type="italics"/> the Water, is the pure Board of Ebony, which <lb/>for that it is more grave than the Water, &longs;inketh, and that which is <lb/>put <emph type="italics"/>upon<emph.end type="italics"/> the Water, is a Compo&longs;ition of Ebony, and of &longs;o much <lb/>Air, that both together are &longs;pecifically le&longs;s grave than the Water, <lb/>and therefore they do not de&longs;cend.</s></p><p type="main"> <s>I will farther confirm this which I &longs;ay. </s><s>Gentlemen, my Antago­ <lb/>ni&longs;ts, we are agreed, that the exce&longs;s or defect of the Gravity of the <lb/>Solid, unto the Gravity of the Water, is the true and proper Cau&longs;e <lb/>of Natation or Submer&longs;ion. <lb/><arrow.to.target n="marg1506"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1506"></margin.target>Great Caution <lb/>to be had in ex­ <lb/>perimenting the <lb/>operation of Fi­ <lb/>gure in Natati­ <lb/>on.</s></p><p type="main"> <s>Now, if you will &longs;hew that be&longs;ides the former Cau&longs;e, there is ano­ <lb/>ther which is &longs;o powerfull, that it can hinder and remove the Sub­ <lb/>mer&longs;ion of tho&longs;e very Solids, that by their Gravity &longs;ink, and if you <lb/>will &longs;ay, that this is the breadth or amplene&longs;s of Figure, you are ob­ <lb/>lieged, when ever you would &longs;hew &longs;uch an Experiment, fir&longs;t to make <lb/>the circum&longs;tances certain, that that Solid which you put into the <lb/>Water, be not le&longs;s grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than it, for if you &longs;hould not do &longs;o <lb/>any one might with rea&longs;on &longs;ay, that not the Figure, but the Levity <lb/>was the cau&longs;e of that Natation. </s><s>But I &longs;ay, that when you &longs;hall di­ <pb xlink:href="040/01/1138.jpg" pagenum="445"/>mit a Board of Ebony into the Water, you do not put therein a Solid <lb/>more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the Water, but one lighter, for be &longs;ides the <lb/>Ebony, there is in the Water a Ma&longs;s of Air, united with the Ebony, <lb/>and &longs;uch, and &longs;o light, that of both there re&longs;ults a Compo&longs;ition le&longs;s <lb/>grave than the Water: See, therefore, that you remove the Air, and <lb/>put the Ebony alone into the Water, for &longs;o you &longs;hall immerge a So­ <lb/>lid more grave then the Water, and if this &longs;hall not go to the Bottom, <lb/>you have well Philo&longs;ophized, and I ill.</s></p><p type="main"> <s>Now, &longs;ince we have found the true Cau&longs;e of the Natation of tho&longs;e <lb/>Bodies, which otherwi&longs;e as being graver than the Water, would de­ <lb/>&longs;cend to the bottom, I think, that for the perfect and di&longs;tinct know­ <lb/>ledge of this bu&longs;ine&longs;s, it would be good to proceed in a way of di&longs;­ <lb/>covering demon&longs;tratively tho&longs;e particular Accidents that do attend <lb/>the&longs;e effects, and,</s></p><p type="head"> <s>PROBL. I.</s></p><p type="main"> <s><emph type="italics"/>To finde what proportion &longs;everall Figures of different<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1507"></arrow.to.target> <lb/><emph type="italics"/>Matters ought to have, unto the Gravity of the <lb/>Water, that &longs;o they may be able by vertue of the <lb/>Contigucus Air to &longs;tay afloat.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1507"></margin.target>To finde the <lb/>proportion Fi­ <lb/>gures ought to <lb/>have to the wa­ <lb/>ters Gravity, <lb/>that by help of <lb/>the contiguous <lb/>Air, they may <lb/>&longs;wim.</s></p><p type="main"> <s>Let, therefore, for better illu&longs;tration, D F N E be a Ve&longs;&longs;ell, <lb/>wherein the water is contained, and &longs;uppo&longs;e a Plate or Board, <lb/>who&longs;e thickne&longs;s is comprehended between the Lines I C and <lb/>O S, and let it be of Matter exceeding the water in Gravity, &longs;o that <lb/>being put upon the water, it dimergeth and aba&longs;eth below the Levell <lb/>of the &longs;aid water, leaving the little Banks A I and B C, which are at <lb/>the greate&longs;t height they can be, &longs;o that if the Plate I S &longs;hould but <lb/>de&longs;cend any little &longs;pace farther, the little Banks or Ramparts would <lb/>no longer con&longs;i&longs;t, but expul&longs;ing the Air A I C B, they would dif­ <lb/>fu&longs;e them&longs;elves over the Superficies I C, and <lb/>would &longs;ubmerge the Plate. </s><s>The height AIBC <lb/>is therefore the greate&longs;t profundity that the <lb/><figure id="id.040.01.1138.1.jpg" xlink:href="040/01/1138/1.jpg"/> <lb/>little <emph type="italics"/>B<emph.end type="italics"/>anks of water admit of. </s><s>Now I &longs;ay, <lb/>that from this, and from the proportion in Gra­ <lb/>vity, that the Matter of the Plate hath to the <lb/>water, we may ea&longs;ily &longs;inde of what thickne&longs;s, at mo&longs;t, we may make <lb/>the &longs;aid Plates, to the end, they may be able to bear up above water: <lb/>for if the Matter of the Plate or <emph type="italics"/>B<emph.end type="italics"/>oard I S were, for Example, as <lb/>heavy again as the water, a <emph type="italics"/>B<emph.end type="italics"/>oard of that Matter &longs;hall be, at the mo&longs;t <lb/>of a thickne&longs;s equall to the greate&longs;t height of the <emph type="italics"/>B<emph.end type="italics"/>anks, that is, as <lb/>thick as A I is high: which we will thus demon&longs;trate. </s><s>Lot the So­ <lb/>lid I S be donble in Gravity to the water, and let it be a regular <pb xlink:href="040/01/1139.jpg" pagenum="446"/>Pri&longs;me, or Cylinder, to wit, that hath its two flat Superficies, &longs;uperi­ <lb/>our and inferiour, alike and equall, and at Right Angles with the o­ <lb/>ther laterall Superficies, and let its thickne&longs;s I O be equall to the <lb/>greate&longs;t Altitude of the Banks of water: I &longs;ay, that if it be put upon <lb/>the water, it will not &longs;ubmerge: for the Altitude <lb/>A I being equall to the Altitude I O, the Ma&longs;s <lb/>of the Air A B C I &longs;hall be equall to the Ma&longs;s of <lb/><figure id="id.040.01.1139.1.jpg" xlink:href="040/01/1139/1.jpg"/> <lb/>the Solid C I O S: and the whole Ma&longs;s A O S B <lb/>double to the Ma&longs;s I S; And &longs;ince the Ma&longs;s <lb/>of the Air A C, neither encrea&longs;eth nor dimi­ <lb/>ni&longs;heth the Gravity of the Ma&longs;s I S, and the Solid I S was &longs;uppo&longs;ed <lb/>double in Gravity to the water; Therefore as much water as the <lb/>Ma&longs;s &longs;ubmerged A O S B, compounded of the Air A I C B, and of <lb/>the Solid I O S C, weighs ju&longs;t as much as the &longs;ame &longs;ubmerged Ma&longs;s <lb/>A O S B: but when &longs;uch a Ma&longs;s of water, as is the &longs;ubmerged part of <lb/>the Solid, weighs as much as the &longs;aid Solid, it de&longs;cends not farther, <lb/><arrow.to.target n="marg1508"></arrow.to.target> <lb/>but re&longs;teth, as by <emph type="italics"/>(a) Archimedes,<emph.end type="italics"/> and above by us, hath been de­> <lb/>mon&longs;trated: Therefore, I S &longs;hall de&longs;cend no farther, but &longs;hall re&longs;t. <lb/>And if the Solid I S &longs;hall be Se&longs;quialter in Gravity to the water, it <lb/>&longs;hall float, as long as its thickne&longs;s be not above twice as much as the <lb/>greate&longs;t Altitude of the Ramparts of water, that is, of A I. </s><s>For I S <lb/>being Se&longs;quialter in Gravity to the water, and the Altitude O I <lb/>being double to I A, the Solid &longs;ubmerged A O S B, &longs;hall be al&longs;o <lb/>Se&longs;quialter in Ma&longs;s to the Solid I S. </s><s>And becau&longs;e the Air A C, <lb/>neither increa&longs;eth nor dimini&longs;heth the pondero&longs;ity of the Solid I S: <lb/>Therefore, as much water in quantity as the &longs;ubmerged Ma&longs;s AOSB, <lb/>weighs as much as the &longs;aid Ma&longs;s &longs;ubmerged: And, therefore, that <lb/>Ma&longs;s &longs;hall re&longs;t. </s><s>And briefly in generall.</s></p><p type="margin"> <s><margin.target id="marg1508"></margin.target>Of Natation <lb/>Lib. 1. Prop. </s><s>3.</s></p><p type="head"> <s>THEOREME. VI.</s></p><p type="main"> <s><emph type="italics"/>When ever the exce&longs;s of the Gravity of the Solid above<emph.end type="italics"/> <lb/><arrow.to.target n="marg1509"></arrow.to.target> <lb/><emph type="italics"/>the Gravity of the Water, &longs;hall have the &longs;ame pro­ <lb/>portion to the Gravity of the Water, that the Alti­ <lb/>tude of the Rampart, hath to the thickne&longs;s of the <lb/>Solid, that Solid &longs;hall not &longs;ink, but being never &longs;o lit­ <lb/>tle thicker it &longs;hall.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1509"></margin.target>The proporti­ <lb/>on of the great­ <lb/>e&longs;t thickne&longs;s of <lb/>Solids, beyond <lb/>which encrea­ <lb/>&longs;ed they &longs;ink.</s></p><p type="main"> <s>Let the Solid I S be &longs;uperior in Gravity to the water, and of &longs;uch <lb/>thickne&longs;s, that the Altitude of the Rampart A I, be in proporti­ <lb/>on to the thickne&longs;s of the Solid I O, as the exce&longs;s of the Gravi­ <lb/>ty of the &longs;aid Solid I S, above the Gravity of a Ma&longs;s of water equall <lb/>to the Ma&longs;s I S, is to the Gravity of the Ma&longs;s of water equall to the <pb xlink:href="040/01/1140.jpg" pagenum="447"/>Ma&longs;s I S. </s><s>I &longs;ay, that the Solid I S &longs;hall not <lb/>&longs;inke, but being never &longs;o little thicker it &longs;hall <lb/>go to the bottom: For being that as A I is <lb/><figure id="id.040.01.1140.1.jpg" xlink:href="040/01/1140/1.jpg"/> <lb/>to I O, &longs;o is the Exce&longs;s of the Gravity of the <lb/>Solid I S, above the Gravity of a Ma&longs;s of water <lb/>equall to the Ma&longs;s I S, to the Gravity of the <lb/>&longs;aid Ma&longs;s of water: Therefore, compounding, as A O is to O I, &longs;o <lb/>&longs;hall the Gravity of the Solid I S, be to the Gravity of a Ma&longs;s of water <lb/>equall to the Ma&longs;s I S: And, converting, as I O is to O A, &longs;o &longs;hall the <lb/>Gravity of a Ma&longs;s of water equall to the Ma&longs;s I S, be to the Gravity <lb/>of the Solid I S: But as I O is to O A, &longs;o is a Ma&longs;s of water I S, to a <lb/>Ma&longs;s of water equall to the Ma&longs;s A B S O: and &longs;o is the Gravity of <lb/>a Ma&longs;s of water I S, to the Gravity of a Ma&longs;s of water A S: Therefore <lb/>as the Gravity of a Ma&longs;s of water, equall to the Ma&longs;s I S, is to the <lb/>Gravity of the Solid I S, &longs;o is the &longs;ame Gravity of a Ma&longs;s of water <lb/>I S, to the Gravity of a Ma&longs;s of Water A S: Therefore the Gra­ <lb/>vity of the Solid I S, is equall to the Gravity of a Ma&longs;s of water e­ <lb/>quall to the Ma&longs;s A S: But the Gravity of the Solid I S, is the &longs;ame <lb/>with the Gravity of the Solid A S, compounded of the Solid I S, <lb/>and of the Air A B C I. </s><s>Therefore the whole compounded Solid <lb/>A O S B, weighs as much as the water that would be compri&longs;ed in the <lb/>place of the &longs;aid Compound A O S B: And, therefore, it &longs;hall make <lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> and re&longs;t, and that &longs;ame Solid I O S C &longs;hall &longs;inke no <lb/>farther. </s><s>But if its thickne&longs;s I O &longs;hould be increa&longs;ed, it would be ne­ <lb/>ce&longs;&longs;ary al&longs;o to encrea&longs;e the Altitude of the Rampart A I, to main­ <lb/>tain the due proportion: But by what hath been &longs;uppo&longs;ed, the Alti­ <lb/>tude of the Rampart A I, is the greate&longs;t that the Nature of the <lb/>Water and Air do admit, without the waters repul&longs;ing the Air ad­ <lb/>herent to the Superficies of the Solid I C, and po&longs;&longs;e&longs;&longs;ing the &longs;pace <lb/>A I C B: Therefore, a Solid of greater thickne&longs;s than I O, and of the <lb/>&longs;ame Matter with the Solid I S, &longs;hall not re&longs;t without &longs;ubmerging, <lb/>but &longs;hall de&longs;cend to the bottome: which was to be demon&longs;trated. <lb/></s><s>In con&longs;equence of this that hath been demon&longs;trated, &longs;undry and va­ <lb/>rious Conclu&longs;ions may be gathered, by which the truth of my prin­ <lb/>cipall Propo&longs;ition comes to be more and more confirmed, and the <lb/>imperfection of all former Argumentations touching the pre&longs;ent <lb/>Que&longs;tion cometh to be di&longs;covered.</s></p><p type="main"> <s><emph type="italics"/>And fir&longs;t we gather from the things demonstrated, that,<emph.end type="italics"/></s></p> <pb xlink:href="040/01/1141.jpg" pagenum="448"/><p type="head"> <s>THEOREME VII. <lb/><arrow.to.target n="marg1510"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1510"></margin.target>The heavie&longs;t <lb/>Bodies may <lb/>&longs;wimme.</s></p><p type="main"> <s><emph type="italics"/>All Matters, how heavy &longs;oever, even to Gold it &longs;elf, the <lb/>heavie&longs;t of all Bodies, known by us, may float upon <lb/>the Water.<emph.end type="italics"/></s></p><p type="main"> <s>Becau&longs;e its Gravity being con&longs;idered to be almo&longs;t twenty times <lb/>greater than that of the water, and, moreover, the greate&longs;t Alti­ <lb/>tude that the Rampart of water can be extended to, without break <lb/>ing the Contiguity of the Air, adherent to the Surface of the Solid, <lb/>that is put upon the water being predetermined, if we &longs;hould make <lb/>a Plate of Gold &longs;o thin, that it exceeds not the nineteenth part ofthe <lb/>Altitude of the &longs;aid Rampart, this put lightly upon the water &longs;hall <lb/>re&longs;t, without going to the bottom: and if Ebony &longs;hall chance to be <lb/>in &longs;e&longs;qui&longs;eptimall proportion more grave than the water, the greate&longs;t <lb/>thickne&longs;s that can be allowed to a Board of Ebony, &longs;o that it may be <lb/>able to &longs;tay above water without &longs;inking, would be &longs;eaven times <lb/>more than the height of the Rampart Tinn, <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> eight times more <lb/>grave than water, &longs;hall &longs;wimm as oft as the thickne&longs;s of its Plate,</s></p><p type="main"> <s><arrow.to.target n="marg1511"></arrow.to.target> <lb/>exceeds not the 7th part of the Altitude of the Rampart.</s></p><p type="margin"> <s><margin.target id="marg1511"></margin.target><emph type="italics"/>He el&longs;ewhere <lb/>cites this as a <lb/>Propo&longs;ition, there­ <lb/>fore I make it of <lb/>that number.<emph.end type="italics"/></s></p><p type="main"> <s>And here I will not omit to note, as a &longs;econd Corrollary dependent <lb/>upon the things demon&longs;trated, that,</s></p><p type="head"> <s>THEOREME VIII. <lb/><arrow.to.target n="marg1512"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1512"></margin.target>Natation and <lb/>Submer&longs;ion, col­ <lb/>lected from the <lb/>thickne&longs;s, exclu­ <lb/>ding the length <lb/>and breadth of <lb/>Plates.</s></p><p type="main"> <s><emph type="italics"/>The Expan&longs;ion of Figure not only is not the Cau&longs;e of the <lb/>Natation of tho&longs;e grave Bodies, which otherwi&longs;e <lb/>do &longs;ubmerge, but al&longs;o the determining what be tho&longs;e <lb/>Boards of Ebony, or Plates of Iron or Gold that will <lb/>&longs;wimme, depends not on it, rather that &longs;ame determina­ <lb/>tion is to be collected from the only thickne&longs;s of tho&longs;e <lb/>Figures of Ebony or Gold, wholly excluding the con­ <lb/>&longs;ideration of length and breadth, as having no way <lb/>any &longs;hare in this Effect.<emph.end type="italics"/></s></p><p type="main"> <s>It hath already been manife&longs;ted, that the only cau&longs;e of the Nata­ <lb/>tion of the &longs;aid Plates, is the reduction of them to be le&longs;s grave <lb/>than the water, by means of the connexion of that Air, which de­ <lb/>&longs;cendeth together with them, and po&longs;&longs;e&longs;&longs;eth place in the water; <lb/>which place &longs;o occupyed, if before the circumfu&longs;ed water diffu&longs;eth <lb/>it &longs;elf to fill it, it be capable of as much water, as &longs;hall weigh equall <lb/>with the Plate, the Plate &longs;hall remain &longs;u&longs;pended, and &longs;inke no <lb/>farther.</s></p> <pb xlink:href="040/01/1142.jpg" pagenum="449"/><p type="main"> <s>Now let us &longs;ee on which of the&longs;e three dimen&longs;ions of the Solid <lb/>depends the terminating, what and how much the Ma&longs;s of that ought <lb/>to be, that &longs;o the a&longs;&longs;i&longs;tance of the Air contiguous unto it, may &longs;uffice <lb/>to render it &longs;pecifically le&longs;s grave than the water, whereupon it may <lb/>re&longs;t without Submer&longs;ion. </s><s>It &longs;hall undoubtedly be found, that the <lb/>length and breadth have not any thing to do in the &longs;aid determina­ <lb/>tion, but only the height, or if you will the thickne&longs;s: for, if we take <lb/>a Plate or Board, as for Example, of Ebony, who&longs;e Altitude hath <lb/>unto the greate&longs;t po&longs;&longs;ible Altitude of the Rampart, the proportion <lb/>above declared, for which cau&longs;e it &longs;wims indeed, but yet not if we <lb/>never &longs;o little increa&longs;e its thickne&longs;s; I &longs;ay, that retaining its thick­ <lb/>ne&longs;s, and encrea&longs;ing its Superficies to twice, four times, or ten times <lb/>its bigne&longs;s, or dmini&longs;ning it by dividing it into four, or &longs;ix, or <lb/>twenty, or a hundred parts, it &longs;hall &longs;till in the &longs;ame manner continue <lb/>to float: but encrea&longs;ing its thickne&longs;s only a Hairs breadth, it will <lb/>alwaies &longs;ubmerge, although we &longs;hould multiply the Superficies a <lb/>hundred and a hundred times. </s><s>Now fora&longs;much as that this is a <lb/>Cau&longs;e, which being added, we adde al&longs;o the Effect, and being remo­ <lb/>ved, it is removed; and by augmenting or le&longs;&longs;ening the length or <lb/>breadth in any manner, the effect of going, or not going to the bot­ <lb/>tom, is not added or removed: I conclude, that the greatne&longs;s and <lb/>&longs;malne&longs;s of the Superficies hath no influence upon the Natation or <lb/>Submer&longs;ion. </s><s>And that the proportion of the Altitude of the Ram­ <lb/>parts of Water, to the Altitude of the Solid, being con&longs;tituted in <lb/>the manner afore&longs;aid, the greatne&longs;s or &longs;malne&longs;s of the Superficies, <lb/>makes not any variation, is manife&longs;t from that which hath been above <lb/>demon&longs;trated, and from this, that, <emph type="italics"/>The Pri&longs;ms and Cylinders which<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1513"></arrow.to.target> <lb/><emph type="italics"/>have the &longs;ame Ba&longs;e, are in proportion to one another as their heights:<emph.end type="italics"/> <lb/>Whence Cylinders or Prifmes, namely, the Board, be they great or <lb/>little, &longs;o that they be all of equall thickne&longs;s, have the &longs;ame proportion <lb/>to their Conterminall Air, which hath for Ba&longs;e the &longs;aid Superficies of <lb/>the Board, and for height the Ramparts of water; &longs;o that alwayes <lb/>of that Air, and of the Board, Solids are compounded, that in Gravity <lb/>equall a Ma&longs;s of water equall to the Ma&longs;s of the Solids, compounded <lb/>of Air, and of the Board: whereupon all the &longs;aid Solids do in the <lb/>&longs;ame manner continue afloat. </s><s>We will conclude in the third place, <lb/>that,</s></p> <pb xlink:href="040/01/1143.jpg" pagenum="450"/><p type="margin"> <s><margin.target id="marg1513"></margin.target>Pri&longs;mes and <lb/>Cylinders ha­ <lb/>ving the &longs;ame <lb/>Ba&longs;e, are to one <lb/>another as their <lb/>heights.</s></p><p type="head"> <s>THEOREME. IX. <lb/><arrow.to.target n="marg1514"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1514"></margin.target>All Figures <lb/>of all Matters, <lb/>float by hep of <lb/>the Rampart re­ <lb/>pleni&longs;hed with <lb/>Air, and &longs;ome <lb/>but only touch <lb/>the water.</s></p><p type="main"> <s><emph type="italics"/>All &longs;orts of Figures of what&longs;oever Matter, albeit more <lb/>grave than the Water, do by Benefit of the &longs;aid Ram­ <lb/>part, not only float, but &longs;ome Figures, though of the <lb/>grave&longs;t Matter, do &longs;tay wholly above Water, wetting <lb/>only the inferiour Surface that toucheth the Water.<emph.end type="italics"/></s></p><p type="main"> <s>And the&longs;e &longs;hall be all Figures, which from the inferiour Ba&longs;e up­ <lb/>wards, grow le&longs;&longs;er and le&longs;&longs;er; the which we &longs;hall exemplifie for <lb/>this time in Piramides or Cones, of which Figures the pa&longs;&longs;ions sre <lb/>common. </s><s>We will demon&longs;trate therefore, that,</s></p><p type="main"> <s><emph type="italics"/>It is po&longs;&longs;ible to form a Piramide, of any what&longs;oever Matter propo&longs;ed, <lb/>which being put with its Ba&longs;e upon the Water, re&longs;ts not only without <lb/>&longs;ubmerging, but without wetting it more then its Ba&longs;e.<emph.end type="italics"/></s></p><p type="main"> <s>For the explication of which it is requi&longs;ite, that we fir&longs;t demon&longs;trate <lb/>the &longs;ub&longs;equent Lemma, namely, that,</s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"/>Solids who&longs;e Ma&longs;&longs;es an&longs;wer in proportion contrarily to<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1515"></arrow.to.target> <lb/><emph type="italics"/>their Specificall Gravities, are equall in Ab&longs;olute <lb/>Gravities.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1515"></margin.target>Solids who&longs;e <lb/>Ma&longs;&longs;es are in <lb/>contrary pro­ <lb/>portion to their <lb/>Specifick Gra­ <lb/>vities, are equall <lb/>in ab&longs;olute Gra <lb/>vity.</s></p><p type="main"> <s>Let A C and B be two Solids, and let the Ma&longs;s A C be to the <lb/>Ma&longs;s B, as the Specificall Gravity of the Solid B, is to the Speci­ <lb/>ficall Gravity of the Solid A C: I &longs;ay, the Solids A C and B are <lb/>equall in ab&longs;olute weight, that is, equally grave. For <lb/><figure id="id.040.01.1143.1.jpg" xlink:href="040/01/1143/1.jpg"/> <lb/>if the Ma&longs;s A C be equall to the Ma&longs;s B, then, by the <lb/>A&longs;&longs;umption, the Specificall Gravity of B, &longs;hall be e­ <lb/>quall to the Specificall Gravity of A C, and being e­ <lb/>quall in Ma&longs;s, and of the &longs;ame Specificall Gravity they <lb/>&longs;hall ab&longs;olutely weigh one as much as another. </s><s>But <lb/>if their Ma&longs;&longs;es &longs;hall be unequall, let the Ma&longs;s A C be greater, and in it <lb/>take the part C, equall to the Ma&longs;s B. And, becau&longs;e the Ma&longs;&longs;es B <lb/>and C are equall; the Ab&longs;olute weight of B, &longs;hall have the &longs;ame pro­ <lb/>portion to the Ab&longs;olute weight of C, that the Specificall Gravity of <lb/>B, hath to the Specificall Gravity of C; or of C A, which is the <lb/>&longs;ame <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>: But look what proportion the Specificall Gravity of <lb/>B, hath to the Specificall Gravity of C A, the like proportion, by the <lb/>A&longs;&longs;umption, hath the Ma&longs;s C A, to the Ma&longs;s B; that is, to the Ma&longs;s C: <pb xlink:href="040/01/1144.jpg" pagenum="451"/>Therefore, the ab&longs;olute weight of B, to the ab&longs;olute weight of C, is <lb/>as the Ma&longs;s A C to the Ma&longs;s <emph type="italics"/>C<emph.end type="italics"/>: But as the Ma&longs;s AC, is to the Ma&longs;s C, <lb/>&longs;o is the ab&longs;olute weight of A C, to the ab&longs;olute weight of C: There­ <lb/>fore the ab&longs;olute weight of B, hath the &longs;ame proportion to the ab&longs;o­ <lb/>lute weight of C, that the ab&longs;olute weight of A C, hath to the ab­ <lb/>&longs;olute weight of C: Therefore, the two Solids A C and B are equall <lb/>in ab&longs;olute Gravity: which was to be demon&longs;trated. </s><s>Having de­ <lb/>mon&longs;trated this, I &longs;ay,</s></p><p type="head"> <s>THEOREME X.</s></p><p type="main"> <s><emph type="italics"/>That it is po&longs;&longs;ible of any a&longs;&longs;igned Matter, to form a Pi-<emph.end type="italics"/> <lb/><arrow.to.target n="marg1516"></arrow.to.target> <lb/><emph type="italics"/>ramide or Cone upon any Ba&longs;e, which being put upon <lb/>the Water &longs;hall not &longs;ubmerge, nor wet any more than <lb/>its Ba&longs;e.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1516"></margin.target>There may be <lb/>Cones and Pira­ <lb/>mides of any <lb/><emph type="italics"/>M<emph.end type="italics"/>atter, which <lb/>demittedinto the <lb/>water, re&longs;t only <lb/>their Ba&longs;es.</s></p><p type="main"> <s>Let the greate&longs;t po&longs;&longs;ible Altitude of the Rampart be the Line D B, <lb/>and the Diameter of the Ba&longs;e of the Cone to be made of any Mat­ <lb/>ter a&longs;&longs;igned B C, at right angles to D B: And as the Specificall Gravity <lb/>of the Matter of the Piramide or Cone to be made, is to the Specificall <lb/>Gravity of the water, &longs;o let the Altitude of the <lb/><figure id="id.040.01.1144.1.jpg" xlink:href="040/01/1144/1.jpg"/> <lb/>Rampart D B, be to the third part of the Piramide <lb/>or Cone A B C, de&longs;cribed upon the Ba&longs;e, who&longs;e <lb/>Diameter is B C: I &longs;ay, that the &longs;aid Cone A B C, <lb/>and any other Cone, lower then the &longs;ame, &longs;hall re&longs;t <lb/>upon the Surface of the water B C without &longs;inking. <lb/></s><s>Draw D F parallel to B C, and &longs;uppo&longs;e the Pri&longs;me <lb/>or Cylinder E C, which &longs;hall be tripple to the Cone <lb/>A B C. And, becau&longs;e the Cylinder D C hath the &longs;ame proportion <lb/>to the Cylinder C E, that the Altitude D B, hath to the Altitude B E: <lb/>But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to <lb/>the third part of the Altitude of the Cone: Therefore, by Equality of <lb/>proportion, the Cylinder D C is to the Cone A B C, as D B is to the <lb/>third part of the Altitude B E: But as D B is to the third part of B E, <lb/>&longs;o is the Specificall Gravity of the Cone A B C, to the Specificall Gra­ <lb/>vity of the water: Therefore, as the Ma&longs;s of the Solid D C, is to the <lb/>Ma&longs;s of the Cone A <emph type="italics"/>B<emph.end type="italics"/> C, &longs;o is the Specificall Gravity of the &longs;aid Cone, <lb/>to the Specificall Gravity of the water: Therefore, by the precedent <lb/>Lemma, the Cone A B C weighs in ab&longs;olute Gravity as much as a <lb/>Ma&longs;s of Water equall to the Ma&longs;s D C: But the water which by the <lb/>impo&longs;ition of the Cone A B C, is driven out of its place, is as much <lb/>as would preci&longs;ely lie in the place D C, and is equall in weight to the <lb/>Cone that di&longs;placeth it: Therefore, there &longs;hall be an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> <lb/>and the Cone &longs;hall re&longs;t without farther &longs;ubmerging. </s><s>And its ma­ <lb/>nife&longs;t,</s></p> <pb xlink:href="040/01/1145.jpg" pagenum="452"/><p type="head"> <s>COROLARY I. <lb/><arrow.to.target n="marg1517"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1517"></margin.target>Among&longs;t Cones <lb/>of the &longs;ame Ba&longs;e, <lb/>tho&longs;e of lea&longs;t Al­ <lb/>titude &longs;hall &longs;ink <lb/>the lea&longs;t.</s></p><p type="main"> <s><emph type="italics"/>That making upon the &longs;ame Ba&longs;is, a Cone of a le&longs;s Altitude, it &longs;hall be <lb/>al&longs;o le&longs;s grave, and &longs;hall &longs;o much the more re&longs;t without Submer&longs;ion.<emph.end type="italics"/></s></p><p type="head"> <s>COROLARY II.</s></p><p type="main"> <s><emph type="italics"/>It is manife&longs;t, al&longs;o, that one may make Cones and Piramids of any Matter <emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1518"></arrow.to.target> <lb/><emph type="italics"/>what&longs;oever, more grave than the water, which being put into the <lb/>water, with the Apix or Point downwards, re&longs;t without Submer&longs;ion. <emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1518"></margin.target>There may be <lb/>Cones and Pira­ <lb/>mides of any <lb/>Matter, which <lb/>demitted with <lb/>the Point down­ <lb/>wards do float a­ <lb/>top.</s></p><p type="main"> <s>Becau&longs;e if we rea&longs;&longs;ume what hath been above demon&longs;trated, of <lb/>Pri&longs;ms and Cylinders, and that on Ba&longs;es equall to tho&longs;e of the <lb/>&longs;aid Cylinders, we make Cones of the &longs;ame Matter, and thrree <lb/>times as high as the Cylinders, they &longs;hall re&longs;t afloat, for that in Ma&longs;s <lb/>and Gravity they &longs;hall be equall to tho&longs;e Cylinders, and by having <lb/>their Ba&longs;es equall to tho&longs;e of the Cylinders, they &longs;hall leave equall <lb/>Ma&longs;&longs;es of Air included within the Ramparts. </s><s>This, which for Exam­ <lb/>ple &longs;ake hath been demon&longs;trated, in Pri&longs;ms, Cylinders, Cones and <lb/>Piramids, might be proved in all other Solid Figures, but it would <lb/>require a whole Volume (&longs;uch is the multitude and variety of their <lb/>Symptoms and Accidents) to comprehend the particuler demon&longs;tration <lb/>of them all, and of their &longs;everall Segments: but I will to avoid prolixity <lb/>in the pre&longs;ent Di&longs;cour&longs;e, content my &longs;elf, that by what I have declared <lb/>every one of ordinary Capacity may comprehend, that there is not <lb/>any Matter &longs;o grave, no not Gold it &longs;elf, of which one may not form <lb/>all &longs;orts of Figures, which by vertue of the &longs;uperiour Air adherent to <lb/>them, and not by the Waters Re&longs;i&longs;tance of Penetration, do remain <lb/>afloat, &longs;o that they &longs;ink not. </s><s>Nay, farther, I will &longs;hew, for removing <lb/>that Error, that,</s></p><p type="head"> <s>THEOREME XI. <lb/><arrow.to.target n="marg1519"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1519"></margin.target>A Piramide or <lb/>Cone, demitted <lb/>with the Point <lb/>downwards &longs;hal <lb/>&longs;wim, with its <lb/>Ba&longs;e downward <lb/>&longs;hall &longs;ink.</s></p><p type="main"> <s><emph type="italics"/>A Piramide or Cone put into the Water, with the Point <lb/>downward &longs;hall &longs;wimme, and the &longs;ame put with the <lb/>Ba&longs;e downwards &longs;hall &longs;inke, and it &longs;hall be impo&longs;&longs;ible <lb/>to make it float.<emph.end type="italics"/></s></p><p type="main"> <s>Now the quite contrary would happen, if the difficulty of Pene­ <lb/>trating the water, were that which had hindred the de&longs;cent, for <lb/>that the &longs;aid Cone is far apter to pierce and penetrate with its &longs;harp <lb/>Point, than with its broad and &longs;pacious Ba&longs;e.</s></p><p type="main"> <s>And, to demon&longs;trate this, let the Cone be <emph type="italics"/>A B C,<emph.end type="italics"/> twice as grave <lb/>as the water, and let its height be tripple to the height of the Rampart <lb/><emph type="italics"/>D A E C<emph.end type="italics"/>: I &longs;ay, fir&longs;t, that being put lightly into the water with the <pb xlink:href="040/01/1146.jpg" pagenum="453"/>Point downwards, it &longs;hall not de&longs;cend to the bot­ <lb/>tom: for the Aeriall Cylinder contained betwixt <lb/><figure id="id.040.01.1146.1.jpg" xlink:href="040/01/1146/1.jpg"/> <lb/>the Ramparts <emph type="italics"/>D A C E,<emph.end type="italics"/> is equall in Ma&longs;s to the <lb/>Cone <emph type="italics"/>A B C<emph.end type="italics"/>; &longs;o that the whole Ma&longs;s of the Solid <lb/>compounded of the Air <emph type="italics"/>D A C E,<emph.end type="italics"/> and of the Cone <lb/><emph type="italics"/>A B C,<emph.end type="italics"/> &longs;hall be double to the Cone <emph type="italics"/>A C B:<emph.end type="italics"/> And, <lb/>becau&longs;e the Cone <emph type="italics"/>A B C<emph.end type="italics"/> is &longs;uppo&longs;ed to be of Matter double in Gra­ <lb/>vity to the water, therefore as much water as the whole Ma&longs;&longs;e <lb/><emph type="italics"/>D A B C E,<emph.end type="italics"/> placed beneath the Levell of the water, weighs as much <lb/>as the Cone <emph type="italics"/>A B C<emph.end type="italics"/>: and, therefore, there &longs;hall be an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> <lb/>and the Cone <emph type="italics"/>A B C<emph.end type="italics"/> &longs;hall de&longs;cend no lower. </s><s>Now, I &longs;ay farther, <lb/>that the &longs;ame Cone placed with the Ba&longs;e downwards, &longs;hall &longs;ink to <lb/>the bottom, without any po&longs;&longs;ibility of returning again, by any means <lb/>to &longs;wimme.</s></p><p type="main"> <s>Let, therefore, the Cone be <emph type="italics"/>A B D,<emph.end type="italics"/> double in Gravity to the <lb/>water, and let its height be tripple the height <lb/><figure id="id.040.01.1146.2.jpg" xlink:href="040/01/1146/2.jpg"/> <lb/>of the Rampart of water L B: It is already <lb/>manife&longs;t, that it &longs;hall not &longs;tay wholly out of <lb/>the water, becau&longs;e the Cylinder being com­ <lb/>prehended betwixt the Ramparts <emph type="italics"/>L B D P,<emph.end type="italics"/> <lb/>equall to the Cone <emph type="italics"/>A B D,<emph.end type="italics"/> and the Matter of <lb/>the Cone, beig double in Gravity to the <lb/>water, it is evident that the weight of the &longs;aid <lb/>Cone &longs;hall be double to the weight of the Ma&longs;s of water equall to the <lb/>Cylinder <emph type="italics"/>L B D P<emph.end type="italics"/>: Therefore it &longs;hall not re&longs;t in this &longs;tate, but <lb/>&longs;hall de&longs;cend.</s></p><p type="head"> <s>COROLARY I.</s></p><p type="main"> <s><emph type="italics"/>I &longs;ay farther; that much le&longs;&longs;e &longs;hall the &longs;aid Cone stay afloat, if one<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1520"></arrow.to.target> <lb/><emph type="italics"/>immerge a part thereof.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1520"></margin.target>Much le&longs;s &longs;hall <lb/>the &longs;aid Cone <lb/>&longs;wim, if one im­ <lb/>merge a part <lb/>thereof.</s></p><p type="main"> <s>Which you may &longs;ee, comparing with the water as well the part <lb/>that &longs;hall immerge as the other above water. </s><s>Let us therefore <lb/>of the Cone A B D, &longs;ubmergeth part N T O S, and advance the <lb/>Point N S F above water. </s><s>The Altitude of the Cone F N S, &longs;hall <lb/>either be more than half the whole Altitude of the Cone F T O, or <lb/>it &longs;hall not be more: if it &longs;hall be more than half, the Cone F N S <lb/>&longs;hall be more than half of the Cylinder E N S C: for the Altitude <lb/>of the Cone F N S, &longs;hall be more than Se&longs;quialter of the Altitude <lb/>of the Cylinder E N S C: And, becau&longs;e the Matter of the Cone is <lb/>&longs;uppo&longs;ed to be double in Specificall Gravity to the water, the water <lb/>which would be contained within the Rampart E N S C, would be <lb/>le&longs;s grave ab&longs;olutely than the Cone F N S; &longs;o that the whole Cone <lb/>F N S cannot be &longs;u&longs;tained by the Rampart: But the part immerged <lb/>N T O S, by being double in Specificall Gravity to the water, &longs;hall <pb xlink:href="040/01/1147.jpg" pagenum="454"/>tend to the bottom: Therefore, the whole <emph type="italics"/>C<emph.end type="italics"/>one F T O, as well in <lb/>re&longs;pect of the part &longs;ubmerged, as the part above water &longs;hall de­ <lb/>&longs;cend to the bottom. </s><s>But if the Altitude of the Point F N S, &longs;hall <lb/>be half the Altitude of the whole Cone F T O, the &longs;ame Altitude of <lb/>the &longs;aid <emph type="italics"/>C<emph.end type="italics"/>one F N S &longs;hall be Se&longs;quialter to the Altitude E N: and, <lb/>therefore, E N S C &longs;hall be double to the Cone F N S; and as much <lb/>water in Ma&longs;s as the <emph type="italics"/>C<emph.end type="italics"/>ylinder E N S C, would weigh as much as the <lb/>part of the <emph type="italics"/>C<emph.end type="italics"/>one F N S. But, becau&longs;e the other immerged part <lb/>N T O S, is double in Gravity to the water, a Ma&longs;s of water equall <lb/>to that compounded of the <emph type="italics"/>C<emph.end type="italics"/>ylinder E N S C, and of the Solid N T O S, <lb/>&longs;hall weigh le&longs;s than the <emph type="italics"/>C<emph.end type="italics"/>one F T O, by as much as the weight of <lb/>a Ma&longs;s of water equall to the Solid N T O S: Therefore, the <emph type="italics"/>C<emph.end type="italics"/>one <lb/>&longs;ha l al&longs;o de&longs;cend. </s><s>Again, becau&longs;e the Solid N T O S, is &longs;eptuple <lb/>to the <emph type="italics"/>C<emph.end type="italics"/>one F N S, to which the <emph type="italics"/>C<emph.end type="italics"/>ylinder E S is double, the propor­ <lb/>tion of the Solid N T O S, &longs;hall be to the <emph type="italics"/>C<emph.end type="italics"/>ylinder E N S C, as &longs;eaven <lb/>to two: Therefore, the whole Solid compounded of the <emph type="italics"/>C<emph.end type="italics"/>ylinder <lb/>E N S C, and of the Solid N T O S, is much le&longs;s than double the <lb/>Solid N T O S: Therefore, the &longs;ingle Solid N T O S, is much graver <lb/>than a Ma&longs;s of water equall to the Ma&longs;s, compounded of the <emph type="italics"/>C<emph.end type="italics"/>y­ <lb/>linder E N S C, and of N T O S.</s></p><p type="head"> <s>COROLARY II. <lb/><arrow.to.target n="marg1521"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1521"></margin.target>Part of the <lb/>Cones towards <lb/>the Cu&longs;pis remo­ <lb/>ved, it &longs;hall &longs;till <lb/>&longs;ink.</s></p><p type="main"> <s><emph type="italics"/>From whence it followeth, that though one &longs;hould remove and take a­ <lb/>way the part of the Cone F N S, the &longs;ole remainder N T O S would <lb/>go to the bottom.<emph.end type="italics"/></s></p><p type="head"> <s>COROLARY III.</s></p><p type="main"> <s><emph type="italics"/>And if we &longs;hould more depre&longs;s the Cone F T O, it would be &longs;o much the<emph.end type="italics"/></s></p><p type="main"> <s><arrow.to.target n="marg1522"></arrow.to.target> <lb/><emph type="italics"/>more impo&longs;&longs;ible that it &longs;hould &longs;u&longs;tain it &longs;elf afloat, the part &longs;ubmerged <lb/>N T O S &longs;till encrea&longs;ing, and the Ma&longs;s of Air contained in the Rampart <lb/>dimini&longs;hing, which ever grows le&longs;s, the more the Cone &longs;ubmergeth.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1522"></margin.target>The more the <lb/>Cone is immer­ <lb/>ged, the more <lb/>impo&longs;&longs;ible is its <lb/>floating.</s></p><p type="main"> <s>That Cone, therefore, that with its Ba&longs;e upwards, and its <lb/><emph type="italics"/>Cu&longs;pis<emph.end type="italics"/> downwards doth &longs;wimme, being dimitted with its Ba&longs;e <lb/>downward mu&longs;t of nece&longs;&longs;ity &longs;inke. </s><s>They have argued farre <lb/>from the truth, therefore, who have a&longs;cribed the cau&longs;e of Natation <lb/>to waters re&longs;i&longs;tance of Divi&longs;ion, as to a pa&longs;&longs;ive principle, and to the <lb/>breadth of the Figure, with which the divi&longs;ion is to be made, as the <lb/>Efficient.</s></p><p type="main"> <s>I come in the fourth place, to collect and conclude the rea&longs;on of <lb/>that which I have propo&longs;ed to the Adver&longs;aries, namely,</s></p> <pb xlink:href="040/01/1148.jpg" pagenum="455"/><p type="head"> <s>THE OREME XII.</s></p><p type="main"> <s><emph type="italics"/>That it is po&longs;&longs;ible to fo m Solid Bodies, of what Figure<emph.end type="italics"/> <lb/><arrow.to.target n="marg1523"></arrow.to.target> <lb/><emph type="italics"/>and greatne&longs;s &longs;oever, that of their own Nature goe <lb/>to the Bottome; But by the help of the Air con­ <lb/>tained in the Rampart, re&longs;t without &longs;ubmerging.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1523"></margin.target>Solids of any <lb/>Figure & great­ <lb/>ne&longs;&longs;e, that natu­ <lb/>rally &longs;ink, may <lb/>by help of the <lb/>Air in the Ram­ <lb/>part &longs;wimme.</s></p><p type="main"> <s>The truth of this Propo&longs;ition is &longs;ufficiently manife&longs;t in all tho&longs;e <lb/>Solid Figures, that determine in their uppermo&longs;t part in a plane <lb/>Superficies: for making &longs;uch Figures of &longs;ome Matter &longs;pecifi­ <lb/>cally as grave as the water, putting them into the water, &longs;o that the <lb/>whole Ma&longs;s be covered, it is manife&longs;t, that they &longs;hall re&longs;t in all <lb/>places, provided, that &longs;uch a Matter equall in weight to the water, <lb/>may be exactly adju&longs;ted: and they &longs;hall by con&longs;equence, re&longs;t or <lb/>lie even with the Levell of the water, without making any Rampart. <lb/></s><s>If, therefore, in re&longs;pect of the Matter, &longs;uch Figures are apt to re&longs;t <lb/>without &longs;ubmerging, though deprived of the help of the Rampart, <lb/>it is manife&longs;t, that they may admit &longs;o much encrea&longs;e of Gravity, <lb/>(without encrea&longs;ing their Ma&longs;&longs;es) as is the weight of as much water <lb/>as would be contained within the Rampart, that is made about their <lb/>upper plane Surface: by the help of which being &longs;u&longs;tained, they <lb/>&longs;hall re&longs;t afloat, but being bathed, they &longs;hall de&longs;cend, having been <lb/>made graver than the water. </s><s>In Figures, therefore, that determine <lb/>above in a plane, we may cleerly comprehend, that the Rampart <lb/>added or removed, may prohibit or permit the de&longs;cent: but in tho&longs;e <lb/>Figures that go le&longs;&longs;ening upwards towards the top, &longs;ome Per&longs;ons <lb/>may, and that not without much &longs;eeming Rea&longs;on, doubt whether <lb/>the &longs;ame may be done, and e&longs;pecially by tho&longs;e which terminate in a <lb/>very acute Point, &longs;uch as are your Cones and &longs;mall Piramids. </s><s>Touch­ <lb/>ing the&longs;e, therefore, as more dubious than the re&longs;t, I will endeavour <lb/>to demon&longs;trate, that they al&longs;o lie under the &longs;ame Accident of going, <lb/>or not going to the Bottom, be they of any whatever bigne&longs;s. </s><s>Let <lb/>therefore the Cone be A B D, made of a matter <lb/>&longs;pecifically as grave as the water; it is manife&longs;t <lb/><figure id="id.040.01.1148.1.jpg" xlink:href="040/01/1148/1.jpg"/> <lb/>that being put all under water, it &longs;hall re&longs;t in <lb/>all places (alwayes provided, that it &longs;hall weigh <lb/>exactly as much as the water, which is almo&longs;t <lb/>impo&longs;&longs;ible to effect) and that any &longs;mall weight <lb/>being added to it, it &longs;hall &longs;ink to the bottom: <lb/>but if it &longs;hall de&longs;cend downwards gently, I &longs;ay, <lb/>that it &longs;hall make the Rampart E S T O, and <lb/>that there &longs;hall &longs;tay out of the water the point A S T, tripple in <lb/>height to the Rampart E S: which is manife&longs;t, for the Matter of the <pb xlink:href="040/01/1149.jpg" pagenum="456"/>Cone weighing equally with the water, the part &longs;ubmerged S B D T, <lb/>becomes indifferent to move downwards or upwards; and the Cone <lb/><emph type="italics"/>A S T,<emph.end type="italics"/> being equall in Ma&longs;s to the water that would be contained in <lb/>the concave of the Rampart <emph type="italics"/>E S T O,<emph.end type="italics"/> &longs;hall be al&longs;o equall unto it in <lb/>Gravity: and, therefore, there &longs;hall be a perfect <emph type="italics"/>Equilibrium,<emph.end type="italics"/> and, <lb/>con&longs;equently, a Re&longs;t. </s><s>Now here ari&longs;eth a doubt, whether the <lb/>Cone <emph type="italics"/>A B D<emph.end type="italics"/> may be made heavier, in &longs;uch &longs;ort, that when it is put <lb/>wholly under water, it goes to the bottom, but yet not in &longs;uch &longs;ort, <lb/>as to take from the Rampart the vertue of &longs;u&longs;taining it that it &longs;ink not, <lb/>and, the rea&longs;on of the doubt is this: that although at &longs;uch time as <lb/>the Cone <emph type="italics"/>A B D<emph.end type="italics"/> is &longs;pecifically as grave as the water, the Rampart <lb/><emph type="italics"/>E S T O<emph.end type="italics"/> &longs;u&longs;taines it, not only when the point <emph type="italics"/>A S T<emph.end type="italics"/> is tripple in <lb/>height to the Altitude of the Rampart <emph type="italics"/>E S,<emph.end type="italics"/> but al&longs;o when a le&longs;&longs;er <lb/>part is above water; [for although in the De&longs;cent of the Cone the <lb/>Point <emph type="italics"/>A S T<emph.end type="italics"/> by little and little dimini&longs;heth, and &longs;o likewi&longs;e the <lb/>Rampart <emph type="italics"/>E S T O,<emph.end type="italics"/> yet the Point dimini&longs;heth in <lb/><figure id="id.040.01.1149.1.jpg" xlink:href="040/01/1149/1.jpg"/> <lb/>greater proportion than the Rampart, in that <lb/>it dimini&longs;heth according to all the three Di­ <lb/>men&longs;ions, but the Rampart according to two <lb/>only, the Altitude &longs;till remaining the &longs;ame; <lb/>or, if you will, becau&longs;e the Cone <emph type="italics"/>S T<emph.end type="italics"/> goes di­ <lb/>mini&longs;hing, according to the proportion of the <lb/>cubes of the Lines that do &longs;ucce&longs;&longs;ively become <lb/>the Diameters of the Ba&longs;es of emergent Cones, <lb/>and the Ramparts dimini&longs;h according to the proportion of the <lb/>Squares of the &longs;ame Lines; whereupon the proportions of the Points <lb/>are alwayes Se&longs;quialter of the proportions of the Cylinders, con­ <lb/>tained within the Rampart; &longs;o that if, for Example, the height of <lb/>the emergent Point were double, or equall to the height of the <lb/>Rampart, in the&longs;e ca&longs;es, the Cylinder contained within the Ram­ <lb/>part, would be much greater than the &longs;aid Point, becau&longs;e it would be <lb/>either &longs;e&longs;quialter or tripple, by rea&longs;on of which it would perhaps <lb/>&longs;erve over and above to fu&longs;tain the whole Cone, &longs;ince the part &longs;ub­ <lb/>merged would no longer weigh any thing;] yet, neverthele&longs;s, when <lb/>any Gravity is added to the whole Ma&longs;s of the Cone, &longs;o that al&longs;o the <lb/>part &longs;ubmerged is not without &longs;ome exce&longs;&longs;e of Gravity above the <lb/>Gravity of the water, it is not manife&longs;t, whether the Cylinder con­ <lb/>tained within the Rampart, in the de&longs;cent that the Cone &longs;hall make, <lb/>can be reduced to &longs;uch a proportion unto the emergent Point, and to <lb/>&longs;uch an exce&longs;&longs;e of Ma&longs;s above the Ma&longs;s of it, as to compen&longs;ate the <lb/>exce&longs;&longs;e of the Cones Specificall Gravity above the Gravity of the wa­ <lb/>ter: and the Scruple ari&longs;eth, becau&longs;e that howbeit in the de&longs;cent <lb/>made by the Cone, the emergent Point <emph type="italics"/>A S T<emph.end type="italics"/> dimini&longs;heth, whereby <lb/>there is al&longs;o a diminution of the exce&longs;s of the Cones Gravity above <pb xlink:href="040/01/1150.jpg" pagenum="459"/>the Gravity of the water, yet the ca&longs;e &longs;tands &longs;o, that the Rampart <lb/>doth al&longs;o contract it &longs;elf, and the Cylinder contained in it doth de­ <lb/>mini&longs;h. </s><s>Neverthele&longs;s it &longs;hall be demon&longs;trated, how that the Cone <lb/><emph type="italics"/>A B D<emph.end type="italics"/> being of any &longs;uppo&longs;ed bigne&longs;&longs;e, and made at the fir&longs;t of a <lb/>Matter exactly equall in Gravity to the Water, if there may <lb/>be affixed to it &longs;ome Weight, by means of which it may de&longs;cend to <lb/>the bottom, when &longs;ubmerged under water, it may al&longs;o by vertue of <lb/>the Rampart &longs;tay above without &longs;inking.</s></p><p type="main"> <s>Let, therefore, the Cone <emph type="italics"/>A B D<emph.end type="italics"/> be of any &longs;uppo&longs;ed greatne&longs;&longs;e, <lb/>and alike in &longs;pecificall Gravity to the water. </s><s>It is manife&longs;t, that <lb/>being put lightly into the water, it &longs;hall re&longs;t without de&longs;cending; <lb/>and it &longs;hall advance above water, the Point <lb/><figure id="id.040.01.1150.1.jpg" xlink:href="040/01/1150/1.jpg"/> <lb/><emph type="italics"/>AS T,<emph.end type="italics"/> tripple in height to the height of the <lb/>Rampart <emph type="italics"/>E S<emph.end type="italics"/>: Now, &longs;uppo&longs;e the Cone <emph type="italics"/>A B D<emph.end type="italics"/> <lb/>more depre&longs;&longs;ed, &longs;o that it advance above wa­ <lb/>ter, only the Point <emph type="italics"/>A I R,<emph.end type="italics"/> higher by half than <lb/>the Point <emph type="italics"/>A S T,<emph.end type="italics"/> with the Rampart about it <lb/><emph type="italics"/>C I R N.<emph.end type="italics"/> And, becau&longs;e, the Cone <emph type="italics"/>A B D<emph.end type="italics"/> is <lb/>to the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> as the cube of the Line <emph type="italics"/>S T<emph.end type="italics"/> <lb/>is to the cube of the Line <emph type="italics"/>I R,<emph.end type="italics"/> but the Cylin­ <lb/>der <emph type="italics"/>E S T O,<emph.end type="italics"/> is to the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> as the Square of <emph type="italics"/>S T<emph.end type="italics"/> to <lb/>the Square of <emph type="italics"/>I R,<emph.end type="italics"/> the Cone <emph type="italics"/>A S T<emph.end type="italics"/> &longs;hall be Octuple to the Cone <lb/><emph type="italics"/>A I R,<emph.end type="italics"/> and the Cylinder <emph type="italics"/>E S T O,<emph.end type="italics"/> quadruple to the Cylinder <emph type="italics"/>C I R N<emph.end type="italics"/>: <lb/>But the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> is equall to the Cylinder E <emph type="italics"/>S T O<emph.end type="italics"/>: Therefore, <lb/>the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> &longs;hall be double to the Cone <emph type="italics"/>A I R:<emph.end type="italics"/> and the <lb/>water which might be contained in the Rampart <emph type="italics"/>C I R N,<emph.end type="italics"/> would be <lb/>double in Ma&longs;s and in Weight to the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> and, therefore, <lb/>would be able to &longs;u&longs;tain the double of the Weight of the Cone <emph type="italics"/>AIR<emph.end type="italics"/>: <lb/>Therefore, if to the whole Cone <emph type="italics"/>A B D,<emph.end type="italics"/> there be added as much <lb/>Weight as the Gravity of the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> that is to &longs;ay, the eighth <lb/>part of the weight of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> it al&longs;o &longs;hall be &longs;u&longs;tained by <lb/>the Rampart <emph type="italics"/>C I R N,<emph.end type="italics"/> but without that it &longs;hall go to the bottome: <lb/>the Cone <emph type="italics"/>A B D,<emph.end type="italics"/> being, by the addition of the eighth part of the <lb/>weight of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> made &longs;pecifically more grave than the <lb/>water. </s><s>But if the Altitude of the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> were two thirds <lb/>of the Altitude of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> the Cone <emph type="italics"/>A S T<emph.end type="italics"/> would be to the <lb/>Cone <emph type="italics"/>A I R,<emph.end type="italics"/> as twenty &longs;even to eight; and the Cylinder <emph type="italics"/>E S T O,<emph.end type="italics"/> to <lb/>the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> as nine to four, that is, as twenty &longs;even to <lb/>twelve; and, therefore, the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> to the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> <lb/>as twelve to eight; and the exce&longs;s of the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> above <lb/>the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> to the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> as four to twenty &longs;even: there­ <lb/>fore if to the Cone <emph type="italics"/>A B D<emph.end type="italics"/> be added &longs;o much weight as is the four <lb/>twenty &longs;evenths of the weight of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> which is a little <lb/>more then its &longs;eventh part, it al&longs;o &longs;hall continue to &longs;wimme, and <pb xlink:href="040/01/1151.jpg" pagenum="460"/>the height of the emergent Point &longs;hall be double to the height of the <lb/>Rampart. </s><s>This that hath been demon&longs;trated in Cones, exactly holds <lb/>in Piramides, although the one or the other &longs;hould be very &longs;harp in <lb/><arrow.to.target n="marg1524"></arrow.to.target> <lb/>their Point or Cu&longs;pis: From whence we conclude, that the &longs;ame <lb/>Accident &longs;hall &longs;o much the more ea&longs;ily happen in all other Figures, <lb/>by how much the le&longs;s &longs;harp the Tops &longs;hall be, in which they deter­ <lb/>mine, being a&longs;&longs;i&longs;ted by more &longs;pacious Ramparts.</s></p><p type="margin"> <s><margin.target id="marg1524"></margin.target>Natatiou ea&longs;i­ <lb/>e&longs;t effected in <lb/>Figures broad <lb/>toward the top.</s></p><p type="head"> <s>THEOREME XIII. <lb/><arrow.to.target n="marg1525"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1525"></margin.target>All Figures &longs;ink <lb/>or &longs;wim, upon <lb/>bathing or not <lb/>bathing of their <lb/>tops.</s></p><p type="main"> <s><emph type="italics"/>All Figures, therefore, of whatever greatne&longs;&longs;e, may <lb/>go, and not go, to the Bottom, according as their Sumi­ <lb/>ties or Tops &longs;hall be bathed or not bathed.<emph.end type="italics"/></s></p><p type="main"> <s>And this Accident being common to all &longs;orts of Figures, without <lb/>exception of &longs;o much as one. </s><s>Figure hath, therefore, no part <lb/>in the production of this Effect, of &longs;ometimes &longs;inking, and &longs;ome­ <lb/>times again not &longs;inking, but only the being &longs;ometimes conjoyned <lb/>to, and &longs;ometimes &longs;eperated from, the &longs;upereminent Air: which <lb/>cau&longs;e, in fine, who &longs;o &longs;hall rightly, and, as we &longs;ay, with both his <lb/>Eyes, con&longs;ider this bu&longs;ine&longs;s, will find that it is reduced to, yea, that <lb/>it really is the &longs;ame with, the true, Naturall and primary cau&longs;e of <lb/>Natation or Submer&longs;ion; to wit, the exce&longs;s or deficiency of the <lb/>Gravity of the water, in relation to the Gravity of that Solid Mag­ <lb/>nitude, that is demitted into the water. </s><s>For like as a Plate of Lead, <lb/>as thick as the back of a Knife, which being put into the water by it <lb/>&longs;elf alone goes to the bottom, if upon it you fa&longs;ten a piece of Cork <lb/>four fingers thick, doth continue afloat, for that now the Solid that <lb/>is demitted in the water, is not, as before, more grave than the water, <lb/>but le&longs;s, &longs;o the Board of Ebony, of its own nature more grave than <lb/>water; and, therefore, de&longs;cending to the bottom, when it is demit­ <lb/>ted by it &longs;elf alone into the water, if it &longs;hall be put upon the water, <lb/>conjoyned with an Expanded vail of Air, that together with the <lb/>Ebony doth de&longs;cend, and that it be &longs;uch, as that it doth make with <lb/>it a compound le&longs;s grave than &longs;o much water in Ma&longs;s, as equalleth <lb/>the Ma&longs;s already &longs;ubmerged and depre&longs;&longs;ed beneath the Levell of the <lb/>waters Surface, it &longs;hall not de&longs;cend any farther, but &longs;hall re&longs;t, for <lb/>no other than the univer&longs;all and mo&longs;t common cau&longs;e, which is that <lb/>Solid Magnitudes, le&longs;s grave <emph type="italics"/>in&longs;pecie<emph.end type="italics"/> than the water, go not to the <lb/>bottom.</s></p><p type="main"> <s>So that if one &longs;hould take a Plate of Lead, as for Example, a finger <lb/>thick, and an handfull broad every way, and &longs;hould attempt to make <lb/>it &longs;wimme, with putting it lightly on the water, he would lo&longs;e his <lb/>Labour, becau&longs;e that if it &longs;hould be depre&longs;&longs;ed an Hairs breadth be­ <pb xlink:href="040/01/1152.jpg" pagenum="461"/>yond the po&longs;&longs;ible Altitude of the Ramparts of water, it would dive <lb/>and &longs;ink; but if whil&longs;t it is going downwards, one &longs;hould make <lb/>certain Banks or Ramparts about it, that &longs;hould hinder the do fu&longs;ion <lb/>of the water upon the &longs;aid Plate, the which Banks &longs;hould ri&longs;e &longs;o <lb/>high, as that they might be able to contain as much water, as &longs;hould <lb/>weigh equally with the &longs;aid Plate, it would, without all Que&longs;tion, <lb/>de&longs;cend no lower, but would re&longs;t, as being &longs;u&longs;tained by vertue of <lb/>the Air contained within the afore&longs;aid Ramparts: and, in &longs;hort, <lb/>there would be a Ve&longs;&longs;ell by this means formed with the bottom of <lb/>Lead. </s><s>But if the thinne&longs;s of the Lead &longs;hall be &longs;uch, that a very <lb/>&longs;mall height of Rampart would &longs;uffice to contain &longs;o much Air, as might <lb/>keep it afloat, it &longs;hall al&longs;o re&longs;t without the Artificiall Banks or Ram­ <lb/>parts, but yet not without the Air, becau&longs;e the Air by it &longs;elf makes <lb/>Banks &longs;ufficient for a &longs;mall height, to re&longs;i&longs;t the Superfu&longs;ion of the <lb/>water: &longs;o that that which in this ca&longs;e &longs;wimmes, is as it were a <lb/>Ve&longs;&longs;ell filled with Air, by vertue of which it continueth afloat.</s></p><p type="main"> <s>I will, in the la&longs;t place, with an other Experimeut, attempt to <lb/>remove all difficulties, if &longs;o be there &longs;hould yet be any doubt le&longs;t in <lb/>any one, touching the opperation of this ^{*}Continuity of the Air, with </s></p><p type="main"> <s><arrow.to.target n="marg1526"></arrow.to.target> <lb/>the thin Plate which &longs;wims, and afterwards put an end to this part of <lb/>my di&longs;cour&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1526"></margin.target>*Or rather Cor­ <lb/>tiguity,</s></p><p type="main"> <s>I &longs;uppo&longs;e my &longs;elf to be que&longs;tioning with &longs;ome of my Oponents.</s></p><p type="main"> <s>Whether Figure have any influence upon the encrea&longs;e or diminu­ <lb/><arrow.to.target n="marg1527"></arrow.to.target> <lb/>tion of the Re&longs;i&longs;tance in any Weight again&longs;t its being rai&longs;ed in the <lb/>Air, and I &longs;uppo&longs;e, that I am to maintain the Affirmative, a&longs;&longs;ert­ <lb/>ing that a Ma&longs;s of Lead, reduced to the Figure of a Ball, &longs;hall be <lb/>rai&longs;ed with le&longs;s force, then if the &longs;ame had been made into a thinne <lb/>and broad Plate, becau&longs;e that it in this &longs;pacious Figure, hath a great <lb/>quantity of Air to penetrate, and in that other, more compacted and <lb/>contracted very little: and to demon&longs;trate the truth of &longs;uch my O­ <lb/>pinion, I will hang in a &longs;mall thred fir&longs;t the Ball or Bullet, and put <lb/>that into the water, tying the thred that upholds it to one end of <lb/>the Ballance that I hold in the Air, and to the other end I by degrees <lb/>adde &longs;o much Weight, till that at la&longs;t it brings up the Ball of Lead <lb/>out of the water: to do which, &longs;uppo&longs;e a Gravity of thirty Ounces <lb/>&longs;ufficeth; I afcerwards reduce the &longs;aid Lead into a flat and thinne <lb/>Plate, the which I likewi&longs;e put into the water, &longs;u&longs;pended by three <lb/>threds, which hold it parallel to the Surface of the water, and put­ <lb/>ting in the &longs;ame manner, Weights to the other end, till &longs;uch time as <lb/>the Place comes to be rai&longs;ed and drawn out of the water: I finde <lb/>that thirty &longs;ix ounces will not &longs;uffice to &longs;eperate it from the water, <lb/>and rai&longs;e it thorow the Air: and arguing from this Experiment, I af­ <lb/>firm, that I have fully demon&longs;trated the truth of my Propo&longs;ition. <lb/></s><s>He re my Oponents de&longs;ires me to look down, &longs;hewing me a thing <pb xlink:href="040/01/1153.jpg" pagenum="462"/>which I had not before ob&longs;erved, to wit, that in the A&longs;cent of the <lb/>Plate out of the water, it draws after it another Plate <emph type="italics"/>(if I may &longs;o <lb/>call it)<emph.end type="italics"/> of water, which before it divides and parts from the inferiour <lb/>Surface of the Plate of Lead, is rai&longs;ed above the Levell of the other <lb/>water, more than the thickne&longs;s of the back of a Knife: Then he <lb/>goeth to repeat the Experiment with the Ball, and makes me &longs;ee, <lb/>that it is but a very &longs;mall quantity of water, which cleaves to its <lb/>compacted and contracted Figure: and then he &longs;ubjoynes, that its <lb/>no wonder, if in &longs;eperating the thinne and broad Plate from the <lb/>water, we meet with much greater Re&longs;i&longs;tance, than in &longs;eperating the <lb/>Ball, &longs;ince together with the Plate, we are to rai&longs;e a great quantity of <lb/>water, which occurreth not in the Ball: He telleth me moreover, <lb/>how that our Que&longs;tion is, whether the Re&longs;i&longs;tance of Elevation be <lb/>greater in a dilated Plate of Lead, than in a Ball, and not whether <lb/>more re&longs;i&longs;teth a Plate of Lead with a great quantity of water, or a <lb/>Ball with a very little water: He &longs;heweth me in the clo&longs;e, that the <lb/>putting the Plate and the Ball fir&longs;t into the water, to make proofe <lb/>thereby of their Re&longs;i&longs;tance in the Air, is be&longs;ides our ca&longs;e, which <lb/>treats of Elivating in the Air, and of things placed in the Air, and <lb/>not of the Re&longs;i&longs;tance that is made in the Confines of the Air and <lb/>water, and by things which are part in Air and part in water: and <lb/>la&longs;tly, they make me feel with my hand, that when the thinne Plate <lb/>is in the Air, and free from the weight of the water, it is rai&longs;ed with <lb/>the very &longs;ame Force that rai&longs;eth the Ball. </s><s>Seeing, and under&longs;tand­ <lb/>ing the&longs;e things, I know not what to do, unle&longs;s to grant my &longs;elf con­ <lb/>vinced, and to thank &longs;uch a Friend, for having made me to &longs;ee that <lb/>which I never till then ob&longs;erved: and, being adverti&longs;ed by this &longs;ame <lb/>Accident, to tell my Adver&longs;aries, that our Que&longs;tion is, whether a <lb/>Board and a Ball of Ebony, equally go to the bottom in water, and <lb/>not a Ball of Ebony and a Board of Ebony, joyned with another <lb/>flat Body of Air: and, farthermore, that we &longs;peak of &longs;inking, and <lb/>not &longs;inking to the bottom, in water, and not of that which happeneth <lb/>in the Confines of the water and Air to Bodies that be part in the <lb/>Air, and part in the water; nor much le&longs;s do we treat of the greater <lb/>or le&longs;&longs;er Force requi&longs;ite in &longs;eperating this or that Body from the Air; <lb/>not omitting to tell them, in the la&longs;t place, that the Air doth re&longs;i&longs;t, <lb/>and gravitate downwards in the water, ju&longs;t &longs;o much as the water (if <lb/>I may &longs;o &longs;peak) gravitates and re&longs;i&longs;ts upwards in the Air, and that the <lb/>&longs;ame force is required to &longs;inke a Bladder under water, that is full of <lb/>Air, as to rai&longs;e it in the Air, being full of water, removing the con­ <lb/>&longs;ideration of the weight of that Filme or Skinne, and confidering the <lb/>water and the Air only. </s><s>And it is likewi&longs;e true, that the &longs;ame Force <lb/>is required to &longs;ink a Cup or &longs;uch like Ve&longs;&longs;ell under water, whil&longs;t it is <lb/>full of Air, as to rai&longs;e it above the Superficies of the water, keeping <pb xlink:href="040/01/1154.jpg" pagenum="463"/>it with the mouth downwards; whil&longs;t it is full of water, which is <lb/>con&longs;trained in the &longs;ame manner to follow the Cup which contains it, <lb/>and to ri&longs;e above the other water into the Region of the Air, as the <lb/>Air is forced to follow the &longs;ame Ve&longs;&longs;ell under the Surface of the wa­ <lb/>ter, till that in this ca&longs;e the water, &longs;urmounting the brimme of the <lb/>Cup, breaks in, driving thence the Air, and in that ca&longs;e, the &longs;aid <lb/>brimme coming out of the water, and arriving to the Confines of the <lb/>Air, the water falls down, and the Air &longs;ub-enters to fill the cavity of <lb/>the Cup: upon which en&longs;ues, that he no le&longs;s tran&longs;gre&longs;&longs;es the Arti­ <lb/>cles of the <emph type="italics"/>Convention,<emph.end type="italics"/> who produceth a Plate conjoyned with much <lb/>Air, to &longs;ee if it de &longs;eend to the bottom in water, then he that makes <lb/>proof of the Re&longs;i&longs;tance again&longs;t Elevation in Air with a Plate of Lead, <lb/>joyned with a like quantity of water.</s></p><p type="margin"> <s><margin.target id="marg1527"></margin.target>An Experi­ <lb/>ment of the op­ <lb/>peration of Fi­ <lb/>gures, in en­ <lb/>crea&longs;ing or le&longs;­ <lb/>&longs;ening of the <lb/>Airs Re&longs;i&longs;tance <lb/>of Divi&longs;ion.</s></p><p type="main"> <s>I have &longs;aid all that I could at pre&longs;ent think of, to maintain the <lb/><arrow.to.target n="marg1528"></arrow.to.target> <lb/>A&longs;&longs;ertion I have undertook. </s><s>It remains, that I examine that which <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath writ of this matter towards the end of his Book <emph type="italics"/>De Cælo<emph.end type="italics"/>; <lb/>wherein I &longs;hall note two things: the one that it being true as hath <lb/><arrow.to.target n="marg1529"></arrow.to.target> <lb/>been demon&longs;trated, that Figure hath nothing to do about the moving <lb/>or not moving it &longs;elf upwards or downwards, it &longs;eemes that <emph type="italics"/>Aristotle<emph.end type="italics"/> <lb/>at his fir&longs;t falling upon this Sp. </s><s>culation, was of the &longs;ame opinion, as <lb/>in my opinion may be collected from the examination of his words. <lb/></s><s>Tis true, indeed, that in e&longs;&longs;aying afterwards to render a rea&longs;on of <lb/>&longs;uch effect, as not having in my conceit hit upon the right, (which <lb/>in the &longs;econd place I will examine) it &longs;eems that he is brought to <lb/>admit the largene&longs;&longs;e of Figure, to be intere&longs;&longs;ed in this operation. <lb/></s><s>As to the fir&longs;t particuler, hear the preci&longs;e words of <emph type="italics"/>Aristotle.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1528"></margin.target><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> opi­ <lb/>nion touching <lb/>the Operation <lb/>of Figure ex­ <lb/>amined.</s></p><p type="margin"> <s><margin.target id="marg1529"></margin.target><emph type="italics"/>Ari&longs;tot de Cælo,<emph.end type="italics"/> <lb/>Lib. 4. Cap. 66.</s></p><p type="main"> <s><emph type="italics"/>Figures are not the Cau&longs;es of moving &longs;imply upwards or downwards,<emph.end type="italics"/> <lb/><arrow.to.target n="marg1530"></arrow.to.target> <lb/><emph type="italics"/>but of moving more &longs;lowly or &longs;wiftly, and by what means this comes to <lb/>pa&longs;s, it is not difficult to &longs;ee.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="marg1530"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> makes <lb/>not Figure the <lb/>cau&longs;e of Motion <lb/>ab&longs;olutely, but <lb/>of &longs;wi&longs;t or &longs;low <lb/>motion,</s></p><p type="main"> <s>Here fir&longs;t I note, that the terms being four, which fall under the <lb/>pre&longs;ent con&longs;ideration, namely, Motion, Re&longs;t, Slowly and Swiftly: <lb/><arrow.to.target n="marg1531"></arrow.to.target> <lb/>And <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> naming Figures as Cau&longs;es of Tardity and Velocity, ex­ <lb/>cluding them from being the Cau&longs;e of ab&longs;olute and &longs;imple Motion, <lb/>it &longs;eems nece&longs;&longs;ary, that he exclude them on the other &longs;ide, from being <lb/>the Cau&longs;e of Re&longs;t, &longs;o that his meaning is this. </s><s>Figures are not the <lb/>Cau&longs;es of moving or not moving ab&longs;olutely, but of moving quickly <lb/>or &longs;lowly: and, here, if any &longs;hould &longs;ay the mind of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> is to <lb/>exclude Figures from being Cau&longs;es of Motion, but yet not from <lb/>being Cau&longs;es of Re&longs;t, &longs;o that the &longs;ence would be to remove from <lb/>Figures, there being the Cau&longs;es of moving &longs;imply, but yet not there <lb/>being Cau&longs;es of Re&longs;t, I would demand, whether we ought with <lb/><emph type="italics"/>Aristotle<emph.end type="italics"/> to under&longs;tand, that all Figures univer&longs;ally, are, in &longs;ome <lb/>manner, the cau&longs;es of Re&longs;t in tho&longs;e Bodies, which otherwi&longs;e would <lb/>move, or el&longs;e &longs;ome particular Figures only, as for Example, broad <pb xlink:href="040/01/1155.jpg" pagenum="464"/>and thinne Figures: If all indifferently, then every Body &longs;hall re&longs;t: <lb/>becau&longs;e every Body hath &longs;ome Figure, which is fal&longs;e: but if &longs;ome <lb/>particular Figures only may be in &longs;ome manner a Cau&longs;e of Re&longs;t, as, <lb/>for Example, the broad, then the others would be in &longs;ome manner <lb/>the Cau&longs;es of Motion: for if from &longs;eeing &longs;ome Bodies of a contracted <lb/>Figure move, which after dilated into Plates re&longs;t, may be inferred, <lb/>that the Amplitude of Figure hath a part in the Cau&longs;e of that Re&longs;t; <lb/>&longs;o from &longs;eeing &longs;uch like Figures re&longs;t, which afterwards contracted <lb/>move, it may with the &longs;ame rea&longs;on be affirmed, that the united and <lb/>contracted Figure, hath a part in cau&longs;ing Motion, as the remover of <lb/>that which impeded it: The which again is directly oppo&longs;ite to what <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aith, namely, that Figures are not the Cau&longs;es of Motion. <lb/></s><s>Be&longs;ides, if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had admitted and not excluded Figures from be­ <lb/>ing Cau&longs;es of not moving in &longs;ome Bodies, which moulded into ano­ <lb/>ther Figure would move, he would have impertinently propounded <lb/>in a dubitative manner, in the words immediately following, whence <lb/>it is, that the large and thinne Plates of Lead or Iron, re&longs;t upon the <lb/>water, &longs;ince the Cau&longs;e was apparent, namely, the Amplitude of <lb/>Figure. </s><s>Let us conclude, therefore, that the meaning of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>in this place is to affirm, that Figures are not the Cau&longs;es of ab&longs;olutely <lb/>moving or not moving, but only of moving &longs;wiftly or &longs;lowly: which <lb/>we ought the rather to believe, in regard it is indeed a me&longs;t true con­ <lb/>ceipt and opinion. </s><s>Now the mird of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> being &longs;uch, and ap­ <lb/>pearing by con&longs;equence, rather contrary at the fir&longs;t &longs;ight, then fa­ <lb/>vourable to the a&longs;&longs;ertion of the Oponents, it is nece&longs;&longs;ary, that their <lb/>Interpretation be not exactly the &longs;ame with that, but &longs;uch, as being <lb/>in part under&longs;tood by &longs;ome of them, and in part by others, was &longs;et <lb/>down: and it may ea&longs;ily be indeed &longs;o, being an Interpretation <lb/>con&longs;onent to the &longs;ence of the more famous Interpretors, which is, <lb/>that the Adverbe <emph type="italics"/>Simply<emph.end type="italics"/> or <emph type="italics"/>Ab&longs;olutely,<emph.end type="italics"/> put in the Text, orght not to <lb/>be joyned to the Verbe to <emph type="italics"/>Move,<emph.end type="italics"/> but with the Noun <emph type="italics"/>Cau&longs;es<emph.end type="italics"/>: &longs;o that <lb/>the purport of <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> words, is to affirm, That Figures are not the <lb/>Cau&longs;es ab&longs;olutely of moving or not moving, but yet are Cau&longs;es <emph type="italics"/>Se­ <lb/>cundum quid, viz<emph.end type="italics"/> in &longs;ome &longs;ort; by which means, they are called <lb/>Auxiliary and Concomitant Cau&longs;es: and this Propo&longs;ition is received <lb/>and a&longs;&longs;erted as true by <emph type="italics"/>Signor Buonamico Lib.<emph.end type="italics"/> 5. <emph type="italics"/>Cap.<emph.end type="italics"/> 28. where he <lb/>thus writes. <emph type="italics"/>There are other Cau&longs;es concomitant, by which &longs;ome <lb/>things float, and others &longs;ink, among which the Figures of Bodies hath <lb/>the fir&longs;t place,<emph.end type="italics"/> &c.</s></p><p type="margin"> <s><margin.target id="marg1531"></margin.target>Lib. 4. Cap. 61 <lb/>Text. </s><s>42.</s></p><p type="main"> <s>Concerning this Propo&longs;ition, I meet with many doubts and diffi­ <lb/>culties, for which me thinks the words of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> are not capable of <lb/>&longs;uch a con&longs;truction and &longs;ence, and the difficulties are the&longs;e.</s></p><p type="main"> <s>Fir&longs;t in the order and di&longs;po&longs;ure of the words of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> the par­ <lb/>ticle <emph type="italics"/>Simpliciter,<emph.end type="italics"/> or if you will <emph type="italics"/>ab&longs;oluté,<emph.end type="italics"/> is conjoyned with the Verb <pb xlink:href="040/01/1156.jpg" pagenum="465"/><emph type="italics"/>to move,<emph.end type="italics"/> and &longs;eperated from the Noun <emph type="italics"/>Cau&longs;es,<emph.end type="italics"/> the which is a great <lb/>pre&longs;umption in my favour, &longs;eeing that the writing and the Text <lb/>&longs;aith, Figures are not the Cau&longs;e of moving &longs;imply upwards or <lb/>downwards, but of quicker or &longs;lower Motion: and, &longs;aith not, <lb/>Figures are not &longs;imply the Cau&longs;es of moving upwards or down­ <lb/>wards, and when the words of a Text receive, tran&longs;po&longs;ed, a &longs;ence <lb/>different from that which they found, taken in the order wherein <lb/>the Author di&longs;po&longs;eth them, it is not convenient to inverte them. <lb/></s><s>And who will affirm that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> de&longs;iring to write a Propo&longs;ition, <lb/>would di&longs;po&longs;e the words in &longs;uch &longs;ort, that they &longs;hould import a <lb/>different, nay, a contrary &longs;ence? </s><s>contrary, I &longs;ay, becau&longs;e under­ <lb/>&longs;tood as they are written; they &longs;ay, that Figures are not the <lb/>Cau&longs;es of Motion, but inverted, they &longs;ay, that Figures are the <lb/>Cau&longs;es of Motion, &c.</s></p><p type="main"> <s>Moreover, if the intent of <emph type="italics"/>Aristotle<emph.end type="italics"/> had been to &longs;ay, that Figures <lb/>are not &longs;imply the Cau&longs;es of moving upwards or downwards, but <lb/>only Cau&longs;es <emph type="italics"/>Secundum quid,<emph.end type="italics"/> he would not have adjoyned tho&longs;e <lb/>words, <emph type="italics"/>but they are Cau&longs;es of the more &longs;wift or &longs;low Motion<emph.end type="italics"/>; yea, the <lb/>&longs;ubjoining this would have been not only &longs;uperfluous but fal&longs;e, for <lb/>that the whole tenour of the Propo&longs;ition would import thus much. <lb/></s><s>Figures are not the ab&longs;olute Cau&longs;es of moving upwards or down­ <lb/>wards, but are the ab&longs;olute Cau&longs;e of the &longs;wift or &longs;low Motion; <lb/>which is not true: becau&longs;e the primary Cau&longs;es of greater or le&longs;&longs;er <lb/>Velocity, are by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in the 4th of his <emph type="italics"/>Phy&longs;icks, Text.<emph.end type="italics"/> 71. attri­ <lb/>buted to the greater or le&longs;&longs;er Gravity of Moveables, compared a­ <lb/>mong them&longs;elves, and to the greater or le&longs;&longs;er Re&longs;i&longs;tance of the <lb/><emph type="italics"/>Medium's,<emph.end type="italics"/> depending on their greater or le&longs;s Cra&longs;&longs;itude: and the&longs;e <lb/>are in&longs;erted by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> as the primary Cau&longs;es; and the&longs;e two only <lb/>are in that place nominated: and Figure comes afterwards to be <lb/>con&longs;idered, <emph type="italics"/>Text.<emph.end type="italics"/> 74. rather as an In&longs;trumentall Cau&longs;e of the force <lb/>of the Gravity, the which divides either with the Figure, or with <lb/>the <emph type="italics"/>Impetus<emph.end type="italics"/>; and, indeed, Figure by it &longs;elf without the force of <lb/>Gravity or Levity, would opperate nothing.</s></p><p type="main"> <s>Iadde, that if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had an opinion that Figure had been in <lb/>&longs;ome &longs;ort the Cau&longs;e of moving or not moving, the inqui&longs;ition <lb/>which he makes immediately in a doubtfull manner, whence it <lb/>comes, that a Plate of Lead flotes, would have been impertinent; <lb/>for if but ju&longs;t before he had &longs;aid, that Figure was in a certain &longs;ort <lb/>the Cau&longs;e of moving or not moving, he needed not to call in <lb/>Que&longs;tion, by what Cau&longs;e the Plate of Lead &longs;wims, and then a&longs;cri­ <lb/>bing the Cau&longs;e to its Figure; and framing a di&longs;cour&longs;e in this manner. <lb/></s><s>Figure is a Cau&longs;e <emph type="italics"/>Secundum quid<emph.end type="italics"/> of not &longs;inking: but, now, if it be <lb/>doubted, for what Cau&longs;e a thin Plate of Lead goes not to the bottom; <lb/>it &longs;hall be an&longs;wered, that that proceeds from its Figure: a di&longs;cour&longs;e <pb xlink:href="040/01/1157.jpg" pagenum="466"/>which would be indecent in a Child, much more in <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; For <lb/>where is the occa&longs;ion of doubting? </s><s>And who &longs;ees not, that if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>had held, that Figure was in &longs;ome &longs;ort a Cau&longs;e of Natation, he <lb/>would without the lea&longs;t He&longs;itation have writ; That Figure is in a <lb/>certain &longs;ort the Cau&longs;e of Natation, and therefore the Plate of Lead <lb/>in re&longs;pect of its large and expatiated Figure &longs;wims; but if we take <lb/>the propo&longs;ition of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> as I &longs;ay, and as it is writte n, and as in­ <lb/>deed it is true, the en&longs;uing words come in very oppo&longs;itely, as well in <lb/>the introduction of &longs;wift and &longs;low, as in the que&longs;tion, which very <lb/>pertinently offers it &longs;elf, and would &longs;ay thus much.</s></p><p type="main"> <s>Figures are not the Cau&longs;e of moving or not moving &longs;imply up­ <lb/>wards or downwards, but of moving more quickly or &longs;lowly: But if <lb/>it be &longs;o, the Cau&longs;e is doubtfull, whence it proceeds, that a Plate of <lb/>Lead or of Iron broad and thin doth &longs;wim, &c. </s><s>And the occa&longs;ion of <lb/>the doubt is obvious, becau&longs;e it &longs;eems at the fir&longs;t glance, that the <lb/>Figure is the Cau&longs;e of this Natation, &longs;ince the &longs;ame Lead, or a le&longs;s <lb/>quantity, but in another Figure, goes to the bottom, and we have <lb/>already affirmed, that the Figure hath no &longs;hare in this effect.</s></p><p type="main"> <s>La&longs;tly, if the intent of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in this place had been to &longs;ay, <lb/>that Figures, although not ab&longs;olutely, are at lea&longs;t in &longs;ome mea&longs;ure <lb/>the Cau&longs;e of moving or not moving: I would have it con&longs;idered, <lb/>that he names no le&longs;s the Motion upwards, than the other down­ <lb/>wards: and becau&longs;e in exemplifying it afterwards, he produceth <lb/>no other Experiments than of a Plate of Lead, and Board of Ebony, <lb/>Matters that of their own Nature go to the bottom, but by vertue <lb/>(as our Adver&longs;aries &longs;ay) of their Figure, re&longs;t afloat; it is &longs;it that <lb/>they &longs;hould produce &longs;ome other Experiment of tho&longs;e Matters, which <lb/>by their Nature &longs;wims, but retained by their Figure re&longs;t at the <lb/>bottom. </s><s>But &longs;ince this is impo&longs;&longs;ible to be done, we conclude, that <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in this place, hath not attributed any action to the Figure <lb/>of &longs;imply moving or not moving.</s></p><p type="main"> <s>But though he hath exqui&longs;itely Philo&longs;ophiz'd, in inve&longs;tigating <lb/>the &longs;olution of the doubts he propo&longs;eth, yet will I not undertake <lb/>to maintain, rather various difficulties, that pre&longs;ent them&longs;elves <lb/>unto me, give me occa&longs;ion of &longs;u&longs;pecting that he hath not entirely <lb/>di&longs;plaid unto us, the true Cau&longs;e of the pre&longs;ent Conclu&longs;ion: which <lb/>difficulties I will propound one by one, ready to change opinion, <lb/>when ever I am &longs;hewed, that the Truth is different from what I &longs;ay; <lb/>to the confe&longs;&longs;ion whereof I am much more inclinable than to contra­ <lb/>diction. <lb/><arrow.to.target n="marg1532"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1532"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> erred <lb/>in affirming a <lb/>Needle dimitted <lb/>long wayes to <lb/>&longs;ink.</s></p><p type="main"> <s><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> having propounded the Que&longs;tion, whence it proceeds, <lb/>that broad Plates of Iron or Lead, float or &longs;wim; he addeth (as <lb/>it were &longs;trengthening the occa&longs;ion of doubting) fora&longs;much as other <lb/>things, le&longs;s, and le&longs;s grave, be they round or long, as for in&longs;tance a <pb xlink:href="040/01/1158.jpg" pagenum="467"/>Needle go to the bottom. </s><s>Now I here doubt, or rather am certain, <lb/>that a Needle put lightly upon the water, re&longs;ts afloat, no le&longs;s than the <lb/>thin Plates of Iron or Lead. </s><s>I cannot believe, albeit it hath been <lb/>told me, that &longs;ome to defend <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;hould &longs;ay, that he intends a <lb/>Needle demitted not longwayes but endwayes, and with the Point <lb/>downwards; neverthele&longs;s, not to leave them &longs;o much as this, though <lb/>very weak refuge, and which in my judgement <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf <lb/>would refu&longs;e, I &longs;ay it ought to be under&longs;tood, that the Needle mu&longs;t <lb/>be demitted, according to the Dimen&longs;ion named by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> which <lb/>is the length: becau&longs;e, if any other Dimen&longs;ion than that which is <lb/>named, might or ought to be taken, I would &longs;ay, that even the Plates <lb/>of Iron and Lead, &longs;ink to the bottom, if they be put into the water <lb/>edgewayes and not flatwayes. </s><s>But becau&longs;e <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aith, broad <lb/>Figures go not to the bottom, it is to be under&longs;tood, being demitted <lb/>broadwayes: and, therefore, when he &longs;aith, long Figures as a <lb/>Needle, albeit light, re&longs;t not afloat, it ought to be under&longs;tood of <lb/>them when demitted longwayes.</s></p><p type="main"> <s><emph type="italics"/>Morcover, to &longs;ay that<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>is to be under&longs;tood of the Needle de­ <lb/>mitted with the Point downwards, is to father upon him a great imper­ <lb/>tinency; for in this place he &longs;aith, that little Particles of Lead or Iron, <lb/>if they be round or long as a Needle, do &longs;ink to the bottome; &longs;o that by <lb/>his Opinion, a Particle or &longs;mall Grain of Iron cannot &longs;wim: and if he <lb/>thus believed, what a great folly would it be to &longs;ubjoyn, that neither <lb/>would a Needle demitted endwayes &longs;wim? </s><s>And what other is &longs;uch a <lb/>Needle, but many &longs;uch like Graines accumulated one upon another? </s><s>It <lb/>was too unworthy of &longs;uch a man to &longs;ay, that one &longs;ingle Grain of Iron could <lb/>not &longs;wim, and that neither can it &longs;wim, though you put a hundred more <lb/>upon it.<emph.end type="italics"/></s></p><p type="main"> <s>La&longs;tly, either <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> believed, that a Needle demitted long­ <lb/>wayes upon the water, would &longs;wim, or he believed that it would <lb/>not &longs;wim: If he believed it would not &longs;wim, he might well &longs;peak <lb/>as indeed he did; but if he believed and knew that it would &longs;loat, <lb/>why, together with the dubious Problem of the Natation of broad <lb/>Figure, though of ponderous Matter, hath he not al&longs;o introduced <lb/>the Que&longs;tion; whence it proceeds, that even long and &longs;lender Fi­ <lb/>gures, howbeit of Iron or Lead do &longs;wim? </s><s>And the rather, for that <lb/>the occa&longs;ion of doubting &longs;eems greater in long and narrow Figures, <lb/>than in broad and thin, as from <emph type="italics"/>Aristotles<emph.end type="italics"/> not having doubted of it, <lb/>is manife&longs;ted.</s></p><p type="main"> <s>No le&longs;&longs;er an inconvenience would they fa&longs;ten upon <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who <lb/>in his defence &longs;hould &longs;ay, that he means a Needle pretty thick, and <lb/>not a &longs;mall one; for take it for granted to be intended of a &longs;mall one <pb xlink:href="040/01/1159.jpg" pagenum="468"/>and it &longs;hall &longs;uffice to reply, that he believed that it would &longs;wim; <lb/>and I will again charge him with having avoided a more wonderfull <lb/>and intricate Probleme, and introduced the more facile and le&longs;s <lb/>wonderfull.</s></p><p type="main"> <s>We &longs;ay freely therefore; that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> did hold, that only the <lb/>broad Figure did &longs;wim, but the long and &longs;lender, &longs;uch as a Needle, <lb/>not. </s><s>The which neverthele&longs;s is fal&longs;e, as it is al&longs;o fal&longs;e in round <lb/>Bodies: becau&longs;e, as from what hath been predemon&longs;trated, may be ga­ <lb/>thered, little Balls of Lead and Iron, do in like manner &longs;wim.</s></p><p type="main"> <s>He propo&longs;eth likewi&longs;e another Conclu&longs;ion, which likewi&longs;e &longs;eems </s></p><p type="main"> <s><arrow.to.target n="marg1533"></arrow.to.target> <lb/>different from the truth, and it is, That &longs;ome things, by rea&longs;on of <lb/>their littlene&longs;s fly in the Air, as the &longs;mall du&longs;t of the Earth, and the <lb/>thin leaves of beaten Gold: but in my Opinion, Experience &longs;hews <lb/>us, that that happens not only in the Air, but al&longs;o in the water, in <lb/>which do de&longs;cend, even tho&longs;e Particles or Atomes of Earth, that <lb/>di&longs;tur be it, who&longs;e minuity is &longs;uch, that they are not de&longs;ervable, &longs;ave <lb/>only when they are many hundreds together. </s><s>Therefore, the du&longs;t <lb/>of the Earth, and beaten Gold, do not any way &longs;u&longs;tain them&longs;elves <lb/>in the Air, but de&longs;cend downwards, and only fly to and again in <lb/>the &longs;ame, when &longs;trong Windes rai&longs;e them, or other agitations of the <lb/>Air commove them: and this al&longs;o happens in the commotion of the <lb/>water, which rai&longs;eth its Sand from the bottom, and makes it muddy. <lb/></s><s>But <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> cannot mean this impediment of the commotion, of <lb/>which he makes no mention, nor names other than the lightne&longs;s of <lb/>&longs;uch Minutiæ or Atomes, and the Re&longs;i&longs;tance of the Cra&longs;&longs;itudes of the <lb/>Water and Air, by which we &longs;ee, that he &longs;peakes of a calme, and <lb/>not di&longs;turbed and agitated Air: but in that ca&longs;e, neither Gold nor <lb/>Earth, be they never &longs;o &longs;mall, are &longs;u&longs;tained, but &longs;peedily de&longs;cend. <lb/><arrow.to.target n="marg1534"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1533"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> af­ <lb/>fir meth &longs;ome <lb/>Bodies volatile <lb/>for their Minu­ <lb/>ity, Text. </s><s>42.</s></p><p type="margin"> <s><margin.target id="marg1534"></margin.target><emph type="italics"/>Democritus<emph.end type="italics"/> pla­ <lb/>ced the Cau&longs;e of <lb/>Natation in <lb/>certain &longs;iery A­ <lb/>tomes.</s></p><p type="main"> <s>He pa&longs;&longs;eth next to confute <emph type="italics"/>Democritus,<emph.end type="italics"/> which, by his Te&longs;timony <lb/>would have it, that &longs;ome Fiery Atomes, which continually a&longs;cend <lb/>through the water, do &longs;pring upwards, and &longs;u&longs;tain tho&longs;e grave Bodies, <lb/>which are very broad, and that the narrow de&longs;cend to the bottom, </s></p><p type="main"> <s><arrow.to.target n="marg1535"></arrow.to.target> <lb/>for that but a &longs;mall quantity of tho&longs;e Atomes, encounter and re&longs;i&longs;t <lb/>them.</s></p><p type="margin"> <s><margin.target id="marg1535"></margin.target><emph type="italics"/>Ari&longs;tot. </s><s>De Cœlo<emph.end type="italics"/> <lb/>lib. 4. cap. 6. <lb/>text. </s><s>43.</s></p><p type="main"> <s>I &longs;ay, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> confutes this po&longs;ition, &longs;aying, that that &longs;hould <lb/><arrow.to.target n="marg1536"></arrow.to.target> <lb/>much more occurre in the Air, as the &longs;ame <emph type="italics"/>Democritus<emph.end type="italics"/> in&longs;tances a­ <lb/>gain&longs;t him&longs;elf, but after he had moved the objection, he &longs;lightly re­ <lb/>&longs;olves it, with &longs;aying, that tho&longs;e Corpu&longs;cles which a&longs;cend in the Air, <lb/>make not their <emph type="italics"/>Impetus<emph.end type="italics"/> conjunctly. </s><s>Here I will not &longs;ay, that the <lb/><arrow.to.target n="marg1537"></arrow.to.target> <lb/>rea&longs;on alledged by <emph type="italics"/>Democritus<emph.end type="italics"/> is true, but I will only &longs;ay, it &longs;eems <lb/>in my judgement, that it is not wholly confuted by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> whil&longs;t he <lb/>&longs;aith, that were it true, that the calid a&longs;cending Atomes, &longs;hould <lb/>&longs;u&longs;tain Bodies grave, but very broad, it would much more be done <lb/>in the Air, than in Water, for that haply in the Opinion of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> <pb xlink:href="040/01/1160.jpg" pagenum="469"/>the &longs;aid calid Atomes a&longs;cend with much greater Force and Velocity <lb/>through the Air, than through the water. </s><s>And if this be &longs;o, as I veri­ <lb/>ly believe it is, the Objection of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in my judgement &longs;eems to <lb/>give occa&longs;ion of &longs;u&longs;pecting, that he may po&longs;&longs;ibly be deceived in more <lb/>than one particular: Fir&longs;t, becau&longs;e tho&longs;e calid Atomes, (whether <lb/>they be Fiery Corpu&longs;cles, or whether they be Exhalations, or in <lb/>&longs;hort, whatever other matter they be, that a&longs;cends upwards through <lb/>the Air) cannot be believed to mount fa&longs;ter through Air, than <lb/>through water: but rather on the contrary, they peradventure move <lb/>more impetuou&longs;ly through the water, than through the Air, as hath <lb/>been in part demon&longs;trated above. </s><s>And here I cannot finde the rea­ <lb/>&longs;on, why <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;eeing, that the de&longs;eending Motion of the &longs;ame <lb/>Moveable, is more &longs;wift in Air, than in water, hath not adverti&longs;ed <lb/>us, that from the contrary Motion, the contrary &longs;hould nece&longs;&longs;arily <lb/>follow; to wit, that it is more &longs;wift in the water, than in the Air: for <lb/>&longs;ince that the Moveable which de&longs;cendeth, moves &longs;wifter through <lb/>the Air, than through the water, if we &longs;hould &longs;uppo&longs;e its Gravity <lb/>gradually to dimini&longs;h, it would fir&longs;t become &longs;uch, that de&longs;cending <lb/>&longs;wiftly through the Air, it would de&longs;cend but &longs;lowly through the <lb/>water: and then again, it might be &longs;uch, that de&longs;cending in the <lb/>Air, it &longs;hould a&longs;cend in the water: and being made yet le&longs;s grave, <lb/>it &longs;hall a&longs;cend &longs;wiftly through the water, and yet de&longs;cend likewi&longs;e <lb/>through the Air: and in &longs;hort, before it can begin to a&longs;cend, though <lb/>but &longs;lowly through the Air, it &longs;hall a&longs;cend &longs;wiftly through the water: <lb/>how then is it true, that a&longs;cending Moveables move &longs;wifter through <lb/>the Air, than through the water?</s></p><p type="margin"> <s><margin.target id="marg1536"></margin.target><emph type="italics"/>Democritus<emph.end type="italics"/> con­ <lb/>futed by <emph type="italics"/>Ari­ <lb/>&longs;totle,<emph.end type="italics"/> text 43.</s></p><p type="margin"> <s><margin.target id="marg1537"></margin.target><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> con­ <lb/>futation of <emph type="italics"/>De­ <lb/>mocritus<emph.end type="italics"/> refuted <lb/>by the Author.</s></p><p type="main"> <s>That which hath made <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> believe, the Motion of A&longs;cent to be <lb/>&longs;wifter in Air, than in water, was fir&longs;t, the having referred the <lb/>Cau&longs;es of &longs;low and quick, as well in the Motion of A&longs;cent, as of <lb/>De&longs;cent, only to the diver&longs;ity of the Figures of the Moveable, and to <lb/>the more or le&longs;s Re&longs;i&longs;tance of the greater or le&longs;&longs;er Cra&longs;&longs;itude, or Ra­ <lb/>rity of the <emph type="italics"/>Medium<emph.end type="italics"/>; not regarding the compari&longs;on of the Exce&longs;&longs;es <lb/>of the Gravities of the Moveables, and of the <emph type="italics"/>Mediums<emph.end type="italics"/>: the which <lb/>notwith&longs;tanding, is the mo&longs;t principal point in this affair: for if the <lb/>augmentation and diminution of the Tardity or Velocity, &longs;hould <lb/>have only re&longs;pect to the Den&longs;ity or Rarity of the <emph type="italics"/>Medium,<emph.end type="italics"/> every Body <lb/>that de&longs;cends in Air, would de&longs;cend in water: becau&longs;e whatever <lb/>difference is found between the Cra&longs;&longs;itude of the water, and that of <lb/>the Air, may well be found between the Velocity of the &longs;ame Move­ <lb/>able in the Air, and &longs;ome other Velocity: and this &longs;hould be its <lb/>proper Velocity in the water, which is ab&longs;olutely fal&longs;e. </s><s>The other <lb/>occa&longs;ion is, that he did believe, that like as there is a po&longs;itive and in­ <lb/>trin&longs;ecall Quality, whereby Elementary Bodies have a propen&longs;ion <lb/>of moving towards the Centre of the Earth, &longs;o there is another like­ <pb xlink:href="040/01/1161.jpg" pagenum="470"/>wi&longs;e intrin&longs;ecall, whereby &longs;ome of tho&longs;e Bodies have an <emph type="italics"/>Impetus<emph.end type="italics"/> of <lb/><arrow.to.target n="marg1538"></arrow.to.target> <lb/>flying the Centre, and moving upwards: by Vertue of which in­ <lb/>trin&longs;e call Principle, called by him Levity, the Moveables which have <lb/>that &longs;ame Motion more ea&longs;ily penetrate the more &longs;ubtle <emph type="italics"/>Medium,<emph.end type="italics"/> <lb/>than the more den&longs;e: but &longs;uch a Propo&longs;ition appears likewi&longs;e un­ <lb/>certain, as I have above hinted in part, and as with Rea&longs;ons and <lb/>Experiments, I could demon&longs;trate, did not the pre&longs;ent Argument im­ <lb/>portune me, or could I di&longs;patch it in few words.</s></p><p type="margin"> <s><margin.target id="marg1538"></margin.target>Lib. 4. Cap. 5.</s></p><p type="main"> <s>The Objection therefore of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> again&longs;t <emph type="italics"/>Democritus,<emph.end type="italics"/> whil&longs;t <lb/>he &longs;aith, that if the Fiery a&longs;cending Atomes &longs;hould &longs;u&longs;tain Bodies <lb/>grave, but of a di&longs;tended Figure, it would be more ob&longs;ervable in <lb/>the Air than in the water, becau&longs;e &longs;uch Corpu&longs;cles move &longs;wifter in <lb/>that, than in this, is not good; yea the contrary would evene, for <lb/>that they a&longs;cend more &longs;lowly through the Air: and, be&longs;ides their <lb/>moving &longs;lowly, they a&longs;cend, not united together, as in the water, <lb/>but di&longs;continue, and, as we &longs;ay, &longs;catter: And, therefore, as <lb/><emph type="italics"/>Democritus<emph.end type="italics"/> well replyes, re&longs;olving the in&longs;tance they make not their <lb/>pu&longs;h or <emph type="italics"/>Impetus<emph.end type="italics"/> conjunctly.</s></p><p type="main"> <s><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> in the &longs;econd place, deceives him&longs;elf, whil&longs;t he will <lb/>have the &longs;aid grave Bodies to be more ea&longs;ily &longs;u&longs;tained by the &longs;aid <lb/>Fiery a&longs;cending Atomes in the Air than in the Water: not ob&longs;erv­ <lb/>ing, that the &longs;aid Bodies are much more grave in that, than in this, <lb/>and that &longs;uch a Body weighs ten pounds in the Air, which will not <lb/>in the water weigh 1/2 an ounce; how can it then be more ea&longs;ily <lb/>&longs;u&longs;tained in the Air, than in the Water?</s></p><p type="main"> <s>Let us conclude, therefore, that <emph type="italics"/>Democritus<emph.end type="italics"/> hath in this particular <lb/>better Philo&longs;ophated than <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/> But yet will not I affirm, that <emph type="italics"/>De-<emph.end type="italics"/> <lb/><arrow.to.target n="marg1539"></arrow.to.target> <lb/><emph type="italics"/>mocritus<emph.end type="italics"/> hath rea&longs;on'd rightly, but I rather &longs;ay, that there is a ma­ <lb/>nife&longs;t Experiment that overthrows his Rea&longs;on, and this it is, That <lb/>if it were true, that calid a&longs;cending Atomes &longs;hould uphold a Body, <lb/>that if they did not hinder, would go to the bottom, it would follow, <lb/>that we may find a Matter very little &longs;uperiour in Gravity to the <lb/>water, the which being reduced into a Ball, or other contracted <lb/>Figure, &longs;hould go to the bottom, as encountring but few Fiery A­ <lb/>tomes; and which being di&longs;tended afterwards into a dilated and <lb/>thin Plate, &longs;hould come to be thru&longs;t upwards by the impul&longs;ion of a <lb/>great Multitude of tho&longs;e Corpu&longs;cles, and at la&longs;t carried to the very <lb/>Surface of the water: which wee &longs;ee not to happen; Experience <lb/>&longs;hewing us, that a Body <emph type="italics"/>v. </s><s>gra.<emph.end type="italics"/> of a Sphericall Figure, which very <lb/>hardly, and with very great lea&longs;ure goeth to the bottom, will re&longs;t <lb/>there, and will al&longs;o de&longs;cend thither, being reduced into what&longs;oever <lb/>other di&longs;tended Figure. </s><s>We mu&longs;t needs &longs;ay then, either that in the <lb/>water, there are no &longs;uch a&longs;cending Fiery Atoms, or if that &longs;uch there <lb/>be, that they are not able to rai&longs;e and lift up any Plate of a Matter, <pb xlink:href="040/01/1162.jpg" pagenum="471"/>that without them would go to the bottom: Of which two Pofitions, <lb/>I e&longs;teem the &longs;econd to be true, under&longs;tanding it of water, con&longs;tituted <lb/>in its naturall Coldne&longs;s. </s><s>But if we take a Ve&longs;&longs;el of Gla&longs;s, or Bra&longs;s, <lb/>or any other hard matter, full of cold water, within which is put a <lb/>Solid of a flat or concave Figure, but that in Gravity exceeds the <lb/>water &longs;o little, that it goes &longs;lowly to the bottom; I &longs;ay, that putting <lb/>&longs;ome burning Coals under the &longs;aid Ve&longs;&longs;el, as &longs;oon as the new Fiery <lb/>Atomes &longs;hall have penetrated the &longs;ub&longs;tance of the Ve&longs;&longs;el, they &longs;hall <lb/>without doubt, a&longs;cend through that of the water, and thru&longs;ting a­ <lb/>gain&longs;t the fore&longs;aid Solid, they &longs;hall drive it to the Superficies, and <lb/>there detain it, as long as the incur&longs;ions of the &longs;aid Corpu&longs;cles &longs;hall <lb/>la&longs;t, which cea&longs;ing after the removall of the Fire, the Solid being a­ <lb/>bandoned by its &longs;upporters, &longs;hall return to the bottom.</s></p><p type="margin"> <s><margin.target id="marg1539"></margin.target><emph type="italics"/>Democritus<emph.end type="italics"/> con­ <lb/>futed by the <lb/>Authour.</s></p><p type="main"> <s>But <emph type="italics"/>Democritus<emph.end type="italics"/> notes, that this Caufe only takes place when we <lb/>treat of rai&longs;ing and &longs;u&longs;taining of Plates of Matters, but very little <lb/>heavier than the water, or extreamly thin: but in Matters very <lb/>grave, and of &longs;ome thickne&longs;s, as Plates of Lead or other Mettal, that <lb/>&longs;ame Effect wholly cea&longs;eth: In Te&longs;timony of which, let's ob&longs;erve <lb/>that &longs;uch Plates, being rai&longs;ed by the Fiery Atomes, a&longs;cend through <lb/>all the depth of the water, and &longs;top at the Confines of the Air, &longs;till <lb/>&longs;taying under water: but the Plates of the Opponents &longs;tay not, but <lb/>only when they have their upper Superficies dry, nor is there any <lb/>means to be u&longs;ed, that when they are within the water, they may <lb/>not &longs;ink to the bottom. </s><s>The cau&longs;e, therefore, of the Supernatation <lb/>of the things of which <emph type="italics"/>Democritus<emph.end type="italics"/> &longs;peaks is one, and that of the Super­ <lb/>natation of the things of which we &longs;peak is another. </s><s>But, returning <lb/><arrow.to.target n="marg1540"></arrow.to.target> <lb/>to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> methinks that he hath more weakly confuted <emph type="italics"/>Democritus,<emph.end type="italics"/> <lb/>than <emph type="italics"/>Democritus<emph.end type="italics"/> him&longs;elf hath done: For <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> having propounded <lb/>the Objection which he maketh again&longs;t him, and oppo&longs;ed him with <lb/>&longs;aying, that if the calid a&longs;cendent Corpu&longs;cles were tho&longs;e that rai&longs;ed <lb/>the thin Plate, much more then would &longs;uch a Solid be rai&longs;ed and <lb/>born upwards through the Air, it &longs;heweth that the de&longs;ire in <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>to detect <emph type="italics"/>Democritus,<emph.end type="italics"/> was predominate over the exqui&longs;itene&longs;s of Solid <lb/>Philo&longs;ophizing: which de&longs;ire of his he hath di&longs;covered in other oc­ <lb/>ca&longs;ions, and that we may not digre&longs;s too far from this place, in the <lb/>Text precedent to this Chapter which we have in hand; where he <lb/><arrow.to.target n="marg1541"></arrow.to.target> <lb/>attempts to confute the &longs;ame <emph type="italics"/>Democritus,<emph.end type="italics"/> for that he, not content­ <lb/>ing him&longs;elf with names only, had e&longs;&longs;ayed more particularly to de­ <lb/>clare what things Gravity and Levity were; that is, the Cau&longs;es of <lb/>de&longs;cending and a&longs;cending, (and had introduced Repletion and Va­ <lb/>cuity) a&longs;cribing this to Fire, by which it moves upwards, and that to <lb/>the Earth, by which it de&longs;cends; afterwards attributing to the <lb/>Air more of Fire, and to the water more of Earth. </s><s>But <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> <lb/>de&longs;iring a po&longs;itive Cau&longs;e, even of a&longs;cending Motion, and not as <emph type="italics"/>Plato,<emph.end type="italics"/> <pb xlink:href="040/01/1163.jpg" pagenum="472"/>or the&longs;e others, a &longs;imple negation, or privation, &longs;uch as Vacuity <lb/><arrow.to.target n="marg1542"></arrow.to.target> <lb/>would be in reference to Repletion, argueth again&longs;t <emph type="italics"/>Democritus<emph.end type="italics"/> and <lb/>&longs;aith: If it be true, as you &longs;uppo&longs;e, then there &longs;hall be a great Ma&longs;s <lb/>of water, which &longs;hall have more of Fire, than a &longs;mall Ma&longs;s of Air, <lb/>and a great Ma&longs;s of Air, which &longs;hall have more of Earth than a lit­ <lb/>tle Ma&longs;s of water, whereby it would en&longs;ue, that a great Ma&longs;s of Air, <lb/>&longs;hould come more &longs;wiftly downwards, than a little quantity of <lb/>water: But that is never in any ca&longs;e &longs;oever: Therefore <emph type="italics"/>Democritus<emph.end type="italics"/> <lb/>di&longs;cour&longs;eth erroneou&longs;ly.</s></p><p type="margin"> <s><margin.target id="marg1540"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;hews <lb/>his de&longs;ire of <lb/>finding <emph type="italics"/>Demo­ <lb/>critus<emph.end type="italics"/> in an Er­ <lb/>ror, to exceed <lb/>that of di&longs;co­ <lb/>veting Truth.</s></p><p type="margin"> <s><margin.target id="marg1541"></margin.target>Cap. 5. Text 41.</s></p><p type="margin"> <s><margin.target id="marg1542"></margin.target>Id. </s><s>ibid.</s></p><p type="main"> <s>But in my opinion, the Doctrine of <emph type="italics"/>Democritus,<emph.end type="italics"/> is not by this alle­ <lb/>gation overthrown, but if I erre not, the manner of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> deduction <lb/>either concludes not, or if it do conclude any thing, it may with e­ <lb/>quall force be re&longs;tored again&longs;t him&longs;elf. <emph type="italics"/>Democritus<emph.end type="italics"/> will grant to <lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that there may be a great Ma&longs;s of Air taken, which con­ <lb/>tains more Earth, than a &longs;mall quantity of water, but yet will deny, <lb/>that &longs;uch a Ma&longs;s of Air, &longs;hall go fa&longs;ter downwards than a little water, <lb/>and that for many rea&longs;ons. </s><s>Fir&longs;t, becau&longs;e if the greater quantity <lb/>of Earth, contained in the great Ma&longs;s of Air, ought to cau&longs;e a greater <lb/>Velocity than a le&longs;s quantity of Earth, contained in a little quantity <lb/>of water, it would be nece&longs;&longs;ary, fir&longs;t, that it were true, that a <lb/>greater Ma&longs;s of pure Earth, &longs;hould move more &longs;wiftly than a le&longs;s: <lb/>But this is fal&longs;e, though <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in many places affirms it to be true: <lb/>becau&longs;e not the greater ab&longs;olute, but the greater &longs;pecificall Gravity, <lb/><arrow.to.target n="marg1543"></arrow.to.target> <lb/>is the cau&longs;e of greater Velocity: nor doth a Ball of Wood, weigh­ <lb/>ing ten pounds, de&longs;cend more &longs;wiftly than one weighing ten Ounces, <lb/>and that is of the &longs;ame Matter: but indeed a Bullet of Lead of four <lb/>Ounces, de&longs;cendeth more &longs;wiftly than a Ball of Wood of twenty <lb/>Pounds: becau&longs;e the Lead is more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the Wood. <lb/></s><s>Therefore, its not nece&longs;&longs;ary, that a great Ma&longs;s of Air, by rea&longs;on of <lb/>the much Earth contained in it, do de&longs;cend more &longs;wiftly than a little <lb/><arrow.to.target n="marg1544"></arrow.to.target> <lb/>Ma&longs;s of water, but on the contrary, any what&longs;oever Ma&longs;s of water, <lb/>&longs;hall move more &longs;wiftly than any other of Air, by rea&longs;on the partici­ <lb/>pation of the terrene parts <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> is greater in the water, than in the <lb/>Air. </s><s>Let us note, in the &longs;econd place, how that in multiplying the <lb/>Ma&longs;s of the Air, we not only multiply that which is therein of terrene, <lb/>but its Fire al&longs;o: whence the Cau&longs;e of a&longs;cending, no le&longs;s encrea&longs;eth, <lb/>by vertue of the Fire, than that of de&longs;cending on the account of its <lb/>multiplied Earth. </s><s>It was requi&longs;ite in increa&longs;ing the greatne&longs;s of the <lb/>Air, to multiply that which it hath of terrene only, leaving its Fire <lb/>in its fir&longs;t &longs;tate, for then the terrene parts of the augmented Air, <lb/>overcoming the terrene parts of the &longs;mall quantity of water, it might <lb/>with more probability have been pretended, that the great quanti­ <lb/>ty of Air, ought to de&longs;cend with a greater <emph type="italics"/>Impetus,<emph.end type="italics"/> than the little <lb/>quantity of water.</s></p> <pb xlink:href="040/01/1164.jpg" pagenum="467"/><p type="margin"> <s><margin.target id="marg1543"></margin.target>The greater <lb/>Specificall, not <lb/>the greater ab­ <lb/>&longs;olute Gravity, <lb/>is the Cau&longs;e of <lb/>Velocity.</s></p><p type="margin"> <s><margin.target id="marg1544"></margin.target>Any Ma&longs;s of <lb/>water &longs;hal move <lb/>more &longs;wiftly, <lb/>than any of Air, <lb/>and why.</s></p><p type="main"> <s>Therefore, the Fallacy lyes more in the Di&longs;cour&longs;e of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> than <lb/>in that of <emph type="italics"/>Democritus,<emph.end type="italics"/> who with &longs;everall other Rea&longs;ons might oppo&longs;e <lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and alledge; If it be true, that the extreame Elements be <lb/>one &longs;imply grave, and the other &longs;imply light, and that the mean <lb/>Elements participate of the one, and of the other Nature; but the <lb/>Air more of Levity, and the water more of Gravity, then there &longs;hall <lb/>be a great Ma&longs;s of Air, who&longs;e Gravity &longs;hall exceed the Gravity of a <lb/>little quantity of water; and therefore &longs;uch a Ma&longs;s of Air &longs;hall de­ <lb/>&longs;cend more &longs;wiftly than that little water: But that is never &longs;een to <lb/>occurr: Therefore its not true, that the mean Elements do partici­ <lb/>pate of the one, and the other quality. </s><s>This argument is fallacious, <lb/>no le&longs;s than the other again&longs;t <emph type="italics"/>Democritus.<emph.end type="italics"/></s></p><p type="main"> <s>La&longs;tly, <emph type="italics"/>Aristotle<emph.end type="italics"/> having &longs;aid, that if the Po&longs;ition of <emph type="italics"/>Democritus<emph.end type="italics"/> <lb/>were true, it would follow, that a great Ma&longs;s of Air &longs;hould move <lb/>more &longs;wiftly than a &longs;mall Ma&longs;s of water, and afterwards &longs;ubjoyned, <lb/>that that is never &longs;een in any Ca&longs;e: methinks others may become de­ <lb/>&longs;irous to know of him in what place this &longs;hould evene, which he de­ <lb/>duceth again&longs;t <emph type="italics"/>Democritus,<emph.end type="italics"/> and what Experiment teacheth us, that <lb/>it never falls out &longs;o. </s><s>To &longs;uppo&longs;e to &longs;ee it in the Element of water, <lb/>or in that of the Air is vain, becau&longs;e neither doth water through <lb/>water, nor Air through Air move, nor would they ever by any <lb/>whatever participation others a&longs;&longs;ign them, of Earth or of Fire: the <lb/>Earth, in that it is not a Body fluid, and yielding to the mobility of <lb/>other Bodies, is a mo&longs;t improper place and <emph type="italics"/>Medium<emph.end type="italics"/> for &longs;uch an Ex­ <lb/>periment: <emph type="italics"/>Vacuum,<emph.end type="italics"/> according to the &longs;ame <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf, there <lb/>is none, and were there, nothing would move in it: there remaine <lb/>the Region of Fire, but being &longs;o far di&longs;tant from us, what Experi­ <lb/>ment can a&longs;&longs;ure us, or hath a&longs;&longs;ertained <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in &longs;uch &longs;ort, that he <lb/>&longs;hould as of a thing mo&longs;t obvious to &longs;ence, affirm what he produ­ <lb/>ceth in confutation of <emph type="italics"/>Democritus,<emph.end type="italics"/> to wit, that a great Ma&longs;s of Air, <lb/>is moved no &longs;wifter than a little one of water? </s><s>But I will dwell no <lb/>longer upon this matter, whereon I have &longs;poke &longs;ufficiently: but <lb/>leaving <emph type="italics"/>Democritus,<emph.end type="italics"/> I return to the Text of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> wherein he <lb/>goes about to render the true rea&longs;on, how it comes to pa&longs;s, that the <lb/>thin Plates of Iron or Lead do &longs;wim on the water; and, moreover, <lb/>that Gold it &longs;elf being beaten into thin Leaves, not only &longs;wims in <lb/>water, but flyeth too and again in the Air. </s><s>He &longs;uppo&longs;eth that of <lb/><arrow.to.target n="marg1545"></arrow.to.target> <lb/>Continualls, &longs;ome are ea&longs;ily divi&longs;ible, others not: and that of the <lb/>ea&longs;ily divi&longs;ible, &longs;ome are more &longs;o, and &longs;ome le&longs;s: and the&longs;e he <lb/>affirms we &longs;hould e&longs;teem the Cau&longs;es. </s><s>He addes that that is ea&longs;ily <lb/>divi&longs;ible, which is well terminated, and the more the more divi&longs;ible, <lb/>and that the Air is more &longs;o, than the water, and the water than the <lb/>Earth. </s><s>And, la&longs;tly, he &longs;uppo&longs;eth that in each kind, the le&longs;&longs;e quan­ <lb/>tity is ea&longs;lyer divided and broken than the greater.</s></p> <pb xlink:href="040/01/1165.jpg" pagenum="474"/><p type="margin"> <s><margin.target id="marg1545"></margin.target><emph type="italics"/>De Cœlo<emph.end type="italics"/> l. </s><s>4. c. <lb/></s><s>6. t. </s><s>44.</s></p><p type="main"> <s>Here I note, that the Conclu&longs;ions of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in generall are all <lb/>true, but methinks, that he applyeth them to particulars, in which <lb/>they have no place, as indeed they have in others, as for Example, <lb/>Wax is more ea&longs;ily divi&longs;ible than Lead, and Lead than Silver, in­ <lb/>a&longs;much as Wax receives all the terms more ea&longs;iler than Lead, and <lb/>Lead than Silver. </s><s>Its true, moreover, that a little quantity of Sil­ <lb/>ver is ea&longs;lier divided than a great Ma&longs;s: and all the&longs;e Propo&longs;itions <lb/>are true, becau&longs;e true it is, that in Silver, Lead and Wax, there <lb/>is &longs;imply a Re&longs;i&longs;tance again&longs;t Divi&longs;ion, and where there is the ab&longs;o­ <lb/>lute, there is al&longs;o the re&longs;pective. </s><s>But if as well in water as in Air, <lb/>there be no Renitence again&longs;t &longs;imple Divi&longs;ion, how can we &longs;ay, that <lb/>the water is ea&longs;lier divided than the Air? </s><s>We know not how to ex­ <lb/>tricate our &longs;elves from the Equivocation: whereupon I return to <lb/>an&longs;wer, that Re&longs;i&longs;tance of ab&longs;olute Divi&longs;ion is one thing, and Re­ <lb/>&longs;i&longs;tance of Divi&longs;ion made with &longs;uch and &longs;uch Velocity is another. <lb/></s><s>But to produce Re&longs;t, and to abate the Motion, the Re&longs;i&longs;tance of <lb/>ab&longs;olute Divi&longs;ion is nece&longs;&longs;ary; and the Re&longs;i&longs;tance of &longs;peedy Di­ <lb/>vi&longs;ion, cau&longs;eth not Re&longs;t, but &longs;lowne&longs;s of Motion. </s><s>But that as well <lb/>in the Air, as in water, there is no Re&longs;i&longs;tance of &longs;imple Divi&longs;ion, is <lb/>manife&longs;t, for that there is not found any Solid Body which divides <lb/>not the Air, and al&longs;o the water: and that beaten Gold, or &longs;mall <lb/>du&longs;t, are not able to &longs;uperate the Re&longs;i&longs;tance of the Air, is contrary <lb/>to that which Experience &longs;hews us, for we &longs;ee Gold and Du&longs;t to go <lb/>waving to and again in the Air, and at la&longs;t to de&longs;cend down­ <lb/>wards, and to do the &longs;ame in the water, if it be put therein, and &longs;e­ <lb/>parated from the Air. </s><s>And, becau&longs;e, as I &longs;ay, neither the water, <lb/>nor the Air do re&longs;i&longs;t &longs;imple Divi&longs;ion, it cannot be &longs;aid, that the water <lb/>re&longs;i&longs;ts more than the Air. </s><s>Nor let any object unto me, the Exam­ <lb/>ple of mo&longs;t light Bodies, as a Feather, or a little of the pith of El­ <lb/>der, or water-reed that divides the Air and not the water, and from <lb/>this infer, that the Ait is ea&longs;lier divi&longs;ible than the water; for I &longs;ay <lb/>unto them, that if they do well ob&longs;erve, they &longs;hall &longs;ee the &longs;ame <lb/><arrow.to.target n="marg1546"></arrow.to.target> <lb/>Body likewi&longs;e divide the Continuity of the water, and &longs;ubmerge in <lb/>part, and in &longs;uch a part, as that &longs;o much water in Ma&longs;s would weigh <lb/>as much as the whole Solid. </s><s>And if they &longs;hal yet per&longs;i&longs;t in their doubt, <lb/>that &longs;uch a Solid &longs;inks not through inability to divide the water, I will <lb/>return them this reply, that if they put it under water, and then let it <lb/>go, they &longs;hall &longs;ee it divide the water, and pre&longs;ently a&longs;cend with no le&longs;s <lb/>celerity, than that with which it divided the Air in de&longs;cending: &longs;o that <lb/>to &longs;ay that this Solid a&longs;cends in the Air, but that coming to the water, <lb/>it cea&longs;eth its Motion, and therefore the water is more difficult to be <lb/>divided, concludes nothing: for I, on the contrary, will propo&longs;e them <lb/>a piece of Wood, or of Wax, which ri&longs;eth from the bottom of the <lb/>water, and ea&longs;ily divides its Re&longs;i&longs;tance, which afterwards being arri­ <pb xlink:href="040/01/1166.jpg" pagenum="475"/>ved at the Air, &longs;tayeth there, and hardly toucheth it; whence I may <lb/>aswell &longs;ay, that the water is more ea&longs;ier divided than the Air</s></p><p type="margin"> <s><margin.target id="marg1546"></margin.target><emph type="italics"/>Archimed. </s><s>De <lb/>In&longs;ident, humi<emph.end type="italics"/> lib. <lb/></s><s>2. prop. 1.</s></p><p type="main"> <s>I will not on this occa&longs;ion forbear to give warning of another fal­ <lb/>lacy of the&longs;e per&longs;ons, who attribute the rea&longs;on of &longs;inking or &longs;wimming <lb/>to the greater or le&longs;&longs;e Re&longs;i&longs;tance of the Cra&longs;&longs;itude of the water again&longs;t <lb/>Divi&longs;ion, making u&longs;e of the example of an Egg, which in &longs;weet water <lb/>goeth to the bottom, but in &longs;alt water &longs;wims; and alledging for the <lb/>cau&longs;e thereof, the faint Re&longs;i&longs;tance of fre&longs;h water again&longs;t Divi&longs;ion, and <lb/>the &longs;trong Re&longs;i&longs;tance of &longs;alt water But if I mi&longs;take not, from the &longs;ame <lb/>Experiment, we may aswell deduce the quite contrary; namely, that <lb/>the fre&longs;h water is more den&longs;e, and the &longs;alt more tenuous and &longs;ubtle, <lb/>&longs;ince an Egg from the bottom of &longs;alt water &longs;peedily a&longs;cends to the <lb/>top, and divides its Re&longs;i&longs;tance, which it cannot do in the fre&longs;h, in who&longs;e <lb/>bottom it &longs;tays, being unable to ri&longs;e upwards. </s><s>Into &longs;uch like perplex­ <lb/>ities, do fal&longs;e Principles Lead men: but he that rightly Philo&longs;ophating, <lb/>&longs;hall acknowledge the exce&longs;&longs;es of the Gravities of the Moveables and <lb/>of the Mediums, to be the Cau&longs;es of tho&longs;e effects, will &longs;ay, that the <lb/>Egg &longs;inks to the bottom in fre&longs;h water, for that it is more grave than <lb/>it, and &longs;wimeth in the &longs;alt, for that its le&longs;s grave than it: and &longs;hall <lb/>without any ab&longs;urdity, very &longs;olidly e&longs;tabli&longs;h his Conclu&longs;ions.</s></p><p type="main"> <s>Therefore the rea&longs;on totally cea&longs;eth, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;ubjoyns in the <lb/><arrow.to.target n="marg1547"></arrow.to.target> <lb/>Text &longs;aying; The things, therefore, which have great breadth remain <lb/>above, becau&longs;e they comprehend much, and that which is greater, <lb/>is not ea&longs;ily divided. </s><s>Such di&longs;cour&longs;ing cea&longs;eth, I &longs;ay, becau&longs;e its not <lb/>true, that there is in water or in Air any Re&longs;i&longs;tance of Divi&longs;ion; be­ <lb/>&longs;ides that the Plate of Lead when it &longs;tays, hath already divided and <lb/>penetrated the Cra&longs;&longs;itude of the water, and profounded it &longs;elf ten or <lb/>twelve times more than its own thickne&longs;s: be&longs;ides that &longs;uch Re&longs;i&longs;tance <lb/>of Divi&longs;ion, were it &longs;uppo&longs;ed to be in the water, could not rationally <lb/>be affirmed to be more in its &longs;uperiour parts than in the middle, and <lb/>lower: but if there were any difference, the inferiour &longs;hould be the <lb/>more den&longs;e, &longs;o that the Plate would be no le&longs;s unable to penetrate <lb/>the lower, than the &longs;uperiour parts of the water; neverthele&longs;s we &longs;ee <lb/>that no &longs;ooner do we wet the &longs;uperious Superficies of the Board or <lb/>thin Piece of Wood, but it precipitatly, and without any reten&longs;ion, <lb/>de&longs;cends to the bottom.</s></p><p type="margin"> <s><margin.target id="marg1547"></margin.target>Text 45.</s></p><p type="main"> <s>I believe not after all this, that any (thinking perhaps thereby to <lb/>defend <emph type="italics"/>Aristotle<emph.end type="italics"/>) will &longs;ay, that it being true, that the much water re­ <lb/>&longs;i&longs;ts more than the little, the &longs;aid Board being put lower de&longs;cendeth, <lb/>becau&longs;e there remaineth a le&longs;s Ma&longs;s of water to be divided by it: be­ <lb/>cau&longs;e if after the having &longs;een the &longs;ame Board &longs;wim in four Inches of <lb/>water, and al&longs;o after that in the &longs;ame to &longs;ink, he &longs;hall try the &longs;ame <lb/>Experiment upon a profundity of ten or twenty fathom water, he <lb/>&longs;hall &longs;ee the very &longs;elf &longs;ame effect. </s><s>And here I will take occa&longs;ion to <pb xlink:href="040/01/1167.jpg" pagenum="476"/>remember, for the removall of an Error that is too common; That <lb/>that Ship or other what&longs;oever Body, that on the depth of an hundred <lb/>or a thou&longs;and fathom, &longs;wims with &longs;ubmerging only &longs;ix fathom of its <lb/>own height, [<emph type="italics"/>or in the Sea dialect, that draws &longs;ix fathom water<emph.end type="italics"/>] &longs;hall <lb/>&longs;wim in the &longs;ame manner in water, that hath but &longs;ix fathom and half <lb/><arrow.to.target n="marg1548"></arrow.to.target> <lb/>an Inch of depth. </s><s>Nor do I on the other &longs;ide, think that it can be <lb/>&longs;aid, that the &longs;uperiour parts of the water are the more den&longs;e, al­ <lb/>though a mo&longs;t grave Authour hath e&longs;teemed the &longs;uperiour water in <lb/>the Sea to be &longs;o, grounding his opinion upon its being more &longs;alt, than <lb/>that at the bottom: but I doubt the Experiment, whether hitherto <lb/>in taking the water from the bottom, the Ob&longs;ervatour did not light <lb/>upon &longs;ome &longs;pring of fre&longs;h water there &longs;pouting up: but we plainly <lb/>&longs;ee on the contrary, the fre&longs;h Waters of Rivers to dilate them&longs;elves <lb/>for &longs;ome miles beyond their place of meeting with the &longs;alt water of <lb/>the Sea, without de&longs;cending in it, or mixing with it, unle&longs;s by the <lb/>intervention of &longs;ome commotion or turbulency of the Windes.</s></p><p type="margin"> <s><margin.target id="marg1548"></margin.target>A Ship that <lb/>in 100 Fathome <lb/>water draweth <lb/>6 Fathome, &longs;hall <lb/>float in 6 Fa­ <lb/>thome and 1/2 an <lb/>Inch of depth.</s></p><p type="main"> <s>But returning to <emph type="italics"/>Aristotle,<emph.end type="italics"/> I &longs;ay, that the breadth of Figure hath <lb/>nothing to do in this bu&longs;ine&longs;s more or le&longs;s, becau&longs;e the &longs;aid Plate of <lb/><arrow.to.target n="marg1549"></arrow.to.target> <lb/>Lead, or other Matter, cut into long Slices, &longs;wim neither more nor <lb/>le&longs;s; and the &longs;ame &longs;hall the Slices do, being cut anew into little <lb/>pieces, becau&longs;e its not the breadth but the thickne&longs;s that operates in <lb/>this bu&longs;ine&longs;s. </s><s>I &longs;ay farther, that in ca&longs;e it were really true, that the <lb/><arrow.to.target n="marg1550"></arrow.to.target> <lb/>Renitence to Divi&longs;ion were the proper Cau&longs;e of &longs;wimming, the Fi­ <lb/>gures more narrow and &longs;hort, would much better &longs;wim than the more <lb/>&longs;pacious and broad, &longs;o that augmenting the breadth of the Figure, <lb/>the facility of &longs;upernatation will be demini&longs;hed, and decrea&longs;ing, that <lb/>this will encrea&longs;e.</s></p><p type="margin"> <s><margin.target id="marg1549"></margin.target>Thickne&longs;s not <lb/>breadth of Fi­ <lb/>gure to be re­ <lb/>&longs;pected in Na­ <lb/>tation.</s></p><p type="margin"> <s><margin.target id="marg1550"></margin.target>Were Reni­ <lb/>tence the cau&longs;e <lb/>of Natation, <lb/>breadth of Fi­ <lb/>gure would <lb/>hinder the <lb/>&longs;wiming of Bo­ <lb/>dies.</s></p><p type="main"> <s>And for declaration of what I &longs;ay, con&longs;ider that when a thin Plate <lb/>of Lead de&longs;cends, dividing the water, the Divi&longs;ion and di&longs;continu­ <lb/>ation is made between the parts of the water, invironing the perime­ <lb/>ter or Circumference of the &longs;aid Plate, and according to the big­ <lb/>ne&longs;s greater or le&longs;&longs;er of that circuit, it hath to divide a greater or <lb/>le&longs;&longs;er quantity of water, &longs;o that if the circuit, &longs;uppo&longs;e of a Board, <lb/>be ten Feet in &longs;inking it flatways, it is to make the &longs;eperation and <lb/>divi&longs;ion, and to &longs;o &longs;peak, an inci&longs;&longs;ion upon ten Feet of water; and <lb/>likewi&longs;e a le&longs;&longs;er Board that is four Feet in Perimeter, mu&longs;t make an <lb/>ince&longs;&longs;ion of four Feet. </s><s>This granted, he that hath any knowledge <lb/>in Geometry, will comprehend, not only that a Board &longs;awed in many <lb/>long thin pieces, will much better float than when it was entire, but <lb/>that all Figures, the more &longs;hort and narrow they be, &longs;hall &longs;o much the <lb/>better &longs;wim. </s><s>Let the Board ABCD be, for Example, eight <lb/>Palmes long, and five broad, its circuit &longs;hall be twenty &longs;ix Palmes; <lb/>and &longs;o many mu&longs;t the ince&longs;&longs;ion be, which it &longs;hall make in the water to <lb/>de&longs;cend therein: but if we do &longs;aw ir, as &longs;uppo&longs;e into eight little <pb xlink:href="040/01/1168.jpg" pagenum="469"/>pieces, according to the Lines E F, G H, <emph type="italics"/>&c.<emph.end type="italics"/> making &longs;even Segments, <lb/>we mu&longs;t adde to the twenty &longs;ix Palmes of the circuit of the whole <lb/>Board, &longs;eventy others; whereupon the eight little pieces &longs;o cut and <lb/>&longs;eperated, have to cut ninty &longs;ix Palmes of water. </s><s>And, if moreover, <lb/>we cur each of the &longs;aid pieces into five parts, re­ <lb/><figure id="id.040.01.1168.1.jpg" xlink:href="040/01/1168/1.jpg"/> <lb/>ducing them into Squares, to the circuit of ninty <lb/>&longs;ix Palmes, with four cuts of eight Palmes apiece; <lb/>we &longs;hall adde al&longs;o &longs;ixty four Palmes, whereupon <lb/>the &longs;aid Squares to de&longs;cend in the water, mu&longs;t <lb/>divide one hundred and &longs;ixty Palmes of water, <lb/>but the Re&longs;i&longs;tance is much greater than that of <lb/>twenty &longs;ix; therefore to the le&longs;&longs;er Superficies, <lb/>we &longs;hall reduce them, &longs;o much the more ea&longs;ily <lb/>will they float: and the &longs;ame will happen in all <lb/>other Figures, who&longs;e Superficies are &longs;imular among&longs;t them&longs;elves, but <lb/>different in bigne&longs;s: becau&longs;e the &longs;aid Superficies, being either demini­ <lb/>&longs;hed or encrea&longs;ed, always dimini&longs;h or encrea&longs;e their Perimeters in <lb/>&longs;ubduple proportion; to wit, the Re&longs;i&longs;tance that they find in pene­ <lb/>trating the water; therefore the little pieces gradually &longs;wim, with more <lb/>and more facility as their breadth is le&longs;&longs;ened.</s></p><p type="main"> <s><emph type="italics"/>This is manife&longs;t; for keeping &longs;till the &longs;ame height of the Solid, with <lb/>the &longs;ame proportion as the Ba&longs;e encrea&longs;eth or demini&longs;heth, doth the &longs;aid <lb/>Solid al&longs;o encrea&longs;e or dimini&longs;h; whereupon the Solid more dimini&longs;hing <lb/>than the Circuit, the Cau&longs;e of Submer&longs;ion more dimini&longs;heth than the Cau&longs;e <lb/>of Natation: And on the contrary, the Solid more encrea&longs;ing than the <lb/>Circuit, the Cau&longs;e of Submer&longs;ion encrea&longs;eth more, that of Natation <lb/>le&longs;s.<emph.end type="italics"/></s></p><p type="main"> <s>And this may all be dedueed out of the Doctrine of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> a­ <lb/>gain&longs;t his own Doctrine.</s></p><p type="main"> <s>La&longs;tly, to that which we read in the latter part of the Text, that <lb/><arrow.to.target n="marg1551"></arrow.to.target> <lb/>is to &longs;ay, that we mu&longs;t compare the Gravity of the Moveable with <lb/>the Re&longs;i&longs;tance of the Medium again&longs;t Divi&longs;ion, becau&longs;e if the force of <lb/>the Gravity exceed the Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> the Moveable will <lb/>de&longs;cend, if not it will float. </s><s>I need not make any other an&longs;wer, <lb/>but that which hath been already delivered; namely, that its not <lb/>the Re&longs;i&longs;tance of ab&longs;olute Divi&longs;ion, (which neither is in Water nor <lb/>Air) but the Gravity of the <emph type="italics"/>Medium<emph.end type="italics"/> that mu&longs;t be compared with the <lb/>Gravity of the Moveables; and if that of the <emph type="italics"/>Medium<emph.end type="italics"/> be greater, the <lb/>Moveable &longs;hall not de&longs;cend, nor &longs;o much as make a totall Submer&longs;ion, <lb/>but a partiall only: becau&longs;e in the place which it would occupy in <lb/>the water, there mu&longs;t not remain a Body that weighs le&longs;s than a like <lb/>quantity of water: but if the Moveable be more grave, it &longs;hall de&longs;­ <lb/>cend to the bottom, and po&longs;&longs;e&longs;s a place where it is more conformable <pb xlink:href="040/01/1169.jpg"/> for it to remain, than another Body that is le&longs;s grave. </s><s>And this <lb/>is the only true proper and ab&longs;olute Cau&longs;e of Natation and Sub­ <lb/>mer&longs;ion, &longs;o that nothing el&longs;e hath part therein: and the Board of the <lb/>Adver&longs;aries &longs;wimmeth, when it is conjoyned with as much Air, <lb/>as, together with it, doth form a Body le&longs;s grave than &longs;o much water <lb/>as would fill the place that the &longs;aid Compound occupyes in the <lb/>water; but when they &longs;hall demit the &longs;imple Ebony into <lb/>the water, according to the Tenour of our Que­ <lb/>&longs;tion, it &longs;hall alwayes go to the bottom, <lb/>though it were as thin as a <lb/>Paper.</s></p><p type="margin"> <s><margin.target id="marg1551"></margin.target>Lib. 4. c. </s><s>6. <lb/>Text 45.</s></p><p type="head"> <s><emph type="italics"/>FINIS.<emph.end type="italics"/></s></p> </chap> <pb xlink:href="040/01/1170.jpg"/> <chap> <p type="head"> <s>THE <lb/>TROUBLESOME <lb/>INVENTION <lb/><emph type="italics"/>OF<emph.end type="italics"/><lb/>Nicolas Tartalea:</s></p><p type="head"> <s>BEING <lb/>A Generall way to recover from the bottome of the <emph type="italics"/>Water,<emph.end type="italics"/><lb/>any <emph type="italics"/>SHIP<emph.end type="italics"/> that's <emph type="italics"/>Sunke,<emph.end type="italics"/> Or any other <emph type="italics"/>Ponderous Ma&longs;&longs;e,<emph.end type="italics"/> though <lb/>it were a <emph type="italics"/>Solid TOWER of Metal.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>TOGETHER WITH<emph.end type="italics"/><lb/>An Artificiall way of DIVING, and &longs;taying a long <lb/>time under <emph type="italics"/>Water,<emph.end type="italics"/> to &longs;eeke any thing <emph type="italics"/>Sunke<emph.end type="italics"/> in the <lb/>greate&longs;t <emph type="italics"/>DEPTHS.<emph.end type="italics"/></s></p><p type="head"> <s><emph type="italics"/>AS ALSO, <lb/>A SVPPLEMENT,<emph.end type="italics"/> Shewing a <lb/>Generall and Secure Way to <emph type="italics"/>Grapple, &c.<emph.end type="italics"/> any <lb/><emph type="italics"/>Submerged SHIP.<emph.end type="italics"/></s></p><p type="head"> <s>Engli&longs;hed, By <emph type="italics"/>THO. SALUSBURY,<emph.end type="italics"/> <expan abbr="E&longs;q;">E&longs;que</expan></s></p><figure id="id.040.01.1170.1.jpg" xlink:href="040/01/1170/1.jpg"/><p type="head"> <s><emph type="italics"/>LONDON,<emph.end type="italics"/><lb/>Printed by WILLIAM LEYBOURN, <emph type="italics"/>Anno Dom.<emph.end type="italics"/><lb/><emph type="italics"/>MDC LXIV.<emph.end type="italics"/></s></p><pb xlink:href="040/01/1171.jpg"/></chap><chap><p type="main"> <s>To the mo&longs;t <emph type="italics"/>Serene,<emph.end type="italics"/> and mo&longs;t <emph type="italics"/>Illustrious<emph.end type="italics"/><lb/>Prince, FRANCESCO DONATO <lb/>Duke of VENICE.</s></p><p type="main"> <s><emph type="italics"/>It having been told me here at<emph.end type="italics"/><lb/>Bre&longs;cia, <emph type="italics"/>Mo&longs;t Serene and Mo&longs;t <lb/>Illu&longs;trious Prince, that about ten <lb/>years &longs;ince, that a Ship full-laden <lb/>did &longs;inke near to<emph.end type="italics"/> Malamoccho, <emph type="italics"/>in <lb/>about<emph.end type="italics"/> 5 <emph type="italics"/>Fathome of Water, and <lb/>that to endeavour the recovering and getting it from <lb/>thence, there had been u&longs;ed all tho&longs;e Means, and boun­ <lb/>tifull Offers and Tenders that could be imagined, a&longs;wel <lb/>by the Illu&longs;trious Signory, for the Pre&longs;ervation of the <lb/>Port, as by the chief Owners of the Ship and its Cargo: <lb/>and that although there were many that had tried, and <lb/>attempted the &longs;ame, by &longs;undry and divers wayes, of no <lb/>&longs;mall expence, and that it had been &longs;ever all times well <lb/>grappled and begirt, yet neverthele&longs;s as far as I could <lb/>hear, none of them were able to rai&longs;e her from that &longs;mall <lb/>depth: And it being al&longs;o told me, that of late there was <lb/>another &longs;unk again in le&longs;s than four Fathome of Water, <lb/>&longs;o that all its Poope and Prow, and a greate part of its <lb/>Hull, was above Water, and that yet not with &longs;tanding this <lb/>al&longs;o was judged by the fruitle&longs;s Experiments and Ex­ <lb/>pen&longs;es made about the former, to be irrecoverable, &longs;o<emph.end type="italics"/><pb xlink:href="040/01/1172.jpg"/><emph type="italics"/>that for the clearing of the Port, it is pre&longs;ently re&longs;olved, <lb/>that the &longs;aid Ship &longs;hould be broken up, & taken to pieces <lb/>at low Water: and &longs;o, for ought that I hear, it hath been. <lb/></s><s>Now I having con&longs;idered of how great prejudice the <lb/>breaking up of &longs;uch a Ve&longs;&longs;el was, be&longs;ides the lo&longs;s of the <lb/>Cargo, I deliberated about the finding of a way or Rule, <lb/>that might remedy &longs;uch detriment all Occurrences: And <lb/>having found out one thats generall and unquestionable, I <lb/>thought fit, for the common benefit of this renowned City, <lb/>to declare, and by Figures to dilucidate the &longs;ame in the <lb/>pre&longs;ent Tractate, and to offer and dedicate the &longs;ame to <lb/>your Highne&longs;s; not as a pre&longs;ent worthy of yon (for indeed <lb/>the&longs;e Mechanicall Matters are exceeding di&longs;proporti­ <lb/>onate to your Highne&longs;s Merits) but only with an Ambi­ <lb/>tion to Enoble and Dignifie my Book with your Glorious <lb/>Name; In confidence that like as the Sun doth not di&longs;­ <lb/>dain that all &longs;orts of Per&longs;ons &longs;hould make u&longs;e of its light <lb/>and heat, &longs;oneither will Your accu&longs;tomed Humanity be <lb/>offended with this my Pre&longs;umption; and therefore I <lb/>humbly lay my &longs;elf at your Highne&longs;s Feet,<emph.end type="italics"/></s></p><p type="main"> <s>Nicolas Tartalea.</s></p><pb xlink:href="040/01/1173.jpg" pagenum="483"/><p type="head"> <s>THE <lb/>Indu&longs;trious or Trouble&longs;ome <lb/>INVENTION <lb/>OF <lb/>Nicolas Tartalea:</s></p> </chap> <chap> <p type="head"> <s><emph type="italics"/>BOOKEI.<emph.end type="italics"/></s></p><p type="caption"> <s><emph type="italics"/>The Figure of a Ship &longs;unke according to the Relation made of that <lb/>which was cau&longs;ed to be broken up neere<emph.end type="italics"/> Malamoccho, <emph type="italics"/>as being <lb/>judged irrecoverable.<emph.end type="italics"/></s></p><figure id="id.040.01.1173.1.jpg" xlink:href="040/01/1173/1.jpg"/><p type="head"> <s><emph type="italics"/>EXPLANATION I.<emph.end type="italics"/></s></p><p type="main"> <s>Before I come to declare the promi&longs;ed way <lb/>to recover any laden or empty Ship when <lb/>it is &longs;unke; I thinke it convenient (<emph type="italics"/>Mo&longs;t <lb/>Serene and Illu&longs;trious Prince,<emph.end type="italics"/>) fir&longs;t to de­ <lb/>clare the reall cau&longs;e of its &longs;inking.<pb xlink:href="040/01/1174.jpg" pagenum="484"/><arrow.to.target n="marg1552"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1552"></margin.target><emph type="italics"/>Archimed.<emph.end type="italics"/> of <lb/>Natation, Lib. 2. <lb/>Prop. </s><s>1.</s></p><p type="main"> <s>I &longs;ay then; That its impo&longs;&longs;ible that the water &longs;hould wholly <lb/>&longs;wallow or receive into it any materiall Body lighter than it &longs;elf (as <lb/>to &longs;pecies;) but it will leave or cau&longs;e one part thereof to lie above <lb/>the Superficies of the &longs;aid water, that is uncovered by it. </s><s>And as <lb/>the whole Body demitted into the water, is to the part thereof, <lb/>which &longs;hall be received or admitted by the water, &longs;o &longs;hall the Spe­ <lb/>cificall Gravity of the water, be unto the Specificall Gravity of the <lb/>&longs;aid Solid Body.</s></p><p type="main"> <s><arrow.to.target n="marg1553"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1553"></margin.target><emph type="italics"/>Archimed.<emph.end type="italics"/> of <lb/>Natation, Lib. 1. <lb/>Prop. </s><s>7.</s></p><p type="main"> <s>But tho&longs;e Solid Bodies which are more grave than the water; be­ <lb/>ing demitted into the &longs;aid water, &longs;uddenly make the water to give <lb/>place; and not only enter wholly into the &longs;ame, but they do go <lb/>continually de&longs;cending, till they arrive at the bottom: And they <lb/>de&longs;cend with &longs;o much greater Velocity, by how much they exceed <lb/>the water in &longs;pecificall Gravity.</s></p><p type="main"> <s><arrow.to.target n="marg1554"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1554"></margin.target><emph type="italics"/>A chimed.<emph.end type="italics"/> of <lb/>Natation, Lib. 1. <lb/>Prop. </s><s>111.</s></p><p type="main"> <s>And tho&longs;e again which happen to be of the &longs;ame Gravity with the <lb/>water, of nece&longs;&longs;ary con&longs;equence being put into it, are admitted <lb/>and received totally into the &longs;ame, but yet they &longs;tay in the Surface <lb/>of the &longs;aid water; that is, they &longs;uffer not any part to lie above the <lb/>Superficies of the &longs;aid water, nor much le&longs;s doth the water con&longs;ent <lb/>to their de&longs;cent to the bottom.</s></p><p type="main"> <s>And all this is demon&longs;trated by <emph type="italics"/>Archimedes<emph.end type="italics"/> of <emph type="italics"/>Syracu&longs;a,<emph.end type="italics"/> in that <lb/>his Tract <emph type="italics"/>De in&longs;identibus aquæ,<emph.end type="italics"/> by us tran&longs;lated. </s><s>And becau&longs;e the <lb/>greate&longs;t part of woods are lighter, or le&longs;s grave than the water; he <lb/>therefore that &longs;hall build a Ship or other Ve&longs;&longs;el meerly of wood, <lb/>lighter than water, its manife&longs;t that he cannot (though he &longs;hould <lb/>fill the &longs;ame with water, as full as it would hold) make the &longs;ame <lb/>totally to &longs;ink, but that nece&longs;&longs;arily &longs;ome one part or other of the <lb/>&longs;aid Ship or Ve&longs;&longs;el &longs;hall &longs;tand above the Surface of the water: For <lb/>its a thing very clear, that all that &longs;ame Body, compounded of wood <lb/>and of water, would be much lighter than if it were all only of water <lb/>without wood: Such a compound Body therefore being le&longs;s grave <lb/>than the water, its nece&longs;&longs;ary (for the rea&longs;ons above produced) that <lb/>a part of the &longs;ame remain above the Surface of the water.</s></p><p type="main"> <s>And if the &longs;aid Ship or Bark &longs;hall be built (as it is u&longs;ual) with <lb/>Bolts, Nailes, and other Materials of Iron, and that &longs;uch Iron­ <lb/>works be not of &longs;uch quantity, as to make that Body compounded <lb/>of wood and Iron, graver than the water, but that it continue &longs;till <lb/>le&longs;s grave than the water (as I judge all Ships and Barks to be;) The <lb/>&longs;ame will follow as did before, namely, that filling the &longs;aid Ship <lb/>with water, as full as is po&longs;ible, it cannot by any means go to the <lb/>bottom If then a Ship or other Ve&longs;&longs;el being wholly fill'd with <lb/>water, cannot be thereby &longs;unk to the bottom; It is a thing evident, <lb/>that if &longs;uch a Ship or Ve&longs;&longs;el &longs;hall be totally fill'd with a Matter <lb/>lighter than the water; not only its totall &longs;inking under that weight <pb xlink:href="040/01/1175.jpg" pagenum="485"/>will be impo&longs;&longs;ible, but al&longs;o its floating in &longs;ome part above the Sur­ <lb/>face of the water will be nece&longs;&longs;ary: And &longs;o much the greater part <lb/>&longs;hall be vi&longs;ible above the water, by how much the Matter of the <lb/>Lading, is lighter than the water.</s></p><p type="main"> <s>Therefore, if all the Cargo of a Ship (for in&longs;tance) Buts of Oyl, <lb/>and that no other Matters of a graver Nature than water were intro­ <lb/>duced, and that the &longs;aid Ship &longs;hould by &longs;ome Accident be filled <lb/>up with water, it is not only manife&longs;t that the Ship cannot be there­ <lb/>by &longs;unk to the bottom, but that a part thereof mu&longs;t nece&longs;&longs;arily float <lb/>above the Surface of the water: Becau&longs;e all that Compo&longs;ition of <lb/>Wood, Water and Oyl, would be lighter than if it had been all <lb/>&longs;imply of water. </s><s>The very &longs;ame would follow, if the Cargo had <lb/>been &longs;oley of Wine, Wax, Camphor, Spices, or the like Matters, <lb/>lighter than the water. </s><s>But becau&longs;e the Merchandizes that fraight <lb/>Ships, or other Ve&longs;&longs;els, are &longs;ome (&longs;pecifically) graver, and &longs;ome <lb/>(&longs;pecifically) lighter than the water: (The graver are all forts of <lb/>Mettals, as Iron, Tinn, Lead, Bra&longs;s, Copper, Silver, Gold, and infi­ <lb/>nite other Species of Commodities; likewi&longs;e the per&longs;ons of Men, <lb/>Stones, Balla&longs;ts, and the like:) And that al&longs;o there are &longs;ome &longs;orts of <lb/>Commodities that chance to differ very little in Gravity from the <lb/>water: Therefore I conclude, that as oft as any Ship accidentally <lb/>is fill'd with water, and &longs;o &longs;inks by degrees to the bottom, it is ne­ <lb/>ce&longs;&longs;ary to grant that all the Compo&longs;ition, namely, of the Fraight, <lb/>of the Ve&longs;&longs;el, and of the water that entered into it, is more grave, <lb/>than if the compo&longs;ition had been all &longs;imply of water, by the rea&longs;ons <lb/>before alledg'd.</s></p><p type="main"> <s>And therefore in &longs;uch a ca&longs;e things graver than the water, mu&longs;t <lb/>of nece&longs;&longs;ity exceed in force tho&longs;e that be lighter: and by how much <lb/>things graver than the water, exceed the lighter, &longs;o much the more <lb/>Force will be required to recover &longs;uch a Ship or other Ve&longs;&longs;el being <lb/>&longs;unk, and on the contrary, &longs;o much le&longs;s Force will be required, <lb/>when the Ma&longs;s of the Materials more grave than the water, &longs;hall <lb/>not differ much from the Ma&longs;s of the le&longs;s grave: provided the Re­ <lb/>covery be undertaken in &longs;ome &longs;hort time after the Ship &longs;hall be &longs;unk, <lb/>For if the Ship lie many dayes under water, the delay will intro. <lb/></s><s>duce many difficulties: One will be, that it will con&longs;olidate with <lb/>and dock or work it &longs;elf farther into the Mudd or Sand, which will <lb/>not a little hinder its Recovery; and again, the water will continu­ <lb/>ally carry into the &longs;aid Ship, Ouze, Mudd, and Sand, which Mat­ <lb/>ter is much graver than the water, whereby the Ship is continually <lb/>made graver as to the water, than it was at the beginning when it <lb/>was fir&longs;t &longs;ubmerg'd. </s><s>And moreover the corruptible Matters, which <lb/>are by nature lighter than the water, will corrupt, and corrupting <lb/>will change into other earthy &longs;ub&longs;tances much graver than the <pb xlink:href="040/01/1176.jpg" pagenum="486"/>water: in&longs;omuch that at the length, it ought to be pre&longs;uppo&longs;ed in <lb/>order to the recovery of the &longs;aid Ship, as if it were &longs;olely laden <lb/>with Mire, Dirt, and Sand: which doing, you will not be deceived <lb/>in the operation, that is to &longs;ay, preparing and working with a Force <lb/>equivalent to that its Gravity. </s><s>The way to know how to prepare <lb/>Forces equivalent to the Gravity &longs;hall be &longs;hewn in the eight Expla­ <lb/>nation of this.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> II.</s></p><p type="main"> <s>Now to give beginning to the bu&longs;ine&longs;s propo&longs;ed, I &longs;ay, that <lb/>in the Recovery of a Foundred Ship laden, or any other la­ <lb/>den Ve&longs;&longs;el that is foundered or &longs;unk, there interveneth more <lb/>e&longs;pecially the&longs;e three great Ob&longs;tructions. </s><s>The fir&longs;t difficulty is, how <lb/>to imbreech and grapple it with &longs;uch, and &longs;o many Ropes, as may <lb/>&longs;uffice to bear it up; for if this either by ill chance cannot be done <lb/>(whether through its being in a place two deep, or too far dockt in <lb/>the Mudd or Sand) all our other labour will be fru&longs;trate and vain.</s></p><p type="main"> <s>The &longs;econd difficulty, when once it is grappled, is how with dex­ <lb/>terity to &longs;eperate it from the bottom of the Sea; and this difficulty <lb/>will be much greater, the Ship being in a Miry or Sandy bottom, <lb/>than if it &longs;hall be in a Stony place; and it &longs;hall be al&longs;o a greater <lb/>difficulty to &longs;eperate it from a very deep bottom, than from a Shal­ <lb/>low; (alwayes &longs;uppo&longs;ing that the two bottoms be both alike, name­ <lb/>ly, either both Stony or both Sandy;) and al&longs;o far greater &longs;hall the <lb/>&longs;aid difficulty be in a Ship long &longs;unk, than in one newly four dered; <lb/>(as we have already &longs;aid in the precedent Explanation:) But when <lb/>&longs;he is once water-born, or &longs;eperated from the bottom, its an ca&longs;ie <lb/>matter to rai&longs;e her up to the Surface of the water; for then &longs;he &longs;hall <lb/>not be a little aleviated in her Gravity: But the truth is, the draw­ <lb/>ing of it after wards above the Superficies of the water, is no very ca­ <lb/>&longs;ie matter, but is extream hard to be done; and this is the third <lb/>difficulty; the principal cau&longs;e of which two la&longs;t difficulties &longs;hall be <lb/>a&longs;&longs;igned by and by.</s></p><p type="main"> <s>But becau&longs;e the means to obviate and &longs;uperate the fir&longs;t difficulties <lb/><arrow.to.target n="marg1555"></arrow.to.target> <lb/>as more ^{*} common, we &longs;hall forbear to &longs;peak of them untill the <lb/>next Book. </s><s>To provide, and that briefly, to the &longs;econd and third <lb/>impediments (which are the lea&longs;t known) that is, not only to &longs;e­ <lb/>perate the Ship from the bottom, but to rai&longs;e it al&longs;o &longs;omewhat above <lb/>the Surface of the water.</s></p> <pb xlink:href="040/01/1177.jpg" pagenum="487"/><p type="margin"> <s><margin.target id="marg1555"></margin.target>* <emph type="italics"/>The Author be­ <lb/>lieved (as he de­ <lb/>clareth in the E­ <lb/>pi&longs;tle to the en&longs;u­ <lb/>ing Suppliment of <lb/>this his<emph.end type="italics"/> Inventi­ <lb/>on) <emph type="italics"/>that the Ma­ <lb/>riners conver&longs;ant in the&longs;e affairs, had many wayes to imbreech a Ve&longs;&longs;el uuder water; and for that rea&longs;on he <lb/>over pa&longs;&longs;eth it here, and is very cur&longs;ive upon the &longs;ame Point, in the &longs;econd Book, but giveth a generall Rule <lb/>for it in the &longs;aid Suppliment: to which the Reader is referred for fuller Satisfaction.<emph.end type="italics"/></s></p><p type="main"> <s>And this is the Rule that you mu&longs;t ob&longs;erve; If the Ship be newly <lb/>&longs;unk, you mu&longs;t immediately, if it be po&longs;&longs;ible, find two other Ships, <lb/>that be each of them rather of greater bulk than the foundered Ship <lb/>than le&longs;s: and when you have found the&longs;e two Ships, you mu&longs;t <lb/>free them of all the inward and outward lading, and rigging, e&longs;pe­ <lb/>cially of tho&longs;e things which are by nature more grave than the water, <lb/>as are the Guns, the Shot, and any kind of Balla&longs;t, which is pre&longs;up­ <lb/>po&longs;ed to be in the Hold, and of other things of impediment; and <lb/>when the&longs;e Ships are thus cleared, you mu&longs;t &longs;top all the Loop-holes, <lb/>Cat-holes, Skuppers and Hau&longs;es, which you &longs;hall finde between or <lb/>above Decks, graving and calking them &longs;o with Okum, and paying <lb/>them with Pitch, that the water can neither get in nor out thereat. <lb/></s><s>And next you mu&longs;t join or grapple the&longs;e two Ships together with five <lb/>or more Tires or Orders of thick and &longs;trong Beames tripplicated; <lb/>that is, that each of the &longs;aid Orders con&longs;i&longs;t of three Beams, joyned <lb/>lengthways; and that each of the three Beams be &longs;omewhat longer <lb/>than the bredth of the Deck or Hull of each Ship; and that theybe <lb/>thick and &longs;trong, as being to &longs;upport the Foundered Ship, as you <lb/>&longs;hall &longs;ee it made to appear pre&longs;ently: and couple the &longs;aid Ships to­ <lb/>gether, at &longs;uch a di&longs;tance from each other, that you give berth, or <lb/>leave room enough betwixt for the foundered Ship to play; and <lb/>you mu&longs;t make this couppling in &longs;uch &longs;ort, that the length or &longs;ide <lb/>of the one Ship, look towards the length or &longs;ide of the other; and <lb/>albeit this conjunction or grappling may be made with many Orders <lb/>or Tires of tho&longs;e Bcams tripplicated lengthways, as was &longs;aid above, </s></p><p type="caption"> <s><emph type="italics"/>The Figurall repre&longs;entation of the two empty Ships, conjoyned with <lb/>five Orders of Beams, and towed ju&longs;t over the place where the <lb/>Foundered Ship is.<emph.end type="italics"/> <lb/><figure id="id.040.01.1177.1.jpg" xlink:href="040/01/1177/1.jpg"/> <lb/>yet that we may not cau&longs;e confu&longs;ion in the Figure, we would have <lb/>this colligation to be made only of five Rows, as appeareth in the <pb xlink:href="040/01/1178.jpg" pagenum="488"/>Scheme: and although the &longs;aid Rows of Beames cannot be all <lb/>placed equidi&longs;tant from the Surface of the water, for that the <lb/>Wailes or Rifings of the two Ships are not flu&longs;h, but cuved, it is <lb/>not of any importance, &longs;o that they be well fa&longs;tened and &longs;trength­ <lb/>ened in tho&longs;e places where they re&longs;t upon the &longs;aid Rifings: upon <lb/>which Ri&longs;ings, you &longs;hall conjoyn the &longs;aid Beams, namely, the two <lb/>ends of them, which two ends &longs;hall be the &longs;tronge&longs;t place, able to <lb/>&longs;upport any great weight. </s><s>Yet the truth is, that to fit the&longs;e Tires <lb/>of Beams, you need not have regard to make them pa&longs;s through from <lb/>&longs;ide to &longs;ide, in that weak part of the Ships Poop and Prow, to re&longs;t <lb/>them on the Rifings or Gun-wales of the Deck of tho&longs;e Ships, and <lb/>to go cro&longs;s the Hull in tho&longs;e places. </s><s>And next you are to make upon <lb/>the&longs;e Beams, that is upon the mouths of both the Ships, a Plat-form <lb/>of Planks for to &longs;tand upon whil&longs;t you are about the work; leaving <lb/>diver&longs;e Scuttles or Spaces open, whereby to de&longs;cend, aud for other <lb/>u&longs;es: And all this being done, you are to tow or hall the&longs;e Ve&longs;&longs;els <lb/>to the place where the Ship is that did &longs;ink, and to lay them Board <lb/>and Board in &longs;uch fa&longs;hion, that the one may lie on one &longs;ide of it, and <lb/>the other upon the other, as in the Scheme is apparent.</s></p><p type="main"> <s>This being done, fill tho&longs;e two Ships as full of water as they can <lb/>hold or &longs;wim, (the way to free them with great facility and expe­ <lb/>dition, &longs;hall be &longs;hewn in the twelfth Explanation;) and being full, <lb/>wait the time of low water; that is, when the Tide returning, the <lb/>Sea doth low as much as it can do; and at that in&longs;tant of time, <lb/>make the Ship very fa&longs;t with tho&longs;e ends of Cords or Cables (with <lb/>which it was Swite or bound) to tho&longs;e five, or more Tires of Beams, <lb/>wherewith the fore&longs;aid two Ships were imbreecht or grappled: And <lb/>having well belayd or fa&longs;tned tho&longs;e Cables, you mu&longs;t bale or take <lb/>out a &longs;mall part of the water out of one of the two Ships, and then <lb/>let it re&longs;t &longs;o, till &longs;uch time as you have baled or taken a little more <lb/>than that quantity out of the other Ship; and then again take a <lb/>little more out of the fir&longs;t Ship, and leave it &longs;o till you have taken <lb/>another &longs;uch a quantity from the other Ship, and thus proceed gra­ <lb/>dually, till you find the Foundered Ship, water-born or loo&longs;ned <lb/>from the bottom: but being water-born (if it be in a Showle bot­ <lb/>tom, as was that at <emph type="italics"/>Malamoccho)<emph.end type="italics"/> you are to take out the &longs;aid water, <lb/>equally from both the Ships, at one and the &longs;aid time, to the end <lb/>the Ship may ri&longs;e evenly without &longs;wagging or &longs;haking; and thus you <lb/>are to proceed till you have taken all the water from the one & the <lb/>other of the two Ships: In &longs;o doing, you &longs;hall &longs;ee the two Shpis lea­ <lb/>&longs;urely and gently rai&longs;e the Ship that was &longs;unk, &longs;o high above the <lb/>Surface of the water, that you may commodiou&longs;ly free it, and <lb/>di&longs;charge it of its lading, as appeareth in the following Figures. <lb/></s><s>And if you would not keep the two Ships &longs;o long imploy'd, you may <pb xlink:href="040/01/1179.jpg" pagenum="489"/>warpe or towe the Foundered Ship at high-water to &longs;ome place <lb/>where it may lie a-ground: and by that means upon the Ebbe or <lb/>Rece&longs;&longs;ion of the Tide, it will lie much more above water; and then <lb/>you may &longs;afely unfa&longs;ten it from tho&longs;e five or more Tires of Beames, <lb/>to which it was at fir&longs;t tyed, to hall it to a place of &longs;afety, as it was <lb/>our purpo&longs;e to do; and this &longs;hall &longs;ucceed as well in an ouzie bot­ <lb/>tom, as in a Stony, This though you may take notice of, that if <lb/>the Cargo of this new Foundred Ship was &longs;uch, that the things more <lb/>grave than the water, did not much exceed the le&longs;s grave, it would <lb/>be ea&longs;ie to effect the recovery with two Ships, very much le&longs;s than <lb/>tho&longs;e which we have &longs;poken of above; yet neverthele&longs;s it will be <lb/>good prudence to take them rather bigger than le&longs;&longs;er, that &longs;o they <lb/>may exceed 200000 pounds in Power, rather than want one only <lb/>ounce in Act; e&longs;pecially in ca&longs;e you would in a deep place at the <lb/>fir&longs;t motion hoi&longs;t it by meer Force &longs;omewhat above the Surface of <lb/>the water, for in that point alone it will require incomparably much <lb/>more force, than in all the other operations.</s></p><p type="main"> <s>How you are to preceed, in ca&longs;e the Ship &longs;hould be &longs;unk in a <lb/>place very deep, &longs;hall be declared in the &longs;eaventh Explanation. </s><s>The <lb/>Figures of this Explanation are the&longs;e two that folllow.</s></p><p type="caption"> <s><emph type="italics"/>The Figure of the two Ships filled with water, to rai&longs;e the Ship that <lb/>is &longs;unk<emph.end type="italics"/> <lb/><figure id="id.040.01.1179.1.jpg" xlink:href="040/01/1179/1.jpg"/></s></p> <pb xlink:href="040/01/1180.jpg" pagenum="490"/><p type="caption"> <s><emph type="italics"/>The Figure of the two Ships emptied as they lie, with the other Ship <lb/>rai&longs;ed up above water.<emph.end type="italics"/></s></p><figure id="id.040.01.1180.1.jpg" xlink:href="040/01/1180/1.jpg"/><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> III.</s></p><p type="main"> <s>But if it &longs;o fall out, that you cannot on &longs;nch an in&longs;tant, finde <lb/>two Ships of the &longs;ame Bulk with the Ship &longs;unk, you may take <lb/>four &longs;maller; provided, that all the four together hold twice <lb/>as much burden as the Ship &longs;unk, and rather more than le&longs;s. </s><s>Which <lb/>four &longs;mall Ships being all fir&longs;t cleer'd of their lading, and well &longs;topt <lb/>in all their Skuppers and Portholes (as was &longs;aid in the two) you mu&longs;t <lb/>couple them with Beams and good Planks, by two and two, as you <lb/>u&longs;e to do with two Lighters, when you would make a Bridge of <lb/>them: and the&longs;e two pair of Hoys or Barkes thus coupled together, <lb/>you mu&longs;t afterwards fa&longs;ten one pair to another, with &longs;even of tho&longs;e <lb/>Tires or Rows of thick and &longs;trong Beams tripplicated, as was &longs;aid in <lb/>the precedent Explanation; and place them at &longs;uch a di&longs;tance one <lb/>pair from another, as that you may leave berth or &longs;pace enough for <lb/>the &longs;unk or foundered Ship to ri&longs;e between them, and &longs;ome what <lb/>more, (as was &longs;aid of the two.) And though this conjunction of the <lb/>two pair of Ships, may be made three &longs;everall wayes, yet I will have <lb/>you make the two Poops or Hin decks of the one couple, to lie op­ <lb/>po&longs;ite to the two Poops of the other couple. </s><s>And to make this <lb/>conjunction, you are to place two Tires of tho&longs;e great Beams along <lb/>the upper parts of the &longs;aid Poops, &longs;o, that they may re&longs;t in the in­ <lb/>&longs;ide on tho&longs;e le&longs;&longs;er Beams and Planks, where with each of tho&longs;e two <lb/>pair of Ships were coupled: and each of the&longs;e Orders or Tires of <pb xlink:href="040/01/1181.jpg" pagenum="491"/>Beames ought to be compo&longs;ed of three Beams conjoyned length­ <lb/>wayes, as was &longs;aid in the precedent Explanation; and make two of <lb/>the Tires lie upon the Ships; and to tho&longs;e Tires, let that &longs;unk Ship <lb/>be grappled: and another Tire of the &longs;aid Beams is to be placed in <lb/>the mid&longs;t between the one and the other couple; and two other <lb/>Tires of the &longs;aid Beams ought to be fa&longs;tened upon the one and other <lb/>&longs;ide, that is, upon the Rifings or Bends of tho&longs;e two couples of <lb/>Ships; and that being done, there will be in all &longs;even Tires or Or­ <lb/>ders of Beams; which &longs;eaven Orders of Beams ought conjunctly to <lb/>be prolonged, on the one and on the other &longs;ide. </s><s>almo&longs;t to the <lb/>length of the Hull of each Ship, as in the Figure is represented: and </s></p><p type="caption"> <s><emph type="italics"/>The Figurall example how to recover a Foundered Ship with four <lb/>&longs;mall Ships<emph.end type="italics"/> <lb/><figure id="id.040.01.1181.1.jpg" xlink:href="040/01/1181/1.jpg"/> <lb/>this being done, you are to proceed, as hath been &longs;hewn in the two, <lb/>that is, fill them top full of water, and at low water, imbreech the <lb/>Ship &longs;unk very well, withall tho&longs;e ends of Ropes or Cables, that <lb/>you did belay to tho&longs;e &longs;even Tires of Beams: and when tho&longs;e <lb/>Grapplings &longs;hall be well made fa&longs;t; you &longs;hall at high water bale or <lb/>free the water by little and little out of the Ships, one pair after a­ <lb/>nother, till you feel the foundered Ship is di&longs;engaged from the bot­ <lb/>tom, and water-born, as was &longs;aid in the two. </s><s>And having &longs;epera­ <lb/>ted it from the bottom (if it be in a &longs;hallow place, as was that where <lb/>the Ship was foundered neer <emph type="italics"/>Malamoccho<emph.end type="italics"/>) you are to proceed to let <lb/>out the re&longs;t of the &longs;aid water, but take it equally and gradually from <lb/>the one and the other pair, that they may de&longs;cend evenly, and with­ <lb/>out heeling, as was &longs;aid of the two; and in &longs;o doing, the &longs;aid Ship <lb/>&longs;hall not only be hoi&longs;ted up to the Surface of the water, but much <pb xlink:href="040/01/1182.jpg" pagenum="492"/>above the &longs;ame; &longs;o that you may in that po&longs;ture free or drain it <lb/>and di&longs;charge it of the Cargo. </s><s>But if you cannot &longs;o long &longs;pare <lb/>tho&longs;e four Ships from other u&longs;es, then you may at high water tow <lb/>it to &longs;ome place, where running it on ground, you may at the ebbe <lb/>of the Tide (for that then there will lie much more of it above wa­ <lb/>ter) &longs;afely loo&longs;e it from tho&longs;e Beames, as was al&longs;o &longs;aid in the prece­ <lb/>dent Explanation of the two Ships.</s></p><p type="main"> <s>But in ca&longs;e the Foundered Ship &longs;hould chance to be in a very deep <lb/>Sea, in the &longs;eventh Explanation (to be the briefer in this place) <lb/>&longs;hall be &longs;hewn how you are to proceed.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> IV.</s></p><p type="main"> <s>And if it happen that it &longs;hould be in a place where there are <lb/>no Ships to be got, either great cr little; you may take of <lb/>other kind of Pinaces, Barks or Barges, but endeavour to <lb/>get &longs;uch as are floaty, and highe&longs;t built in there Rifings, that &longs;o they <lb/>may, at &longs;uch time as they are full of water, de&longs;cend very far under <lb/>water, (or according to the Mariners phra&longs;e, may draw much wa­ <lb/>ter) and of the&longs;e you mu&longs;t &longs;top all the Skuppers, Haw&longs;es, Cat-holes <lb/>and Port holes, that you finde, as in the Ships, that they may hold <lb/>the more water, and con&longs;equently draw the more water, or be de­ <lb/>pre&longs;&longs;ed deeper into the &longs;ame; and take &longs;o many couple of the&longs;e <lb/>Botes, that they may all together contain double the burden of <lb/>the Ship to be recovered, and rather much more, than any thing <lb/>le&longs;s. </s><s>And of all the&longs;e Boats or Barks, make two Squadrons, conjoyning <lb/>each Squadron with good &longs;mall Timbers & Planks, as you u&longs;e to do, <lb/>when you would make a Bridge of Boats: And the&longs;e &longs;ame Ve&longs;&longs;els of <lb/>the one and other divi&longs;ion, &longs;hould be placed board and board, that &longs;o <lb/>the great Beams, which are to conjoyn one Squadron to the other, <lb/>may bear upon the Rifings, Bends or Wales, of the &longs;aid Ve&longs;&longs;els. </s><s>And <lb/>this being done, you are to couple the&longs;e two Squadrons, to each other <lb/>with tho&longs;e thick and &longs;trong Tires of Beams, mentioned in the former <lb/>Explanations, which Orders of Beams &longs;hould be fixed between two & <lb/>two of tho&longs;e Botes, as is &longs;aid above, to the end, that they may bear or <lb/>re&longs;t upon the Bends of tho&longs;e Boats; and place another Tire upon the <lb/>out&longs;ides of both the Divi&longs;ions, upon the ends of the cro&longs;s &longs;mall Beams <lb/>which hold the &longs;everall Ve&longs;&longs;els together: So that if the Squadrons con­ <lb/>&longs;i&longs;ted each of four Barks, the Tires of the &longs;aid Beams would come to <lb/>be five,; and if there &longs;hould be five in a Squadron, the Tires of <lb/>Beams would be &longs;ix, and &longs;o forwards; that is, the Orders of Beams, by <lb/>this means, &longs;hall be alwayes one more than the number of Botes in <lb/>each Squadron. </s><s>But in the Ships you mu&longs;t ob&longs;erve another method, <lb/>becau&longs;e of tho&longs;e two Orders, which are placed in each Poop; by </s></p> <pb xlink:href="040/01/1183.jpg" pagenum="493"/><p type="caption"> <s><emph type="italics"/>The way to recover a Foundered Ship with many Barks or Wherryes.<emph.end type="italics"/> <lb/><figure id="id.040.01.1183.1.jpg" xlink:href="040/01/1183/1.jpg"/> <lb/>which means in every two Ships to a Divi&longs;ion (which in all make <lb/>four Ships) there mu&longs;t be &longs;even Orders of Beams, and in three Ships <lb/>to a Squadron, there mu&longs;t be ten Orders of Beams, and in four <lb/>Ships to a Squadron thirteen; and thus proceeding forwards to a <lb/>greater number of Ships in a Squadron. </s><s>And having under&longs;tood the <lb/>way of coupling many Barks or Wherryes in Squadrons; as al&longs;o the <lb/>manner how to joyn or fa&longs;ten them to each other, and with how <lb/>many Orders of Beams; you are to proceed in the re&longs;t, as in the <lb/>precedent Explanations hath been demon&longs;trated in &longs;howle bottoms, <lb/>but the directions how to manage this affair in deep places, &longs;hall be <lb/>declared in the &longs;eventh Explanation.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> V.</s></p><p type="main"> <s>To remove this inconvenience of taking Ships or other Ve&longs;&longs;els; <lb/>and of &longs;tanding to lighten them of their Guns & lading, and of <lb/>&longs;topping their Loop-holes; you may in&longs;uch a misfortune cau&longs;e <lb/>to be made two great Ve&longs;&longs;els, almo&longs;t in form of ^{*} Che&longs;ts without co­ <lb/><arrow.to.target n="marg1556"></arrow.to.target> <lb/>vers, the length of each to be equal to the Hull of a middle rate Ship, <lb/>and the breadth equall to that of the &longs;ame Ship at the Main-ma&longs;t, <lb/>and the height al&longs;o the &longs;ame with that of the Ship in the Bow, &longs;o <lb/>that each of the&longs;e Plat forms or Che&longs;ts, &longs;hall hold much more than <lb/>a common Ship, and thus both will contain more than the double <lb/>burden of &longs;uch a Ship. </s><s>And for the making of the&longs;e Ve&longs;&longs;els, you <lb/>mu&longs;t fir&longs;t make the Models in Carvel-manner of thick and &longs;trong <lb/>Timber, with their Eutertaces, Tran&longs;omes and Knees, to hold their <lb/>&longs;ides and ends together: and this done, &longs;pike down to them certain <pb xlink:href="040/01/1184.jpg" pagenum="494"/>thick and &longs;trong Planks; and then cau&longs;e them to be well graved and <lb/>calked in the Seames or Strakes by a Calker, with Okum, and paid <lb/>with Pitch, as you u&longs;e to do Ships or Gallyes, and then apply them <lb/>to your purpo&longs;e. </s><s>And when you would u&longs;e them, you need only <lb/>fa&longs;ten them together with tho&longs;e five or more Orders of thick and <lb/>lu&longs;ty Beams, trippled lengthwayes, that is, prolonged both wayes, <lb/>&longs;o as that they may lie athwart the Decks of the &longs;aid two Ve&longs;&longs;els, <lb/>and place the &longs;aid Ships &longs;o far di&longs;tant from each other, as you gue&longs;&longs;e <lb/>the bredth of the Foundered Ship to be, and &longs;omething more: And <lb/>then make upon the Deck of each of them, that is, upon tho&longs;e <lb/>Beams, a Plat-form of Planks, as was &longs;aid in the two Ships of the <lb/>&longs;econd Explanation, and afterwards proceed as in tho&longs;e two Ships.</s></p><p type="margin"> <s><margin.target id="marg1556"></margin.target>* Of the&longs;e Ve&longs;­ <lb/>&longs;els Cardinall <lb/><emph type="italics"/>Richleiu<emph.end type="italics"/> made <lb/>u&longs;e at the Siege <lb/>of <emph type="italics"/>Rochell<emph.end type="italics"/> to &longs;hut <lb/>up the Haven.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> VI.</s></p><p type="main"> <s>And inca&longs;e you think the making of a couple of &longs;uch great <lb/>Modles or Ve&longs;&longs;els, as we mentioned in the foregoing Ex­ <lb/>planation, would be too great a trouble or expence; you <lb/>may make two pair of &longs;uch Che&longs;ts, each of them but of hal&longs; the <lb/>bulk of one of the former: but if you judge the&longs;e two pair too <lb/>trouble&longs;ome, you may make three, four, or more pairs; alwayes <lb/>provided, that among&longs;t them all they hold about twi&longs;e the burden <lb/>of the Ship &longs;unk; and the&longs;e Frames when you would u&longs;e them, mu&longs;t <lb/>be joyned together in two Ranks, with le&longs;&longs;er Beams and Planks, <lb/>as was &longs;aid of the four Boats or Wherryes; and then fa&longs;ten the&longs;e <lb/>two Ranks to each other at the requi&longs;ite di&longs;tance, with great and <lb/>&longs;trong tripplicated Beams, as was &longs;aid of the Ships, Barks and Boats; <lb/>and then operate as you was to do with tho&longs;e: alwayes remembring <lb/>in the freeing or emptying the &longs;aid Ve&longs;&longs;els, to bale out the water by <lb/>little and little fir&longs;t from one Rank, and then from the other; and <lb/>&longs;o proceed interchangeably till you percieve that the Ship is clear of <lb/>the bottom: and being di&longs;engaged, if it be in a &longs;hallow place, <lb/>continue taking the water equally out of the one and other Divi&longs;i­ <lb/>on of Ve&longs;&longs;els, till all the water be drained out of them, as was requi­ <lb/>red upon the former Explanations: but if it be &longs;unk in a deep Sea, <lb/>the next Explanation &longs;hall &longs;hew how you are to proceed; and that <lb/>briefly.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> VII.</s></p><p type="main"> <s>And in ca&longs;e the &longs;aid Ship newly &longs;unk, chance to be in a very <lb/>deep bottom; It will be nece&longs;&longs;ary fir&longs;t to fix upon tho&longs;e <lb/>two or four Ships, or upon tho&longs;e two Squadrons of Barks, <lb/>Fly-boats or Wherryes, at lea&longs;t &longs;ix or eight Cap&longs;tains, Ship-Cranes <pb xlink:href="040/01/1185.jpg" pagenum="495"/>or Windla&longs;&longs;es, with their nece&longs;&longs;ary Garnets or Pullies, requi&longs;ite to <lb/>&longs;nch a weight: and you may ea&longs;ily accomodate the&longs;e Pullies, to tho&longs;e <lb/>Orders of great Beams, wherewith the &longs;aid Ve&longs;&longs;els were conjoyned. <lb/></s><s>And having prepared the&longs;e Cap&longs;tains, you are to proceed in all <lb/>things, as hath been directed you in the precedent Explanations, <lb/>excepting only in this, that whil&longs;t you are freeing the water alter­ <lb/>nately by degrees out of the two or more Ships, or from the two <lb/>Squadrons of Barks, Fly-boats or Wherryes, as &longs;oon as you finde <lb/>the Foundered Ship to be water-born or got clear of the bottom of <lb/>the Sea, I would have you cea&longs;e to take any more water forth of <lb/>the &longs;aid Ships, or le&longs;&longs;er Ve&longs;&longs;els before filled; and I would have you <lb/>with tho&longs;e Cap&longs;tains, attempt to draw the &longs;aid Ship that was funk <lb/>unto the Levell or Surtace of the water, or to lie Horizontal unto it, <lb/>which may be ea&longs;ily done, for that its pondero&longs;ity will be much di­ <lb/>mini&longs;hed. </s><s>And when you have drawn it to the Surface of the water, <lb/>then I would have you di&longs;charge all the other water out of the two <lb/>Ships, or the two Squadrons of &longs;mall Ve&longs;&longs;els. </s><s>And this &longs;econd wa­ <lb/>ter, I would have raken equally, and at the &longs;ame time, from the one <lb/>and the other Ship, or from each Rank of Barks or Boats, as hath <lb/>been &longs;aid of the other. </s><s>And thus tho&longs;e Ships or Squadrons of Boats <lb/>&longs;hall hoi&longs;t the &longs;aid Foundered Ship, &longs;o high above the Superficies of <lb/>the water, that you may free it of the water which was got into it, <lb/>and unlade its Cargo, which was our purpo&longs;e.</s></p><p type="main"> <s>You mu&longs;t note, that all that hath been hitherto &longs;aid of a Ship <lb/>newly &longs;unk, ought to be under&longs;tood of all other kind of Foundered <lb/>Ships, proceeding alwayes proportionately as was directed in that <lb/>Ship. </s><s>And again, I give you no Figure how you are to fit and fix <lb/>the Cap&longs;tains and Pullies, as being a thing common and manife&longs;t.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> VIII.</s></p><p type="main"> <s>But if it &longs;o fall out, that the &longs;aid Ship or other Ve&longs;&longs;el hath been <lb/>&longs;unk many Months; albeit that there might have been many <lb/>matters in the Cargo of a lighter nature than water, yet you <lb/>mu&longs;t &longs;uppo&longs;e the ca&longs;e as if the Ship were as heavy as if it had been <lb/>fil'd with Sand or Gravel; yea and much heavier, for many Rea&longs;ons, <lb/>as hath been alledg'd in the fir&longs;t Explanation. </s><s>Therefore that you <lb/>may not deceive your &longs;elves in the de&longs;igned recovering of it, you <lb/>would do well to double the Forces required to the recovery of a <lb/>new &longs;unk Ship; that is, you mu&longs;t take four Ships, each as big as <lb/>the Foundered <emph type="italics"/>S<emph.end type="italics"/>hip, and combine the&longs;e four <emph type="italics"/>S<emph.end type="italics"/>hips, as you were re­ <lb/>quired to joyn the four &longs;mall <emph type="italics"/>S<emph.end type="italics"/>hips in the third Explanation. </s><s>And <lb/>if you cannot procure them of that burthen, take eight le&longs;&longs;er, pro­ <lb/>vided that altogether they be quadruple in contence to the <emph type="italics"/>S<emph.end type="italics"/>hip to <pb xlink:href="040/01/1186.jpg" pagenum="496"/>to be recovered: and divide the&longs;e eight le&longs;&longs;er <emph type="italics"/>S<emph.end type="italics"/>hips or Barks into <lb/>two <emph type="italics"/>S<emph.end type="italics"/>quadrons, of four in a <emph type="italics"/>S<emph.end type="italics"/>quadron, according as you was di­ <lb/>rected in the four Ships in the third direction. </s><s>And if you cannot pro­ <lb/>cure <emph type="italics"/>S<emph.end type="italics"/>hips great or &longs;mal, take &longs;o many pair of other Ve&longs;&longs;els, Fly boats <lb/>or Wherryes, that in all they may at lea&longs;t contain four times the bur­ <lb/>then of the Foundered <emph type="italics"/>S<emph.end type="italics"/>hip: And reduce the&longs;e Barks, Boats or <lb/>Wherryes into two Divi&longs;ions, as you are taught in the fourth Ex­ <lb/>planation: and in all other particulars, proceed according to the <lb/>method pre&longs;cribed in the recovery of the <emph type="italics"/>S<emph.end type="italics"/>hip newly &longs;unk; and <lb/>that as well in deep, as &longs;hallow places; that is, placing in a deep <lb/><emph type="italics"/>S<emph.end type="italics"/>ea upon the &longs;aid Ships, or <emph type="italics"/>S<emph.end type="italics"/>quadrons of Boats, at lea&longs;t twelve or <lb/>&longs;ixteen Cap&longs;tains, which it will be ea&longs;ie to do, for that you will have <lb/>a large &longs;pace upon tho&longs;e <emph type="italics"/>S<emph.end type="italics"/>hips or ranks of Boats, as al&longs;o there will <lb/>not want room to fa&longs;ten their Pullies to tho&longs;e Tires of Beams, which <lb/>combine the &longs;aid <emph type="italics"/>S<emph.end type="italics"/>hips or ranks of Boats. </s><s>In all things el&longs;e proceed <lb/>preci&longs;ely according as you have been directed in the &longs;econd, third, <lb/>fourth, fifth, &longs;ixth and &longs;eventh Explanations.</s></p><p type="main"> <s>This indeed mu&longs;t be granted, that inca&longs;e the &longs;aid <emph type="italics"/>S<emph.end type="italics"/>hip long &longs;unk, <lb/>&longs;hould be in a <emph type="italics"/>S<emph.end type="italics"/>tony bottom, or where &longs;he hath a great current, the <lb/>which current &longs;uffereth not any great bed or &longs;helves of Mudd to <lb/>gather about the &longs;aid <emph type="italics"/>S<emph.end type="italics"/>hip, it may then ea&longs;ily be got clear of the bot­ <lb/>tom, with the &longs;ame Forces as were imploy'd in that newly &longs;unk, to <lb/>recover it; and al&longs;o may as ea&longs;ily be drawn to the Surface of the <lb/>water: But whether you can rai&longs;e it with part of its Hull above <lb/>the <emph type="italics"/>S<emph.end type="italics"/>uperficies of the water, is a thing much to be doubted; <lb/>yet if it &longs;hould prove &longs;o upon the Experiment, namely, that you <lb/>cannot elevate its Hull above the <emph type="italics"/>S<emph.end type="italics"/>urface of the water, you may in <lb/>&longs;uch a ca&longs;e hall it at high water to &longs;hore, or to &longs;ome place where it <lb/>may lie a ground, whereby at the retreat of the Tide, it will lye with <lb/>part of its Hull above water, &longs;o that you may commodiou&longs;ly clear <lb/>it of the imbibed water and Cargo.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> IX.</s></p><p type="main"> <s>And to the end that this invention may be of generall u&longs;e <lb/>for the re covery or rai&longs;ing any kind of Collo&longs;&longs;us, that may <lb/>happen to be &longs;unk, to wit, of all <emph type="italics"/>S<emph.end type="italics"/>pecies of <emph type="italics"/>S<emph.end type="italics"/>olid Bodies, <lb/>whether of <emph type="italics"/>S<emph.end type="italics"/>tone, Iron, Pewter, Bra&longs;s, Lead, <emph type="italics"/>S<emph.end type="italics"/>ilver or Gold (as you <lb/>may have many occa&longs;ions voluntarily to &longs;ink them in time of war, to <lb/>pre&longs;erve them) and then that you may know how to get them up <lb/>again, you mu&longs;t ob&longs;erve this Rule: If the <emph type="italics"/>S<emph.end type="italics"/>olid long time &longs;ubmer­ <lb/>ged were of Brick; &longs;o &longs;oon as it is imbreecht, you mu&longs;t take &longs;o ma­ <lb/>ny couple of <emph type="italics"/>S<emph.end type="italics"/>hips, Barks, Hoyes or Wherryes, that the &longs;um of their <lb/>contents put together, may exceed the <emph type="italics"/>S<emph.end type="italics"/>quare of the <emph type="italics"/>S<emph.end type="italics"/>olid Area <lb/>of the &longs;ubmerged <emph type="italics"/>S<emph.end type="italics"/>olid: and if the <emph type="italics"/>S<emph.end type="italics"/>olid &longs;o long &longs;unk were of Mar­ <pb xlink:href="040/01/1187.jpg" pagenum="497"/>ble, the <emph type="italics"/>S<emph.end type="italics"/>olid Content of all the <emph type="italics"/>Vacua<emph.end type="italics"/> of tho&longs;e <emph type="italics"/>S<emph.end type="italics"/>hips or Ve&longs;&longs;els ad­ <lb/>ded together, mu&longs;t not be le&longs;s than Septuple to the Solid Content <lb/>of the &longs;ubmerged Body; namely, &longs;even times as much. </s><s>And if <lb/>that long &longs;unk Solid chance to be of Iron; you mu&longs;t make the Solid <lb/>Content of all the <emph type="italics"/>Vacuum's<emph.end type="italics"/> of tho&longs;e Ve&longs;&longs;els to be no le&longs;&longs;e in the <lb/>Aggregate than 12 3/2 times as much as the Solid Content of that &longs;ub­ <lb/>merged Solid: and the like mu&longs;t be done, if the &longs;ubmerged Solid <lb/>be of Pewter, for that Iron and Pewter differ not much in Gravity. <lb/></s><s>But and if the drowned <emph type="italics"/>S<emph.end type="italics"/>olid be of Copper, it is requi&longs;ite that the <lb/><emph type="italics"/>S<emph.end type="italics"/>olid Content of all the Ve&longs;&longs;els Cavities in &longs;um, be no le&longs;s than <lb/>thirteen times as much as the <emph type="italics"/>S<emph.end type="italics"/>olid Content of the &longs;aid <emph type="italics"/>S<emph.end type="italics"/>olid &longs;unk. <lb/></s><s>And if the &longs;ubmerged <emph type="italics"/>S<emph.end type="italics"/>olid were of Lead, the <emph type="italics"/>S<emph.end type="italics"/>olid Content of all <lb/>the <emph type="italics"/>Vacua<emph.end type="italics"/> of tho&longs;e <emph type="italics"/>S<emph.end type="italics"/>hips, wherewith you would recover it, &longs;hould <lb/>be no le&longs;s than twenty times as much as the <emph type="italics"/>S<emph.end type="italics"/>olid content of the <lb/>drowned <emph type="italics"/>S<emph.end type="italics"/>olid, and rather more than le&longs;s; and almo&longs;t the &longs;ame <lb/>proportion ought to be ob&longs;erved, if the &longs;ubmerged Solid were of fine <lb/>Silver, for that Lead and pure Silver differ not much in Gravity: <lb/>truth is, that Lead is &longs;omewhat more weighty than Silver, but not <lb/>much.</s></p><p type="main"> <s>But if the Solid which was &longs;unk, &longs;hould chance to be of pure <lb/>Gold, you mu&longs;t for its recovery take &longs;o many couple of Barks or <lb/>Boats, that the Solid Content of their <emph type="italics"/>Vacua,<emph.end type="italics"/> taken in aggregate, <lb/>may be no le&longs;s than 34 times as much as the Solid content of the <lb/>&longs;aid Golden Solid &longs;ubmerged. </s><s>And that you may the better under­ <lb/>&longs;tand me, I will put an Example, that you were to recover or rai&longs;e <lb/>out of the water, a Solid Body re&longs;embling a great Tower, which I <lb/>imagine to be in length an 100 Paces, and in breadth 10, and in <lb/>thickne&longs;s al&longs;o ten: and I &longs;uppo&longs;e that it is all one <emph type="italics"/>S<emph.end type="italics"/>olid, that is to <lb/>&longs;ay, not hollow within. </s><s>And fir&longs;t we put the ca&longs;e that this Tower <lb/>were made of Brick. </s><s>Now becau&longs;e the <emph type="italics"/>S<emph.end type="italics"/>olid Content of this &longs;up­ <lb/>po&longs;ed <emph type="italics"/>S<emph.end type="italics"/>olid would be 10000 cubical Paces: therefore in this ca&longs;e, <lb/>if you would recover this &longs;ame Body, that is, not only loo&longs;en it from <lb/>the bottom of the <emph type="italics"/>S<emph.end type="italics"/>ea, but al&longs;o rai&longs;e it a good height above water, <lb/>it will be requi&longs;ite, as is &longs;aid above, to take &longs;o many pair of Ships, <lb/>Barks, Boats, or other Ve&longs;&longs;els, (as hath been &longs;hewn in the 5 and 6 <lb/>Explanation) that the <emph type="italics"/>S<emph.end type="italics"/>olid Content of all the <emph type="italics"/>Vacua<emph.end type="italics"/> of them put <lb/>together, be not le&longs;s than four times the &longs;aid &longs;um of 10000 cubick <lb/>Paces; that is, it mu&longs;t not be under 40000 cubicall Paces, as was <lb/>above determined. </s><s>And &longs;o ìf it happen that the &longs;aid &longs;ubmerged So­ <lb/>lid &longs;hould be all of Marble, the <emph type="italics"/>S<emph.end type="italics"/>olid Content of all the Vacuities <lb/>of the &longs;aid <emph type="italics"/>S<emph.end type="italics"/>hips, ought not to be le&longs;s than 70000 cubicall Paces, <lb/>namely Septuple, as was before concluded. </s><s>And thus if the &longs;unk. <lb/><emph type="italics"/>S<emph.end type="italics"/>olid were all of Iron or Pewter, the aggregate of all the <emph type="italics"/>S<emph.end type="italics"/>olid Con­ <lb/>tent of all tho&longs;e <emph type="italics"/>Vacuums<emph.end type="italics"/> put together, mu&longs;t be rather more than <pb xlink:href="040/01/1188.jpg" pagenum="498"/>le&longs;s then 126666 2/3 cubical Paces. </s><s>And in ca&longs;e the Solid were all of <lb/>Copper, the Solid Content of the &longs;aid <emph type="italics"/>Vacua<emph.end type="italics"/> ought to be about <lb/>130000 cubick Paces. </s><s>And likewi&longs;e if the Solid were all of Lead <lb/>or Silver, the Solid Content of all the &longs;aid <emph type="italics"/>Vacua<emph.end type="italics"/> is to be no le&longs;s than <lb/>200000 Paces cubical. </s><s>La&longs;tly, if &longs;uch &longs;ubmerged Solid be pro­ <lb/>pounded all of fine Gold, the &longs;um of tho&longs;e Cavities ought to be no <lb/>le&longs;s than 340000 cubick Paces.</s></p><p type="main"> <s>The manner how to proceed in the recovery of tho&longs;e &longs;everall <lb/>kinds of Solids, is to be under&longs;tood to be like to that which was <lb/>pre&longs;cribed in the recovery of the Ship: and that as well in deep, as <lb/>&longs;hallow waters. </s><s>And the greater number of Ships or Boats are re­ <lb/>quired to opperate in the recovery of the &longs;aid &longs;ubmerged Solid in a <lb/>deep Channell, &longs;o much the more room mu&longs;t yon take upon the <lb/>one and the other Squadron, for to be able to pitch &longs;uch a number <lb/>of Cap&longs;tens as &longs;hall be needfull, and more if occa&longs;ion be. </s><s>Yet you <lb/>mu&longs;t ob&longs;erve, that in the taking the water alternately from the one <lb/>and other Squadron, when you perceive the &longs;aid Solid to be di&longs;­ <lb/>engaged from the bottom, you are to forbear taking out any more <lb/>from either of them; as was appointed touching the Ship, in the <lb/>&longs;eventh Explanation. </s><s>And make u&longs;e of as many Pullies as you &longs;hall <lb/>&longs;ee cau&longs;e for, not only to lift it to, but al&longs;o to draw it above the <lb/>waters Surface: and that if notwholly, yet for the greater part: <lb/>and when it is lifted as high as is po&longs;ible, then take the remaining <lb/>water by equall mea&longs;ures, out of the one and other Squadron, or <lb/>Rank of Ships; which being done, it &longs;hall be hoi&longs;ted &longs;o high out of <lb/>the water, that you may put under it as many Lighters or Flat-boats, <lb/>as &longs;hall be &longs;ufficient to bear it up, and to carry it to any place, as <lb/>occa&longs;ion &longs;hall require.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION X.<emph.end type="italics"/></s></p><p type="main"> <s>Albeit <emph type="italics"/>Vitruvius, Vegetius<emph.end type="italics"/> and <emph type="italics"/>Valturius<emph.end type="italics"/> do teach diver&longs;e and &longs;un­ <lb/>dry wayes to carry water up on high, many whereof may <lb/>&longs;tand us in much &longs;tead in this our Invention, for the commo­ <lb/>dious filling and emptying all the &longs;everall kinds of Ve&longs;&longs;els &longs;poken of <lb/>above; of which al&longs;o, many are very well known and familiar to <lb/>every one; to wit, with Bur-pumps, Chain pumps, common-pumps, <lb/>and many others: yet neverthele&longs;s to fill the &longs;aid Ships or other <lb/>Ve&longs;&longs;els with water, with great facility and dexterity; I judge this <lb/>more expedient than any of them; namely, to make a Hole in the <lb/>bottom of each of tho&longs;e Ships or other Ve&longs;&longs;els, of two or three inches <lb/>Diameter at lea&longs;t, and for every Ship to appoint a Boome or long <lb/>tapered Pole like a Plugg or Tapp, &longs;o that being thru&longs;t into the &longs;aid <lb/>Hole, it will &longs;top it &longs;o clo&longs;e, that unle&longs;s you con&longs;ent thereto, no <pb xlink:href="040/01/1189.jpg" pagenum="499"/>water can enter in thereat, and this Pole is to be &longs;omewhat longer <lb/>than to reach from the Keel to the upper deck of the &longs;aid Ship; and <lb/>near the other end, put another piece of a Pole cro&longs;s wayes; that <lb/>you may be able by means of that to rule it; namely, to pull it up, <lb/>when you would un&longs;top the Hole, to let in the water that &longs;hould <lb/>fill the Ship, and to thru&longs;t it down when you would &longs;top the Hole <lb/>that no more water may enter; and this &longs;ame Pole &longs;hould pa&longs;s <lb/>through two Rings, fixed in the Hold of the Ship, which are to <lb/>keep the &longs;aid Pole directly over the Hole, that if you would &longs;top it, <lb/>the Plugg or Spiggot may not go be&longs;ides the Hole, when you thru&longs;t <lb/>the Pole downwards. </s><s>And that I may be the better under&longs;tood, I <lb/>have here below drawn the &longs;ame Pole, with its Tapp or Plugg at the <lb/>end. </s><s>And when you go about to recover any Ship, you mu&longs;t &longs;top <lb/>the &longs;aid Holes, till &longs;uch time as the &longs;aid Ships are carried <lb/><figure id="id.040.01.1189.1.jpg" xlink:href="040/01/1189/1.jpg"/> <lb/>and fitted upon the place, as is &longs;hewn above. </s><s>And <lb/>when you would fill them with water, it is but with­ <lb/>drawing the &longs;aid Poles, and opening the Holes; and <lb/>fa&longs;ten them at that &longs;tay, till you have a mind to &longs;top <lb/>the Holes; and then look downwards, and ob&longs;erve <lb/>when the Ships are as full as they can &longs;wim, or when <lb/>they are full enough, which will be in a very &longs;hort <lb/>time: and then let down tho&longs;e Poles, and &longs;top the <lb/>Holes very clo&longs;e. </s><s>And when they are as full as they <lb/>need, in the ebb of the Tide, combine the Ship with the Pullies, to <lb/>tho&longs;e five or more Orders of Beams often mentioned: and then draw <lb/>out the water with Pumps by little and little, and one while out of <lb/>one, and another while out of the other Ship, as was appointed in <lb/>the &longs;econd Explication: and in all other particulars proceed, as was <lb/>al&longs;o there directed But if the Gravity of tho&longs;e Ve&longs;&longs;els, cau&longs;eth <lb/>them not to fill fa&longs;t enough, you mu&longs;t fill them at the top, that is <lb/>by baling in water by the Deck (I mean the &longs;aid Poles being fir&longs;t <lb/>thru&longs;t down) to make the &longs;aid Ve&longs;&longs;els to de&longs;cend fa&longs;ter, and to rai&longs;e <lb/>the Matter &longs;ubmerged with more Force; many other new wayes <lb/>might be &longs;hewn, as well to empty, as to fill the&longs;e Ve&longs;&longs;els; but for <lb/>the pre&longs;ent this &longs;hall &longs;uffice.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> XI.</s></p><p type="main"> <s>If you would attempt to recover a Ship or other Ve&longs;&longs;el by the <lb/>wayes here pre&longs;cribed: you mu&longs;t go about the &longs;ame, when the <lb/><arrow.to.target n="marg1557"></arrow.to.target> <lb/>Moon is in the Auge of the Excentrick, for at that time the Sea <lb/>ebbeth and floweth more than at any other time in the Moneth; <lb/>and this happens in her Coujunction and Oppo&longs;ition, which is a <lb/>matter of great avail in the&longs;e operations: and herewith we conclude <lb/>this our fir&longs;t Book.</s></p> <pb xlink:href="040/01/1190.jpg" pagenum="500"/><p type="margin"> <s><margin.target id="marg1557"></margin.target><emph type="italics"/>i.e.<emph.end type="italics"/> At a &longs;pring, <lb/>tide, which is <lb/>greate&longs;t the third <lb/>day after the fuil <lb/>and change.</s></p><p type="head"> <s>THE <lb/>Indu&longs;trious or Trouble&longs;ome <lb/>INVENTION <lb/>OF <lb/>Nicholaus Tartalea:</s></p><p type="head"> <s><emph type="italics"/>BOOKE<emph.end type="italics"/> II.</s></p><p type="main"> <s>In which are taught, &longs;ome artificial wayes of <emph type="italics"/>Diving<emph.end type="italics"/> <lb/>and &longs;taying long under Water: whereby one may <lb/>ea&longs;ily de&longs;cend to the Bottom, to finde out, not on­ <lb/>ly a Ship &longs;unke, but al&longs;o, any other &longs;mall thing of <lb/>Value: And the place being darke, many wayes <lb/>are &longs;hewn how to enlighten it: And the thing <lb/>&longs;unk being found, &longs;everall wayes and means are <lb/>pre&longs;cribed how to imbreach them, as well in a <lb/>Deepe, as Shallow Channel.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> I.</s></p><p type="main"> <s>Having under&longs;tood, <emph type="italics"/>Mo&longs;t Serene Prince,<emph.end type="italics"/> from &longs;un­ <lb/>dry Sea men, that there are many now adayes, <lb/>who without any particular Artifice or help, do <lb/>upon occa&longs;ion dive and continue a long time <lb/>under Water, and in places very deep; I had <lb/>thought to have added nothing touching the <lb/>way of Artificiall Diving, and &longs;taying under <lb/>water, to &longs;eeke and finde out a Ship, Boare, <lb/>or other thing of Value &longs;ubmerged, and that for two Rea&longs;ons. </s><s>Fir&longs;t, <lb/>Fearing that I &longs;hould be derided by tho&longs;e kinde of men, it being to <lb/>them a &longs;uperfluous thing to go about to do tho&longs;e things by Art, <lb/>which they know how to execute without any arrificiall help. <pb xlink:href="040/01/1191.jpg" pagenum="501"/>Secondly, doubting, by rea&longs;on of my &longs;mall experience in Maratine <lb/>Affairs, to incurre &longs;ome Soleci&longs;me: but there coming into my mind <lb/>an excellent expre&longs;&longs;ion of a famous Philo&longs;opher of this Renowned <lb/>City; who upon a time per&longs;wading me to write &longs;omething that <lb/>was new, and I having an&longs;wered (it being incident for humanly to <lb/>erre) that I was afraid lea&longs;t my &longs;o great de&longs;ire to publi&longs;h my fund y <lb/>new Conjectures, might run me into &longs;ome fanta&longs;tical conceits, that <lb/>might make me become the &longs;ubject of vulgar di&longs;cour&longs;e, this excel­ <lb/>lent per&longs;on replied: That if Nature &longs;hould forbear her operations for <lb/>fear of producing &longs;ometimes &longs;ome mon&longs;trous things, the worlds de­ <lb/>&longs;truction would en&longs;ue, for that they onely are free from erring who <lb/>do nothing, who&longs;e &longs;peech hath emboldened me to &longs;peak of a point, <lb/>which I never thought to have medled with; namely, To declare <lb/>&longs;ome of my conjectural wayes of artificial diving, and continuing <lb/>under water, to &longs;eek out any thing that was &longs;unk in the &longs;ame, though <lb/>in places very deep. </s><s>And I judge the&longs;e the mo&longs;t expedient that can <lb/>be devi&longs;ed: and becau&longs;e the&longs;e and the like wayes may be varied <lb/>into &longs;everal forms, and &longs;orts, one more ingenious, and artificial than <lb/>another; the prettie&longs;t, and mo&longs;t ingenious is this, I would have you <lb/><arrow.to.target n="marg1558"></arrow.to.target> <lb/>get, made at <emph type="italics"/>Murano,<emph.end type="italics"/> a hollow Globe of Tran&longs;parent Gla&longs;&longs;e, the di­ <lb/>ameter of which I would have to be at lea&longs;t two foot, with a round <lb/>mouth, that the Diameter of the &longs;aid mouth may be at lea&longs;t one <lb/>foot, or wrather more; that is, &longs;o much as one may ea&longs;ily put his <lb/>head therein, and at plea&longs;ure draw it forth; and next you mu&longs;t <lb/>make two round Boards of a Diameter &longs;omething bigger then that <lb/>of the &longs;aid Globe, and with the&longs;e two round Boards, and four &longs;len­ <lb/>der pieces of Wood, as long as a man is high, and a little more, you <lb/>mu&longs;t make a little Modell for a man to &longs;tand betwixt the&longs;e four pie­ <lb/><arrow.to.target n="marg1559"></arrow.to.target> <lb/>ces of Wood; and with one of the round Boards above, and the o­ <lb/>ther beneath; and the&longs;e round Boards are to be very fa&longs;t nailed or <lb/>otherwi&longs;e fa&longs;tened to the four pieces of the Frame, and in the top of <lb/>this Machine, you mu&longs;t fit and fix the &longs;aid Sphere of Gla&longs;&longs;e with the <lb/>mouth downwards, &longs;o, that if a man &longs;tand upright in the &longs;aid Frame, <lb/>he may hold his head in the &longs;aid gla&longs;&longs;e without &longs;tooping. </s><s>And this <lb/>being done, take neer upon as much Lead as all this Machine weighs, <lb/>and make it into a round figure, of the compa&longs;&longs;e of the round <lb/>Boards, and then fa&longs;ten and nail it to the bottome of the &longs;aid Mo­ <lb/>dell, namely, underneath the lowermo&longs;t Board on which your feet <lb/>&longs;tand when you put it into the Water: And then, (or before) <lb/>make an hole as big as a Shilling in the Centre of this Lead and <lb/>Board, pa&longs;&longs;ing through them both; and this &longs;ame Lead will be able <lb/>to draw almo&longs;t all the Machine together with him that &longs;hall be <lb/>therein under Water. </s><s>Truth is, that the Experiment requireth that <lb/>the &longs;aid Lead be &longs;o limitted that it may be able to draw the Ma­ <pb xlink:href="040/01/1192.jpg" pagenum="502"/>chine and per&longs;on in it under Water, but &longs;o, that the &longs;upreme or up <lb/>per part of the &longs;ame, that is the uppermo&longs;t round Board, may &longs;tay at <lb/>the Superficies of the Water; that is, if the Lead chance to be &longs;o <lb/>ponderous, that it cau&longs;e the Engine to &longs;ink lei&longs;urely to the bottome, <lb/>you mu&longs;t take away &longs;ome of the &longs;aid Lead; and on the contrary, <lb/>if it chance that the Lead be not able to draw it all in that manner <lb/>under Water, &longs;o as to make the &longs;aid upper round Board to lye and <lb/>&longs;tay exactly level with the Surface of the Water, but that a part of it <lb/>re&longs;ts vi&longs;ible above the Water, you mu&longs;t encrea&longs;e the &longs;aid Lead &longs;o, <lb/>that the upper Board may lye and abide preci&longs;ely, as was &longs;aid be­ <lb/>fore, in the Surface of the Water: and when you have thus adju­ <lb/>&longs;ted the &longs;aid Lead, I would have you take a Ball or Bullet of Lead <lb/>weighing two or three pounds, (that is to &longs;ay of &longs;uch a weight, that <lb/>it may be &longs;ufficient to make the Machine and per&longs;on diving to de­ <lb/>&longs;cend to the bottome as oft as it is interpo&longs;ed, or added,) with an <lb/>Iron Ring in the &longs;aid Ball, to which bend or fa&longs;ten a Rope as long as <lb/>the &longs;aid Water is deep, in which the Diver is to de&longs;cend, and &longs;ome­ <lb/>what more; and reeve or pa&longs;&longs;e the other end of the &longs;aid <lb/>Cord through the hole <lb/>made in the Board and <lb/>Lead through the bot­ <lb/><figure id="id.040.01.1192.1.jpg" xlink:href="040/01/1192/1.jpg"/> <lb/>tom of the Model; and <lb/>fa&longs;ten that &longs;ame end <lb/>of the Cord in a place <lb/>of the Machine, &longs;o, that <lb/>the Diver may take it, <lb/>and draw it, or &longs;lack <lb/>it as he plea&longs;eth: and <lb/>this being done, the <lb/>&longs;aid Machine will be <lb/>fini&longs;hed. </s><s>And that you <lb/>may better under­ <lb/>&longs;tand it, I have here in­ <lb/>&longs;erted it graphically: <lb/>yet I &longs;hould have told <lb/>you, that for many rea­ <lb/>ons you &longs;hould in the beginning have fa&longs;tened a Ring in the Cen­ <lb/>tre of the upper Board, on the out&longs;ide, to tye a Cord to the &longs;ame as <lb/>occa&longs;ion &longs;erveth.</s></p> <pb xlink:href="040/01/1193.jpg" pagenum="503"/><p type="margin"> <s><margin.target id="marg1558"></margin.target>A Place near to <lb/><emph type="italics"/>Venice,<emph.end type="italics"/> where the <lb/>famous Glahes <lb/>are made.</s></p><p type="margin"> <s><margin.target id="marg1559"></margin.target>Like the Frame <lb/>of an Houre­ <lb/>gla&longs;&longs;e.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> II.</s></p><p type="main"> <s>Having under&longs;tood the manner how to make this &longs;ame En­ <lb/>gine, it remains to &longs;hew how it is to be u&longs;ed; And for your <lb/>direction therein, I &longs;ay, That he that would dive or go under <lb/>Water to &longs;eek any thing that was &longs;unk, &longs;hould carry the &longs;aid Ma­ <lb/>chine to the place where he re&longs;olves to de&longs;cend, and fir&longs;t to let that <lb/>Ball of Lead with the Line go to the bottome, and then to put in <lb/>the Machine it &longs;elf, which by means of its heavy bottome of Lead <lb/>will re&longs;t upright in the Water, with almo&longs;t all the Globe of Gla&longs;&longs;e <lb/>above Water, in &longs;uch &longs;ort, that he that would may ea&longs;ily enter into <lb/>the &longs;ame: yet you mu&longs;t be dexterous in going into it, that you do <lb/>not much &longs;way the Machine &longs;idewayes, for that, if it lye too oblique <lb/>the Water will enter into the Globe of Gla&longs;&longs;e, and drive the Aire <lb/>thence that was in the &longs;ame, or at lea&longs;t in part, but holding it up­ <lb/>right when you enter the &longs;ame, the Water &longs;hall keep in the Aire on <lb/>all &longs;ides, whereby the water will be kept from entring. </s><s>And therefore <lb/>if he that &longs;hall enter into the &longs;aid Machine, do nimbly thru&longs;t his head <lb/>into the &longs;aid Globe by the hole thereof, he &longs;hall finde it quite fil­ <lb/>led with Ayre; in which place he may breath for verry many Re­ <lb/>&longs;pirations, without the lea&longs;t ob&longs;truction from the Water: And be­ <lb/>cau&longs;e this Machine will &longs;tay with its upper end level with the Wa­ <lb/>ters &longs;urface (the affixed Lead having been &longs;o limited) therefore <lb/>de&longs;iring to de&longs;cend to the bottom, the Diver &longs;hould hale the Ball <lb/>and Line upwards, which was &longs;ent before to the Bottom, in haling <lb/>of which the &longs;aid Machine will de&longs;cend as much under Water as he <lb/>hales the Corde; and if he continue haling it, till there be none of <lb/>it left, he &longs;hall de&longs;cend to the Bottome; and in the de&longs;cent, and after <lb/>that he &longs;hall be got to the bottom, he mu&longs;t look round about him <lb/>through that tran&longs;parent Globe for to finde out the thing he &longs;eeks, <lb/>and &longs;eeing it, he may many wayes with ca&longs;e transferre him&longs;elf <lb/>thither without ri&longs;ing again to the top; And when he would re­ <lb/>turn upwards to the toppe of the Water, he needs do no more but <lb/>&longs;lacken that corde fa&longs;tned to the Ball of Lead, for thereupon the <lb/>Machine &longs;hall begin to ri&longs;e upwards, and letting the &longs;aid Corde goe, <lb/>it &longs;hall not &longs;tay till the Machines upper parte arrive at the &longs;urface of <lb/>the Water; and being a&longs;cended thither, the Diver may come out <lb/>thereof, and &longs;wim to the top, and provide him&longs;elf afterwards of <lb/>&longs;uch things as are nece&longs;&longs;ary for embreching the &longs;aid Ship or other <lb/>matter &longs;unke: And in ca&longs;e the Diver cannot &longs;wim, it will be nece&longs;&longs;a­ <lb/>ry to fa&longs;ten a Corde to the Ring placed in the Centre of the upper <lb/>Board, and thereby to draw the Modell above the Surface of the <pb xlink:href="040/01/1194.jpg" pagenum="504"/>Water; but knowing how to &longs;wim, he may enter, a&longs;cend, and <lb/>de&longs;cend of him&longs;elf, without any help.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> III.</s></p><p type="main"> <s>But if you chance to be in a place where you cannot procure <lb/>the &longs;aid Globe to be made of Gla&longs;&longs;e, it may be made of Wood; <lb/>but then you mu&longs;t make therein great Sights, or Eyeholes of <lb/>clear Gla&longs;&longs;e of each &longs;ide to look four &longs;everall wayes; and pay it <lb/>without, and al&longs;o within if you &longs;ee cau&longs;e with Pitch. </s><s>And if you <lb/>cannot get &longs;uch a Ball of Wood, you may make &longs;hift with a little <lb/>Cubicall Che&longs;t or Boxe, like one of tho&longs;e Che&longs;ts wherein they plant <lb/>Ceaders, which mu&longs;t be well joyned graved and pitch't, with four <lb/>&longs;uch Sights of Gla&longs;&longs;e as before, namely one upon every lateral flat <lb/>or plain, &longs;o placed, that the Diver may &longs;ee through them every way, <lb/>and be able to look downwards, it would be good to make the <lb/>Box &longs;omewhat narrower towards the mouth, that &longs;o the four late­ <lb/>rall Planes may look &longs;omewhat &longs;loping: and in the entrance, de­ <lb/>&longs;cent, a&longs;cent, and coming forth, you are to u&longs;e the &longs;ame Rules as be­ <lb/>fore; aud if you have a de&longs;ire to de&longs;cend fa&longs;ter, you mu&longs;t make the <lb/>Ball of Lead &longs;omewhat heavier, that was tyed to the end of the <lb/>Corde, and this done the Machine &longs;hall de&longs;cend fa&longs;ter to the bottom <lb/>upon halling the &longs;aid Corde and Ball; and when you vere or let <lb/>loo&longs;e the Cord, the Engine will re-a&longs;cend but according to its former <lb/>&longs;peed: But if you would al&longs;o make it &longs;wifter in its a&longs;cent you are <lb/>to proceed quite contrary, that is, you mu&longs;t &longs;omewhat dimini&longs;h the <lb/>Lead, which is under the Ba&longs;e of the fiame; and the more you di­ <lb/>mini&longs;h the &longs;aid Lead, the &longs;wifter &longs;hall it be in a&longs;cending. </s><s>But you <lb/>mu&longs;t remember withall to encrea&longs;e the Ball of Lead, &longs;o that it may <lb/>be able to draw the &longs;aid Machine to the bottome &longs;peedily or lei&longs;ure­ <lb/>ly according as occa&longs;ion requires.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> IV.</s></p><p type="main"> <s>But if there be any likelihood of any obnoxious Fi&longs;h in the place <lb/>where the Diver is to de&longs;cend, that may hurt him, being quite na­ <lb/>ked; though that in the former kind of Machine with four pillars you <lb/>may &longs;e u e him with a wire Grate, made in the manner of doors to the <lb/>&longs;ame, yet to the end that you may know that this Invention may be <lb/>varied &longs;undry ways; you may in this ca&longs;e have a Globe of tran&longs;parent <lb/>gla&longs;s made at <emph type="italics"/>Murano,<emph.end type="italics"/> of &longs;uch a bigne&longs;s, that a man &longs;tanding on his feet, <lb/>or el&longs;e &longs;itting, may be contain'd therein, having amouth or round hole <lb/>of capacity &longs;ufficient for a man, commodiou&longs;ly to enter and goe out <lb/>thereby, and &longs;omewhat larger: & then coffin or enclo&longs;e the &longs;aid Globe <pb xlink:href="040/01/1195.jpg" pagenum="505"/>between two round Boards of &longs;omewhat a greater Diameter than <lb/>the Globe, with four pillars, as in the en&longs;uing figure doth graphically <lb/>appear. </s><s>But in the round Board which is put over the hole or mouth <lb/>of the &longs;aid Globe, you mu&longs;t al&longs;o make a round hole &longs;omewhat nar­ <lb/>rower than that of the Globe, but yet big enough for a man to pa&longs;&longs;e <lb/>in and out thereat. </s><s>Afterwards under this round Board &longs;o bored, <lb/>you mu&longs;t place and fix another round bored piece of Lead of &longs;uch <lb/>thickne&longs;&longs;e, as that it may be able to draw the &longs;aid Ball or Globe of <lb/>Gla&longs;&longs;e, together with the Diver in &longs;uch manner under Water, that <lb/>the upper round Board do re&longs;t in the Surface of the Water, namely, <lb/>that it may not be &longs;o heavy as to &longs;ink the Globe and Diver to the <lb/>bottome, but only to retain it beneath the Surface of the Water, <lb/>which by tryal may be ea&longs;ily proportioned, namely, by adding or <lb/>taking away Lead from the Ba&longs;e, according as occa&longs;ion &longs;hall require. <lb/></s><s>Next you are to frame a &longs;eat for the Diver to &longs;it commodiou&longs;ly in <lb/>the &longs;aid Ball or Globe, and next fa&longs;ten a Ball of Lead to the end of <lb/>a Rope, as many fathom long as the water is deep into which you <lb/>would de&longs;cend, and &longs;omewhat more, as was &longs;aid in the preceding <lb/>Explanation. </s><s>And that Ball of Lead &longs;hould be of &longs;uch bigne&longs;&longs;e, that <lb/>applied to the &longs;aid Model, it may be &longs;ufficient to make it de&longs;cend to <lb/>the bottome lei&longs;urely, or &longs;wiftly, as he &longs;eeth cau&longs;e who is to dive. <lb/></s><s>And make an handle or peg in the &longs;aid Globe whereat to fa&longs;ten or <lb/>belay the other end of <lb/>the &longs;aid Rope, and to <lb/>draw it ea&longs;ily upwards, <lb/><figure id="id.040.01.1195.1.jpg" xlink:href="040/01/1195/1.jpg"/> <lb/>or let it loo&longs;e at the <lb/>plea&longs;ure of him that is <lb/>within, and this may be <lb/>ea&longs;ily done by joyning <lb/>and fa&longs;tening four <lb/>pieces of wood upright <lb/>in the mouth or hole of <lb/>that bored Board and <lb/>Lead, which &longs;hall be <lb/>about the mouth of the <lb/>&longs;aid Globe; and that <lb/>I may be the better <lb/>under&longs;tood, I will give <lb/>it you in figure with the <lb/>Diver &longs;itting therein. <lb/></s><s>If you would de&longs;cend to the bottome of &longs;ome deep water by help <lb/>of this Machine, you are to proceed according to the directions gi­ <lb/>ven in the precedent Explanation.</s></p> <pb xlink:href="040/01/1196.jpg" pagenum="506"/><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> V.</s></p><p type="main"> <s>In ca&longs;e you &longs;hould be in a place where you could not have &longs;uch <lb/>a Globe made of Gla&longs;&longs;e, you may procure one of Copper or <lb/><arrow.to.target n="marg1560"></arrow.to.target> <lb/>Lead, round in fa&longs;hion of a greater ^{*} Churne, wide in the bot­ <lb/>tome and narrow in the mouth, and at lea&longs;t five foot high, and four <lb/>foot broad. </s><s>It may indeed be made quadrangular, that is, &longs;o that <lb/>the mouth be at lea&longs;t three foot &longs;quare every way, and the bottome <lb/>at lea&longs;t four foot every &longs;ide, and not under five foot high, and this <lb/>&longs;ame ve&longs;&longs;el, making it of Lead, mu&longs;t be &longs;o contrived, or proportio­ <lb/>ned, that the corporeal or &longs;olid <emph type="italics"/>Area,<emph.end type="italics"/> or Content of its interiour va­ <lb/>cuity, or &longs;pace, be about <gap/>oruple to the &longs;olid <emph type="italics"/>Area<emph.end type="italics"/> of the Lead, <lb/>which is imployed in making the &longs;aid Ve&longs;&longs;el; that is, make the Lead <lb/>of &longs;uch a thickne&longs;&longs;e, that the Ve&longs;&longs;els vacuity may be nine tenths of <lb/>the &longs;olid Area of all the whole Frame, which may be ea&longs;ily done by <lb/>any one that is not ignorant of practical Geometry: and this Ve&longs;&longs;el <lb/>being made, you &longs;hould place or &longs;et therein four great Fye holes or <lb/>Sights of tran&longs;parent or cri&longs;taline Gla&longs;&longs;e, &longs;o placed as to &longs;ee any way <lb/>as you &longs;hall need or de&longs;ire: and furthermore, in the framing of this <lb/>&longs;ame Ve&longs;&longs;el, you mu&longs;t make &longs;ome provi&longs;ion for the &longs;etling or &longs;tay­ <lb/>ing your feet, and to &longs;it down, and likewi&longs;e you mu&longs;t make a <lb/>Pulley to hall the Ball of Lead up, or let it down, which is fa&longs;tened <lb/>to the end of the long cord, as was &longs;aid in the two precedent ca&longs;es. <lb/></s><s>And moreover, in the making of this Ve&longs;&longs;el, you are to fa&longs;ten four <lb/>Rings of Iron to the bottome without, namely, to the four Angles, <lb/>it being Quadrangular; (and being round, let them divide the Cir­ <lb/>cumference into four equal parts) and betwixt the&longs;e four Rings, <lb/>you mu&longs;t place a &longs;quare or round Deal Board. </s><s>And this Ve&longs;&longs;el thus <lb/>modellized &longs;hall be &longs;o contrived, that putting it into the water with <lb/>the mouth downwards, with him in it who is to Dive, it &longs;hall but ju&longs;t <lb/>&longs;tay in the Surface of the water with that bottome of wood; but if <lb/>it chance that it &longs;hall not &longs;tay at the Surface of the water by helpof <lb/>that bottome of Board, but that it will de&longs;cend, you mu&longs;t upon that <lb/>bottome fa&longs;ten another, or two, or more &longs;quare or round Boards to <lb/>the four Rings, in &longs;uch wi&longs;e, that by means of the &longs;aid Boaids it may <lb/>be reduced to &longs;uch a quality, that it may re&longs;t with the &longs;aid round <lb/>Boards in the Surface of the water, and de&longs;cend no farther. </s><s>Having <lb/>with judgement and experience provided all the&longs;e things, and the <lb/>Diver being de&longs;irous to de&longs;cend of him&longs;elf, and likewi&longs;e to return <lb/>to the top when he plea&longs;eth, this may be performed with that Ball <lb/>of Lead tied to the end of that long Rope, as hath been &longs;aid in the <lb/>precedent Explanations, that is, to &longs;end the Ball fir&longs;t to the bottom in <lb/>he place where the Diver would de&longs;cend, and then to enter into the <pb xlink:href="040/01/1197.jpg" pagenum="507"/>Machine, and to &longs;ettle him&longs;elf therein; and then to pull the Ball <lb/>upwards, which &longs;hould be of that Gravity, that it may be apt to <lb/>make &longs;uch a Ve&longs;&longs;el or Machine de&longs;cend together with the Diver; and <lb/>if the Machine chance to be ju&longs;tly contrived, as hath been &longs;aid a­ <lb/>bove, I hold that a Ball of &longs;ive or &longs;ix pounds may be &longs;ufficient to <lb/>make it de&longs;cend nimbly upon the pulling of the Cord, and lifting <lb/>the Ball from the bottome, and continuing to draw the &longs;aid Cord, <lb/>as long as there is any remaining, he &longs;hall arrive at the bottome; and <lb/>whenever he would return upwards, he need but only vere or &longs;lack­ <lb/>en that Cord, and letting it all go he will not cea&longs;e a&longs;cending till the <lb/>Machine attains with its top (covered with tho&longs;e &longs;quare or round <lb/>Boards) unto the Surface of the Water, as hath been &longs;aid of the o­ <lb/>thers. </s><s>I will not &longs;tand to &longs;hew you the many particularities which <lb/>might be in&longs;erted for the tran&longs;porting your &longs;elves from one place to <lb/>another, keeping at the bottome, that is, without returning to the <lb/>top, for that they are almo&longs;t infinite, but it &longs;hall &longs;uffice to let you <lb/>know, that he may ea&longs;ily do it, carrying with him a long Hitcher, or <lb/>a Boom, or a Spike with a Hook at the end.</s></p><p type="margin"> <s><margin.target id="marg1560"></margin.target>* <emph type="italics"/>Brenta,<emph.end type="italics"/> a Ve&longs;&longs;el <lb/>in which they <lb/>in Italy carry <lb/>Grapes to the <lb/>Pre&longs;s.</s></p><p type="main"> <s>Many other particulars there might be in&longs;i&longs;ted on, and e&longs;pecially <lb/>how many may &longs;imply (that is, without any of the forsaid Ma­ <lb/>chines) go to the bottome, and &longs;tay for many hours under Water, <lb/>which, be&longs;ides the many profitable conclu&longs;ions that might from <lb/>thence be inferred for Diving in indifferent depths, being accompa­ <lb/>nied with the helps pre&longs;cribed in the foregoing Explanations, they <lb/>would be much to the purpo&longs;e, for that the Liver being once condu­ <lb/>cted with the Machine near unto the thing &longs;unk, he might come out <lb/>of the &longs;aid Machine, and go and &longs;tay for a long time about the &longs;ame, <lb/>to fa&longs;ten, or prepare tho&longs;e things that are nece&longs;&longs;ary for the rai&longs;ing <lb/>it: And farthermore, there is &longs;omething to be &longs;aid, when the thing <lb/>&longs;unk is in a muddy or dark Water, how the Diver may in &longs;undry <lb/>wayes, kindle there a great and flaming light, which flaming fire, <lb/>be&longs;ides that it would make him di&longs;cern the thing &longs;unk, it would al&longs;o <lb/>&longs;ecure him in his going forth of the Machine from any devouring <lb/>Fi&longs;hes, for that all &longs;uch as &longs;hould chance to be near that place would <lb/>be affrighted at &longs;uch an unu&longs;ual &longs;pectacle, and would make far <lb/>from it. </s><s>I might al&longs;o &longs;hew many wayes to embreech and grapple a <lb/>Ship when it is found, as well in deep as &longs;hallow Channels, which <lb/>particulars I &longs;hall re&longs;erve for another time.</s></p><p type="main"> <s>I will not &longs;tand to &longs;hew how this kind of Diving Machine might <lb/>be made of Boards, and that in &longs;undry fa&longs;hions, well calked and <lb/>pitcht, with four Lights or Sights, fa&longs;tening about the mouth of the <lb/>&longs;ame as much Lead as &longs;hould be nece&longs;&longs;ary, ora&longs;inuch as by what <lb/>hath been &longs;poken in the third Explanation, it is &longs;ufficiently manife&longs;t. </s></p> <pb xlink:href="040/01/1198.jpg" pagenum="508"/><p type="head"> <s>A <lb/>SUPPLEMENT <lb/>OF THE <lb/>Indu&longs;trious or Trouble&longs;ome <lb/>INVENTION <lb/>OF <lb/>Nicholaus Tartalea:</s></p><p type="main"> <s>In which is &longs;hewn a general and &longs;afe way to im­ <lb/>breech Cables, and hitch Grappling irons to any <lb/>Ship that's &longs;unk, a&longs;well in a deep as &longs;hallow Bot­ <lb/>tome, provided you know the exact place where <lb/>the &longs;aid Ship is. </s><s>Together with another new way <lb/>of rai&longs;ing or recovering the &longs;ame.</s></p><p type="main"> <s><emph type="italics"/>Whereunto is, la&longs;t of all, added &longs;ome new ways to conduct a Light, or <lb/>Flaming Matter, unto the Bottome of the Water, to enlighten, upon oc­ <lb/>ca&longs;ion, any dark Bottome, for the di&longs;covery, not onely, of a Ship or Bark, <lb/>but al&longs;o any &longs;mall thing of value that is &longs;unk, and that in the night as <lb/>well as in the day.<emph.end type="italics"/></s></p><p type="head"> <s>To the Mo&longs;t <lb/>Illu&longs;trious and mo&longs;t Serene</s></p><p type="head"> <s>PRINCE <lb/>France&longs;co Donato, <lb/>Duke of <lb/>VENICE.</s></p><p type="main"> <s><emph type="italics"/>Having not long &longs;ince, Most Serene, and Mo&longs;t <lb/>Illu&longs;trious Prince, publi&longs;hed under the Glorious <lb/>Name of your Highne&longs;&longs;e, &longs;undry and diver&longs;e <lb/>way storai&longs;e a Ship &longs;unk, with its Cargo in it (when once<emph.end type="italics"/> <pb xlink:href="040/01/1199.jpg" pagenum="509"/><emph type="italics"/>it is Grappled) I mu&longs;t confe&longs;&longs;e I was not then &longs;ollicitous to <lb/>find a way to imbreach or grapple the &longs;aid Ship (though <lb/>it is nece&longs;&longs;ary to be known) and the cau&longs;e thereof was, for <lb/>that I concluded that among&longs;t Mariners there were a <lb/>thou&longs;and means to effect it, and I was loath to enquire af­ <lb/>ter &longs;uch things as are commonly known to many, although <lb/>I be ignorant of them; but delight to &longs;earch into tho&longs;e <lb/>things which none el&longs;e can do. </s><s>Now, having been &longs;ince <lb/>told and a&longs;&longs;ured by many, that Mariners, and all other <lb/>per&longs;ons of ingenuity find far greater difficulty in imbrea­ <lb/>ching and Grappling &longs;uch a Ship, than they do, (when <lb/>once they have hold of it) to rai&longs;e the &longs;ame: I under&longs;tan­ <lb/>ding the &longs;ame, pre&longs;ently deliberated upon &longs;ome way that <lb/>&longs;hould be general and &longs;ecure, and to adde it in the end of <lb/>my Treati&longs;e, that &longs;o it might not, for want thereof, be vain <lb/>and u&longs;ele&longs;s. </s><s>And thus; of many that I have found, that <lb/>which to me hath &longs;eemed mo&longs;t univer&longs;al and ea&longs;y to be <lb/>explained by writing; I have here &longs;ubjoined, together <lb/>with another new way to recover the &longs;aid Ship: and the <lb/>manner how to illuminate the bottome of a dark Water, <lb/>but still under the Illustrious Name of your Serene <lb/>Highne&longs;&longs;e, at who&longs;e feet I once more humbly throw my <lb/>&longs;elf<emph.end type="italics"/></s></p><p type="main"> <s>NICOLO TARTAGLIA.</s></p> <pb xlink:href="040/01/1200.jpg" pagenum="510"/><p type="head"> <s>A Supplement.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> I.</s></p><p type="main"> <s>To hitch therefore, and &longs;ling, or grapple fa&longs;t a laden Ship <lb/>that is &longs;unk, being in a &longs;howle bottome, as was that broken <lb/>up near to <emph type="italics"/>Malamoccho,<emph.end type="italics"/> you are to take a very &longs;trong <lb/>Sheat-anchor Cable, of &longs;uch a length as is &longs;ufficient for <lb/>the U&longs;es hereafter to be under&longs;tood, and at one end of <lb/>&longs;uch a Cable you are to &longs;eiz or fa&longs;ten very well a thick and &longs;trong Iron <lb/>Ring, big enough for the other end of the Cable to pa&longs;&longs;e through with <lb/>ea&longs;e, and make thereof a running Parbunckle: and then, near to this <lb/>Ring (that is under this Cable at the place where it &longs;hall be bent to <lb/>the Ring) you mu&longs;t &longs;eiz or fa&longs;ten one of the Flooks of a thick and <lb/>&longs;trong Anchor, and about three fathoms &longs;pace from that fir&longs;t An­ <lb/>chor hitch the Flook of another &longs;econd Anchor into the &longs;aid Cable, <lb/>&longs;eizing or fa&longs;tening it that it &longs;tir not: and about two fathoms di­ <lb/>&longs;tance from this &longs;econd Anchor, &longs;eiz, as before the Flook of a third <lb/>Anchor, and &longs;o two fathom from that a fourth Anchor; and &longs;o pro­ <lb/>ceed, placing in that manner as many Anchors as &longs;uffice to go round <lb/>the Hull of the &longs;aid Ship under its Wails, and rather le&longs;&longs;e than more, <lb/>to the end the la&longs;t Anchor may be no hinderance to the running of <lb/>the Parbunckle at the Ring at &longs;uch time as it is to be rou&longs;ed or vered, <lb/>that is, to be drawn or let &longs;lip. </s><s>The truth is, that in the part of the <lb/>Cable marked E, in the Figure following, and in the oppo&longs;ite <lb/>part marked G (which parts you are to place &longs;o that they may fall <lb/>one at the Stem, the other at the Stern) no Anchor is to be placed, <lb/>but you mu&longs;t leave at lea&longs;t three fathom interval betwixt tho&longs;e An­ <lb/>chors at G, as was required to be done betwixt the fir&longs;t and &longs;econd <lb/>at E. </s><s>And then form the &longs;aid Running Parbunckle, that is, reeve the <lb/>other end of the Cable through the Ring of Iron; and, that being <lb/>made, you are to place many per&longs;ons upon Flat-bottome Boats fa­ <lb/>&longs;tened in an Oval Figure round the place where the Ship lyeth: and <lb/>then vere or &longs;lacken the Parbunckle, but in an Oval Form, to that <lb/>widene&longs;&longs;e, that it may at four or five foot di&longs;tance, inviron the foun­ <lb/>dered Ship: and this done, you mu&longs;t let all the Anchors, together <lb/>with this Girdle or Parbunckle, (being kept at that widene&longs;&longs;e) gent­ <lb/>ly and equally fall to the bottome of the Sea, keeping the Ship in <lb/>the mid&longs;t of the Ovall: and when you perceive all the Anchors de­ <lb/>&longs;cended to the bottome, you mu&longs;t vere there &longs;everal Cables, that <lb/>they may &longs;ink deep into the &longs;and or Ouze; and then after this you <pb xlink:href="040/01/1201.jpg" pagenum="511"/>mu&longs;t draw, and bring them by degrees clo&longs;e underneath the Hull of <lb/>the Ve&longs;&longs;el, and then hall or &longs;train hard the end of the Sheat Anchor <lb/>Cable which was reeved through the Ring; and begirt the Hull <lb/>of the Ship therewith, as with a Girdle (and to &longs;train it very taught, it <lb/>would not be ami&longs;&longs;e to make u&longs;e of a Cap&longs;tan) and when this <lb/>Girdle is drawn to its due exactne&longs;&longs;e, to the end it may not &longs;lip (in <lb/>the elevation of the Ship) fa&longs;ten to that part which you hold above <lb/>Water another Ring of Iron, and pa&longs;&longs;e through this Ring one of <lb/>the Anchor-Cables that is on the &longs;ame &longs;ide as the fir&longs;t Ring is on, <lb/>and almo&longs;t as far from the &longs;aid Ring, as the &longs;econd Ring is di&longs;tant <lb/>from the fir&longs;t; whereupon making this &longs;econd Ring to &longs;lip along <lb/>the &longs;aid Anchor Cable, and then in the Elevation halling the &longs;ame, <lb/>it &longs;hall make the &longs;aid Girdle taught under the &longs;aid Ship: and that I <lb/>may be the better under&longs;tood, I have here underneath repre&longs;ented <lb/>the &longs;aid Girdle pul'd together in an Oval Figure as it is to lye under <lb/>the Rake of the Ships Hull with fourteen Flooks of fourteen An­ <lb/>chors under the &longs;ame (except in the part inked E, and in its oppo­ <lb/>&longs;ite part G,) well &longs;ea&longs;­ <lb/>ed; of which Girdle, or <lb/>Parbunckle, the fir&longs;t <lb/><figure id="id.040.01.1201.1.jpg" xlink:href="040/01/1201/1.jpg"/> <lb/>Ring &longs;hall be A, <lb/>through which the <lb/>Sheat-Anchor Cable <lb/>pa&longs;&longs;eth, namely, the <lb/>Cable A B, to which <lb/>Cable was fa&longs;tened a <lb/>&longs;econd Ring in the <lb/>point B, through which <lb/>&longs;econd Ring, (to the <lb/>end the Girdle might <lb/>not &longs;lio) we will reeve <lb/>the Cable of the An­ <lb/>chor C; which Anchor <lb/>C we &longs;uppo&longs;e to be <lb/>&longs;omewhat farther from <lb/>the Ring A, than the &longs;econd Ring B is from the fir&longs;t Ring A, and <lb/>then make the &longs;aid Ring B to &longs;lip along the Cable of the &longs;aid <emph type="italics"/>A<emph.end type="italics"/>nchot <lb/>C, till it come to the point C. <emph type="italics"/>A<emph.end type="italics"/>nd thus the Ship &longs;hall be &longs;ecurely <lb/>and &longs;trongly grappled and begirt. <emph type="italics"/>W<emph.end type="italics"/>hich done, proceeding as we <lb/>directed in the fir&longs;t Book of our <emph type="italics"/>Indn&longs;trious Invention,<emph.end type="italics"/> you will exe­ <lb/>cute your purpo&longs;e; That is, when the two or more coupled Ships <lb/>&longs;hall be full of water, at the ebbing of the Tide you are to fa&longs;ten <lb/>and belay to tho&longs;e Tires of Beams that couple the &longs;aid Ships, all <lb/>tho&longs;e fourteen Cables, taking a little more care in tying, and belay­ <pb xlink:href="040/01/1202.jpg" pagenum="512"/>ing that of the Anchor C, which will keep the Girdle from &longs;lipping <lb/>in the Elevation.</s></p><p type="main"> <s>But if you doubt that that &longs;ingle Cable, to which the Anchors <lb/>are fa&longs;tened, is not &longs;ufficient for &longs;o great a weight, you may above <lb/>that, place another with a Ring al&longs;o, through which (as before) the <lb/>end of it may pa&longs;&longs;e, by that means begirting the Ship with two of <lb/>tho&longs;e Girdles, and ob&longs;erving the &longs;ame Rules you may take three or <lb/>four of tho&longs;e &longs;lipping &longs;heat-anchor Cables, each with its Ring <lb/>wherein to run in the manner of a Noo&longs;e. <emph type="italics"/>A<emph.end type="italics"/>nd when the &longs;aid new <lb/>Girdle is pulled &longs;trait and clo&longs;e to the Ship, fa&longs;ten to the &longs;aid Cable, <lb/>(or to each of them if you u&longs;e more) another &longs;econd Ring, to gird <lb/>and hold the &longs;aid Noo&longs;e fa&longs;t, that it &longs;lip not with the Cable of the <lb/><emph type="italics"/>A<emph.end type="italics"/>nchor C, or with more of tho&longs;e <emph type="italics"/>A<emph.end type="italics"/>nchor-Cables if there be occa­ <lb/>&longs;ion.</s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/>nd in ca&longs;e that tho&longs;e fourteen Cables be thought in&longs;ufficient <lb/>to bear &longs;o great a burden, you may take twenty or thirty of them, or <lb/>as many as you plea&longs;e, tying them clo&longs;er to one the other, under <lb/>the running Cable, and make half of them to be placed on one &longs;ide, <lb/>and the other half on the other &longs;ide of the &longs;aid Ship.</s></p><p type="main"> <s><emph type="italics"/>A<emph.end type="italics"/>nd if again it be doubted that the &longs;ingle Cable of the <emph type="italics"/>A<emph.end type="italics"/>nchor <lb/>C s not able to hold the Noo&longs;e fa&longs;t, you may take two or three of <lb/>them, for you may judge what the &longs;tre&longs;s of that anchor is by means of <lb/>the height of the water. </s><s>Truth is, this office might be di&longs;tributed <lb/>among&longs;t more <emph type="italics"/>A<emph.end type="italics"/>nchors, by adding a third Ring to the main Cable, <lb/>as far from the &longs;econd, as the <emph type="italics"/>A<emph.end type="italics"/>nchor D is di&longs;tant from the <emph type="italics"/>A<emph.end type="italics"/>nchor <lb/>C, &longs;o that the Cable of the <emph type="italics"/>A<emph.end type="italics"/>nchor D, pa&longs;&longs;ing through that third <lb/>Ring, and &longs;lipping the &longs;aid Ring along till it come to D, it will fol­ <lb/>low that tho&longs;e two Cables of tho&longs;e two Anchors C and D, will keep <lb/>the Parbunckle &longs;traight; aud in this manner you may proceed by ad­ <lb/>ding new Rings, and imploying more Anchor-Cables, for the great­ <lb/>er &longs;ecurity.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> II.</s></p><p type="main"> <s>The &longs;ame method may al&longs;o be ob&longs;erved when the Ship is in a <lb/>deep place, provided that the depth exceed not the length of the <lb/>Hull of the Ship, becau&longs;e then there may be alwaies found &longs;ome one <lb/>or more Cables &longs;ufficient to reeve through the &longs;econd and follow­ <lb/>ing Rings of the Main Cable to &longs;ecure the Noo&longs;e from &longs;lipping, or <lb/>growing &longs;lack, as in the preceding declaration hath been &longs;aid. </s><s>But if <lb/>it chance that the depth of the place be far greater than the length <lb/>of the Ship, you can no longer &longs;ecure the Noo&longs;e with that &longs;econd <lb/>Ring, but mu&longs;t find out &longs;ome other way, and though there might be <lb/>many found out, I &longs;hall in&longs;tance but in this one.</s></p> <pb xlink:href="040/01/1203.jpg" pagenum="513"/><p type="main"> <s>After you have &longs;trained, drawn the &longs;aid Girdle as taught as you <lb/>can, you may take the Cable thereof, and the Cable of the anchor <lb/>next adjoyning on the &longs;ame &longs;ide that the fir&longs;t Ring is on (namely, <lb/>the Cable marked F,) and twi&longs;t and wind them together, and then <lb/>reeve the &longs;ingle Cable of the Girdle <emph type="italics"/>A B,<emph.end type="italics"/> through the Ring of a <lb/>Sheat-anchor, (without its Cable) and let the anchor &longs;lide down­ <lb/>wards along the &longs;aid Main Cable, which by rea&longs;on of its weight will <lb/>run almo&longs;t clo&longs;e to the Ring <emph type="italics"/>A,<emph.end type="italics"/> of the Main Cable, pre&longs;&longs;ing the twi&longs;t <lb/>of the two Cables clo&longs;e at <emph type="italics"/>A<emph.end type="italics"/>; and this done, once more twine or <lb/>twi&longs;t a little the two former Cables, namely the Sheat anchor-cable <lb/>B, and the le&longs;&longs;er Cable F, and then &longs;ea&longs;e tho&longs;e two Cables &longs;everally <lb/>to the Orders of Beams, that is, one to one Order, and the other to <lb/>another at &longs;ome di&longs;tance from the former, to the end they drive <lb/>down the twi&longs;ting near to the Ring of the anchor: which twi&longs;ting <lb/>will keep the Noo&longs;e from &longs;lipping or opening in elevating the Ship. <lb/><emph type="italics"/>A<emph.end type="italics"/>nd if there be any occa&longs;ion to u&longs;e a Cap&longs;tain (as was &longs;aid in the <lb/>&longs;eventh Explanation of the fir&longs;t Book) you mu&longs;t always take care <lb/>to &longs;train the&longs;e two Cables equally, and much a&longs;under, which doing, <lb/>the Girdle &longs;hall be kept &longs;trait. </s><s>Many other ways might be &longs;hewen <lb/>for to keep the &longs;aid Grand Cable from &longs;lipping, but e&longs;teeming them <lb/>&longs;uperfluous, I omit them.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> III.</s></p><p type="main"> <s>He that is de&longs;irous to recover a foundered Ship laden with <lb/>Fraight, by other ways than tho&longs;e pre&longs;cribed in the fir&longs;t Book, <lb/>namely, without &longs;tanding to fill tho&longs;e two or more Ships, or other <lb/>Ve&longs;&longs;els with water, and then to empty them, may only by force of <lb/>Cap&longs;tains or Cranes ea&longs;ily effect the &longs;ame in the manner following, <lb/>(&longs;till making u&longs;e of the Parbunckle and flooks of anchors explained <lb/>in the fir&longs;t Explanation of this) namely: By taking from their an­ <lb/>chors Rings all their Cables, except that which is to make fa&longs;t the <lb/>Main-Cable Noo&longs;e that begirts the Ship, and in their places make <lb/>fa&longs;t to each Ring a &longs;trong Pulley or Block, in &longs;uch &longs;ort, that all the <lb/>&longs;aid Pulleys or Blocks have equal number of Shivers, or wheels, and <lb/>tho&longs;e as many as you can make them: and through the&longs;e Shivers or <lb/>wheels reeve their proper and convenient Cables or Ropes, incatena­ <lb/>ting each Pulley with its &longs;uperiour; and this done, make two &longs;qua­ <lb/>drons of Barks, or Lighters, or Flat-boats, according to the method <lb/>laid down in the fourth Explanation of the fir&longs;t Book, collated and <lb/>bound together with tho&longs;e Tires of thick and &longs;trong Beams tripled, <lb/>and with a great and &longs;pacious platform of thick Planks upon each <lb/>&longs;quadron, and upon tho&longs;e two &longs;pacious platforms place as many <lb/>Cap&longs;ters or Ship-cranes as you &longs;hall judge nece&longs;&longs;ary for &longs;uch a <pb xlink:href="040/01/1204.jpg" pagenum="514"/>weight, and rather much more, then ever &longs;o little le&longs;s, and then let <lb/>fall the &longs;aid Anchors lei&longs;urely, with the Girdle opened in an Oval <lb/>Figure, untill they come to the bottome of the Sea, &longs;o that the Girdle <lb/>do encircle or &longs;urround the foundered Ship. </s><s>And having once be­ <lb/>girt it carefully, approximate all the Anchors with the Girdle to the <lb/>Hull of the Ship, and then &longs;harpen or make taught the Girdle-cable <lb/>by halling it hard and &longs;treight to the Ships hull, and when it is <lb/>drawn clo&longs;e, belay it that it may not &longs;lacken, with that &longs;ingle An­ <lb/>chor-cable, or more, according to that &longs;ecure way &longs;poken of but <lb/>now, or by &longs;ome other than &longs;hall &longs;eem more expedient, (for many <lb/>more, if one think thereon may be found:) and this being done, <lb/>&longs;eek to loo&longs;en the Ship by degrees from its bed of Ouze, a little on <lb/>one &longs;ide, and a little on the other with the afore&longs;aid Cap&longs;ters, and, <lb/>being once water born, then draw it upwards equally on both &longs;ides, <lb/>and proceed in this manner till &longs;uch time as you have hoi&longs;ted it &longs;uf­ <lb/>ficiently above the Waters &longs;urface, and then pump out the Water, <lb/>and unlade its Cargo.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> IV.</s></p><p type="main"> <s>Having in the &longs;econd Book &longs;hewn &longs;everal ways of Diving under <lb/>Water in &longs;earch of things &longs;unk, in this place I have thought <lb/>fit to add, in ca&longs;e that &longs;ome little thing of value &longs;hould fall <lb/>into a Water in &longs;ome &longs;hady place, and where its bottome is ob&longs;cure <lb/>and dark, a way how to conveigh a Light thither that may give light <lb/>enough for the di&longs;cerning of that little thing, provided that it be not <lb/>buried in, or covered with the old Ouze. </s><s>Now to perform this, and <lb/>that with expedition, we may in &longs;mall depths take one of tho&longs;e bra&longs;s <lb/>Buckets or Pails, which are u&longs;ed in carrying and keeping of Water <lb/>for hou&longs;ehold u&longs;es: and tho&longs;e of them that are &longs;haped long and <lb/>deep, with feet &longs;hall be better then tho&longs;e that are made round and <lb/>&longs;hallow, without feet; and the bigger and higher it is, &longs;o much the <lb/>better it &longs;hall be. </s><s>And having made choice of &longs;uch a Bucket, you <lb/>are to fa&longs;ten to the Ears of it two &longs;mall Ropes of about two yardes <lb/>apiece, in &longs;uch a fa&longs;hion, as that they may one cro&longs;s the other at the <lb/>mouth of the Bucket, making upon it a perfect cro&longs;s, and that the <lb/>Knot of the Ropes may be in the mid&longs;t of the Buckets bottom with­ <lb/>out, making of the ropes a Hoop over the bottome whereat to fa&longs;ten <lb/>another Rope of greater length; &longs;o that the Bucket being held by <lb/>that la&longs;t Rope may come to hang with its mouth perpendicularly <lb/>downwards. </s><s>And this done, fa&longs;ten as much Lead to the two Eares of <lb/>the Bucket as may ju&longs;t make it &longs;ink to the Bottome, and then &longs;et <lb/>and fa&longs;ten a little Wax candle lighted in the inter&longs;ection that tho&longs;e <lb/>two Ropes make over the mouth of the Bucket, that is, in the centre <pb xlink:href="040/01/1205.jpg" pagenum="515"/>of that perfect cro&longs;s; &longs;o that the candle with its light may be with­ <lb/>in, and near the bottome of the &longs;aid Bucket. </s><s>This being done, let <lb/>down the Bucket, with the candle in it gently unto the bottome, <lb/>which doing, you &longs;hall &longs;ee the burning candle clearly enlighten the <lb/>bottome of the Water. </s><s>And this Bucket you may remove from <lb/>place to place, without drawing it upwards. </s><s>The truth is, that this <lb/>candle will not long continue burning, but will &longs;erve for a little <lb/>while, and when it &longs;hall go out of it &longs;elf, it may be drawn up, re­ <lb/>lighted, and let down, as occa&longs;ion requires: but the greater that the <lb/>Bucket, and the le&longs;&longs;er that the candle &longs;hall be, &longs;o much the longer <lb/>time &longs;hall it keep its light under Water: and therefore if the &longs;aid <lb/>bottome were very deep, it would be requi&longs;ite to perform that e&longs;&longs;ect <lb/>with &longs;o much a greater Ve&longs;&longs;el, as a great Caldron, but yet of Brals, <lb/>or by that means the candle &longs;hall continue longer lighted.</s></p><p type="head"> <s><emph type="italics"/>EXPLANATION<emph.end type="italics"/> V.</s></p><p type="main"> <s>But in ca&longs;e that a Ship or Bark were foundered in &longs;ome &longs;pacious <lb/>and profound Gulph, and that the exact place where it &longs;unk <lb/>were unknown, and that the bottome of the &longs;aid &longs;pacious Gulph <lb/>were very ob&longs;cure, it is manife&longs;t that &longs;o little a light as that &longs;poke <lb/>of in the precedent Explanation would hardly &longs;erve. </s><s>And therefore <lb/>if you would convey thither one much bigger, you may do it &longs;eve­ <lb/>rall wayes, of which one is this. </s><s>Take nine ounces of refined Salt­ <lb/>peter, &longs;ix ounces (Greek weight) of Brim&longs;tone that is clear and <lb/>tran&longs;parent, three ounces of Camphire refined, and one ounce of <lb/>Ma&longs;tick; and beat all the&longs;e things &longs;everally, not very &longs;mall; and <lb/>when you have beaten them, mix them all together in an Earthen <lb/>Pan; and when they are well mingled, put thereto three pounds of <lb/>common Gunpowder, and then remingle them very well together; <lb/>and afterwards put therein four ounces of oyl of Stone, and mix all <lb/>very well; and this done, take a Cartredge thereof, and give fire to <lb/>it; and if it burn too &longs;lowly, put a little more Gunpowder to it, <lb/>but if it burn too vehemently and &longs;uddenly, add thereto more oyl. <lb/></s><s>Put this Compo&longs;ition, after this, into a little Bag of double Canvis, <lb/>of &longs;uch a widene&longs;&longs;e, that when all the mixture is out, therein it may <lb/>be as broad, as high, and cram the Compo&longs;ition hard down into the <lb/>Bag; and then with very good Pack thread &longs;ew up the mouth of the <lb/>Sack, cutting away the &longs;uperfluous Canvas. </s><s>Then winde a good <lb/>hempen cord round about it very hard every way, reducing it to the <lb/>form of a round Ball, and after it is very well bound and &longs;wathed a­ <lb/>bout many &longs;everall times, you mu&longs;t melt Brim&longs;tone into a great Ve&longs;­ <lb/>&longs;el, and when it is melted, roll the &longs;aid Ball therein &longs;o, as that it may <lb/>be covered all over with a cru&longs;t of Brim&longs;tone. </s><s>And this being done <pb xlink:href="040/01/1206.jpg" pagenum="516"/>affix a piece of Lead unto the Ball by an iron Wire, and make it ve­ <lb/>ry fa&longs;t, and frame in the top of the Ball a Bow or Noo&longs;e with the <lb/>&longs;aid Wire, and to that fa&longs;ten a long Rope, and then in the oppo&longs;ite <lb/>place where the Lead is fixed, make an hole with an iron rod into <lb/>the middle of the Ball, and &longs;top that hole with a little fine Gunpow­ <lb/>der, holding it &longs;u&longs;pended by the Rope: and when you would have <lb/>that Light de&longs;cend into the bottome of the Sea or Gulph, goe to the <lb/>place, and give fire to the little hole, and when it is inkindled, let <lb/>down the Ball and Lead, lengthwayes, almo&longs;t to the bottome, where <lb/>he &longs;hall be that would find the thing &longs;unk, and you &longs;hall find that <lb/>the &longs;aid fire will illuminate very much round about the &longs;aid bottom, <lb/>and &longs;hall la&longs;t a long time, and more or le&longs;s, according to the hole <lb/>made in the Ball. 'Tis to be noted, that the Ball is to be held over <lb/>the head of him that diveth, for that the &longs;moke proceeding from it <lb/>will much ob&longs;cure the Waters above it, &longs;o as that it will give Light <lb/>only downwards; and this fire will be a dreadful &longs;ight unto the Fi&longs;h, <lb/>&longs;o that they will fly from &longs;o new a &longs;pectacle.</s></p><p type="head"> <s><emph type="italics"/>The END of the fir&longs;t part <lb/>of the Second TOME.<emph.end type="italics"/></s></p> </chap> </body> <back></back> </text></archimedes>